Thermal Analysis and Calorimetry · 2020. 4. 14. · Thermal Analysis and Calorimetry STEPHEN B....

� 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Thermal Analysis and Calorimetry

STEPHEN B. WARRINGTON, Formerly Anasys, IPTME, Loughborough University,

Loughborough, United Kingdom

G€uNTHERW. H. H€oHNE, Formerly Polymer Technology (SKT), Eindhoven University

of Technology, Eindhoven, The Netherlands

1. Thermal Analysis . . . . . . . . . . . . . . . . . . 415

1.1. General Introduction . . . . . . . . . . . . . . . 415

1.1.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 415

1.1.2. Sources of Information . . . . . . . . . . . . . . 416

1.2. Thermogravimetry. . . . . . . . . . . . . . . . . 416

1.2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . 416

1.2.2. Instrumentation . . . . . . . . . . . . . . . . . . . . 416

1.2.3. Factors Affecting a TG Curve . . . . . . . . . 417

1.2.4. Applications . . . . . . . . . . . . . . . . . . . . . . 417

1.3. Differential Thermal Analysis and

Differential Scanning Calorimetry. . . . . 418

1.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . 418

1.3.2. Instrumentation . . . . . . . . . . . . . . . . . . . . 419

1.3.3. Applications . . . . . . . . . . . . . . . . . . . . . . 419

1.3.4. Modulated-Temperature DSC (MT-DSC) . 421

1.4. Simultaneous Techniques. . . . . . . . . . . . 421

1.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . 421

1.4.2. Applications . . . . . . . . . . . . . . . . . . . . . . 421

1.5. Evolved Gas Analysis. . . . . . . . . . . . . . . 422

1.6. Mechanical Methods . . . . . . . . . . . . . . . 422

1.7. Less Common Techniques . . . . . . . . . . . 423

2. Calorimetry . . . . . . . . . . . . . . . . . . . . . . 424

2.1. Introduction . . . . . . . . . . . . . . . . . . . . . 424

2.2. Methods of Calorimetry. . . . . . . . . . . . . 424

2.2.1. Compensation of the Thermal Effects . . . . 425

2.2.2. Measurement of a Temperature Difference 425

2.2.3. Temperature Modulation . . . . . . . . . . . . . 426

2.3. Calorimeters . . . . . . . . . . . . . . . . . . . . . 427

2.3.1. Static Calorimeters . . . . . . . . . . . . . . . . . 4272.3.1.1. Isothermal Calorimeters . . . . . . . . . . . . . . 4272.3.1.2. Isoperibolic Calorimeters . . . . . . . . . . . . . 4282.3.1.3. Adiabatic Calorimeters . . . . . . . . . . . . . . 430

2.3.2. Scanning Calorimeters . . . . . . . . . . . . . . . 4302.3.2.1. Differential-Temperature Scanning

Calorimeters . . . . . . . . . . . . . . . . . . . . . . 4312.3.2.2. Power-Compensated Scanning Calorimeters 4322.3.2.3. Temperature-Modulated

Scanning Calorimeters . . . . . . . . . . . . . . . 432

2.3.3. Chip-Calorimeters . . . . . . . . . . . . . . . . . . 433

2.4. Applications of Calorimetry. . . . . . . . . . 433

2.4.1. Determination of Thermodynamic Functions 433

2.4.2. Determination of Heats of Mixing . . . . . . 434

2.4.3. Combustion Calorimetry . . . . . . . . . . . . . 435

2.4.4. Reaction Calorimetry. . . . . . . . . . . . . . . . 436

2.4.5. Safety Studies . . . . . . . . . . . . . . . . . . . . . 437

References . . . . . . . . . . . . . . . . . . . . . . . 438

1. Thermal Analysis

1.1. General Introduction

1.1.1. Definitions

Thermal analysis (TA)hasbeendefinedas ‘‘agroupof techniques in which a physical property of asubstance and/or its reaction products is measuredas a function of temperature while the substance issubjected to a controlled temperature programme’’[1]. The formal definition is usually extended toinclude isothermal studies, in which the property ofinterest is measured as a function of time.

The definition is a broad one, and coversmany methods that are not considered to fall

within the field of thermal analysis as it isusually understood. The present chapter willbe restricted to major techniques. Since allmaterials respond to heat in some way, TAhas been applied to almost every field ofscience, with a strong emphasis on solvingproblems in materials science and engineering,as well as fundamental chemical investiga-tions. TA is applicable whenever the primaryinterest is in determining the effect of heatupon a material, but the techniques can also beused as a means of probing a system to obtainother types of information, such as composition.

The following list summarizes quantities sub-ject to investigation and the corresponding ther-mal analysis techniques:

Article No : b06_001

DOI: 10.1002/14356007.b06_001.pub3

Mass Thermogravimetry (TG)

Temperature difference Differential thermal analysis (DTA)

Heat flow rate Differential scanning calorimetry (DSC)

Evolved gas Evolved gas analysis (EGA)

Dimensions (length,

volume)

Thermodilatometry (TD)

Mechanical deformation Thermomechanical analysis (TMA)

Complex modulus Dynamic mechanical analysis (DMA)

Optical properties Thermoptometry

Electrical properties Thermoelectrometry

Magnetic properties Thermomagnetometry

1.1.2. Sources of Information

Two journals (the Journal of Thermal Analysisand Calorimetry and Thermochimica Acta) de-vote their contents entirely to TA; the Proceed-ings of the (now) four-yearly Conferences of theInternational Confederation for Thermal Analy-sis and Calorimetry (ICTAC) constitute anexcellent additional source of research papers.Specific information regarding Proceedings vo-lumes for the nine ICTAC Conferences between1965 and 1991 is available in [1]. The mostcomplete listing of worldwide TA literature isalso found in the ICTAC handbook [1], which inaddition gives addresses for national TA socie-ties and important equipment suppliers. Themostuseful textbooks include [2–5, 40].

There is a wealth of information available onthe Internet; see, for example, ‘‘Thermal Analy-sis’’ in Google or another search engine. [6]

1.2. Thermogravimetry

1.2.1. Introduction

Thermogravimetry (TG) is used to measure varia-tions inmass as a function of temperature (or time).Processes amenable to study in this way are listedin Table 1. TG is one of the most powerful TA

techniques from the standpoint of quantitativedata, and for this reason it is often employed incombination with other measurements.

1.2.2. Instrumentation

The instrument used is a thermobalance. Theschematic diagram in Figure 1 presents the maincomponents of a typical modern unit. Compo-nent details vary according to the design, andchoice of a particular instrument is usually dic-tated by requirements of the problem underinvestigation (temperature range, sensitivity,etc.). The balance mechanism itself is usually ofthe null-deflection type to ensure that thesample’s position in the furnace will not change.The balance transmits a continuous measure ofthe mass of the sample to an appropriate record-ing system, which is very often a computer. Theresulting plot of mass vs. temperature or time iscalled a TG curve. Balance sensitivity is usuallyof the order of one microgram, with a totalcapacity of asmuch as a few hundredmilligrams.Furnaces are available that operate from subam-bient (e.g., �125 �C) or room temperature up toas high as 2400 �C. A furnace programmer nor-mally supports a wide range of heating andcooling rates, often in combination, as well asprecise isothermal control. The programmingfunctions themselves are increasingly being as-sumed by computers. Most applications involveheating rates of 5 – 20 K/min, but the ability toheat a sample as rapidly as 1000 K/min can be

Figure 1. Schematic diagram of a thermobalance a) Sam-ple; b) Sample temperature sensor; c) Furnace temperaturesensor; d) Furnace; e) Recorder or computer, logging samplemass, temperature, and time; f) Balance controller; g) Re-cording microbalance; h) Gas; i) Furnace temperatureprogrammerThe computer may also control the furnace programmer

Table 1. Processes that can be studied by thermogravimetry

Process Weight gain Weight loss

Ad- or absorption *

Desorption *

Dehydration/desolvation *

Sublimation *

Vaporization *

Decomposition *

Solid – solid reactions *

Solid – gas reactions * *

416 Thermal Analysis and Calorimetry Vol. 36

useful in the simulation of certain industrialprocesses, for example, or in flammability stud-ies. Special control methods, grouped under theterm controlled-rate thermal analysis (CRTA),are receiving increasing attention [7], and offeradvantages in resolving overlapping processesand in kinetic studies. One of thesemethods is therecently commercially available High-Resolu-tion TG, in this case the heating rate is controlledby the measured mass change rate.

The quality of the furnace atmosphere de-serves careful attention. Most commercial ther-mobalances operate at atmospheric pressure.Vacuum and high-pressure studies normally re-quire specialized equipment, either commercialor home-made, as do experiments with corrosivegases [8]. The ability to establish an inert (oxy-gen-free) atmosphere is useful, as is the potentialfor rapidly changing the nature of the atmosphere.

The mode of assembly of the componentsvaries; for example, the furnace might be above,below, or in line with the balance. Sample con-tainers also vary widely in design; cylindricalpans are common, typically 5 – 8 mm in diame-ter and 2 – 10 mm high, though flat plates andsemisealed containers may be used to investigatethe effects of atmospheric access to a sample.Compatibility between the constructionmaterialsand the system under investigation must be care-fully considered. Materials commonly availableinclude aluminum, platinum, alumina, and silica.Temperature indication is normally provided by athermocouple located near the sample container.Because of inevitable thermal gradients withinthe apparatus, an indicated temperature can neverbe taken as an accurate reflection of the tempera-ture of the sample. Reproducible location of thethermocouple is vital; recommended calibrationprocedures have been described in [9]. Only insimultaneous TG – DTA instruments is directmeasurement of the temperature possible.

1.2.3. Factors Affecting a TG Curve

WENDLANDT [2] has listed 13 factors that directlyaffect a TG curve, both sample- and instrument-related, someofwhich are interactive.Theprimaryfactors are heating rate and sample size, an in-crease in either of which tends to increase thetemperature at which sample decomposition oc-curs, and to decrease the resolution between suc-

cessive mass losses. The particle size of the sam-ple, the way in which it is packed, the crucibleshape, and the gas flow rate also affect the progressof a thermal reaction. Careful attention to consis-tency in experimental details normally results ingood repeatability. On the other hand, studying theeffect of deliberate alterations in such factors asheating rate can provide valuable insights into thenature of observed reactions. All these considera-tions are equally applicable to other techniques aswell, including DTA (Section 1.3).

1.2.4. Applications

TG has been applied extensively to the study ofanalytical precipitates for gravimetric analysis[10]. One example is calcium oxalate, as illus-trated in Figure 2. Information such as extent ofhydration, appropriate drying conditions, stabil-ity ranges for intermediate products, and reactionmechanisms can all be deduced from appropriateTG curves. Figure 2 also includes the first deriv-ative of the TG curve, termed the DTG curve,which is capable of revealing fine details moreclearly.

A TG method has also been devised for theproximate analysis of coal, permitting four sam-ples per hour to be analyzed with results of thesame precision and accuracy as BS and ASTMmethods [11]. A typical curve is shown in Fig-ure 3. The approach taken here can be general-ized to the compositional analysis of many ma-terials [12]. TG also facilitates comparisons ofthe relative stabilities of polymers (Fig. 4) andothermaterials. An analysis of curves prepared atdifferent heating ratesmakes it possible to extract

Figure 2. TG (A) and DTG (B) curves for calcium oxalatemonohydrateSamplemass 30 mg, heating rate 20 K/min, argon atmosphere

Vol. 36 Thermal Analysis and Calorimetry 417

kinetic data for estimating the service lifetimes ofsuch materials. In another coal-related applica-tion, an empirical correlation has been estab-lished between characteristic temperatures ob-tained fromDTG curves of coals examined underair and the performance of the same coals insteam-raising plants [13], permitting the rapidassessment of new fuels (Fig. 5). The simulationof industrial processes, particularly heteroge-neous catalysis, is another important area ofapplication.

1.3. Differential Thermal Analysis andDifferential Scanning Calorimetry

1.3.1. Introduction

Both differential thermal analysis (DTA) anddifferential scanning calorimetry (DSC) are con-cerned with the measurement of heat changes,and as such are applicable in principle to a widerrange of processes than TG. From a practicalstandpoint DSC may be regarded as the methodfrom which quantitative data are most easilyobtained. The use of DSC to determine absolutethermodynamic quantities is discussed in Sec-tions 2.3.2 and 2.4.1. Types of processes amena-ble to study by these methods are summarized inTable 2.

Figure 3. TG curve (A) illustrating a programmed-temper-aturemethod for the proximate analysis of coal,where the lineB defines the temperature program a) Moisture; b) Volatiles;c) Fixed carbon; d) Ash; e) Point at which the atmosphere waschanged to air

Figure 4. TG curves for four polymers in air, showing theirrelative stabilities a) Silicone rubber; b) PVC; c) PTFE;d) Perspex

Figure 5. DTG curves for four ASTM standard coal sam-ples heated in air [13] a) Lignite ‘‘A’’; b) Sub-bituminous‘‘A’’; c) High-volatility bituminous ‘‘A’’; d) Buckwheatanthracite

Table 2. Processes that can be studied by DTA/DSC

Process Exothermic Endothermic

Solid – solid transitions * *

Solid – liquid transitions * *

Vaporization *

Sublimation *

Adsorption *

Desorption *

Desolvation *

Decomposition * *

Solid – solid reactions * *

Solid – liquid reactions * *

Solid – gas reactions * *

Curing *

Polymerizations *

Catalytic reactions * *


1.3.2. Instrumentation

Figure 6 shows the components of a typical DTAapparatus. The sample and an inert referencematerial (commonly alumina) are subjected toa common temperature program while the tem-perature difference between the two is moni-tored. In an ideally designed instrument, thetemperature difference DT remains approximate-ly constant if no reaction is taking place in thesample. When an endothermic process such asmelting occurs, the sample temperature Ts lagsbehind that of the reference Tr; DT ¼ Ts � Tr isthus negative, so a (negative) peak is produced onthe corresponding DTA curve, which is a recordof DT against either temperature or time (Fig. 7).

Exothermic processes lead to peaks in the oppo-site direction. The peak area is related to both theheat change DQ and the sample size according tothe relationship

DH�m ¼ K

ZDT�dt

where m is the sample mass, and DH is theenthalpy of reaction (which is the reactionheat DQ in the case of constant pressure). Theproportionality constant K is always tempera-ture-dependent, it is also influenced by thermalproperties of the sample and container. Certainapparatus designs minimize these influences, sothat once the characteristics of K ¼ f (T) havebeen determined the DT signal can be condi-tioned (electronically or digitally) to give anoutput signal calibrated directly in heat flow rateunits; i.e., the sensitivity is nominally indepen-dent of temperature. This is the principle under-lying heat-flux DSC. For a more complete de-scription of this technique, as well as power-compensated DSC, see Section 2.3.2. A widevariety of commercial devices covers the tem-perature range from ca. �150 – 2500 �C, buthigh-temperature instruments are less sensitivethan low-temperature designs due to constraintsimposed by thermocouple technology. DSC in-struments are usually limited to a maximumtemperature of 700 �C, though heat-flux DSChas been extended to 1400 �C.DTAhead designsvary enormously, but most accommodate sam-ples in the range 5 – 200 mg in metal or ceramiccontainers. The thermocouples usually take theform of beads that fit into recesses in the contain-ers, or plates upon which the containers rest.Nowadays the thermocouple is never actuallyplaced in the sample, in contrast to the ‘‘classi-cal’’ arrangement shown in Figure 6.

1.3.3. Applications

DSC is used extensively in polymer science [14](! Plastics, Properties and Testing). A general-ized DSC curve for a polymer is shown in Fig-ure 8. Most polymers display a glass transition,in the course of which the material passes from aglassy to a rubbery state with a simultaneousincrease in specific heat capacity (! Plastics,Properties and Testing). Glass-transition temper-ature measurements are used for material

Figure 6. Schematic diagram of a classical DTA apparatusa) Reference thermocouple; b) Sample thermocouple;c) Heating block; d) DT amplifier; e) Recorder or computer,logging Ts, DT, and time; f) Furnace; g) Temperature pro-grammer, which may be linked to the computer; h) Gas inletTs, sample temperature; Tr, reference temperature;DT ¼ Ts � Tr

Figure 7. TypicalDTAcurve for themeltingof apurematerial


characterization and comparison, often provid-ing information about such factors as thermalhistory, crystallinity, extent of cure, and plasti-cizer content of a polymer. Amorphous polymersusually exhibit a crystallization exotherm, andthermosetting polymers a curing exotherm, bothof which can be analyzed kinetically to establishthe thermal treatment required to obtain desiredproperties in a particular product. The meltingendotherm is a measure of the extent of crystal-linity, an important parameter related tomechan-ical properties. The temperature at which exo-thermic degradation begins under an oxidizingatmosphere is used to compare oxidative stabili-ties of different polymers or different stabilizers.Discrimination can be improved by isothermalmeasurements, in which the material under in-vestigation is heated initially in an inert gas, afterwhich the atmosphere is changed to air or oxygenand the time lapse prior to exothermic deflectionis measured. The same approach is applicable tostudies of oils, greases, fats, etc., though high-pressure cells may be necessary to preventvolatilization.

The particular temperatures at which peaksare observed can be used for the identification ofcomponents in a mixture, and the size of aparticular peak can be used for quantitativeevaluation. Examples include the determinationof quartz in clays and analysis of the constituentsof polymer blends, both of which would bedifficult to achieve by other means. DTA hasbeen used to determine the presence and degreeof conversion of high-alumina cement concrete(HAC), a material subject to severe loss ofstrength under certain atmospheric conditions

due to solid-state reactions in the cement matrix.Figure 9 shows a DTA curve for partially con-verted HAC together with the way the data areused for a conversion measurement.

An analysis of the shape of the fusion peakfrom a relatively pure material (e.g., a pharma-ceutical agent) can, with certain restrictions, leadto an estimate of purity [15]. Figure 10 shows anidealized melting curve for an impure material.By calculating the fraction (F) ofmaterialmeltedat a series of temperatures, and applying severalsimplifying assumptions, the mole fraction of animpurity can be calculated from the expression:

Ts ¼ T0�RT20X2

DHf � 1

F

where Ts ¼ sample temperature, T0 ¼ meltingpoint of the pure material, R ¼ gas constant,X2 ¼ mole fraction of impurity, DHf ¼ enthal-pyof fusion, and F ¼ the fraction melted attemperature Ts. The calculations are readily per-formed by commercial software.

Figure 8. Generalized DSC curve for a polymer a) Glasstransition; b) Crystallization; c) MeltingThe subsequent reactions may be endothermic or exothermic

Figure 9. DTAcurve for a partially converted high-aluminacement concrete from a test drillingDegree of conversion ¼100 y/(x þ y)

Figure 10. Generalized DSC curve for the melting of animpure materialFraction melted at temperature Tx ¼ (area ABE)/(area ADC)


DTA curves can be used to construct phasediagrams for mixtures. Measurement of a singlepoint on the phase diagram may be sufficient forquality-control purposes. Figure 11 shows theDTA curve for a nickel-based superalloy, wherethe solvus temperature (the temperature corre-sponding to complete solution of one solid phasein another) of the g 0

phase characterizes the heattreatment to which the alloy has been subjected.

Solid – solid reactions have also been suc-cessfully studied by these techniques, as havedecompositions of high explosives. The applica-bility of DTA/DSC to very small samples is ofobvious value here. Similarly, preliminaryscreening of potentially hazardous reaction mix-tures is conveniently carried out in this way as aguide to the likelihood of exothermic reaction,the corresponding temperature range and magni-tude, and possible effects of pressure and atmo-spheric conditions (see also Section 2.4.5).

1.3.4. Modulated-Temperature DSC(MT-DSC)

MT-DSC is an important development (see alsoSection 2.2.3) which offers significant advan-tages in the quality of results and gives additionalinformation, particularly for polymers [16]. Asinusoidal modulation is superimposed on thenormally linear temperature ramp, and the result-ing signals are analyzed by a Fourier Transformtechnique. This allows the separation of ‘‘revers-ing’’ and ‘‘nonreversing’’ thermal events andsimplifies the analysis of overlapping transitionssuch as those often found in the glass transitionregion. Other benefits include the ability to mea-sure heat capacity changes pseudo-isothermally,

as in, e.g., curing systems, and improved signal-to-noise ratio and baseline linearity.

1.4. Simultaneous Techniques

1.4.1. Introduction

TG or DTA/DSC alone rarely gives sufficientinformation to permit a complete interpretationof the reactions in a particular system; resultsmust usually be supplemented by other thermalmethods and/or general analytical data. Alterna-tive thermal methods are best applied simulta-neously, leading, for example, to TG and DTAinformation from the same sample under identi-cal experimental conditions. This avoids ambi-guity caused bymaterial inhomogeneity, but alsoproblems attributable to different experimentalconditions with different instruments, whichsometimes markedly affects the correspondencebetween TG and DTA curves. Other advantagesinclude: (1) indication of the thermal stability ofmaterials examined by DTA, which in turnmakes it possible to correct measured heats ofreaction for partially decomposed samples; (2)accurate temperature measurement in TG work,which is vital in kinetic studies; and (3) thedetection of unsuspected transitions in a con-densed phase, which may help explain puzzlingfeatures of the corresponding TG curve.

The range of simultaneous techniques hasbeen reviewed by PAULIK [17]. TG – DTA andTG – DSC are the commonest simultaneousmethods, followed by evolved gas analysis (Sec-tion 1.5).

1.4.2. Applications

TG – DSC curves showing the curing and de-composition of a polyimide resin are presented inFigure 12. Following a glass transition (a) andsubsequent fusion of the material at ca. 120 �C(b), which are detected by DSC, the TG curvereveals the initial stages of an exothermic curingreaction (c) that occurs with a 7% mass loss.Endothermic decomposition of this resin doesnot take place until ca. 430 �C, as shown again byTG (d), a finding that permitted assignment of theappropriate baseline for measuring the heat ofcuring.

Figure 11. DTA curve for a nickel-based superalloya) Solution of the g 0 phase; b) Melting 250 mg sample heatedat 10 �C min�1 in argon


1.5. Evolved Gas Analysis

Evolved gas analysis (EGA) measures the natureand/or quantity of volatile products released onheating. In practice it is often performed simul-taneously with TG or TG – DTA, and is partic-ularly useful in furnishing direct chemical infor-mation to augment the physical measurements ofTG or DTA. Additional advantages that haveemerged include specificity – a single decompo-sition can be followed against a background ofconcurrent processes – and sensitivity, which canbe far greater than with TG alone [18, 19].

Instrumentation. Almost every imaginabletype of gas detector or analyzer has been utilized inEGA, including hygrometers, nondispersive infra-red analyzers, and gas chromatographs. Absorp-tion of the products into solution permits analysisby coulometry, colorimetry, ion selectiveelectrodemeasurements, or titrimetry. The most importantanalyzers are Fourier transform infrared (FTIR)spectrometers and, preeminently, mass spectro-meters [20]. The two latter methods can be usedto record spectra repetitively, thereby producing atime-dependent record of the composition of thegas phase, from which EGA curves can be con-structed for selected species.

Applications. Simultaneous TG – MScurves for a brick clay are shown in Figure 13,which simulates a set of firing conditions [21].After an initial loss of moisture, combustion of

organic matter at ca. 300 �C gives characteristicpeaks for CO2, H2O, and SO2. More SO2 resultsfrom the oxidation of iron sulfides. Clay dehy-droxylation occurs in the range 350 – 600 �C,and calcite dissociates to give the CO2 peakobserved at higher temperatures. EGA is of greatvalue in the interpretation of complex TG andDTA curves.

In another example (Fig. 14), the evolution ofbenzene from two samples of PVC, one containinga smoke retardant, was compared quantitatively byinjecting knownamounts of benzene into the purgegas stream before and after the experiments, there-by providing a standard for estimating the amountof benzene produced by the polymer [21]. Thesmoke retardant was found in this case to reducebenzene evolution by a factor of ca. 20.

1.6. Mechanical Methods

This section covers a family of techniques leadingto dimensional or mechanical data for a material

Figure 12. Simultaneous TG – DSC curves for an uncuredpolyimide resin a) Glass transition; b) Melting; c) Curing;d)Degradation 10 mg sample heated at 10 �C min�1 in argon

Figure 13. Simultaneous TG – MS curves for a brick clayA) TG curve; B) MS dataEvolution of a) Water (M, 18); b) Carbon dioxide (M, 44);c) Sulfur dioxide (M, 64)40 mg sample heated at 15 �C min�1 in air


as a function of temperature or time. For a suc-cinct review of the application areas see [23].

Thermodilatometry (TD) measures di-mensional changes (expansion) as a function oftemperature in materials subject to negligibleloads. A probe, which is held in light contactwith the heated sample, is connected to a sensi-tive position sensor, usually a linear variabledifferential transformer (LVDT). In another typeof dilatometer the volume change on heating orcooling can be measured in a similar way. Inaddition to providing expansion coefficients thetechnique can also indicate phase changes, sin-tering, and chemical reactions.Major applicationareas include metallurgy and ceramics.

Thermomechanical Analysis. The equip-ment used in thermomechanical analysis (TMA)is similar in principle to that for TD, but provisionis made for applying various types of load to thespecimen, so that penetration, extension, andflexure can be measured. This approach to ana-

lyzing such modes of deformation is illustratedschematically in Figure 15. The technique findsmost use in polymer studies, as in the determi-nation of glass-transition and softening tempera-tures for thin films and shrinkage characteristicsof fibers.

Dynamic Mechanical Analysis. Polymersexhibit both elastic and viscous behavior understress. In dynamic mechanical analysis (DMA) asinusoidally modulated stress, often flexural(though measurement is also possible under ten-sile, compressive, shear, or torsional conditions)is applied to a specimen of material maintainedunder a specified temperature regime. Displace-ment transducers measure strain induced in-phase with the stress, as well as strain that lagsbehind. The former gives a measure of thesample’s modulus, or stiffness, and the latterreflects damping characteristics. Like most otherthermoanalytical techniques, DMA can be usedto generate quantitative physical data, but it isalso invoked in a comparative sense: to monitorthe effects of additives, for example, or in qualitycontrol. It is particularly well suited to the ex-amination of engineering composites, since ge-lation and curing behavior is sometimes moreeasily followed by DMA than by alternativetechniques such as DSC.

1.7. Less Common Techniques

Thermoptometry. This group of techni-ques includes:

Figure 14. Simultaneous TG – MS curves showing the evo-lution of benzene (m/e, 78) A) TG curve; B)MS curve a) PVCwithout a smoke retardant; b) PVC with a smoke retardant(4% MoO3)15 mg samples heated at 10 �C min�1 in argon

Figure 15. Modes of deformation subject to examination byTMA A) Penetration; B) Extension; C) Flexure a) Sample;b) Probe; c) Clamps; d) Load


1. Thermomicroscopy, in which a material isobserved under reflected, transmitted, or po-larized transmitted light. The correspondingapparatus is referred to as a hot stage, whichmay also incorporate a DSC sensor for addi-tional information.

2. Thermophotometry, in which the intensity ofreflected or transmitted light is measured.

3. Thermoluminescence, which provides a mea-sure of the intensity of light emitted by thematerial itself.

Electrical and Magnetic Techniques.Thermomagnetometry is used to study the mag-netic properties of materials by revealing appar-ent weight changes that accompany phase transi-tions in the presence of an appliedmagnetic field,or variations in the amount of a magneticsubstance.

Thermoelectrometry comprises methodsfor the measurement of resistance or capacitanceduring heating. Some equipment in this categoryprovides remote probes for in situ monitoring ofthe curing of thermosets.

Microthermal analysis (m-TA) enables arange of thermal methods to be applied toregions of a material only a few micrometerswide. They are based on the use of an atomicforce microscope (AFM) with a heatable tip.Many materials are heterogeneous, and themicrostructure can influence the material prop-erties on the macroscale. After acquiring theconventional AFM topographic image, selectedfeatures can be subjected to DTA and TMAwiththe probe tip. The tip can also be used to pyro-lyze the selected area, and the vapors are thenanalyzed by GC-MS [24].

2. Calorimetry

2.1. Introduction [25–45]

Calorimetry in the broadest sense means thequantitative measurement of energy exchangedin the form of heat during a reaction of any type.By contrast, thermal analysis (Chap. 1) is con-cerned only with the measurement and recordingof temperature-induced changes or temperaturedifferences in dependence on time. Since all

chemical reactions and many physical changes(e.g., deformation, phase transformations) areassociated with the uptake or release of heat, thequantitative investigation of heat exchange is arelatively simple and universal method for char-acterizing particular processes both in an overallsense and with respect to time.

Nevertheless, only in recent decades has cal-orimetry emerged from the laboratories of a fewthermodynamicists and specialists to become awidespread, convenient analytical method. Thedevelopment of commercial calorimeters sincethe 1950s has led to rapid dissemination andapplication of the method even beyond thebounds of universities.

The explanation of this phenomenon, as withmany other apparatus-based developments, liesin the refinement in measurement techniquesmade possible by modern electronics. As a rule,heat cannot be measured directly, but must bedetermined instead on the basis of a temperaturechange in the system under investigation. Veryaccurate classical thermometers tend to be veryslow measuring devices. Resistance thermo-meters and thermocouples respond much morerapidly, but they require electronic amplification,and amplifiers with the required precision havebecome available only in recent decades.

A further explanation for the increasing im-portance of calorimetry is the development ofpersonal computers, which relieve the user of theoften laborious task of evaluating the experimen-tal results, thereby opening the way for the meth-od to become a routine laboratory technique.

In the sections that follow, calorimetry andthe present state of instrument development willbe described in such a way as to reveal both thepossibilities and the limits of the method. Thescope of the chapter rules out exhaustive treat-ment of the subject, so the goal is rather todelineate the method and guide the interestedreader to other relevant technical literature.

2.2. Methods of Calorimetry

As noted above, heat that is released or consumedby a process cannot be measured directly. Unlikematerial quantities such as amount of substance,which can be determined with a balance, or thevolume of a liquid, which can be establishedwith a liter measure, the quantity heat must be


measured indirectly through its effect on a sub-stance whose temperature it either raises or low-ers. The fundamental equation for all of calorim-etry describes the relationship between heat ex-changed with a calorimeter substance and acorresponding temperature change:

DQ ¼ CðTÞ�DT ð1ÞwhereDQ ¼ exchanged heat (J),DT ¼ observedtemperature change (K), and C (T) ¼ heat ca-pacity (J/K).

For heats (and therefore temperature changes)that are not too large, the temperature change isdirectly proportional to the exchanged heat. Theproportionality constant is the heat capacity ofthe calorimeter substance (previously referred toas the ‘‘water value’’). However, if the tempera-ture change exceeds a few Kelvin, the tempera-ture dependence of heat capacity stands in theway of a linear relationship, and a knowledge ofthe temperature function of the particular heatcapacity in question is required in order to deter-mine heat on the basis of a measured temperaturedifference.

The relationship above leads directly to thestandard calorimetric methods for determiningthe heat of a process: either temperature is heldconstant by appropriate compensation for theheat effect, and the required compensation poweris measured, or a temperature change is deter-mined and used to calculate a correspondingvalue for exchanged heat. A precondition for thelatter approach is accurate knowledge of the heatcapacity aswell as the heat transport properties ofthe measurement system.

2.2.1. Compensation of the ThermalEffects

In the first method of heat measurement, temper-ature changes in the calorimeter substance areavoided by supplying or dissipating heat exactlyequal in magnitude (but opposite in sign) to thatassociated with the process under investigation.As a rule, electrical energy is used to provide thiscompensation, either by introduction in the formof Joule’s heat or dissipation through the Peltiereffect. A combination approach is also possible,with an appropriate constant level of cooling andsimultaneous controlled electrical heating. Therequisite amount of compensation power can

today be determined with a high degree of preci-sion. It was once customary to invoke for com-pensation purposes ‘‘latent’’ heat derived from aphase change; in other words, heat released in aprocess was measured by using it to melt asubstance such as ice, with subsequent weighingof the resulting water and conversion of the datainto energy units based on the known heat offusion for ice.

Themethod of compensation is advantageous,since it permits measurements to be carried outunder quasi-isothermal conditions, therebyavoiding heat loss from the calorimeter to thesurroundings by heat transport processes. Fur-thermore, there is no need for a calibrated ther-mometer, only a sensor sufficiently sensitive totemperature changes to provide adequate controlover the compensation power.

2.2.2. Measurement of a TemperatureDifference

In this alternative method of heat measurement,which is also indirect, a measured temperaturedifference is used to calculate the amount of heatexchanged. A distinction can be made betweentemporal and spatial temperature-differencemeasurements. In temporal temperature-differ-ence measurement the temperature of a calorim-eter substance is measured before and after aprocess, and a corresponding heat is calculatedon the basis of Equation (1) (which presupposesan accurate knowledge of the heat capacity). Inthe spatial method a temperature difference be-tween two points within the calorimeter (orbetween the calorimeter substance and the sur-roundings) is the quantity of interest. The basisfor interpretation in this case is from Fourier’slaw the equation for stationary heat conduction(Newton’s law of cooling):

F ¼ lðTÞ�A�DT �l�1 ð2ÞwhereF ¼ heat flow rate (W), l (T) ¼ thermalconductivity (W m�1 K�1),A ¼ cross-sectionalarea (m2), DT ¼ temperature difference (K), andl ¼ length (m).

From this expression it follows that the heatflow rate through a heat-conducting material isproportional to the corresponding temperaturedifference. If this temperature difference is re-corded as a function of time, then for a given


thermal conductivity one acquires a measure ofthe corresponding heat flow rate, which can beintegrated to give a total heat. The techniqueitself is very simple, but the result will be correctonly if the measured temperature difference ac-curately reflects the total heat flow rate and noheat is lost through undetected ‘‘heat leaks’’.Careful calibration and critical tests of the calo-rimeter are absolutely necessary if one hopes toobtain reliable results.

A fundamental disadvantage of the tempera-ture-difference method is the fact that noni-sothermal conditions prevail, so the preconditionof a stationary state is fulfilled only approximate-ly. The potential therefore exists for nonlinearphenomena in the heat-transport process, whichmight result in conditions outside the range ofvalidity for Equation (2). Furthermore, with non-isothermal studies it is impossible to rule outcompletely the presence of undetected leaks. Itmust also be pointed out that in the case ofnonisothermal studies the thermodynamic quan-tities of interest cannot be established accordingto the methods of reversible thermodynamics, atleast not without further consideration. Strictlyspeaking, irreversible thermodynamics shouldbe applied to nonisothermal calorimetry. Al-though the distinction is generally unimportantin normal calorimetric practice, it becomes es-sential in cases where time-dependent processesare involved with timescales which are compa-rable to those of the experiment, e.g., in thetemperature-modulated mode of operation.

2.2.3. Temperature Modulation

The temperature-modulated mode of operationhas been well known for many decades in calo-rimetry [46], but became well established onlyduring the 1990s, when commercial DSC wasmodified thisway [47]. The idea is to examine thebehavior of the sample for periodic rather thanfor isothermal or constant-heating-rate tempera-ture changes. In this way it is possible to obtaininformation on time-dependent processes withinthe sample that result in a time-dependent gen-eralized (apparent) heat capacity function or,equivalently, in a complex frequency-dependentquantity. Similar complex quantities (electricsusceptibility, Young’s modulus) are knownfrom other dynamic (dielectric or mechanical)

measurement methods. They are widely used toinvestigate, say, relaxation processes of thematerial.

In calorimetry there are three establishedtemperature modulation methods:

1. The sample is heated with a periodicallychanging heat flow from a electrical heater[48] or chopped light beam [49], and thetemperature change of the sample (magnitudeand phase shift) is measured as the responsesignal (AC calorimetry).

2. A thermal wave is sent into the sample from ametallic film that is evaporated onto its sur-face and which heats it periodically. Thetemperature change is measured by using thesame metal film as a resistance thermometer.The third harmonic of the resulting tempera-ture oscillations is proportional to the powerinput and depends on the product of the heatcapacity and thermal conductivity of thesample in a characteristic way (3w method[50]).

3. The sample (or furnace) temperature is con-trolled to follow a set course with super-imposed periodical changes, and the heatflow rate is measured via the differentialtemperature between sample and reference(temperature-modulated differential scan-ning calorimetry, TMDSC [47, 51, 52]).

In all three cases, both the magnitude of theperiodic part of the response signal and its phaseshift with respect to the stimulating signal aremeasured, and this results in a complex quantity(temperature, heat flow rate, and heat capacity,respectively). As heat transport always requirestime, the frequency of temperature modulationis normally limited to a maximum of 0.2 Hz toallow the heat to flow through the sample prop-erly. For the 3w method, however, frequenciesof several kilohertz are possible because the heatsource and the temperature probe are identicalin this case. At the lower end, the frequencyrange is only limited by the noise threshold(sensitivity) of the sensors in question. As arule only two decades are available. Conse-quently, only time-dependent processes withtimescales within this window can be followedin the calorimeter.

For quasistatic conditions it follows fromEquation (1) that:


dQ

dt¼ F ¼ Cp� dT

dtð3Þ

where the real quantities heat flow rate F andtemperature change (heating rate) are strictlyproportional, with the real heat capacity Cp asproportionality factor. This implies an infinitepropagation velocity of thermal waves and aninfinitely fast excitation time of the vibrationalstates that characterize the (static) heat capacityof a sample. Both conditions are fulfilled fornormal solids within the above-mentioned fre-quency range. In cases where processes are in-volved which need time, the heat flow rate andthe temperature change are no longer proportion-al, and the process in question causes the heatflow to lag behind the temperature. This resultsformally in a time-dependent apparent heat ca-pacity, and Equation (3) no longer holds; in-stead:

FðtÞ ¼ CpðtÞ* dTðtÞdt

ð4Þ

This appears very similar, but the operator *stands for the convolution product, which is anintegral operator rather than a product [44, 53].

Equation (4) can be Fourier transformed andthen reads:

FðwÞ ¼ CpðwÞ�Fourier dTðtÞdt

� �ð5Þ

The (complex) heat flow rate is given as anormal product of the complex heat capacity andthe (complex) Fourier-transformed heating rate inthe frequency domain. For a given T(t) course(normally periodical with underlying constantheating rate), the complex heat capacity can bedetermined from the measured complex (magni-tude and phase) heat flow rate function. The result-ingCp function is given either as real and imaginarypart or as magnitude (absolute value) and phase.The two forms are mathematically equivalent.From the frequency dependence of these quantitiesthe Cp(t) behavior can be derived [44].

2.3. Calorimeters

There are many diverse types of calorimeters,differing with respect to measuring principle,mode of operation, and general construction.Measuring principles have been described in the

preceding sections. In terms of mode of opera-tion, two approaches can be distinguished: staticcalorimeters, in which the temperature remainsconstant or changes only in consequence of theheat of reaction, and dynamic calorimeters, inwhich the temperature of the calorimeter sub-stance is varied deliberately according to a pre-scribed program (usually linear with time).

With regard to construction, a distinction canbe made between single and differential calori-meters. Twin design is characteristic of the latter:that is, all components are present in duplicate,and the two sets are arranged as identical aspossible. The reaction under investigation takesplace in one side of the device,while theother sidecontains an inert reference substance. The outputsignal represents the difference between signalsoriginating in the sample and reference side.Withsuch a difference signal all symmetrical effectscancel (e.g., the heat leaks to the surroundings).

2.3.1. Static Calorimeters

Considering first the static calorimeters, threetypes can be distinguished depending uponwhether they are operated in an isothermal, iso-peribolic (isoperibolic ¼ uniform surround-ings), or adiabatic manner.

2.3.1.1. Isothermal Calorimeters

In the isothermal mode of operation it is impera-tive that all thermal effects be somehow compen-sated. This is achieved either electrically or withthe aid of a phase transition of some pure sub-stance. Only phase-transition calorimeters can beregarded as strictly isothermal. In this case ther-modynamics ensures that the temperature willremain precisely constant since it is controlledby a two-phase equilibrium of a pure substance.The most familiar example is the ice calorimeter,already in use by the end of the 18th century anddeveloped further into a precision instrumentabout 100 years later by BUNSEN (Fig. 16). Theliquid – gas phase transition has also been usedfor thermal compensation purposes; in this case aheat of reaction can be determined accurately bymeasuring the volume of a vaporized gas.

Phase-transformation calorimeters are easy toconstruct, and for this reason they are not availablecommercially. Such a device permits very precise


determinationof the heat releasedduringaprocess.An important drawback is the fact that the isother-malmethod is limited to the fewfixed temperaturescorresponding to phase transitions of suitable puresubstances.

This disadvantage does not apply to an iso-thermal device based on electrical compensation.Nevertheless, calorimeters of the latter type op-erate only in a quasi-isothermal mode, sinceelectronic control systems depend for their re-sponse upon small deviations from an estab-lished set point, and a certain amount of time isrequired for changing the prevailing tempera-ture. The use of modern circuits and componentsensures that errors from this source will benegligible, however. Electrical compensationmakes it possible to follow both endothermicand exothermic processes. In both cases thecompensation power is readily measured andrecorded or processed further with a computer.Isothermal calorimeters are used quite generallyfor determining heats of mixing and solution.Commercial devices are available that also sup-port the precise work required for multiphasethermodynamics. As a rule such calorimeters areof the single rather than the differential type.

2.3.1.2. Isoperibolic Calorimeters

An isoperibolic calorimeter is distinguished bythe fact that it is situated within a thermostatedenvironment. As a result, the temperature of thesurroundings is kept constant, as is the effect ofthe surroundings on the calorimeter vessel. A

well-defined thermal conduction path is main-tained between the calorimeter vessel and itssurroundings so that the temperature differencebetween the calorimeter vessel and the environ-ment will be proportional to the heat flow rate.Temperature equilibration usually adheres to anexponential time function, and an integral takenover the entire course of this function is propor-tional to the heat of reaction. Such instrumentsoften have exceptionally large time constants;that is, temperature equilibration occurs veryslowly. Indeed, the greater the equilibration time,the more sensitive is the calorimeter. It is ofcourse difficult with an exponential function toidentify precisely the end point, so the integralover the measurement function and therefore theheat of interest are subject to correspondingdegrees of uncertainty. The advantages lie insimplicity of construction and ease of producinga measurement signal (a straightforward temper-ature difference), which might for example bederived from a differential thermocouple and asimple set of amplifiers.

The best-known calorimeter of this type wasdeveloped by TIAN and CALVET (Fig. 17). Here

Figure 16. Ice calorimeter (based on [54]) a) Sampleholder; b) Calorimeter vessel; c) Capillary with mercurythread; d) Water; e) Ice; f) Ice – water mixture; g) Mercury

Figure 17. Tian – Calvet calorimetera, b) Heat conduction paths between measuring cells andblock; c, d) Sample and reference containers; e) Isoperibolicblock; f ) Thermostatic jacket; g) Thermal insulation;h) Thermopiles


the defined heat-conduction path to the thermo-stated surroundings (a large aluminum block)consists of a large number of differential thermo-couples coupled in series (thermopile). Thisarrangement permits optimum determinationof the heat flow rate to the surroundings, andsuch an instrument can be very sensitive(microcalorimeter).

If heat transport to the surroundings is restrict-ed by suitable insulation, temperature equilibra-tion becomes so slow that –with small correc-tions – temperature changes in the calorimetersubstance alone can serve as the basis for deter-mining the heat of a reaction. Calorimeters in thiscategory include the classicalmixing calorimeter(with heat exchange) in which the sample sub-stance is brought into contact with a (usually)colder calorimeter substance, whereupon an in-termediate ‘‘mixing temperature’’ is established(Fig. 18). Other examples of mixing calori-meters include the simpler types of combustioncalorimeters, in which the calorimeter substanceis water, and the drop calorimeter (see Fig. 24).The latter consists of a metal block whose tem-perature change subsequent to introduction of asample of accurately known temperature pro-vides information about the sample’s heat capac-ity. The category of isoperibolic calorimetersalso includes flow calorimeters, in which two

fluid media (usually liquids containing the reac-tants) are first brought to the temperature of thethermostated surroundings and then combined.The ensuing reaction causes a measurable tem-perature change, the extent of which is propor-tional to the heat of the reaction (Fig. 19).

Figure 18. A classical mixing calorimeter (from MeyersConversationslexikon, 1893) a) Calorimeter vessel; b) Con-vection and radiation shield; c) Cover; d) Jacketing vessel(thermostated); e) Lifting mixer

Figure 19. Flow calorimeter, with a chemical reaction occurring in the liquidA, B reactants, A þ B reaction product; a) Differential thermocouple


2.3.1.3. Adiabatic Calorimeters

An adiabatic calorimeter is equipped with anelectronic control system designed to ensure tothe greatest extent possible that the surroundings ofthe calorimeter cell remain at all times at preciselythe same temperature as the substance underexamination. The object is to prevent virtually allheat transport to the surroundings, thereby makingit possible to establish the total heat effect from thechange in temperature of the calorimeter sub-stance. Good adiabatic calorimeters are difficultto construct, and they are not available commer-cially. Nevertheless, precision instruments ofthis type permit quantities such as specific heatcapacities, as well as associated anomalies, to bemeasured very accurately (Fig. 20). The method

entails an extraordinary level of effort, and it ispracticed only by specialists working in a fewlaboratories in the world [55].

Simpler adiabatic calorimeters are distribut-ed commercially in the form of adiabatic mixingand combustion calorimeters. These constitutevery satisfactory routine instruments, especiallysince the adiabatic mode of operation (whichentails measurement of only a single temperaturedifference) facilitates automated data acquisitionand interpretation.

2.3.2. Scanning Calorimeters

Scanning calorimeters are devices in which thesample temperature is deliberately changed dur-ing the course of an experiment according to aprescribed program. As a rule, heating or coolingof the sample is caused to occur linearly withtime, and the heat flow rate required to accom-plish the desired change is determined and outputas a function of time or temperature. Any chemi-cal or physical change in the sample at a particu-lar temperature will manifest itself as a change inthe heat flow rate, leading to a ‘‘peak’’ in themeasurement curve whose area is proportional tothe heat of the process (see also Section 1.3.2).

Such instruments havebeen on themarket sincethe 1950s. Their great advantage is that they permitheats of reaction and transformations of every typeto be measured both rapidly and with reasonableprecision. Heating rates usually fall in the range5 – 20 K/min, so a measurement extending over300 K can be completed within an hour, providinga reliable indication of all changes in the sampleover this temperature range, including heats ofreaction. The rapid development of calorimetry inrecent years is due largely to the perfection of thistype of calorimeter.

Scanning calorimeters are designed almostwithout exception as differential devices. Withregard to the principle of measurement, twovarieties can be distinguished: differential-tem-perature and power-compensated calorimeters.Although the two types rely upon very differentapproaches to determining heat flow rates withrespect to the sample, and are therefore subject todifferent sources of error, they are marketedunder the single heading differential scanningcalorimeter (DSC). They can even be operated intemperature-modulated mode.

Figure 20. Construction of an adiabatic calorimeter (basedon [56]) a) External radiation shield; b) Internal radiationshield; c) Adiabatic jacket; e) Calorimeter vessel; f) Samplesuspension platform with resistance thermometer and heater;g) Electrical leads; h) Calorimeter suspension system


2.3.2.1. Differential-Temperature ScanningCalorimeters

In a differential-temperature scanning calorimeterthe heat necessary for raising the sample tempera-ture reaches the sample position via one well-defined heat conduction path (cf. Fig. 21). Themeasured signal is derived from a temperaturedifference generated along this path, which isproportional to the heat flow rate [see Eq. (2)].Thismeasuring and operating principle leads to thealternative designation heat-flux calorimeter forsuch a device. In order to minimize errors fromheat leaks and other influences of the surroundings,calorimeters of this type are always based on adifferential design, with full duplex construction.Many commercial models are available.

Any temperature difference between the sam-ple and the reference is directly proportional tothe corresponding differential heat flow rate, andso this is the quantity to be measured. Theappropriate functional relationship follows di-rectly from Equation (2):

F ¼ KðTÞ�DT ð6ÞThe heat flow rate of interest, F (in W), is

proportional to the measured temperature differ-

ence DT (in K). Unfortunately, the proportionali-ty constant K (the calibration factor for thecalorimeter in K W�1) is itself a function of thethermal conductivity of the sample [see Eq. (2)],and therefore temperature dependent. Moreover,temperature differences between the sample andthe reference result in variable amounts of heatloss to the surroundings via inevitable heat leaks.Heat exchange with the environment also occursvia radiation and convection. Since the twotransport processes are linked to temperaturedifferences in a nonlinear way, the calibrationfactor in the presumably linear calorimeter equa-tion necessarily depends on DT, which is thequantity to be measured. Consequently, the cali-bration factor depends upon such sample para-meters asmass, thermal conductivity, and specificenthalpy difference [44], so heats measured withthese instruments must realistically be assignedan uncertainty of about five percent unless con-siderable effort has been expended in calibration[57]. Repeatability of the results is generallymany times better, but the user should not makethe mistake of assuming an equally high level ofcertainty. Another source of systematic error maydevelop during the measurement if some reactioncauses a change in the heat capacity and/or theextent of heat transfer to the sample holder. Bothphenomena contribute to changes in the baseline,with the result that the course of the latter cannotbe plotted accurately (Fig. 22). This in turnmeansthat the area corresponding to the heat of reactionalso cannot be determined exactly, leading to

Figure 21. Operating principle of a temperature-differencescanning calorimeter (heat-flux calorimeter)TF furnace temperature, TS sample temperature, TR referencetemperature, T0 initial temperature, DT differential tempera-ture TS � TR, b heating rate, t time

Figure 22. Output curve from a scanning calorimeter show-ing a shift in the baseline caused by variability in either cp orthe coefficient of heat transfera) Original baseline; b) Peak; c) Unknown baseline path;d) Final baseline


uncertainty in the associated heat [44]. Despitethese restrictive comments, differential-tempera-ture scanning calorimeters offer the advantages ofa simple, transparent mode of operation andrelatively low cost, and for this reason theyaccount for a large share of the market. Withappropriately critical supervision they are capa-ble of fulfilling their assignment admirably. In2002 a new type of heat-flux calorimeter with‘‘Tzero� technique’’ [58] became commerciallyavailable. This DSC uses the power of moderncomputer technology to correct for some of thementioned sources of error resulting in a highercertainty and better resolution of the measuredcurves and an excellent (almost zero) baseline.

2.3.2.2. Power-Compensated ScanningCalorimeters

Like differential-temperature devices, power-compensated scanning calorimeters always fea-ture duplex construction, with sample and refer-ence holders heated in such a way that at everyinstant the temperature of each corresponds al-most exactly to a programmed set temperature.Any temperature differences that arise betweensample and reference by reason of thermal eventsin the sample are compensated immediately byappropriate changes in the electrical heating(Fig. 23). The output signal is proportional to theinstantaneous differential heat flow rate. Sincetemperature differences between sample and ref-erence are essentially compensated at once, mea-surement errors due to undetected heat leaks canbe largely avoided. Instruments of this type, themost widely distributed of which are manufac-tured by Perkin – Elmer instruments, require avery complicated electronic control system, andare therefore rather expensive. The principal dis-advantage lies in the fact that the electronicsystem is a black box for the average layman,therebyobscuringpossible sources of error.Theseinstruments also require that there be some devi-ation, albeit minimal, from the set temperature toguide the control circuit, so just as in the preced-ing case some systematic error must be anticipat-ed (although certainly to a lesser degree), associ-ated once again with temperature differencesbetween sample and reference and nonlinear heatexchange. Accordingly, the level of systematicuncertainty for heats measured by power-com-pensated DSC can be estimated at 1 – 3%.

2.3.2.3. Temperature-ModulatedScanning Calorimeters

Differential-temperature and power-compensat-ed scanning calorimeters are now commerciallyavailable to run in the temperature modulatedmode (TMDSC). In both cases the temperature iscontrolled to follow the normal (linear in time)course but with an additional periodical temper-ature change of particular amplitude and frequen-cy. The measured heat flow rate function is thesum of the ‘‘underlying‘‘ part and the periodicalpart. The former can be extracted by calculatingthe ‘‘gliding average‘‘ integral over a periodalong the measured curve. It is identical to thecurve that would be obtained in this DSC whenthe temperature modulation is switched off. Theperiodical part, on the other hand, is the differ-ence of the measured and the underlying curves[44]. From the periodic part the complex Cp canbe calculated by using Fourier analysis or other

Figure 23. Operating principle of a power-compensateddifferential scanning calorimeter (Perkin – Elmer)T0 initial temperature; TS sample temperature; TR referencetemperature; hT imean temperature between sample and refer-ence; DP differential power PS � PR; b heating rate; t time


mathematical techniques. This enables time de-pendent-processes to be investigated in caseswhere their timescale falls within the frequencywindow of the TMDSC method [44].

For precise measurements it is necessary tocorrect (calibrate) the measured heat flow ratemagnitude and phase shift for influences from theapparatus, as well as from the heat transport,which also is a time-dependent process andtherefore influences the measured heat flow ratefunction [44, 59, 60].

2.3.3. Chip-Calorimeters

In the early 2000s a huge progress has been madein miniaturization of electronic equipment, inparticular in the field of integrated circuits. Itbecame more and more easy to produce ‘‘chips’’with thin Si or SiNmembranes as basis which canbe used as micro- or nanocalorimeters. Suchchip-calorimeters have on the one hand a veryfast response time (in the milliseconds region)and open the possibility to measure very smallsamples (nanograms) at heating and cooling ratesup to 5000 K/s [61] (for details see [62] and otherarticles in this special issue of ThermochimicaActa). This technology opens very new fields ofresearch on thermodynamic behavior of smallparticles as well as membranes on the one handand the detection of very small amounts of sub-stances with the help of specific chemical reac-tions on the other hand. The latter can be a largestep toward the development of an ‘‘artificialnose’’ which may serve as a sensor to detect,say, dangerous gases in the surroundings.

2.4. Applications of Calorimetry

Modern calorimeters permit relatively rapid andtruly precise measurement of heat exchanges in awide variety of reactions. Since heat evolution isproportional to the conversion (extent of reac-tion) in a chemical, physical, or biological reac-tion, calorimetric measurement constitutes onemethod for quantitative evaluation of the reac-tion itself. Measurement is possible not only ofthe total heat (and therefore the total conversion)of a reaction but also of the course of the reactionwith respect to time. This opens the way tostudies of kinetics, problems related to stability

and safety, and other areas in which temperatureand time-dependencies in a reaction play a part.

The sections that follow describe several pos-sible applications of calorimetry, although theseshould be regarded only as illustrative, since thescope of the present article rules out any treat-ment that is even approximately exhaustive. Nosuch limits apply to the reader’s imagination,however, and any process that generates (orconsumes) heat can in principle be followedwith a calorimeter. Enzymatic and bacterialmanufacturing processes have assumed increas-ing importance in industry, and interest in bio-calorimetry is growing accordingly [63–65].

2.4.1. Determination of ThermodynamicFunctions

Various thermodynamic potential functions (en-thalpy, entropy, free energy, etc.) can be deter-mined by integration on the basis of specific heatcapacities. The accurate establishment of specif-ic heat capacities at constant pressure, cp, as afunction of temperature is thus of fundamentalimportance. Different types of calorimeters areused for determinations of cp depending uponaccuracy requirements and the temperature rangein question.

The most accurate results are obtained withadiabatic calorimeters, which are useful over atemperature range from fractions of a Kelvin toabout 1000 K. These instruments permit specificheat capacities to be determined with very smalluncertainties (<1%). Nevertheless, such mea-surements are so complex that they are rarelyapplicable to normal laboratory practice in in-dustry, especially given the lack of commercialinstruments.

The standard approach to cp measurementtherefore relies on the less precise butmore easilyconstructed and operatedmixing calorimeters, inparticular drop calorimeters (Fig. 24). A (mean)specific heat capacity is calculated in this casefrom the heat released when a sample of knowntemperature is introduced (dropped) into an iso-peribolic calorimeter. Charging temperaturesmay exceed 2500 K. Determining the tempera-ture dependence of cp requires many individualmeasurements at various charging temperatures.The uncertainty in such measurements is usually3 – 5%.


A truly elegant method for determining cp at<1000 K takes advantage of a scanning calo-rimeter [44], preferably a power-compensatedDSC. The procedure involves raising the tem-perature of a sample in the calorimeter at adefined rate (typically 10 K/min). The samemeasurement is subsequently repeated, this timewith empty crucibles. The difference between thetwo measurement curves provides a record ofthe heat flow rate into the sample, fromwhich thespecific heat capacity can be calculated. Thismethod makes it possible conveniently to mea-sure the cp(T) of a material over a temperaturerange of several hundred Kelvins within thecourse of a single day. However, it does demanda very high level of repeatability (baseline sta-bility) for the DSC in question. In the case ofdifferential-temperature (heat-flux) DSC – evenwith careful calibration – uncertainties of 5 –10% in the results must be anticipated. Withpower-compensated DSC the systematic uncer-

tainties tend to be in the range of 3 – 5%. Un-certainties in the calculated thermodynamic po-tential functions of interest are comparable.

The TMDSC enables another elegant possi-bility of cp (magnitude) determination from theamplitude of the modulated part of the measuredheat flow rate function both in the isothermal andscanning modes of operation. This method isespecially advantageous in cases of noisy signalswith low sample masses or low heating rates.Precise calibration of the heat flow rate ampli-tude is a prerequisite for obtaining reliable results[44, 60, 61].

However, a calorimeter operating dynamical-ly always indicates a temperature that deviates toa greater or lesser extent from the true sampletemperature, resulting in further uncertainty. Itmust in any case be borne in mind that potentialfunctions determined on the basis of thermody-namic equilibrium, and thus defined statically,may differ from functions determined dynami-cally, since equilibrium conditions are not main-tained in DSC, and in the case of a reaction evenstationary conditions are lacking.

If time-dependent processes are involved,then the process is clearly outside the scope ofclassical thermodynamics. The time-dependent(apparent) heat capacity, measured with, say,TMDSC would lead to time-dependent potentialfunctions which must be interpreted in terms ofirreversible thermodynamics. In such cases, anonzero imaginary part of the complex heatcapacity exists which is linked to the entropyproduction of the process in question (for detailssee [45]). Thus, temperature-modulated calorim-etry makes it possible to determine time-depen-dent (irreversible) thermodynamic quantities.

2.4.2. Determination of Heats of Mixing

For liquid systems consisting of several compo-nents, multiphase thermodynamics provides thetheoretical background for computing phase dia-grams from heats of mixing for the relevantcomponents. Phase diagrams in turn are interest-ing not only to thermodynamicists; they are alsoof great importance in chemical process engi-neering practice.

The determination of heats of mixing is aclassical field of investigation for calorimetry,one that at the required level of precision is today

Figure 24. High-temperature drop calorimeter (based on[67]) a) Sample; b) Heated corundum tube; c) Magnesiainsulation; d) Cooling coils; e) Sample mounting device;f) Copper block; g) Hole for receiving sample; h) Resistancethermometer; i) Level of the thermostated oil bath


incomparably less laborious than previously.Enthalpies of mixing were formerly determinedin some cases indirectly via vapor pressure mea-surements, but today they are measured directlyin (quasi)isothermal or isoperibolic calorimeters.Recently also chip-calorimeters have been usedfor this purpose [66].

The art of conducting such an experimentsuccessfully lies in rigorously excluding vapori-zation during the measurement, since specificheats of vaporization are orders of magnitudelarger than the effects of mixing that are to bemeasured. As excess quantities (which charac-terize deviations from ideal behavior), heats ofmixing are invariably small, and they must bedeterminedwith high precision in order to permitthe construction of sufficiently precise phasediagrams. Isothermal calorimeters are thereforedefinitely to be preferred, since here the problemof incomplete determination of a heat ofmixing –owing perhaps to undetected heat leaks – is lesssevere than with an isoperibolic instrument.Moreover, the isothermal heat of mixing is de-fined more precisely, and it lends itself morereadily to mathematical treatment than in thecase of parallel temperature changes.

Phase transitions in solid mixtures can befollowed directly in a scanning calorimeter, sincevapor pressures associated with the componentsare here so low that vaporization plays virtuallyno role and therefore does not interfere. Corre-sponding phase diagrams (i.e., liquidus –soliduscurves) can be inferred from heat flow rate curvesobtained by controlled heating and cooling ofappropriatemixtures (cf. Section 1.3.3). Thermo-dynamically relevant quantities can in turn bedetermined indirectly by comparing measuredphase diagrams with calculated diagrams.

2.4.3. Combustion Calorimetry

The determination of heats of combustion forfuels of all types is prescribed in detail by gov-ernment regulation, since the ‘‘calorific value’’ or‘‘heat content’’ of a particular coal, oil, or naturalor manufactured gas determines its economicvalue. Combustion calorimeters or ‘‘bomb ca-lorimeters’’ (usually operated adiabatically) areused for suchmeasurements, whereby the sampleis combusted in a ‘‘calorimetric bomb’’ (likewisestandardized; cf. Fig. 25) in pure oxygen at

3 � 106 Pa to a defined set of end products.Methods of measurement and interpretation arealso standardized, and they have been simplifiedto such an extent that the entire procedure can beautomated.

The same instruments are useful for determin-ing heats of combustion for a wide variety of(usually organic) substances, from which stan-dard enthalpies of formation can be determined.For these calorimetric methods errors in mea-surement are very small (< 1 ‰), with a level ofprecision that is also appropriate for analyticalpurposes (e.g., purity or composition checks onbatches of chemicals). Combustion calorimetryis useful in biology as well. For example, indeterminations of the nutrient content of leavesand fruits as a function of season and place basedon appropriate heats of combustion.

Many combustion calorimeters are availablecommercially. Instruments utilizing water as thecalorimeter substance generally operate adiabat-ically, thereby avoiding the somewhat compli-cated Regnault – Pfaundler procedure (cf. [42])for determining and interpreting prior and sub-sequent temperature patterns. ‘‘Dry’’ combustioncalorimeters that avoid the use of water or otherliquids have also come onto the market.

Figure 25. Example of a calorimetric bomb for use in acombustion calorimeter a) Pressure vessel; b) Screw cap;c) Sealing ring; d) Inlet valve; e) Outlet valve; f) Samplecrucible with sample; g) Crucible holder; h) Heat shield


2.4.4. Reaction Calorimetry

Every chemical process is associated with sometype of heat effect. Accurate knowledge of heatreleased or consumed is of great importance inprocess engineering. Moreover, heat evolution isstrictly coupled with the particular course of areaction. If one is able to determine unambigu-ously the time dependence of the heat flow rateassociated with a particular sample, one alsogains access to the corresponding reaction ratelaw, which in turn opens the way to the reactionkinetics [44]. Knowledge of the appropriate ki-netic parameters permits one to predict the courseof the reaction under other sets of conditions,which is of great practical value. Heat of reactiondeterminations as well as kinetic studies are bestcarried out under isothermal (and isobaric) con-ditions, and for this reason it is advisable to selecta (quasi)isothermal calorimeter with compensa-tion for effects of the measurement process. One

practical difficulty lies in the fact that reactionbegins immediately after introduction of thesample at the appropriate temperature, eventhough the calorimeter itself is not yet at thermalequilibrium (and therefore not ready for use).Oneway out of this dilemma is to devise a systemfor bringing the components of the reactiontogether only after isothermicity has beenachieved. With liquids the challenge is not par-ticularly great, since pumps and stirrers canensure rapid (and thorough) mixing of the reac-tants at any desired time. The piercing of amembrane (or an ampoule) is also a commonexpedient. Another possibility is the use of aspecially designed reaction calorimeter. Withone device of this type the first reactant is presentfrom the outset in a suitable glass or metallicvessel, to which a second reactant is added withmixing after stationary conditions have beenestablished (Fig. 26). With the aid of electronictemperature control the reaction can then be

Figure 26. Operating principle of a reaction calorimeter (Contraves) a) Reaction vessel; b)Heating and cooling bath; c) Stirrer;d) Balance; e) Pressure sensor for internal pressure; f) pH probe; g) Temperature sensor; h) Dosing valve; i) Control unit;j) Control and monitoring signals; k) Measured signal


carried out in any way desired: isothermally,adiabatically, or under the influence of sometemperature program. Measurement of therelevant quantities, process control, and ther-mochemical data interpretation are all accom-plished with the aid of a personal computer. Asecond type of special reaction calorimeter,suitable only for liquid components, is soconstructed that each reactant is pumped inthrough its own system of tubing, with thestreams uniting after temperature equilibration(Fig. 27). The ensuing reaction causes a tem-perature change, from which the correspondingheat of reaction can be calculated.

Transport and mixing of liquid or gaseouscomponents is accomplished rather easily, butthe situation is more complex for solid sub-stances or mixtures. Here there is little hope ofsatisfactorily mixing the components inside anormal calorimeter, so one is forced to resort toa scanning calorimeter. The calorimeter ischarged at a temperature below that at whichthe substances react, after which the temperatureis increased linearly with time until reaction iscomplete. From a heat flow rate – time functionacquired at a well-defined heating rate it is pos-sible to establish both the heat of reaction and, ifneed be, kinetic parameters for the process. Oneprerequisite, however, is that the recorded func-tion reproduces in an unbiased way the true heatproduction of the sample. This presents seriousproblems, since heat must inevitably flow fromthe point at which it is generated to the site of thetemperature sensors before any measurementsignal can appear. In the case of a fairly rapid

chemical process, where the rate constant iscomparable to the time constant of the calorime-ter, the measurement signal from the recordingdevice must be treated mathematically (‘‘des-meared’’) [44] before it can be utilized for akinetic analysis.

2.4.5. Safety Studies

Calorimetric methods applicable to safety stud-ies are also concerned with clarifying the kineticbehavior of substances, but in this case from asafety engineering viewpoint.

The vast majority of chemical substances areendothermic materials; that is, they release heatwhen they decompose, and their decompositionis accelerated by heat. Chemical reaction kineticsteaches that any reaction is capable of proceedingat temperatures considerably lower than the tem-perature at which the maximum reaction rate isachieved. Usually, however, the reaction rateunder these conditions is so low that the processis not apparent. The more unstable a substance,the lower is its decomposition temperature, andtherefore the greater its decomposition rate atroom temperature. In the event that heat evolvedduring storage – attributable to traces of reac-tion occurring under storage conditions – ex-ceeds the level at which heat is emitted to thesurroundings, then the decomposition rate mayincrease very rapidly, possibly to the point of anexplosion.

Thorough knowledge of decomposition kinet-ics is therefore essential for ensuring safe storageand handling. The requisite information can, inprinciple, be gained through the methods de-scribed in Section 2.4.4, but it is often impossibleto avoid an uncontrolled outcome and simulta-neous destruction of the measuring system. Thisobviously rules out the use of expensive appara-tus, which has led to the development of specialsafety calorimeters that are either inexpensiveand disposable or designed to withstand theeffects of violent reactions.

Simple arrangements of this type clearly pre-clude precision measurements, but they are en-tirely adequate from the specific viewpoint ofassessing storage safety at particular tempera-tures or with particular types of packaging. Thesimplest example is an exceedingly primitiveisoperibolic calorimeter consisting of a glass

Figure 27. Schematic diagram of a flow calorimeter afterP. PICKER (Setaram)A, B) Reactants; A þ B) Reaction mixture; C) Heat-exchange liquid a) Reaction tube (sample tube); b) Referencetube; c, d) Heat-exchange tubes; e) Vacuum jacket;f ) Thermostated liquid; g) Thermistor; h) Flow divider;i, k)Heating elements; l)Measurement and control electronics;m) Output signal


ampoule, either open or fitted with a pressure-tight closure, mounted together with a thermo-couple inside a small furnace – a device thatanyone can easily assemble and calibrate. Moreambitious designs differ from standard calori-meters in that the sample holder (or measuringhead) is incorporated into an autoclave of suffi-cient stability to permit studying the thermalbehavior even of explosives. Included in thiscategory are the so-called accelerating rate ca-lorimeters (ARC), in which a sample is heatedvery slowly under quasiadiabatic conditions untilthe reaction intensifies by itself as a result ofexothermic decomposition. The resulting tem-perature – time function can then be used toestablish the corresponding heat effect and sta-bility behavior.

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M. E. Brown, p. K. Gallagher: Handbook of Thermal

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Calorimetry, informa healthcare, New York, NY 2007.

G. Kaletunc:Calorimetry in Food Processing, Wiley-Black-

well, Ames, Iowa 2009.

S. R. Magill, R. Yoshida: Calorimetry in High Energy

Physics, AIP American Inst. of Physics, Melville, NY

2006.

J. Sest�ak, J. J. Mares, p. Hubik: Glassy and Amorphous

Materials, 1st ed., Springer, Berlin 2009.


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