DSC Resolution and Dynamic Response Improvements Obtained by a New Heat Flow Measurement Technique. Robert L. Danley, Peter A.

Transcription

1 DSC Resolution and Dynamic Response Impovements Obtained by a New Heat Flow Measuement Technique Robet L. Danley, Pete A. Caulfield TA Instuments, 109 Lukens Dive, New Castle DE ABSTRACT Diffeential Scanning Caloimete heat flow measuements include significant instument effects that educe the dynamic esponse of the signal to sample effects. Fo example, a shap fist ode tansition, like a metal melt displays a potacted exponential decay of the heat flow signal following completion of the melt. This exponential decay is the esult of heat stoage within the DSC senso and the sample pan. A new technique fo measuing DSC heat flow is descibed that yields geatly impoved dynamic esponse. The new measuement technique accounts fo heat stoage within the senso assembly and the sample pan. Dynamic esponse of the heat flow signal is significantly enhanced, impoving the ability of the DSC to sepaate themal events that occu within a small tempeatue ange. INTRODUCTION It is well known that the heat flow signal fom a DSC duing a tansition is an inexact epesentation of the actual sample heat flow. The measued heat flow is delayed and distoted in time (1). This distotion o smeaing of the heat flow signal is the esult of heat stoage within the sample pan and the senso. These heat stoage effects ae pesent in all DSCs, heat flux o powe compensation. Heat stoage within a themal system is analogous to capacitance within an electical cicuit, so that the heat capacity of the sample pan and the senso effectively filte the measued heat flow. Fo many DSC expeiments, the smeaed heat flow is a sufficiently accuate measuement, fo example when heat flow is integated ove a baseline to obtain the enthalpy of a tansition. Howeve, in expeiments whee patial aea integations ae equied, fo example kinetics and puity, the heat flow signal must be de-smeaed (2). The DSC esolution, i.e. the ability to sepaate closely spaced tansitions is impoved when the heat stoage effects of pan and senso ae emoved fom the heat flow signal. Two de-smeaing methods, modeling and numeical deconvolution have geneally been used. The modeling appoach seeks to epesent the DSC by diffeential equations whee the measued signal i.e. the diffeential tempeatue and it s deivatives ae the 1 TA269

2 inputs and the coefficients of the equations epesent the themal chaacteistics of the DSC. De-smeaing using fist and second ode diffeential equations has been demonstated (3,4). A difficulty in pacticing these methods is the detemination of appopiate values fo the instument coefficients (2). Numeical deconvolution seeks to econstuct the sample heat flow by employing the convolution integal equation and the appaatus function, which is detemined by the esponse to an impulsive heat input (1). Numeical deconvolution inceases noise in the heat flow signal and can only be pefomed afte the measuement is complete (2). This pape pesents anothe appoach to obtaining the actual sample heat flow, using a new heat flow measuement. It is based on epesentation of the DSC heat flow measuement by two diffeential equations that use two diffeential tempeatue measuements and the senso tempeatue as input signals. A calibation pocedue is used to detemine the diffeential equation coefficients epesenting the instument. This method also accounts fo slight imbalances in the measuement system that contibute to instument baseline defects (5). The DSC is a twin instument compising two nominally identical caloimetes within an enclosue, the tempeatue of which is contolled to match a desied themal pogam. Heat exchange within the caloimete may be modeled using the lumped heat capacity method whee discete themal esistances and heat capacities epesent the components of the system (6). Figue 1 shows an electical netwok that is analogous to sam Sample and Pans m ps c pan m p c pan T ps T p s R p R p T s R s C s C T R Senso T 0 heat flow within the DSC. Figue 1 DSC Heat Flow Measuement Model The model is divided into two pats, the potion below the boken line (labeled senso) epesents the DSC while the potion above the line epesents the sample and 2 TA269

3 pans. Each caloimete compises a themal esistance and a heat capacity; subscipts s and indicate the sample o efeence caloimete. T s and T ae the measued tempeatues of the sample and efeence caloimetes and T 0 is the tempeatue at the base of the senso, which is epesentative of that of the DSC enclosue. The measued heat flows ae q s, the heat flow to the sample and it s pan and q, the heat flow to the efeence and it s pan. The actual sample heat flow is q sam. A heat capacity C ps and a themal esistance R p epesent the sample pan and the themal esistance between pan and senso. The efeence pan is assumed to be empty, a heat capacity C p and a themal esistance R p epesent the efeence pan and the themal contact esistance between pan and senso. The sample and efeence pan tempeatues ae T ps and T p. Pefoming a heat balance gives the measued sample and efeence heat flows in tems of measued tempeatues T s, T, T 0 and senso themal paametes R s, C s, R, C : T Ts dts T T qs 0 dt & Cs 0 C Rs R substitute the two measued diffeential tempeatues: T T s T T0 T0 Ts into the sample and efeence heat flow equations to obtain the heat flow measuement equations: T0 dts T0 + T dts d T s Cs C Rs R Themal esistances and heat capacities ae obtained using a two pat calibation method (5). The measued sample heat flow includes the sample and pan heat flow and, likewise, the measued efeence heat flow is the sum of the pan and efeence heat flows. The objective of the measuement is to ecove the tue sample heat flow q sam. The measued sample heat flow is the sum of the sample and sample pan heat flows: dtps s sam + m psc pan The measued efeence heat flow is just the pan heat flow because the efeence pan was assumed to be empty: dt q & p m pc pan Using the efeence heat flow equation to eliminate the pan specific heat capacity and solve fo q sam : dtps m ps sam s dtp m p This equation gives the actual sample heat flow and accounts fo pan mass imbalances and diffeences in heating ate between the sample and efeence pans. The heat flow measuement equations include imbalances and diffeences in heating ate between the sample and efeence caloimetes. Conventional DSC heat flow measuements do not include the senso imbalances o the diffeences in heating ate between the sample and efeence caloimetes and pans. The heating ate atio accounts fo the fact that duing a DSC expeiment the heating ates of the sample and efeence pans may be diffeent, fo example duing a tansition. In conventional DSC, the heat 3 TA269

4 flow measuement is in eo because the efeence pan always heats at the pogammed heating ate. When the sample pan heating ate is highe o lowe than the pogammed heating ate, the efeence heat flow offsetting the sample pan heat flow is too low o too high. The same comments apply to the senso heat flow. The heat capacity tems in the heat flow measuement equations account fo diffeences between the sample and efeence senso heating ates. To use this heat flow measuement method, the sample and efeence pan tempeatues ae needed, they ae not measued diectly but may be obtained fom the measued quantities. Heat flow between the sample and efeence pans and thei sensos ae given by: Ts Tps T Tp s R R Which ae solved to find the pan tempeatues: T T R p ps s s p T p T qrp Senso tempeatues and heat flows ae measued, the pan contact esistance R p is needed to detemine the pan tempeatues. A model equation is used to calculate the contact esistance between the pan and senso. The model assumes that thee ae two paallel heat conduction paths between the pan and the senso, one is solid conduction though the senso and pan whee they contact one anothe and the second is conduction though the gas laye between the pan and senso. The equation used fo the contact esistance is: 1 Rp R + R R pan Whee, the component themal esistances ae calculated fom: 1 R α k K is the themal conductivity of the pan, senso o puge gas and α is a geometic facto fo the pan, senso o puge gas that is equivalent to the atio of an aea to a length. Themal conductivities fo each component as a function of tempeatue ae known, the geometic factos have been detemined fom a cuve fit of expeimental data. The geometic factos ae dependent upon the pan and senso shape. Typical values of the geometic factos ae supplied in the instument softwae fo selected pan types. These capabilities ae incopoated in the TA Instuments Q1000 DSC (5,7). EXPERIMENTAL A TA Instuments Q1000 with a RCS (mechanical efigeation cooling system) was used to pefom the expeiments shown below. The instument was calibated pe the manufactue s instuctions, including calibation of the senso themal coefficients. The DSC cell was puged with nitogen, cimped aluminum pans wee used with 5.64mg indium and 1.13mg dotiacontaine samples. RESULTS AND DISCUSSION Figue 2 shows an indium melt at 20 C/min. Two heat flows ae plotted, the conventional DSC heat flow and the heat flow accoding the Advanced Tzeo heat sen gas p & 4 TA269

5 flow measuement of this pape. The conventional DSC heat flow signal is popotional to the Diffeence between sample and efeence tempeatue. E( T ) T Compaing the Advanced Tzeo heat flow to the conventional heat flow, the peak height inceased fom 23.2mW to 29.9 mw and the peak wih at half height has deceased damatically fom 2.26 to 0.82 C, epesenting a thee fold eduction in peak wih. The onset and peak tempeatues ae slightly lowe due to the elimination of themal lag of the sample caloimete and sample pan. The baseline etun at the completion of the melt is much faste, coesponding to impoved dynamic esponse that yields bette esolution. Heat Flow (mw) C 0.82 C mW C C 2.26 C mW C Conventional DSC Advanced Tzeo Tempeatue ( C) Figue 2 Indium Melt Tzeo vs. Conventional DSC Figue 3 shows the esult of a 10 C/min DSC expeiment with a 1.13mg sample of dotiacontane, a C32 hydocabon. Two heat flow signals ae shown; Advanced Tzeo and conventional DSC. This sample has thee closely spaced tansitions demonstating the sepaation ability of a DSC (i.e. the esolution). The fist two tansitions ae baely sepaated fom one anothe by conventional DSC, wheeas Advanced Tzeo shows a substantial impovement in the sepaation. Howeve, between the second and thid tansitions, Advanced Tzeo clealy achieves a baseline, whee conventional DSC does not. In this case, the ability to accuately detemine the enthalpy of the thid tansition is impoved by Advanced Tzeo as compaed to conventional DSC. All peak heights ae substantially inceased while peak wih is consideably educed. Analysis of additional expeiments confims the impoved esolution (8). 5 TA269

6 Heat Flow (mw) Advanced Tzeo Conventional DSC Tempeatue ( C) Figue mg Dotiacontane at 10 C/min CONCLUSIONS A new method of measuing heat flow in DSC is descibed that impoves the measuement by including the heat stoage effects of the senso and the pans. The heat stoage effects manifest themselves in any DSC expeiment whee the sample and efeence heating ates ae not identical. That includes tansitions in DSC and geneally all MDSC expeiments. A key featue of this new measuement is that the sample and efeence heat flows may be measued sepaately, allowing the diffeence in heating ates between sample and efeence senso and pans to be accounted fo. The esult is that the actual sample heat flow is measued. A calibation method is used that allows the chaacteistics of the DSC to be detemined. REFERENCES 1. G. W. H. Höhne, Themochimica Acta, 1978, 22, G. W. H. Höhne, W. Hemminge H.-J. Flammesheim, Diffeential Scanning Caloimety, 1996, K. H. Schönbon, Themochimica Acta, 1983, 69, K.-R. Löblich, Themochimica Acta, 1985, 85, R. L. Danley, P. A. Caulfield, Poc. 29 th Conf. N. Ame. Them. Anal. Soc., J. P. Holman, Heat Tansfe, 4 th Edition, 1976, L. Waguespack, R. L. Blaine, Poc. 29 th Conf. N. Ame. Them. Anal. Soc., P. A. Caulfield, R. L. Danley, Poc. 29 th Conf. N. Ame. Them. Anal. Soc., TA269