SOLID-STATE NMR FOR ADVANCED MATERIALS CHARACTERIZATION

Transcription

1 SOL-STTE NM FO VNCE MTELS CHCTEZTON Von er Fakutät für Matheatik, nforatik un Naturwissenschaften er heinisch- Westfäischen Technischen Hochschue achen zur Erangung es akaeischen Graes einer oktorin er Naturwissenschaften genehigte issertation von PL.-PHYS. LN EGHN U aus Targu Lapus (oania) erichter: Universitätsprofessor r. rer. nat. ernhar üich Universitätsprofessor r. rer. nat. Martin Möer Tag er ünichen Prüfung:. Jui 004 iese issertation ist auf en nternetseiten er Hochschubibiothek onine verfügbar.

2 ie voriegene rbeit wure in er Zeit von Mai 00 bis Juni 004 a Lehrstuh für Makrooekuare Cheie er heinisch-westfäischen Technischen Hochschue achen angefertigt. Herrn Prof. r.. üich anke ich für ie Übernahe er wissenschaftichen etreuung ieser Prootionsarbeit. Für ie freuniche Übernahe es Korreferats anke ich Herrn Prof. r. M. Möer.

3 The iportant thing is not to stop questioning. Curiosity has its own reason for existing. One cannot hep but be in awe when he contepates the ysteries of eternity, of ife, of the arveous structure of reaity. t is enough if one tries erey to coprehen a itte of this ystery every ay. Never ose a hoy curiosity. bert Einstein

4 Contents bbreviations an Sybos V ntrouction Spin-iffusion NM.. ntrouction an otivation Principes of spin-iffusion NM....3 Genera anaytica soutions of spin-iffusion equations in three-oain systes with aear orphoogy Theory Particuar case for a two-oain systes The effect of the interface oain Tests of the soutions of the spin-iffusion equations Singe- an oube-quantu ipoar fiters Experienta.. Sapes..... NM Experients oube-quantu ipoar fiter MPE ipoar fiter eaxation of ongituina agnetization Proton spin-iffusion Concusions nvestigation of copex orphoogies by spin-iffusion NM Nyon-6 fibres ntrouction an otivation Experient.... Sape... NM easureents

5 Contents 3..3 Proton spectra of Nyon-6 fibres Spin iffusivities Evience for aggregates of fibris MPE ipoar fiter efficiency Proton spin-iffusion using a MPE ipoar fiter C. Morphoogy of Nyon-6 fibres etaie escription of the Nyon-6 orphoogy base on spiniffusion experients using a Q fiter Theory Efficiency of the oube-quantu ipoar fiter C. Proton spin-iffusion experients using a Q fiter ibock copoyers ntrouction Theory of ibock copoyers Experienta. 55. Sapes NM experients Proton spectra Proton spin-iffusion using a MPE ipoar fiter Concusions NM stuy of shape-eory poyers.. 4. ntrouction an otivation.. 4. Experienta escription of the sapes NM easureents Characterization of the networks H spectra C spectra Longituina reaxation easureents oube-quantu bui-up curves WSE experients. 4.4 nvestigation of the kinetic of the UV-curing process naysis of shape-eory properties

6 Contents 4.5. The concept of shape eory NM investigation of the shape-eory effect nvestigation of in vitro egraation Concusions Moecuar ynaic heterogeneities of confine thin ipi fis ntrouction an otivation Experienta Sapes. 5.. NM experients Mutipe-quantu bui-up curves an eite spectra Proton agnetization-exchange experients Theory oube-quantu ipoar fiter Proton agnetization-exchange NM on ipi fis istribution function of resiua ipoar coupings Concusions nvestigation of orere tissues by NM ntrouction an otivation Experienta Theoretica backgroun NM etection of protein. Magnetization transfer process coagen an water. 6.5 entification of exchangeabe protons Concusions Concusions ppenix. Sapes naytica soutions of the spin-iffusion process in a aear orphoogy eferences.. 4

7 V Contents

8 List of abbreviations an sybos V List of abbreviations an sybos 0 surface coverage static agnetic fie c CP eff SC Q E a LG M n M w MPE MS NM P PEO PS t T T g T concentration cross-poarization spin-iffusion coefficient vaue of the resiua ipoar couping Scanning eectron icroscopy oube-quantu coherences activation energy intensity of the ongituina agnetization Oigo[(L-actie)-ran-gycoie]iethacryate concentration of z-agnetization Nuber average oecuar weight Weight average oecuar weight Magic an Poarization Echoes Magic nge Sape Spinning Nucear Magnetic esonance Poyaie Poy(ethyene-b-oxie) Poystyrene Universa gas constant tie absoute teperature gass transition teperature aboratory frae spin-attice reaxation tie T rotating frae spin-attice reaxation tie T transverse reaxation tie

9 V List of abbreviations an sybos SNS SXS UV WSE WX Sa-ange neutron scattering Sa-ange X-ray scattering Utra-vioet Wie-ine separation spectra Wie-ange X-ray iffraction ν / fu ine with at haf height ν Q spitting of the oube-quantu eite spectra τ c proton ensity / ensity correation tie

10 ntrouction Since its iscovery in 946 by F. och an E. Purce, Nucear Magnetic esonance (NM) was continuousy expaning its ethos an appications. This progress is a resut of a continuous technica eveopent an perhaps, the ost iportant, fro the unique opportunities provie by NM itsef [ys96, Sie99, ü0, Fry, Wi, Law]. ifferent NM ethos appie to the sae sape can provie structura an ynaica inforation which can then be correate with the acroscopic properties. Therefore, it is not at a surprising that NM cou go so eepy into iverse reas ike ateria science, cheistry, rug iscovery, bioogy, eicine, an we ogging technoogy. n recognition of the iportance of NM severa Nobe prices were aware to scientists working in this exciting an chaenging fie uring the ast ecaes. t starte in 95 with och an Purce an it continue in 99 with. Ernst for his work concerning the ethooogica eveopent of high resoution NM. More recenty, in 00, K. Wüthrich was aware for his work on the euciation of the protein structure. itionay, the Nobe Price in Meicine was aware to P. Lauterburg an P. Mansfie in 003 for their iscoveries which e to the eveopent of agnetic resonance iaging as one of the inispensabe toos for eica iagnostic an research. The potentia an the wie range of appicabiity of soi state NM spectroscopy is aso we pointe out in the present work by the two ain covere topics. They focus on (i) appication of NM in aterias characterization an (ii) ethooogica eveopents in the fie of spin-iffusion NM. (i) Cassica an avance soi state NM ethos were successfuy appie for the investigation of a broa range of systes with iportant appications such as Nyon-6 fibres, ibock copoyers, confine ipis, bioaterias, an bioogica tissues. n unerstaning of their icroscopic structure an ynaics is necessary in orer to anufacture aterias with iprove acroscopic properties. Poyaie (P) is the ost coon engineering theropastic in use toay ue to an exceent cobination of properties such as high stiffness an strength at eevate teperatures, exceent heat ageing resistance, goo abrasion, an wear an cheica

11 Chapter. ntrouction resistance [s]. P is suitabe for a ajor processing techniques, such as injection ouing, bow ouing an extrusion [s]. Particuary, Nyon-6 (P6) is one of the ost iportant synthetic fiber-foring aterias use for high-spee et spinning [Zia76]. These fibres have a orphoogy consisting of a copex istribution of obie aorphous, ess-obie aorphous, an crystaine regions which is ifficut to characterize by cassica techniques ike X-rays. The vaues of their sizes as we as their spatia istributions irecty infuence the acroscopic properties of the fibres an therefore an investigation of the is necessary. n NM approach base on spin-iffusion NM epoying ifferent types of ipoar fiters which seect in separate experients the agnetization coing fro ifferent regions in cobination with anaytica soutions of the spin-iffusion equations was epoye to characterize the orphoogy of these fibres an to estiate the oain sizes of the crystaine, ess-obie aorphous an obie aorphous regions. These istribute icroheterogeneities were then correate with the processing conitions, i.e. wining spee an raw ratio. n iportant cass of poyeric ateria is represente by ibock copoyers. Particuary, ibock copoyers of PEO-b-PHEM represent suitabe aterias for use in the bioeica fie for rug eivery [ei]. The sizes of the obie aorphous, the interface, an the rigi aorphous oains of these copoyers with ifferent oecuar weights were estiate with the hep of spin-iffusion NM experients. itionay, the ong perio was correate with the oecuar weight. Further on, our attention was focuse on supporte thin ipi fis ue to a their increasing nuber of appications in the ast years. They represent a reativey copatibe structure for the eveopent of new types of eectrocheica sensors an biosensors with a fast response in tie, on the orer of a few secons, an with high sensitivity (nanooar etection iit). The function of these biocopatibe oecuar ayers on soi substrates is strongy associate with their structure, their packing, an their ynaics. The oecuar ynaic heterogeneities of thin ecithin fis of controe thickness ranging fro a onoayer to subonoayers in subicron cyinrica pores of ifferent iaeters were investigate by proton utipe-quantu bui-up curves an eite spectra as we as agnetization-exchange NM. The effect of various paraeters such as the oecuar area coverage, the pore size an the teperature on the overa chain ynaics was investigate. nother interesting an chaenging topic covere in this work is reate to bioegraabe poyers having shape eory properties. Poyers base on poygycoie, poy(actie), an their copoyers constitute proising aterias for the use in the fie of

12 Chapter. ntrouction 3 surgery an pharaceutics [Str0, Wit0, bi97, Len]. esie biocopatibiity an bioegraabiity, these type of copoyers have a eory that aows the to be efore into a teporary configuration an then to be restore to the origina parent geoetry by appying heat for a few secons [Len]. n coparison with other shape eory aterias, such as shape eory aoys, they offer uch greater eforation capabiities, substantiay easier shaping proceure, higher shape stabiity, they are cheaper, an for the eica use provie better biocopatibiity an bioegraabiity. Severa acroscopic properties ike the transition teperature an the echanica properties can be varie in a wie range by ony sa changes in their cheica structure an coposition [Fen99, Len]. Therefore nowaays, they represent a cass of aterias with high potentia in any appications. n investigation of the structura characteristics, the oecuar ynaics an the echaniss responsibe for the shape eory behavior an for the changes in physica properties associate with hyroytic egraation was carrie out using cassica an avance NM ethos. f the poyaie fibres are the ost coon engineering theropastic in use toay, coagen is the ost abunant protein on earth an one of the ajor constituents in aas, constituting 5% of the tota protein ass in these anias [b]. t pays a crucia roe for the stabiity an function of ifferent bioogica tissues such as bones, tenons, skin, igaents, boo vesses, an cartiages. ts echanica properties are strongy reate to the interaction between the protein an its water of hyration. itionay, a characterization of the spin ynaics in the two states is of iportance for generating better contrast in agnetic resonance iaging [Neu3]. n investigation of this interaction was ae with the hep of agnetization transfer experients. The ientification an characterization of the steps of this process as we as the ientification of the functiona groups responsibe for it was one. (ii) The other irection of the present work is reate to ethooogica eveopents in the fie of spin-iffusion NM. t represents an estabishe etho to investigate oain sizes an orphoogy of heterogeneous poyers an it is base on the agnetization exchange after prouction of a z agnetization graient by a ipoar fiter [Sch93, Sch94, e95, Van96, Che96]. These spin-iffusion experients are suitabe to investigate ifferent aspects of structura heterogeneities in a broa range of spatia iensions fro 0. n to about 00 n [Sch93, Van94, e95, Van96]. n spite of the ipressive efforts to anayze quantitativey the spin-iffusion process in the ast ecaes severa funaenta probes reain to be sove [Che8, Hav95, i96]. eiabe vaues of the spin-iffusion coefficients are requeste for a correct estiation of the oain sizes as we as the use of a proper

13 4 Chapter. ntrouction anaytica oe. n any cases the anaytica soutions consiere earier an which provie ore physica insight into the spin-iffusion process were use in the short-tie regie to obtain inforation about the oain sizes [Sch93, Sch94]. naytica soutions for the evoution of agnetizations in the oains characterize by an average spin-iffusion coefficient were propose for the spin-iffusion process taking pace in two oains with aear, cyinrica an spherica orphoogies [e95]. Later, genera anaytica soutions of the iffusion-equations were erive for a two-oain aear orphoogy characterize by ifferent spin-iffusion coefficients [Wan96]. itionay, none of the above oes takes into account the interfaces which are usuay present an which have a strong infuence on the acroscopic properties of the aterias. n the present work anaytica soutions of the spin-iffusion equations for a oneiensiona orphoogy copose of three oains are introuce. They are vai in the whoe range of the ixing ties an for arbitrary oain sizes, iffusivities an proton ensities. They can be easiy extene for investigating the spin-iffusion processes in higher iensions. n orer to perfor a spin-iffusion experient a graient of agnetization has to be create. The ajority of spin-iffusion investigations one in the past use ipoar fiters which ainy seect the signa fro the oains with high oecuar obiity. However, there are copex orphoogies for which the use of such type of fiters cannot ea to the esire inforation. One way to overcoe this probe is the use of ipoar fiters base on the excitation of utipe-quantu coherences. This approach was first reporte in [Gra97] where it was shown that by the appropriate seection of excitation/reconversion perios of the utipe-quantu coherences the agnetization of the oains with stronger ipoar coupings in a heterogeneous sape wi pass through the fiter whereas that with the weaker ipoar coupings wi be fitere out. fiter base on the excitation of oube-quantu coherences was ipeente. t was teste by coparing the oain sizes of two ibock copoyers with those obtaine in a spin-iffusion experient epoying a MPE (Mgic an Poarization Echoes) ipoar fiter. Further on, the cobination of these two types of fiters in conjunction with anaytica soutions of the spin-iffusion equations can be use to euciate the orphoogy of copex poyeric systes such as Nyon-6. This approach represents a big step forwar in the fie of spin-iffusion NM an can be extene to a broa cass of heterogeneous aterias.

14 Spin-iffusion NM. ntrouction an otivation The properties of poyers are often eterine by the existence of heterogeneities on ifferent ength an tie scaes. Typica exapes for heterogeneous poyers are seicrystaine poyers, poyer bens, bock copoyers an organic-inorganic hybri aterias. ynaic heterogeneities even occur in aorphous hoopoyers an ow oar ass gass forers. Whie the priary structure of the acrooecuar chain eterines the oca behaviour, acroscopic properties often refect the inherent heterogeneity of the orphoogy ike oain sizes, structure of grain bounaries, an interna interfaces. These istribute icrostructures can be probe by a variety of ethos ike transission eectron icroscopy (TEM), fie ion an atoic force icroscopy (FM), sa-ange X-rays scattering (SXS) an of neutron scattering (SNS). Soi state NM has been especiay usefu to iprove our unerstaning of heterogeneous aterias, ue to the correation of high structura resoution with severa ecaes of ynaic inforation [Sch94, Ki97, e0, ü0]. One estabishe NM etho to investigate oain sizes an orphoogy of heterogeneous poyers is base on the agnetization exchange after prouction of a z agnetization graient by a ipoar fiter [Sch93, Sch94, e95, Van96, Che96] (an references therein). These spin-iffusion experients are suitabe to investigate ifferent aspects of structura heterogeneities in a broa range of spatia iensions fro 0. n to about 00 n [Sch93, Van94, e95, Van96]. n spite of the ipressive efforts to anayze quantitativey the spin-iffusion process severa funaenta probes reain to be sove [Che8, Hav95, i96]. t is ainy the one-iensiona or aear oe, with a two- or three-phase orphoogy, that has been consiere earier in anaytica [Sch93, e95, Che8, Hav95, i96] an nuerica soutions [ss78, Ki9, Ken96] of the spin-iffusion equations. n any cases the anaytica soutions which provie ore physica insight into the spin-iffusion process were use in the short-tie regie to obtain inforation about the oain sizes [Sch93, Sch94]. naytica soutions for the evoution of agnetization in the oains were propose for the spin-iffusion process taking pace in two oains with 5

15 6 Chapter. Spin-iffusion NM aear, cyinrica an spherica orphoogies [e95]. n average spin-iffusion coefficient was assue in orer to sipify the copex reationships an to investigate the possibiity to use spin-iffusion experient to ifferentiate between ifferent orphoogies. This sipifie escription prove aequate for perforing spatiay resove spin-iffusion easureents on soi poyers [Wei96]. Later, genera anaytica soutions of the iffusionequations were erive for a two-oain aear orphoogy characterize by ifferent spin-iffusion coefficients [Wan96]. n orer to perfor a spin-iffusion experient a graient of agnetization has to be create. The ajority of spin-iffusion investigations one in the past use ipoar fiters which seect ainy the signa fro the oains with high oecuar obiity. To this category beong, for exape, the Goan-Shen [Go66] an the MPE (Mgic an Poarization Echo) ipoar fiters [e95]. However, there are situations, such as the case of copex orphoogies, where the use of such type of fiters cannot ea to the esire inforation. Mutipe-quantu coherences of ipoar coupe spin-/ nucei in the sois [Ern87, Mun87] have aso been expoite as a fiter to separate ifferent agnetization coponents in a spatiay heterogeneous syste. The first investigation of this type is reporte in ef. [Gra97] where it was shown that by the appropriate seection of excitation/reconversion perios of the utipe-quantu coherences the agnetization of the oains with stronger ipoar coupings in a heterogeneous sape wi pass through the fiter whereas that of the weaker ipoar coupings wi be fitere out. The experient was perfore on 3 C spin pairs in oube-abee poy(ethyene). y using short excitation/reconversion tie in the Q fiter, ony the spectru of the crystaine regions reains. Later, a an ipeester [a98] iscusse the possibiity to use oube-quantu an four-quantu (FQ) ipoar fiters in connection with a one-iensiona experient an seective etection. The FQ ipoar fiter was appie for a H spin iffusion experient on high-ensity poy(oxyethyene) but no oain sizes were reporte. The ain objectives of this chapter are: (i) To obtain genera anaytica soutions for the spin-iffusion equations escribing the process of ongituina agnetization transfer in an one-iensiona orphoogy copose of three oains with arbitrary sizes an iffusivities. The spin-iffusion equations nees to be sove taking into account proper initia an bounary conitions. The oain sizes obtaine by using these anaytica soutions are teste using previousy pubishe spin-iffusion ata on ibock copoyers an seicrystaine poyers. itionay, the effect of the interface size an of the approxiations ae on the evauation of the corresponing spin-iffusion coefficient on the

16 Chapter. Spin-iffusion NM 7 spin-iffusion curves is iscusse. (ii) To copare the oain sizes in heterogeneous poyers obtaine fro H spin-iffusion experients perfore using a cassica singequantu (SQ) ipoar fiter an a oube-quantu (Q) fiter. s oe syste for our investigation two ifferent ibock copoyers with aear orphoogy were seecte More etais can be foun in ref. [u]. Further on, we show how the cobination of ipoar fiters an anaytica soutions for the spin-iffusion process eas to an approach for testing the aear orphoogy of heterogeneous poyers.. Principes of spin-iffusion NM Spin-iffusion experients are typica spatia exchange experients [Sch93, Sch94] of the nucear agnetization eiate by the ipoar couping. The transfer of agnetization epens on the strength of the ipoar couping, the nuber of spins invove, an the istance between the nucei transferring the agnetization. The experienta set-up (Fig..) starts with a seection or fiter perio, foowe by a ixing perio of uration t uring which the spin-iffusion process takes pace, an a etection perio. For a better unerstaning et s have the situation epicte in Fig.. with a oe syste which has aternating oains an. nitiay the agnetization is hoogenousy istribute into the syste. For spin-iffusion to occur a graient of agnetization has to be create. Usuay this is achieve base on a ifference in one of the NM paraeters ike T, T, T or cheica shift of the two coponents [Sch93, Sch94]. s a resut the agnetization of one of the coponent is kept whie that of the other is fitere out so that after the seection perio ony the signa fro the seecte coponent is present. Once seecte the agnetization is aowe to re-equiibrate in the syste by fowing fro the source () into the sink () which was initiay evoi of agnetization. The istribution of the integra intensities of these two coponents is then onitorize in tie by recoring the NM spectru at ifferent vaues of the ixing tie t. The integra intensity corresponing to the source ecreases in tie whie that corresponing to the sink increases unti both reach equiibriu vaues. The tie epenence of the integra intensities is eterine by the orphoogy of the syste an by the oain sizes. One of the probes very often encountere in spin-iffusion experients is reate to T reaxation [Sch93, Sch94]. The reaxation of the agnetization coponents initiay suppresse can ea to signa contributions that are inistinguishabe fro those prouce by spin-iffusion an therefore no quantitative ata anaysis can be one.

17 8 Chapter. Spin-iffusion NM Figure.. Scheatic representation of the spin-iffusion process in a two-phase syste. fter the seection perio the NM spectru shows ony the signa corresponing to the phase. With increasing ixing tie, the intensity of the signas fro region ecreases whie those fro region increases unti equiibriu is reache. Severa authors were iscussing possibe canceation schees of the T effect on the spin-iffusion ata [Zha89, Ken90, New9]. Unfortunatey, none of these schees eas to a copete suppression of the reaxation effect. Later on a schee base on the storage of the z- agnetization after the ixing perio aternating between the (z) an (-z) irections an subtraction of the (-z) contribution fro the (z) contribution on the etection perio was propose by Spiess et a [Sch93, Sch94]. For a given vaue of the ixing tie t the etecte agnetization has the for where M r iffusion z ( r, t M ) z r t ( ) = iffusion r, t M ( r, t ) exp T z r (.) is the contribution without the effect of the reaxation. Fro the above equation is obvious that the effect of the reaxation can be sipy correcte by utipication of the spin-iffusion ata of each coponent fro the syste with the t corresponing factor exp T seection of agnetization. using the T vaue obtaine in a easureent without

18 Chapter. Spin-iffusion NM 9.3 Genera anaytica soutions of spin-iffusion equations for three oain systes with aear orphoogy.3. Theory We consier that the spin-iffusion process takes pace in a aear orphoogy (Fig..). The nucear agnetization transfer occurs fro a source an fows into a finite sink via an interface. The process is one-iensiona aong the x irection corresponing to the saest istance. ctuay, the interface can be, in principe, a oain with a size coparabe to the sizes of oains an. Figure.. The scheatic representation of the finite-source/interface/finite-sink syste with aear orphoogy. The spin-iffusion is consiere to be one-iensiona aong the x axis across the oain bounaries. The source, interface an sink oains have the inear iensions,, an, respectivey an they have been suppose to be uch saer than the iension perpenicuar to the iffusion irection. The spin-iffusion iffusivities are,, an, an the spin ensities are enote by,, an. n each region the spin-iffusion process is suppose to be governe by the acroscopic aw of Fick, i.e., x ( x,t) ( x,t) t = 0, x ( x,t) ( x,t) t = 0, (.)

19 0 Chapter. Spin-iffusion NM x ( x,t) ( x,t) t = 0, where, an are the space (x) an tie (t) epenent concentrations of the nucear z agnetization in the corresponing oains., an are the spin-iffusion coefficients in the oains, an, respectivey. t is assue that they are inepenent of space an the aount of agnetization. The inear sizes of the oains, an aong the irection of the poarization transfer are enote by, an, respectivey. ecause of the syetry of the orphoogy, the cacuations are ae ony for positive x coorinates so that for the region we have 0 x <, for region, x <, an for region, x < 3 (cf. Fig..). t zero spin-iffusion tie the whoe agnetization is suppose to be concentrate in the oain (source), i.e., ( t ) 0 = 0 =, (.3) ( t = 0) 0, an ( t = 0) 0 =. (.4) = Then the agnetization fows fro to via the oain respecting the bounary conitions. The first bounary conitions are reate to the continuity of the z agnetization (or nucear poarization oriente parae with the irection of the static agnetic fie) concentration at the oain bounaries. They can be written as (,t) (,t) =, (.5),t) = (, t). (.6) ( The secon bounary conitions require that the z-agnetization fuxes have to be equa at the oain interfaces, i.e.,,t,t ( ) ( = ), (.7) x x (,t) (,t) =, (.8) x x where, an are the nuber ensities of spins in the, an oains, respectivey. t is aso evient that ( x,t) x = x= 0 ( x,t) 0, an = 0. (.9) x The soutions of the above ifferentia equations with the initia an the bounary conitions can be obtaine using the Lapace transforation. They are presente in the appenix [Cra86, Car86]. x= 3

20 Chapter. Spin-iffusion NM We are finay intereste in the tie epenence of the NM signa intensity (NM observabe) of each oain which is nothing ese other than the integra of the concentration of the z agnetization over the reevant iension of each oain. Using the tie an space epenent agnetization concentrations, an given in the appenix (see Eqs. (.5-.7)) we finay get () ( ) ( ) ( ) ( ) { ( ) ( ) ( ) ( ) ( ), sin sin F sin e x t t = = = β β β β β (.0) () ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ), sin sin sin sin sin F e x t t = = = β β β β β β β (.) an, () ( ) ( ) ( ) ( ) ( ). sin F sin e x t t = = = β β β β (.) These soutions of the spin-iffusion process in a aear orphoogy copose of three oains are vai for arbitrary vaues of oain sizes an spin-iffusion coefficients. generaization of these soutions was ae for the case of an inefficient fiter i.e. when there is soe resiua agnetization at zero spin-iffusion tie aso in the interface an sink regions. etaie cacuations are given in [u]. The first test of the vaiity of the spin-iffusion NM observabes escribe by the Eqs. (.0) - (.) is reate to the aw of conservation of z agnetization in tie, i.e.,

21 Chapter. Spin-iffusion NM () ( ) ( ) ( ) 0 0 t t t = =. (.3) n any poyer systes we have to consier an ensebe average over a istribution of sizes in each oain. The tie evoution of the spin-iffusion observabes oes not criticay epen on the for of the size istribution function [e95] (an references therein) an can easiy be incorporate in our genera soutions Eqs. (.0) - (.). n the interpretation of the spin-iffusion ata given beow we wi negect this oain size istribution. The soutions for a two ()- an a three (3)-iensiona probe can be erive as proucts of the soutions if the phase structure can be expresse as a prouct of oneiensiona structures [Sch93]. Nevertheess it is evient that the exact soutions for the spiniffusion equations for cyinrica or spherica orphoogies are ifferent fro those taken fro a aear orphoogy [e95, Cra86, Car86]. For exape, in the case of a cyinrica orphoogy, the exact anaytica soutions ipies a copex cobination of esse functions. Work aong this irection is in progress..3. Particuar case for a two oain systes n the particuar situation of a vanishing interface the NM observabes an have the foowing fors ) ( t ) ( t () ( ) ( ) ( ) ( ), sin sin cos cos t exp sin sin x x t i = = = 0 i i i i i i i i β β κλ β β λ κ β β β β (.4) () ( ) ( ) ( ) ( ), sin sin cos cos t exp sin sin x x t i = = = 0 i i i i i i i i β β κλ β β λ κ β β β β (.5) where = κ an κ λ =. The vaues β i are the soutions of the trigonoetric equation

22 Chapter. Spin-iffusion NM 3 sin β cos β cos β sin β = 0. (.6).3.3 The effect of the interface oain The genera escription of spin-iffusion for a three oain syste with arbitrary sizes an iffusivities aows us to siuate the effect of the approxiations use for the vaue of the spin iffusivity of the interface oain. The spin-iffusion ecay an bui-up curves are siuate in Fig..3a for ifferent vaues of fufiing the conition. t is evient that the spin-iffusion curves are not very sensitive to the vaues taken for. Hence, the arithetic average = use in previous stuies is justifie. Figure. 3. The effects of the spin-iffusion coefficient (a) an the size of the interface oain (b) on the ecay an bui-up spin-iffusion curves siuate using Eqs. (.0) an (.). For a the siuations the foowing paraeters were use: = 5 n, = 0 n, = 0.5 n /s, an = 0.8 n /s. For the siuations shown in a) the size of the interface oain was taken to be = 5 n an in b) the iffusion coefficient of the interface was = 0.5 n /s. The intercept of the tangent to the inear region of the spin-iffusion bui-up curve an the tie axis is enote by. / t 0 The effect of the interface oain size is siuate in Fig..4b. f the range of the vaues changes about one orer of agnitue a cear change in the shape of the spin-iffusion curves is observe. t is shown in Fig..3b that for intereiate vaues of the spin-iffusion tie t the bui-up curves have a goo inear behavior. n approxiate evauation of the interface size can be obtaine fro the intercept of the tie axis an the tangent to the inear region of the spin-iffusion bui-up curves [e95]. This vaue is given by t 0 (cf. Fig..3b). n Fig..4 the vaues are shown versus t 0 obtaine fro a set of spin-iffusion

23 4 Chapter. Spin-iffusion NM siuations. t is evient that a inear epenence t0 exists ony for the interface sizes up to about n. For a orphoogy represente by three oains with of the sae orer of agnitue as those for the source or the sink the intercept t 0 has a copex epenence on the interface oain size. Figure.4. nterface size versus the intercept / t 0 (see Fig..3b) obtaine fro a set of siuations base on Eq. (.) with = 5 n, = 0 n an spin-iffusion coefficients = 0.5 n /s, = 0.8 n /s, an = 0.5 n /s. The straight ine shows that a inear epenence exists between an / t 0 for sa vaues of the interface size..3.4 Tests for the soutions of the spin-iffusion equations n orer to check the accuracy of anaytica soutions for spin-iffusion equations erive above we sha appy the for the evauation of the oain sizes in poyer systes with aear orphoogies using ata which have areay been pubishe in the iterature. The first case is represente by the sape C of a poy(styrene-b-ethyphenysioxane), (PS-b- PMPS) ibock copoyer fro [Cai93]. ts orphoogy is aear an ha been eterine by transission eectron icroscopy. The previous stuy [Cai93] aso inicates the presence of an interface in this syste which can be inferre fro the sigoia shape of the spiniffusion bui-up curve at the beginning of the spin-iffusion process (see aso Fig..3b) [e95, Sch93].

24 Chapter. Spin-iffusion NM 5 Figure. 5. Experienta ata for the H spin-iffusion bui-up curve of PS in a PS-b-PMPS ibock copoyer (sape C fro [Cai93]). The integra intensity of the fitere spectru is (0). The soi ine represents the fit of the experienta ata using Eq. (.). The best fit paraeters are given in Tabe.. The siuations obtaine using Eq. (.) with the iffusivities an oain sizes reporte in [Cai93] (ashe ine) an [Wan96] (ash-pointe ine) are aso shown. The spin-iffusion buiup curve an the experienta ata were noraize to the quasi-equiibriu vaue. n Fig..5 the experienta ata taken fro [Cai93] as we as the siuations base on our anaytica soutions (cf. Eq..) are shown using the spin-iffusion coefficients an oain sizes given in [Cai93] an [Wan96] (see Tabe.). The tie-epenent spiniffusion curves siuate with the paraeters fro [Cai93] an [Wan96] are both in the goo agreeent but the experienta ata are not reprouce accuratey. The bui-up curve given by Eq. (.) is aso shown in Fig..5 an the agreeent with the experienta ata is satisfactory for a vaues of the spin-iffusion ties. The iffusion coefficients an the oain sizes which give the best fit with the experienta ata are reporte in the Tabe.. They are cose to the vaues reporte previousy [Cai93, Wan96]. Moreover, the ong perio of the aear orphoogy obtaine fro our ata, i.e., NM = PMPS interface PS, is NM [Cai93].. ± n an ies in the range of the vaue easure by SXS, SXS 9-5 n

25 6 Chapter. Spin-iffusion NM Tabe.. Spin-iffusion coefficients () an oain sizes () for a PS-b-PMPS ibock copoyer (first rows) [Cai93, Wan96]. The vaues of the iffusivities use for the siuation of the spin-iffusion ata shown in Fig..5 an the oain sizes obtaine are shown in the ast row PMPS interface PS PMPS interface PS (n /s) (n /s) (n /s) (n) (n) (n) a 5.5 b 4 a b b a c.3 c.8 c a ata fro ef. [Cai93] b ata fro ef. [Wan96] c the uncertainities are ess than 0% Tabe.. Spin-iffusion coefficients () an oain sizes () for the PEO syste (first row) [e95]. The vaues of the iffusivities use for siuation of the spin-iffusion ata shown in Fig..6 an the oain sizes obtaine are shown in the ast row aorphous interface crystaine aorphous interface crytaine (n /s) (n /s) (n /s) (n) (n) (n) 0.5 a 0.5 a 0.8 a 4. a 0.3 a 7. a b 0.5 b 8 b a ata fro ef. [e95] b the uncertainities are ess than 0% The secon case stuie is a high-oecuar-weight poy(ethyene oxie) (PEO). t has crystaine an aorphous aear oains which have been investigate by spin-iffusion NM [e95]. The easure spin-iffusion ecay an bui-up curves for the aorphous an the crystaine regions fro [e95] are shown in Fig..6. The tie evoution of the NM signas fro aorphous an crystaine oains generate using Eqs. (.0) an (.) an spin-iffusion coefficients as we as the oain sizes reporte in [e95] (see Tabe.) are shown in Fig..6 (ashe ines).

26 Chapter. Spin-iffusion NM 7 Figure. 6. The tie evoution for the H spin-iffusion observabes of aorphous a) an crystaine b) coponents of PEO fro [e95]. The ashe ines show the curves obtaine fro Eqs. (.0) an (.) with the paraeters fro [e95]. The soi ines represent the fit of the spin-iffusion ata using Eq. (.0) for (a) an Eq. (.) for (b). The best fit paraeters are presente in Tabe.. The spin-iffusion bui-up curve an the experienta ata were noraize to the quasi-equiibriu vaue. The ifferences between the experienta ata an the siuate spin-iffusion curves using our genera soutions are ue to the fact that sipifie soutions of the spin-iffusion equations with an average spin-iffusion coefficient [Cra86] were use for estiating the oain sizes in [e95]. The best fit of the spin-iffusion ata [e95] using the Eqs. (.0) an (.) are given by soi ines ( cf. Fig..6). The best fit paraeters are iste in Tabe.. The use of exact soutions for the spin-iffusion process in which each region is characterize by a ifferent iffusivity in the case of seicrystaine PEO eas to arger oain sizes copare to the case of an average iffusivity [e95]. This is ue to the fact that the fronts of the z-agnetization in the crystaine oains which have the argest size wi trave faster because the iffusivity of this oain is arger copare to the average iffusivity.

27 8 Chapter. Spin-iffusion NM.4 Singe- an oube-quantu ipoar fiters.4. Experienta. Sapes Proton spin-iffusion experients using singe-quantu (SQ) an oube-quantu (Q) fiters were perfore on poy(ethyene oxie)-bock-poy(styrene) (PEO-b-PS) ibock copoyer an on poy(ethyene oxie)-bock-poy(hyroxyethyethacryate) (PEO-b- PHEM) ibock copoyer. For both copoyers a onofunctiona poy(ethyene oxie) acroinitiator with a oecuar weight of 000 was use for the ato transfer raica poyerization (TP) of styrene in buk an of hyroxyethy ethacryate (HEM) in ethyene gyco as sovent, respectivey [ei, ei3]. The egrees of the poyerization of the poystyrene bock an of poy(hem) bock, respectivey were esigne to be equa to that of the corresponing PEO bock [ei, ei3]. The conversions as we as the oecuar weights an the poyispersities M w M n of the sapes eterine by eans of GPC are given in Tabe.3. Further etais of the poyerization proceure are given in ef. [ei] an [ei3]. Tabe.3. Characteristics of the PEO-b-PS an PEO-b-PHEM ibock copoyer Conversion a Sape (%) M n b g/o M w /M n b PEO-b-PS PEO-b-PHEM a Conversion of the viny onoer eterine by eans of H NM spectroscopy b M n vaue of the bock copoyer evauate by eans of GPC n orer to anayse the phase behaviour of the two copoyers a ifferentia scanning caorietry anaysis was ae within the range 80 o C to 0 o C with a heating rate of 0 K/in. For both sapes a weak transition aroun 56 0 C was etecte, in agreeent with the gass teperature T g of PEO which is a seicrystaine poyer with T g = C an a eting teperature T = 67 0 C. None of the two sapes shows an enother near 67 0 C which inicates that they are copetey aorphous.

28 Chapter. Spin-iffusion NM 9. NM Experients H soi-state NM spectra, Q bui-up curves, an spin-iffusion spectra were easure using a ruker SX-500 spectroeter operating at MHz for H. The ata were coecte at roo teperature for non-spinning sapes. The ength of a π/ puse was about 5.5 µs, the we tie was.5 µs, an the recyce eay was 5.5 s for a easureents. Proton ongituina agnetization reaxation (T ) easureents were perfore uner static conitions at roo teperature using the saturation recovery etho. Typicay, tie increents were use, an the tota integra intensities of the NM absorption spectra were evauate in a east-squares fit with a su of two exponentias. The fast ecaying coponent was attribute to the obie aorphous phase an the other one to the rigi aorphous phase. Proton spin-iffusion easureents were perfore using the genera schee consisting of a z agnetization fiter, a spin-iffusion perio, an an acquisition perio as presente in Fig..7a. The graient of agnetization was create by using two types of fiters accoring to the poyer phase to be seecte. Figure.7. a) Genera schee use for the spin-iffusion experient. b) Puse sequence use for a spin-iffusion experient with a Q fiter. c) Puse sequence use for a spin-iffusion experient with a MPE fiter.

29 0 Chapter. Spin-iffusion NM The fiter epicte in Fig..7b excites oube-quantu coherences [Ern87, Mun87] an seects ainy the agnetization of the rigi phase. The vaue of t Q is 5 µs an the vaue of τ correspons to the axiu of the Q bui-up curve. n orer to seect the obie aorphous phase a MPE ipoar fiter [e95] (Fig..7c) was use which is base on refocusing SQ coherences with a fiter perio of τ = 00µs..4. oube-quantu ipoar fiter H Q bui-up curves of the two ibock copoyers were recore using the five-puse sequence [Ern87, Mun87] (Fig..8). The axiu of the curves appear at very short excitation ties τ, in the range fro 0 to 0 µs, inicating the presence of strong H ipoar interactions. These interactions are stronger in PEO-b-PS than in PEO-b-PHEM. Figure.8. Proton Q bui-up curves of a) PEO-b-PS an b) PEO-b-PHEM recore using the puse sequence fro Fig..7b with t Q = 5µs an t = 0µs. Proton NM spectra PEO-b-PS an PEO-b-PHEM are shown in Figs..9a an.0a, respectivey. Each spectru shows a narrow an a broa coponent. n orer to assign the coponents to the corresponing bock, a proton spectru of pure PEO with the sae oecuar weight as the PEO bock in the copoyers was recore. Taking into account that no crystaine phase of PEO is present in the copoyers, the coparison of this spectru with the proton spectra of the two copoyers inicates that the narrow peak is ue to the obie aorphous PEO coponent. Thus, the broa coponent is ue to the PS bock in PEO-b-PS an to the PHEM bock in PEO-b-PHEM. The proton spectra of each sape were ecopose in ters of a Gaussian an a Lorentzian ine. The resuts (Tabe.4) inicate that the obiity of the poyer chains in the obie aorphous phase is about one

30 Chapter. Spin-iffusion NM orer of agnitue higher than in the rigi aorphous phase. This aows a goo seection of the z agnetization of the forer oain using a ipoar fiter (see beow). Tabe.4. eative integra intensities (), ine positions an the fu-with at haf intensity ν / of the two coponents of PEO-b-PS an PEO-b-PHEM ibock copoyers obtaine fro ecoposition of proton spectra. PEO-b-PS PEO-b-PHEM Mobie igi Mobie igi orph. orph. orph. orph. (%) a 78 a 30 a 70 a Line pos. (pp) ν / (khz) a The uncertainties are saer than 0%. Figure.9. ipoar fiter efficiency for PEO-b-PS ibock copoyer using a Q fiter. Proton spectru: a) after a 90 0 puse, an for an excitation tie of b) τ = 5 µs corresponing to the axiu of the Q bui-up curve, an c) τ = 55 µs.

31 Chapter. Spin-iffusion NM Figure.0. ipoar fiter efficiency for PEO-b-PHEM ibock copoyer using a Q fiter. Proton spectru: a) after a 90 0 puse, an for an excitation tie of b) τ = 8 µs corresponing to the axiu of the Q bui-up curve, an c) τ = 75 µs. Figures.9b,.9c an Figs..0b,.0c show the fitere H spectra recore at the axiu of the Q bui-up curves an far away fro the for the PEO-b-PS an PEO-b- PHEM ibock copoyers, respectivey. n the case of the PEO-b-PS syste the Q fiter acts quite efficienty an aost ony the rigi phase corresponing to the PS coponent is seecte. The Q fiter is not so efficient in fitering out the obie aorphous coponent in PEO-b-PHEM, a sa contribution of about 0% of PEO being sti present. This eans that for this copoyer the Q coherences can quite easiy be excite in the obie an in the rigi aorphous phases. For the vaues of the excitation tie τ far away fro the vaue corresponing to the axiu of the Q bui-up curves, the fiter starts to act as a T fiter in both cases, an the obie coponents can be seecte. The rawback of the Q fiter use as a T fiter is the reuce intensity of the fitere spectra which eas to a sa signa/noise ratio for the spin-iffusion ata..4.3 MPE ipoar fiter Spin-iffusion experients copeentary to those with the Q fiter were ae using a MPE ipoar fiter [e95]. ecause of the ifferences of the obiity between the two

32 Chapter. Spin-iffusion NM 3 phases, the MPE fiter is abe to seect the obie aorphous coponent in both copoyers. The resuts are shown in Fig.. an Fig... Figure.. ipoar fiter efficiency for PEO-b-PS using a MPE ipoar fiter with ifferent free evoution perios: a) τ = µs, b) τ = 0 µs, an c) τ = 50 µs. For a free evoution perio of τ = 00 µs () the agnetization of the rigi phase is copetey fitere out. Figure.. ipoar fiter efficiency for PEO-b-PHEM using a MPE fiter ipoar with ifferent free evoution perios: a) τ = µs, b) τ = 0 µs, an c) τ = 50 µs. For a free evoution perio of τ = 00 µs () ony the signa fro the obie aorphous phase is present.

33 4 Chapter. Spin-iffusion NM Litte fitration is achieve in the case of both sapes when the MPE fiter with a free evoution tie of τ = µs is epoye (Figs..b an.b). The fitration efficiency is increasing when the free evoution tie is increase. For τ = 00 µs the rigi coponent is copetey fitere out an ony the obie aorphous coponent gives rise to a signa in the spectru (Figs.. an.)..4.4 eaxation of ongituina agnetization ecause at ong ixing ties the spin iffusion process is affecte by ongituina agnetization reaxation an estiation of the reaxation ties T of each phase is necessary. The experienta reaxation curves were fitte by a su of two exponentias. The resutant vaues of the reaxation ties T an the corresponing reative intensities are given in Tabe.5. With reference to the reative intensities obtaine fro the ecoposition of the proton spectra (Tabe.4) the arge vaue of the reaxation tie is attribute to the PEO bock in both cases an the short one to the PS an respectivey to the PHEM bocks. The obtaine vaues for the reaxation ties of the two coponents are not too ifferent fro each other inicating that the spin-attice reaxation is strongy affecte by the spin-iffusion process. Tabe.5. eative apitues an proton ongituina reaxation ties of PEO-b-PS an PEO-b-PHEM ibock copoyers. Sape T ong ( s ) ( s) T short ong (%) (%) short PEO-b-PS 0.64 a 0.4 a a 78 a PEO-b-PHEM 0.6 a 0.55 a 7 a 73 a a The uncertainties are saer than 0%..4.5 Proton spin-iffusion Proton spectra recore after ifferent ixing ties using the Q fiter are shown in Figs..3 an.4 for PEO-b-PS an PEO-b-PHEM, respectivey. n both cases the fow of ongituina agnetization fro the rigi oain into the obie oain is observe with increasing ixing tie. fow of the agnetization in the opposite way is observe when the MPE fiter is use (Figs..5 an.6). n both cases, the equiibration of agnetization takes pace on a tie scae saer than the reaxation of the ongituina agnetization, hence a correction of the spin-iffusion ata corresponing to the reaxation effects has not been perfore.

34 Chapter. Spin-iffusion NM 5 Figure.3. Proton spectra of PEO-b-PS recore after ifferent ixing ties t in the spin-iffusion experient using a Q fiter: a) t = 500 µs, b) t = 5 s, an c) t = 50 s. Figure.4. Proton spectra of PEO-b-PHEM recore after ifferent ixing ties t in the spiniffusion experient using a Q fiter: a) t = 500 µs, b) t = s, an c) t = 5 s.

35 6 Chapter. Spin-iffusion NM Figure.5. Proton spectra of PEO-b-PS recore after ifferent ixing ties in the spin-iffusion experient using a MPE fiter: a) t = 00 µs, b) t = 500 µs, c) t = 0 s, an ) t = 00 s. Figure.6. Proton spectra of PEO-b-PHEM recore after ifferent ixing ties in the spiniffusion experient using a MPE fiter: a) t = 00 µs, b) t = 500 µs, c) t = 0 s, an ) t = 00 s. The tie epenent integra spin-iffusion intensities obtaine for PEO-b-PS with the MPE an Q fiters are presente in Fig..7. n the first case, the agnetization fows fro the obie aorphous regions into the rigi aorphous regions. The quasi-equiibriu

36 Chapter. Spin-iffusion NM 7 is reache approxiatey at 00 s. n the atter case, the agnetization fows fro the rigi aorphous phase to the obie phase an the equiibriu is reache in about the sae tie. The integra spin-iffusion intensities obtaine for PEO-b-PHEM with the MPE an Q fiters are presente in Fig..8. n the first case, the agnetization fows fro the PEO regions into the PHEM regions an in the secon case in the reverse irection. Quasiequiibriu is reache faster in the case of the Q ipoar fiter copare to the case of the MPE fiter because of fiter efficiency ifferent fro one. Figure.7. Proton spin iffusion bui-up an ecay curves of PEO-b-PS obtaine using a) a MPE fiter an b) a Q fiter. Figure.8. Proton spin iffusion bui-up an ecay curves of PEO-b-PHEM obtaine using a) a MPE fiter an b) a Q fiter. For both copoyers the spin-iffusion ecay an bui-up curves are crossing each other for the MPE ipoar fiter (Figs..7a an.8a). This is not the case for the spiniffusion experients perfore with the Q fiter (Fig..7b an.8b). These facts can be

37 8 Chapter. Spin-iffusion NM expaine by the arger nuber of protons in the rigi oains copare to that in the obie oains (Tabe.4). The oain sizes for both copoyers were estiate using Eqs. (.0) an (.) in the case of MPE fiter. n the case of the Q fiter the sae equations were epoye for the PEO-b-PS syste. The equations reporte in [u] an which took into account a 0.85 vaue for the fiter efficiency were use for the PEO-b-PHEM syste. The vaues for the proton ensities were estiate base on the oecuar ensity. They are PEO = 0.03 g / c 3 3 3, = 0.08g / c, an = g / c. The vaues for the PS PHEM spin-iffusion coefficients of the PEO an the PS bock were assue to be equa to those reporte previousy [e95, Jac98, Me99, Yu] PEO = 0.5 n /s an PS = 0.8 n /s. ecause in the case of PEO-b-PHEM the ine with for the PHEM bock is in the sae range as that of the PS bock an, oreover, because the proton ensities of the two coponents are cose to each other we can assue that a vaue of 0.8 n /s is a reasonabe choice for the spin-iffusion coefficient of the PHEM phase. For both systes, the proton ensity an spin-iffusion coefficient corresponing to the interface have been taken as the arithetic average of the corresponing vaues of the source an the sink. The oain sizes obtaine fro the evauation of the spin iffusion ata acquire with the SQ an Q ipoar fiters are given in Tabe.6 for both ibock copoyers. Tabe.6. oain sizes in the PEO-b-PS an PEO-b-PHEM ibock copoyers easure by the MPE an Q fiters PEO-b-PS PEO-b-PHEM PEO interface PS PEO interface PHEM (n) (n) (n) (n) (n) (n) MPE fiter 4. a.8 a 4.5 a.6 a 0.5 a 6.7 a Q fiter 3.6 a 0.8 a 4.8 a.5 a 0.3 a 6. a a The uncertainties are saer than 0%. There is goo agreeent between the vaues estiate for the oain sizes of either syste using the two types of fiters. This is an inication that the Q fiter is abe to give the sae inforation as the ipoar fiters which are usuay use in spin-iffusion experients. The ifferences that exist, in the case of the PEO-b-PS ibock copoyer, for the vaues of

38 Chapter. Spin-iffusion NM 9 the estiate size of the interface can be expaine by inaccuracies in the evauation of the integra signas of the rigi phase when the MPE ipoar fiter is use. Nevertheess, the vaues of the oain sizes obtaine using the two types of fiters are cose to each other which inicates that the spin-iffusion process fro the obie phase to the rigi phase is equivaent to the process in the reverse irection. Such an equivaence shows that the assuption of a aear orphoogy for the two systes is correct. Therefore, such types of spin-iffusion experients using a cobination of ipoar fiters that seect the z agnetization fro regions with ifferent obiity can be use for probing if the orphoogy of a syste is aear or not..5 Concusions The spin-iffusion process has been investigate in systes with a oe orphoogy represente by three ifferent oains with arbitrary sizes, iffusivities, an proton ensities. Genera anaytica soutions vai for the fu range of spin-iffusion ties were erive for an one-iensiona process. n the aopte oe, the nucear agnetization transfer occurs fro a source an fows into a finite sink via an interface. The theoretica approach was base on the use of the Lapace transforation. The integra intensities corresponing to each oain were evauate, an a C progra was written for their generation. The obtaine soutions were teste for a poy(styrene-b-ethyphenysioxane) ibock copoyer an seicrystaine poy(ethyene oxie) by preicting the oain sizes an coparing then with the previousy reporte ata. For the first tie, the effect of the interface in ters of the size an the spin-iffusion coefficient on the spin-iffusion curves was irecty investigate. The siuations showe that the presence of the interface has a stronger effect on the signa obtaine fro the sink region than on the signa obtaine fro the source region. The vaue of the spin-iffusion coefficient in the interface has ony a sa effect on the spin-iffusion bui-up an ecay curves an therefore, an arithetic average of the spin-iffusion coefficients in the source an sink is a goo approxiation for its vaue. The appicabiity of these soutions can be extene for stuying the iffusion of iquis, an for ass or heat transfer in systes having the sae orphoogy. n the ast part of this chapter, spin-iffusion experients were perfore for two ifferent copoyers in orer to test a ipoar fiter base on the excitation of Q coherences. This ipoar fiter uses specific excitation/reconversion ties an seects ony (or ainy) the agnetization of the rigi oains with ower oecuar obiities. t was shown that the

39 30 Chapter. Spin-iffusion NM oube-quantu fiter is abe to give the sae inforation about the oain sizes as a traitiona ipoar fiter which seects the agnetization of the obie oains. The rigiphase fiter has severa avantages: (i) the narrow NM signa which correspons to the obie oains can be etecte ore easiy an the integra intensity is evauate ore accuratey copare to the case of traitiona spin-iffusion experients in which the increase in the intensity of the broa NM signa is easure. (ii) high-orer utipequantu fiter can be appie to iprove the efficiency of the initia z agnetization graient prouce in the rigi oains. Nevertheess, the ipoar fiter base on the seection of utipe-quantu coherences prouces weak initia NM signas because of the ow excitation efficiency of such coherences. Moreover, the easureent tie is onger because of the phase cycing necessary for seection of the utipe-quantu coherences. Spin-iffusion experients epoying Q an T fiters were perfore on the sae copoyers proucing coparabe vaues for the oain sizes. Moreover, it was shown that inforation about the aear orphoogy of systes can be obtaine inepenent of other techniques using such a cobination of ipoar fiters. This represents a big step forwar in the fie of spin-iffusion NM.

40 3 nvestigation of copex orphoogies by spin-iffusion NM 3. Nyon-6 fibers 3.. ntrouction an otivation Poyaie (P) is the ost coon engineering theropastic in use toay [s]. The annua consuption of poyaie for engineering pastic appications excees 000 ktons [s]. Poyaies cover a broaer range of appications than any other engineering pastic. They are suitabe for a ajor processing techniques, such as injection ouing, bow ouing an extrusion [s]. Nyon-6 (P6) is one of the ost iportant synthetic fiberforing aterias use for high-spee et spinning [Zia76]. Thus, high-spee et spinning raises both scientific interest an technica iportance. Therefore, it is necessary to unerstan the reationship between the spinning spee an the fiber properties on the basis of the icroscopic structure an oecuar otion. The segenta ynaics of Nyon-66 was investigate by euteriu NM spin-attice reaxation an ine-shape siuations. They reveae the existence of free an constraine aorphous popuations [Hir90, Miu90]. This resut is confire by stuies by X-ray iffraction which inicate that there are three ifferent phases in Nyon-6 fibers: crystaine, unorientate aorphous ocate in the aear stack, an orientate aorphous ocate between the fibris [Mur93a, Mur93b]. Furtherore, the existence of a obie aorphous phase in aition to the crystaine an rigi aorphous phases in Nyon-6 fibers has been prove by easureents of the H spin-attice reaxation in the rotating frae ( ), an a processing-icrostructure an chain-otion reationship was estabishe [Kwa0, Kwa]. The fraction of each phase was estiate fro the agnetization ecay. t was shown that it epens on the processing spinning spee. The NM obie aorphous phase represents a sa fraction of a few percent copare to the crystaine an NM rigi aorphous phases. t can be inferre fro NM spin-attice reaxation easureents that the rigi aorphous 3 T T

41 3 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM regions, rather than the obie aorphous ones, transfor into the crystaine regions uring high-spee spinning of Nyon-6 fibers. n aition to NM spectroscopy an reaxoetry, agnetic resonance iaging has been aso use to investigate the fracture behavior of two ifferent types of extrue poyaie 6 / aeic anhyrie grafte ethyene-propyene (EPMg-M) bens [r]. ecenty, an investigation of the changes in the crystainity an orphoogy of soe paraagnetic Nyon-6 cay nanocoposites copare with the corresponing pure Nyon-6 sapes was ae by using H spin-iffusion easureents [Van]. However, no inforation about the istribution of the crystaine, rigi aorphous an obie aorphous phases insie the fibers as we as the corresponing oain sizes were given. The ain goa of this subchapter is to show how the new eveopent in the spiniffusion ethooogy reate to ipoar fiters can ea to a ore etaie escription of the copex orphoogy of Nyon-6 fibres. The new approach aopte in this stuy is base on the use of a MPE fiter which seects the agnetization fro the obie aorphous phase in conjunction with a oube-quantu ipoar fiter that seects the initia nucear poarization in the crystaine oains together with anaytica soution of the spin-iffusion equation. 3.. Experient. Sapes Nyon-6 utifiaent yarns use in this stuy were obtaine by et-spinning at SM (Geeen, The Netherans). Fibers with ifferent wining spee an raw ratio were investigate. The fibers with ifferent wining spees were obtaine fro a coercia Nyon-6 grae (GL030 by SM) with a reative viscosity of.45 an a oecuar weight of M n = 6400 kg/ko. The as-spun fibers were not subjecte to further hot-rawing. The fibers with ifferent raw ratios were obtaine fro a uti-fiaent yarn spun at a ow spee of 500 /in, using a coercia Nyon-6 grae (GL000 by SM) with a reative viscosity of.85 an a oecuar weight of M n = 400 kg/ko. The characteristics of the investigate Nyon-6 fibers are suarize in Tabe 3.. To avoi copications in the interpretation of NM spin-iffusion ata introuce by the presence of absorbe water, the Nyon-6 fibers were saturate with O by putting the in contact with the iqui O. Equiibriu was reache after one week when no weight change was recore on successive ays. For Nyon-6 fibers at roo teperature an a reative huiity of the surrouning air of 00% an 40% the fiber ass increases by about 0% an %, respectivey. The hyration water is present ony in the aorphous phase of the

42 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 33 Nyon-6 fibers [Hut96, Mur89] an because the aount of water uptake is oerate [r] no rastic changes in the oain sizes is expecte. Tabe 3.. Processing paraeters of Nyon-6 fibers Wining Eongation M Spee n Tenacity raw atio Poyer at break (g/o) (cn/tex) (/in) (%) 500 a GL b GL a GL b GL b 3. GL b 4.4 GL a 4.5 GL a MPE ipoar fiter was use b Q ipoar fiter was use. NM easureents Proton soi-state NM spectra an spin-iffusion ata were easure using a ruker SX- 500 spectroeter operating at MHz for H. The ata were coecte for static sapes at roo teperature. The ength of the π/ puse was about 5.5 µs an the we tie was set to.5 µs. The recyce eay was 5 s for a easureents. The NM experients with the Nyon-6 fibers ierse in O an those hyrate with O essentiay showe the sae H spectra. The H spectra can be ecopose in the three coponents (see beow) using the ruker WinFit progra. Proton ongituina agnetization reaxation (T ) easureents for non-rotating sapes were perfore at roo teperature using the inversion recovery etho. n orer to avoi agnetization transfer fro the obie aorphous phase to the rigi aorphous an crystaine phases aitiona easureents uner agic-ange sape spinning (MS) were ae at a rotor frequency of ν = 5 khz, this tie using the saturation recovery etho. Typicay tie increents were use, an the tota integra intensities of the NM absorption spectra were fitte with a su of two exponentias by a east-squares proceure.

43 34 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM The fast ecaying coponent was attribute to the obie aorphous phase an the other one to the rigi aorphous an crystaine phases. These easureents o not aow us to separate the ongituina agnetization reaxation of the ast two phases. The spin-iffusion experient foows the genera schee z-agnetization fiter - spin-iffusion perio etection as shown in Fig..7. The graient of agnetization was create by using two types of fiters epening on the poyer phase to be seecte. MPE ipoar fiter (Fig..7c) with a free evoution tie τ = 0 µs was use for seecting the agnetization fro the obie aorphous regions. For seecting the agnetization fro the crystaine regions a fiter base on the excitation of the oube-quantu coherences was epoye. The vaue of the paraeter τ epoye for the Q ipoar fiter (Fig..7b) in Nyon-6 sapes was τ = µs. The spin-iffusion process using a Q fiter is copete for a tie scae saer than the T vaue so that no correction of the spin-iffusion ata ue to ongituina reaxation effect was perfore. This is fuy justifie for the crystaine an ess-obie aorphous oains because of ong T vaues of the orer of s (see beow). For the obie aorphous oains T is of orer of 00 s but the renoraization proceure appie uring the ata anaysis (see beow) partiay copensates its effect on the spiniffusion curves of the crystaine an the ess-obie aorphous regions Proton spectra of Nyon-6 fibers Typica proton NM spectra of static Nyon-6 hyrate in O are shown in Figure 3.. The NM spectra of the poyer can be ecopose into three coponents. One has the saest fu with at haf height ν / in the range khz (see Tabe 3.). t correspons to the NM-obie aorphous phase, an fro the integra intensity it is cear that its content is uch ow than that of the other two coponents. The coponent with an intereiate ν / was attribute to the ess-obie aorphous regions. The coponent with the higher ν / is reate to the crystaine regions an a sa fraction of the aorphous phase that is rigi at the roo teperature [Lit3]. n increase in the wining spee or raw ratio eas to an increase in the crystaine content. This is ue to the fact that a part fro the aorphous regions transfors into crystaine ones. This effect is uch ore obvious when the raw ratio increases. n this situation aso an increase in the iobiization of the chains in both ess-obie an crystaine regions can be seen, as refecte in the increase of the ine with. The ata presente in Tabe 3. show that for a sapes the content of the ess-obie aorphous an crystaine phases represents ore than about 90%.

44 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 35 Figure 3.. Proton spectra for Nyon-6 fibers hyrate in O. a) Spun at 000 /in, b) spun at 5800 /in, c) spun at 500 /in an rawn to = 3., ) spun at 500 /in an rawn to = 4.4. NM spectra corresponing to the crystaine, ess-obie aorphous an obie aorphous phases obtaine by the ecoposition of the origina spectra are represente by ashe ines. Tabe 3.. eative contribution of the obie aorphous, ess-obie aorphous (LM) an crystaine (C) phases as we as the corresponing H spectra ine withs at haf height. eative apitue (%) a Line with (khz) a Mobie LM Cryst. Mobie LM Cryst. 000 /in /in = = a The uncertainties are ess than 0% 3..4 Spin iffusivities To evauate the oain sizes of the ess-obie aorphous an crystaine regions, the corresponing spin-iffusion coefficients have to be estiate. For this purpose we sha use the approach propose in [e95].

45 36 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM The spin-iffusion coefficient can be evauate by taking into account that, to a goo approxiation, the NM ine shapes in the rigi an obie phases are approxiate by Gaussian an Lorentzian curves, respectivey. The spin-iffusion coefficients can be reate to the secon van Veck oent of the NM absorption ines which in return is reate to the fu ine with at haf height ν /, so that [e95], an obie r / / [ α ν ], (3.) 6 rigi π r ν/, (3.) n where r is the ean square istance between the nearest spins an α is a cut-off paraeter for the Lorentzian ine shape, i.e., the absorption spectru intensity is zero for the frequency range ω > α. To evauate r for Nyon-6 we have use a vaue of 0.8 n for the istance between the protons of the ethyene group an 0.5 n for the nearestneighbour protons in a CH -CH oecuar fragent [Nor70, o67]. Finay, the estiate weighte ean istance is r / 0. n. To estiatie of the spin-iffusion coefficients of the obie aorphous an the crystaine phases of Nyon-6, Eq. (3.) an Eq. (3.) respectivey were use. The ess-obie aorphous phase has a obiity intereiate to the obiities of a rigi an a obie phase so that an average of the spin-iffusion coefficients base on the Eqs. (3.) an (3.) was use for the spin-iffusion coefficient corresponing to this phase. The vaiity of this approxiation can be justifie a posteriori base on the coparison of oain sizes estiate fro spin-iffusion experients an X-rays ata (see beow). Typica vaues of the spin-iffusion coefficients for the obie aorphous, ess-obie aorphous an crystaine phases in Nyon-6 fibers are given in Tabe 3.3. The ifference between the vaues obtaine for the spin-iffusion coefficient of crystaine phase of the Nyon-6 sapes an the propose vaues in the iterature of 0.8 n /s for rigi systes is ue to the ifference in the fu ine with at haf height (copare ν = 76 khz fro ef. [Sch93] with the corresponing / ν / estiate for Nyon-6 fibres).

46 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 37 Tabe 3.3. H spin-iffusion coefficients estiate base on the ine withs at haf height fro Tabe 3.. M (n /s) a LM (n /s) a C (n /s) a 500 /in /in /in /in = = = a The uncertainties are ess than 0% 3..5 Evience for aggregates of fibris. MPE ipoar fiter efficiency n orer to perfor a spin-iffusion experient, a graient in the Zeean spin orer has to be create by using a cheica shift or a ipoar fiter. Two types of ipoar fiters were epoye in this stuy: (i) a Goan-Shen ipoar fiter [Go66] or a T -fiter using the ifferences between the transverse agnetization ecays of ifferent oains an (ii) a MPE fiter (see Fig..7c) [e95]. The atter one is base on the agic-, Hahn-, an poarization echoes [hi7, e73, Zha9]. Copare to the T fiter, for which the efficiency in seecting the transverse agnetization is proportiona to the ratio T, obie / T,rigi coherences of the rigi phase given by agic sanwiches [e95]., the MPE fiter has an efficiency in fitering out the singe-quantu 6 ( T / T ) N, obie,rigi where N is the nuber of the The efficiency of the T - an MPE ipoar fiters was easure for the Nyon-6 fiber spun at 5000 /in an hyrate in O, an the resuts are shown in Fig. 3.. The Goan- Shen fiter with the puse separation of 0 µs is quite efficient in fitering out the crystaine coponent (copare Figs. 3.a an 3.b). Nevertheess, a sa contribution fro the rigi aorphous phase can be etecte (cf. Fig 3.b). partia fitration is obtaine when the MPE fiter is use with the free evoution tie of τ = µs as shown in Fig. 3.c. For τ = 0

47 38 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM µs ony the obie aorphous coponent is present (cf. Fig. 3.). The spectru is not istorte (copare with Fig. 3.b) an its intensity is coparabe to the intensity of the T fitere H spectru. Therefore, the MPE fiter wi be use for a the spin-iffusion experients perfore in this stuy. Figure 3.. ipoar fiter efficiency for a Nyon-6 fiber spun at 5000 /in: a) Proton spectru obtaine after Fourier transforation of the free inuction ecay recore after a 90 0 raio-frequency puse. b) Spectru obtaine using a Goan-Shen fiter with a puse separation of 0 µs. c) Spectru obtaine using MPE fiter with the free evoution perio of τ = µs (cf. Fig..7c). ) Spectru after a MPE fiter with τ = 0µs.. Proton spin-iffusion using a MPE ipoar fiter on Nyon-6 fibers The spin-iffusion experient using the puse sequence shown in Fig..7c was appie to Nyon-6 fibers hyrate in O. The source of the z agnetization was seecte by the MPE ipoar fiter in the obie aorphous regions. The saer nuber of protons in the obie aorphous regions copare to that in the crystaine an ess-obie aorphous regions eas to broa signas with ow integra intensity even at onger vaues of the spin-iffusion tie (cf. Fig. 3.3). Therefore, ony the noraize intensities of the H spectra corresponing to the obie aorphous region as a function of the square root of the iffusion tie t are epicte in Fig. 3.4.

48 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 39 Figure 3.3. Proton NM spectra recore at ifferent ties t, for a spin-iffusion experient (cf. Fig..7c). MPE ipoar fiter with τ = 0 µs was use. Figure 3.4. The noraize spin-iffusion ecay curves for Nyon-6 fibers obtaine in a spiniffusion experient using a MPE ipoar fiter. The intercept of the inear part of the ecay curve with the tie axis provies * ( ) / t 0 iffusivities given in Tabe 3.3 are shown by ines.. The best fit of the ata using Eq. (.0) an the

49 40 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM The first etho which is use for the evauation of the size of the obie aorphous oains is base on the intercept of the inear part of the spin-iffusion ecay curve with the abscissa axis which yies the vaue reation [Me99] M * t 0 an which is reate to the oain size by the ε * * = eff t0, (3.) π where ε is the iensionaity of the spin-iffusion process (ε = for aear orphoogy, ε = for cyinrica orphoogy an ε = 3 for spherica orphoogy), an eff =, where eff correspons to the effective spin-iffusion M eff * M ( )/ eff coefficient of the sink. The sink corresponing to the oains was consiere to be represente by the crystaine an ess-obie aorphous oains which have reativey cose vaues of the iffusivities (cf. Tabe 3.3). These coposite oains have an effective iffusivity given by NC NLM eff = C LM, (3.) N N where the vaues of an were taken fro Tabe 3.3. The corresponing reative fractions N C N an LM N N LM phases were taken fro Tabe 3.4. C of the protons for the crystaine an ess-obie aorphous Tabe 3.4. eative proton fractions of crystaine an ess-obie aorphous oains to the obie aorphous oain aong the fiber in Nyon-6 fibers hyrate in O, using the reative integra intensities reporte in Tabe 3.3. Spun at 500 /in Spun at 500 /in = 4.5 Spun at 5000 /in N N C LM N N 0.6 a a 0. a a a 0.9 a a the uncertainities are ess than 0% t shou be note that the use of the paraeter * t 0 instea of the paraeter s t use in [Sch94] eiinates the epenence of obie on the voue ratio of the sink to the source

50 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 4 [Me99]. The estiate size of the obie aorphous region for the three Nyon-6 sapes base on a aear orphoogy an Eq. (3.) are given in Tabe 3.5. ore genera etho for evauation of the oain sizes of a oains invove in the process of z-agnetization transfer is provie by Eq. (.0), which is vai for a aear orphoogy an which escribes the tie evoution of the Zeean poarization in the agnetization source in the iit of an iea fiter. The ines in Fig. 3.4 are obtaine fro Eq. (.0) using the iffusivities given in Tabe 3.3. For the sink we have use the sae effective iffusion coefficient as for the previous estiation. For the interface, the corresponing spiniffusion coefficient has been taken to be an arithetic average between the iffusivity of the coposite oain an the iffusion coefficient of the obie aorphous phase. The vaue of the proton ensity has been obtaine base on the oecuar weight of the Nyon-6 an on the 3 ensities of the aorphous an crystaine phases =.09 g/c an aorphous crystaine =.8 g/c 3, respectivey [ra89]. We have estiate a vaue of 0.05 g/ c 3 for the proton ensity of the aorphous phase an 0.08 g/ c 3 for the crystaine phase. n average vaue was use for the coposite oain anaogous to the vaue estiate for the spin-iffusion coefficient. Moreover, an average vaue fro the proton ensity of coposite oain an that of the obie aorphous phase was use for the proton ensity of the interface. The best fit of the spin-iffusion ata using the above paraeters gives the oain sizes of the three oain orphoogy presente in Tabe 3.5. Fro Fig. 3.4 it is evient that the siuate curves o not fit the spin-iffusion ata in the ong tie regie. This fact cou be reate to the uncertainities in the H NM ineshape ecoposition at ow signa-to-noise ratio an to the errors inuce by the correction of the ongituina agnetization reaxation at onger spin-iffusion ties. However, the oain size of the obie aorphous region estiate using the two ethos are cose to each other an are varying in the sae way with the processing conitions. C. Morphoogy of the Nyon-6 fibers Our particuar set-up of the spin-iffusion experient in which the source of agnetization is seecte for the obie aorphous oains aows us to expore ony soe aspects of the copex orphoogy of the Nyon-6 fibers. The structura oe which can expain the easure oain sizes presente in Tabe 3.5 is shown in Fig. 3.5.

51 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 4 Tabe 3.5. oain sizes of the obie aorphous, interface an aggregate of fibris in the Nyon-6 fibers in O obtaine fro H spin-iffusion experient, the erive anaytica * soutions of the spin-iffusion equations an the tie intercept ( ) / t. 0 Spun at 500 /in Spun at 500 /in = 4.5 Spun at 5000 /in Mobie aorphous 3.69 n a 3.46 n b 5.6 n b 3.64 n b 5.55 n 3.79 n a a nterface 0.5 n b 0.75 n b 0.5 n b ggregate of fibris 48 n b 40 n b 7 n b a using Eq. (3. ). The uncertinities are of the orer of 0% b using Eq. (.0). The uncertinities are of the orer of 0% The highy obie aorphous phase is situate at the surface of an aggregate of fibris an separate fro this aggregate by an interface. The agnetization transfer is taking pace in a irection aong the iaeter of the fibris. nsie of the aggregate the fibris are separate by the ess-obie aorphous oains. The fibris have a aear structure with aternating crystaine an ess-obie aorphous oains [Mur96]. The egree of fibriar an aear orientation is about the sae as that of the crystaine orientation [Mur96]. t was shown by sa-ange X-ray scattering (SXS) that the interfibriar regions, unike the interaear regions essentiay consist of aorphous chain segents, ay have icro-vois in aition to aorphous chain segents [Mur96]. The orphoogy is siiar to that iscusse by Hu an Schit-ohr [Hu0] for utrarawn utra-high oecuar weight poyethyene fibers to expain their H spin-iffusion experients. The obie aorphous phase has oain sizes in the range of n for the investigate Nyon-6 fibers. The process of hot rawing increases the size of these oains by a factor of about two an aso the size of the interface copare to that of the fiber spun at 500 /in (cf. Tabe 3.5). t the sae tie the size of the aggregate of fibris ecreases copare to that when the fiber is not rawn. Not ony the oain sizes are changing upon rawing but of course aso the nuber of protons present in each oain is changing (cf. Tabe 3.). For instance, the aount of obie aorphous oain is increasing about twice in the hot rawn Nyon-6 fiber copare to the unrawn fiber. This shows that the obie

52 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 43 aorphous phase fore in the process of hot rawing ainy originates fro the aggregate of fibris an not fro an extension of the poyer chains in this phase. These resuts are supporte by SXS investigation of rawing effect on Nyon-6 fibers [Mur96]. t was shown that the iaeter of the fibris ecreases sighty upon rawing in agreeent with our reuce vaue of the size of the aggregate of fibris (cf. Tabe 3.5). Moreover, the coherence ength or the crystaite size begins to increase at a raw ratio of.5 3 [Mur96]. This fact is supporte by an increase of the reative nuber of protons etecte by NM in the crystaine phase of rawn fiber (see Tabe 3.). ase on the sizes given in Tabe 3.5 an the reporte vaue of about 5 n for the interfibri spacing of a Nyon-6 fiber rawn to = 4.5 [Mur96], the average nuber of fibris present in the aggregates can be estiate to be in the range of 4 8. Figure 3.5. The oe of the average phase orphoogy use for interpreting the spin-iffusion experients with the source of the z agnetization in the obie aorphous phase. The nuber of protons in the obie aorphous phase is in the range of about %-0% for investigate Nyon-6 fibers hyrate in O. The ajority of protons are concentrate in the fibris. The etais not reveae by our spin-iffusion easureents about the aggregate of fibris, but by SXS, are aso shown [Mur96]. The istance between the fibris is. The fibris are separate within the aggregate by essobie aorphous oain. The axes of the fibris are suppose to be oriente approxiatey parae to the argest iension of the interface an the obie aorphous regions. ong the fibris the aear stack of crystaine/ess-obie aorphous oains is present being we organize within a coherence ength L c.

53 44 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM The ata presente in Tabe 3.5 show that for Nyon-6 fibers spun at 5000 /in the aggregate sizes increase by about 30% copare to the fibers spun at 500 /in. This is in agreeent with the arger vaue of the nuber of protons shown in Tabe 3.. so the oain sizes of the obie aorphous phase an interface are increasing. The resuts fro the H ineshape ecoposition show that the ess-obie aorphous an obie aorphous phases transfor into the crystaine phase uring high-spee spinning of the Nyon-6 fibers (copare the vaues for sapes spun at 500 /in an at 5000 /in in Tabe 3.). The sae resut was reporte by Kwak et a. [Kwa0] for high-spee et-spun Nyon-6 fibers using various physica ethos incuing soi-state H NM spectroscopy an reaxoetry etaie escription of Nyon-6 orphoogy base on spiniffusion experients using a Q fiter. Theory n the previous chapter genera anaytica soutions vai for a tie ranges of the spiniffusion equations were eveope for systes with arbitrary oain sizes an iffusivities with a aear orphoogy. Very often the investigate coposite aterias have a uch ore copex orphoogy. One exape, reevant for the present investigation is shown in Fig The source (crystaine, hereafter C), characterize by a spin-iffusion coefficient an a proton ensity with a spin-iffusion coefficient C is surroune by a sink (ess-obie aorphous, hereafter LM) LM an a proton ensity C LM. The iffusion process has a iensionaity of three. One way to escribe the spin-iffusion process for this orphoogy is by expressing the corresponing soutions as a prouct of one-iensiona soutions [Cra86, Car86]. When interfaces are present the nuber of paraeters to be estiate for a copete characterization of the orphoogy epicte in Fig. 3.6 is nine. Usuay the sizes of interfaces are uch saer than the sizes of the oains theseves so that in a first approxiation the presence of interfaces can be negecte. itionay, the syetry of the syste ipies that the iffusion processes are equivaent in the x an y irections so that four quantities (enote in Fig. 3.6 by,,, an ) are sufficient to characterize the agnetization transfer aong x, y, an z irections. C LM C LM

54 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 45 Figure 3.6. Scheatic representation of the orphoogy of Nyon-6 fibres use for oeing the spin-iffusion process. The fow of agnetization fro the crystaine oain (C) into the ess-obie aorphous oains (LM) is consiere to be a three-iensiona process taking pace in a rectanguar orphoogy. The source an sink oains have iensions C an LM aong the fiber irection an C an LM in the irection perpenicuar to the fiber axis. n such a situation the integra intensity at ifferent iffusion tie t, corresponing to the source (cf. Fig. 3.6) can be written as C () t ( z) z ( x) x, z x = C C C (3.3) z x where ( ) an C ( z) are the concentrations of the agnetizations aong the x an z C x irections, with C z = an C x =, respectivey. The integra intensity corresponing to the sink can be estiate base on the conservation of the z agnetization in tie LM () t (), t C 0C C C = (3.4) C

55 46 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 0 C C where is the concentration of agnetization at spin-iffusion tie zero, the size of the source aong the z irection, an C the size of the source on the irections x an y (cf. Fig. 3.6). f we negect the interfaces, the tie evoution of the concentration of the agnetization in the source oain aong the x an y irections has the for C C 0C C( x ) = sin C LM LM β i cos C ( x β ) exp ( β t) 4 LM i i 0C C i= 0 C i ( ) cos i cos C C C β κ LM i ( ) sin LM C λ LM β β κλ LM LM C C LM LM βi sin (3.5), β i where κ = C an LM λ = κ C LM. The vaues β i are the soutions of the trigonoetric equation C C LM C C LM C sin β cos β LM LM cos β sin β 0. LM LM (3.6) C = naogous foruae escribe the tie evoution of the concentration of the agnetization aong z irection.. Efficiency of the oube-quantu ipoar fiter ecenty it was shown that by using a ipoar fiter base on the excitation of oube-quantu coherences the agnetization fro the ore rigi part of a heterogeneous poyer can be seecte [a98]. The efficiency of the Q fiter was easure for the Nyon-6 fiber rawn at = 3. an hyrate in O. The resuts are shown in Fig t sa excitation ties the fiter seects the agnetization ainy fro the crystaine regions. t onger excitation ties the fiter starts to act ike a T fiter an the agnetization fro the ess-obie an obie aorphous regions can be seecte. n a three situations the fiter has high efficiency in seecting the agnetization corresponing to ifferent oains. Q ipoar fiter can be use in cobination with ipoar fiters for obie oains to increase the confience in the estiate oain sizes. This fiter prouces a sa z agnetization as a resut of ow efficiency in seecting Q coherences. However, the use of this type of fiter eas to a better evauation of the integra intensities corresponing to

56 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 47 ifferent coponents ue to the ore accurate etection of the narrow signas on the top of a broa coponent copare to the etection of a broa coponent uner a narrow signa. Figure 3.7. Efficiency of the Q ipoar fiter for a Nyon-6 fiber spun at 500 /in an rawn to = 3.. Proton spectru after an excitation tie τ of a) µs corresponing to the axiu of Q bui-up curve, b) 8 µs, an c) 73 µs. The use paraeters were t Q = 5 µs an t = 30 µs. The tie evoution of the nucear agnetization in the syste is shown by H NM spectra in Fig The agnetization front eanating fro the crystaine regions first reaches the ess-obie aorphous regions an ony after onger iffusion ties aso the obie aorphous regions. This resut is consistent with the previous oe, which shows that the obie aorphous phases are separate by istances equa to the average iension of an aggregate of fibris.

57 48 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM Figure 3.8. Proton NM spectra evoution for Nyon-6 fiber spun at 500 /in an rawn to = 3. uring the spin-iffusion process. Spectra recore after iffusion ties t of a) 50 µs, b) 500 µs, an c) 00 s. Q ipoar fiter with an excitation tie τ of µs was use for a experients. C. Proton spin-iffusion experients using a Q fiter s we have seen previousy, the particuar set-up of the spin-iffusion experient in which the source of agnetization is seecte for the obie aorphous oains aows us to expore ony soe aspects of the copex orphoogy of the Nyon-6 fibers. This type of spin-iffusion easureents provies ony goba inforation even if the aggregates have a we-efine structure accoring to SXS [Mur96]. nsie an aggregate the ess-obie aorphous oains separate the fibris so that the fibris have a aear structure with aternating crystaine an ess-obie aorphous oains [Mur96]. To get a ore etaie picture of the orphoogy of Nyon-6 fibers, spin-iffusion experients were conucte with the puse sequence fro Fig..7b The source of z agnetization was seecte by the oube-quantu fiter ainy in the crystaine regions (enote by C in Fig. 3.6). ecoposition of the proton spectra corresponing to ifferent ties in the spin-iffusion evoution was ae in ters of three coponents, one corresponing to obie aorphous regions, another one to the ess-obie aorphous regions, an the thir one to the crystaine phase. The presence of the obie aorphous regions at the surface of the aggregates copicates the interpretation of the spin-iffusion

58 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 49 ata. ue to the fact that its aount is ess than 0% for a sapes (see Tabe 3.) an that the fow of agnetization is reaching it ony after onger spin-iffusion ties, our approach wi ainy focus on the transfer of agnetization between the crystaine an the ess-obie aorphous regions. Therefore, a renoraization of the integra intensities corresponing to these two phases was ae by subtracting the signa fro obie aorphous phase. The evoution of the integra intensities of the crystaine an ess-obie aorphous coponents is epicte in Fig. 3.9 as a function of the square root of the spin-iffusion ties. The equiibriu vaues, which are irecty reate to the aount of each phase inicate a goo agreeent with the vaues estiate by the ecoposition of the proton spectra. Figure 3.9. Noraize spin-iffusion ecay curves for Nyon-6 fibers with ifferent wining spees an raw ratios () obtaine with the puse sequence of Fig..7b. The experienta ata were fitte with Eqs. (3.3) an (3.4). To estiate the oain sizes for the crystaine an ess-obie aorphous oains base on the anaysis of spin-iffusion ata we have ae the foowing assuptions: (i) the orphoogy of the fibris can be approxiate with the orphoogy epicte in Fig. 3.6, (ii) the presence of the interfaces can be negecte, an (iii) the ess-obie aorphous oains insie an outsie the aear stack are in a first approxiation ientica an therefore they can be characterize by the sae proton ensity LM an spin-iffusion coefficient LM. fit of the experienta ata epicte in Fig. 3.9 was ae base on the Eqs. (3.3), an (3.4). Vaues for the proton ensity of the aorphous phase of.09 g/c 3 an for the crystaine phase.8 g/c 3 as reporte before an the spin-iffusion coefficients fro Tabe

59 50 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 3.3 were use. The estiate vaues for the oain sizes aong the fibri axis as we as perpenicuar to this irection are given in Tabe 3.6. The theoretica curves corresponing to the obtaine oain sizes provie a goo fit of the experienta ata at the beginning of the spin-iffusion process but show a poorer fit for onger iffusion ties. This isatch was attribute to the existent transfer of agnetization to the obie-aorphous phase. Tabe 3.6. Estiate oain sizes for Nyon-6 fibers with ifferent processing conitions base on the fitting of spin-iffusion ata with Eq. (3.3) an (3.4). C a LM a Long perio C a LM a (n) (n) C LM (n) (n) (n) 000 /in /in = = a The uncertainties are ess than 5% s expecte, the oain sizes of ifferent phases are infuence by the processing conitions. The foowing trens are observe with increasing of wining spee an raw ratio (cf. Tabe 3.6): (i) the size of the crystaine regions insie the aear stack increases, (ii) the size of the ess-obie aorphous regions insie an outsie the aear stack ecreases, (iii) the ong perio in the fiber irection increases sighty with wining spee but ecreases with raw ratio, an (iv) the iaeter of the fibris ecreases. The increase in the size of the crystaine regions aong the fiber axis with wining spee an raw ratio can be correate with the sizes of aorphous regions, either insie or outsie the aear stack. The tren in the estiate vaues of the oain size of the crystaine regions aong the fibris is supporte by the WX ata reporte in Tabe 3.7. The WX an SXS easureents [Pen3] were ae for ry Nyon-6 sapes with processing conitions cose to those of the sapes investigate in the present stuy.

60 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 5 Tabe 3.7. Sizes of the crystaine regions aong the chain irection an perpenicuar to it fro X-ray ata (cf. Fig. 3.6). C (n) C (n) Guinier iaeter (n) 00 /in.8 a 4. a /in 5. a 6.3 a - = a 4.8 a - = a 4.9 a 6.0 b = a 5.7 a 4.5 b a WX ata b SXS ata The iaeter of the fibris ecreases with raw ratio as cou be seen by coparing an unrawn sape with a sape rawn at = 4.5. The estiate sizes fro NM spiniffusion experients are in sae orer of agnitue with the WX ata (copare Tabes 3.6 an 3.7). However, it is interesting to see that the so cae Guinier iaeter estiate base on the SXS ata is showing the sae tren as the spin-iffusion ata whie the WX an SXS ata are showing the opposite behaviour. This apparent iscrepancy can be reconcie when we reaize the possibiity that as the fiber is rawn the fibri iaeter cou ecrease whie the crystas becoe uch ore orere [Mur96]. The sae expanation can be appie aso for the ata corresponing to sapes with ifferent wining spee ue to the observe increase in the ine with (see Tabe 3.). The vaues obtaine for the essobie aorphous regions outsie the aear stack inicate that the space between two ajacent fibris is occupie ony by a few aorphous chains. This observation is in agreeent with the resuts fro [Mur96] where very cose vaues for the fibri iaeter an inter-fibri istances were reporte for sapes prouce with ifferent raw ratios.

61 5 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 3. ibock copoyers 3.. ntrouction ock copoyers represent a subject of broa current research ephasis across the fu spectru of acrooecuar cheistry an physics, ranging fro eveopent of new synthetic strategies an oecuar architectures to appication of avance theoretica an coputationa ethos [Ha98, Lo3]. They are wiey use coerciay. n the soi an rubbery states they are use as theropastic eastoers with appications such as ipact oification, copatibiization an pressure-sensitive ahesion [Ha98, Jac98b, Lo3]. More recenty a ot of attention was pai to appications in the bioeica fie for rug eivery [99, Kat, Ots, ei]. n soutions, their surfactant properties are expoite in foas, oi aitives, soubiizers, thickeners, an ispersion agents. For a these appications aterias with particuar physica properties such as tensie strength, torsiona oui, extensibiity, ensity an ong-ter stabiity are require [Ha98]. Therefore, to engineer these aterias for a particuar set of properties an unerstaning of the structure-properties reationship is necessary. Moecuar an structura characterization, the unerstaning of the factors that contro phase behaviour, an euciation of the response of copoyer aterias to externa fies are require steps. t is argue that ue to the rapi progress in a these areas bock copoyers are nowaays on the verge of a new generation of sophisticate aterias appications, in which particuar nanostructures wi pay a crucia roe [Lo3]. biion oar annua arket for bock copoyer aterias ay aso refect the potentia an the significance of these aterias [Lo3]. ock copoyer icrostructures have oain iensions that can be varie continuousy fro nanoeter size to hunres of nanoeters, by sipy changing the oecuar weight, the onoer structure, an the teperature [Lo3]. epening on the weight fraction of one of the onoers, the ibock copoyers exhibit ifferent equiibriu syetries such as aeae, cyiners, an spheres [Suh98, Ha98]. These various structures provie new thera an echanica properties that are not seen in the hoopoyers fore by ony or onoers [Oth86]. This process is riven by the tota free energy iniization [He76, He80, Lei80, Oth86, Suh98]. For exape, in the case of a aear orphoogy the theoretica stuies preict that the oecuar weight epenence of the aear spacing is given by a power aw as M where the exponent α is /3 in the strong segregation iit or / in the case of weak segregation iit [He76, Oth86]. α

62 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 53 The ais of this subchapter are (i) to estiate the sizes of the obie aorphous, the interface an the rigi aorphous regions of a series of aorphous PEO-b-PHEM ibock copoyers with ifferent oecuar weight by using spin-iffusion NM which have potentia appications in the rug eivery fie an (ii) to correate the ong perio with the oecuar weight of the copoyers an to copare the resut with the theoretica preictions. 3.. Theory of ibock copoyers The funaenta theroynaics of the phase separation in bock copoyers shows that the phase behaviour of a two-coponent bock copoyers in buk is eterine by three experientay controabe factors: the overa egree of poyerisation N, the architectura constrains (ibock, tribock, star bock etc.) an the coposition φ (overa voue fraction of coponent ), an the segent-segent interaction paraeter χ. t equiibriu, the bock copoyer chains assue the owest free energy configuration. Two iiting regies have been postuate in the bock copoyer phase. For χn<0, the interaction is sufficienty ow so that the iniviua chains assue unperturbe Gaussian statistics. The coposition profie is aost sinusoia, an the oain perioicity ong scaes as [Lei80, Oth86, Suh98]: / ong g an (3.7) where a is the characteristic segent ength, g an N stan for the gyration raius of the copoyer oecue an the poyerisation inex (oecuar weight M w of the bock), respectivey. This regie is cae weak segregation iit an the copoyers which are showing this behaviour are characterise by a wiene interface ue to an enhance phase ixing. f the vaue of χn is greater than 00, neary pure an oains are fore. n this case the chain conforation is not onger a Gaussian one but rather perturbe (stretche chain conforation). This regie is tere as strong segregation iit. The interface between the constituent icrooains in strongy segregate systes is quite narrow with the onoer coposition profie resebing a sharp step. The bounaries eineating the ifferent icrophases are expecte to be vertica. The interaction energy associate with the contacts is ocaise in the interfacia regions. The syste wou ike to iniise the tota area of such an interface by ecreasing the energeticay unfavourabe contacts, but it has to o this uner the constraint of incopressibiity an entropic penaty of extene chain conforations. These opposing forces ea to perturbe chain configurations, an the perioicity ong can be scae as [He76, He80, Oth86, Suh98]:

63 54 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM ong / 3 / 6 g an χ (3.8) wie variety of icrostructures in bock copoyer systes eveops uner icrophase separation. This process is a resut of two copeting effects. First, the bocks prefer to segregate ue to their inherent cheica incopatibiity. The spatia extent of phase separation is, however, iite by the connectivity of the bocks ipose by the architecture of the oecues. s a coproise of both effects, perioic icrostructures evove. Therefore, the geoetry of the icro-phase separate structure is very sensitive to the cheica nature an the oecuar structure of the copoyer as we as to its tota coposition. One of the ost iportant factors eterining the phase orphoogy in bock copoyer is their coposition. t is easiy unerstoo that the shape of the poyer/poyer interface varies with the reative chain ength of the coponent poyer. copositionay syetric ibock copoyer (i.e., when the voue fractions of both coponents are the sae) fors a fat interface as shown in Fig. 3.0a. s the voue fraction of a coponent continues to increase (say of ) reative to the other (i.e., as the copoyer becoes copositionay asyetric) a curve interface is fore because the chains ust stretch sufficienty (Fig 3.0b) to aow the foration of a panar interface. n this case the oss of the conforationa entropy of the ajor coponent (here ) is too high. Therefore, the chains ten to expan parae to the irection to the interface to gain the conforationa entropy uner the conition that segent ensities of both of the bock chains have to be kept constant an they ust be the sae as those of the buk ensities of the hoopoyers. s a consequence, the interface becoes a convex towars the inor coponent (Fig 3.0c). This effect of interface curvature becoes ore an ore pronounce as the coposition of the bock copoyer becoes further asyetric. The ost asyetric bock copoyer possesses a spherica orphoogy coprising centre spheres of the inor coponent isperse into the atrix of the ajor coponent. cyinrica orphoogy appears when the voue fraction of the inor coponent increases. Syetric bock copoyers exhibit a aear orphoogy consisting of aternating ayers of the two coponents. With increasing voue fraction of the PS coponent the orphoogy appears in reverse orer (i.e. P cyiners in the PS atrix an P spheres in the PS atrix) [Ha98]. n the strong segregation iit, the foowing sequence of phases is observe for PS-P ibock copoyers [Ha98]: φ PS <0.5, spherica; 0.5< φ PS <0.35, cyinrica; 0.35< φ PS <0.65, aear; 0.65< φ PS <0.85, cyinrica; an 0.77< φ PS, spherica.

64 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 55 Figure 3.0. Scheatics of chain conforation at the icrophase-separate state: a) stabe fat interface fro a copositionay syetric bock copoyer i.e. φ = φ, b) an unstabe fat interface in the case φ >> φ, an c) a stabe curve interface in the case of φ >> φ [Ha98]. The orphoogica changes observe in a two-coponent bock copoyer by varying the coposition are shown in Fig 3. [Ha98]. Figure 3.. TEM iages fro [Ha98] showing the cassica orphoogy of the bock copoyers exepifie by that observe in a PS-P ibock copoyer. The voue fractions correspon to the PS coponent Experienta. Sapes H spin-iffusion easureents were perfore on a series of poy(ethyene oxie)-bockpoy(hyroxyethyethacryate) (PEO-b-PHEM) ibock copoyers with ifferent oecuar weights. onofunctiona poy(ethyene oxie) acroinitiator with a oecuar weight of 000 was use for the ato transfer raica poyerization (TP) of hyroxyethy ethacryate (HEM) in ethyene gyco as sovent [ei]. The egrees of the poyerization of poy(hem) bock were esigne to be equa to that of the corresponing

65 56 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM PEO bock. The conversions as we as the oecuar weights an the poyispersities M w M n of the sapes eterine by eans of GPC are given in Tabe 3.8. Further etais of the poyerisation proceure are given in ef. [ei]. Tabe 3.8. Characteristics of the aorphous PEO-b-PHEM ibock copoyer Sape a Conversion M n (%) g/o b M w M n a Conversion eterine by eans of H NM spectroscopy b b M n vaue of the bock copoyer easure by GPC n orer to anayse the phase behaviour of these copoyers, ifferentia scanning caorietry easureents were ae for the sapes with the ower an higher oecuar weight. The anaysis was ae within the range fro 80 o C to 0 o C with a heating rate of 0 K/in. For both sapes a weak transition aroun 56 0 C was etecte, in agreeent with the gass teperature T g of PEO which is a seicrystaine poyer with T g = C an a eting teperature T = 67 0 C. None of the two sapes show an enother near 67 0 C which inicates that they are copetey aorphous.. NM Experients H soi-state NM spectra an the spin-iffusion ata were easure on a ruker SX-500 spectroeter operating at MHz for H. The ata were coecte at roo teperature for non-spinning sapes. The ength of a π/ puse was about 5 µs, the we tie was.5 µs, an the recyce eay was 5 s for a easureents. Proton spin-iffusion easureents were perfore using the genera schee consisting of a z agnetization fiter, a spin-iffusion perio, an an acquisition perio as presente in Fig..7. The graient of agnetization was create by a MPE ipoar fiter. The tota integra intensity is constant in the range of the use ixing ties for the spin-iffusion experients for a investigate sapes. Therefore, no correction of the spiniffusion ata ue to the spin-attice reaxation was perfore.

66 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM Proton spectra The proton spectra of the investigate sapes are epicte in Fig. 3.. Each spectru shows the existence of a narrow an a broa coponent. They correspon to regions with high an ow obiities, respectivey. Tabe 3.9. eative integra intensities () an the fu-with at haf intensity ν / of the two coponents of aorphous PEO-b-PHEM ibock copoyers obtaine fro a ecoposition of proton spectra Sapes Mobie orphous (%) igi orphous Mobie orphous ν / (khz) igi orphous ase on the coparison with the proton spectra corresponing to the pure bock the narrow coponent was attribute to the PEO bock an the broa one to the PHEM bock. The proton spectru of each sape was ecopose in ters of a Gaussian an a Lorentzian ine. The resuts given in Tabe 3.9 inicate that in both systes the obiity of the poyer chains in the obie aorphous phase is about one orer of agnitue higher than in the rigi aorphous phase. This high ifference aows for a goo seection of the agnetization fro one of the regions, as we wi see in the next paragraph Proton spin-iffusion using a MPE ipoar fiter The efficiency of the MPE fiter for the sape 3 is epicte in Fig For sa vaues of the free perio τ the fiter has ony itte effect an aost no fitration is achieve. The agnetization fro the rigi phase starts to ephase with increasing τ vaue. For a free evoution perio of 00 µs the agnetization coponent of the rigi PHEM bock is copetey fitere out whie the agnetization given by the obie region passe the fiter.

67 58 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM Figure 3.3. ipoar fiter efficiency for PEO-b-PHEM using an MPE fiter with ifferent free evoution perios a) τ = µs, b) τ = 0 µs, an c) τ = 50 µs. fter a free evoution perio of τ = 00 µs () ony the signa fro the obie aorphous phase is present. Figure 3.4. Proton spectra of PEO-b-PHEM recore after ifferent ixing ties in the spiniffusion experient using a MPE fiter: a) t = 00 µs, b) t = 500 µs, c) t = 0 s, an ) t = 00 s.

68 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 59 Once the seection was ae the agnetization is aowe to fow into the syste. The evoution of the agnetization front at ifferent oents in tie is epicte in Fig With increasing ixing tie the PS signa appears an increases unti equiibriu is reache. The anaysis of the spin-iffusion ata was ae in ters of two coponents corresponing to the two phases. For the quantitative estiation the oain sizes of the two phases a fit of the experienta ata has to be one. This was ae taking into account that the bock copoyers aopt a aear orphoogy as was prove before an using Eq. (.0) an (.). The vaues for the proton ensities were estiate base on the oecuar ensity. 3 3 They are = 0.03 g / c an = g / c. The vaues of the spin-iffusion PEO PHEM coefficients were assue to be PEO = 0.5 n /s an PHEM = 0.8 n /s base on the iscussion fro the previous chapter. The proton ensity an the spin-iffusion coefficient corresponing to the interface have been taken as an arithetic average of the corresponing vaues of the source an the sink. The oain sizes estiate base on the spin iffusion ata for a investigate sapes are given in Tabe 3.0. Tabe 3.0. oain sizes of aorphous PEO-b-PHEM ibock copoyers easure in a spin-iffusion experient epoying a MPE ipoar fiter (n) Sapes PEO nterface PHEM Long perio The sizes of the two bocks increases with the oecuar weight. The vaues obtaine for the interface oain are saer copare to the sizes of the PEO an PHEM an they are ainy inepenent of the changes in the oecuar weight. The inepenence of the interfacia thickness fro the oecuar weight is in agreeent with the theoretica preictions [He75, He76, He80]. The sae resut was reporte aso for bock copoyers of Poystyrene-Poyisoprene [Has80, Jac98, Yu99].

69 60 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM Figure 3.5. epenence of the ong perio of the PEO-b-PHEM bock copoyers on the α oecuar weight. α is the exponent of the power aw reationship ong M w. To further verify the reiabiity of the NM easureents of the icrooain structure, a pot of the epenence of the ong perio = on ong PEO interface PHEM the oecuar weight was ae. The resut epicte in Fig.3.5 in a oube-ogarithic scae inicates goo agreeent with the two/thirs power aw theoreticay preicte in the strong segregation iit. s note by Schit et a. [Sch93] the vaue of α estiate by NM easureents is inepenent of any caibration ipose on the NM easureents through the choice of the spin-iffusion coefficients. 3.3 Concusions n this chapter we have showe that soi state spin-iffusion NM can successfuy be appie to characterize the orphoogy an oain sizes of fibres an bock copoyers. n NM approach to carify the copex orphoogy of seicrystaine poyer systes was introuce an appie to stuy Nyon-6 fibers. t expores spin-iffusion NM using a cobination of ipoar fiters base on the excitation of singe an oube-quantu coherences which seect in separate experients the agnetization coing fro regions with ifferent obiity. The particuar set up of the spin-iffusion experient using a MPE ipoar fiter reveas ony the spatia istribution of the obie aorphous oains an the aggregates of fibris as a whoe. These spin-iffusion ata were interprete in ters of a oe in which z

70 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM 6 agnetization transfer takes pace towars sinks of crystaine an ess-obie aorphous oains which are connecte in series an in parae an which for aggregates. These crystaine/aorphous aggregates separate by obie aorphous oains invove about 4-0 fibris. ore etaie picture of the Nyon-6 fiber orphoogy was obtaine by the spiniffusion experients using a oube-quantu ipoar fiter. This type of fiter seects the rigi oains in Nyon-6 fibers. n this way inforation about the iensions of the crystaine an ess-obie aorphous oains was obtaine aong the fibri irection as we as perpenicuar to it. s a first approxiation the three-iensiona soutions of the spiniffusion equation were use in ters of a prouct of one-iensiona soutions escribing a aear orphoogy. ore reaistic oe base on a cyinrica orphoogy can be use. Moreover, the oain sizes of the Nyon-6 fibers aong an perpenicuar to the irection of the fibris as we as the changes prouce by the variation of the wining spee an raw ratio are in agreeent with the ata provie by WX an SXS. The correation between the changes in oain sizes, easure by such copeentary spin-iffusion experients for a fu series of Nyon-6 sapes with ifferent raw ratios an wining spees can be expoite to estabish processing-structure reationships. series of aorphous PEO-b-PHEM ibock copoyers with ifferent oecuar weights was investigate by spin-iffusion NM. The graient of the z agnetization was create epoying a MPE ipoar fiter, which estroys the agnetization fro the rigi PHEM phase. The sizes of the obie aorphous, the interface, an the rigi aorphous phase were estiate base on the genera anaytica soutions of the spin-iffusion equation in a aear orphoogy copose of three oains. The sizes of the PEO an PHEM regions epen on the oecuar weight whie the thickness of the interface is inepenent of these paraeters. This resut is in agreeent with the theoretica preictions an with the experienta resuts reporte for other bock copoyers. itionay, the correation of the ong perio of the bock copoyer inicates aso a goo agreeent with the theoretica /3 ong M w preictions.

71 6 Chapter 3. nvestigation of copex orphoogies by spin-iffusion NM

72 4 NM stuy of shape-eory poyers 4. ntrouction an otivation ioegraabe poyers are an iportant cass of synthetic bioaterias that are wiey use in teporary therapeutic appications such as woun cosure, tissue regeneration, an rug eivery. ong the bioabsorbabe poyers eveope thus far, poygycoie, poy(actie), an their copoyers constitute proising aterias for the use in the fie of surgery an pharaceutics [Str0, Wit0, bi97, Len]. Unike non-egraabe ipants, these aterias egrae to haress proucts an therefore obviate the nee for surgica reova after they have serve their purpose. esie biocopatibiity an bioegraabiity, this type of copoyers has a eory that aows the to be efore into a teporary configuration an then to be restore to the origina parent geoetry by appying heat in few secons (Fig. 4.) [Len]. Figure 4.. estoration of the parent shape within 35 secons of a ben shape-eory poyer uner the infuence of 70 0 C hot [Len]. Copare to other shape-eory aterias, such as shape-eory aoys, the poyers offer uch greater eforation capabiities, substantiay easier shaping proceure, high shape stabiity, they are cheaper, an in the case of the eica use biocopatibiity an bioegraabiity. They aow arger eforation of the peranent shape to the teporary shape (fro 50% to 500% copare to 7% to 8% in the case of aoys) [Tob96, Len, Len, ou3]. Severa acroscopic properties such as transition teperature an echanica properties can be varie in a wie range by ony sa changes in their cheica structure an coposition [Fen99, Len]. Therefore, they represent nowaays a cass of aterias with high potentia in any appications. 63

73 64 Chapter 4. NM stuy of shape-eory poyers Poyeric aterias showing shape eory properties can be esigne by taking poyer networks in which the poyer chains are abe to fix a given eforation by cooing beow a certain transition teperature. This transition teperature can be a gass transition teperature or a eting point. Upon reheating above this transition teperature the chains oose their teporary orientation an regain their origina shape. Shape-eory poyers are characterize by two features, triggering segents having a thera transition within the range of interest an cross-inks eterining the peranent shape. epening on the kin of cross-inking, shape eory poyers can be theropastic eastoers or therosets. To esign poyers with suitabe properties for a given appication, the unerstaning of the structura characteristics, oecuar ynaics an the echaniss responsibe for changes in physica properties associate with hyroytic egraation is requeste. Therefore, we have carrie out soi-state NM stuies of aorphous copoyers of L,L-iactie an igycoie. The ais of this chapter are: (i) to characterize the effect of the oecuar weight an the onoer ratio of actie to gycoie on the structure an the oecuar ynaics of the fina networks, (ii) to investigate the crossinking process uner the action of UVirraiation, (iii) to characterize the shape eory behavior an to unerstan the oecuar echanis associate with this effect, an (iv) to stuy the echaniss responsibe for the egraation in vitro. 4. Experienta 4.. escription of the sapes Figure 4.. eaction schee for the synthesis of the network precursor oigo[(l-actie)-rangycoie]iethacryate. The network precursor was obtaine using the reaction schee fro Fig. 4.. The acroio () is obtaine by ring-opening poyerization of L,L-iactie an igycoie, using ethyene gyco as initiator an ibutyin oxie as a catayst. The catayst prootes

74 Chapter 4. NM stuy of shape-eory poyers 65 transesterification, the extent epening on the reaction tie an teperature. The acroiethacryates () are obtaine by the en-group oification of the acroios with ethacryoychorie. The raica is =CH-CH 3 for the iactie onoer an =CH for the gycoie. Network foration is achieve by photopoyerizing bifunctiona acryates by UV-irraiation. This is a fast an easy etho to obtain a network with a high iensiona stabiity an iprove shape recovery. The use of raiation instea of heat presents avantages such as high reaction rates an ow energy consuption [Lit]. ore etaie escription of the reaction steps an conitions are escribe in [Cho]. Figure 4.3. Poyethacryate crossink points in the network LG. enotes the oigo[(l-actie)-rangycoie] ain chain. Tabe 4.. Nuber average oecuar weight of oigo[(l-actie)-ran-gycoie] ios eterine by ifferent ethos [Cho]. Sape M n (g/o) M n (g/o) M n (g/o) (cacuate) ( H NM) (GPC) LG LG LG LG LG We are expecting that the acroscopic properties of the fina network are strongy reate to the segent ength of the network precursor an the oar ratio of L,L-actie to gycoie. Therefore, oigoers with oar ratio of L,L-actie to gycoie of 85:5, 75:5 an 60:40 were synthesize. For a oar ratio 85:5 oigoers with oecuar weight fro 000 to 7000 were aso synthesize. The fina networks obtaine base on these oigoers wi be cae fro now on LGi where i=-7 correspons to the oecuar weight i000 g/o.

75 66 Chapter 4. NM stuy of shape-eory poyers n a cases the SC easureents inicate that the sapes are copetey aorphous [Cho]. The T g vaues of the networks are higher than those of the corresponing network precursors, ue to the ecrease in nuber of the free chain ens. They are aroun 55 0 C an their vaues sees to be inepenent of the oecuar weights in the investigate range [Cho] even if other authors report a inear epenence [Coh97]. This inicates that for our sapes the crossink ensity has no arge effect on the teperature transition. For UV curing the sapes were processe as fis an then irraiate with a Heraeus Nobe Light Excier Laborsyste (308 n) Laser. Figure epenence of the gass transition teperature of the precursors an of the networks on the oecuar weight of the precursors. 4.. NM experients Soi state NM experients were perfore on a ruker SX-500 spectroeter. The Laror frequency is 500 MHz for protons an 5 MHz for 3 C. The H spectra an T ( H) easureents were ae using puse engths in the range of µs, a we tie of.5 µs, an a recyce eay of 5 s were use. The 3 C spectra were recore using crosspoarization. The oube-quantu bui-up curves were obtaine using the puse sequences escribe in Fig..7b with a fiter tie of s. The easureents were ae in the teperature range fro 95 K to 350 K.

76 Chapter 4. NM stuy of shape-eory poyers Characterization of the networks 4.3. H spectra Typica proton spectra recore uner static an MS conitions are shown in Fig. 4.5 for the sape LG3. fast ook at the proton spectru in static conitions inicates the existence of a broa coponent ue to regions with ow obiity an a narrow coponent ue to regions with high obiity. However, a ecoposition of the spectru in ters of two coponents oes not ea to a proper fit of the experienta ata. Therefore, a fit in ters of three coponents was one by supposing the existence of a rigi phase, an intereiate one, an a obie phase. The ine shapes of the rigi an intereiate phases were fitte with Gaussians, whie the ine of the obie phase was fitte with a Lorentzian. The resuts are given in Tabe 4.. Tabe 4.. ntegra intensity () an fu-with at haf height ( ν / ) of each phase of the ifferent LG networks. (%) ν / (khz) Mobie ntere. igi Mobie ntere. igi LG LG LG LG LG The fraction of the tota integra intensity containe in the narrow peak is about -3% for the investigate sapes. ue to the arge ifference between the ine with of this coponent an the other two this signa shou be given by protons which are sufficienty isoate fro other protons to experience a significant reuction of the their ipoar interaction. Having in view the coposition of the chain we are attributing this signa ainy to the protons fro soe CH 3 groups or to anging chains. The rigi part of the network was attribute to a part of the backbone which is fore by CH an CH groups an the corresponing CH 3 groups with restricte obiity which are ocaize coser to the crossink points. The region with intereiate obiity was attribute to the ie part of the backbone an the corresponing CH 3 groups. The ow obiity of the CH 3 groups can be ue

77 68 Chapter 4. NM stuy of shape-eory poyers to the presence of the CH groups as we as to a squeezing of the poyeric chains which hiners their otions. With increasing the oecuar weight (chain ength) the foowing trens can be seen: (i) the fraction an the obiity of the obie phase an the fraction of the intereiate phases increase an (ii) the fraction of the rigi phase an the corresponing obiity ecrease. y increasing the chain ength the crossink ensity ecreases. Therefore, the chains are ess constraine an therefore they gain obiity. However, the resuts show that this change in obiity is ainy experience by the rigi part of the chain. The effect on the intereiate part is refecte ony in an increase of its aount. Uner MS a part of the ipoar interactions is average out, an the spectru shows the presence of two ines (see Fig. 4.5). The peak at.6 pp is ue to the ethys of the actie whie the peak at 4.8 pp is reate to the ethyenes of the gycoie [Eng0]. The ethyns of the actie give a signa at 5. pp [Eng0] but in our spectru it is not resove. Figure 4.5. H spectra of LG3 recore at roo teperature a) in static conitions, an b) uner MS at 5 khz. The stars inicate the positions of spinning siebans. n orer to investigate the thera stabiity of the sapes an the ynaica changes inuce by teperature in the range of interest proton spectra were recore uner static an MS conitions for ifferent teperatures. The resuts are shown in Figs. 4.6 an 4.7.

78 Chapter 4. NM stuy of shape-eory poyers 69 Figure 4.6. H spectra of LG3 recore in static conitions at a) roo teperature, b) T = 35 K beow T g, c) T = 330 K aroun T g, an ) T = 350 K above T g. Figure 4.7. H spectra of LG3 recore uner MS (5kHz) at a) roo teperature, b) T = 35 K beow T g, c) T = 330 K aroun T g, an ) T = 350 K above T g. The starts inicate the position of spinning siebans. The MS spectra inicate that the sapes o not experience structura changes with the teperature. The ony changes are ue to the enhance obiity with increasing teperature. raatic increase of the chain obiity can be seen for teperatures above T g. This is refecte by both static an MS spectra. n the first situation the evient changes are

79 70 Chapter 4. NM stuy of shape-eory poyers irecty reate to the ine with whie uner MS a change in the ine shape of the spinning sie bans can aso be seen. For teperatures high enough, the fuctuations ue to the theray activate otion ouate the ipoar interactions an they ea to an average of the. s a consequence, the spectru in static conitions shows a structure (see Fig. 4.6). The two peaks have the sae positions as in the MS spectru C spectra Typica cross-poarization carbon spectra recore uner static an MS conitions with a contact tie of s are represente in Fig. 4.8 for the sape LG3. n the static spectru, three ain peaks with ifferent shapes are observe. The carbony peaks observe at the owest fie show arge cheica shift anisotropies. The ethy peaks at the highest fie have shouers on both sies an thus show cheica shift anisotropies athough the egree of anisotropy is not arge. This inicates that their obiity is higher than that of the other functiona groups. The ines o not show a spitting uner both static an MS conitions, in agreeent with the aorphous state of these sapes, even if the presence of a sa egree of crystainity was reporte for sapes with the sae onoer ratio [Kis98]. Figure C CP spectra of LG3 recore at roo teperature a) in static conitions, an b) uner MS at 5 khz. The stars inicate the positions of spinning siebans.

80 Chapter 4. NM stuy of shape-eory poyers 7 Uner spinning conitions the anisotropy of the cheica shift is average out. ue to the arge ifferences in the cheica shift the signas given by the iniviua functiona groups are resove (Fig. 4.8b). The 3 C spectru shows a peak at 8 pp reate to the ethys of the acti aci, one peak at 6 pp reate to the ethyenes of the gycoi aci, one peak at 65 pp ue to the ethyns of the acti aci, two peaks at 66 pp an 7 pp reate to the carboxyic groups of the two co-units an of the cross-inker, respectivey. coparison between the 3 C spectra of the network precursors an the fina network inicates that the signa fro 44 pp is ue to the crossinker. n orer to assign it to a functiona group of the ethacryate crossinker a ipoar ephasing experient was perfore. This experient akes use of the strong istance epenence of the 3 C/ H ipoar couping an the fact that the 3 C ine with, in the absence of proton ipoar ecouping, is arger for those 3 C spins with H spins near to the, usuay as irecty bone protons [ri93]. The ony ifference fro the stanar CP sequence is that after the CP ook puse the ipoar ecouping is switche off for a tie τ. The 3 C signa is then recore in the usua way. The effect of this eay is to aow the signas coing fro the carbons cose to the protons with concoitant broa ines to ephase copetey. fter a ephasing tie of 40 µs the 3 C spectru contains ony signas coing fro CH 3, C=O an the signa at 44 pp. The obtaine resut inicates that the signa at 44 p is ue to the quaternary carbon of the crossinker. The fact that the signa fro CH 3 is not estroye ike that of CH an CH is ue to the oveent of the protons aroun the their C3 syetry axis which eas to a weaker ipoar interaction. typica ethy group at roo teperature jups ore than 0 9 ties per secon aroun this three fo axis [Sch94]. n aitiona proof for the correct assignent of the peaks beonging to the crossinker was ae by recoring 3 C spectra of sapes with various crossink ensity. The variation of the signa intensities for ifferent sapes is epicte in Fig The signas are higher for sapes with shorter chain engths (higher crossink ensity) whie they becoe ifficut to be etecte for sapes with ong chain ength (ower crossink ensity). The intensity of the other signas reain constant over the whoe range of oecuar weights. These resuts confir that inee the two signas are given by the crossinker. ase on the signa at 44 pp an investigation of the efficiency of the cross-inking process for sapes having ifferent chain engths was one. pot of the behavior that it exhibits with the oecuar weight of the acroios is shown in Fig s expecte, a inear epenence of the 3 C signa intensity with the oecuar weight of the network chains is seen.

81 7 Chapter 4. NM stuy of shape-eory poyers Figure C CP spectra of networks with ifferent crossink ensity a) LG, b) LG3, an c) LG5 recore at roo teperature an using a contact tie of s. Figure 4.0. epenence of the reative intensity of the cross-inker signa fro 3 C CP easureents on the oecuar weight M n of the acroios.

82 Chapter 4. NM stuy of shape-eory poyers 73 The integra intensities of the 3 C signas at 6 pp an at 65 pp (see Fig. 4.) aow the estiation of the oar coposition of sapes with ifferent onoer ratio actie/gycoie base on the equation: CH Lactie (%) = 00 (4.) CH CH Figure 4.. Cross-poarization spectra recore uner MS at 5 khz of the fina networks with a onoer ratio actie/gycoie of a) 85 to 5, an b) 60 to 40. cross-poarization tie of s was use. Tabe 4.3. Moar istribution of the actie an gycoie onoers fro 3 C ata. Cacuate Estiate fro 3 C spectra Sape Lactie (%) Gycoie (%) Lactie (%) Gycoie (%) LG7a LG7b LG7c

83 74 Chapter 4. NM stuy of shape-eory poyers The resuts obtaine for sapes with a oecuar weight of 7000 g/o an having three ifferent onoer ratio of actie an gycoie are given in Tabe 4.3. The oar istribution reveae by NM shows a goo agreeent with the expecte vaues. For a better unerstaning of the of the ynaic processes inuce by teperature, 3 C spectra uner static an MS conitions were recore in the teperature range fro 95 K to 355 K. They are shown in Fig. 4. an Fig raatic changes in the shape of the spectra in both static an MS conitions can be seen for teperatures higher than T g. Uner static conitions the frequency of the chain otion ue to teperature eas to a partia averaging of the cheica shift anisotropy for the CO, CH an CH groups. itionay, a ecrease of the intensity for these groups is seen. This effect can be attribute to the fact that at high teperature the iniviua peaks are characterize by ifferent cross poarization conitions. n the case of CH 3 the thera otion eas to an average of the cheica shift anisotropy an therefore to a narrow ine. Figure C spectra of LG3 recore in static conitions at a) roo teperature, b) T = 35 K beow T g, c) T = 330 K aroun T g, an ) T = 350 K above T g. n the case of the MS spectra, a broaening of the ines corresponing to the CO, CH an CH functiona groups appears at T = 350 K even if with increasing teperature an aitiona narrowing of the ine is expecte. esie the theray activate otion, MS iposes aso a tie epenence of the anisotropic interactions. The tie epenence generate externay an that arising fro theray riven, interna otions ea to a ine narrowing. However, when both effects are present the effectiveness in achieving ine

84 Chapter 4. NM stuy of shape-eory poyers 75 narrowing can be reuce [ri93]. This reuction is greatest when interna an externa tie epenencies have siiar tiescaes, that is, when τ ( c ω H ) τ ω ( H ) c an ω MS [ri93]. For the ipoar ecouping becoes uch ess effective an the 3 C ines broaen as the ipoar inewith is reintrouce [ri93]. When τ c ω MS, the cheica shift anisotropy wi not propery be average, again eaing to broaer ines [ri93]. s seen fro the proton spectra, the thera otion an MS have sae siiar effects on the behavior of the sapes at T = 350 K. Therefore, the resuts obtaine fro 3 C spectra inicate that the functiona groups of the backbone have a correation tie s. None of the above effects were etecte in the case of the signa fro CH3. However, such a ine broaening can be seen, as reporte for poypropene, a oecue which has a ethy group in the sae neighborhoo ike our sapes, aroun 05 K [ri93]. τ c = 0 4 Figure C spectra of LG3 recore uner MS (5 khz) at a) roo teperature, b) T = 35 K beow T g, c) T = 330 K aroun T g, an ) T = 350 K above T g.

85 76 Chapter 4. NM stuy of shape-eory poyers Longituina reaxation easureents nother type of easureents base on the proton spin-attice reaxation was use to characterize the oecuar otion an to estabish the effect of various paraeters such as oecuar weight of the network an teperature on the chain ynaics. The experients were perfore using the inversion-recovery etho. The ata were fitte with the su of two exponentias by a east-squares proceure. The estiate vaues for the two coponents of the reaxation ties an the corresponing fractions for sapes with ifferent oecuar weight are given in Tabe 4.4. ifference of aost one orer of agnitue between the vaues of the reaxation ties of the two coponents can be seen. ase on the coparison with the resuts obtaine fro the proton ineshape ecoposition, the reaxation ties with the higher vaues were attribute to the rigi phase whie the short reaxation ties beong to the intereiate phase. The vaues of the reaxation ties an the corresponing apitues show the sae epenence on the oecuar weight as that refecte by the ine with in the proton spectra. oth reaxation ties ecrease with the oecuar weight but the exhibite variation is pretty weak. However, the resuts suggest an increase in the obiity of the whoe chain with increasing ength. Tabe 4.4. Proton ongituina reaxation tie (T ) an the reative coponents apitue () for the LG networks easure uner static conitions. (%) T (s) Short cop. Long cop. Short cop. Long cop. LG LG LG LG LG oube-quantu bui-up curves esiua ipoar coupings represent sensitive paraeters to the hinrance of the oecuar otion ue to the cross-inking, topoogica constraints, an externa factors ike echanica stress [Sch99]. oube-quantu bui-up curves were recore for sapes with ifferent oecuar weight (crossink ensity) using the five puse sequence epicte in Fig..7b. The

86 Chapter 4. NM stuy of shape-eory poyers 77 fiter tie was set to s. Typica resuts for two sapes with ifferent crossink ensity are shown in Fig The axiu of the bui-up curves appears at a short excitation tie of about 9 µs. This inicates the presence of strong ipoar interactions. Figure 4.4. oube-quantu bui-up curves for the LG an the LG5 networks. Each curve exhibit a axiu at short excitation ties. The insert represents a zoo of the initia part of the curves for a better view of the positions of the axia. The spin response can reaiy be escribe using the ensity atrix forais. n the iit of short excitation an reconversion regies, i.e., ϖ τ <<, where ϖ is the resiua ipoar couping an τ noraize Q signas can be expresse as [Sch99] Here is the uration of the excitation an reconversion perios, the S ( τ ) ( ), Q eff τ (4.) are the effective resiua ipoar coupings consiering contributions fro the CH eff an the CH 3 groups, respectivey, an aso fro intergroup resiua ipoar coupings. Nevertheess, the ain contributions to these coherences are fro the CH [Sch99] an the initia sopes of the bui-up curves provie a irect estiate of eff. pot of the effective resiua ipoar coupings estiate base on Eq. (4.) versus the inverse of the oecuar weight is shown in Fig The resuts refect irecty the effect of the oecuar weight on the chain ynaics. The resiua ipoar coupings ineary increase with the crossink ensity. This epenence is in agreeent with the resuts reporte in [Sch99] for,4-cis-poyisoprene.

87 78 Chapter 4. NM stuy of shape-eory poyers Figure 4.5. epenence of the resiua ipoar coupings estiate fro the oube-quantu buiup curves on the crossink ensity WSE experients For a etaie unerstaning of the ateria properties on a icroscopic eve, it is essentia to obtain knowege about the istribution of the obiity in the ateria. Usuay this type of inforation cannot be propery obtaine by cassica techniques such as, for exape, H spectru. The proton ine shapes of rigi oecues represent a superposition of any ipoar spectra an therefore they cannot be quantitativey anayse. soution to this probe is the use of WSE (wieine separation) experients [Sch9, Sch93, Sch94]. The WSE experient estabishes a correation, naey of cheica structure an segenta obiity, as refecte in the 3 C cheica shifts an in the H ine shapes, respectivey. For every resove 3 C resonance, it yies a proton wieine spectru which refects the ipoar coupings of the protons in the proxiity of the respective 3 C nucei [Sch9]. Figure 4.6 shows a WSE spectru of LG3 recore uner static conitions at roo teperature. Sices in the proton iension corresponing to ifferent 3 C cheica shifts yie ifferent proton ine shapes. The narrow coponent seen in the proton spectra was not observe in any of the of the WSE sices. The corresponing proton ine shapes of the CH 3, CH an CH groups were fitte with two Gaussian functions. The attept to ake the fit in ters of ony one coponent ea to a ba atch with the experienta spectru. The resuts are given in Tabe 4.5. The vaues for the ine withs of each functiona group are in goo agreeent with those estiate fro the proton spectra (Tabe 4.) an which correspon to the so cae rigi an intereiate phases. This is an aitiona confiration

88 Chapter 4. NM stuy of shape-eory poyers 79 for the assignent ae fro anaysis of the proton spectra. For a teperature of T = 350 K, above T g, sices in the proton iension yie the sae ine shape regaress of position in the carbon iension. n this case, the estiate ine withs were.49 khz for CH 3, 4. khz for CH an 4.34 khz for CH. This inicates that teperatures higher than T g inuce a otiona average of the ipoar interactions for a functiona groups. Figure 4.6. contour pot of the WSE spectru for LG3 recore uner static conitions at roo teperature. Sices in the proton iension corresponing to ifferent 3 C cheica shifts are shown on the right sie. Tabe 4.5. Fu ine withs at haf height of H sice spectra of the LG3 network at roo teperature corresponing to ifferent 3 C signas. CH 3 CH CH ν / (khz) ' ν / (khz)

89 80 Chapter 4. NM stuy of shape-eory poyers 4.4 nvestigation of the kinetic of the UV-curing process n orer to anufacture crossink poyers with esire properties, the knowege of the kinetics of the cross-inking process is necessary. The irraiation tie an the teperature are the ost iportant paraeters to be seecte in the curing process [Lit]. They wi utiatey eterine the acroscopic properties of the poyers. Therefore, a proper seection of their vaues is requeste. Our stuy focuses on the effect of the irraiation tie on the kinetics of the UV-curing process. Sapes with ifferent oecuar weight (chain ength) an irraiation ties were stuie. The cross-inking process can be onitore by observing the changes in the signa of the crossinker. 3 C spectra for sapes with ifferent irraiation ties are represente in Fig They are recore at roo teperature an uner 5 khz spinning. For a better view, a pot of the 3 C intensities versus the irraiation ties is shown in Fig t sa irraiation ties the signa given by the crossinker is very weak. This eans that ony few chains are cross-inke. The intensity increases with increasing irraiation tie ue to the fact that ore an ore chains are cross-inke. itionay, an increase in the ine with is seen because of the iobiization ipose by the cross-ink points. However, for onger irraiation ties the signa intensity ecreases. This inicates that there is a iite range of irraiation ties in which the raiation eas to efficient cross-inking of the chains. For ties onger than an optia irraiation tie, the raiation starts to act in a estructive way, an a part of the chains break (Fig. 4.8). This process epens on the chain ength as refecte in Fig Figure C CP spectra recore uner MS at 5 khz for the LG7 networks with UV irraiation ties of a) 5 in, b) 5 in, c) 30 in, an ) 45 in.

90 Chapter 4. NM stuy of shape-eory poyers 8 Figure 4.8. Kinetics of the UV-curing process for a) the LG5 an b) the LG7 networks. The resuts fro Fig. 4.8 inicate aso that the engths of the chains are responsibe for the rate of the photocuring process. The sapes with shorter chain engths cross-ink faster than those with onger chains. However, a higher aount of ata is necessary to get the kinetic constant. Nevertheess, we are expecting that the cross-inking is a type of thresho process. t starts above a specific irraiation tie. Work in this irection is in progress. 4.5 naysis of shape-eory properties 4.5. The concept of shape-eory Shape-eory poyers are stiui-responsive aterias [Tob96, Fen98, Jeo0, Len, Lena]. They have the capabiity to change their shape upon appication of externa stiuus. change in shape cause by teperature is cae a theray inuce shape-eory effect. The process of prograing an recovery is scheaticay shown in Fig Figure 4.9. Scheatic representation of the theray inuce shape-eory effect. n the prograing process the teporary shape is obtaine. Heating the sape above the transition teperature resuts in recovering the peranent shape.

91 8 Chapter 4. NM stuy of shape-eory poyers First, the poyer is conventionay processe to receive its peranent shape. uring the prograing process the poyer is efore an the esire teporary shape is fixe. This is usuay one by heating up the sape, eforing it, an cooing it own, or rawing the sape at ow teperature. The sape is now in the teporary shape. Further on, heating up the sape above a transition teperature, the sape recovers its peranent shape. This effect of recovering is cae shape eory effect. Cooing now the sape own, beow the transition teperature, the teporary shape is not recovere again. This can ony happen when a new prograing proceure is one [Lenb]. The change in shape uring the shape eory transition is epicte in Fig. 4.. The teporary shape of the copoyers which is a spira retrieves its peranent shape, a ro, within 35 secons uner the infuence of hot air having a teperature of 70 o C. The peranent shape is recovere with a precision of ore than 99% [Len]. More an ore aterias with very ifferent cheica structure can be foun nowaays uner the generic nae of shape-eory poyers. This category incues poyurethane [Tob96], ifferent copoyers such as poyethyene/nyon-6 graft an ethyeneviny acetate [Fen98, Fen99] or base on oigo(ε-caproactone) [Len], an ore recenty iqui crystas [ou3]. these aterias show at east two separate phases. The phase with the highest thera transition T g,h acts as a physica cross-ink an it is responsibe for the peranent shape [Lenb]. bove this teperature the poyer ets an can be processe by conventiona processing techniques. secon phase serves as a oecuar switch an enabes the fixation of the teporary shape. The transition teperature for the fixation of the switching segents can either be a gass transition (T g ) or a eting teperature (T ) NM investigation of the shape-eory effect The experienta approach epoye to obtain inforation about the shape eory characteristics of our LG networks was base on the investigation of the teperature behavior of sapes with ifferent stretching ratios. This behavior was copare with that exhibite by an unstretche sape. itionay, a coparison of the characteristics of the stretche sapes before an after heating above the transition teperature was carrie out at roo teperature in orer to estiate the recovery of the peranent shape. We have stuie sapes with two ifferent stretching rates: 30% an 80%. Stretching rates above 80% cou not be reache ue to the breaking of the fis. Severa NM ethos

92 Chapter 4. NM stuy of shape-eory poyers 83 were epoye but in the foowing we wi present ony those which show the ost reevant inforation. n investigation of the variation of the ongituina reaxation ties with the teperature was perfore for a sape stretche at 80%. The resuts were copare with those corresponing to the unstretche sape. They are epicte in Fig The vaues of the two coponents of the reaxation tie T (see paragraph 4.3.3) ecrease with increasing the teperature. oth coponents show a change in the behavior aroun T g = 37 K. However, the phase with the onger reaxation tie exhibits a ore raatic change in the sope. This correspons to a transition fro the teporary shape to the peranent shape. The recovery of the peranent shape above T g is confire when the behavior of the stretche sape is copare with that of an unstretche sape. eow the transition teperature, the vaues of T short an T ong are higher for the stretche sape than for the unstretche one. Once the teperature goes above 37 K the vaues of the reaxation ties for the two sapes are, within the error iits, equa. This areay inicates that the recovery of the peranent shape has goo efficiency. nother test of the recovery of the peranent shape consiste of the coparison of the reaxation ties for the unstretche sape an the stretche sapes at roo teperature after they were heate above T g (Fig. 4.0). The vaues of the T ong for the two sapes are in goo agreeent whie those corresponing to T short show soe ifferences. This can be ue to the fact that the peranent shape is not copetey recovere. Figure 4.0. Evoution of the ongituina reaxation ties with the teperature for a LG3 network stretche at 80% in coparison with the corresponing unstretche sape: a) the coponent with the short reaxation tie an b) the coponent with the ong reaxation tie. The easureents were ae using the inversion-recovery etho uner static conitions. The ashe ines inicate the position of the transition teperature.

93 84 Chapter 4. NM stuy of shape-eory poyers The above type of easureents areay suggest that the stretche an the unstretche sapes exhibit ifferent egree of obiity. For a better unerstaning of the oecuar echaniss invove in the shape eory effect an in the stabiization of the teporary shape utipe-quantu spectroscopy has aso been use. oube-quantu bui-up curves for unstretche sapes an sapes with ifferent egrees of stretching are shown in Fig. 4.. For a sapes, the axiu of the curves appears at short excitation ties of about 8 0 µs. This inicates the presence of strong ipoar interactions. Nevertheess, the interactions are stronger in the sape with the higher stretching ratio. The anaysis of the curves was ae in the initia tie regie base on Eq. (4.). The resuts are presente in Tabe 4.6. Figure 4.. oube-quantu bui-up curves recore at roo teperature for the LG3 network: a) with ifferent egrees of stretching an b) stretche at 80% before an after heating. The easureents were ae uner static conitions. The ash ines inicate the positions of the axiu of the curves. Tabe 4.6. esiua ipoar coupings for LG3 with ifferent stretching ratios evauate base on the initia tie regie of the oube-quantu bui-up curves. Unstretche T = 95 K Stretche at 30% Stretche at 80% efore heating fter heating efore heating fter heating T = 350 K eff (khz) k 8.06 n increase in the strength of the ipoar interactions is seen by increasing the stretching ratio. This is ue to an orering process of the chains uner the action of the externa stress. The orering is higher for higher stretching ratios. raatic change in the

94 Chapter 4. NM stuy of shape-eory poyers 85 strength of the resiua ipoar couping is seen for the sape stretche at 80% at T = 350 K above T g. t this teperature the chains oose their orientation ue to the stronger chain otion an to the recovery of the peranent shape. oss in orientation is aso seen when both stretche sapes are cooe own to roo teperature after being heate above T g. n estiation of the efficiency of the recovering of the peranent shape can be ae by coparing the vaues of the resiua ipoar coupings of the unstretche an the stretche sapes after heating. The recovery of the peranent shape is ore than 99% for the sape stretche by 30% whie it is aroun 98% for the sape stretche by 80%. The above T vaues an the vaues of the resiua ipoar coupings together with the previous resuts (section 4.3) support the foowing echanis for the shape-eory effect (see aso Fig. 4.). The peranent shape is stabiize by the cheica crossink points. bove T g, ue to the shaping proceure, the (L_actie)-ran-gycoie chains get orientate an the interactions between the becoe stronger. y ecreasing the teperature the interactions are frozen an therefore the chains act ike physica cross-inks for the network an they keep the teporary shape. n increase now of the teperature above T g eas to a oss in the chain orientation an to a recovery of the peranent shape. Figure 4.. Scheatic representation of the oecuar echanis responsibe for the shape-eory behavior of the LG networks. The ots represent the cheica cross-ink points.

95 86 Chapter 4. NM stuy of shape-eory poyers 4.6 nvestigation of the egraation process in vitro The egraation an the ageing of poyers are copex cheica processes that occur uner the infuence of heat, oxygen or echanica stress, an resut in a tie-epenent change in their cheica an physica properties [Noz]. n the particuar case of the hyroytic egraation, it epens not ony on paraeters ike ph, ionic strength, an teperature, but aso on poyer characteristics such as oecuar weight, cheica coposition, an structura properties such as onoer stereocheistry, co-onoer ratio, orphoogy an configurationa structure [Kis98]. Therefore, a better unerstaning of the echaniss responsibe for changes in physica properties associate with egraation, which wou utiatey perit the esign of poyers with bioegraation rates, an other properties, suitabe for a given appication is requeste. soi-state NM investigation of the structura an orphoogica changes of the [(L-actie)-ran-gycoie]iethyacryates inuce uring hyroytic egraation in vitro was ae. teperature of T = 37 o C an a buffer soution with ph = 7 were chosen in orer to iic the egraation in vivo. Proton spectra corresponing to ifferent egraation ties for the LG3 networks are represente in Fig The presence of a highy obie coponent can be seen. t is associate with the buffer ingress into the sapes an the reease of the egraation proucts. The ecoposition of the spectra gives irect inforation about the evoution of this coponent an its obiity (Fig. 4.4). Figure 4.3. Proton spectra of the LG3 networks recore uner static conitions a) before egraation an after ifferent hyroytic egraation ties b) 6 ays, c) 49 ays, an ) 06 ays.

96 Chapter 4. NM stuy of shape-eory poyers 87 t initia stages of egraation the aount of the obie coponent is ow. t correspons ainy to the buffer ingress into the sape (see beow). ue to the strong interactions between the poyeric chains the water uptake is oerate at this stage. This hinerance is we ephasize aso in the high vaues of the corresponing ine with. The aount an obiity of the obie coponent increases after about two onths. t this stage the signa shou be a contribution fro the water signa an fro the egraation proucts which are not copetey reease into the buffer soution. The corresponing ine with inicates an increase in the obiity but however, it is sti hinere. Figure 4.4. a) Fraction of the obie coponent an b) the variation of the corresponing inewith uring the hyroytic egraation of LG3 obtaine fro the proton spectra recore uner static conitions. n orer to get inforation about the behavior of the poyeric chains ue to the hyroytic egraation WSE spectra were recore. Sices in the proton iension corresponing to the 3 C cheica shift of the CH 3 groups are presente in the Fig The spectra corresponing to ifferent stages of the egraation process present siiar shapes inicating the presence of two coponents. None of the spectra shows a highy obie coponent corresponing to ow oecuar weight egraation proucts. The sae behaviour was aso exhibite by the spectra corresponing to the CH groups. n anaysis of the was carrie out in ters of two coponents for both functiona groups. The resuts of the ecoposition are shown in Fig.4.6.

97 88 Chapter 4. NM stuy of shape-eory poyers Figure 4.5. Proton spectra corresponing to the CH 3 groups evauate fro WSE recore uner MS using a spinning spee of 5 khz a) before egraation an after ifferent egraation ties of b) 6 ays, c) 49 ays, an ) 06 ays. Figure 4.6. Effect of the hyroytic egraation on the CH an CH 3 groups evauate base on the WSE spectra recore uner MS using a spinning spee of 5 khz. Variation of the ine with with the egraation tie corresponing to: a) the intereiate an b) the rigi phase. The two coponents were attribute to the intereiate an to the rigi phases, respectivey (see section 4.3.). The increase in the ine withs for both phases copare to those reporte previousy can be ue to an ageing process. n the present situation, a ecrease of the ine with of the two phases for both functiona groups can be seen. ue to the water ingress the sapes were sweing an therefore the chains cou ove uch ore freey. However, it is interesting to note that the effect sees to be higher for the rigi phase.

98 Chapter 4. NM stuy of shape-eory poyers 89 Nevertheess, a ecrease in the fraction of the rigi phase in the favor of the intereiate one cou be seen. For exape, before egraation the rigi fraction was aroun 67% whie after 76 ays of egraation the fraction was aroun 30%. The sweing effect is refecte aso in an increase in the acroscopic size of the pieces which were use uring the easureent. itionay, a change in the coor of the sapes cou be seen with increasing egraation tie. ue to the fact that aways the sae aount of the origina sape was egrae the changes in the aounts of the ifferent functiona groups with the egraation tie cou be foowe. The resuts are epicte in Fig The three functiona groups exhibit the sae behavior. The hyroytic process acts by rano scission of the ester bons [Tsu97, Zon99, Str0, Fu] being a buk process an not a surface one [Tsu97]. Figure 4.7. Effect of the hyroytic egraation on the proton fraction corresponing to the ifferent functiona groups incuing the CO groups. The ata were estiate fro the WSE spectra. Severa groups propose a egraation echanis which favors the appearance of a crystaine phase fro the ore obie aorphous chains through so cae ceavageinuce crystaization [Zon99, Ki0, Fu]. The recoring of carbon spectra is a we estabish etho to euciate the existence of functiona groups in aorphous an crystaine phase ue to a ifference in the cheica shifts. Therefore, the sei-crystaine aterias show a spitting of the ines. The carbon spectra recore for our sapes exhibit no spitting (see Fig. 4.8). This inicates the absence of a crystaization process.

99 90 Chapter 4. NM stuy of shape-eory poyers Figure C CP spectra recore uner MS at 5 khz with a contact tie of s for the LG3 network a) before egraation an b) after 49 ays of egraation. oth spectra were noraize to the intensity of the CH 3 ine. ase on the above resuts, the foowing egraation echanis can be propose. t consists of two ajor steps. First, the water oecues iffuse into the aorphous regions resuting in the scission of soe isorere chains. itionay, the sapes get swoen. n the secon stage, the water attacks the chains an ceavage of the ue to the hyroysis of the ester group happens. This process ust be occurring on the networks prior to the start of the ass oss [Tzu97]. When the egraation proucts are sa enough to be soube they are reease into the surrouning aqueous eiu. 4.7 Concusions n this chapter networks of [(L-actie)-ran-gycoie]iethacryate were characterize in ters of structure, obiity, shape eory properties, an egraation behavior with the hep of NM. ifferent techniques such as proton an carbon spectra, ongituina reaxation tie, oube-quantu bui-up curves, an WSE recore uner static an MS conitions were epoye. n the first part of this work, the effect of ifferent paraeters such as the cross-ink ensity an the teperature on the networks properties was anayze. n increase in the cross-ink ensity ea to a ecrease in the chain obiity. The vaues of the resiua ipoar coupings show a inear epenence of the cross-ink ensity. However, the ongituina reaxation ties exhibit ony a weak epenence on the chain ength. Changes in the chain ynaics take pace aso with increasing teperature. goo agreeent is seen between the T g vaue etecte by NM an that estiate by SC. itionay, base on the 3 C spectra, the onoer coposition was evauate. t is in goo agreeent with the theoretica preictions.

100 Chapter 4. NM stuy of shape-eory poyers 9 The investigation of the cross-inking kinetics uner the action of UV irraiation reveae that there is a range of optia curing tie on which the raiation acts for buiing up the [(L-actie)-ran-gycoie]iethacryate network. Furtherore, it was shown that the rate of the cross-inking is higher for sapes with shorter chain engths. n anaysis of the shape eory properties of the networks was carrie out by coparing the behavior of sapes with ifferent stretching ratios an the corresponing unstretche sapes. The sapes behave ifferent beow T g but, in the error iit, they exhibit the sae behavior above T g. Moreover, the recovery of the peranent shape has a goo efficiency. itionay, the NM ata support the oecuar echanis which was suppose to be responsibe for the shape eory effect was. ase on it, the peranent shape of the sapes is ue to the cross-ink points. The poyeric chains act ike physica crossink points when the sapes is stretche ue to an orering effect an therefore they are responsibe for the teporary shape. The ast part of this work focuses on the investigation of the echaniss responsibe for the egraation in vitro. The egraation process invoves two ain steps. First the water oecues iffuse insie the aorphous networks. This eas to an increase in the chain obiity. Further on, egraation proucts wi appear through the hyroysis of the ester bons. They wi be reease into the aqueous surrounings after severa tie. The egraation process evoves in a hoogeneous way through the sape. itionay, no crystaine phase was etecte.

101 9 Chapter 4. NM stuy of shape-eory poyers

102 5 Moecuar ynaic heterogeneities of confine thin ipi fis 5. ntrouction an otivation Moecuar fis of sef-assebe singe biayer ipi ebranes on soi panar supports [Ta85, Nau9, Gro97, Cre99] an ore recenty ipi onoayers on siica beas [Käs99], have attracte consierabe attention ue to their potentia appications in biosensing an biosepartion as we as ue to their interesting physica properties [Sac96, Cor97, Nik99, Goo0, Wan]. The function of these biocopatibe oecuar ayers on soi substrates is associate with their structure, packing, an ynaics. recent H NM stuy by Zaar et a. [Za0, Za] on iqui crysta fis in porous hosts has suggeste that upon reucing the effective ayer thickness to an orer of one oecuar ength or even ess, a eviation fro the orer an ynaics of a 3 buk phase towars -iqui or -gas behavior occurs. n the ight of these investigations an aso ue to soe siiarities that iqui crystas [Xue9] have with ipi oecues it is interesting to stuy utra thin fis of phosphoipis. Furtherore, knowege of the roe that the soi substrate pays with regar to the ipi oecuar orering an ynaics ay serve as iportant inforation in the anufacture of biosensors. Hence the stuy of the ynaics of ipi oecues at various surface coverage ranging fro buk-ike thick fis to subonoayer effective thickness is essentia for unerstaning the properties of ipi fis at a oecuar eve, an our work is aie in this irection. The ain objectives of this chapter are to expore the surface inuce ynaic heterogeneity of utra thin ipi fis an to unerstan the behavior of the overa ynaics of confine ipi oecues an the effect of oecuar area coverage, pore size an teperature. The experienta techniques invove: (i) excitation of utipoar spin states represente by oube-quantu (Q) an tripe-quantu (TQ) coherences an easureent of the spitting of Q eite spectra, in orer to extract resiua ipoar coupings an ynaic orer paraeters. The existence of ynaic heterogeneities aong the grafte oecues are evience ony inirecty in these experients as oppose, for instance, to 93

103 94 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis those perfore on poy(iethysioxane) ayers cheicay attache to the surface of hyrophiic siica [Wan3]. (ii) For a irect evience of the existence of the ynaic heterogeneities aong the oecuar chain the H agnetization - exchange etho was use [Ern87, Sch94]. The istribution of the resiua ipoar coupings aong the fatty chains is escribe by a heuristic Gaussian function. The egree of oecuar ynaic heterogeneities can be quantify by the with of the Gaussian istribution function that is correate with the pore sizes, oecuar area coverage an teperature. 5. Experienta 5.. Sapes Lipi fis absorbe on hyrophiic porous substrates (nopore ebranes) were prepare with an effective thickness ranging fro a onoayer to a subonoayer with a ow coverage own to ~ 80 Å per oecue. nopore (Structure Probe nc, US) esignates coerciay avaiabe ebranes, noray use for fitration appications. They are ae of cheicay pure auina ( O 3 ). Their structure consists of open, parae cyinrica channes with efine iaeters that exten through the entire ebrane [Za0, Za] (Fig.5.). 60 µ thickness of the Figure 5.. Scanning eectron icrocopy of the cyinrica structure of the nopores: a) cross-section an b) ongituina section. The ipi use in the present stuy is egg-yok ecithin, 99 % pure, with a oecuar weight M eci = 760 g/o, purchase fro rich Cheicas, US. t was coate onto the inner surfaces of the nopore ebranes using the sovent (hexane) evaporation etho [Za0, Za]. The use of this technique ensures the preparation of oecuar fis with an effective thickness of ess than a onoayer in a controabe way [Za0, Za]. n other wors, thin oecuar epositions with a we efine area per oecue can be fore on a soi surface.

104 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 95 scheatic representation of the ecithin oecue is shown in Fig. 5.. t consists of a poar hea group an two fatty aci chains which are ainy copose of CH groups. One of the chains shows a kink ue to the presence of a carbon oube bon. Figure 5.. Scheatic rawing of a ecithin oecue. The cose circes an sa vertica ines are CH 3 an CH groups, respectivey. The nopore ebranes have unifor iaeters of = 00 n an = 0 n, hereafter cae 00 an 0. On the sooth surfaces of the ebrane [Cra9] the oecuar eposition is expecte to be unifor an the thickness of the eposition epens on the concentration of ecithin in the sovent. For utra thin fis the appropriate quantity to characterize the surface coverage is which is reate to the concentration c, the weight percentage of ecithin in the sovent. ccoring to Zaar et a., [Za0, Za] the reation between the require concentration c (weight percentage of ecithin in the sovent), an can be expresse as, c Meci = λ, (5.) c rn eci where eci is the ass ensity of ecithin, N is the vogaro nuber, an λ is eci hexane. n the orere phase of ecithin, for a one onoayer thickness, the area per oecue at the air-water interface is = ~ 5 Å (47 Å < < 54 Å ) [Hau8] an one ay expect siiar coverage on the hyrophiic surface of nopore aso. pproxiating λ, the require concentration for this coverage in 00, is ~ Sapes with five ifferent concentrations, c = 0.08 ( = 3 Å ), c = 0.06 ( = 39 Å ), c = ( = 5 Å ), c = 0.0 ( = 8 Å ), an c = ( = 54 Å ) were prepare in 00. Curvature effects on the organization an ynaics of ipi fis in 00 are expecte to be absent [Cra9] whereas the saer raius of curvature in the saer pores of 0, can

105 96 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis introuce eastic eforations [Zen98] which in turn can infuence the overa ynaics of the ipi oecues. n view of investigating the roe of the geoetrica constraints, we extene our stuies to sapes with c = 0.0 in 0 pores yieing a fi coverage of = 80 Å. 5.. NM experients Soi-state NM proton spectra an agnetization-exchange ata were easure using a ruker SX-500 spectroeter. The ength of the π/ puse was about 5 µs an the we tie was.5 µs. The recyce eay was 5 s for a easureents. The Q an TQ bui-up curves an the oube-quantu eite spectra were perfore using the puse sequence fro Fig. 5.3b with the appropriate phase cycing. The eite spectra were recore using τ = t = 0 µs.the spin-iffusion experient foows the genera schee agnetization fiter agnetization-exchange perio etection (Fig. 5.3a). n a easureents a ipoar fiter base on the seection of the oube-quantu (Q) coherences with τ = 0 µs an a very short evoution tie of tq = 5 µs was use (cf. Fig. 5.3b). The resutant H spectra can be ecopose in the three coponents (see beow) with ifferent ine shapes using the ruker WinFit progra. For the ine shape of the rigi coponent a Gaussian fit function was chosen, an average between a Gaussian an a Lorentzian ine shape for the intereiate coponent, an a Lorentzian ine shape was assue for the obie coponent. Figure 5.3. a) Genera schee of a agnetization-exchange experient with a utipe-quantu (MQ) ipoar fiter. b) Puse sequence for the agnetization-exchange experient with a oubequantu fiter.

106 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 97 For a sapes uner investigation, the integra intensity of the agnetizationexchange experients was constant in the whoe range of agnetization-exchange ties. This inicates that the agnetization-exchange process is copete on a tie scae shorter than T. Therefore, no correction of the agnetization-exchange ata ue to ongituina reaxation was perfore. The sapes were anipuate an seae in NM MS rotors uner nitrogen. Highresoution H MS spectra o not show any signas fro sovent oecues or hyration water. For unerstaning the effect of the teperature on the chain ynaics, the easureents were perfore in a teperature range fro 95 K to 63 K. 5.3 Mutipe-quantu bui-up curves an eite spectra oube- an tripe-quantu buiup curves recore at T = 95K for buk ecithin an for fis with varying surface coverage (c = 0.06 to 0.005) in 00 are shown in Fig. 5.4a an 5.4b. The corresponing oube-quantu (Q) eite spectra in the short excitation an reconversion regie are shown in Fig The sopes of the Q, an TQ bui-up curves (hence the respective vaues of resiua ipoar coupings) an the spitting of the Q eite spectra are rearkaby ower for the fis copare to those in the buk, inicating faster ynaics in the fis. n the buk state, ipi oecues are tighty packe an the ynaics of the fatty aci chains experience steric hinrances which ea to a stronger ipoar interaction. The arger ν Q interactions ike a power pattern. ν Q in the buk is refecting a continuous istribution of H-H pair Figure 5.4. oube-quantu (a) an tripe-quantu (b) bui-up curves for ecithin fis confine in 00. The easureents were ae at roo teperature using the puse sequence fro Fig. 5.3b with the appropriate phase cycing.

107 98 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis n the buk state two axia are observe in TQ bui-up curves, one at 8 µs an one at 40 µs. This observation suggests the presence of two ynaicay ifferent types of CH 3 groups in the oecue. This cou be ue to the ynaic heterogeneity aong the CH 3 groups on the either ens of the oecue (Fig. 5.) which is we pronounce in the buk phase. s the ynaics of the hea group cou be reativey sow copare to the fatty aci chains, the first axiu can be assigne to the CH 3 groups of the poar hea. n principe, the TQ coherence between two ajacent CH groups can aso contribute to the observe axia. However the efficiency of such puping is very ow copare to that of a three-spin tria in a CH 3 group [Sch99]. Figure 5.5. oube-quantu eite spectra of buk ecithin an ecithin fis of various concentrations confine in 00 pores. The ata were recore at roo teperature using the puse sequence epicte in Fig. 5.3b in short excitation/reconversion perio an with a fiter tie of 0 µs. ue to the sef assebing nature of the zwitterionic ipi oecues, the hyrophiic nopore surface wi first be covere copetey with the hyrophiic poar hea groups oriente towars the surface. t c = 0.06, (38 Å ) is ess than that of onoayer coverage (5 Å ). Then the ipi oecues have to accooate theseves in a space saving configuration [Hau8], possiby sighty tite away fro the surface whie the chains point towars the surface nora. t has to be entione that the kink in one of the fatty aci chains (Fig. 5.) prevents the copete orientation of the chains aong the surface nora. The excess ipi has to be covere on the top of this initia coverage with partia intercaation. Q eite spectra for this coverage (Fig. 5.5) exhibit a shouer ike structure suggesting a superposition of at east two istinct phases, a scenario that resebes a ewetting of the excess of iqui crystas at interfaces [Va96, Va99, Zih0] an utiaear ipi biayers [Per]. We ca this fi as supersaturate coverage. However such an excess coverage ay not be unifor.

108 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 99 siiar observation is ae (not shown in Fig. 5.5) for c = 0.08 ( =3 Å ). t has to be entione that in the presence of oisture, a foration of a secon ayer on the top of the onoayer ay not be rue out. n aition to the intra CH an CH 3 group rotations, in an uniaxia environent the possibe ynaic oes that the surface oriente ipi oecues can exhibit are, (i) rotations about the ong oecuar axis, (ii) fuctuations aong their oecuar axis, about their ean positions, (iii) reorientationa tubing with their base (hea group) fixe at the surface an (iv) surface iffusion. For c = 0.06, the ynaic processes (i) an (ii) are ore probabe copare to (iii) an (iv) an the reuction in ν Q an the corresponing eff inicate a partia averaging of the ipoar interactions with respect to the buk. t c = ( = 5 Å ) a hoogeneous onoayer coverage with hoeotropic aignent is expecte (Fig. 5.4b) which can be consiere a -iqui phase [Za0, Za]. t can be seen that the position of the Q eite spectru atches that of the shouer ike structure for c = 0.06, confiring that the excess ipi in c = 0.06 ewetts the buk ike phase [Per]. The sope of the Q bui-up curve an the position of its axiu (~50 µs) for c = are arginay ower than those for c = 0.06 suggesting that the reative contributions of the ynaic processes are aost siiar in both the cases. The otiona hinrances cou be ue to the geoetry of the oecue (Fig. 5.). t c = 0.0, as (8 Å ) is ore than that of the saturate onoayer coverage, the oecues tit towars the nopore surface in orer to occupy ore area, which is effectivey equivaent to a subonoayer thickness. nterestingy, the overa ynaics at this coverage sees to be faster than that in the saturate onoayer (c = 0.048) as is evient fro Fig.5.4 an Fig This sees to be pausibe because of the reuction in the ensity of oecues eas to a cear separation of the pivots of the hea groups. Such a situation favors the ynaic oes (iii) an (iv) an hence an efficient averaging of the ipoar interaction. We assue that on average the interfacia area of the hea group is sti cose to (~5 Å ) an base on a sipe cacuation estiate that in orer to achieve an excess coverage of about 77 Å (so as to reach a tota of 8 Å ), the fatty aci chains have to tit by ~6 0 fro the surface nora. However, ue to the kink in the fatty aci chain (Fig. 5.) the effective tit cou be ess than this vaue. The - iqui ike characters see to be ore pronounce for fi concentrations aroun c = 0.0, an this configuration with space pivot groups resebes a bioogicay reevant iqui crystaine aear phase [Hau8]. Upon reucing the fi coverage fro onoayer to subonoayer an eventuay to an utra thin fi, the cooperative nature of the ipi oecues ay iinish an the effect of

109 00 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis the surface on the oecuar properties can be ore significant. t ~ 54 Å (c = 0.005), the sopes of the Q an TQ buiup show again an increase copare to those for = 8 Å, which is rather interesting. siiar increase in ν Q of the corresponing Q eite spectru is observe (Fig. 5.5). The ratio of ( = 54 Å ) to ( = 8 Å ν Q ν Q ) inicates that the ynaic orer paraeter has increase by a factor ~.5 in the sape with = 54 Å. t this ow coverage, the ipi oecues shou ie fat on the nopore surface, with their ong oecuar axis aong the surface pane, in orer to have the high surface area per oecue. n a fat ying configuration the ost probabe ynaic processes that ipi oecues can unergo are fast reorientations about their ong axis aong the surface pane siiar to ynaic process (i) an the surface iffusion (iv), whie the reorientationa tubing (iii) is negigibe. Such a phase can be represente as an oriente iqui [Za0, Za]. We interpret that the increase vaues of eff an the restricte ynaics ipose by the surface orering. ν Q at this coverage are ue to The quaitative anaysis of the TQ bui-up curves at a concentrations has aso yiee siiar inforation that supports the anaysis of the Q bui-up curves. The aitiona inforation that is obtaine fro the TQ ata is about the inequivaence in the CH 3 group ynaics. For fis with > 3 Å, in aition to the weak signature of a shouer or change in the sope aroun 5 µs, two cosey pace axia in the region of 50 to 5 µs are observe (cf. Fig. 5.4). The sopes an positions of the axia are consistent with the possibe ynaics iscusse above. Upon ecreasing the surface concentration fro = 8 Å to = 54 Å, these two axia are better resove inicating that the sowy rotating CH 3 groups (first axiu) are being sowe own further, whie the fast rotating groups o not experience any change in their ynaic state. This observation suggests that the surface inuce oecuar orering at c = not ony iposes hinrance for the overa ynaics (process (iii)) but aso gives rise to further ynaic inequivaence aong the terina CH 3 groups. Nevertheess, the rearkabe feature is, espite the possibiity that the oecues ie fat on the surface an experience surface inuce orering, the rotationa as we as the surface iffusion processes see to be surprisingy fast copare to than in the onoayer thick fi. The effect of increasing in the confineent on the ynaics of -iqui fi is teste for the saer pores 00 an 0. Proton Q an TQ bui-up curves an Q eite spectra of ecithin fis of c = 0.0 in 00, 00 an 0 are shown in Fig. 5.6 an Fig ccoring to Eq. (5.), c = 0.0 shou yie vaues of of 56 Å an 80 Å in 00 an 0, respectivey.

110 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 0 Figure 5.6. oube-quantu (a) an tripe-quantu (b) bui-up curves of ecithin fis in pores of various sizes. The easureents were perfore at roo teperature. Figure 5.7. oube-quantu eite spectra of ecithin fis confine in pores of various sizes. The ata were recore at roo teperature using the puse sequence epicte in Fig. 5.3b in the short excitation/reconversion perio an with a fiter tie of 0 µs. The ashe ines are guies to the eye to estiate the reative change in ν Q with respect to 00. n coparison to 00 (6.54 khz), the respectivey (Fig. 5.7). The increase ν Q in 00 an 0 are 9.78 an.8 khz, ν Q (.8 khz) for 80 Å in the saer 0 pore, copare to that for = 56 Å (00) suggests an increase surface orering in 0. s this coverage correspons to the ecithin oecue ying fat on the surface, one wou expect that the ynaics an hence ν Q shou be coparabe to that of = 54 Å in 00. The ratio ν Q (80 Å ) to ν Q (54 Å ) is ony.4, suggesting that oecues ay not be experiencing uch the presence of other oecues, but rather surface inuce orering. However, it appears that the increase raius of curvature in 0 has ony a noina effect on the ynaic hinrance. The sae picture is supporte by the changes in the initia sopes of

111 0 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis the Q bui-up curves (Fig. 5.6a). nterestingy, the TQ bui-up curves (Fig. 5.6b) for 0 i not exhibit the effects of ynaic inequivaence in the CH 3 groups. The effect of teperature was aso investigate in the teperature range fro 95K to 63K for buk ecithin an ecithin fis confine in 00 an 0. The oube-quantu bui-up curves (not shown here) exhibit for a sapes an increase in the sope with ecrease of the teperature. The sae effect is aso presente by the oube-quantu eite spectra. pot of the ogarithic vaues of ν Q confine in 0 is epicte in Fig versus teperature for buk ecithin an ecithin fis Figure 5.8. Variation of the ogarithic vaues of the spitting ν Q of the oube-quantu eite spectra versus the inverse of the teperature. The easureents were ae with a fiter tie of 5 µs. n increase of the strength of the resiua ipoar coupings can be seen with ecreasing teperature for both sapes (an aso for fis confine in 00). However, the effect is higher for the confine fis than for the buk. Nevertheess, even at very ow teperature the oecuar ynaics exhibite by the confine fis is faster than in buk. The spitting of the oube-quantu eite spectra can be reate to a resiua spitting with the hep of the rrhenius aw ν Q Ea = ν 0 exp, (5.) T where E a represent the activation energy, the universa gas constant an T the teperature. ase on this equation the activation energies for buk an the ecithin fis confine in 00 an 0 were estiate. Their vaues are.59 kj/o, 4.3 kj/, an 5.84 kj/o, respectivey. This inicates that the teperature has a higher effect on confine ecithin than in buk state an for saer pores. This is ue to the orering effect ipose by the surface which is accentuate by the ow teperatures.

112 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis Proton agnetization-exchange experients 5.4. Theory Uner confineent the ecithin oecues aopt ifferent anchoring orientations epening on the surface coverage an the pore size [Za0, Za]. The oecues experience geoetrica constraints an surface inuce orientation that ea to a change in the chain ynaics copare to that in the buk state, as seen before, as we as to a istribution of the oecuar ynaics aong the ipi chains. One way to characterize these heterogeneities is with the hep of resiua ipoar coupings. NM agnetization-exchange in the iit of spin-iffusion is a we estabishe etho for estiating oain sizes when the spin-iffusion coefficients are known [Sch94]. On the other han, if the sizes are known an evauation of the spin-iffusion coefficients can be ae. These quantities are irecty reate to the resiua ipoar coupings. This ast approach was aopte here to investigate the heterogeneity of the oecuar otion of the confine ecithin oecues. Figure 5.9. a) Scheatic representation of the ecithin oecue. b) Spin-iffusion oe aopte to escribe the agnetization-exchange process aong the ecithin chains. The process is consiere to be one-iensiona in a finite source-intereiate-finite sink syste aong the x axis across the oain bounaries. The source, intereiate, an sink oains have the inear iensions,, an M. The average spin-iffusion coefficients are by,, an M.,, an M, an the spin ensities are enote

113 04 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis n the oe aopte for anaysing the agnetization-exchange experients (see Fig.5.9) severa assuptions were ae: (i) n a particuar set-up of the agnetization-exchange experient the source of the agnetization can be seecte in the rigi part of the oecue which is the poar hea an soe of the CH groups fro the fatty aci chains. t this point we assue that the agnetization-exchange process is an intra-oecuar one an not interoecuar between ifferent oecues. This assuption is unnecessary for sa ipi concentrations where the oecues are too istant for an interoecuar agnetizationexchange to procee. Furtherore, we o not assue a agnetization graient between the two chains of the oecue. Therefore, the front of agnetization wi procee aong the oecuar chains through a fip-fop process of the ajacent proton spins. The spee of this process epens not ony on the vaue of the resiua ipoar couping but aso on the istance between protons. s shown in Fig. 5.9a there are three bons which separate the CH an CH groups ocate at the en of the poar hea fro the first CH groups of the fatty aci chains. ue to the arger inter-proton istances we can consier that this region fors a botte neck to the poarization transfer fro the poar hea to the fatty chains so that this transfer is negigibe copare to the agnetization-exchange aong the fatty chains. (ii) Furtherore, we assue that the agnetization-exchange process aong the fatty chains can be escribe by a one-iensiona () spin-iffusion process taking pace in a three oain syste with a aear orphoogy (see Fig. 5.9b). Taking into account a C-C bon ength of 0.54 n, a C=C bon ength of 0.34 n, an a C-H bon ength of 0. n insie the CH 3 group, the estiate ength of the fatty chains is of.5 n. This esoscopic size of the fatty chains justifies the spin-iffusion oe aopte above. n this oe the agnetization front procees fro a source into a sink via an intereiate region. The source correspons to a rigi part () of the fatty chains, the intereiate region () to a part of the chains with intereiate obiity whie the sink (M) is the obie en of the chains. Each region is characterize by an average spin-iffusion coefficient,, an M whie the corresponing sizes are enote by,, an, M respectivey. The carbon oube bon in one of the two chains of a ipi oecue akes this chain stiffer than the other. Therefore, the aopte spin-iffusion coefficient wi be an average of the vaues corresponing to the two chains. Within this oe, the tie-epenent ongituina agnetization (t) of each region is given by the soution of the spin-iffusion equation (for ore etais see chapter ),

114 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 05 () ( ) {( ) ( ), sin sin F sin e x t t x = = = M M M M M M M M 0 0 M M 0 4 β β β β β (5.3) () ( ) ( ) ( ) ( ) ( ), sin sin sin sin sin F e x t t x x = = = M M M M M M M M 0 M M 0 β β β β β β β (5.4) an () ( ), sin F sin e x t t x x = = = M M M M 0 M M M M 0 M M M 3 8 β β β β (5.5) where, an M are the space (x) an tie (t) epenent concentrations of the nucear z agnetization in the source, intereiate, an sink oains respectivey, 0 is the initia concentration of the agnetization, an,, an M are the proton ensities in the,, an M oains, respectivey. Furtherore, β are the soutions of the foowing trigonoetric equation,

115 06 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis ( )( ) ( )( ) ( )( ) ( )( ), β sin β sin β sin β sin 0 M M M M M M M M M M M M M M M M = (5.6) an ( )( ) ( )( ) ( )( ) ( )( ). β cos β cos β cos β cos F = M M M M M M M M M M M M M M M M M M M M M M M M (5.7) The above NM signas obey the aw of conservation of z agnetization at any tie t, () () ( ) ( ). t t t 0 (5.8) 0 M = = (iii) n orer to quantitativey characterize the effect of ifferent paraeters ike pore size, teperature an surface coverage on the heterogeneity of the oecuar otion aong the obie part of the fatty aci chains, inforation about the vaues of the spin-iffusion coefficients at each position in the chain is neee. Therefore, the average vaue of the corresponing spin-iffusion coefficient has to be reate to the iffusion-coefficients at each position on the chain by a istribution function ( ) ( ). x x, P x ) ( x * = M 0 M M σ (5.9) To a first approxiation, a heuristic Gaussian istribution with a with σ can be consiere

116 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 07 where P * ( x,σ) P( x,σ), = π σ (5.0) P x σ ( x,σ) exp. = Fro this, the otion average spin-iffusion coefficient of the obie region is given by (5.) M = M ( 0) π σ M 0 x exp σ x, (5.) where M ( 0) is the spin iffusion-coefficient at the bounary between the intereiate an obie regions which is nothing ese than oube-quantu ipoar fiter t was previousy shown that the particuar set-up of a spin-iffusion experient with a ipoar fiter base on the excitation of proton oube-quantu (Q) coherences can be use for seecting the rigi part of a poyeric chain. The efficiency of a Q fiter for ecithin confine in 00, at roo teperature an for a concentration c = 0.0 is iustrate in Fig t sa excitation ties τ the Q fiter seects the agnetization fro the rigi regions as refecte by the ine with (Fig. 5.0a). These regions are attribute to the poar hea an to soe of the CH groups ocate at the beginning of the fatty aci chains. The oubet spitting exhibite by this spectru resuts fro the eiting of Q coherences insie the CH an CH 3 groups. Such a structure appears at sa vaues of the excitation tie of τ = 0 µs an fiter tie of t = 0 µs. t onger excitation ties (Fig. 5.0b,c) the fiter acts ike a T fiter, an the agnetization fro regions with intereiate an higher obiity can be seecte. n a these situations the fiter has high efficiency in seecting the agnetization corresponing to ifferent parts of the oecue. The Q fiter prouces a sa z agnetization as a resut of the ow efficiency in creating oube-quantu coherences. However, as escribe in chapter two, the use of this type of fiter eas to a better evauation of the integra intensities corresponing to ifferent coponents ue to the ore accurate etection of the narrow signas on the top of a broa coponent copare to the etection of a broa coponent uner a narrow signa.

117 08 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis Figure 5.0. oube-quantu fitere spectra eonstrating the efficiency of the Q ipoar fiter for ecithin in 00, at roo teperature an for a concentration of c = 0.0. Proton spectru with an excitation tie of: a) τ = 0 µs, b) τ = 30 µs, (c) τ = 00 µs, beyon the axiu of the Q bui-up curve. The puse sequence paraeters were t Q = 5 µs an t = 0 µs for a easureents (see Fig. 5.3b) Proton agnetization-exchange NM on ipi fis The agnetization-exchange evoution of the NM signas using the puse sequence fro Fig. 5.3 for ipi fis confine in the 00 nopore ebrane is shown in Fig. 5.. The agnetization front first reaches a region with intereiate obiity an after onger exchange tie oves to the ore obie regions (cf. Fig. 5.9). ecoposition of the proton spectra corresponing to ifferent ties in the agnetization-exchange evoution was carrie out in ters of three coponents. One correspons to poar hea an rigi regions of the fatty aci chains, another one to the intereiate regions, an the thir one to the obie part. t was assue that the poar hea oes not contribute to the agnetization-exchange process. However, it aways gives a constant signa. The intensity of this signa can be evauate base on the equiibriu signa intensity given together by the poar hea an the rigi region of the fatty aci chains an the nuber of protons corresponing to these two regions. Therefore, a renoraization of the

118 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 09 integra intensities corresponing to the ifferent regions of the fatty aci chain was ae by subtracting the signa fro the poar hea group. Figure 5.0. Proton NM spectra for ecithin in 00 at roo teperature an for a concentration of c = 0.0 as a function of the agnetization-exchange tie. The spectra were recore for iffusion ties t of a) 30 µs, b) 500 µs, an c) 5 s. Q ipoar fiter with an excitation tie τ of 0 µs was use in a experients (cf. Fig. 5.3b). Typica agnetization-exchange bui-up an ecay curve are shown in Fig. 5.. The curves fro rigi an obie parts of the ecithin chains have a onotone epenence on tie whie the curve corresponing to the intereiate region shows a axiu. This is ue to an accuuation of agnetization in this part of the oecue which is then reease into the obie part of the chain. For the evauation of the spin-iffusion coefficients a fit of the agnetizationexchange curves was ae with the hep of Eqs. (5.3) (5.5). The input paraeters use in the siuation progra for generating the integra intensities were the engths of the three parts of the fatty chain an the corresponing proton ensities. ue to the fact that the fatty chains are ainy copose of CH groups we can consier to a goo approxiation that the proton ensities for the three parts are equa. Therefore, if the intensities given by Eqs. (5.3) (5.5) are noraize to (0) they o not epen on these paraeters any onger. The engths of the oains were estiate base on the ength of the fatty aci chains an the equiibriu

119 0 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis signa intensities taken fro the agnetization-exchange curves. The vaues obtaine for the oain engths as we as the corresponing spin-iffusion coefficients are given in Tabes 5. an 5.. Figure 5.. Noraize agnetization-exchange ecay an bui-up curves for ecithin in 00 with c = 0.0 an at a) T = 93 K an b) T = 63 K obtaine with the puse sequence of Fig. 5.3b. The experienta ata were fitte with Eqs. (5.3), (5.4), an (5.5). The sizes of the three ain regions of the fatty chains showing ifferent obiities strongy epen on the surface coverage, teperature, an pore size. These iensions are areay an inication of the heterogeneity of the oecuar otion aong the fatty chains. However, one can obtain a better unerstaning of the heterogeneity of the chain ynaics inuce by ifferent paraeters such as surface coverage, pore size, an teperature with the hep of the resiua ipoar coupings via the spin-iffusion coefficients. The ynaics of the ecithin fis shows a strong epenence on the surface coverage (see Tabe 5.). The effect is sprea out in a oains of the fatty chains. The higher vaues of the spin-iffusion coefficients in the sape with a surface coverage of 54 Å inicate a stronger interaction of each part of the chain with the wa suggesting that at this ow concentration the oecues ie fat on the wa. This sees to be a characteristic anchoring irection not ony for ipi utra thin fis but aso for iqui crystas an poyers in interaction with surfaces when their concentration is very ow [Za0, Za, Pri]. raatic ecrease of the spin-iffusion coefficients arise when the surface coverage ecreases to 8 Å. further ecrease of the surface coverage to 5 Å again eas to higher vaues of the spin-iffusion coefficients. This effect correspons to an anchoring transition fro a fat orientation in the case of a surface coverage of 54 Å to a tite orientation for a surface coverage of 8 Å an further on to an axia orientation in the case of a surface coverage of 5 Å (see Fig. 5.). n this ast situation, it sees that the observe segenta orering is not a singe chain process but

120 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis instea invoves orientationa correation ue to the interactions between the chain segents corresponing to ifferent oecues [Zeg95, Zeg97]. The tenency of the oecues to have ifferent anchoring irections was aso reveae by Monte Caro siuations for ipi onoayers grafte to a surface [Haa96]. The reason for the existence of tite structures is that at ow concentrations the ensity in the onoayer increases by titing of the chains as its height ecreases. n this way a ower energy state can be reache[haa96]. Conversey, the tenency of the syste to eveop a tite structure is ess pronounce the higher the ensity of the chains [Haa96]. Figure 5.. ifferent anchoring irections that the ecithin fis can aopt uner confineent conitions: a) fat on the surface, b) tite, an c) axia. Tabe 5.. Effect of the surface coverage on the oain sizes an on the corresponing spiniffusion coefficients as we as on the with of the Gaussian istribution function for ecithin fis confine in 00 at T = 93 K c (n) a a (n) M (n) a a (n /s) a (n /s) M a (n /s) σ a (n) a The uncertainties are ess then 0% The pore size has aso an iportant effect on the ynaic of the fatty aci chains. ecrease fro 00 n to 0 n eas to an increase of the resiua ipoar coupings as

121 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis refecte in the vaues of the average spin-iffusion coefficients (Tabe 5.). These ata inicate that the geoetrica confineent is ainy fet by the rigi an intereiate regions whie the effect sees to be inia on the obie part of the fatty chains. Here, we have to point out that the appropriate quantity to characterize the effect of ifferent paraeters on the chain ynaics of the obie part is not the average spin-iffusion coefficient but the with of the istribution function (see beow). This is ue to the fact that the iension of the obie region changes with the pore size an the teperature. s a consequence, the corresponing average spin-iffusion coefficient refects the oecuar ynaics corresponing to regions with ifferent sizes. Tabe 5.. Effect of the pore size an teperature on the oain sizes an on the average spin-iffusion coefficients as we as on the with of the Gaussian istribution function for a ecithin concentration of c = 0.0 T = 93 K T = 63 K (n) a (n) a M (n) a (n /s) a (n /s) a M (n /s) a σ (n) b a The uncertainties are ess then 0% For the sae concentration of ecithin oecues, a ecrease in the pore size correspons to an increase of the surface coverage an to the occurrence of eastic eforations. n a 0 nopore ebrane the oecues ie fat on the surface whie in 00 they are tite at an ange of about 6 0 fro the nora irection to the surface. Therefore, in 0 the interactions with the surface are stronger than in 00 which eas to an increase in the vaues of the resiua ipoar coupings.

122 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 3 The chain otion is sowe own by ecreasing the teperature (Tabe 5.). so in this case the effect of the teperature sees to be higher on the obiity of the rigi an intereiate parts of the fatty chains an very week on the obie part. itionay, by coparing the sizes an the spin-iffusion coefficients between 00 an 0 is sees that the teperature has a higher effect on the oecuar ynaics of ecithin confine in 00 than on ecithin in saer pores because of the saer orering effect of the pore surface. Siiar resuts concerning the effect of surface coverage, pore size, an teperature on the ynaics of confine ipi fis are reporte in the previous section base on the anaysis of oube- an tripe-quantu bui-up curves an oube-quantu eite spectra. This type of easureents is uch easier to anayse because the interpretation is oe free. However, the ata refect ony the behaviour of a part of the chain (the rigi part in this case) an cannot quantify the istribution of the heterogeneity of the chain ynaics. The agnetization-exchange experient is inee not oe free but it is a powerfu etho in showing how the oecuar obiity is istribute aong the fatty aci chains. Therefore, this experient shows ceary which anchoring irection the ipi fis aopt uner ifferent conitions istribution function of resiua ipoar coupings Unti now the heterogeneity of the chain ynaics aong the fatty chains was escribe in ters of oain sizes an average spin-iffusion coefficients. better unerstaning of the effect of surface coverage, pore size an teperature on the oecuar otion of confine oecues can be achieve by obtaining inforation on the vaues of the resiua ipoar couping at each position in the fatty chain. To a first approxiation, we can consier that the heterogeneity of the otion in the rigi an intereiate regions is not very arge an therefore sufficienty we escribe by the average spin-iffusion coefficients. This is not any onger the case for the obie part of the fatty chains. The appropriate quantity taken in this stuy to escribe the heterogeneity of the chain ynaics in the part of the oecue with intense oecuar otion is the with σ of the Gaussian istribution function. n evauation of σ for a sapes was ae using Eq. (5.) an the corresponing vaues of M, M an fro Tabe 5. an 5.. The estiate vaues are iste in Tabe 5. an 5.. t is evient that the with of the istribution function epens on the surface coverage, the pore size, an the teperature. The istribution of the chain ynaics aong the fatty chains can be visuaise by a pot of the epenence of the Gaussian istribution function of the istance. The effect of the

123 4 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis surface coverage on the chain ynaics is epicte in Fig. 5.3a whie the effect of the pore size an the teperature is shown in Fig. 5.3b. The heterogeneity of the chain ynaics is affecte ost by the surface coverage. The otion is uch ore unifor at ow an high ecithin concentrations, c = an c = 0.048, respectivey. n the first case the otion is hinere ue to the oecues ying fat on the surface. The otions that the oecues can experiences in such an anchoring position are rotations about the ong oecuar axis, an surface iffusion [Za]. y increasing the concentration to c = 0.0 the oecues can aso experience reorientationa tubing with their hea group fixe at the surface [Za]. For a concentration of c = the ost probabe ynaic oes are fuctuations aong the oecuar axis, about their ean positions an surface iffusion. ecrease in the heterogeneity of the chain ynaics is aso observe when the pore size ecreases. The heterogeneity of the chain ynaics of the oecues in a 0 nopore ebrane shows a behaviour siiar to that of the oecues at a concentration of c = in 00. Therefore, the preferre otions of the oecues are rotations about the ong oecuar axis an surface iffusion. The eastic eforations ue to the curvature of the pores in 0 have ony a sa effect on the chain ynaics copare to than in 00. change in the heterogeneity of the chain ynaics is aso seen with ecreasing teperature (Fig. 5.3b). The chains becoe ore rigi in both pores. However, the chains are ore rigi in 0 than 00. Figure 5.3. epenence of the Gaussian istribution function on a) surface coverage in 00 an at T = 93 K, an b) pore size an teperature for a concentration of c = 0.0. We shou note that the epenence of the spin-iffusion coefficients an the with of the istribution function on surface coverage, pore size, an teperature inicates that each part of the chain can inepenenty give inforation how these paraeters affect the chain

124 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis 5 ynaics. n other wors, the surface inuce orer an the geoetrica confineent affect the ynaics of the entire oecue. 5.5 Concusions n this chapter the oecuar ynaic heterogeneities of onoayer to subonoayer thin ecithin fis confine to subicron cyinrica pores were investigate using proton oubean tripe-quantu bui-up curves, oube-quantu eite spectra an agnetizationexchange experients. quaitative anaysis base on the sope of the bui-up curves as we as the spitting of the oube-quantu eite spectra inicates that the surface inuce orientation of the ipi chains such that their oecuar otion is faster than in buk. The ipi oecues aopt ifferent anchoring irections epening on the concentration an pore size. For sa concentrations of ipis the ost favorabe conforation is a fattene structure, whie for higher concentrations the oecues aopt an axia orientation. quantitative characterization of the heterogeneity in resiua ipoar coupings ue to a spatia istribution of apitue an frequency of the oecuar otions of ipi fis was ae using proton agnetization-exchange experients an oee in the approxiation of one-iensiona spin-iffusion in three connecte oains. oubequantu ipoar fiter prouces the agnetization graient. The fit paraeters of the oe are the average spin-iffusion coefficients corresponing to the ifferent regions of the fatty aci chains. The estiate vaues of these paraeters inicate a strong epenence of the chain ynaics on the average area per oecue, the pore iaeter, an the teperature. The chain ynaics aong the ore obie parts of the fatty chains were quantifie in ters of a Gaussian istribution function of the resiua ipoar coupings. The effects of various paraeters on the heterogeneity of the resiua ipoar coupings can be escribe by the with of the Gaussian istribution function. For the ipi fis investigate in this stuy the surface inuce orer an the geoetrica confineent affect the chain ynaics of the entire oecue. Therefore, each part of the chain inepenenty refects the effect of surface coverage, pore size, an teperature. The characterization of the spatia istribution of the oecuar otion using a spin-iffusion oe can be extene to the investigation of the surface effects on chain-segent orer of poyer fis an grafte poyers.

125 6 Chapter 5. Moecuar ynaic heterogeneities of confine ipi fis

126 6 nvestigation of orere tissues by NM 6. ntrouction an otivation Coagen is the ost abunant protein on earth an one of the ajor constituents in aas, constituting 5% of the tota protein ass in these anias [b]. There are at east tweve types of coagen which can be foun in bones, tenon, skin, igaents, boo vesses, cartiages, an other tissues [b]. Coagen pays a crucia roe for the stabiity an function of these bioogica tissues. For instance, coagen oecues for a rigi network in cartiage, which provies the scaffo for the echanica stabiity of these tissue an restricts the sweing [ei4]. The funaenta higher orer structure of coagens is a ong an thin iaeter roike protein which is fore by three coie subunits that are about.5 n in iaeter an 300 n in ength (Fig. 6.). Each chain consists of about 050 aino acis organize in a right-hane tripe heix with an average of 3 resiues by turn [b]. The repetitive pattern of the chain is of the type [Gy-X-Y] n, i.e. every thir aino aci ust be a gycine (Gy) because of the ense packing in the tripe heica arrangeent which oes not aow ore extene sie chains [b]. arge proportion of the resiues are proine (Pro) an hyroxyproine (Hyp) which are essentia for the stabiization of the heices (Fig. 6.). Thus, the coagen typicay contains aroun 33% Gy, 3% Pro, % of both aanine an Hyp. Figure 6.. The tripe heix structure of coagen. 7

127 8 Chapter 6. nvestigation of orere tissues by NM Tenon is a non-contractie coponent of the uscuoskeeta syste that connects usces to the bones (Fig. 6.). t transits a tensie force fro the usce to the bone to cause joint oveent. Coagen is the ost significant protein in tenons coprising percent or ore of the ry weight of the tenon [b]. This coagen consists osty (greater than 95 percent) of type coagen. The other 5 percent is type an type V coagen. Other coponents of tenons are water, proteogycans, ces, eastin, an other extraceuar atrix coponents. of these coponents are arrange in a fibrous structure as iagrae in Figure 6.3. Figure 6.. Huan chies tenon. Figure 6.3. The hierarchica organization of the tenon structure: fro coagen fibris to the entire tenon [Kas78]. The ynaics of the coagen fibers as we as the interaction between the coagen an its water of hyration are of iportance since the echanica properties are strongy reate to these characteristics. Unerstaning the reation between the bioogica function, the oecuar structure, an the ynaics of the coponents of tenon, in particuar of the coagen, is thus a request for the eveopent of treatent strategies. itionay, they can ea to a better contrast in M of tissues [Neu3]. The roe of proton exchange between water an proteins has been the subject of intensive work in the past few years [Sto78, en83, en94, Woj99, Ei99, Ei, Hus, Zij3]. Seective excitation of either the protein or the water is require for easuring the agnetization transfer rate between the. Such type of transfer can be achieve base on the ifference of cheica shift between the signas of ifferent functiona groups an water. For arge proteins, such as coagen, the strong ipoar interactions ea to a very broa spectru whie the abunant aount of water gives a arge narrow peak. Therefore, in such conitions, the functiona groups of the protein cannot be separate.

128 Chapter 6. nvestigation of orere tissues by NM 9 The ais of this chapter are: (i) to etect the protein an to estiate the rate of spiniffusion within, (ii) to investigate the agnetization transfer between the coagen fibres an water by seectivey exciting the protein using a oube-quantu ipoar fiter, an (iii) to ientify the functiona groups responsibe for this process. This ast goa can be achieve by spinning the sape at the agic ange an suppressing the water peak with the WTEGTE etho. 6. Experienta The experients were conucte on sheep chies an cow igitoru counis tenons. The sapes were purchase fro the butcher an use without further purification. They have been kept in the freezer at 7 0 C an efreeze before each easureent, cut in sa pieces an tighty packe into the rotors. The easureents were ae at roo teperature on a ruker SX-500 MHz spectroeter using 7 an 4 probeheas. The 4 probehea has a z graient attache. For the first probe the 90 0 puse ength was 5.5 µs an the secon one about 7.5 µs. 6.3 Theoretica backgroun For arge proteins ike tenon, in which the overa an the interna otions are sow or anisotropic, the ipoar interactions between the protons are not scae own to a significant egree an the spin states escribe by high rank spherica tensors that invove two or ore protons can be fore on a very short tie scae. n water, these tensors evove over a uch onger tie scae ue to the reuction of the intraoecuar ipoar interaction, which resuts fro the reorientationa otion in the free an boun states as we as fro the cheica exchange between these two states [Nav, Ei]. Furtherore, proton exchange aong water oecues causes an aitiona reuction of the proton-proton intraoecuar ipoar interaction [Ei]. The ifferent tie scaes of the evoution of the high rank tensors in the protein an in water akes possibe to retain the ongituina agnetization of either the protein or the water using utipe-quantu fiters. etaining the agnetization of ony one of the two species enabes the etection of the MT (agnetization transfer) between the. The reaxation ties of the singe-quantu coherence tensors of the protein are expecte to be uch shorter than those of water an they aso reax on a tie scae that is uch shorter than the cheica exchange between the water an the exchangeabe protons of the protein [Ez78, Hi9]. Thus, it is ipossibe to observe the foration of singe-quantu

129 0 Chapter 6. nvestigation of orere tissues by NM coherences of the protein by cheica exchange with water an vice versa. However, given that the reaxation ties of the ongituina agnetization can be ong for both water an the protein, the reconversion of the oube-quantu signa to its initia poarization state (aigne aong the agnetic fie) enabes the etection of the cheica exchange between water an protein [Ei]. escription of the agnetization transfer process can be one using the approach propose by Ezes an Sauski [Ez78] which incorporates the presence of the crossreaxation for a two phase syste (Fig. 6.4). These equations are erive by incuing exchange ters in the och equations for the z agnetization for both phases. efining M zw () t an () t as the tie-epenent z agnetization of the water an the protein phases M zp ( ) with the equiibriu vaues zw 0 an zp( 0), w = Tw an p = Tp as the intrinsic ongituina reaxation rates, an k an k as the exchange rates constants eas to the w p coupe ifferentia equations M t zw () t = w [ ], [ M () t ( )] k [ M () t ( 0) ] k M () t ( 0) zw zw 0 w zw zw p zp zp (6.) M zp t () t = p [ M () t ( )] k M () t ( 0) zp [ ] k M () t ( 0) zp 0 p zp zp w zw zw [ ], (6.) with the conition that z p 0) kp = zw (0) ( k w which can aso be written in ters of the fractions of the protons beonging to the water phase k p k p k w = p w an protein phase k p k w k w = p p respectivey. The soutions for the ongituina agnetization of the two coponents were foun to be where zp t t t t () t = ( )( a e a e ) ( 0) b ( e e ), M (6.3) zw zp 0 zw p M (6.4) w t t t t () t = ( ) b ( e e ) ( 0)( a e a e ), zp 0 zw pp a ± = ± k kp ( k) 4kp ( ) p p w w p p p w, (6.5)

130 Chapter 6. nvestigation of orere tissues by NM kpp b =, (6.6) 4 ( k) kp ( p w p p w ) = k ± ( k) kp ( ). ± p w p w 4 p p w (6.7) The MT rate k is the su of the forwar an backwar exchange rates. Fro above equations it is cear that if either the protein or the water are seectivey excite, the ongituina agnetization corresponing to the other coponent is recovering in a process escribe by a ifference of two exponentias [Ei]. n the iit of fast agnetization transfer, i.e., k >> p, w, an for the seective excitation of the protein an fitration of the water signa, i.e. zw (0) = 0 [Ei] the foowing foruas escribe the recovery of ongituina agnetization corresponing to the protein an water zp t () ( 0)( t t = p e p e ), M (6.8) zp w p with zw t () ( 0) ( t t = p e e ), M (6.9) zp w = k, an = pw w ppp. (6.0) The foration rate of the signa is given by the agnetization transfer rate an its ecay rate is a weighte average of the ongituina rates of the proton an water, respectivey. s can be seen fro Eqs. (6.8) - (6.0) if one seectivey excites the protein uner fast exchange, on a tie scae saer than the vaue of the ongituina reaxation, the two ongituina agnetizations are equa to that of the protein. We can concue that uner fast exchange the tie scae of MT process can be ivie into a short one where the exchange oinates an a ong one where the reaxation oinates [Ei]. 6.4 NM etection of protein. Magnetization transfer between coagen an water typica proton spectru of the fresh tenon recore uner static conitions is epicte in Fig. 6.4a. t consists of an high narrow peak centere at 4.75 pp corresponing to the water an a sa peak centere to ower vaues of the frequencies corresponing to the aiphatic protons. The eite spectru obtaine by appying the puse sequence fro Fig..7b which

131 Chapter 6. nvestigation of orere tissues by NM excites the oube-quantu coherences by using the proper phase cycing is represente in Fig. 6.4b. The spectru exhibits a structure which consists of a narrow ine superipose on a broa oubet. The narrow ine is ue to the boun water, the free water being fitere out. For easureents ae at anges ifferent of the agic ange the signa exhibits a spitting. This is ue to the fact that the boun water oecues present an anisotropic orientation which eas to an averaging of the ipoar interactions at agic ange [Mig73, Nav]. The broa oubet (tens of kiohertz) was attribute to the protons fro the coagen fibres. ts spitting exhibits aso an anguar epenence but the variation is uch weaker than that of the boun water. This inicates that the aino-acis insie the coagen fibres posses ony soe egree of orer [Nav]. Figure 6.4. a) Proton spectru of fresh tenon after a 90 0 puse an b) Q eite spectru for an excitation tie of τ = 0 µs. The spectru was recore using the puse sequence epicte in Fig..7b with t Q = µs an t = µs. The easureents were perfore in static conitions at the agic ange an at roo teperature. n orer to check if the broa oubet is inee ue to the protein protons an not to soe strongy boun water popuations the oube-quantu eite spectra were aso recore for tenon ierse in euterate water for one onth an for tenon kept in the open atosphere for 48 hours. n both situations a ecrease of the intensity of the narrow coponent can be seen but no change in the shape of the broa oubet. However, an increase in the spitting happens when the sapes were kept in open atosphere ue to the evaporation of soe water which eas to a ecrease in the obiity of the coagen fibres. The above assignents are supporte aso by the oube- an tripe-quantu bui-up curves shown in Fig The oube-quantu curve (Fig. 6.5a) shows two axia. The first

132 Chapter 6. nvestigation of orere tissues by NM 3 axiu appears at a very short excitation tie of 7 µs. t beongs to the protons of the protein. The secon axiu is ocate at an excitation tie of 50 µs an it beongs to the boun water. n the case of the tripe-quantu bui-up curves ony one axiu, at short excitation ties of 4 µs, can be seen. t correspons to the protons of the protein. Figure 6.5. a) oube- an b) tripe-quantu bui-up curves of fresh tenon recore at roo teperature using the 5 puses sequence epicte in Fig..7b with the appropriate phase cycing. The experienta paraeters were t Q = µs an t = µs. Figure 6.6. ipoar fiter efficiency using a Q fiter with t Q = µs an t = µs. Proton spectru after an excitation tie of a) τ = 0 µs, b) τ = 7 µs corresponing to the axiu of the bui-up curve of the coagen fibres, c) τ = 50 µs corresponing to the axiu of the bui-up curve of the bounwater an ) τ = 500 µs beyon the secon axiu. n orer to stuy the agnetization transfer between the coagen fibres an the water the seective excitation of either the protein or the water is require. s we cou see above

133 4 Chapter 6. nvestigation of orere tissues by NM this cou be achieve by appying a oube-quantu fiter. The effect of seective excitation is epicte in Fig For short excitation ties (Fig. 6.6a,b) the broa coponent is the oinant coponent. With increasing excitation tie the contribution of this coponent gets saer an the water signa gives the ain contribution (Fig. 6.6c,). Once the agnetization of the protein was seecte (situation presente in Fig. 6.6a), the agnetization is aowe to reequiibrate within the syste. This process is epicte in Fig Figure 6.7. Evoution of the agnetization in the experients using a Q fiter with τ = 0 µs an t Q = µs. Proton spectru recore after tie of a) t = 0 µs, b) t = 00 µs, c) t = 350 µs, an ) t = 7 s. Severa steps can be seen uring the agnetization transfer. For short vaues of the transfer tie t, the spectru consists ainy of the signa given by the protein. raatic change of its shape happens with increasing vaue of the transfer tie ue to an equiibration of the agnetization insie the protein through a spin-iffusion process. This equiibration is very fast an it is achieve in about 00 µs (Fig. 6.7b). uring this tie the water signa changes very itte. t onger vaues of t the water signa starts to increase as a resut of a agnetization transfer fro the protein. The variation of its signa is epicte in Fig The curve can be escribe by a ifference of two exponentias. The increasing part of the curve correspons to a agnetization transfer process between the coagen protons an the water whie the ecreasing part of the curve is associate with a ongituina reaxation process. fit of these ata was ae using the Eq. (6.9). rate of k = 40 s - was estiate for the water signa bui-up an a rate of 0.9 s - for the ecreasing part of the signa. The vaue of k is in

134 Chapter 6. nvestigation of orere tissues by NM 5 agreeent with those reporte in [Ez78, en94, Ei99] for easureents ae at roo teperature. Figure 6.8. Variation of the apitue of the water signa with the transfer tie t. ase on the above resuts we can concue that two types of ynaic processes occur in the hyrate tenon. The first one happens on a tie scae of hunres of icrosecons an it is reate to a spin-iffusion process insie the protein. t assures the equiibriu insie the protein at any oent of tie in the agnetization transfer process. The secon process invoves a agnetization transfer between the protein an the water. This process takes pace on a tie scae fro hunres of icrosecons to tens of iisecons. These tie ranges are in agreeent with those reporte in [Ei99]. Two types of echaniss were propose for the observe agnetization transfer [Ei99, Zij3]. One is reate to the exchange between the exchangeabe protons of the protein an the water oecues. The other one is reate to a ipoar interaction ue to a partia averaging of the first orer ipoar interactions between the protein an the water (coon situation encountere in sois) or of secon orer coony foun in iquis (NOE). t roo teperature the MT process is governe by the exchange whie at ow teperatures the ipoar interaction is the ajor echanis. The oinance of one of the two echaniss is reate to the resience tie of the water in the near of the protein, the rate of cheica exchange between the exchangeabe protons of the protein an the water protons, an the rate of the spin-iffusion within the protein. The agnetization fows fro the protein to the water via soe of the functiona groups an therefore a graient of the agnetization is create insie the protein. This is cancee by fast spin-iffusion.

135 6 Chapter 6. nvestigation of orere tissues by NM 6.5 entification of the exchangeabe protons Unti now we foowe the transfer of agnetization fro the seectivey excite protein to the water. This process procees through soe of the functiona groups of the protein. However, no inforation about the nature of these functiona groups cou obtaine ue to the strong ipoar interactions insie the protein which yie to a broa spectru superipose by a arge water signa. This probe can be sove by using MS in orer to average the ipoar interactions insie the protein an by using a sovent suppression etho to eiinate the water signa. Figure 6.9. a) WTEGTE puse sequence for seective peak suppression using a inversion puse an a pair of puse fie graients. b) Puse sequence epoye to easure the agnetization transfer process. WTEGTE sequence is epoye in the seection an in the etection perio. The WTEGTE (water suppression by graient taiore excitation) (Fig 6.9a) is a we estabish etho for suppressing the water signa [Sk93, Fis3]. The frequency-seective inversion puse consists of a sequence of six puses with urations of 3α 9α 9α 9α 9α 3α with 6 α = π [Sk93] an it is usuay referre as coposite puse. n cobination with the two ientica graients appie before an after the puse, WTEGTE suppresses the signa ocate at the carrier frequency of the

136 Chapter 6. nvestigation of orere tissues by NM 7 puse train [Sk93]. The purpose of the graient puses is to reove the unesire coherences rather than to seect the appropriate coherence-transfer pathway. n investigation of the agnetization transfer between the water an coagen fibres can be achieve by using the puse sequence epicte in Fig. 6.9b. The first WTEGTE is use to estabish non-equiibriu popuations by suppressing either the water or one of the exchangeabe protons peaks, an thus initiating agnetization transfer is subsequenty eaing to a reestabishent of equiibriu. The secon WTEGTE was use to suppress the water peak so that the peaks of the exchangeabe protons can be etecte. The efficiency of this puse sequence in suppressing the water signa is epicte in Fig The intensity of the water signa is reuce by a factor of about 64 when the suppression etho is appie copare to the signa obtaine after a nora 90 0 puse (copare Figs. 6.0b an c). n this case the signas corresponing to ifferent functiona groups are resove. The peaks at ow frequencies are ue to the aiphatic protons, those cose to 5.8 pp beong to the OH groups whie the signas in the range fro 6.8 to 8.7 pp are ue to the NH groups [Woj99, Me0]. Figure 6.0. Efficiency of the WTEGTE puse sequence in suppressing the water signa. Proton spectru a) after a 90 0 puse, b) spectru fro (a) utipie by 64, c) after appying the puse sequence fro Fig. 6.9b with a syetric WTEGTE characterize by the paraeters p G = G = W = 00 µs an a short vaue for the agnetization transfer tie t MT = 50 µs, ) spectru fro (c) utipie by 8. easureents were perfore on bovine tenon at roo teperature uner MS (5 khz). The chain of processes which foows the seective excitation of the protein protons at ifferent oents of the agnetization transfer process is represente in Fig. 6..

137 8 Chapter 6. nvestigation of orere tissues by NM ecrease of the signas corresponing to the functiona groups an to the water can be seen by increasing the agnetization transfer tie t MT. The OH an NH groups exhibit a raatic change in the intensity whie the aiphatic protons exhibit ony a weak change (Fig. 6.). This inicates that the peaks of the exchangeabe protons are ocate in the range of pp. ase on previous stuies on pepties the peak at 5.8 pp was attribute to the hyroxy proton of the hyroxyproine resiue an the peaks aroun 8 pp to the NH protons of resiues such as gycine, aanine an asparagines [Woj99, Me0, Zij3]. n anaysis of the ecays corresponing to a functiona groups base on the Eq. (6.8) reveae that the cheica exchange tie of the OH groups is aroun 50 s whie that of the NH groups are ess than 50 s. This correspons to an exchange rate of 6.66 s - for OH an 0 s - for NH, respectivey. The ong vaue for the exchange rate of OH is in agreeent with the resuts reporte in [Me0] whie that for the NH is in agreeent with the resut obtaine uner static conitions an with that reporte in [Woj99]. This inicates that the agnetization transfer process between the protein an the water ainy procees via the cheica exchange of the NH protons. Figure 6.. Proton spectra corresponing to ifferent oents in the agnetization transfer process between protein an water: a) after t MT = 6 s an b) after t MT = 50 s. The spectra on the are the sae as those on the eft but agnifie by a factor of 8. They show ony the region of the OH an the NH functiona groups.

138 Chapter 6. nvestigation of orere tissues by NM 9 Figure 6.. Evoution of the signas corresponing to ifferent functiona groups uring the agnetization transfer process as epicte in Fig. 6.. The changes of the peaks at.3 pp (aiphatic protons), at 5.8 pp (OH groups), an at 8.0 pp (NH groups) are shown. 6.6 Concusions n this chapter the interaction between the coagen an its water of hyration was investigate with the hep of agnetization transfer experients. Uner static conitions the graient of agnetization was create by a oube-quantu fiter which seects the agnetization fro the protein. The transfer of agnetization invoves two steps. The first one is reate to spin-iffusion insie the protein. t happens very fast, on a tie scae of hunres of icrosecons. The secon process invoves a agnetization transfer between the protein an water. This process takes pace on a tie scae fro hunres of icrosecons to tens of iisecons, an at roo teperature it ainy procees via cheica exchange with a constant of the orer 40 s -. The estiate rate is in agreeent with the previous resuts. The secon step in our approach was the ientification of the exchangeabe protons. Therefore, a new etho to assign the peaks of the exchangeabe coagen protons an to easure the exchange rates of the with water was introuce. The etho ipeente uner MS uses the WTEGTE sequence for on-resonance peak suppression in the seection an the etection perios. The resuts base on the suppression of the water signa inicate that the exchangeabe protons are ocate in the range fro 5.5 pp to 8.7 pp. ase on previous stuies on pepties, an assignent of these protons to ifferent aino acis was ae. itionay, the easure exchange rates corresponing to ifferent

139 30 Chapter 6. nvestigation of orere tissues by NM functiona groups ea to the concusion that at roo teperature the agnetization transfer procees ainy via the exchange of the NH groups which is happening on a tie scae shorter than 50 s.

140 7 Concusions Soi state NM spectroscopy was successfuy appie for the characterization of a broa range of iportant poyeric an bioogica aterias such as Nyon-6 fibers, ibock copoyers, shape eory eastoers, confine ipis, an tenon. The approaches use to obtain inforation about the structure an the oecuar ynaics of the investigate systes can be further extene to other poyeric an bioogica systes. The origina resuts obtaine are suarize as foows:. The spin-iffusion process in a oe orphoogy syste represente by three ifferent oains with arbitrary sizes, iffusivities, an proton ensities has been investigate. Genera anaytica soutions vai for the fu range of spin-iffusion ties were erive for an one-iensiona process. The obtaine soutions were teste for a poy(styrene-b-ethyphenysioxane) ibock copoyer an for seicrystaine poy(ethyene oxie) by preicting the oain sizes an coparing the with previousy reporte ata. ase on these anaytica soutions, the effect of the interface in ters of the size an the spin-iffusion coefficient on the spin-iffusion curves was investigate. These soutions can be use for an approxiate escription of the spiniffusion processes which take pace in two an three iensions. itionay, the appicabiity of the propose anaytica soutions can be extene to characterize heat transfer an iqui iffusion in systes with siiar orphoogies.. ipoar fiter base on the excitation of oube-quantu (Q) coherences was ipeente. This fiter seects ainy the agnetization fro the rigi oains. t was teste by estiating the oain sizes of the obie aorphous, the interface an the rigi aorphous regions of a PEO-b-PS ibock copoyer an coparing the with those obtaine in a spin-iffusion experient epoying a fiter which seects the agnetization of the obie phase. The avantages of using one or the other type of fiter were iscusse. 3

141 3 Chapter 7. Concusions 3. n NM approach to carify the copex orphoogy of seicrystaine poyer systes was introuce. This approach uses a cobination of ipoar fiters that seect in separate experients the obie an the rigi oains of a heterogeneous sape in cobination with one-iensiona an uti-iensiona anaytica soutions of the spin-iffusion equations aapte to a specific orphoogy. itionay, it was shown that inforation about the aear orphoogy of systes can be obtaine inepenent of other techniques using such a cobination of ipoar fiters. This represents a big step forwar in the fie of spin-iffusion NM. 4. The NM approach base on the cobination of ipoar fiters was successfuy appie to carify the orphoogy of Nyon-6 fibres. The particuar set up of the spiniffusion experient using a MPE ipoar fiter reveas ony the spatia istribution of the obie aorphous oains an the aggregates of fibris as a whoe. n estiation of oain sizes of crystaine an ess-obie aorphous oains aong the fibris as we as the iaeter of the fibris an the inter-fibri istance cou be achieve in a spin-iffusion experient epoying a oube-quantu fiter. The changes etecte in the oain size iensions with the processing conitions show the sae tren as the ata fro wie-ange X-ray iffraction an sa-ange X-ray scattering. 5. The oains sizes of the rigi aorphous, the interface an the obie aorphous regions of a series of poy(ethyene oxie)-bock-poy(hyroxyethyethacryate) (PEO-b-PHEM) ibock copoyers with ifferent oecuar weights were estiate by using H spin-iffusion easureents epoying a MPE ipoar fiter. The correation of the aear ong perio with the oecuar weight shows a epenence of / 3 ong M w in agreeent with the theoretica preiction. 6. Networks of [(L-actie)-ran-gycoie]iethacryate with potentia eica appications were characterize in ters of structure, obiity, shape eory properties, an egraation behavior in vitro. The effects of various paraeters such as the cross-ing ensity, teperature, an UV irraiation tie on the icroscopic properties of the networks were iscusse. itionay, oecuar echaniss responsibe for the shape eory behaviour an for the egraation in vitro were corroborate.

142 Chapter 7. Concusions The oecuar ynaic heterogeneities of onoayer to subonoayer thin ecithin fis confine to subicron cyinrica pores were investigate using proton utipequantu an agnetization-exchange experients. The surface inuce orientation of the oecuar chains which eas to the chain ynaics faster than in buk. The buiup an ecay agnetization-exchange curves were anayze in the iit of an oneiensiona spin-iffusion process which takes pace in a three oain orphoogy. The effect of the surface coverage, the pore size, an the teperature on the heterogeneity of the chain ynaics was iscusse. The etho escribe can aso be appie to characterize the surface inuce orer of ifferent poyer aterias, ipis, an iqui crystas. 8. The interaction between the coagen an its water of hyration was investigate with the hep of agnetization transfer experients. Uner static conitions the graient of agnetization was create using a oube-quantu fiter which seects the agnetization corresponing to the protein. Two steps in the agnetization transfer process were ientifie. The first one is reate to a fast spin-iffusion process insie the protein. t takes pace in hunre of icrosecons. The secon step is a cheica exchange process between the coagen an the water. t happens in a tie range fro hunre of icrosecons to tens of iisecons an it is characterize by an exchange rate of 40 s new etho to assign the peaks of the exchangeabe coagen protons an to easure the exchange rates of the with water was introuce. The etho ipeente uner MS uses the WTEGTE sequence for an on-resonance peak suppression in the seection an etection perio. The resuts base on fitering out the water signa inicate that the exchangeabe protons are ocate in the range fro 5.5 to 8.7 pp. t roo teperature, the agnetization transfer procees ainy via the exchange of the NH groups with exchange rate higher than 0 s -.

143 34 Chapter 7. Concusions

144 ppenix 35 ppenix : Sapes Shape eory eastoers: egraation experients For the egraation in vitro of the [(L-actie)-ran-gycoie]iethyacrytes networks a phosphate buffer soution was prepare by issoving 35,8 g of soiu phosphate (Na HPO 4 H O) an 8,57 g of potassiu phosphate (KH PO 4 ) in one iter of istie water. For avoiing the foration of icroorganiss 0,5 g of soiu azie (NaN 3 ) was ae. The obtaine ph vaue was 7. The sapes were cut in sa pieces, weighte an pace into bottes which were fie with buffer soution. The bottes were incubate into a oving water bath at T = 37 o C. efore each easureent the sapes were took out fro the buffer, paying specia attention to pick a pieces. Then they have been rie fro the superficia water an easure using a 7 rotor.

145 36 ppenix

146 ppenix 37 ppenix : naytica soutions of the spin-iffusion process in a aear orphoogy n orer to obtain anaytica soutions for the spin-iffusion equations () with the initia an bounary conitions given by Eqs. (.) - (.9) we introuce the Lapace transforation of the concentration of the z-agnetization i ( x, t), where i =, an, efine as pt i = e i ( x,t)t, (.) 0 where p is a nuber whose rea part is positive an arge enough to ake the above integra convergent. fter the appication of the Lapace transforation an taking into account that initiay the agnetization is istribute ony in oain, we have to sove the foowing inear ifferentia equations x q t = 0, where q p =, x x q p =, an q q t t = 0, (.) q p =. = 0, ppication of the Lapace transforation to the continuity conitions, Eqs. (.5) an (.6) yies (,t) (,t) =, (,t) (,t) =, (.3) an to the foowing equations for the fux equaities, (cf. Eqs. (.7) an (.8)) i.e.,

147 38 ppenix ( ) ( ) x,t x,t =, ( ) ( ) x,t x,t =. (.4) The bounary conitions, Eq. (.9), have the for ( ) 0 0 = x= x x,t, an ( ) 0 3 = x= x x,t. (.5) The first of the equations (.) is an inhoogeneous inear ifferentia equation with a soution of the for 0 q e e x q x q =, (.6) where the first two ters represent the soution of the hoogeneous ifferentia equation an the ast ter is a particuar soution. The other two equations (.) are hoogeneous ifferentia equations an we search soutions of the foowing for x q x q e e =, x q x q e e =. (.7) Using the bounary conitions, Eqs. (.5), an foowing soe agebra a the unknown coefficients can be evauate so that we obtain the foowing expressions for the Lapace transforation of the concentration of the nucear spin z-agnetization in a three oains ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) [ ], E q q sh E q q sh x q ch q = (.8) ( ) [ ] ( ) ( ) ( ) [ ] ( ) ( ) ( ) [ ] ( ) ( ) [ ] [ ( ) ( ) [ ]]}, x q q ch x q q ch E q q sh E q q sh x q ch q = (.9) an

148 ppenix 39 ( ) ( ) [ ], E x q ch q sh q 0 4 = (.0) where the quantity E is given by ( )( ) ( ) ( ) [ ] ( )( ) ( ) ( [ ] ) ( )( ) ( ) ( ) [ ] ( )( ) ( ) ( [ ]. q q q sh q q q sh q q q sh q q q sh E = ) (.) The next step is to appy the inverse Lapace transforation to the Eqs. (.8) - (.0). Our integrans have sipe poes at 0 = p an, where are the roots of the trigonoetric equation p β = ± β ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ). β sin β sin β sin β sin = (.) The resiue of integrans (.8) (.0) at 0 = p is ( ) ( ) ( ) ( ) for an ( ) ( ) 3 0 for. n the case of we observe that for the first ter we can irecty appy the inverse Lapace transforation so that we ust fin the resiue at ony for the secon part of whose vaue is given by = 0 p ( ) ( ) ( ) ( ) n orer to cacuate the resiues at we have to evauate: p β = ( ), p E p E p p p p β β = = = or, F iβ p E p p = = β (.3) where

149 40 ppenix ( )( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ). β cos β cos β cos β cos F = (.4) ppying now the inverse Lapace transforation to Eqs. (.8) - (.0) we get the tie epenent z-agnetization concentration uring the spin-iffusion process ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ), ) sin sin F x cos e x,t t = = β β β β β (.5) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ), x cos x cos sin sin F e x,t t = = β β β β β β (.6) an ( ) ( ) ( ) ( ) ( ). x cos F sin e x,t t = = β β β β (.7) These quantities are use for the evauation of the integra z-agnetization of each oain given by Eqs. (.0) - (.). The above sus are ae over a soutions of the trigonoetric equation (.4). β

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164 Pubications by the author as part of this work: [u]. ua,. E. eco, M. erter,. üich, V. M. Litvinov, an J. P. Penning, Genera anaytica escription of spin-iffusion for a three oain orphoogy. ppication to et-spun Nyon- 6 fibers, J. Phys. Che., 07 (003) [u]. ua,. E. eco, M. erter,. üich,. eining, H. Keu, an H. Höcker oain sizes in heterogeneous poyers by spin-iffusion using singe-quantu an oube-quantu ipoar fiters, Soi State Nuc. Magn. eson., 4 (003) [u3]. ua,. E. eco,. üich, V. M. Litvinov, an J. P. Penning, Copex orphoogy of et-spun Nyon-6 fibers investigate by H oubequantu-fitere NM spin-iffusion, ChePhysChe (in press). [u4]. Jagaeesh,. Prabhakar,. ua,. E. eco, an. üich, Surface an confineent inuce oecuar ynaics of thin ipi fis: a H utipe-quantu NM stuy, Phys. ev. Lett. (in press). [u5]. ua, J. harata,. E. eco, an. üich, Moecuar ynaics heterogeneities of confine ipi fis by H agnetization - exchange NM, J. Phys. Che. (subitte). [u6]. ua,. E. eco,. üich, H. Keu, an H. Höcker, Moecuar weight epenence of the oain spacing of aorphous PEO-b-PHEM ibock copoyer systes using NM spin-iffusion (in preparation). [u7]. ua,. E. eco, an. üich, naytica soutions of spin-ifffusion equation in a two-oain syste with cyinrica orphoogy (in preparation). [u8]. ua,. E. eco,. üich, V. M. Litvinov, an J. P. Penning, Effect of the wining spee an raw ratio on the oain sizes of Nyon-6 fibres. n spin-iffusion NM stuy (in preparation). [u9]. ua, M. erter,. oenkap,. üich, an. Lenein, Characterization of the structure an the oecuar ynaics of bioegraabe oigo[(l-actie)-ran-gycoie] by soi state NM (in preparation). 55

165 56 Pubications by the author [u0] [u]. ua, M. erter,. oenkap,. üich, an. Lenein, ioegraabe ipants of oigo[(l-actie)-ran-gycoie]: egraation stuies in vitro using soi state NM (in preparation). U. Eiav,. ua,. E. eco,. üich, an G. Navon, MS etho for the assignent an the easureent of exchange rates of protons in rigi proteins, eonstrate on coagen in tenon (in preparation).

166 cknowegeents cknowegeents wou ike to express y eepest gratitue to Prof. ernhar üich, a great scientist an person. t was an honour an in sae tie a great peasure to work uner his guiance. have aways beneficiate fro his support, scientific avices, constant otivation an isponibiity. wou ike to aress any thanks to Prof. Martin Möer for being the co-referee of this thesis. oresc sa aresez cee ai cae utuiri onuui Prof. an eco. ansuui ii atorez faptu ca astazi pot scrie aceste ranuri. avut area sansa e a ucra cu ansu, o persoana eosebita atat in punct e veere stiintific cat si uan si e a invata enor e ute e a ansu in tipu interesanteor iscutii espre stiinta si viata. esea, optiisu si energia ansuui i-au at puterea e a erge inainte. Many thanks are aresse to r. Marko erter for his support an for the interesting iscussions we ha. With his hep know to operate a ruker spectroeter toay. This work cou not be achieve without y coaborators. want here to thanks for the support fro r. Victor Litvinov an r. Jean-Pau Penning fro SM, r. Heut Keu an Prof. H. Höcker fro W, r. Jags aratha, Hyeraba, nia, r. nreas Lenein, r. Nokyong Choi an ip.-che. ris oenkap fro University of Potsa, an r. Uzi Eiav fro the University of Te viv, srae. so, want to thank r. nette Wiesath, r. Sophia nferova, Prof. Vaiir nferov an Günther Schröer for the nice iscussions we ha an for being goo friens. thank aso Kaus Kupferschäger for his hep in severa cases. cou not achieve a part of y work without the hep of Christian Köker which was aways fighting to fin new tenons for y easureents. t was a peasure to share the office with y coegue an frien Kai Kreer. have aways enjoye the nice reaxing iscussions we ha uring rinking a cup of coffee an eating ars.

167 cknowegeents For sure o not forget y roanian coegues an friens i Voa an Gabi ata. Many thanks for their support an the goo tie spen togheter. want to say thanks to Markus Küppers, Mirko Krügger, Mingfei Wang, r. Siegfrie Stapf, r. Christa Gehen, r. Feerico Casanova, r. Xiaohong en, Nicu Goga, Kerstin Münneann, nreea ar, Sobiroh Kayiro, Juan Pero, an Shatru Shara for the nice coegia atosphere. wou ike to aress y thanks aso to y roanian coeagues an friens: Prof. O. Cozar, r. V. Chis, Prof. S. stiean, Prof. M. Toica, Prof. C. Cosa, Prof. L. avi, Prof.. Ciurchea, an to a the other coeagues fro the epartent of toic Physics where spen the first years of y scientific carrier. oresc sa utuesc prietenei ee Prof. Mihaea Lese care i-a eschis portie catre fascinanta ue a stiintei si pentru suportu constant eaungu tipuui. Vreau sa utuesc e aseenea parintior ei Viorica si Gavri, frateui eu in si unchiuui eu Gusti pentru sprijinu si iubirea pe care i-au oferit-o eaungu tuturor acest ani. Nu as fi ajuns nicioata aici fara sfaturie si inenurie or. n at the en, but not the east, y specia thinking is for Michae as, y best frien, y coeague an y ife partner. want to thank hi for being near e, for giving e the power of going further on, for his constant support an hep, for sharing with e the goo an the ba oents.

168 Curricuu vitae Surnae: First Nae: ate an pace of birth: ua ina eghina th October 974, Targu Lapus, oania Eucation: Priary schoo, Targu Lapus, oania Liviu ebreanu theoretica high schoo, Targu Lapus, oania Facuty of Physics, abes-oyai University, Cuj-Napoca, oania Master in iophysics an Meica Physics at Facuty of Physics, an stuent at Facuty of Matheatics abes-oyai University, Cuj- Napoca, oania Ph stuent, epartent of toic an Nucear Physics, Facuty of Physics, abes-oyai University, Cuj-Napoca, oania esearch stage at NM Poyer Laboratory, Universite Joseph Fourier, Grenobe, Supervisor Prof. r. J. P. Cohen-a esearch stage at NM Poyer Laboratory, Universite Joseph Fourier, Grenobe, Supervisor Prof. r. J. P. Cohen-a Ph stuent at nstitute for Technica Cheistry an Macrooecuar Cheistry WTH achen, Gerany, Supervisor Prof. r.. üich st Juy 004 efense for the octora egree in natura science Professiona Positions: ssistant professor at the epartent of toic an Nucear Physics, Facuty of Physics, abes-oyai University, Cuj-Napoca, oania Scientific assistant in the epartent of Macrooecuar Cheistry (Prof.. üich), WTH achen