Adortion t the olid/g interfce Introduction Mny hyicl nd chemicl rocee occur t different interfce. Adortion (not to be confued with bortion) i one of the min nd bic urfce henomen. Adortion i found to occur in mny nturl hyicl, biologicl, nd chemicl ytem. It i widely ued in lbortory reerch nd indutril liction.
Adortion t the olid/g interfce Solid urfce how trong ffinity for g molecule tht come in contct with them, nd ome of them re tred on the urfce. In dortion roce ontneou ccumultion of g or vour (dorbte) tke lce t the olid urfce (dorbent or ubtrte) comred to the bulk he. Fig. 1. Adortion of g molecule on the rticle of dorbent. The revere roce of dortion i clled deortion.
1. Adortion roce Adortion t the olid/g interfce Adortion - ontneou ccumultion of g or vour (dorbte) t the olid urfce (dorbent or ubtrte) comred to the bulk he. Adorbent - olid on which dortion occur (uully it i orou mteril of lrge ecific urfce (m 2 /g)). Adorbte - ubtnce (g or vour) which i dorbed on olid urfce (dorbent). Abortion - roce in which g diffue into the olid borbing medium. It i often difficult to find the difference between dortion nd bortion, nd tht i why the term ortion i ued.
Adortion t the olid/g interfce The mount of the ubtnce dorbed t equilibrium deend on: temerture g vour reure ecific urfce re of the olid (dorbent). The nture of olid or g lo ly ignificnt role. The nture of the dorbent h rofound effect on the dortion roce. The bic feture of good dorbent i lrge ecific urfce re. The bigger the urfce re, the more molecule re tred on it urfce. Generlly, thi men tht good dorbent i very orou. The ecific re of n dorbent i the urfce re vilble for dortion er grm of the dorbent.
Adortion t the olid/g interfce Adortion iotherm The reltionhi t contnt temerture between the equilibrium dorbed mount of g dorbed nd the g reure Adortion reduce the imblnce of ttrctive force which exit t the urfce, nd hence the urfce free energy of heterogeneou ytem i formed. Accordingly, in olid-g ytem the reltion exreing energy chnge re imilr to thoe in liquid-g ytem. The min difference in the dicued ytem i urfce heterogeneity with regrd to energy.
Adortion t the olid/g interfce In the ce of olid/g dortion, the Gibb urfce i equivlent to the dorbent urfce, nd there i no need to inert hyotheticl urfce in the ce of liquid/g ytem. However, in thi ytem one cn conider n interfcil lyer coniting of two region: dortion ce the rt of the g he reiding in the force field of the dorbent urfce the urfce lyer of olid dorbent. Schemtic concentrtion rofile of ubtnce t olid/g interfce function of the ditnce from the olid urfce i reent in Fig. 1.1. Fig. 1.1. Adortion t the olid/g interfce. Concentrtion rofile of ubtnce i function of the ditnce from the olid urfce in the rel ytem nd in the reference ytem (the overled ytem. The urfce exce mount i given by the hded re.
Adortion t the olid/g interfce The urfce exce mount of the dorbed g (Gibb dortion) n iσ i the exce number of mole of tht ubtnce reent in the rel ytem over the number reent in reference ytem, where dortion doe not er t the me equilibrium g reure. The exce number of mole n iσ cn be clculted in the following wy: n σ i = ( g c c ) i i dv + c i dv (1) where g ( c c ) i i dv i the dortion ce, c idv i the urfce lyer of the dorbent, c i g c i i the locl concentrtion of ubtnce i in volume element dv of the interfcil lyer, i the concentrtion of tht ubtnce in the bulk he.
The econd term of eqution (1) i uully umed to be zero, nd hence: n ( g c c ) = dv σ i i i (2) Adortion t the olid/g interfce For g mixture the totl urfce exce mount i given by the um of the urfce exce mount of dorbed individul comonent: σ σ n = n (3) i i If n iσ i the urfce exce of ubtnce i er 1 g of dorbent whoe ecific urfce re i, then Γ σ = i σ n i (4)
Adortion t the olid/g interfce The quntity of dorbed mole n iσ i given n σ i = n i c g i V g (5) where n i i the totl number of mole of ubtnce i in the ytem, c i g i it concentrtion in the g he, V g i the volume of g t equilibrium with the dorbent. Art from the urfce exce it i oible to determine the totl mount of ubtnce i in the urfce lyer with reference to 1 g of dorbent n i defined : n i = cidv (6) V where V = l i the volume of the interfcil lyer, rcticlly it i the volume of the dorbed lyer, l i the thickne of the dorbed lyer, i the ecific re of the dorbent.
Adortion t the olid/g interfce The quntity n i cn be conveniently defined : n + c i = n σ i g i V,g (1) where V,g i the volume of the dortion lyer. When dortion of ubtnce i i recible nd it equilibrium reure i ufficiently mll, the term c ig V,g in eqution (1) i negligibly mll, then: n i n σ i (2) Such roximtion i jutified in the ytem under norml (low) reure. In tudie of dortion t the olid/g (vour) interfce vriou ymbol hve been ued to denote the mount of dortion, e.g. the ymbol (mol/g) or the ymbol v (cm 3 /g). So, we ume tht: n = i (3)
2. Phyicl nd chemicl dortion Adortion t the olid/g interfce The dortion roce i generlly clified either hyiortion (hyicl dortion) or chemiortion (chemicl dortion). Phyiortion i the mot common form of dortion. Phyiortion (hyicl dortion) Adortion in which the force involved re intermoleculr force (vn der Wl force) of the me kind thoe reonible for the imerfection of rel ge nd the condention vour, nd which do not involve ignificnt chnge in the electronic orbitl ttern of the ecie involved. Chemiortion (chemicl dortion) Chemiortion (or chemicl dortion) i dortion in which the force involved re vlence force of the me kind thoe oerting in the formtion of chemicl comound. [IUPAC Comendium of Chemicl Terminology 2nd Edition (1997)]
Adortion t the olid/g interfce The roblem of ditinguihing between chemiortion nd hyiortion i biclly the me tht of ditinguihing between chemicl nd hyicl interction in generl. The rincil differece between chemiortion nd hyiortion: het of dortion (enthlhy of dortion) reveribility thickne of the dorbed lyer
Adortion t the olid/g interfce Comrion between hyiortion nd chemiortion Phyiortion Low enthly of dortion (5 50 kj/mol) Thi roce i reverible Intermoleculr force of ttrction re vn der Wl force, hydrogen bonding, etc. Multi-moleculr lyer my be formed Thi roce i oberved under condition of low temerture It i not ecific Chemiortion High enthly of dortion (200 400 kj/mol) Thi roce i irreverible Vlence force of ttrction re chemicl bond force Generlly, monomoleculr lyer i formed Thi roce tke lce t high temerture It i highly ecific Fig. 1.2. Phyiortion Fig. 1.3. Chemiortion
Adortion t the olid/g interfce Phyiortion WEAK, LONG RANGE BONDING Vn der Wl interction (e.g. London dierion, diolediole), hydrogen bonding. NOT SURFACE SPECIFIC Phyiortion tke lce between ll molecule on ny urfce roviding the temerture i low enough. H d = 5 50 kj/mol Non ctivted with equilibrium chieved reltively quickly. Increing temerture lwy reduce urfce coverge. No urfce rection. MULTILAYER ADSORPTION BET iotherm ued to model dortion equilibrium
Adortion t the olid/g interfce Chemiortion STRONG, SHORT RANGE BONDING Chemicl bonding invoving orbitl overl nd chnge trnfer SURFACE SPECIFIC e.g. chemiortion of hydrogen tke lce on trnition metl but not gold nd mercury H d = 50 500 kj/mole Cn be ctivted, in which ce equilibrium cn be low nd increing temerture cn fvour dortion Surfce rection my tke lce: diocition, recontruction, ctlyi MONOLAYER ADSORPTION Lngmuir iotherm ued to model equlibrium
Thermodynmic conidertion A ontneou roce require G < 0. S i negtive for the dorbte Therefore, from G = H T S In order for G be ngtive H mut be negtive i.e. the roce hould be exothermic nd the degree of dortion incree with decreing temerture Adortion t the olid/g interfce
3. Equilibrium of dortion Adortion t the olid/g interfce Between the dorbte nd dorbent dynmic equilibrium i etblihed, which reult from equliztion of the number of dorbed molecule with tht of molecule undergoing deortion: A A d where A re the dorbte molecule in the g he, A d re in the dorbed tte. Thi follow in the me time unit the me number of dorbte molecule i undergoing dortion nd deortion. A dortion meure the mount of the dorbed ubtnce i i umed tht i exreed in grm, mole or cm 3 er the dorbent m unit. In dortion equilibrium thee quntitie deend on the g nd temerture reure. Equilibrium contnt of dortion K d cn be rewritten : K [Ad ] [A] d = (1)
Adortion t the olid/g interfce Adortion equilibrium i etblihed fter coniderble dortion of the g on the dorbent urfce, nd cn be written generl eqution: (,, T) 0 f = = f (, T) (2) where i the quntity of g dorbed on the urfce er 1 g (or mol) of the dorbent, i the equilibrium reure of the g in the bulk he (the equilibrium reure), nd T i the temerture. When tudying dortion equilibrium one of the rmeter remin unchnged, deending which of the vrible i left on the contnt level, we obtin: or dortion iotherm (T = cont) = f () T dortion iobr ( = cont) = f(t) dortion iotere ( = cont) = f(t)
Adortion t the olid/g interfce Adortion iotherm T = cont An dortion iotherm for ingle geou dorbte on olid i the function which relte t contnt temerture the mount of ubtnce dorbed t equilibrium to the reure (or concentrtion) of the dortive in the g he. The urfce exce mount rther thn the mount dorbed i the quntity cceible to exerimentl meurement, but, t lower reure, the difference between the two quntitie become negligible. [htt://www.iuc.org/goldbook/a00165.df] Fig. 1.4. Iotherm of dortion The degree of dortion incree with the decreing temerture.
Adortion t the olid/g interfce Adortion iobr = cont The function relting the mount, m or volume, or correonding exce of ubtnce dorbed by given mount of olid, to the temerture t contnt reure. Fig. 1.5. Iobr of dortion [htt://www.iuc.org/goldbook/a00165.df] The degree of dortion incree with the increing reure
Adortion t the olid/g interfce Adortion iotere = contnt The function relting the equilibrium reure to the temerture t contnt vlue of the mount, or exce mount of ubtnce dorbed by given mount of olid. Fig. 1.6. Iotere of dortion [htt://www.iuc.org/goldbook/a00165.df] The degree of dortion incree with increing reure
4. Henry eqution Adortion t the olid/g interfce Adortion equilibrium cn be conidered ccording to the cheme: Molecule in the g he Molecule on the dorbent (dortion comlex) On homogeneou urfce the concentrtion of dorbte in the urfce lyer i contnt over the whole urfce. The equilibrium condition in uch ytem i given by: f c fc = K (3) where c i the dorbte concentrtion in the urfce lyer (urfce concentrtion), c i the dorbte concentrtion in the g he f nd f re the ctivity coefficient in the urfce lyer nd in the g he, K i the equilibrium contnt, which i function of temerture only. c Kf f c = (4) Eqution (4), relting c to c t T = cont, i the dortion iotherm.
Adortion t the olid/g interfce Becue the ctivity coefficient f nd f re concentrtion deendent, therefore the dortion iotherm i nonliner. At low concentrtion of dorbte (g reure u to 10 5 N/m 2 ) we cn lo ume tht f = f = 1, nd then c = Kc (5) On lying the idel g eqution (V=nRT =(n/v) RT nd c=n/v) c = /RT one obtin: c = K RT (6) Inted of the urfce concentrtion it i oible to clculte the totl mount of dorbte (mol/g) in the volume of the urfce lyer V = l ( i the ecific urfce re of dorbent nd l i the thickne of the urfce lyer): = V c = l c
Adortion t the olid/g interfce In the tudie of dortion roce, beide the vlue (mol/g), the dorbed mount, the mount of dortion er unit re (µmol/cm 2 ), or number of molecule er nm 2 i lo ued: = = Subtituting uitble deendence it i ey to how tht: l c = V Kc = V K RT For given dortion ytem t T = cont, V nd K re lo contnt, therefore: K V = K, (9) RT nd = K, (7) (8) (10) or = K, (11) where K =, K,
Adortion t the olid/g interfce It follow from eqution (6), (10) nd (11) tht t low reure (the mount er 1 g of dorbent) nd (the mount er unit urfce re) re roortionl to the concentrtion or reure of g in the g he. Thi dortion lw i formlly identicl with the well known Henry lw for g bortion in liquid (which, in turn, i the conequence of the more generl Nernt rtition lw): v b = K (Henry lw for g bortion) Eqution (6), (10) nd (11) reent different form of the imlet dortion iotherm eqution known the Henry dortion iotherm, nd the correonding contnt i clled the Henry contnt. It w found tht t room temerture, when the g reure doe not exceed tmoheric reure, the dortion iotherm for rgon, nitrogen nd oxygen on ctivted crbon, ilic gel nd ditomceou erth were liner.
Adortion t the olid/g interfce Inted of the urfce concentrtion c or the totl dorbed mount the frctionl coverge of urfce defined by the quntity θ (the urfce coverge) i often ued. urfce coverge θ The number of dorbed molecule on urfce divided by the number of molecule in filled monolyer on tht urfce: θ = number of occuied dortionite totl number of oibleite c = c m = m = θ (12) m where, c m, m nd m re the quntitie correonding to the comlete coverge of the dorbent urfce by the filled monolyer of the dorbte.
Adortion t the olid/g interfce The Henry dortion iotherm (eqution (6), (10) nd (11)) cn be exreed in term of urfce coverge: K K K,, θ = = = (13) c RT m m m Thi men tht the coverge of the dorbent urfce in the Henry region i roortionl to the reure of the dorbte in the g he.
5. Freundlich dortion iotherm Adortion t the olid/g interfce In 1895 Boedecker rooed n emiricl eqution for the dortion iotherm in the following form: 1/ = k where k, n re the contnt whoe vlue deend uon dorbent nd g t given temerture. Thi eqution i known the Freundlich dortion eqution becue Freundlich oulrized it liction. n (1) The Freundlich iotherm remind tht of the Lngmuir one, however, it differ by lck of the tright roortionlity line between the mount of the dorbed ubtnce, the g reure in the rnge of low reure: Fig. 1.7. Freundlich iotherm. d d n 1 e
Adortion t the olid/g interfce Tking both log ide of the Freundlich eqution, we get: log = logk + 1/ n log (2) Plotting grh between log nd log, we get tright line with the loe vlue equl to 1/n nd log k y-xi intercet. Fig. 1.8. Determintion of the contnt from the logritmic form of Freundlich ioterm.
Adortion t the olid/g interfce The vlue n chnge from 0.2 to 0.9 nd incree with temerture incree to 1. The vlue k chnge within wide rnge deending on the kind of dorbent nd dorbed ubtnce. In contrt to the theoreticlly jutified the Lngmuir iotherm, the Freundlich iotherm i of urely emiricl chrcter. The Freundlich iotherm differ lo from the Lngmuir one in limited liction rnge. It cnnot be ued for tright liner iotherm rt occurring either t low reure the vlue n =1 hould be then umed, or t high reure the curve incree unreervedly, where urfce h limited vlue nd it mut be in the condition of turtion.
Adortion t the olid/g interfce The Freundlich eqution i imle, however, it doe not exctly decribe the iotherm in wide reure rnge. It w rther ued to decribe dortion qulittively. Then the eqution ered to be ometime ueful in theoreticl conidertion nd it cn be derived uing the method of ttiticl mechnic. Limittion of the Freundlich dortion iotherm: It i licble within certin limit of reure. At higher reure it how devition. The vlue of contnt k nd n chnge with the temerture. The Freundlich iotherm i n emiricl one nd it doe not hve ny theoreticl bi.
6. Lngmuir theory nd dortion iotherm Adortion t the olid/g interfce In 1916, Irving Lngmuir ublihed new model iotherm for ge dorbed onto olid, which retined hi nme. The Lngmuir dortion model i the mot common one ued to quntify the mount of dorbte dorbed on n dorbent function of rtil reure t given temerture.
Adortion t the olid/g interfce The Lngmuir dortion iotherm i bed on the following umtion. 1. The dorbent urfce conit of certin number of ctive ite (roortionl to the urfce re), t ech of which only one molecule my be dorbed. Ech dorbte molecule occuie only one ite 2. No lterl interction between the dorbed molecule, thu the het of dortion i contnt nd indeendent of coverge.
The Lngmuir dortion iotherm i bed on the following umtion. Adortion t the olid/g interfce 3. The dorbed molecule remin t the ite of dortion until it i deorbed (i.e. the dortion i loclized). 4. At mximum dortion, only monolyer i formed: molecule of dorbte do not deoit on the other, lredy dorbed, molecule of dorbte, only on the free urfce of dorbent. Fig. 1.9. Monolyer model of Lngmuir dortion.
Adortion t the olid/g interfce The dortion equilibrium t, T = cont i exreed follow: g molecule in the bulk he + ctive ite on the dorbent urfce = loclized dortion comlex The iotherm w formulted on the bi of dynmic equilibrium between the dorbed he nd the g or vour he. Kinetic derivtion Equilibrium rereent tte in which the rte of dortion of molecule onto the urfce i exctly counterblnced by the rte of deortion of molecule bck into the g he, i.e. when the rte of dortion equl the rte of deortion, dynmic equilibrium occur.
Adortion t the olid/g interfce The rte of dortion deend on: 1. the chnge of urfce coverge due to dortion which i roortionl to the reure, 2. the colliion robbility with free ctive ite: 1 m where i the concentrtion of the occuied ctive ite on the urfce, i.e. the urfce concentrtion of the dorbte, m i the urfce concentrtion t the monolyer coverge of the dorbte. 3. the ctivtion energy of n dortion ex ( E/RT)
Adortion t the olid/g interfce The rte of deortion deend on: 1. frctionl coverge of the urfce 2. the ctivtion energy of deortion ex ( E /RT) m At equilibrium the dortion rte certinly equl the deortion rte: 1 m ex E RT = k' m ex E' RT (1) where k i the roortionl coefficient. Hence = k' ex where H d = E E i the het of dortion ( ). H RT d 1 m m (2)
Adortion t the olid/g interfce If we ume tht the het of dortion doe not deend on the urfce coverge we cn write: where k i the contnt deending on the temerture. From the definition it reult tht or where θo = o m k = 1 m ( ) m Hd k' ex = RT m + o = i the frction of the urfce with free ctive ite 1 k k = ( ) m (3) (4) m (5) θ + θ =1 (6) o θ= m = θ m
Tking into ccount the urfce coverge we obtin: θ = 1 k i.e. θ = k ( 1 θ) ( θ) Adortion t the olid/g interfce (7) Trnforming eqution (7) for θ the following reltionhi i obtined: k = 1+ k θ i.e. θ = k ( 1 θ ) (8) mk = 1+ k mk = 1+ k (9) (10) Eqution (8) (9) nd (10), re different form of the Lngmuir dortion iotherm decribing dortion on homogeneou urfce when no interction tke lce between the dorbte molecule, which were derived in kinetic wy. Thi iotherm cn be lo derived thermodynmiclly or ttiticlly.
Adortion t the olid/g interfce I ce If dortion occur t low reure k 1 then: θ k = = m m k k (11) (12) (13) Adortion i roortionl to the reure, o in thi reure rnge the Lngmuir eqution i trnformed to tht of the Henry eqution. II ce If the reure of the dorbing ubtnce i ufficiently high, then k >> 1, nd we cn neglect unity in the denomintor of eqution (11)-(13) yielding: θ 1,... m,... m (14) It follow from the bove reltion tht the mount of dorbed g initilly incree linerly with the increing reure, then grdully decree, nd t roritely high reure the dortion reche contnt vlue.
Adortion t the olid/g interfce The Lngmuir dortion iotherm eqution, e.g. eqution (10) cn be reented in the liner form: m K = 1+ K ( 1+ K ) = K m (15) (16) 1+ K = m K Fig. 1.10. Lngmuir dortion iotherm. (17) = 1 m + 1 m K (18) Fig. 1.11. Determintion of the contnt m nd k from the liner form of the Lngmuir iotherm.
Adortion t the olid/g interfce The quntity m, i.e. the mount of dorbte (mole/g) covering the urfce re of the dorbent in monomoleculr coverge, i known the monolyer ccity. The quntity m llow u to clculte the ecific urfce re of the dorbent if we know the urfce ω m occuied by molecule in the monolyer: S = m N ω m (19) where N i the Avogdro number.
Adortion t the olid/g interfce In mny ytem the Lngmuir dortion iotherm decribe well the exerimentl reult. However, in the ce of temerture decree nd heterogeneity incree of the dorbent urfce, thi cue multilyer dortion which the Lngmuir dortion iotherm doe not nticite. If dortion tke lce from mixture of ge, then dortion of given comonent incree with it increing rtil (molr) reure. For uch ytem the dortion iotherm h the form: θ i = 1 kii k + i i i (20)
7. Potentil theory of dortion Adortion t the olid/g interfce Bic wekne of the Lngmuir theory w the umtion of monomoleculr dortion. The rllel to Lngmuir theory, theory of multimoleculr dortion lyer the o-clled otentil theory, w develoed, whoe uthor were Eucken nd Polnyi. Polnyi umed tht the dortion force ct t longer ditnce thn the molecule ize, the force re not creened by the firt ler of dorbed molecule, the dortion lyer h diffuive chrcter nd it denity chnge with the ditnce from the urfce. In the otentil theory ignificnt role i lyed by the two rmeter: the dortion otentil ε nd the volume of the dorbed lyer V.
Adortion t the olid/g interfce The dortion otentil i relted with the chnge of molr free energy connected with the chnge of the vour reure from tht over the ure liquid he o to the equilibrium reure t given coverge of the dorbent urfce: o = RT ln ε (1) On the dorbent urfce there i force field known the dortion otentil field. ε = RT d ln (2) o It i umed tht in the ce round ech olid one my find ome equiotentil urfce (for flt homogeneou urfce they re lne) delimiting the dorbte which i dorbed t reure lower thn thoe correonding to the otentil vlue nd tht uch equiotentil urfce re ecific for given olid urfce.
Adortion t the olid/g interfce The dortion otentil correond to the chnge of molr free energy connected with the chnge of the vour reure from tht over the ure liquid he o to equilibrium reure t given coverge of the dorbent urfce: equiotentil urfce Fig. 13. Cro-ection of the urfce lyer in term of the otentil theory. The ce between ech et of equiotentil urfce correond to defined volume, nd thu the deendence between the dortion otentilεnd the urfce lyer volume V i: ε = f ( V ) (3) V = V (4) m where i the dorbed mount (mol/g), nd V m i the molr volume of liquid whoe vour i dorbed t the temerture of the exeriment.
Adortion t the olid/g interfce In the otentil theory the lyer of the dorbed g re conidered qui liquid. With increing ditnce from the urfce incree volume of the urfce lyer V nd decree the dortion otentil ε. According to Polnyi the dortion otentil in given temerture rnge, irreective of the temerture, i contnt, thu: ε T V = 0 (5) o,1 ε = RT 1 ln = 1 RT 2 ln o,2 2 (6) Thi theory doe not yield define dortion iotherm, but give the o-clled chrcteritic dortion curve, nd the function ε = f (V ) i chrcteritic function of dortion.
Adortion t the olid/g interfce 30000 Potentil curve ε = RT ln(/), [J] 25000 20000 15000 10000 5000 0 B2=3,0E-8 B2=1,0E-8 B2=3,0E-9 0 0,2 0,4 0,6 0,8 1 V/V A.W. Mrczewki The exerimentl jutifiction of hi theory conit in clculting the chrcteritic curve from exerimentl reult of one exerimentl iotherm, nd hence determining the iotherm t different temerture. Fig.14. Chrcteritic otentil curve. The volume of the dorbed lyer V, it denity ρ nd the mount of dorbed ubtnce re relted by: V = ρ (7)
Adortion t the olid/g interfce If we determine exerimentlly nd, nd know the vlue o nd ρ t given temerture, we cn determine ε = f (V ), nd on thi bi the iotherm t other temerture cn be found. At the me ditnce from the urfce (V 1 = V 2 ) for two different dorbed vour on the me dorbent, the rtio of the dortion otentil ε i contnt: ε = β (8) ε o where β i the convergence (ffinity) coefficient of the chrcteritic curve, ε o i the dortion otentil for vour of tndrd dorbte. V If the condition of the dortion lyer cn be decribed by vn der Wl eqution, it er tht t uitbly low temerture g concentrtion incree u to it condention.
8. Dubinin-Rduhkevich dortion iotherm Adortion t the olid/g interfce Dubinin nd Rduhkevich found tht the chrcteritic dortion curve w correlted to the orou tructure of the dorbent. The convergence coefficient β roximtely become: V β V c c,o P P o α α c c,o (1) where V c nd V c,o re the molr volume of dorbte nd tndrd dorbte, reectively, P nd P o re their rchor; α c nd α c,o re their olrizbilitie. The ttemt w mde to jutify theoreticlly the chrcteritic curve for the microorou dorbent. There w rooed n eqution, which w clled the eqution of Dubinin- Rduhkevich dortion iotherm (R D eqution): V = V o e b RTln o 2 (2) where b=k/β 2, V i the volume of the dorbed lyer, V o i the o-clled limiting volume t the otentil ε =0, roximtely equl to the volume of the microore.
Adortion t the olid/g interfce Dividing both ide of eqution (2) by the molr volume of the liquid dorbte we obtin nother form of thi eqution: = o e b o RT ln 2 (3) where o i the number of mole of liquid dorbte required to fill the microore of 1 g of the dorbent. From hi eqution liner form cn be finlly obtined: or log log V = log o D log o 2 2 (4) o = log Vo D log (5) where D 0,4343BT 2 = nd 2 2 2 B= kr 2,303 β
Adortion t the olid/g interfce 0 log 2 ( /) 0 10 20 30 40 50 If the exerimentl dt re reented in the form of log or log V veru log 2 ( o /) lot, tright line from it o or V o nd D vlue re obtined. log(v) -5-10 -15-20 -25 DR liner lot B2(RT*ln(10))^2=3,15E-1 B2(RT*ln(10))^2=9,44E-1 B2(RT*ln(10))^2=9,44E-2 A.W. Mrczewki It w hown tht the vlue of contnt B in the R D dortion iotherm re directly connected with orou tructure of the dorbent. In ome ytem tright line form w found only in nrrow temerture rnge, where in other in full reure rnge, e.g. benzene/ctive crbon.
9. The BET theory of multilyer vour dortion Adortion t the olid/g interfce Mny exerimentl dortion iotherm could not be decribed by the theory of Lngmuir nd Polnyi. In 1938 Brunuer, Emmet i Teller reented the multilyer dortion theory (BET theory) bed on the Lngmuir model. The bic umtion of the BET theory i the Lngmuir eqution lied to ech lyer with the dded otulte tht for the firt lyer the het of dortion Q 1 my hve ecil vlue, where for ll ubequent lyer it i equl to Q C, i.e. the het of condention of the liquid dorbte.
Adortion t the olid/g interfce Molecule getting onto the dorbte urfce form n dortion comlex with it even in the ce when t given ite molecule h lredy been dorbed. When vour reure (or g) incree nd reche tht of turted vour o the number of free dortion ite decree, forming double or trile dortion comlexe. vour + free urfce re ingle comlex vour + ingle comlex double comlex vour + double comlex trile comlex Fig. 15. Multilyer model of BET dortion.
Adortion t the olid/g interfce Brunuer, Emmet nd Teller derived n eqution of multilyer dortion on the bi of kinetic conidertion, which cn be lo derived ttiticlly. Moreover, it cn be lo derived be on the nlyi of dortion equilibrium. Mking conidertion imilr to the ce of derivtion of the Lngmuir iotherm, n exreion for the urfce coverge θ cn be obtined: θ= 1 0 C 1 + 0 ( C 1) 0 (1) = 1 0 m C 1 + 0 ( C 1) 0 (2) where i the totl mount of dorbed vour, m i the monolyer ccity, θ i the urfce coverge of dorbte molecule, C i the contnt connected with the difference between the enthly of the firt lyer (Q 1 ) nd the enthly of condention (Q C ) nd exreed by the deendence: 2.3 log C = Q 1 Q C.
Adortion t the olid/g interfce C = g o ex ( L H H ) m RT m (3) where H m H L m i the ure enthly of dortion, H m L H m g o = ex i the molr enthly of the firt lyer, i the molr enthly of condention, S m S R L m i the o-clled entroic fctor. Eqution (1) or (2) i the Brunuer, Emmet nd Teller (BET) iotherm eqution of multilyer vour dortion.
Adortion t the olid/g interfce (4) Eqution (58) cn be written in the liner form = + = 0 0 0 m C) (1 1 1 C + 0 0 C) (1 1 1 0 m C = + 0 0 m 0 1 C C) (1 1 (5) (6) 0 m m 0 0 C 1 C C 1 1 + = (7)
Fig. 16. Determintion of the contnt of the BET dortion iotherm. Preenting the dortion iotherm in the coordinte ytem (/ o) /(1 / o ) nd / o, the m nd C contnt cn be determined from the loe of tright line nd the oint of it interection with y- xi, i.e. tg α=c 1/ m nd the ection b=1/( m C). Knowing the vlue m, the ecific urfce re of the tudied dorbent cn be clculted from the eqution: S = m N ω Meurement of the ecific urfce re of dorbent by the BET method i mde by men of low temerture dortion iotherm of nitrogen, uming ω m = 0.162 nm 2. The monolyer ccity i found from the iotherm he. m Adortion t the olid/g interfce (8)
Adortion t the olid/g interfce According to Brunuer ll dortion iotherm cn be clified into 5 rincil tye: Fig. 17. Tye of g nd vour dortion iotherm ccording to Brunuer I NH 3 + chrcol, II N 2 + ilic, III Br 2 + ilic, IV benzene + ilic, V H 2 O + chrcol.
Adortion t the olid/g interfce Tye I i the Lngmuir tye, roughly chrcterized by monotonic roch to limiting dortion tht reumbly correond to comlete monolyer. Tye II i very common in the ce of hyicl dortion nd undoubtedly correond to multilyer formtion. Point B mrked on the curve correond to the comlete monolyer. Fig. 17. Tye of g nd vour dortion iotherm ccording to Brunuer (I NH 3 + chrcol, II N 2 + ilic, III Br 2 + ilic, IV benzene + ilic, V H 2 O + chrcol) Tye III i reltively rre (n exmle i tht of the nitrogen dortion on ice) nd eem to be chrcterized by het of dortion equl to or le thn the het condention of the dorbte (Q d Q con ). Tye IV nd V re conidered to reflect cillry condention henomen in tht they level off before the turtion reure i reched nd my how hyterei effect.
Adortion t the olid/g interfce The BET eqution concern the firt three of uch dortion iotherm tye. When the het of dortion H m i much L greter thn the het of condention H m L ( H m» H m ), then the contnt C i very lrge, nd eqution (58) i reduced to the Lngmuir iotherm, i.e. tye I iotherm. Fig. 17. Tye of g nd vour dortion iotherm ccording to Brunuer (I NH 3 + chrcol, II N 2 + ilic, III Br 2 + ilic, IV benzene + ilic, V H 2 O + chrcol) For C vlue in the rnge form 3 to 4 to everl hundred, the BET eqution yield iotherm correonding to Tye II. If C i equl to or mller thn unity, i.e. L if H m «H m, the BET eqution yield Iotherm of tye III.
Adortion t the olid/g interfce Amount of dorbte Condention in mcroore Adortion in mcroore Formtion of multilyer in mcroore BET re Condention in microore 0 reltive reure (/ o) 1 dorbte molecule dorbte molecule Fig. 18. Schemtic reenttion of dortion rocce ccording to tye IV.
Adortion t the olid/g interfce Exerimentl greement with the BET theory exit only in reltively nrrow rnge of / o (from 0.05 to 0.3). Tye II doe not often gree in the rnge 0.3 0.5 / o, which i connected with coniderble difference in the dorbent dorbte interction for 2 nd 3 monolyer. A tyicl devition from the theory conit in too mll dortion nticited by BET under low reure nd too gret under high one. There re everl modifiction of the BET eqution, but generlly they re not widely ued. The min flw of ll theorie, which hve been dicued, i negligence of interction between the dorbed molecule, o-clled horizontl or lterl interction which re ignificnt in mny ytem, e.g., they cn form urfce ocited molecule. In generl, the decrition of dortion h not been fully done yet.
10. Cillry condention In the ce of orou dorbent there cn er henomenon clled cillry condention. At low reltive reure / o nd if the cillrie re not too nrrow on the moleculr cle the dortion occur in imilr wy in the ce of nonorou dorbent. When the reure incree inj the cillrie multilyer dortion tke lce nd the dorbed dorbt roertie re imilr to liquid nd the het o dortion i imilr to the het of condention. Thi henomenon cn be exlined tking into ccount vor reure over curved urfce. Deending on the menicu curvture of the liquid different force ct on the liquid molecule being on the curved urfce. Schemtic rereenttion of the force cting on liquid molecule on flt nd curved urfce.
If the menicu i: concve If the menicu lrger the i: moleculr force field lie on the liquid he, convex lrger the moleculr force field lie on the g he. concve lrger moleculr force field occur on the liquid he, convex lrger moleculr force field er on the g he. Therefore the molecule being on the concve urfce re tronger bonded with the liquid thn in ce of the molecule on the convex menicu. Hence, t given temerture the turted vor reure i lower over concve menicu thn convex nd flt one. In uitbly nrrow cillrie the dorbed liquid molecule hve concve menicu nd therefore lower the vor reure thn over flt urfce. In reult, t the me temerture, the liquid vor condente t lower reure thn o bove flt urfce. Thi henomenon of vour condention in cillrie before it reche the reure chrcteritic for the turted vor reure o bove the lnr urfce of thi liquid t given temerture, i clled cillry condention.
The cillry condention cn be exlined uing Kelvin (W. Thomon) eqution derived in 1871. o γ Vm r RT ln = 2 (1) Where: r i the rdiu of the urfce curvture (of the menicu) meured from the g he, for concve: r > 0, for convex: r < 0, nd for lnr: r = ; γ i the liquid urfce tenion, nd V m i the molr volume of the liquid. For liquid being in cylindricl cillry there i reltionhi between the cillry rdiu r nd the menicu curvture rdiu r 1 : Whereθ i the wetting contct ngle r = r 1 coθ (2)
Fig.2. Deendence between cillry rdiu r nd the menicu curvture rdiu r 1 Introducing Eq.2 into Eq.1 one cn obtin the reltionhi between turted vor reure nd the cillry rdiu. (3) If the liquid wet the cillry urfce then the contct ngle i lmot zero θ = 0 nd coθ = 1. In uch ce the cillry rdiu i rcticlly equl to the menicu curvture rdiu. Eqution (1) hd been derived for hericl menicu. If it i concve my be conidered rt of outer here urfce nd In the ce of convex menicu it my be treted rt of inner urfce of the here. Therefre Eq.1 cn be written follow:
(4) where: k nd r k refere to hericl urfce. If the menicu i cylindricl then Eq.1 red: o γ r c Vm RT c ln = (5) Eg.5 i clled Cohn eqution, from which it reult tht the turted vor reure bove the cylindriclly hed (concve) urfce i le decreed thn bove hericl one, i.e. c > k. Becue of the cillry condention er lo henomenon of cillry condention hyterei. Deending on the he of the cillry different he of the hyterei er.
Fig.3.The he of cillry hyterei deending on the cillry tructure of dorbent; r d rdii of the menicu forming during dortion in n oen on both ide cylindricl cillry r de - rdii of the hericl menicu forming during the deortion roce. In ce C of the oen cillry the hyterei loo er. Thi i becue the menicu of the liquid cloing the cillry brek in ome moment of the deortion roce nd the rdii incree uon the liquid evortion. In rel dorbent the he of cillrie re more comlicted. If the hericl rticle touch ech other the cillrie form wedge he. Becue of non-uniform tructure of commercil dorbent the cillrie do not fill in imultneouly. De Boer (1958) clified the hyterei loo into 5 tye, hown in Fig. 4. The mot imort nt re three tye: A, B, E.
Ry.4. Clifiction of the cillry condention hyterei loo fter De Boer. According to de Boer: Tye A er in double-oen cillrie hving he of regulr or irregulr cylinder rim. Tye B er In the reence of lit ore hving rlel wll. Tye E uch hyterei er in the ce of ink-bottle he of the cillrie or deformed tube with nrrow outlet. Tye C nd D reult from the ore he A nd B which re rtilly deformed. Uing rel dorbent the hyterei loo re uully combintion of 2 or 3 tye.
11. Prertion nd tructure of dorbent Nowedy mny dorbent re mnufctured tht differ in reect of their chemicl nture nd tructure of the urfce. There re two cle of dorbent: nonorou nd orou. Nonorou dorbent 1. Preciittion of critlline deoit, e.g. BSO 4 or by grindiing crytlline olid. Thi tye of dorbent chrcterize mll ecific urfce re, u to 10m 2 /g. Mot often, however, the ecific urfce i u to1 m 2 /g. Nonorou dorbent hving lrger ecific urfce cn be obtined in the following wy: 2. Prtil combution of orgnic comound blck oot, or orgnoilicon comound, o clled white oot. Or by: 3. Hydrolyi of hlogen nhydride of orthoiliceou cid (SiCl 4, SiF 4 ) in trongly overheted queou tem iliceou erogel. By thi method it i oible to obtin nonorou dorbent u to everl hundred m 2 /g. They hve imortnt liction filler for olymer, lubricnt, wx, e.t.c. 72
4. Grhite oot it i obtined by heting u to tem. 3000 C in tmohere of nonrective g nd under reduced reure. An reducing tmohere i lo lied. Here the recrytlliztion roce occur nd the oot urfce cover with grhite tructure. The ecific urfce of uch dorbent mount everl dozen m 2 /g. Porou dorbent They hve gret rcticl liction in technic: g nd vor borbnce, uort of ctlit or ctlit, drying, ertion of mixed ge by dortion. The ecific urfce ot thi dorbent my mount more thn 1000 m 2 /g. Thi kind of dorbent re mnufctured grnule or here hving 0,1 2 mm dimeter, to rovide their needed durbility. There re two bic method of orou dorbent mnufcturing. Formtion of tiff keleton of tiny rticle of colloidl ize tht hve very lrge internl urfce, chemicl tretment of orou or nonorou olid (e.g. coke, gl) with liquid or ge.. 73
By firt merhod re obtined gel - xerox ilicgel, Al 2 O 3, MgO. The keleton rtriucle mot often re morhic here.the cillrie ize i detetrmed by the rticle ize nd their king. By the econd method re obtined dorbent from nonctive chrcol by tretment it with H 2 O lub CO 2 t the temerture of 1100 1200 C. A rt of the chrcol burne nd the remining rt i n ctive chrcol hving lrge ecific urfce re (the ore re of everl to everl dozen nm). Other dorbent i obtined by tretment of odium-boron gl with cid. The ore ize deend on therml tretment nd finl tretment with NOH or KOH olution. The dorbent ore differ for their he nd ize. The imortnt rmeter i the dimeter (cylindricl ore) or bredth (the lit ore). Following ore re ditinguihed: microore r < 2 nm (20 Å) mezoore (middle ize ore) r > 2 nm; r < 200 nm mkroore r > 200 nm 74
Tyicl dorbent lied in rctice: ilic gel, - the generl formul i SiO 2 nh 2 O, there re different tye obtined by olycondention of ortho-ilicic cid nd further roceing. Aluminium oxide (lumin) grou of different tructure of Al 2 O 3 often with imuritie of oxide of lkli metl nd lkline erth metl nd different wter content. They re mnufctured motly by dehydrttion of luminium hydroxide. Mot often i ued γ Al 2 O 3 whoe ecific urfce re i S = 100 200 m 2 /g. Activted chrcol thee re the longet time known dorbent. Mot often they re obtined by removing trry (molity) ubtnce from rw wooden col nd rtil burnning in the reence of H 2 O nd CO 2. The urfce i heterogenic chemiclly nd energeticlly, it mount S = 400 900 m 2 /g. Moleculr ieve thee re o clled orou critl which ct moleculr ieve. They ly very eentil role nd mong them mot imortnt re zeolite., which re critl luminoilicte of lkli metl nd lkline erth rrnged the tereo- tetrhedron of SiO 4 i AlO 4. Their generl formul i following: Me 2/n Al 2 O 3 msio 2 H 2 O; n metl vlency Me, m, fctor chrcterizing given zeolite.. 75
The tereo octhedron unit conit of twenty four SiO 4 i AlO 4 tetrhedron. About 40 nturl nd 40 rtificil zeolite re known. They re termed A, X i Y which differ tructurlly.nmely, o clled window dimeter which re gte to the interior of the tructure. The window dimeter i in the rnge of 0,4 nm (4 Å) 1,0 nm (10 Å). The mechnim of the zeolite ction relie on elective llownce ing to the interior of the tructure dorbte molecule, which i determined by the molecule ize. The lrger molecule cnnot enter to the inide. Porou gle they re obtined by therml nd cid tretment of odium-boron-ilic gl. In thi wy it i oible to obtin the dorbent oeing oroity of everl u to everl thound Å. 76
12. Determintion of dorbent tructure by dortion Porou mteril cn be chrcterized with hel of everl rmeter decribing their tructure. Thee rmeter re follow: Men rdii of ore, R. Men rdii (mot often meured in Å or nm) i verge rdii of given orou mteril, nd it men tht there i ome ditribution of the ore ize reltive to thi men rdii. In the literture it i termed by cronym PSD, tht i: Pore Size Ditribution. Secific urfce re, S. Secific urfce of olid (mot often exreed in m 2 /g of olid) i equl to um of externl S e nd internl S i urfce. The externl urfce, S e correond to geometricl urfce of orou grin of 1 g of the dorbent. It i reverily roortionl to the grin ize.. 77
Internl urfce, S i, conit the ore wll. Becue the ore h to be oen, therefore S i vlue doe not involve urfce of the wll of the cloed ore. A rule, S i vlue i much bigger thn S e vlue. For exmle, in the ce of ilicge thi difference mount u to everl order of mgnitude. It hould be keot in mind tht generlly, there i revere reltionhi between ecific urfce nd men ore rdiu. The lrger i ecific urfce S the mller re the ore rddi R. Big ecific urfce(s > 500 m 2 /g) indicte for nrrow ore, while mll ecific urfce (S < 10 m 2 /g) i chrcteritic for mcroorou olid. Totl volume of ore, V, Totl ecific volume of the ore, V (exreed in cm 3 of liquid dorbt er grm of orou olid) i the volume of liquid dorbte which fill in the ore reent in unit m of orbent. 78
A firt roch the vlue V hould be indeendent on the kind of liquid dorbnt if the urfce i erfectly wetting. Among the rmeter chrcterizing the dorbent only ore volume V h cler hyicl ene. It cn be eily determined without ny reumtion, while clcultion of the rdii R well the ecific urfce S need lwy uitble model umtion. Therefore there my be oen roblem whether the determined rmeter re relble. Secilly, the determined men rdii my rie ome doubt for given orbent becue of imlifiction tht re umed in the model, e.g. for ore he Neverthele, knowledge of the vlue of thee rmeter chrcterizing the orou tructure of olid i very ueful for dortion roertie evlution of dorbent. It i imortnt to ue everl indeendent exerimentl method imultneouly nd tndrize the nlyticl method. 79
Pore clifiction Klyfikcj orów ort jet n róŝnicy zchodzących w nich zjwik dorcyjnych i kilrnych. Efektywne romienie njbrdziej zerokoorowtej odminy orów mkroorów rzewyŝzją 500 Å, ich owierzchni włściw zwrt jet w grnicch 0.5 2 m 2 /g. Zzwyczj dorcję n owierzchni mkroorów moŝn ominąć, zś z rzyczyn technicznych częto rzyjmuje ię, Ŝe kondencj kilrn jet rktycznie niemierzln. Dltego, mkroory odgrywją tylko rolę orów trnortowych. Efektywne romienie zncznie drobniejzych orów rzejściowych mezoorów ą duŝo więkze niŝ rozmiry dorbujących ię cząteczek. N owierzchni tych orów zchodzi jedno- i wielocząteczkow dorcj r, tzn. tworzenie ię kolejnych wrtw dorcyjnych, kończąc ię objętościowym zełnieniem orów według mechnizmu kondencji kilrnej. Wrtości efektywnych romieni mezoorów zwrte ą w grnicch 20 500 Å. Dolny zkre romieni krzywizny meniku (15 16 Å) w orch tych rozmirów, odowid grnicy toowlności równni Kelvin. 80
W zleŝności od toni rozwinięci objętości mezoorów i wielkości ich romieni, owierzchnie włściwe tych orów mogą ię mieścić w grnicch 10 500 m 2 /g. N ogół róŝnice w dorcji r n dorbentch jednkowych od względem chemicznym (nieorowtych, czy z mkro- i mezoormi) mją chrkter ilościowy i wynikją z róŝnych wrtości owierzchni włściwych, oniewŝ krzywizn owierzchni (do oczątku kondencji kilrnej) wykzuje tylko niewielki wływ n dorcję. We wzytkich tych rzydkch owierzchni dorbentu m wyrźny en fizyczny i dorcj r rowdz ię do tworzeni kolejnych wrtw dorcyjnych. Efektywne romienie njdrobniejzych orów mikroorów leŝą oniŝej dolnej grnicy rozmirów mezoorów. Jk wynik z dnych uzyknych metodą nikokątowego rozrzni romieni X, główn objętość rzyd zwykle n mikroory o efektywnych romienich leŝących w zkreie 5 10 Å, więc wółmiernych z wielkościmi dorbownych cząteczek. Jednym z odtwowych rmetrów chrkteryzujących mikroory jet ich ogóln objętość w jednotce my dorbentu, w krjnym rzydku rzekrczjąc niezncznie 0.5 cm 3 /g.
Jednym z odtwowych rmetrów chrkteryzujących mikroory jet ich ogóln objętość w jednotce my dorbentu, w krjnym rzydku rzekrczjąc niezncznie 0.5 cm 3 /g. PoniewŜ kŝdy or tnowi ewną rzetrzeń geometryczną, jego kztłt mui być równieŝ brny od uwgę odcz interretcji odowiednich dnych doświdczlnych. Z owodu nieregulrności truktury orów więkzości cił tłych, rzeczywity ich kztłt znny jet tylko w niektórych rzydkch. Konieczne ztem tje ię toownie modeli tnowiących ewne rzybliŝenie rzeczywitego kztłtu orów. Njbrdziej oulrnym modelem jet model orów cylindrycznych jednotronnie bądź obutronnie otwrtych. Ntęny odnoi ię do orów zwnych ink-bottle butelk trmentu, które ą oiywne rzez dw romienie: zerokość wąkiej zyi, zerokość dolnej części butelki. Trzeci, model zczelinowy, odowid orom, których ściny tnowią równoległe łzczyzny. Ry. 1. Modele orów: ()ory cylindryczne obutronnie i jednotronnie otwrte (b) ory ink-bottle, (c) ory zczelinowe. 82
Poroity of dobent, tht i their ize nd the ore volume, cn be invetigted tking into ccount the cillry condention henomenon. During dortion roce hericl nd cylindricl menicu re formed, but during deortion only hericl one. Therefore the deortion iotherm i ued for determinition of efective ize of the cillrie correonding to the dimenion of cylindricl cillrie. The exerimentl oint on the deortion curve in the rnge of hyterei loo correond to dorbed mount t given reltive reure / o. Multilying nd V m (the liquid molr volume) one cn clculte the cilrie volume V filled with the liquid. Then tking / o correonding to thee vlue nd Kelvin eqution the effective rdiu r k of hericl menicu in the cilltrie cn be obtined, if comlete wetting of the cillry wll i umed. 83
Hving determined everl vlue of V nd r one cn lot o clled tructurl curve of the dorbent, then by it differentition curve of cllrie volume ditribution veru their effective rdii i obtined. The derivtive dv/dr llow conclude bout oroity chrcter of invetigted dorbent. Fig.1. ) Structurl curve, b) Ditribution curve of the cillrie volume function of their effective rdii (mot cillrie hve rdiu r = 5 nm) The he of the ditribution curve of the cillrie volume in Fig. 2b how tht thi dorbent i quite homogenouly orou nd mot robbly their rdiu i bout 5 nm. 84
However, lredy qulittive nlyi of the dortion-deortion iotherm low conclude bout the dorbent tructure. If t l ow vlue of / o the dortion incree hrly nd the hyterei loo er t low reure, thi ugget tht thi dorbent i nrrow-ore nd it ecific urfce deend uon the height of the reverible rt of the iotherm (Fig. 3). If in brod rnge of / o the dortion i mll nd the hyterei loo trt cloe to / o = 1, it indicte for brod-ore dorbent (Fig. 3b). Fig.2. Adortion-deortion iotherm; )on nrrow-ore dorbent, b) on brod-ore dorbent nrrow-ore brod-ore 85
Some method od determintion of ge nd vor dortion The dorbed mount of ge nd vor on olid dorbent nd correonding iotherm re determined by two method: ttic or dynmic. Sttic method: the dorbent i lced in cloed veel with ome mount of g or liquid vor. When the equilibrium i ttined the reure nd dorbed mount re meured. The dorbed mount i determined by the incree of the dorbent mle m or doed mount nd tht remined in the gou he in equilibrium. Before the dortion roce the dorbent h to be outged. The m incree i red out from the ring enlrgement. Fig.3. Method for g or liquid vor dortion determintion uing McBin blnce: 1 cloed gl tube, 2 qurtz ring, 3 n with weighed dorbent, 4 moule with liqid dorbte, 5 mnometer, 6 i 7 thermott. 86
Dynmic method they hve been develoed imultneouly with theory of g chromtogrhy. In fct thee method re chromtogrhic one. Fig.4. Dcheme of g chromtogrh. 1 tnk with buoynt g, 2 vlve, 3 urifind nd dehumidifing filter, 4 mnometer, 5 feeder, 6 column with dorbent, 7 detector, 8 recorder (dt cquition), 9 thermott, 10 g fluometer. The chromtogrhic method relie on jet flow of mixture of n inert g (He, N 2 ) clled buoynt g nd ome mount of dorbing g )or vor through column of dorbent. The ge flowing out of the column re nlyzed until the mximum content of the dorbing g in the inert g i reched, tht i no dortion occure. In thi wy the o clled outut curve re lotted
It i lo oible to elute with the hel of the inert g the lredy dorbed n dorbnt, or concentrtion of the dorbed g cn be nlized in the inert g outlet from the column. From thu lotted curve the mount of dorbed g cn be clculted t given reure, i.e. it i oible to determine the dortion iotherm. 88