thermal analysis

31

Differential Thermal

Analysis, Scanning

Calorimetry and

Thermometric

Titrations

UNIT 11 DIFFERENTIAL THERMAL

ANALYSIS, SCANNING

CALORIMETRY AND

THERMOMETRIC TITRATIONS

Structure

11.1 Introduction Objectives

11.2 Differential Thermal Analysis (DTA) Principle

Characteristics of DTA Curves

Instrumentation

Factors Affecting DTA Curves

Sources of Errors

Interpretation of DTA Curve

Applications

11.3 Differential Scanning Calorimetry Principle Instrumentation

Factors Affecting DSC Curves

Sources of Errors

Interpretation of DSC Curve

Applications

Advantages of DSC

11.4 Thermometric Titrations Principle

Instrumentation

Applications

11.5 Summary

11.6 Terminal Questions

11.7 Answers

11.8 Further Readings

11.1 INTRODUCTION

In the previous Unit we discussed thermagravimetric analysis and its applications.

You have learnt that TGA has many applications, but they are limited to the reactions

where mass change should have occurred. Now we will consider two similar thermal

techniques, differential thermal analysis (DTA) and differential scanning calorimetry,

both these techniques have much wider applications than TGA. In the last section of

this unit, thermometric titrations and their applications have been briefly discussed.

As defined earlier, in DTA, the heat changes within a material are monitored by

measuring the difference in temperature (∆T) between the sample and the inert

reference. This differential temperature is then plotted against temperature or time to

get DTA curve (see Fig. 11.1). In differential scanning calorimetry (DSC), the initial

temperatures of the sample and the reference are kept same. The amount of heat that

has to be supplied to the sample or reference to achive this equivalence in temperature

is constantly measured over the temperature range employed. This basically measures

of the amount of energy absorbed or evolved in a particular transition, and hence gives

calorimetric measurements directly. Similar to DTA Curve, DSC Curve can be

obtained by plotting differential heat input to the sample (expressed as a heating rate

dH/dt) against temperature and time (t) (see Fig. 11.2). With this background, now we

will consider the instrumentation and applications of DTA technique.

32

Thermal Methods Objectives

After studying this unit, you should be able to:

• explain the principle of DTA, DSC and thermometric titration,

• describe the experimental setup of DTA, DSC and thermometric titration,

• interpret the analytical information from DTA and DSC curves and

enthalpogram,

• describe the applications of DTA, DSC and thermometric titration, and

• distinguish between thermometric and classical titrimetry.

11.2 DIFFERENTIAL THERMAL ANALYSIS (DTA)

Differential thermal analysis is the most widely used and is probably a very suitable

method for the identification and estimation purposes especially in the case of soils

(clays) and minerals. The chemical or physical changes which are not accompanied by

the change in mass on heating are not indicated in thermogravimetric but there is a

possibility that such changes may be indicated in DTA.

Fig. 11.1: Typical DTA Curve Fig. 11.2: DSC Curve

11.2.1 Principle

Differential thermal analysis is a technique in which the temperature of the substance

under investigation is compared with the temperature of a thermally inert material

such as α-alumina and is recorded with furnace temperature as the substance is

heated or cooled at a predetermined uniform rate. The range of temperature

measurable in the course of DTA is much larger than TG determination. Thus, during

TG, pure fusion reactions, crystalline transition, glass transition and crystallization and

solid state reactions with no volatile product would not be indicated because they

provide no change in mass of the specimen. However, these changes are indicated

during DTA by endothermal or exothermal departure from the base line. Since DTA is

a dynamic method, it is essential that all aspects of the technique be standardized in

order to obtain reproducible results. These include pretreatment of specimen, particle

size and packing specimen, dilution of the specimen and nature of the inert diluent.

The principle of method consists in measuring the change in temperature associated with physical or chemical changes during the gradual heating of the substance.

Thermal changes due to fusion, crystalline structure inversions, boiling, dissociation or

decomposition reactions, oxidation and reduction reactions, destruction of crystalline

lattice structure and other chemical reactions are generally accompanied by an

appreciable rise or fall in temperature. Hence, all these are accounted in DTA.

Generally speaking, phase transitions, dehydration, reduction and some decomposition reactions produce endothermic effects whereas crystallization, oxidation and some

decomposition reactions produce exothermic effects.

In DTA a sample of material under investigation (specimen) is placed by the side of

thermally inert material (the reference sample) usually calacite or α- alumina in

33


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

suitable sample holder or block. The temperature difference between the two is

continuously recorded as they are heated. The block is heated in an electric furnace

i.e. both are heated under identical conditions.

11.2.2 Characteristics of DTA Curves

An idealized representation of the two major processes observable in DTA is

illustrated in Fig. 11.3, where ∆T is plotted on y-axis and T on x-axis. Endotherms are

plotted downwards and exotherms upwards. Similarly, the temperature of the sample

is greater for an exothermic reaction, than that of the reference, for endotherms the sample temperature lags behind that of the reference.

Fig. 11.3: A representation of the DAT Curve showing exotherm, endotherm and base

line changes

When no reaction occurs in the sample material, the temperature of the sample

remains similar to that of reference substance. This is because both are being heated

exactly under identical condition i.e. temperature difference ∆T (Ts–Tr) will be zero for

no reaction. But as soon as reaction starts, the sample becomes either hot or cool

depending upon whether the reaction is exothermic or endothermic. A peak develops

on the curve for the temperature difference ∆T against temperature of furnace or

time. Let us consider the DTA curve in Fig. 11.3 again, where ∆T along the line AB

is zero indicating no reaction but at B where the curve begins to deviate from the

base line corresponds to the onset temperature at which the exothermic reaction starts

and give rise to a peak BCD with a maximum at point C. Where rate of heat

evolution by the reaction is equal to the difference between the rate of evolution of

heat and inert reference material. The peak temperature C corresponds to the

maximum rate of heat of evolution. It does not represent the maximum rate of

reaction nor the completion of the exothermic process. Thus, the position of C does

not have much significance in DTA experiments.

At some determinant point the heat of evaluation process is completed and after this

point heat evaluation goes on decreasing up to D. The usefulness of the method arises

from the fact that peak temperature is normally characteristic of the material in the

sample. Area of the peak BCD is proportional to the amount of reacting material. For endothermic reaction the peak EFG will be obtained as shown in the idealised curve.

This peak shows that the ∆T i.e. (Ts–Tr) will be negative because heat is absorbed and

consequently Ts will be smaller than Tr. Note the levels of base lines of extotherm

curve, AB and DE. Both are at different levels above x-axis. This is due to the fact that

heat capacity of the sample has changed as a result of the exothermic process. Similar

explanation can be given for the difference in levels of base lines of endotherm curve

i.e. DE and GH. DTA curves are not only help in the identification of materials but

their peak areas provide quantitative information regarding mass of sample (m), heat

of reactions (enthalpy change, ∆ H) and factors such as sample geometry and thermal

34

Thermal Methods conductivity. If latter two factors are expressed by a factor K called calibration factor,

then peak area can be express as follows.

Peak area (A) = ± ∆ H m K …(11.1)

We will use +ve sign for endothermic reaction (∆H > 0) i.e. when the temperature of

the sample will lag behind the that of the reference, and negative sign for exothermic

reaction (∆H < 0) the temperature of the sample will exceed that of reference, factor

K is called calibration constant which is temperature dependent. It can be

determined by calibrating DTA with some standard. Once we know the value of K at a

particular temperature, the peak area can be used for quantitative analysis to determine

the mass of sample or energy (enthalpy changes) of a reaction. Beside this DTA curve

also helps in estimating heat capacity of a sample. As you can see in Fig. 11.3 that

there is always a difference in the base lines. The changes in heat capacity ( ∆ Cp) may

be determined at a particular temperature by measuring the difference in base lines i.e.

displacement (d) since:

mmdC 1

orrateheating

p ××

=∆(dT/dt)

d … (11.2)

SAQ 1

Write an expression, which relate the peak area with the amount of the sample. Give

the unit of calibration factor, Kr.

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

11.2.3 Instrumentation

In Fig. 11.4 is shown a block diagram of a differential thermal analyzer. It consists of

following basic components:

1. Furnace Assembly

2. Sample and reference holder with temperature detector

3. Temperature programmer

4. Amplifier and recorder

5. Atmosphere control equipment for furnace and sample holder

The instrument measures the differential temperature of the sample as a function of

temperature or time where the temperature rises at a constant linear rate.

Source of Uniform heating:

Nichrome (nickel and chromium alloy) furnace can be used up to 1300 °C, platinum

and its alloys up to 1750 °C and molybdenum (Mo) for higher range up to 2000 °C. A

special type of higher frequency induction heating may be used for higher

temperatures.

Temperature regulating System:

Uniform rate of heating of the furnace is ensured through electronic temperature

regulators.

If area (A) is measured in

cm2 and unit of ∆ H is

J g–1

, the unit of K will be

cm2 J

–1.

1J

2cm

1gJg

2cm −

=−

=K

In DTA/DSC Cp is

commonly expressed in

mJ g –1

°C-1

. Though in

the SI units, it is

expressed as J mol-1K-1.

SI units of change in

enthalpy, ∆ H, is kJ mol–

1. It is also express as kcal

mol–1

1 calorie = 4.2 J

35


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

(a)

(b)

Fig. 11.4: Schematic diagram of a differential thermal analyzer (a) complete layout (b)

furnace part sharing continuous heating of sample and standard

Specimen Holder

It is designed to accommodate even a small quantity of material and to give maximum

thermal effect. It can be of Pt, Ni, stainless steel, Ag and alloy such as Pt-Rh. Certain

ceramic materials such as sintered alumina , silica, fire clay, heat resistant glass and

even graphite have been recommended as material specimen holder for the sample

under investigation and reference material like (α-alumina).

Measurement of Temperature

Rare metal alloy such as Pt- (Pt-10-13% Rh) are commonly used as thermocouple for

measuring the temperature. For higher temperature up to 2000 0C W-Mo thermocouple

may also be used. Very thin thermocouple is inserted in the sample and reference

holder.

Temperature Recording System

Visual galvanometric observations, though inconvenient can also be used when only a

few samples are to be investigated. Nowadays automatic pen and ink electronic

recorder have been found to be more convenient.

Direct recording of the heating curve

When a sample is heated at a constant rate, the temperature function T, is linear up to

the moment when the sample undergoes change, its slope represents the rate of heating

which remains constant.

36

Thermal Methods At the moment, when an exothermic or endothermic change takes place, the shape of

curve changes as shown in Fig. 11.3. An exothermic reaction causes an increase in

heating rate while endothermic reaction causes a decrease in heating rate. The main

disadvantage of this method is its sensitivity, because small changes in the temperature

causes small deviation in linearity of the curve which some times are not observable.

So, small temperature changes occurring in the sample are generally not detected by

this method. Since detector thermocouples are opposed to each other, small difference

between Ts and Tr can be detected after suitable voltage amplification (Fig.11.4). Thus

very small sample size may be used in this method.

Thus recording of the differential curve is advantageous because it can record the

small change in enthalpy that is not accompanied by a change in weight.

11.2.4 Factors affecting DTA curves:

DTA is a dynamic temperature technique. Therefore, a large number of factors can

affect the resulting experimental curves. Similar to TGA curves, these factors can be

divided into the two groups:

i) Sample factors, and

ii) Instrumental factors

The Instrumental factors such as size and shape of sample holder, sample holder

material, heating rate of the sample, sensitivity of recording system, location of

thermocouple in the sample and atmosphere around sample. Most of these factors are

associated with instrumental design. We have very little control on these factors.

Sample characteristics includes amount of sample, particle size, packing density, heat

capacity and thermal conductivity, degree of crystallinity, dilutes of diluents, swelling

and shrinkage of the sample. In following lines we will concentrate on some of the

important factors in some detail.

1. Amount of Sample: In DTA analysis, peak area of DTA Curve is proportional

to the mass of the sample. Certainly this assumption is valid only over a certain

range of amount of the sample. Generally in DTA experiments, a few mg of

powdered solid sample is used.

2. Particle Size: In DTA experiments, Samples in the form of fine powers are

generally preferred except polymers, in which case we might have to use plastic

fragments or chopped fibers. When we are comparing between two materials,

their sample should have similar particle size.

3. Sample packing: Packing density of sample influences the shape of DTA

Curve. Tight packing influences the escape of volatiles and interaction of

sample with atmosphere of furnace due thermal experiments. Therefore, a

reproducible method of packing the sample is desirable.

4. Heating rate: It is observed that an increase in heating rate increases, the

procedural peak temperature, and some time it also increases peak area. Often

high heating rate results in poor resolution of fine peak in DTA curve. Therefore

slower heating rate is preferred for DTA experiments. Heating rate of 10° C

min-1

and 5° C min-1

are commonly preferred.

5. Atmosphere around sample: Similar to DTG, a flowing gas is preferable to a

static atmosphere as in static atmosphere. There is a possibility of change of

atmosphere around sample on its degradation or decomposition especially in

case of a volatile sample. In such a case we generally use flowing gas technique.

Flowing gas sweeps away volatile by products and keeps homogenous

atmosphere around sample. In Table 11.1, we have summarized the major factor

which can affect the DTA curve.

37


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

Table 11.1: Factors that influence DTA Curve

Factor Effect Suggestions

1. Heating rate Change in peak size and

position

Use a low heating rate

2. Location of

thermocouple

Irreproducible curve Standardise thermocouple

location

3. Atmosphere around sample

Change in the curve Inert gas should be allowed to flow

4. Amount of sample Change in peak size and

position

Standardise sample mass

5. Particle size of

sample

Irreproducible curves Use small, uniform particle size

6. Packing density Irreproducible curves Standardise packing technique

7. Sample container Change in peak Standardise container

Rather empirical nature of the method gives rise to many difficulties originating from

small differences in technique e.g. the peak temperature normally used for reporting

differential thermal results as well as for identification is variable depending upon

the rate of heating, amount of active material, packing of specimen, type of specimen

holder etc. Thus standardization of technique is essential. In general, it is essential that

each apparatus should be calibrated from the mineral expected to be the sample under

investigation.

SAQ 2

List the main factors which affect DTA curves.

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

11.2.5 Sources of Errors

There are a number of sources of errors in DTA, and they can lead to inaccuracies in the recorded temperature and weight data. Some errors may be eliminated by placing

the thermocouple at proper place and handing it with the care. For understanding we

discuss some common sources of errors during operation of a DTA.

i) Buoyance effect: If a thermally inert crucible is heated when empty there is

usually an apparent mass change as temperature increases. This is due to effect

of change in buoyancy of the gas in the sample environment with the

temperature, the increase convection and possible effect of heat from the furnace

in the balance itself. Now, in most modern instruments, this effect is negligible.

However, if necessary, a blank run with empty crucible can be performed over

the appropriate temperature range and calibrate the base line through mentioned

procedure by individual instruments . The resultant record can be used as a

correction curve and results for subsequent experiment performed in the same

condition.

ii) Condensation on Temperature Sensor: Condensation of the sample will also

affect the sensitivity of a thermocouple for temperature measurement. This can

be avoided by maintaining a dynamic atmosphere around the sample in the

furnace so that all the condensable products may be driven by the flowing gases.

iii) Fluctuation of thermostats.

iv) Reaction between sample and container

38

Thermal Methods v) Convection effect from furnace

vi) Turbulence effect from gas flow

vii) Induction effect from furnace

It may noted that errors of type (iii) may be eliminated by properly placing balance in

the laboratory and maintaining constant power supply and error (v) can be avoided by

sensible choice of sample container. Last three types of errors (v-vii) have to be

considered in the design of the furnace, the balance and its suspension system. By

avoiding excessive heating rate and proper gas flow rate some of above mentioned

errors may be eliminated. To further minimize errors, DTA equipment should be

calibrated both for temperature and peak area determination with appropriate

standards. For temperature substances like KNO3, In, Sn, SiO2, BaCO3, etc. are used

depending upon the temperature range used for the experimental condition. For area

calibration indium is often employed as a standard, but as calibration factor K in case

of DTA is temperature dependent, therefore, dependium upon the temperature range of

the experimental condition other standard are also used.

11.2.6 Interpretation of DTA Curve

DTA curves of a pure compound represent characteristic of that compound for

physical chemical changes. Using DTA curve one can co-relate the changes in energy

because of thermophysical and chemical change occurring in a compound because of

heating the material. This can often provide us directly to the temperature at which

the physico- chemical transition are occurring and which is also used to identify the

presence of respective elements or compounds qualitatively. The change in DTA curve

further gives information about the thermophysical changes associated with mass

change e.g. melting point, glass transition temperature, crystallization temperature etc.

To further illustrate, let’s consider the example of CaC2O4.H2O for which DTA curve

is shown in Fig. 11.5. This curve indicates that out of three DTA peaks first is

endothermic in nature, second is exothermic and third one is again endothermic in

nature. The correlates the TGA results and confirms that the nature of reactions

occurring in the endothermic are because of desolvation and decarboxylation while

exothermic is due to decomposition followed by oxidation and finally formation of

stable oxide CaO with evolution of carbon dioxide gas. This can be explained by the

chemistry of decomposition of CaC2O4.H2O when it is heated.

Fig. 11.5: DTA curve of CaC2O4.H2O in the presence of O2

39


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

DTA curves are useful both qualitatively and quantitatively. Similar to TGA, the

position and shapes of the peaks (curve) can be used to determine the composition of

the sample. As discussed earlier, Eq. 11.1 can be used to relate peak area with the heat

of the reaction and amount of sample used for analysis. But before using this equation

we should know the value of calibration constant, K, at the temperature concerned.

This can be achieved by the calibration of instruments with known standards.

However, the value of the calibration factor, K, may be eliminated from the

quantitative calibration by comparison of peak area of unknown sample with the

known sample under identical condition. For example if A1 is the peak area of known

mass (m1) and A2 is the peak area of unknown sample having mass equal to m2, then

using Eq. 11.1 we can write.

2

1

2

1

A

A

m

m=

or

=

1

212

A

Amm … (11.4)

Similarly, the heat of reaction of a unknown sample can also be calculated by

comparison with a sample of known heat of reaction. One thing keep in mind that the

calibration factor, K, in Eq. 11.1 is temperature dependent in DTA situation, therefore

both known and unknown sample should be run at identical temperature.

You may have noticed in Fig 11.3 and 11.6 that the initial and final baselines of peaks

do not coincide. Therefore, determination of the area under the peak may be subject to

ambiguity. To resolve this problem a method for determination of the peak area is

illustrated in Fig. 11.6. Both baselines are extended to a perpendicular line drawn from

the maximum of the curve and the area under the two halves of the curve are

determined and added to give the total area.

Fig. 11.6: Illustration depicting the determination of DTA peak areas. The difference in

the initial and final base indicates a change in heat capacity

The heat of reaction observed in DTA can be further used to calculate molar enthalpy

of reactions by using the formula:

∆Hm = ∆Hr × Mr / m … (11.3)

where, ∆Hm = molar enthalpy of reaction, ∆Hr = enthalpy of reaction, Mr = related molar mass of the compound, m = Mass of substance used for analysis.

Determination of Heat Capacity

The DTA curve is conveniently used to measure the heat capacity (specific heat). For

this purpose first a DTA curve is recorded for an empty container and then for the

sample placed in container is recorded in identical condition. The absolute change in

temperature (∆Tx) has been measured and put in the equation for calculations:

40

Thermal Methods

mH

TTKC 12

p

−= … (11.5)

where Cp is the heat capcity at temperature T, T1 and T2 are diffenrential temperature

generated when the instrument is first run without any sample at all and then with the test sample in position, H is the heating rate (dT/dt) and K is calibration factor. It can

be determined by calibration against standard substance of known enthalpy change.

Construction of Phase Diagram:

The Melting point can be recorded by DTA curve for a eutectic mixture of different

sample with variable composition. These melting points can be used to construct a

phase diagram The critical temperature of organic compounds can be determined by

DTA if sealed sample holder is used. The determination is used of cooling curve, a

discontinuity is observed at the critical temperature Tc. Curie point temperature

making a sudden change at this point can also be determined by this technique . The

specific heat increases gradually upon the curie point e.g 357 oC for nickel,

observed simply by ploting dQ/dT or dT against temperature .

Estimation of Transition temperature:

The precise determination of a transition temperature (e.g. M. P. and B.P.) up to a

precision of ± 0.3 oC over a wide range of heating rate. The temperature estimated for

M.P. Tm or B.P. TB, were most often selected from the portion peak as shown in Fig.

11.7. In this figure first a base line meeting low and high temperature sides of the peak

is drawn where A is the intersection of extrapolated straight line portion of the low

temperature side of the peak with the base line. Further, point B is the inflection point

of low temperature side of the peak and point C is the extrapolated peak, while D is

the extrapolated return to the base line. Melting point Tm is measured by the using

sample is closest to the temperature of point C for sample and temperature at B for

reference. In exceptional cases it may closer to point D.

Fig. 11.7: The different temperature of DTA curve.

SAQ 3

Compound X has a relative molar mass of 98.4 K and heat of fusion )( xH∆ of

6.85 kJ mol–1

. Compound Y has a relative molar mass of 64.3 and having same

melting point as X. 500 gm samples of each yield DTA peak areas of 60.0 cm2 and

45.0 cm3 for X and Y, respectively. Calculate the heat of fusion of Y.

…………………………………………………………………………………………...

…………………………………………………………………………………………...

41


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

11.2.7 Applications

Now we study in some more examples to understand how DTA is used in chemical identification of a material (qualitative interpretation) comparing and for thermal

stability of materials. Such informations can be used to select material for certain end-

use application, predict product performance and improve product quality.

Qualitative and Quantitative Identification of Minerals

For the detection of any minerals in a sample, it is essential that it undergoes

measurable energy changes in the temperature range used. Since most of the minerals undergo such changes, choice of an appropriate temperature range should have

priority. However, assuming a suitable range variation occurring in the minerals

themselves may frequently lead to difficulties in the interpretation of curves. Another complication arises from the fact that certain minerals give reasonably characteristic thermal effect, sometimes clays do not show similar result. Other difficulties may arise

by the presence of organic matter.

Oxidation of organic materials if present masks the thermal effect of substance.

Consequently the analysis of such cases should preferentially be carried out in inert atmosphere or in vacuum. Organic material some times be removable by a suitable

solvent or may be oxidized by treating with H2O2. When clays or ore contain organic material then a broad exothermic peak appears between 200 – 600

0C. Thus the

appearance of a broad exothermic peak between 200-600 0C indicates the presence of

organic material in a given sample. In practice however, difficulties do arise in a case where peak areas for two distinct

samples of same mineral give peaks at two different temperatures. It is, therefore, necessary for qualitative work to know the peak area given by pure mineral identical

to that in the sample under investigation. This, however, is not possible. Another

limitation in the quantitative work in the occurrence of overlapping of peaks e.g. when

Kaolinite and Illite are present in the same sample almost completely overlapping takes place. A representative DTA curve of some minerals are shown in Fig. 11.8. It may be observed that none of these miners show an exothermic peak in the range 200-

600 °C corresponding to organic material as mentioned above.

Fig. 11.8: DTA curves for (A) : kaolinite, (B): Mortmonillonite, (C): Illite

42

Thermal Methods Polymeric Materials

DTA is a very useful technique for the characterization of polymeric materials in the light of identification of thermophysical , thermochemical, thermo mechanical and

thermo elastic changes or transitions. It provides important parameters for polymer processing and its end use. The DTA also provides useful information about

quantitative aspect, degree of fusion, crystallinity, phase equilibrium, heat of polymerization, degree of curing etc. A typical DTA curve of a polymer is shown in

Fig. 11.9 with labeled four transitions: glass transition, crystallisation, melting and

oxidation, abbreviated as Tg, Tc, Tm and Td respectively.

Fig.11.9. DTA curve of a typical polymeric sample

The DTA technique is also used for analyzing a polymeric mixture qualitatively and quantitatively. The individual polymers exhibit their own characteristic peaks. The

Fig. 11.9 is differential thermal curve of seven components polymeric mixture for

their melting points: Polytetrafloroethylene (PTFE), High Pressure (high dencity) Polypropylene (LPPE), Low Density Polypropylene (LPPE), Polypropylene (PP),

Polypropylene POM, Nylon 6, Nylon 66.

Fig. 11.10: DTA curve of a typical polymeric mixture

It is shows characteristics peaks of all the polymers and hence confirm the presence of individual polymers in the analyzed sample. The area under the peak is related to the

heat of reaction and related to the quantity of material present in the mixture. The DTA graph of ethylene propylene block copolymer indicates two peaks for ethylene and propylene. On comparing areas under the peaks it is found that 51 % ethylene and

49 % propylene present in the analysed block copolymer . The peak height technique

has been also employed to measure the quantity of polysebacic anhydride in a epoxy

resin- sebacic anhydride mixture. Another important parameter determined from by DTA is glass transition (Tg), a

second order transition caused by relaxation of chain segment in the amorphous portion of a polymer. The first evidence that a glass transition could be detected by

DTA was provided in (1957), where a transition at 28 °C was shown but not

43


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

interpreted. As such this transition is not associated with latent heat but rather a sudden change in specific heat to bring a liquid into the glassy state. The necessary condition is to cool it rapidly to approximately two third of its melting point.

Tg/Tm =0.66

The glass transition of a polymer can be obtained using number average molecular

mass M ranging from 8 × 103 to 3 × 10

6 from expression:

Tg = [ ( 96.5 +/- 1.0 ) –( 2.8 +/- 0.1)] × 10 3 / M

The deduction about the slope of the glass transition as depicted by DTA curve:

a) The slope of the curve ∆T surface temperature should be sigmoidal.

b) The maximum value of ∆T at the glass transition temperature should be linearly dependent on the heating rate.

c) The inflection point Tg should rise in temperature with the heating rate. It has

been shown that glass transition is associated with a sudden shift in base line.

The Tg depends on heating rate, volume fraction and molar mass. The DTA results provide important information about polymerization reaction , mainly about heat of

polymerization, degree of curing, effect of catalysts, decomposition reaction and radiation effects.

11.2.8 Measurement of Crystallinity:

A common application of DTA is the measurement of the mass fraction of crystalline

material in semi crystalline polymers. The method is based upon the measurement

of the polymer’s heat of fusion , ∆Hf, and the plausible assumption that this

quantity is proportional to the crystalline content . If by some process of

extrapolation the heat of fusion , ∆Hf*, of a hypothetical crystalline sample is known then the mass fraction of a crystallinity is

Mass fraction = *f

f

H

H

∆

∆

Thus, crystallinity of a polymer sample (X) can be determined by measuring the total

energy absorbed by the sample per gram ( H∆ ) and subtracting the amount of

energy which would be absorbed by one gram of totally amorphous material

[ (a)fH∆ ] in the temperature interval, and then dividing by the heat of fusion of one

gram of a perfectly crystalline sample [ (c)fH∆ ], as expressed by following

equation.

X = ∆H – ∆Hf (a)/ ∆Hf(c)

Another method for the determination of polymer crystallinity is based upon the ability of the instrument to cool a molten sample rapidly and reproducibility to a

selected temperature where isothermal crystallization is allowed to occur. A number

of crystallization curves may be obtained at different temperatures. The difference in crystallinity may be caused by branching, nucleation and molecular effect.

Degree of Polymerisation:

The area observed in DTA curve is directly related to heat of polymerization and can be expressed in terms of per mole or per g. Consider the DTA graph of

polymerization process of trialkylcyanurate and triallylisocyanurate. Samples were prepared by mixing two parts Al2O3 , one part monomer 0.1 part catalyst as a 50 %

paste in tricresyl phosphate and heating the mixture at a rate of 8 0C per minute.

Typical values of heat of polymerization as estimated from the peak area, are given in

Table 11.1.

44

Thermal Methods Table 11.2: Estimated Heat of Polymerization

Materials heat of polymerization (∆H1) heat of polymerization (∆H2)

trialkylcyanurate 35 107

triallylisocyanurate 56

Further the area (size) of peak appears in DTA curve had a great value in assessing the degree of curing. This is done by the residual cure remaining in a polymer system

after various treatments. This approach has been applied for estimation of degree of

curing in an unsaturated polyester-styrene copolymer cured at ambient temperature . The variation in the size of the curve represents the percentage of curing in 2 hours

63 % , 3 hours 68.6 % 4 hours 74.3% , 5 hours 77.0 % and 6 hours 78.2%. Similarly the relative change in the heat of reaction measured by DTA also gives information

regarding role of catalyst , degree of crystallinity and decomposition of polymer samples.

Analysis of Biological Materials

DTA has been widely used in the determination of thermal characteristics of bio-organic molecules, the main constituent of body of living being. The bio materials are

having heterogenity as a significant feature. This describes it as

multicomponent, molecular non homogenous materials, in which component exist as

continuous , separate and inter mixed structures. Biological systems present complexity even in static state and then difficulty in obtaining meaningful results and

establishing correlation between thermal characteristics and other physical chemical

properties. However, the investigations carried out under variable experimental condition indicate that DTA curve should be of value as ‘fingerprint’ of biological

materials. The thermal characteristics of a number of biological materials such as fresh

biological materials and decomposed materials determined under different atmospheric condition have been studied.

Fresh biological material consists of materials of active body of plants and animals. It

is always difficult to elucidate the chemical constituents of the plant materials. Information obtained from the study of the simple molecules can not be necessarily

applied directly to heterogeneous system . In the study of such system indirect method has been applied e.g. complete combustion, dilution effect, environmental effect etc. The DTA curves of four leave samples of different plant in oxygen exhibit

two pronounced exothermic effect in the range 240-270 0C region. The first peak is

invariably smaller than second one at least in height always not in area apart from variation in peak temperature. The general similarity in these curves may be inferred

that leaves of the plants have at least same micro-chemical composition.

The DTA curves for some plant materials have also been obtained in a static or air or dynamic oxygen atmosphere, since it is difficult to distinguish between

decomposition and oxidation effects, which may overlap. Endothermic reaction such

as dehydration or volatilization while exothermic accompany combustion under inert atmosphere condition, with oxidation reaction suppressed, such endothermic effect can

be detected. Similarly the analytical method is useful for analysis of high energy materials, explosives, ceramic, cement and pharmaceuticals.

SAQ 4

List the melting point of individual polymer samples from the DTA curve of

Fig. 11.10.

…………………………………………………………………………………………...

…………………………………………………………………………………………...

45


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

11.3 DIFFERENTIAL SCANNING CALORIMETRY

In previous section we have studied DTA techniques in these methods, thermal reactions are observed by measuring the deviation of the sample temperature from that

of the reference material. This deviation effects the DTA curve and decreases the sensitivity. There is another technique called Differential Scanning Calorimetry (DSC)

which have the advantage of keeping the sample and reference at the same temperature and heat flow into sample and reference is measured. This can be

achieved by placing separate heating devices in the sample and reference chambers.

This is in contras to the DTA scheme, where both sample and reference are heated by the same source.

11.3.1 Principle

In DSC the heat flow is measure and plotted against temperature of furnace or time to get a thermogram. This is the basis of Differential Scanning Calorimetry (DSC). The

curve obtained in DSC is between dH/dt in mJ s-1 or mcal s-1 as a function of time or

temperature. A typical DSC curve is shown in Fig. 11.11. The deviation observed above the base (zero) line is called exothermic transition and below is called

endothermic transition. The area under the peak is directly proportional to the heat

evolved or absorbed by the reaction, and the height of the curve is directly proportional to the rate of reaction. Therefore Eq. 11.1 is equally valid for DSC scheme also. The only difference is the calibration factor K in case of DSC is

independent of temperature. This is a major advantage of DSC over DTA.

Fig. 11.11: A typical DSC Curve


The block diagram of a DSC instrument as shown in Fig. 11.12a, essentially works on

the temperature control of two similar specimen holder assembly. The left half of the block diagram represents the circuit for differential temperature control while right

hand side indicates that for average temperature control. In the average temperature

control circuit, the temperature of the sample and reference are measured and averaged and the heat output of the average heater is automatically adjusted so that the average temperature of the sample and reference increases at a linear rate. The differential

temperature use control circuit monitors the difference in temperature between the sample and reference and automatically adjust the power to either the reference or

sample chambers to keep the temperatures equal. For getting a thermogram, the

temperature of the sample is put on the x-axis and the difference in power supplied (in

terms of J s-1

or cal. s–1

) to the two differential heaters is displayed on the y-axis.

Fig. 11.12 b illustrates the heating arrangement in sample and reference compartments.

Here the sample and reference compounds are provided with their own separate heaters, as well as their own temperature sensors so that both S and R are maintained

at identical temperature by controlling electrically the rate at which heat is transferred

to them.

46

Thermal Methods In DSC, samples for analysis range in size from 1 to 100 mg are placed in a sealed sample container. A wide range of heating rate (0.5 to 80°C/min) can be used, DSC instruments are generally sensitive energy detect heat evolution or absorption at a rate

less than one millicalories per second. Electrical signals are amplified and recorded

similar to TGA and DTA.

Fig. 11.12: (a) Block diagram of a DSC instrument (b) Heating arrangement in DSC

compare this with Fig. 11.4 b

During thermal process reactions either liberate or absorb heat. Thus, when ∆ H is

positive (endothermic reaction), the sample heating device is energized and a positive

signal is obtained; when ∆ H is negative the reference heating device is energized and a negative signal is obtained. An idealized representation of the three major processes

observable in DSC is given in Fig. 11.13. The peak area in DSC are proportional to the

amount of sample, the heat of reaction and similar to DTA peak area can be expressed by following equation.

47


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

Fig. 11.13: An idealized representation of the three processes observed in DSC

Peak area (A) = HmK∆± … (11.6)

where ∆ H represents sample enthalpy change and m is the mass of sample and K is a

constant called calibration factor. Unlike DTA it is independent of temperature. Using above Eq. 11.6, we can determine enthalpy change for a reaction directly from peak

area, if we known the value of K. We can also determine enthalpy change by

comparing the ∆ H of the sample with the known ∆ H of the standard. i.e.,

ss

Skk

smA

HmAH

∆×=∆ … (11.7)

where ∆ Hs is the enthalpy change for sample, ∆ Hk is the enthalpy change for known

standard, ms and mk are masses of sample and known standard respectively, and As

and Ak represents the area of peaks of sample and standard materials, respectively.

DSC technique is not only sensitive for the determination of ∆ H, but it is also very

sensitive for the determination of heat capacities (Cp). when a sample is subjected to a heating programme is DSC, the rate of heat flow into the sample is proportional to its

heat capacity. This may be detected by the displacement of the base line as illustrated

in Fig. 11.13. The value of Cp may be determined at a particular temperature by measuring this displacement (d). :

m

dC

×=

rateheatingp … (11.8)

mtT

tH 1)d/d(

)/dd(×=

… (11.9)

Using Eq. 11.9, we can deduce the unit of Cp. In DSC curve displacement (d) will be measured in mJ s

–1. If heating rate is in °C s

–1- and m is expressed in g, then,

11

1

1

p CgmJsC

1

g

smJ −−

−

−

=×=o

C

Cp can also be expressed in term of mcal. as 11CgmCal

−− [conversion factor for J

and Cal. is: 1 calorie = 4.2 J].

In practice we normally measure the base line shift by reference to a base line obtained

for empty sample and reference pans. To further minimize experimental error we

usually determine heat capacity of the sample by comparing with the known heat

capacity of the standard.

48

Thermal Methods ( )

dt

dp12

TmCHHK =−′ … (11.10)

or dt

dd p

TmCK =′

where, H1 and H2 are differential heat generated when the instruments is first run

without any sample at all and then with the test sample in position (in DSC curve

(H2 – H1) is expressed as displacement, d). K ′ is calibration factor, it can be

determined by calibration against standard substance. However, K ′ from the Eq.

11.10 can be eliminated, if a material with a known heat capacity is used to calibrate

the instrument.

Once of the commonly used standard is α -aluminium oxide (Al2O3) or synthesized

sapphire for which specific heat has been determined to five significant figures in the

temperature range 0 to 1200 K. After the base line and sample program, a third

program is run with a weighed sapphire structure. At any temperature T, following

equation applies:

K ′ d = dt

dp

TCm … (11.11)

dK ′′ = dt

dp

TCm ′′ … (11.12)

where d and d ′ are ordinate deflections (displacements) due to the sample and the

standard respectively, PCm ′′ are mass and heat capacity of the standard. Dividing the

Eq. (11.11) by (11.12) we get

md

md

C

C

C

C

m

m

d

d

′

′=

′′′=

′ p

p

p

por … (11.13)

Thus the calibration requires only the comparison of the two displacement values at

the same temperature . We can easily calculate value of Cp on putting the rest values

in the Eq. 11.13. The basic components of DSC are quite similar except the

differential energy measuring system. In DSC, two principle works: one based on

power compensation and other heat flow method. In power compensation method

smaller secondary heater are attached two equalize the generated energy difference

between sample and reference materials. While in heat flow technique heat flux

passing through sample and reference are evaluated and their difference is related

energy consumed or released in the thermal reactions.

SAQ 5

Write the essential differences between a DTA and DSC.

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

11.3.3 Factors Affecting DSC Curve

In the beginning of this block we talked about the lowest temperature, Ti at which the

onset can be detected by the instrument operating under particular conditions. We

may like to call this as transition temperature, which is not correct. Actually in a DSC

experiment, both Ti , Tf and Tc (the final temperature at which the decomposition is

49


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

completed) do not have fundamental significance, but they can still be a useful

characteristic of a DSC curve. The term procedural thermogram, often used for the

temperature at which temperature change appears to commence. This indicates that a

start of thermal reaction, temperature does not have a fixed value, but depends on the

experimental procedure employed to get it. Similar to this there are many factors

which influence a DSC curve. These factors may be due to instrumentation or nature

of sample. We have listed the main factors which affect the shape, precision and

accuracy of the experimental results:

1. Instrumental factors:

a) Furnace heating rate.

b) Recording or chart speed

c) furnace atmosphere

d) Geometry of sample holder/ location of sensors

e) Sensitivity of recording mechanism.

f) Composition of sample container.

2. Sample Characteristics:

a) Amount of sample

b) Solubility of evolved gases in sample.

c) Particle size

d) Heat of reaction

e) Sample packing

f) Nature of sample

g) Thermal conductivity.

Some of these factors we have are already described in sec.11.2.4 in detail.

11.3.4 Sources of Error

There are a number of sources of error in DSC, and they can lead to inaccuracies in the

recorded data of heat. Some of the errors may be corrected by placing the thermo

balance at proper place and handing it with the care. For understanding we are

discussing some common source of errors during operation or common as discussed in

DTA except the in accuracy caused by secondary heaters and thermostats.

Errors can be avoided by proper placing of instrument in the laboratory, maintaining

operating temperature, and constant power supply. By avoiding excessive heating rate

and proper gas flow rate other errors can be also avoided.

To further minimize the errors during experiments, similar to DTA, DSC instruments

are also be calibrated for the temperature and peak area measurements with suitable

standards. The only difference is that calibration constant in DTA situation is

temperature dependent to a significant degree. Therefore in DTA measurement, we

should calibrate peak areas using a standard which provide a reference peak in a same

temperature range as the test sample. In DSC situation, K is independent of

temperature. Therefore, it requires simple steps for the calibration of the instrument.

For peak area calibration we require standard of high purity and accurately known

enthalpy of fusion ( fH∆ ) are required. Few examples of calibration standards are

indium (In), benzoic acid, tin, lead, silver, gold, etc.

50

Thermal Methods SAQ 6

DTA and DSC, which method you will prefer for quantitative purposes and why?

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

11.3.5 Interpretation of DSC Curve

DSC curve of a pure compound is a fingerprint of that compound in the context of

transition temperature as well as heat required for that transition. Therefore, DSC

curve can be used to infer about the presence of a particular compounds and its

thermal behaviour. The peaks observed shifting of base line either up or down. A typical DSC curve is shown in Fig 11.11. The peak above the base line is exothermic

while down the base line is endothermic.

We have seen above how area under DSC Curves is related to the amount of energy

released or absorbed in a physico-chemical change. It has been shown that under

certain conditions the area under the peak is proportional to the amount of heat

evolved in a reaction.

So this area under the curve is used for stochiometric ratio of analyzed compounds

(quantitative interpretation). Now we see in next example how it can be used to

compare thermal stability of a material for physical state and chemical states .This can

be used for chemical identification of a material (qualitative interpretation). Such

information can be used to select material for certain end-use application, predict

product performance and improve product quality. DSC Curves of a polymeric

mixture and probable transitions are shown in Fig. 11.14 for illustration about

probable change in behaviour of a polymer sample.

Fig. 11.14: Change in Behavior of Polymeric Materials in DSC

The DSC technique is more sensitive than DTA and it provides clear presence of a

thermal events occurring during course of heating of time ageing of material . Thus,

the information acquired by DSC is more realistic. The technique is used for the

presence of polymorphism, degree of crystallinity, curing fraction etc. Curves clearly

indicate that Fig. 11.13is showing the peaks for the glass transition, ordering, melting

and decomposition of individual polymers. The ratio of areasunder the curve by

dividing the enthalpy of heat of decomposition, provides the ratio of individual

monomers in a analysed copolymer sample .

The heat of reaction (∆Hr) observed in DSC can be further used to calculate molar

enthalpy of reactions by using following formula:

51


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

∆Hm = ∆Hr × Mr /m

Where, (∆Hm = molar enthalpy of reaction ,

∆Mr = relative molar mass of analysed compound,

m = Mass of substance used for analysis.

11.3.6 Applications

Differential scanning Calorimetry (DSC) used to measure energy changes as a

function of temperature or time. A typical graph is shown in Fig. 11.13. Using this

technique it is possible to observe a number of characteristic properties of a sample

like fusion, crystallization, glass transition temperatures (Tg) as well as other thermo

chemical reactions. DSC can also be used to study oxidation, as well as other chemical

reactions. Glass transitions may occur as the temperature of an amorphous solid is

increased. These transitions appear as a step in the baseline of the recorded DSC

signal. This is due to the sample undergoing a change in heat capacity; no formal

phase change occurs. As the temperature increases, an amorphous solid will become

less viscous. At some point the molecules may obtain enough freedom of motion to

spontaneously arrange themselves into a crystalline form. This is known as the

crystallization temperature (Tc). This transition from amorphous solid to crystalline

solid is an exothermic process and results in a peak in the DSC signal. As the

temperature increases the sample eventually reaches its melting temperature (Tm). The

melting process results in an endothermic peak in the DSC curve. The ability to

determine transition temperatures and enthalpies makes DSC an invaluable tool in

producing phase diagrams for various chemical systems. The technique is widely used

across a range of applications, both as a routine quality test and as a research tool. The

equipment is easy to calibrate, using low melting indium for example, and is a rapid

and reliable method of thermal analysis. The few notable specific applications of DSC

are:

The result of a DSC experiment is a curve of heat flux versus temperature or time.

There are two different conventions: exothermic reactions in the sample shown with a

positive or negative peak. This curve can be used to calculate enthalpies of transitions.

This is done by integrating the peak corresponding to a given transition. It can be

shown that the enthalpy of transition can be expressed using the following equation:

∆H = KA

where ∆H is the enthalpy of transition, K is the calorimetric constant, and A is the area

under the curve. The calorimetric constant will vary with the instrument and can be

determined by analyzing a well-characterized sample with known enthalpies of

transition.

Most of well known spectroscopic methods of great value in the qualitative and

quantitative chemical analysis are based on our ability to measure energy absorption or emission caused by transition from one energy state to another. The

great potential of thermal spectroscopy for quantitative analysis was not realized in

the past because of the absence of a suitable, fast scanning, the calibration run for

the synthetic compounds and the base line technique used in the area measurement

and can be used for the quantitative analysis of constituents present in the fiber

blend.

Many materials can exist in two or more different crystal line forms. The chemical

reactivity and physical properties of different forms vary frequently one to another.

Technological handling requires one of the perfect suitable form, hence the

phenomenon is of great importance in chemistry and conveniently studied by

DSC.

52

Thermal Methods DSC may also be used in the study of liquid crystals. As matter transitions between

solid and liquid it often goes through a third state, which displays properties of both

phases. This anisotropic liquid is known as a liquid crystalline or mesomorphous state.

Using DSC, it is possible to observe the small energy changes that occur as matter

transitions from a solid to a liquid crystal and from a liquid crystal to an isotropic

liquid.

DSC curves may also be used to evaluate puriting of a drug and polymer. This is

possible because the temperature range over which a mixture of compounds melts is

dependent on their relative amounts. This effect is due to a phenomenon known as

freezing point depression, which occurs when a foreign solute is added to a solution.

(Freezing point depression is what allows salt to de-ice sidewalks and antifreeze to

keep your car running in the winter.) Consequently, less pure compounds exhibit a

broadened melting peak that begins at lower temperature than a pure compound. DSC

is used widely for examining polymers to check their purity and composition. Melting

point and glass transition temperature for most polymers are available from standard

compilations, and the method can show up possible polymer degradation by the

lowering of the expected melting point, Tm. It depends on the molar mass of the

polymer, so lower grades will have lower melting points than expected.

In pharmaceutical industry it is necessary to have well-characterized drug compounds

in order to define processing parameters. For instance, if it is necessary to deliver a

drug in the amorphous form, it is desirable to process the drug at temperatures below

those at which crystallization can occur. The above mentioned transition are well

observed in DSC curve and used in industry regularly

There are two important criteria for characterization of waxes and fats by DSC:

1. Although melting peak shape of wax and wax formulations can be quite

complex , they are much less sensitive than fats to variation in the

crystallization condition.

2. The crystallization of waxes is easily nucleated with the result that solidification

occurs readily with little or no super cooling. In fact the crystallization peak for

most waxes is virtually mirror image to its melting point. Although reading of

DSC thermogram and applying to these criterion, we can easily make

statement whether the supplied material is wax or fat.

Using differential scanning calorimetry to study the oxidative stability of samples

generally requires an airtight sample chamber. Usually, such tests are done

isothermally (at constant temperature) by changing the sample atmosphere. First, the

sample is brought to the desired test temperature under an inert atmosphere, usually

nitrogen or organ. Then, oxygen is added to the system. Any oxidation that occurs is

observed as a deviation in the baseline. Such analysis can be used to determine the

stability and optimum storage conditions of a compound

A more specific application of DSC where DTA cannot be employed is the detection

of magnetic transition in the materials. The magnetic transition are of second order

with ∆H=0 but with the a maximum heat capacity at the transition temperature.

Technique is sensitive to detect these minor variations. A typical DSC curve for a

magnetic transition is shown in Fig. 11.15. Similarly glass transition can be detected easily with DSC.

53


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

Fig 11.15: A Typical magnetic transition observed in DSC

11.3.7 Advantages of DSC

1. Small sample size 1 to 10 mg.

2. Simple and rapid procedure of analysis, typically 15 to 30 min. per

determination.

3. Ideal for comparison of sample purity for example in quality control.

4. Does not require high absolute temperature accuracy ( in contrast with melting

point depression method.

5. Does not require calibration with known impurity levels, cryoscopic constant

is obtained simultaneously.

6. The use of melting rather than a freezing curve avoid problems associated

with super cooling of sample , poor crystallizability from melt , instability in

the melt etc.

11.4 THERMOMETRIC TITRATIONS

In the earlier section you have learnt about thermogravimertric analysis (TGA),

different thermal analysis (DTA) and differential Scanning Calorimetry (DSC)

methods. We hope that you have clearly understood the principle of TGA, DTA and

DSC its analytical applications. We assume that you can apply the knowledge of TGA,

DTA and DSC to derive analytical information about simple and complex compounds.

In this section we will introduce you to thermometric titration and familiarize you with

the instrumentation including experimental details. At the end we will discuss some

typical analytical applications of thermometric titration methods.

11.4.1 Principle

Similar to the case of thermogravimetry, basic principle of thermometric titrations is

based on the change in temperature with the addition of titrant and determine the end

point from a plot of temperature vs. volume of titrant. The titrant is added to an

isothermal titrate in an adiabatic titration calorimeter. In most instances there occurs a

change in enthalpy concomitantly, yielding a corresponding heat of reaction. As a

result these are also called enthalpy titrations and the titration curves are called

enthalpograms. It can be exothermic or endothermic. In thermometric titration,

change in temperature occurs only when titration is in progress and sample reactant is

present. Thus, start and end point of a titration are readily observed and the number of

moles titrated is calculated as in regular titration. By determining the heat capacity of

the system under study, heat of reaction can be readily determined. In addition,

equilibrium constant can be evaluated under appropriate experimental conditions.

54

Thermal Methods

Fig. 11.16: Tupical Enthalpogram for (a) exothermic reaction and (b) endothermic

reaction, showing start of titration, progress of titration, end point and excess reagent line

Typical shapes of enthalpogram are shown in Fig. 11.16 a and b. On both

enthalpograms, the base line represents temperature-time blanks recorded prior to the

start of the actual titration, B corresponds to the beginning of addition of titrant, C is

the end point and CD the excess reagent line. Thus BC is the titration branch proper of

the enthalpograms. In cases where ∆H <0, it has an ascending slope shown in as Fig.

11.16 a whereas for ∆H >0, it has a descending slope as showing Fig. 11.16 b both

cases the excess reagent branches of the enthalpograms (CD) are drawn with

ascending slope because the dilution of most titrants is an exothermic process. In order

to minimize variations in heat capacity during titration, it is customary to use titrants

50-100 times more concentrated than the unknown titrated. Thus the volume of titrate

solution is maintained virtually constant, but the titrants are diluted appreciably. The

heat of dilution can be corrected for conveniently by the linear back extrapolation CB´.

Under these conditions, the extrapolated ordinate height BB´ represents a measure of

the change of temperature. ∆T, due to the titration reaction, as well as of integral heat,

Q, evolved or absorbed viz.,:

BB´ ∝ ∆T

∆T = K

HN.

K

Q ∆−= … (11.14)

where K denotes the effective heat capacity and N is the number of moles reacted in

the titration. From Eq.(11.14), it is evident that the quantity BB’ can be used for

obtaining the following informations;

• Heat of titration reaction, ∆H, whenever a known amount of titrate is used.

• Concentration of an unknown ‘titration’, whenever ∆H is known (∆T is

proportional to concentration and independent of tirate sample size).

• Quantity of an unknown in a known volume of titrate.

55


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

Nomenclature

Operationally enthalpograms are thermometric titration curves, where temperature is

experimentally observable variable upon addition of titrant. The basic property which

determines the shape of an enthalpogram is change in enthalpy. This accounts for the

designation “Thermomatic titration” (TT) and “enthalpy titration” used in literature.

Other similar terms include “Calorimetric titration, thermochemical titration, thermal

titration, similar to the usage for potentiometric/amperometric techniques.

Another type of thermometric titration includes direct injection enthalpimetry (DIE)

which yields a plot of temperature vs the time following injection of the titrant. In this

case end point is not obtained but the magnitude of the temperature change is

proportional to the concentration. The speed of analysis is enhanced and processes

with equilibrium unfavourable for titration are readily studied by using a large excess

of one reagent.

SAQ 7

What does enthalpogram represent and what type of information it provides?

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...


Experimental setup of TT consists of a reagent delivery system (motor driven

automated buret), an adiabatic reaction cell (such as Dewar flask with stirring device),

an electronic temperature sensing system and an amplifying and data processing

system. A typical experimental assembly and adiablatic cell are illustrated in Fig 11.17

and 11.18 respectively. In TT temperature control is most important and depends upon

the results required. Often, it is possible to obtain and paint in titrations simply by

bringing both the sample and the titrant to rooms temperature. However, for precise

calorimetric results the titrant and sample must be close to the same temperature as far

as possible and this is achieved by a thermostat.

Fig. 11.17: Schematic layout for thermometric titration assembly and bridge circuit

56

Thermal Methods

Fig. 11.18: An efficient adiabatic cell for thermometric titrations

A. Delivery Pump: A constant delivery pump permits the time axis of a strip chart

recorder to be used as the volume of titrant axis. Typically a syringe driven by a

synchronous motor which drives the screw is used and solution is delivered at a

constant rate ranging down to few µdm3 per min.

In DIE the syring is rapidly emptied at the start of the experiment to deliver the

titrant instantaneously into the sample cell.

B. Adiabatic Cell: These have widely varying designs ranging from an insulated

beaker to a Dewar flask type cell (Fig. 11.18). All the cells are designed to

minimize the heat transfer from the cell to the environment thus maximizing the

temperature change observed. When only titration end point is of interest, the

simple cell is sufficient. However, if quantities such as heat of reaction,

equilibrium constant or kinetic parameters are sought, it becomes essential to

use better cells which have thin walls to minimize the heat capacity and

maximize the speed of response to temperature change.

C. Calibration Unit: In order to bring the cell quickly to thermal equilibrium, it is

essential to use calibration heater. It has two purposes, to determine the heat

capacity of the system and to control the temperature in the cell itself. The heat

evolved or absorbed is calculated from the temperature change using the

relationship.

∆Q = ∆TC´p … (11.15)

Where C´p is the heat capacity of the system which is measured as the amount of

heat necessary to raise the cell temperature by an unit.

D. Temperature Sensing System : It is the heart of thermometric titrator. The

principal temperature sensor is a thermistor which is temperature sensitive

semiconductor whose resistance obeys the Eq. 11.16.

RT = A B/Te … (11.16)

57


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

where A and B are constants whose values depend on the nature of the thermistor. A thermistor has the advantage of being small size, fast response to temperature change and chemical resistance.

E. Amplification and Recording: It is often advantageous to amplify the signal

obtained from the thermistor. ADC amplifier is used to obtain good signals for temperature changes of the order of 10

-4 °C or less. For still lower temperature

changes of the order of 10-6 °C, and AC, Wheatstone bridge with a lock in

amplifier is used. The two most popular data acquisition systems are the strip chart recorder the digital data storage system.

Fig. 11.19: Idealized representation of the four major regions of the TT curve. With a

constant-delivery pump, the x-axis can be in units of time or moles of titrant

Experimental Considerations: An idealized thermometric titration curve is

represented in Fig.11.19 showing four region: region 1 is the baseline which is ideally

horizontal but in practice it always has finite slope due to frictional heat added by stirring, resistive heat added by the thermistor and the transfer of heat from the cell to

the thermostat. If heating due to friction and resistance are constant and equal to W, the slope of region I is represented by

W C(Tc-Te) d

d+=

t

T … (11.17)

where c = the heat leak modulus, Tc = the temperature of the cell, Te = the temperate of

the environment.

In case of Region 2 slope is due to similar effects as a in Region 1 and following cases; temperature change generated by the reaction, the heat of dilution of the

reactants ∆Hd) and the difference in temperature where between titrant and sample

after the start of titration (∆Tr), It is represent by

kTC

H

t

n

C

HWTTC

t

Tr

p

Dp

ecd

d

p)(

d

d∆+

′′

∆+

′

∆−++−−= … (11.18)

58

Thermal Methods where k is a constant and np is the fraction product. In Region 3, equivalence point has

been passed and the slope of the curve is described by

rp

d∆T

C'

∆HW)TC(T

dt

dT+++−= ec … (11.19)

After this no more titrant in added and the slope in Region 4 obeys Eq. (11.17). In real

titration, however, a rounding is observed at the equivalence point and this case is

dealt separately.

The Eq. 11.17-11.19 can be combined to obtain the heat of reaction ∆H and if the

production of product (np) is equilibrium, controlled, equilibrium constant K of the

reaction can be calculated as-

–∆G = RT In K = – ∆H + T∆S ... .(11.20)

Analytical Calculations: Knowing the concentration of either the titrant or the

sample, concentration of unknown may be calculated from the volume added to reach

the end point. Heat of reaction is, in general, obtained from the Eq. 11.17 - 11.19.

However, in practice a graphical method is followed. Heat capacity at the mid point of

the curve is obtained by extrapolating the part of the curve in Region III back to region

II and thus measuring Q from the baseline to the extrapolated line at the mid point of

titration (see Example 2 and Fig.11.18)

SAQ 8

What are the essential components of the experimental setup for carrying out

thermometric titration.

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

SAQ 9

Explain why reaction cell should be adiabatic and continuous stirring is required when

the reaction is in progress?

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

11.4.3 Application

Since heat of reaction is the most general property of chemical processes,

thermometric titrations have a wide range of applicability in quantitative analysis. It

includes the determination of the concentration of an unknown substance, the reaction

stoichiometry, equilibrium constant and the thermodynamic quantities ∆G, ∆H and

∆S. These have been applied successfully to all types of titration processes including

acid-base (neutralization) reactions, redex reactions, precipitation reactions, and

complexometric reactions in media ranging from aqueous at room temperature to

molten salt at 350°C. Precision and accuracy of measurements depends largely on the

enthalpy of the reaction involved ranging from 0.2%. Lowest limit of concentration

that can be successfully titrated is 10-4

M. The main limitation of the method is that it

59


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

is non selective. The nature of information derived from the judicious mathematical

analysis of thermometric titration curves is summarized in Table.11.2.

Example 1

A classical example of thermometric titration is in the titration of boric acid

(Ka = 6.4 × 10-10) with a strong base (such as NaOH) which is otherwise very difficult

to perform.

Table 11.2: Summary of Application of Thermometric Titrations

Type of Application Information Obtained Procedure

Fundamental

Analytical

Heat of reaction

Free energy of reaction

Entropy of reaction

Reaction Stoichiometry

Concentration of

unknown

From extrapolated ordinate heights

From curvature in equivalence pt.

Region.

From the modynamic equation

End point determination

Direct enthalpimettry

As an illustration, Fig.11.20 shows comparision of potentiometric (pH) and

thermometric titration curves for HCl and H3BO3 with NaOH in dilute Aqueous

solution. The potentiontiometric curves of the two acids (fig.11.20 a) are very different

yielding a large end point inflexion ‘for the HCl (Ka~ ∞) and virtually none for boric

acid. However, corresponding enthalpograms (Fig.11.20 b) are strikingly similar,

because the heats of neutralization of the two acids are comparable, -13.5 kcal/mole

for HCI and –10.2 kcal/mole for H3BO3. As a result H3BO3 can be determined with

better precision and accuracy by thermometric titration compared to potentiometric

method. In the enthalpogram for H3BO3 and NaOH (Fig.11.20 b), AB represents a trace of the temperature of the solution before the addition of titrant and C is the end

point. Line BC shows the gradual evolution of heat of reaction. Linear portions of the

curves are extrapolated to give the initial and equivalence points and the vertical

distance between them (BB´) gives temperature difference (∆T) used to evaluate

enthalpy [Eq.(11.14)].

(a) (b)

Fig. 11.20: Comparision of (a) potentiometric and (b) thermometric titration curves for

HCl and H3BO3 with NaOH solution

60

Thermal Methods Thermometric titraions possess extraordinary potentiality for determining heat of

reaction in a dilute solution rapidly and conveniently so that ∆H values can be set

virtually equal to the ideal thermodynamic parameters corresponding to infinite

dilution.

Non aqueous systems are well suited for thermometric titrations though heat of mixing

of solvent and dilution pose a problem. The lower specific heat of many organic

solvents introduces a favorable sensitivity factor. Under strictly anhydrous conditions,

even diphenylamine, urea, acetamide and acetanilide are readily titrated with

perchloric acid in glacial acetic acid. Lewis bases such as dioxane, morpholine,

pyridine and tetrahydrofuran may be titrated with a Lewis acid such as SnCl4 in CCl4,

benzene and nitrobenzene. TT is very useful for titrating acetic anhydride in acetic

acid Sulfuric acid acetylating bath water in conc. acids by dilution with fuming acids

and free anhydrides in fuming acids.

Analysis of mixtures is possible when the two species have different equilibrium

constants and heats of reaction with the titrant. For example, in the titration of mixture

of calcium and magnesium with EDTA. Calcium (Kf = 1011

) reacts first and

exothermally (∆H = –5.7 kcal/mole) and then magnesium (Kf = 109.1

) reacts endothermally (∆H = 5.5 kcal/mole) as illustrated in Fig. 11.21.

Fig. 11.21: Typical curve for thermometric titration of a mixture of Ca2+

and Mg2+

with

EDTA

Precipitation and ion-recombination reactions by TT also yield good results. For

example, halide reacts with silver or mercury (II), and cations such as Mn(II) with

EDTA and oxalate. Titration of silver with halide can be carried out at elevated

temperatures in molten state.

Example 2 : To Determine equilibrium constant of complex formation by

thermometric titration. Equilibrium constant of complex formation reaction may be

estimated from enthalpograms when there is distinct curvature near the equivalence

point as shown in (where is Fig. 11.22) Let us consider the reaction.

A + B ⇋ AB

61


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

Fig. 11.22: Equilibrium curvature of enthalpograms, illustrating parameters h and ht

used to estimate equilibrium constants

where equilibrium concentrations [A] and [B] can be calculated using analytical

concentration (A) and (B). Thus we have

[ ] )(ABt

Ah

h=

[A] = (A) - [AB]

[B] = (B) - [AB] … (11.21)

These concentrations are then used to calculate quilibrium constant (K) using the

expression

[ ][ ][ ] [ ] [ ][ ][ ]AB)(AB)(

)(

BA

AB

t −−==

BAh

AhK

… (11.22)

Consider the reaction between a metal (M) with a ligand (L) to form a complex ML

Initial concentrations for both are given to be 0.015 M. It gives an enthalpogram

similar to Fig. 11.22 where h and ht were measured to be 58.2 and 67.9 (0ºC, cm, mV

or in any other units) respectively wherefrom stability constant of the complex can be

estimated as described in following lines.

At the end point, following relationship holds.

CL = 0.0015 = [ML] + [L]

and CM = 0.0015= [ML] + [M]

but [ ]

−=

−=t

Lt

MMLh

hC

h

hC

[L] = [M] = CM - [ML] = CL - [ML]

Thus stability constant may be calculated as

[ ][ ][ ] [ ]( ) ( )[ ]

3

22Mt

M 108.29.67/2.58015.0015.09.67

2.58015.0

MLLM

ML×=

−

×=

−==

Ch

hCK

When dilute solutions are used, it may be safely assumed that the measured

thermodynamic parameters are essentially the same as in standard state of infinite

dilution (∆Hmean ≈ ∆Hº).

62

Thermal Methods SAQ 10

What is the chief limitation of thermometric titrations.

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

SAQ 11

Even after the equivalence point, an increase in temperature is observed. Why?

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

11.5 SUMMARY

• In this unit, basic principles, instrumentations and applications of differential

thermal analysis (DTA), differential scanning calorimetry (DSC) techniques and

thermometric titrations are described.

• The applications of DTA and DSC are discussed by taking different examples

related to different properties e.g. quantitative and qualitative analysis,

polymorphism , crystallinity, physico chemical transitions etc. The elementary

calculations are discussed to elaborate the topics.

• The probable cause of errors, their remedies, interpretation of result and

comparison of DTA and DSC has been discussed keeping the identical

objective of both the techniques.

• Thermometric titrations are based on the change in temperature with the

addition of titrant where two quantities are plotted to yield an enthalpogram

involving the determination of heat of reaction used for quantitative

determination of an unknown.

• Experimental setup of thermometric titration consists of a reagent delivery

system, an adiabatic reaction cell and an amplifying and data processing system.

• Thermometric titrations can be used for studying all types of reactions such as

neutralization, redox, precipitation and complelxometric. It can also be used for

the determination of reactions toichiometry and thermodynamic quantities ∆G,

∆H, and ∆S.

• Non aqueous systems are well suited for thermometric titrations.

• In TT, precision and accuracy of the measurements range from 0.2% to 2% with

lowest limit of concentration being 10-4

M.

11.6 TERMINAL QUESTIONS

1. Calculate the change in entropy for melting of Indium metal at 157.6 oC the

heat absorbed is 13.6 Cal per gram.

63


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

2. All the thermal analysis instruments have features in common. Discuss these

common features and the way in which the individual techniques differs form

others

3. Estimate the purity of a materials which melts during DSC melting endotherm.

Describe the procedure.

4. What type of standard do you need for the calibration of heat and temperature

of DSC?

5. How DSC can be used for measuring the heat capacity of solid samples. Is a

particular standard required?

6. Explain how thermometric titrations are different than classical titrations.

Discuss their advantages.

7. Why is it essential to calibrate the thermometric titration unit. How is it done?

8. What are the various heat terms involved in different stages of an enthalpogram.

Derive an expression to determine ∆S for a reaction.

9. In a thermometric titration of acid A with a base B, the slopes of four regions

were found to be 1.0x10-5

, 8.0x10-4

, and –0.5x10-5

ºC/sec respectively. The

overall temperature change was 0-100ºC and heat capacity of the cell was

determined to be 1.00 cal/ºC. The titration rate was 6.0 x 10-8 moles B/sec. And

the titration of B into pure water gave a slope of 2.0 x 10-5 ºC/sec. Calculate the

heat of reaction.

11.7 ANSWERS

Self Assessment Questions

1. The relationship is given by Eq. 11.1

A = ± HmK∆

where K is the calibration factor. The unit of K can be calculated as:

Hm

AK

∆

±=

If A is in cm2, m in g and ∆ H is J g

–1, then unit of K are given by

12

1

2

JcmgJg

cm −

−=

2. Important factors are listed in Table 11.1.

3. Using Eq. 11.1 we can get following equation.

∆=∆

x

y

x

y

xym

m

A

AHH

Before substituting mx and my, they should be converted in molar quantities.

mx = 500/98.4 moles, my = 500/64.3 moles

Therefore,

=∆

4.98/500

3.64/500

0.60

0.4585.6yH

= 7.85 kJ mol.

4. PTFE melts ∼ 350 °C

HPPE melts ∼ 100 °C

64

Thermal Methods LDPP melts ∼ 125 °C

PP melts ∼ 175 °C

POM melts ∼ 210 °C

Nylone 6 ∼ 160 °C

Nylone 66 ∼ 300 °C

5. i) In DSC, the sample and reference materials are provided with their own

heating arrangements, as well as their own temperature sensor. In DTA

scheme both sample and reference are heated by the same source.

ii) Calibration factor in DTA is temperature dependent, on the other hand in

DSC, it is independent of temperature in DTA.

6. DSC is preferred for quantitative methods. In DTA, the calibration constant K, is

temperature dependent, therefore, it require extra calibration steps. Further, DSC

is more sensitive technique.

7. Enthalpogram is a titration curve which represents a plot between the volume of

titrant added on x-axis and change in temperature on y-axis.

It provides information as the star and end point of a titration. With its help we

can determine heat of reaction, equilibrium constant of the reaction and kinetic

parameters.

8. Experimental set up of thermometric titration consists of an adiabatic cell

(Dewar flask), delivery pump, and recording unit including ADC amplifier.

9. An adiabatic with negligible or minimum heat transfer losses is required for

accurate determination of heat of reaction and other parameters. It started

maximize the temperature changes as quickly as possible.

10. Thermometric titrations are not suitable for all types of titrations except where a

change in temperature occurs.

11. In most cases dilution of titrant in an exothermic process. Hence after the end

point, if excess amount of reagent is added then it gets diluted resulting in

increase in temperature.

Terminal Questions

1. Entropy change = 13.6 /157.6 =86.29 cal per gram per °C.

2.

TGA DTA DSC

Measures thermal effect Measures thermal effect Measures thermal effect

Provide range thermal

stability of materials




stability of mat

erials

Contains : furnace ,

temperature measuing unit,

atmosphere control unit

and recorder




and recorder




and recorder

65


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

Dissimilarity

TGA DTA DSC

Measures thermo –

Chemical effect

Measures thermo –physical

thermo –Chemical effect

Measures thermo –

physical thermo –

Chemical effect with

more sensitively


chemical stability of

materials

Provide range thermal:

physical and chemical



physical and chemical

stability and also transition

temperature e.g Curie

tempraure.

Contains Thermbalance Contains : Thermocouple

for measuring ∆ T

Contains : Seacodary

heater for measure ∆H

3. The heat of fusion ∆Hf and temperature during melting are measured and a

curve is plotted, the slope gives the melting point, depression (∆T) due to

presence of impurities in sample and Zero intercept represents the melting point

of a theoretical sample without impurity (To).

Depression of melting point ( T∆ ) can be expressed as

sf

2oT x

H

RT

∆

−=∆

where , yH∆ is the heat of fusion in mol–1

, To is the melting point of the pure

solvent system (substances) in Kelvins and, R is the gas constant and xs is the

mole fraction of solute (impurity). This expression can be used to calculate %

impurity in the sample.

Mole % impurity = TRT

H

2∆×

∆×

o

f100

Area under DSC curve gives heat of fusion for the sample.

4. It is recommended to use pure metal standards (99.999% pure) for the

temperature and heat calibration of DSC and DTA. According to the

manufacturers of thermal analysis equipment, one or more standards are needed. Indium (In) is the commonly used standard for the calibration of temperature

and peak area.

5. For such a measurement sapphire has to be used as a standard. The Cp

determination using DSC requires a run of three different tests as follows: 1-

two pans empty, 2- one pan with the sample, the reference pan remaining empty,

3- one pan with the standard, the reference pan remaining empty. The pans need

to have the same mass, and an identical heating rate has to be used for the three

runs.

6. Thermometric titrations can be performed only for the systems where heat is evolved or absorbed. In other words these involve change in enthalpy. Further,

these do not require any indicator for the detection of end point. However,

classical titration through require an indicator but these are good for all kinds of

reaction i.e. neutralization, precipitation, redox, complexometric etc. It has the

added advantage that equilibrium constant of reaction can be determined.

66

Thermal Methods 7. It is essential to calibrate the thermometric titration unit so that its heat capacity

may be determined. Further it helps in the earliest of cell temperature.

8. In an enthalpogram represents primarily change in enthalpy and temperature due

to the titration reaction. However, it also involves internal heat evolved or

absorbed.

As per eq. (11.20) RT ln K = STH ∆+∆− . which as rearrangement gives

T

HKR

T

HKRTS

∆+=

∆+=∆ ln

ln

9. Use Eq. (11.17) and correct Fig. 11.19

The slope in Region 1 corresponds to because Tc=Te. Same equation applies to

Region 4. In this case, however, constant C can be evaluated since w and (Tc -

Te) are known. Value of c is found to be 1.5 × 10-4 sec –1. Heat of dilution factor

in eqn. (11.19) is the difference between the slope f the titration of B into pure

water and the slope in Region 1.

sec/C100.1100.1100.2 555

P

Do

−−− ×=×−×=′

∆

C

H

Thus Eq. (11.19) can be solved for TR and a value of –1.2×10–4

sec–1

is obtained.

Finally, are the above information is used in Eq. (11.18) to obtain.

4P

P

101.8d

d −×=

′

∆−

t

H

C

H

The term dt

d PH is equal to the titration rate as PC′ is already given. Thus heat of

reaction is

mol/kcal5.13ormole/cal105.13100.6

101.8 3

8

4

−×−=×

×−=∆

−

−

H

Ans: ∆H = -13.5 Kcal/mole

11.8 FURTHER READING

1. H.H.Willard , L.L.Merrit Jr., J.A. Dean , F.A.Settle Jr., Instrumental Method

of Analysis, Wadsworth Publishing company , USA, 1986.

2. M.E. Brown, Introduction to Thermal Analysis, Kluwer Academic Publisher ,

London, 2001.

3. P.D.garn, Thermoanalytical Methods of Investigations, Academic Press , New

York , 1965.

4. W.W. Wandlandt, Thermal Analysis, Wiley, New York, 1986.

5. A.Blazek, Thermal Analysis, Van Nostrand Reinhold, London,1972 .

6. H.Kmaber , P.D.Garn , Thermal Analysis: Comparative studies on Materials,

John Wiley & Sons, New York, 1974.

67


Analysis, Scanning

Calorimetry and

Thermometric

Titrations

7. H.Gunzzler and A.Williams, Hand Book of Analytical Techniques, Wiley –VCH , Weinheim , Vol -2, 2001.

8. G.W.Ewing, Analytical Instrumentation Handbook, Marcel Dekker Inc, New

York, 1990.

9. J.Jiordan, J.Chem. Education, 40, A5(1963)

10. J. Batethel, Thermometric titrations, John Wiley, New York, 1975.

11. N. Jespersen in Instrumental Analysis Eds. H.H.Bauer, G.D.Christian, and J.E.O’ Reilly, Second Edn.Allyn and Bacon. Inc. Boston, 1986,p.523.

12. H.H. Willard, L. L. Meritt, J. A. Dean and F.A. Settle, Instrumental Methods of

Analysis, Seventh Edn, Wadsworth Publishing company, Belmont, 1988.

13. R.A. Meyer, Encyclopedia of Analytical Chemistry, John Wiley & Sons Ltd ,

Vol 15, 2000.

14. R.C. Mackenzie, Differential Thermal Analysis, Academic press London, 1970.

15. Skoog, Douglas A., F. James Holler and Timothy Nieman, Principles of

Instrumental Analysis. Fifth Edition. New York. 1998..

16. Dean, John A., The Analytical Chemistry Handbook. New York. McGraw Hill,

Inc. 1995.

thermal analysis

Documents

principle of dta

differential temperature

applications of dta

typical dta curve

experimental setup of

thermometric titrations

differential heat input

wider applications