UNIT 11 DIFFERENTIAL THERMAL ANALYSIS, SCANNING CALORIMETRY AND THERMOMETRIC TITRATIONS

Transcription

1 UNIT 11 DIFFERENTIAL THERMAL ANALYSIS, SCANNING CALORIMETRY AND THERMOMETRIC TITRATIONS Differential Thermal 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 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. 31

2 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 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 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 32

3 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 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. Differential Thermal 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 (T s T r ) 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 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. (T s T r ) will be negative because heat is absorbed and consequently T s will be smaller than T r. 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 33

4 Thermal Methods If area (A) is measured in cm 2 and unit of H is J g 1, the unit of K will be cm 2 J 1. 2 cm K = = g J g 1 2 cm J 1 In DTA/DSC C p is commonly expressed in mj g 1 C -1. Though in the SI units, it is expressed as J mol -1 K -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 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 that there is always a difference in the base lines. The changes in heat capacity ( C p ) may be determined at a particular temperature by measuring the difference in base lines i.e. displacement (d) since: SAQ 1 d d 1 C p = or heating rate m (dt/dt) m (11.2) Write an expression, which relate the peak area with the amount of the sample. Give the unit of calibration factor, K r Instrumentation In Fig 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. 34

5 Differential Thermal (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 C 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. 35

6 Thermal Methods At the moment, when an exothermic or endothermic change takes place, the shape of curve changes as shown in Fig 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 T s and T r 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 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. 36

7 Table 11.1: Factors that influence DTA Curve Factor Effect Suggestions 1. Heating rate Change in peak size and Use a low heating rate position 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 Standardise sample mass position 5. Particle size of Irreproducible curves Use small, uniform particle size sample 6. Packing density Irreproducible curves Standardise packing technique 7. Sample container Change in peak Standardise container Differential Thermal 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 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) iii) iv) 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. Fluctuation of thermostats. Reaction between sample and container 37

8 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 KNO 3, In, Sn, SiO 2, BaCO 3, 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 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 CaC 2 O 4.H 2 O for which DTA curve is shown in Fig 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 CaC 2 O 4.H 2 O when it is heated. Fig. 11.5: DTA curve of CaC 2 O 4.H 2 O in the presence of O 2 38

9 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 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 A 1 is the peak area of known mass (m 1 ) and A 2 is the peak area of unknown sample having mass equal to m 2, then using Eq we can write. m 1 = m 2 A A 1 2 Differential Thermal or A 2 m 2 = m1 (11.4) A1 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 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 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: H m = H r M r / m (11.3) where, H m = molar enthalpy of reaction, H r = enthalpy of reaction, M r = 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 ( T x ) has been measured and put in the equation for calculations: 39

10 Thermal Methods C p T2 T1 = K (11.5) mh where C p is the heat capcity at temperature T, T 1 and T 2 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 T c. 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 o C 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 o C over a wide range of heating rate. The temperature estimated for M.P. T m or B.P. T B, were most often selected from the portion peak as shown in Fig 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 T m 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 ( H x ) 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 cm 2 and 45.0 cm 3 for X and Y, respectively. Calculate the heat of fusion of Y. 40

11 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 enduse application, predict product performance and improve product quality. Differential Thermal 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 H 2 O 2. When clays or ore contain organic material then a broad exothermic peak appears between C. Thus the appearance of a broad exothermic peak between C 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 It may be observed that none of these miners show an exothermic peak in the range C corresponding to organic material as mentioned above. Fig. 11.8: DTA curves for (A) : kaolinite, (B): Mortmonillonite, (C): Illite 41

12 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 with labeled four transitions: glass transition, crystallisation, melting and oxidation, abbreviated as T g, T c, T m and T d respectively. Fig 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 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 : 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 (T g ), 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 42

13 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. T g /T m =0.66 The glass transition of a polymer can be obtained using number average molecular mass M ranging from to from expression: T g = [ ( /- 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 T g 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. Differential Thermal 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, H f, and the plausible assumption that this quantity is proportional to the crystalline content. If by some process of extrapolation the heat of fusion, H f*, of a hypothetical crystalline sample is known then the mass fraction of a crystallinity is Mass fraction = H H f f * 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) ] in the temperature interval, and then dividing by the heat of fusion of one H f gram of a perfectly crystalline sample [ equation. X = H H f (a)/ H f (c) H f (c) ], as expressed by following 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 Al 2 O 3, one part monomer 0.1 part catalyst as a 50 % paste in tricresyl phosphate and heating the mixture at a rate of 8 0 C per minute. Typical values of heat of polymerization as estimated from the peak area, are given in Table

14 Thermal Methods Table 11.2: Estimated Heat of Polymerization Materials heat of polymerization ( H 1 ) heat of polymerization ( H 2 ) trialkylcyanurate 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 bioorganic 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 C 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

15 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. Differential Thermal 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 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 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 Instrumentation Fig : A typical DSC Curve The block diagram of a DSC instrument as shown in Fig a, 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 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. 45

16 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 : (a) Block diagram of a DSC instrument (b) Heating arrangement in DSC compare this with Fig 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 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. 46

17 Differential Thermal Fig : 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., Ak mk H S H s = (11.7) A m s s where H s is the enthalpy change for sample, H k is the enthalpy change for known standard, m s and m k are masses of sample and known standard respectively, and A s and A k 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 (C p ). 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 The value of C p may be determined at a particular temperature by measuring this displacement (d). : d Cp = (11.8) heating rate m = (dh /dt) 1 (dt / dt) m (11.9) Using Eq. 11.9, we can deduce the unit of C p. 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, C p = mj s g 1 o 1 Cs 1 = mj g 1 C 1 C p can also be expressed in term of mcal. as and Cal. is: 1 calorie = 4.2 J]. mcal g 1 1 C [conversion factor for 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. 47

18 Thermal Methods dt K ( H 2 H1 ) = mcp (11.10) dt or K d = mc p dt dt where, H 1 and H 2 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 (H 2 H 1 ) is expressed as displacement, d). K is calibration factor, it can be determined by calibration against standard substance. However, K from the Eq 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 (Al 2 O 3 ) 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: dt K d = m Cp (11.11) dt K d = dt m Cp (11.12) dt where d and d are ordinate deflections (displacements) due to the sample and the standard respectively, m CP are mass and heat capacity of the standard. Dividing the Eq. (11.11) by (11.12) we get d m Cp Cp dm = or = (11.13) d m Cp Cp d m 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 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 Factors Affecting DSC Curve In the beginning of this block we talked about the lowest temperature, T i 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 T i, T f and T c (the final temperature at which the decomposition is 48

19 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: Differential Thermal 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 in detail 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 ( H f ) are required. Few examples of calibration standards are indium (In), benzoic acid, tin, lead, silver, gold, etc. 49

20 Thermal Methods SAQ 6 DTA and DSC, which method you will prefer for quantitative purposes and why? 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 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 for illustration about probable change in behaviour of a polymer sample. Fig : 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 is 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 ( H r ) observed in DSC can be further used to calculate molar enthalpy of reactions by using following formula: 50

21 H m = H r M r /m Where, ( H m = molar enthalpy of reaction, M r = relative molar mass of analysed compound, m = Mass of substance used for analysis. Differential Thermal Applications Differential scanning Calorimetry (DSC) used to measure energy changes as a function of temperature or time. A typical graph is shown in Fig Using this technique it is possible to observe a number of characteristic properties of a sample like fusion, crystallization, glass transition temperatures (T g ) 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 (T c ). 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 (T m ). 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. 51