DTA & DSC

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    Chapter 3

    Differential Thermal Analysis andDifferential Scanning Calorimetry

    P. G. LayeCe ntre o r Thermal Studies, University of Huddersfield, U K

    INTRODUCTION

    Differential therm al analysis (DT A) an d differential scanning calorim etry(DSC)ar e the m ost w idely used of all th e therm al analysis techniques. Theconcept underlying the techniques is simple enough: to o bta in informa-tion o n thermal changes ina sample by heating o r cooling it alongside aninert reference. Historically the techniques have their origin in themeasurement of temperature. Figure1 is a schematic representation ofthe main par ts of an instrum ent. The sample an d reference are containedin the D TA /DS C cell. Temperature sensors and the m eans of heating thesample an d reference a re incorporated in th e cell. O th er terms which havebeen used to describe this part of the instrument include specimenholder assembly an d more recently instru men t test chamb er. A singlecom pute r unit operates the various contro l functions, da ta cap ture an danalysis. Th e term differential emphasises an im po rta nt featureof thetechniques: two identical measuring sensors ar e used, one for the samp leand on e for the reference, an d the signal from the instrum ent depe nds o nthe difference between the response of the two sensors. In this way thesignal represents the thermal change to be studied free from diversetherma l effects which influence both sensors equally. This ha s the c on -siderable merit of allowing high sensitivities to be designed into instru-ments. Th e natu re of the measuring sensors an d the form of the instru-

    men t signal are discussed later in the ch apter.It is the link with thermal energy which is responsible for the wide

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    56 Chapter 3

    Data capture

    analysisOutput device

    Figure 1 Schematic representation of a DTA or D S C instrument

    ranging applicability of both DTA and DSC. Unlike thermogravimetrythe techniques are not dependent on the sample undergoing a change inmass. DSC is the more recent technique and was developed for quantitat-ive calorimetric measurements. DTA does not lend itself to such measure-ments and has progressively been replaced by DSC even for measure-ments in the range 750-16OO0C, which at one time were the sole provinceof DTA. DTA still finds application in the measurement of characteristictemperatures and in the qualitative identification of materials. It remainsthe technique for measurements above 1600C where the high tempera-tures impose considerable design constraints on equipment. The tech-niques are most readily applied to the study of solids and whilst theirapplication to liquids is not uncommon more careful attention to experi-mental practice is required. The small size of samples, often only a few mg,and the rapidity with which experiments can be carried out have played

    an important part in establishing the popularity of the techniques.The present chapter concentrates on the basic features of the tech-

    niques and the use of commercial equipment to make various measure-ments. Theoretical considerations have been limited to setting out theessential ideas. In contrast experimental procedures are discussed at somelength. It is not possible to derive explicit working equations whichpermit the interpretation of experimental data by anything approachingfirst principles. However, calibration may be used to circumvent limita-tions in the theory and forms the basis of all quantitative measurements.In this context it is important to remember that no determination can bemore precise than the calibration and this remains true even with the use

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    58 Chapter 3

    Beparate sample ana reference temperaturesensars a+drnaces

    iample and reffrence thermocouples Singie furnace

    Figure 2 (a) Power-compensation diflerential scanning calorimeter.(b )Hea t JEux differen-tial scanning calorimeter

    perature difference established when the sam ple an d reference a re heatedin the same furnace. The temperature difference is measured by thetemperature sensors - usually thermocouples arranged back-to-back.Figure 2(b) shows the arrang eme ntof the thermocouples and the singlefurnace. The difference between heat fluxDSC and DTA lies in theconversion of AT in to differential power. T he algo rithm for this conver-sion is contained in the instrumen t software. Th e designof the DSC cell is

    critical if the algorithm is to be transferable from one experiment toano ther, independent of the sample. The heat flux app roa ch isa develop-ment of older forms of quantitative DTA .

    Bo th types of differential scan ning calorimeters m ak e useof a crucibleto contain the sample. The reference is either an inert material inacrucible of the same type as that used for the sample or simply the em ptycrucible. Crucibles com mo nly m easure5-6 mrn in diameter, which givessome idea of the overall dimensions of theDSC cell.

    It is the provision of dynamic conditions in which the sample issubjected to a controlled heating or cooling program which setsDSCapart from other calorimetric techniquesand is a key factor in its wide

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    Diflerential Ther mal Analysis and Differential Scanning C alorim etry 59

    range of different applications. Most differential scanning calorimetersare of the heat flux type. Recently a differential scanning calorimeter hasbeen designed which incorporates features of both power compensation

    and heat flux instruments.The results from DTA and DSC experiments are displayed as a thermal

    analysis curve in which the instrument signal is plotted against tempera-ture - usually the sample temperature - or time. Figure 3 shows some ofthe terminology relating to the results from DSC experiments. The de-scription heat flow is frequently used for the instrument signal. Analysisof the thermal analysis curve is carried out using the instrument software.Of particular importance is the extrapolated onset temperature T , which isdefined as the temperature of intersection between the extrapolated initial

    base line and the tangent or line through the linear section of the leadingedge of the peak. This temperature rather than the peak maximumtemperature T, is frequently used to characterise peaks because it ismuch less affected by the heating rate. The temperatures Ti and Tf re theinitial and final temperatures of the peak which are sometimes moredifficult to pin-point precisely. The terms isothermal and dynamicrefer to the operating mode of the instrument. In the figure the peakrepresents an exothermic event (exotherm)and has been represented as apositive displacement. This is the usual convention for DTA and heat fluxDSC. In the case of power-compensation DSC exotherms are negativedisplacements. Where confusion is likely to arise the direction of theexotherms/endotherms should be shown on the thermal analysis curve.In the present chapter the thermal analysis curves have been represented

    Figure 3

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    60 Chapter 3

    using the DTA convention with the exception of Figure 7 where theoryrequires a positive displacement for the endotherm of fusion,

    The alternative format for the thermal analysis curve is the plot of the

    instrument signal against time. The quantitative advantage of DSC overDTA lies in the relationship between the area enclosed by peaks meas-ured in this format and the corresponding heat change: unlike DTA, withDSC the proportionality is independent of the heat capacity of thesample.

    APPLICATIONS

    The versatility of DTA and DSC can be seen in both the range ofmaterials studied and the type of information obtained. From the stand-point of materials studied the techniques may be regarded as virtuallyuniversal in their applicability. Some idea of the range is given in Table 1.Although DSC is a quantitative technique it finds application alongsideDTA as a qualitative tool whereby the thermal analysis curve is used as afingerprint for identifying substances. The techniques may form part of aquality control procedure in which the presence or absence of a peak inthe thermal analysis curve is all that is relevant. The identification ofpolymorphs in the context of pharmaceuticals is particularly relevant

    since different species may have quite different physiological actions. Theinvestigation of potential reactivity between components of drugs asrevealed by changes in the thermal analysis curve represents anothersignificant application of these techniques. DTA and DSC have foundvaluable application in the study of phase diagrams both in pharmaceuti-cals and more widely in the general area of material science.

    The greatest impact of the techniques has been seen in the study ofpolymeric materials with crystallinity and melting behaviour, glass tran-sitions, curing processes and polymerisation representing the differenttypes of thermal behaviour under investigation. A measure of the import-ance of this area of activity is reflected in the considerable number ofpublications and conference presentations it has generated.

    Figure 4 illustrates the application of DSC to the study of polymers.

    Table 1 Mate rials studied by D T A and D SC

    Polymers, glasses and ceramics PharmaceuticalsOils, fats and waxesClays and MineralsCoal, lignite and woodLiquid crystals CatalystsExplosives, propellants a nd pyrotechnics

    Biological materialsMetals and alloysNatural products

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    Diferential T h e r m a l Analysis an d Diferential Scan ning Calori metry 61

    50 100 150 200 250 30 0Temperature/'C

    Figure 4 Thermal analysis cum e o r poly(ethy1ene terephthalate)

    Th e curve is for poly(ethy1ene terephthalate)(PET) heated in N, at 10Cmin-'. The curve shows a displacement at60-70C arising from the glasstransition a nd peaks a t extrapolated onset temperatures of abo ut110Cand 255 "C for crystallisation an d m elting respectively. In the figure thetransitions are particularly well defined. However, both the physicalproperties and the composition and history of polymers affect glasstransitions a nd crystallisation. T he tem peratureof the glass transition isno t fixed but is depen dent on the rate of heating. Th e displacement oftenshows additional structure making the analysis much less straightfor-ward than in the present example. At higher temperatures the thermalanalysis curve would reveal the onset of degradation- hermal analysisoffers a com paratively simple way of assessing the relative thermal stabil-ity of polymers.

    The study of clays and minerals played an important role in thedevelopment of DTA as an investigative technique. In some instancesDTA and DSC provide one of the few routes to the identificationofminerals. An ingenious m e t h ~ d , ~legant in its simplicity, whereby theidentity of a component in a mixture can be confirmed is to add thesuspected m ineral to thereference crucible an d repeat the thermal analy-sis experiment. The relevant peaks should show a diminu tion in size.

    One of the most celebrated examplesof the application of DTA andDS C to m aterial science, which ha d a pub lic impact som e30 years ago, isshown in Figure 5. It relates to the use of high a lum ina cement which insome circumstances led to the weakening and in extreme cases the

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    62 Chapter 3

    1

    100 200 300 400 50 0TemperaturelC

    Figure 5 Thermal unulysis curvefor high alumina cement

    collapse of concrete structures. The problem arose from the conversion ofthe initial product of setting CaO~Al,O,~lOH,O nto the hexahydrateand gibbsite (hydrated alumina). The issue became acute and DTA andDSC offered a rapid route to the determination of the extent of conver-sion. Many thousands of determinations were carried out to identifythose cases where further structural investigations were needed. In thefigure the endothermic peaks are for the dehydration of the decahydrate,gibbsite and hexahydrate in order of increasing temperature. The extentof conversion is defined as the amount of gibbsite/(amount of decahyd-rate + gibbsite). The height of the peaks is taken as a measure of theamounts so that the extent of conversion becomes y/(x + y ) . In practice acalibration is carried out using a sample of known composition. The useof peak heights instead of the more correct use of areas to determine

    amounts is convenient where peaks overlap. DTA and DSC continue tofind application in the investigation of the complex reactions in cementsys ems.

    Figure 6 illustrates the application of DSC to the determination of theoxidative stability of Figure 6(a) shows the thermal analysis curvefor the isothermal test in which the time to oxidation (toxid)is measuredwhen the sample is maintained at a constant temperature in an atmos-phere of 0 ,. An alternative test is dynamic where it is the temperature ofoxidation which is measured. Specialised equipment is necessary for theisothermal test, which usually employs a pressure of about 3.5 MPa. Anobvious advantage of both tests is that the performance of oils can be

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    Differential Thermal Analysis and Differential Scanning Ca lorimetry 63

    0

    9-.I

    c-8

    7

    6

    a

    '

    200 OC

    250 500 750 1000 1250Timeh

    RT S + DODPA

    RTS

    t 2. 0 2.1 2. 2 2-;03T.l,Kl 2 I

    Figure 6 Oxid ative stability of oils. (a) sothermal test experime nt.(b) Determination of th eactivation energy of the induction reuction (abbreviations defined in the t e x t)

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    64 Chapter 3

    monitored without recourse to expensive and time-consuming enginetests. Furthermore it is possible to study the catalytic effects of metalsurfaces on the oxidation. The reciprocal of time to oxidation has been

    taken as a measure of the rate of an induction reaction which has allowedthe kinetics to be explored. Figure 6(b) shows the results for an ester basestock (LPE) and a synthetic base stock made from oligomerisation ofdec-1-ene (RTS) and mixtures containing 1.5% by mass of the anti-oxidant dioctyldiphenylamine (DODPA). The activation energies rangefrom 70 to 130 kJ mol -l . Regardless of the precise significance of thesevalues the true focus of interest lies in the variation from one base stock toanother, with and without the addition of antioxidants.

    Table 2 lists some of the quantitative measurements that can be under-taken by DSC. With modern equipment and software some of these havebecome largely a matter of routine. Even so some thought is necessary!Computer software has the propensity to produce answers to an im-pressive number of figures which may well be totally unrealistic. It is alltoo easy to forget that calorimetric measurements involve ther-modynamic principles and that only by adhering to these can properlydefined thermodynamic quantities be obtained. In spite of these reserva-tions many determinations can be carried out with a minimum of diffi-culty. The American Society for Testing and Materials (ASTM) hasdescribed in considerable detail the use of DTA and DSC for a number ofdifferent measurements.

    The use of DSC to investigate chemical kinetics deserves special men-tion. It has excited more interest and more controversy than perhaps anyother area of application. It continues to generate an enormous output ofliterature. The basis for obtaining kinetic parameters is to identify the rateof reaction with the DSC signal and the extent of reaction with thefractional area of the peak plotted against time. It is possible to obtain thethree variables, rate of reaction, extent of reaction and temperature bycarrying out a series of isothermal experiments at different temperatures

    in much the same way as in classical kinetic investigations. The experi-mental procedure is not without its difficulty but the interpretation of theresults is less contentious than with the alternative dynamic procedures.

    Table 2 Quantitative measurements b y DSC

    Heat capacityEnthalpies of transitions and transformationsPurityChemical kineticsVapour pressure

    Thermal conductivity

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    Differential Thermal Analysis and Diflerential Scanning C alorime try 65

    However, it is these very procedures which exploit the unique capabilityof DSC. There has been something of a drive towards obtaining kineticconstants from a single dynamic experiment. Although the results ob-

    tained in this way may fulfil a useful function further tests are invariablyneeded to explore the possibility of limitations to their applicability.Advantages have been claimed for sample controlled kinetic experimentsin which the experimental conditions are varied in order to maintain therate of reaction constant. This has proved a popular method of tempera-ture control in thermogravimetry although in principle it can be appliedto DSC.

    A standard test method for the determination of the kinetic constantsfor thermally unstable substances is one of the procedures published by

    ASTM E 698 (1999). The development of the test originally in 1979highlighted the use of DTA and DSC for the investigation of potentiallyhazardous materials. This is an area of application which has continuedto gain in importance with the heightened awareness of safety issues.Once again it is the need for small samples and the rapidity of theexperiments which makes the techniques invaluable often as a prelimi-nary to longer term and larger scale experiments such as adiabaticstorage tests. Software is available which allows the assignment of kineticparameters and the calculation of hazard potential. ASTM E 1231 (1996)describes standard practice for calculating the time-to-thermal runaway,critical half-thickness, critical temperature and adiabatic decompositiontemperature rise.

    THEORETICAL CONSIDERAT IONS

    Theoretical considerations can provide useful pointers to the interpreta-tion of thermal analysis curves, can account for many of the empiricalobservations and offer guidance for good experimental practice. A theor-etical approach requires spatial and temporal descriptions of the heat flux

    within the DTA/DSC cell from all forms of heat transfer across allinterfaces. It is hardly surprising that explicit working equations cannotbe derived. However, a great deal can be achieved using a simple ap-proach which has the advantage of being easy to visualise. Such anapproach was that adopted by Gray where well established heat transferequations were used to obtain expressions for DTA and power compen-sated DSC signals. Whilst Grays analysis was concerned with bothtechniques our attention will be focused on DSC.

    The aim was to derive an expression for the instrument signal inresponse to the evolution of heat from a sample as represented by dhldt.The sample and its crucible were considered as one with a total heat

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    66 Chapter 3

    capacity C,. A similar assumption was made regarding the referencematerial and its crucible, which together had a total heat capacity C,. Itwas assumed that there is a source of thermal energy at temperature T p

    and a single thermal impedance R between the sample and the source ofthermal energy and between the reference and the source of thermalenergy. The heat flow between the thermal energy source and the samplewas represented as dq/dt as measured by the instrument. The heating ratewas represented by dT,/dt = p and assumed to be linear. Gray obtainedthe equation,

    dh/dt = - dq/dt + (C s - CR)dTP/dt - CS d2q/dt2. (1)I I1 I11

    Thus the heat evolution from the sample is given by the instrument signalmeasured from zero (term I), a heat capacity displacement (term IT) and athird term which includes the product RC,. This product has units of timeso that term 111 represents a thermal lag. Included in the publication was arecipe for obtaining dh/dt from the experimental curve by making allow-ance for thermal lag. For inert samples dh/dt = 0 and the displacement(term 11) provides a route to the determination of heat capacity.

    The model serves to focus attention on the need to reduce thermal lagas much as possible. Although the contribution to thermal lag from the

    instrument is fixed by the nature of its design the practitioner has somecontrol over the contribution from the sample and crucible. For example,the use of small samples and slow heating or cooling rates, good contactbetween the sample and crucible and between the crucible and thetemperature sensor will all reduce thermal gradients.

    Gray also discussed the shape of the leading edge of the peak for amelting transition,

    dq/dt = (Cs - CR)dTp/dt + R-l(dT,/dt)t.I I1

    Thus the gradient depends on the product of R -' nd the heating rate(dT,ldt) (term 11) and provides a method which has been used to correctfor thermal lag in assigning temperatures. Figure 7 shows the meltingcurve as described in Gray's theory.

    Amongst the plethora of papers which have followed Gray's work thatof Baxter' is interesting in that it presents a different perspective on DSC.Using a similar approach to that of Gray but involving two thermalimpedance terms Baxter was able to relate the heat flux DSC signal to

    AT.Bearing in mind that differential power in power compensation DSC

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    Differential Thermal Analysis and Diferentia l Scanning Calo rimetry 67

    w

    \-0

    m-0 Gradient = R-(dT, , /d t )

    Time

    arises in response to an outer balance AT the distinction between the twotypes of DSC becomes blurred. For most purposes the results from thetwo approaches can be regarded as indistinguishable.

    MTDSC represented something of a revolution in thermal analysiswith an impact which has been compared to that of the original introduc-tion of power compensation DSC. Numerous publications have ap-peared devoted to the complexity of the theory and the data manipula-tion techniques needed before useful information can be obtained.Fortunately all the hard work is done by the instrument software.Rather like conventional DSC, useful information can be obtained with-out recourse to the detailed theory.

    The starting point adopted by Reading and co-workers is a descrip-tion of the heat flow into the sample which occurs as a result of thesinusoidal modulation of the temperature program,

    Q / d t = C& + f ( t , T ) .I I1

    ( 3 )

    Term I represents the heat capacity component of the signal. It is assumedthat this component follows the periodically changing heating rate and isreferred to as the reversing signal. The term f ( t , T ) is any kineticallyhindered thermal event and is regarded as non-reversing. ConventionalDSC provides a measure of the total thermal power dq/dt whereasMTDSC allows the two components to be determined. The terms revers-ing and non-reversing relate to the conditions of the experiment. For

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    68 Chapter 3

    E ,s

    i!

    example the sample size and the period of modulation will influence theability of the sample to follow the temperature modulation and hence theapparent value of the heat capacity. It follows that the choice of experi-

    mental conditions is critical in MTDSC, far more so than in conventionalDSC since it involves the selection of the period and amplitude of themodulation in addition to the underlying heating rate. To some extentthese variables are interdependent. The aim is to achieve 4-6 cyclesduring the thermal event of interest The underlying heating rate can beset to zero in which case measurements are carried out under quasi-isothermal conditions. The software produces an output of the experi-mentally measured modulated heat flow and the modulated heating ratewhich can be used to judge whether the experiment has been carried outunder satisfactory control. A plot of modulated heat flow against tem-perature should show a smooth modulation.

    MTDSC has become very much the established technique in the studyof polymeric materials where its advantages over conventional DSC canbe exploited. Figure 8 illustrates the use of MTDSC for the separation ofoverlapping thermal events in a poly(ethy1ene terephtha1ate)-acrylonit-rile butadiene styrene (PET-ABS) blend. The thermal analysis curve forPET alone was shown in Figure 4. The present figure shows the total heatflow for the blend and its separation into the reversing and non-reversing

    c

    Exotherms

    ;on-reversing

    Reversing\40 60 80 100 12 0 140 160 1

    Temperature/ O C

    Figure 8 Modulated D SC curve fr om u sample of P E T-A B S blend. (T he kar e difleerent o r the three curves)

    0

    xtjlo w scules

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    Diferential Thermal Analysis and Differential Scanning Calorimetry 69

    components. The glass transition temperature for P E T is shown at abo ut65 "C and for ABS at 105"C. Crystallisation of P E T is shown a s a peak inthe non-reversing curve and is also at ab ou t 105"C, which would mask

    the glass transition ofABS in conventional DSC .

    INSTRUMENTATION

    Specification

    Th e aim here is simply to present a n overview of the va rious features onoffer. The range of instruments extends from differential scanningcalorimeters in a suitcase for on-site use to spatially resolved micro-thermal analysis equipm ent for samples as minute as 2x 2 pm. Betweenthese rather extreme examples there is a wide choice of comm ercial DTAand D SC eq uipm ent which allows samples to be studied a t tempe raturesranging from - 50C to abou t 1600C. F or higher temperaturemeasurements (above1600 "C) the e quipm ent becomes increasingly m orespecialised. The detailed specificationof equipment is often difficult(sometimes impossible!) to decipher- here appears to be no commonpractice between manufacturers. Information can best be obtained byraising questions directly with the manufacturers. Evenso, hands-onexperience is to be recom mended when ch oosing equipmen t.

    Temperature Sensors

    In pow er com pensated D SC the small size of the individual sample andreference holders m akes for rapid response. Th e tem perature sensors areplatinum (Pt) resistive elements. The individual furnaces are made ofPt/R h alloy. It is imp ortan t th at the thermal characteristics of the sam pleand reference assemblies be m atched precisely. The m aximu m operatingtempe rature is limited to a bo ut 750 "C. High tempe rature D SC m easure-

    ments (750-1600C) are made by heat flux instruments using ther-mocouples of P t and Pt/Rh alloys. Th e thermocouples often inco rpora tea plate to sup port the crucible. The use of precious metal thermoco uplesis at the expense of a small signal strength. Both chromel/alumel andchromel/constantan are usedin heat flux D SC equipment for measure-ments a t temperatures to abo ut 750 "C. M ultiple thermocouple assem-blies offer the possibility of an increased sensitivity- recently a20-junction Au/Au-Pd thermocouple assembly has been developed.Thermocouples of W and W/Re are used in D TA equipment for measure-ments above 1600C. The operating temperature is the predominantfeature which determines the design and the materials used in the con-

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    70 Chapter 3

    struction of the D TA /DS C cell. Th e performance of therm ocoup les canchange with time d ue to chemical contam ination a nd mechanical stressan d as a result it is not possible to a do pt a once an d for all calibration.

    Crucibles

    M ention has already been made th at samples can be as smallas a few mgalthough such a size can raise considerable problems in obtaining arepresentative sample. The choiceof crucibles depends o n the construc-tion of the DT A/ DSC cell, the reactivity of the samp le an d the tem pera -ture range over which me asurem ents are to be mad e. The most frequentlyused crucibles for low and moderate temperatures,- 50C to abou t

    600C, are made of aluminium a nd can be ofa shallow or deep design.Th e tem perature, 60 0C , is still well below th e m elting tem perature ofaluminium (660C) bu t a t higher tem pera tures th ere is the risk of irrevers-ible (and very expensive!) dam age to temperature sensors arising fromalloying reactions. Lids are available which c an be crimped into positionusing a specially designed press. In som e experiments, such as mea suringboiling tem peratures,a fine hole is pierced in the lid. Crim ped c ruciblescan withstand a n internal pressure of ab ou t0.3 M P a. Crucibles made ofplatinum are used for high temperature measurements but it should beremembered th at p latinum is not entirely resistant to chemical attack a thigh temperatures. Crucibles madeof silver, gold, qua rtz, alum ina a ndgrap hite a re all available com mercially. Also available a re stainless steelcrucibles with lids which screw down on a gasket. These will retain apressure of 10 M P a but are relatively massive(1 g) and considerablyincrease the effective response time of the equipment. More specialisedare glass capillary tubes which fit snugly inside a small m etal block thattakes the p lace of a con ven tional crucible. Liquid sa mp les can be d istilledinto the capillary tubes o r introducedvia a syringe. Introducing a solidcan be mu ch m ore time-consuming! Th e tubes are sealed usinga very fine

    flame whilst cooling the sam ple.

    Temperature and Atmosphere Control

    Co mp uter software is responsible for the en tire operatio n of equ ipmen t-a t one time th e emph asis seemedto be more on presentation of results.Heating rates from0.1 to 500C m i 6 a n be selected depending on theparticular equipment: the high rates are seldom used in measurementsbut do allow temp erature reg ions of interest to be reached quickly. Evenso M atho t and co-workers7 have pointed ou t that there is a need formu ch higher heating and cooling rates in o rder to investigate polymers

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    Differential Thermal Analy sis and Differential Scanning Ca lorimetry 71

    under conditions similar to those used in processing. High cooling ratesare also important since these increase the through-put of work - often animportant commercial consideration. All equipment is designed to allow

    close control of the atmosphere in the DTA/DSC cell. Most experimentsare done with a flowing atmosphere using flow rates from 10 to 100 cm3min? Atmospheres may be reactive or inert but in the case of reactiveatmospheres the possibility of reaction with materials used in the con-struction of the DTA/DSC cell needs to be taken into account. Someequipment has the in-built facility to switch from one gas to anotherduring the course of an experiment.

    Cooling Systems and Accessories

    A variety of optional cooling systems is available from manufacturers tomeet different needs. They are essential if controlled heating or coolingexperiments are to be carried out below room temperature. More modestcooling may be used to enhance control at room temperature or justabove. In MTDSC, cooling may be needed to ensure that the selectedtemperature modulations are attainable. Cooling systems are also used tofast-cool equipment following high temperature experiments. In thiscontext a simple electric fan may be all that is necessary or top-coolingby means of a cooled metal block which fits into the DTA or DSC cell. Anumber of manufacturers have marketed robotic systems for automaticloading of samples. Commercial equipment is also available for highpressure DSC (HPDSC) in which the entire DSC cell can be pressurisedto about 7 MPa and for photoDSC in which samples can be illuminatedwith UV radiation in order to initiate reactions. Most thermal analyserscan be linked to analytical equipment such as mass spectrometers andsome allow both DSC or DTA and thermogravimetry to be carried outsimultaneously on the same sample.

    Calvet-type Equipment

    An alternative approach to the design of differential scanningcalorimeters is to place the sample and reference inside a relativelymassive calorimetric block which acts as a heat sink. The main features ofthe apparatus are shown in Figure 9. The instrument signal is obtained bymeasuring the heat flux between the sample and calorimetric block, andthe reference and calorimetric block using thermopiles. The temperaturesignal is derived from a sensor in the block. The design based on that ofCalvet has been used in calorimeters operating at a single temperaturebut is also used in DSC instruments where the temperature of the block

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    72 Chapter 3

    Separate sample and referenceFurnace windings

    thermopiles \

    Figure 9 Calvet-type dife rentia l scanning calorimeter

    may be raised or lowered. This type of DSC has the advantage of beingable to accommodate very much larger samples and allows for moreversatile experiments. The increased sample size and stable temperatureenvironment increases the effective sensitivity of the apparatus but thedownside is a very much longer response time and very slow heating andcooling rates. Mackenzie* has provided a comprehensive discussion ofthe relationship between the design of equipment and the nature of theinstrument signal.

    EXPERIMENTAL CONSIDERATIONS

    Variables

    Wendlandtg identified some 16 variables which influence the results fromDTA and DSC experiments. Whilst many are attributable to the designof the equipment or to the inherent properties of the sample there remains

    a core of variables where the practitioner is able to exert some control.Sample preparation and containment, heating rate and atmosphere allcome within this core and even small refinements in technique can oftenenhance the quality of the results. Two somewhat extreme examplesillustrate the need for careful control of experimental technique. The firstis the well-known example of the decomposition of an oxalate to carbon-ate and CO. This is an endothermic process but the thermal analysiscurve will show an exotherm due to combustion of CO if there is a trace ofair remaining in the apparatus. The second example illustrates how theuse of a crucible with an ill-fitting lid may give rise to ambiguous results.Thus, in the study of emulsion explosives the vaporisation of the sample

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    Dif ere ntia l Th ermal Analysis and DifSerential Scanning Calo rimetr y 73

    can lead to an extreme distortion in the shape of the exotherm.

    DOS nd Do nots

    Crucibles should be clean and free from all traces of contaminants fromtheir manufacture. Pre-treating the crucible by heating over the tempera-ture range of the experiment beforehand is a useful ploy for ensuring theabsence of unwanted signals during the experiment. The nature of acrucible surface may be another variable that needs to be considered.There are situations where the crucible may act as a catalyst as in themeasurement of oxidation temperatures of oils.

    Remember the importance of ensuring good contact between thesample and crucible and between the crucible and the thermocouple orother measuring sensor. It may be possible to flatten the base of thecrucible by pressing it against a flat metal block. Whenever practicable,samples should be pressed into the crucible, perhaps by means of a lid oreven a second crucible.

    Contact between a sample and crucible in fusion experiments can beimproved by pre-melting the sample to give a uniform coating over thebase of the crucible. This has the effect of enhancing the shape of thesubsequent endotherm with the proviso that no reaction has occurred.However, even here care is needed: the opposite effect is observed whenpowdered gold is melted to give globules which have poor thermalcontact with the crucible.

    A liquid may be introduced into a crucible using a syringe. Care isneeded not to wet the outside of the crucible, particularly when crimpinga lid into place. A tall sided crucible may be selected where there is atendency for a liquid to spread over the surface or if reaction productstend to creep.

    When a crucible is to be used more than once in a series of measure-

    ments it must be replaced each time in precisely the same position. Onesuch example is in the measurement of heat capacity. Thermocoupleassemblies are often designed to facilitate the repositioning of the cru-cible.

    A cautionary dont is to pre-treat the sample without prior knowl-edge of the relevance of its history. Grinding a sample to a fine powder togive good contact with the crucible may introduce spurious thermaleffects. The form of crystals, their size and shape, may be importantfactors in the kinetic behaviour of a sample.

    When selecting an experimental procedure bear in mind the previouscomments regarding aluminium crucibles and avoid their use above

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    74 Chapter 3

    400C. Be aware that alloying reactions can also occur when usingplatinum crucibles. Take into account the possibility of corrosive attackon thermocouples by some reaction products. A well-known example is

    HCl, which is evolved in the degradation of chlorinated polymers andreadily attacks some thermocouple combinations even at modest tem-peratures. Poor reproducibility of the base line is often an indication of acontaminated cell. Don't attempt to clean DTA and DSC cells by scour-ing the surfaces. Gentle cleaning by brushing and heating in air should beall that is necessary. If alloying has taken place it is probably too late toretrieve the situation.

    Be aware of the need to examine thermal analysis curves before subject-ing the results to detailed analysis. Spurious signals are all too frequent

    and can arise for a number of reasons-

    amples bubbling, a spasmodicescape of gas from the crucible and even the movement or distortion ofthe crucible itself.

    The choice of temperature program often involves a compromise. Thedesire for a large signal by use of large samples or high heating (orcooling) rates may lead to an unacceptable thermal lag. However, ther-mal lag is less of a problem now with the high sensitivity of modernequipment which allows the use of small samples. A heating rate of 10Cmin-' is commonly used - at least in a preliminary investigation. Experi-ments should be started some 30C below the temperature of interest sothat a quasi-steady-state can be established before making measure-ments.

    Figure 10 shows the effect of heating rate on the fusion peak of indiumdisplayed against temperature (a) and against time (b). The curves illus-trate the efficacy of extrapolated onset temperature compared with thepeak temperature as already discussed.

    The nature and flow rate of the atmosphere in the DTA/DSC cell canhave a significant effect on the thermal analysis curve. With samples in anopen crucible the atmosphere can be reactive but is more commonly inert-

    N, or Ar being used to blanket the sample and sweep out evolvedgaseous products. The atmosphere also plays a significant role in heatexchange and control of the flow rate is important even in those experi-ments where the sample is in a sealed crucible. The reduction of thermallag remains as a priority in MTDSC. In spite of the expense, the highconductivity of He makes it the preferred choice of atmosphere inMTDSC. Fine control of the flow rate becomes even more importantwith the use of He. Changes in the nature of the atmosphere, whether bydesign or during the course of a reaction, may affect the thermal conduc-tivity sufficiently to alter the peak shapes. A dry atmosphere must be usedfor measurements below room temperature otherwise condensation will

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    Differential The rma l Ana lysis and Differential Scanning C alorim etry 75

    I50 15s 160 165 170

    Temnerature/ "C

    Figure 10 The injuence of heating rate on the thermal analysis curvesf o r the fusion ofindium: (a) plotted against temperatu re,(b) plotted against tinze

    occur in the sample holder, giving rise to spurious signals. With someequipment it may be advantageous to mou nt theDTA/DSC cell in a dr ybox.

    Reference

    The choice of a reference presents few difficulties.In the past, calcined

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    76 Chapter 3

    alumina (heated to1500C o remove adsorb ed m oisture) was common lyused an d still remains the favoured choice when samples are large. Fo rsmall samples the tendency is to use no reference ma terial at all, merely an

    emp ty crucible - s mentioned earlier.

    CALIBRATION

    Preliminaries

    So far the comments concerning experimental aspects have been ingeneral terms - his is the part of the chapter where they become morespecific. Although ca libration is primarily co ncerned with temp eratu re

    an d energy (or enth alpy ) it is also the stage a t which the practitioner getsto know the equipment. It is a good idea to start with preliminaryexperiments as a precursor to the d etailed calibration.

    It is false economy to short-change calibration. The point has beenmade that it is not a once and for all procedure. However, following acomprehensive calibration it is usually only necessary to carry out peri-odic checks. It seems to be th e case th at eq uipm ent functions better if itsuse is limited to a restricted ran ge of tempe rature s rather th an being usedfor all temperatures- but this has financial implications!It is impo rtantto keep a full record of the calibration procedures, periodic checks and allthe results.

    Preliminary experiments should aim to answer basic questions aboutthe behaviour of equipment:

    (1) How reproducible is the instrument signal when a sample crucible

    (2) Ho w sensitive is the signal to the precise placingof the crucible in

    (3) Ho w sensitive is the signal to t he a tmo spheric flow rate?

    (4) Ho w doe s temperatu re affect these experiments?

    is removed a nd subsequently replaced in the appa ratus?

    the apparatus?

    To some extent at least the answ ers may be a n indicationof the prowessof the practitioner.

    The resolution of the equipment can be examined by recording thethermal analysis curve for a mixtureof substances which have closetransition temperatures - the greater the resolution the sharper thedistinction between the two peaks. Quartz and potassium sulfate withsolid-state transition temp eratures of573C and 583C respectively areoften used for this purpose.

    It is important to check the signal range for which the instrument

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    DifSerentiul T herma l Analysis and Di fere ntial Scanning C alorime try 77

    response is linear. This may be carried out by recording the fusion peak ofa suitable calibrant - ndium is often used - and determining the massrange for which the area of the peak is directly proportional to the sample

    mass. With modern equipment the response is likely to be linear over anextensive range of operation.

    Temperature Calibration

    The object is to assign the correct temperature to the temperature in-dicated by the instrument. The method depends on recording the thermalanalysis curve for substances which exhibit a suitable transition tempera-ture. Substances of well established transition temperatures are availablewhich cover much of the temperature range of

    DSCinstruments. It is

    important that any substance used as a calibrant should be available inpure form, be stable and if possible have a negligible vapour pressure.Many of the substances are metals and some have temperatures ofmelting which are fixed points on the International Practical Tempera-ture Scale. Organic calibrants should always be used in sealed crucibles toavoid any loss of sample through vaporisation. This will ensure a sharppeak and at the same time will avoid damage to the equipment fromvapour. Table 3 lists some of the substances for which the temperaturesare either fixed points or are well established.

    A standard procedure for the temperature calibration of differentialthermal analysers and differential scanning calorimeters has been pub-lished as ASTM E 967 (1999).In the two point method two calibrants arechosen to bracket the temperature range of interest. It is assumed that thecorrect temperature T is related to the experimental temperature Texp ythe relationship,

    T = Texp + I . (4)

    S and I are defined by the relationships,

    Table 3 Calibra tion standards

    Cyclopentane,s --+ sCyclopentane, s+ 1Gallium,s +Benzoic acid, s +Indium, s tTin, s +

    Aluminium, s +

    - 35.1 4.9 1- 3.4 8.63

    29.8 79.9123 148156.6 28.623 1.9 60.4660.3 398

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    78 Chapter 3

    where the subscripts 1 and 2 refer to the two calibrants. S should be closeto unity.

    In principle the method is simple enough - mall quantities of the twocalibrants in turn are allowed to equilibrate 30C below the temperatureof the transition as indicated by a constant instrument signal. The calib-rants are then heated through the transition and the extrapolated onsettemperatures obtained from the endotherms. These temperatures corre-spond to Texpl nd Texp2. he calibration will be affected by heating rateand possibly the nature of the atmosphere and its flow rate. The experi-mental conditions for the calibration should be chosen to match those forsubsequent measurements. Calibration over more than two points maybe carried out and the relationship between T and Texpdeterminedstatistically. The extent to which the instrument output can be correctedby the software will depend on the detailed design of the computersystem.

    The process of temperature calibration and measurement has beenconsidered in considerable detail in connection with a program of work

    by GEFTA (German Thermal Analysis Society). The authors raise thefundamental issue that whereas the temperatures of the fixed points aredefined for the substances in phase equilibrium the experimental resultsare measured under dynamic conditions. The authors recommend aprocedure based on extrapolation of results to zero heating rate. Thedetails are contained in a series of publications.'O~' ' The authors12 havealso considered the problem of temperature calibration under conditionsof decreasing temperatures.

    An approach to obtaining the melting temperature under quasi-iso-thermal conditions is by stepwise heating (Figure 11). As the temperatureis increased the peaks initially reveal only a heat capacity displacement.As the melting temperature is approached this displacement is combinedwith some pre-melting and finally at the melting temperature the fusionpeak itself is obtained. Thereafter only a heat capacity displacement isobserved. The procedure can be used to identify the experimental meltingtemperature to a fraction of a degree.

    Figure 12 shows the variation of the solid-solid transition temperatureof K,CrO, with heating rate as part of a study into the feasibility of usingK2Cr0 , as a temperature standard.' The transition temperature of

    K2Cr0, was determined within a closely defined experimental protocol

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    Diferential Thermal Analysisand Differential Scanning C alorime try 79

    Time

    Figure 11 Schematic representation of stepwise heating to obtain melting temperaturesunder quasi-isothermal conditions

    10 2 4 6 8 10

    67

    Heating rate/ 'Cmiri'

    Figure 12 Variation of the extrapolated onset temperature with heating rate f o r thesolid-solid transition peak of K,CrO,

    in three labo rator ies o n five different the rm al analysers (b ot h differentialthermal analysers and differential scanning calorimeters). The value669.1 & 0.2"C was obtained relative to a single point calibration withaluminium for a heating rate of 3C min-' an d an atmosphere of nitro -gen.

    Energy Calibration

    Th e object here is to relate the instrumen t signal to th ermal pow er. The

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    80 Chapter 3

    use of electrical heating is not possible for the majority of differentialscanning calorimeters with the result that calibration is dependent on theavailability of chemical calibrants. A number of the temperature stan-

    dards have well established enthalpies of transition, permitting bothtemperature and energy calibration to be performed together (Table 3). Inpractice the transitions employed are almost invariably fusions. Theprocess of energy calibration has been reviewed by Sarge et al.14 as part ofthe GEFTA programme of work on calibration.

    The starting point is the relationship between the experimental thermalpower (dAq/dt),,, and the correct value dAq/dt,

    where K is the calibration constant. The use of equation (7) implies thatthe instrument signal has already been converted into experimentalthermal power and K is dimensionless. Alternatively the instrument signalmay be read simply as a voltage, in which case K will have the units J s-V- l .

    The integral of the instrument signal with respect to time over a fusionpeak is the total heat change,

    (dAq/dt) dt = Q = K (dAq/dt),,,dt, (8)s swhere Q is the heat change. It is assumed that K does not vary with time(and hence temperature) over the temperature range of the peak - akingfor granted that the peak is sharp. Thus K can be determined from theheat change Q = mAfusHwhere m is the mass of the sample and Afu,H isthe specific enthalpy of the fusion.

    The area of the fusion peak is obtained using the available softwarepackage but care is needed to ensure that the integration extends over the

    entire peak. The sample should be weighed using a balance capable ofweighing to at least 0.01mg. Results obtained in experiments where aweight loss occurs should be regarded as suspect. The inclusion of thedetermined calibration constant into the software once again depends onthe design of the computer system. The calibration constant should bedetermined over the temperature range of interest in subsequentmeasurements.

    The initial determination of the linearity of the instrument responsewill be important in determining the extent of sample mass or thermalpower for which the calibration holds true. Even so it is sensible toinvestigate whether the calibration constant shows any dependence on

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    Diflerential Thermal An alys is and DifSerential Scanning Calorim etry 81

    heating rate, the nature and flow rate of the atmosphere, the type ofcrucible and the thermal characteristics of the sample - metal versusnon-metal.

    It is also possible to use the area enclosed by a peak which is obtainedwhen a sample of known heat capacity is heated through an accuratelyknown temperature range. Sapphire (a-alumina) finds almost universalapplication in this approach. It has a well established heat capacity overthe working temperature range of differential scanning calorimeters andhas the added advantage of being commercially available in the form ofdiscs to fit snugly in crucibles. Alternatively the instrument signal can becalibrated directly - hermal power dAq/dt rather than through total heatQ. This alternative will be referred to later in the context of heat capacity

    measurements. The use of heat capacity measurements to extend themore conventional calibration based on enthalpies of fusion has beendescribed by ASTM [E 968 (1999)l.Figure 13 shows the linear responseof a differential scanning calorimeter by means of recording the instru-ment signal (in mV) for a number of discs of sapphire.

    700 1>8

    .I

    c,

    85 2 5 -

    c,

    eC I

    350

    175

    0Mass of sapphire/mg

    Figure 13 Test,for the linear response of a dflerent iul scanning calorimeter (see tex tf o rdetails)

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    82

    MEASUREMENTS

    Chapter 3

    Reference has already been madeto the range of applications of DTA

    and DSC. This section is concerned with a closer look at calori-metric measurements which link thermal power to heat capacity,dAq/dt = (C, - C,)p, an d its integral, JdAq/dt)dt, to energy or e nthalpy.These linkages together with tempe rature form the basis of quantitativeDSC . Com pute r systems for the con trol of equipment, da ta capt ure andsubsequent analysis have combined to give increased versatility andresults of far greater precision than was possible previously with chartrecorders.

    Measurement of Heat Capacity

    This represen ts on e of the early successes of conv entio nalDSC and morerecently of MTDSC. Heat capacity is a key thermodynamic quantitybecause of its intrinsic importance an d its relationship t o o ther quantities- enthalpy, entro py and G ibb s energy. Its measurement continues to bean important application of DSC where results can be obtained havingan uncertainty of only1-2%, often with a minimu mof difficulty. At theoth er end of the scale with rigorou s atte nti on to detail an d with suitablesamples results can be obtained with uncertainties a pp roa chi ng those ofadiabatic calorimetry.'

    The classical metho d of me asurin g heat capac ities usingDSC involvesthree experiments. In each experiment the isotherm al base-line is estab-lished and the calorimeter then programmed over a temperature rangebefore establishing the final isothermal base-line. Experiments can becarried out using an increasing or decreasing temperature. The samecrucible is used for the three ex perimen ts an d each experim ent is carriedout over the same temperature range an d a t the same heating o r coolingrate. The DSC cell contains (1) the empty crucible, (2) the cru-

    cible + calibrant an d (3) the crucible + sample. Th e reference, an emp tycrucible, is left und isturb ed th ro ug ho ut th e sequence of experimen ts.Figure 14 shows the therm al analysis curves for the three experiments.

    Th e difference between the isoth ermal signals at the beginning a nd end ofthe experiments arises from the temperature dependence of the heattransfer coefficients. The isothermal signals from the three experimentshave been adjusted to be coincident. Modern equipment with its moresecure base-line enables the temperature range of the experiment to be100C or more. The selection of the sample mass is somethingof acompromise - large sample will increase the mag nitud e of the signal bu twill give a greater uncertainty in the temperature due to increase in

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    Digerential Thermal Analysis and Differential Scanning Calorimetry

    B

    0 .t l

    z

    83

    -

    t sothermal - ynamic & Isothermal -

    thermal lag. A sample mass of 10-20mg has been recommended with aheating (or cooling) rate of 10-20C min-'. As indicated in the previoussection, sapphire is almost invariably used as the calibrant. To reiteratethe point already made, the crucible should be in precisely the sameposition in the DSC cell for each experiment. A lid should be used for thecrucible to cover the calibrant and sample and the DSC cell should beclosed by a lid. The signal for each experiment at temperature T can berepresented by the relationships,

    where C is the heat capacity of the empty crucible, C,, C, and C, the heatcapacity of the calibrant, sample and reference respectively.

    The difference between the signals for experiments 1 and 2 serves tocalibrate the thermal power,

    The heat capacity of the sample is obtained from the formula,

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    84 Chapter 3

    It is seen that the calibration constant disappears, which assumes that it isconstant over the experimental conditions. The calculation is carried outusing dedicated software. In some circumstances the crucible used for the

    sample may have to be different from that used for the calibrant. Thismeans that a correction will be required to take into account the differ-ence between the heat capacity of the two crucibles - eadily calculatedwith sufficient accuracy. Measurements can be made at a series of tem-peratures but are meaningful only within the quasi-steady-state region ofthe experiment. The specific heat capacity of sapphire has been listed byASTM in connection with the standard test method E 1269 (1999) fordetermining specific heat capacity by differential scanning calorimetry.

    A number of difficulties can arise. The first is that it is rarely possible to

    adjust the isothermal signals at the beginning of the experiment and findthat they are coincident at the end. Richardson16 has summarised hisseries of papers dealing with this mismatch which may limit the tempera-ture range of the experiments. The second difficulty is uncertainty in theassignment of temperature arising from thermal lag. Again Richardson'has indicated a method of assessing thermal lag from the area of the tailfollowing the change from dynamic to isothermal mode of operation atthe end of the experiment. It corresponds to an energy C,6T whereby thetemperature correction can be calculated.

    The measurement of heat capacity changes through glass transitionsoften presents difficulties when using the classical technique. The increaseis small - often less than 1 J K -' g-' - but the importance of the glasstransition is paramount marking as it does significant changes in theproperties of polymeric substances. A number of alternative approacheshave been devised to improve the resolution of glass transitions. Theseinclude the variety of modulated heating programmes. It was in themeasurement of glass transitions that MTDSC made such an earlyimpact. The approach differs from that of the classical route in that itdepends on the comparison between thermal power recorded at different

    heating rates. In MTDSC the heating rate is continually changing as aresult of the temperature modulation and the heat capacity is obtained bydividing the modulated heat flow by the modulated heating rate. Thedetailed calculation depends on a rather complicated manipulation of theraw da ta but again all this is in the software! The reversing component ofthe total heat flow is then obtained by multiplying the heat capacity bythe average heating rate. A feature of the new techniques is that measure-ments can be carried out under quasi-isothermal conditions - mpossibleto achieve with the conventional technique. In this way it is possible tomonitor the time dependence of the heat capacity during reactions.

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    Difierential Therm al Analys is and Diflerential Scanning C alorime try 85

    Measurement of Energy

    The area of peaks is determined by software with the input of the timescorresponding to the start and finish of the peak. The software mayprovide different options for constructing the base-line. The calculation isstraightforward if the peak is reasonably sharp and the heat capacity ofthe product does not differ greatly from that of the initial sample. Astraight line from start to finish of the peak is constructed to represent thebase-line. Some difficulty may occur in identifying the precise startingpoint of a peak - a problem often encountered when determining thecrystallinity of a polymer from the crystallisation peak. The real complex-ity arises when there is a marked change in heat capacity and the base-lineno longer even approximates to a straight line. The construction of the

    base-line must reflect the changing heat capacity of the sample which inturn will depend on the proportion of the initial sample (reactant) and theproduct. Recipes have been pu b l i ~ h e d ' ~ ? ' ~ hich enable the base-line tobe calculated from an analysis of the shape of the peak and a knowledgeof the heat capacity of the reactant and product over the temperaturerange of the peak. The heat capacity of reactant can be obtained byextrapolating the base-line recorded before the peak. A similar construc-tion can be applied to the product or it may be possible to recycle it overthe temperature range of the peak.

    The energy of the isothermal event may be obtained conveniently usingthe construction shown in Figure 15 in which heat capacity,C = (dq/dt)/P, is plotted against temperature for an exothermic reaction.Area ABEA represents the energy change for the fractional conversion ofreactant into product at temperature T. The area ABCDEA correspondsto the energy of complete conversion of reactant into product at tempera-ture T. The variation of this area over the temperature range of the peak isthe temperature dependence of the energy. The construction also pro-vides a secure route to kinetic data. The total area corresponds to thetransformation a = 0 to a = 1 where a is the fractional extent of reaction.The fractional area ABEA/ABCDEA is the extent of reaction sc at tem-perature T. The values of a obtained in this way may be used to constructthe curve AFD which represents the contribution to the instrument signalof the instantaneous heat capacity of the composition defined by a. Therate of reaction da/dt at temperature Ti s proportional to the distance FE.Treatment of the entire curve yields da/dt, a and T - the triplet whichforms the starting point for a conventional approach to obtaining adescription of the kinetics. The derivation of kinetic data in this wayassumes that the instrument is perfect, with no thermal lags.

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    88 Chapter 3

    C

    Temperature, time

    Figure 17 Determination ojpurity: a)fusionendotherm (b) plot o temperalure ugainst 1/ f(see textfo r details)

    correction is added to all the areas to obtain a straight line, A B D . Thecorrection is usually about 10% of the total area. The curve ABE is anexample of over-correcting the initial curve. The mole fraction impurity isthen calculated from the value of the gradient.

    The method has proved popular, not least because of its rapidity andthe simplicity of the analysis, and has been adopted by ASTM as a

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    Diflerential Thermal Analysis and Dl feren tial Scanning Calorimetry 89

    standard test method [E 928 (1996)l. Nowadays the analysis is in-cluded in the software package. A note of caution however: it may not beobvious whether the ideal solution theory represents the melting be-

    haviour of a particular sample. As might be expected a number of effortshave been made to refine the method and extend its range of applicability.One such method is based on stepwise heating which has already beenmentioned Although it detects melting within finer temperature limits it ismuch more time-consuming.

    Kinetics

    The application of thermal analysis to the study of kinetics involves somany ramifications that few would dispute that it could fill a book of itsown. In principle at least the determination of kinetic parameters requiresan investigation of the rate of reaction over all values of extent of reactionand temperature. Only in this way can potential changes in the reactionmechanism be identified. It cannot be accomplished by a single experi-ment but if the experimental conditions are sufficiently extensive theresults are capable of providing useful information. Even so, extrapola-tion of rate data outside the conditions of the experiment needs to beundertaken with care. Results may be used to obtain predictive curveswhich relate extent of conversion, time and temperature. The isothermallaw has been linked to a variety of mechanistic models but the ultimatedetermination of mechanisms depends on the input of results from avariety of techniques.

    The experimental study of kinetics, as mentioned earlier, has as its basisthe identification of the rate of reaction with instrument signal and theextent of reaction with fractional area of the peak. Analysis of experimen-tal data often makes use of named approaches which exploit theadvantages of dynamic experiments to achieve results without recourseto protracted experimental effort. Two popular but very different

    methods are those of Borchardt and Daniels and Ozawa2 and bothappear in ASTM methods. Both are supported by commercial software.The concern here is with the Borchardt and Daniels method [ASTM E2041 (1999)l which had a considerable impact on kinetic evaluation bothby DTA and subsequently DSC. The analysis was devised originally forDTA experiments in which the thermocouples were in large volumes ofstirred liquids. This is in direct contrast to the current application of themethod to DSC studies of solids. A number of assumptions were madewhich were met more readily in stirred liquid systems than with solids. Asa result there are a number of caveats associated with its application tosolids. In particular the analysis assumed the absence of temperature

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    90 Chapter 3

    gradients and thermal lag. From the standpoint of DSC this means smallsamples and slow heating rates - not the ideal experimental scenario toobtain a large signal! A sample mass of a few mg and heating rates no

    greater than 10C min-l should prove to be effective.

    analysis based on equation (15):The Borchardt and Daniels approach is usually associated with

    ln(da/dt) = In A - EJRT + ln(1 - ),

    an

    15)

    which assumes first order kinetics. A and E , are the pre-exponentialfactor and the Arrhenius activation energy respectively and the tempera-ture T is in kelvin. As before, a is the fractional extent of reaction. Theoriginal assumption of first order kinetics was one of a number made tosimplify the expression originally derived by Borchardt and Daniels forDTA. The rate of reaction da/dt at a given temperature is obtained fromthe thermal power, da/dt = (dq/dt)/AH where AH may be obtained fromthe total area enclosed by the thermal analysis peak. The value of a isobtained from the fractional area at the corresponding temperature. Aplot of ln[(da/dt)/(l - ) ] against l / T should be a straight line whichconfirms the order of reaction to be unity and leads to values for theactivation energy and pre-exponential factor.

    Once again the advantage of the method is its speed and simplicity.

    However, it is applicable only to first order reactions which lead to asmooth well shaped thermal analysis peak. Nevertheless be wary of usingsoftware to smooth thermal analysis curves - detail may be lost whichmight be critical in deciding whether the method is applicable. Althoughallowance should be made for the effect of thermal lag on the shape of thethermal analysis curve in practice it is seldom carried out. Instead theexperimental procedure aims to minimise temperature gradients, ASTMrecommend that the maximum heat evolution should be restricted to lessthan 8 mW. Furthermore the base-line is usually a straight line drawn

    from the start to the finish of the peak. The use of the approach has beenextended by assuming a more general isothermal lawf(a), whence equa-tion (15) becomes

    ln(da/dt) = In A - EJRT + lnf(a) . (16)

    It is impossible to summarise the determination of kinetics on the basis ofsuch a short section devoted to one approach. What is patently obvious isthat the determination of kinetics by DSC is a veritable minefield: differ-ent methods often seem to lead to different results despite the best effortson the part of practitioners.

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    92 Chapter 3

    And for the future, reference 40 is to a special issue ofThermochimicaActa entitled Tow ards the New C entury.

    REFERENCES

    1. M. Reading,D. Elliott an d V. L. Hill, J . Thermal Anal., 1993,40,949.2. E. S. W atson, M . J. ONeill,J. Justin a nd N . Brenner,Anal. Chem.,

    1964,36,1233.3. P. D. Ga r n , Thermoanalytical Methods of Investigation,Academic

    Press, New York, 1965, p. 606.4. D. J . Rose, Analysis of Antioxidant Behaviour in Lubricating Oils,

    P h D Thesis, Scho ol of Chem istry, Unive rsity of Leeds, 1991.5. A.

    P. Gray inAnalytical Calorimetry,

    ed. R. S. Porter and J.F.

    Johnso n, P lenum Press, New York, 1968, p. 209.6. R. A, Baxter, in Thermal Analysis,ed. R. F. S. Schwenker and P . D .

    Ga rn, Academic Press, New York , 1969,p. 65.7. T. F. J. P ijpers, V. B. F. Mathot , B. Goderis and E. van der Vegte,

    Proceedings 0 f2 8 th NATAS Oct 4-6,2000, Orland o, Florida,U SA .8. R. C. Mackenzie,Ana l. Proc., 1980,217.9. W. Wm. Wendlandt, Thermal Analysis, Wiley-Interscience, New

    York, 3rd edn., 1985,227.10. G. W. H. Hohne, H. K. Cammenga, W. Eysel, E. Gmelin and W.

    Hemminger, Thermochim. Ac ta,1990,160, 1.11. H . K. Cammenga, W. Eysel,E. Gmelin, W. Hemminger, G. W. H.

    Hohne and S. M . Sarge, Thermochim. A cta ,1993,219,333.12 . S. M . Sarge, G . W. H. Hohne, H. K. Cammenga, W. Eysel andE.

    Gmelin, Thermochim. Ac ta,2000,361, 1.13 . E. L. Charsley, P. G. Laye a nd M . Richardson,Thermochim. Acta ,

    1993,216,331.14. S. M. Sarge, E. Gmelin, G. W. H. Hohne, H. K. Cammenga, W.

    Hemminger and W. Eysel, Thermochim. Ac ta,1994,247,129.

    15. J. E. Callahan,K. M. M cDermot t,R. D. Weir and E . F. Westrum, J .Chem. Thermodyn.,1992,24,233.16. M. J. Richardson, in Compendium of Thermophysical Property

    Measurement Methods,ed. K . D . Maglic, A. Cezairliyan and V. E.Peletsky, Plen um , 1992, Vol. 2, p.519.

    17. W. P. Brennan, B. Miller andJ . C. Whitwell, Ind. Eng . Chem . (Fund.),1969 ,8, 314.

    18. H. M . Heuvel an d K. C. J . B. Lind, Anal. Chem.,1970,42,1044.19. H. J. Borchardt and F Daniels, J . Am . Chem. SOC.,957,79,41.20. T. Ozawa, J . Thermal Anal.,1970 ,2, 301.21. M. E. Brown (ed.),Handbook of Thermal Analysis and Calorimetry,

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    Diflerential Thermal An alysis and DifSerential Scanning Ca lorim etry 93

    22.

    23.

    24.

    25.

    26.

    27.

    28.

    29 .

    30.

    31.

    32.33.34.

    35.

    36.37.38.39.40 .

    Principles an d Prac tice, Elsevier, Am sterdam , 1998, Vol.1.G. W. H . Hohne, W. Hem minger and H.-J. Flammersheim,Diferen-tial Scanning Calorim etry, A n Introductiono r Practitioners, Springer,

    Berlin, 1996.W. Wm. Wendlandt, Thermal Analysis, Wiley-Interscience, NewYork , 3rd edn., 1985.V. R. Harw alker and C. Y. M a (ed.),Thermal Analysis of Foods,Elsevier, Amsterdam , 1990.W. Smykatz-Kloss and S. St. J. W arne (ed.),Thermal Analysis in theGeosciences,Springer-Verlag, Berlin, 1991.H. Kopsch, Thermal Methods in Petroleum Analysis,VCH, Wein-heim, 1995.

    J. L. Fo r d a nd P. Timmins, Pharmaceutical Thermal Analysis: Tech-niques and Applica tions,Ellis Ho rwo od, Chichester, 1989.V. B. F . Ma th ot (ed.),Calorimetry and Thermal Analy sis of Polymers,Han ser, M unche n, 1994.E. A. Turi (ed.), Thermal Characterisation of Polymeric Materials,Academ ic Press, New Yo rk, 2nd edn., 1997.C. Schick and G. W. H. Hohne (ed.), Special Issue: TemperatureModulated Calorimetry,Thermochim. Ac ta,1997,304/305,1-378.C. Schick an d G .W. H. Ho hn e (ed.), Special Issue: InvestigationofPhase Transitions by Temperature-Modulated Calorimetry,Ther-mochim. Act a,1999 ,330, 3-200.J. Paulik a nd F. Paulik, Anal. Chim. Act a,1971 ,56, 328.J. Rouquerol,Bull. SOC. him.Fr. , 1964,31.M . Reading, in Thermal An alysis: Techniques and Ap plications,ed. E.L. Charsley and S. B. W arrington, T he R oyal Societyof Chemistry,Cambridge, 1992,p. 126.M . E. Brow n, M . Maciejewski,S. Vyazovkin, R. Nom en, J . Sempere,A. Burnham , J. Opfermann, R. Strey, H .L. Anderson, A. Kemm ler, R.Keuleers, J. Janssens, H . 0 . Desseyn, Chao-Rui Li, To ng B Tang , B.

    Roduit, J. Malek and T. Mitsuhashi, Thermochim. Ac ta,2000, 355,125.M . M aciejewski, Thermochim. Ac ta,2000,355, 145.S. Vyazovkin, Thermochim. Ac ta,2000,355,155.B. Rodu it, Thermochim. Ac ta,2000,355, 171.A. K. Galwey and M. E. Brown, Thermochim. Ac ta,1995,269/270,1.W. Hem minger (ed.) Special Issue: Towards th e New Century ,Ther-mochim. Acta ,2000,355, 1-253.

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