Thermal Analysis of Polymeric Materials Part 7 doc

4 Thermal Analysis Tools ___________________________________________________________________ 346 Fig. 4.70 Fig. 4.69 calorimeter material. Checking the precision of several analyses with sample holders of different masses, it was found, in addition, that matching sample and reference sample pans gives higher precision than calculating the heat capacity effect of the different masses. In Fig. 4.70 the expression for the heat capacity is completed by inserting the top equations into the equation for T of Fig. 4.69. The basic DSC equations contain the 4.3 Differential Scanning Calorimetry ___________________________________________________________________ 347 Fig. 4.71 assumptions that the change of reference temperature with time is in steady state, i.e., dT r /dt = q. Introducing the slope of the recordedbaseline,dT/dT r , one obtains a final equation thatcontains onlyparameters easilyobtained, andfurthermore, can be solved for the heat capacity of the sample as shown. The correction term of the basic DSC equation has two factors. The factor in the first set of parentheses represents close to the overall sample and sample holder (pan) heat capacity, C s . The factor in the second set of parentheses contains a correction accounting for the different heating rates of reference and sample. For steady-state (and constant heat capacity), a horizontal baseline is expected with d T/dT r =0;the heat capacity of the sample is then simply represented by the first term. If, however, T is not constant, there must be a correction. Fortunately this correction is often small. Assuming the recording of T is done with 100 times the sensitivity of T r ,as is typical, then, for a T recording at a 45° angle the correction would be 1% of the overall sample and holder heat capacity. This error becomes significant if the sample heat capacity is less than 25% of the heat capacity of sample and holder. Naturally, it is easy to include the correction in the computer software. The online correction Tzero™, which is described in more detail in Appendix 11 accounts for this correction by separately measuring TandT b =T b  T r . Similarly, the heat-flow rates measured in the DSC of Fig. 4.57 should automatically make this correction. The second important measurement with a DSC is the determination of heats of transition. One uses the baseline method for this task. Of special interest is that during such transitions, steady state is lost. The sample undergoing the transition remains at the transition temperature by absorbing or evolving the heat of transition (latent heat). Figure 4.71 represents a typical DSC trace generated during melting. The temperature difference, T, is recorded as a function of time or reference temperature. The melting starts at time t i and is completed at time t f . During this time 4 Thermal Analysis Tools ___________________________________________________________________ 348 Fig. 4.72 span, the reference temperature increases at rate q, while the sample temperature remains constant at the melting point. The temperature difference T, thus, must also increase linearly with rate q. At the beginning of melting the temperature difference is T i . At the end of melting, when steady state has again been attained, it is T f , reaching the peak of the DSC curve. The general integration of C p to enthalpy goes over temperature, as shown in the top equation in Fig. 4.71. The second part of the top equation illustrates the insertion of the expression for mc p from Eq. (3) of Fig. 4.69, changed to the variable time and partially integrated. The final integration to t f is shown in the second equation of Fig. 4.71. The first term of the equation is K times the vertically shaded area, C,in the graph. The second term is the horizontally shaded area, B, multiplied by K. Again, the heat of fusion is not directly proportional to the area under the DSC curve up to the peak. There is, this time, a substantial third term, C p 'q(t f  t i ), marked with a“?”. An additional difficulty is that area C is not easy to obtain experimentally. It represents the heat the sample would have absorbed had it continued heating at the same steady-state rate as before. For its evaluation one needs the zero of the T recording which only is available by calibration for asymmetry (see Fig. 2.29). Next, one may want to calculate the cross-hatched area, A. The calculation is carried out in Fig. 4.72. Area A represents the return to steady state and can be described by using the approach to steady state which was derived in Fig. 4.68. The result represents the first and the last term of the expression for H f as it was given in Fig. 4.71. This means that under the conditions of identical Ti and T f , one can make use of the simple baseline method for the heat of fusion determination: The heat of fusion, H f , is just the area above the baseline in Fig. 4.71, multiplied with K, the calibration constant. If the baseline deviates substantially from the horizontal, corrections must be made which are discussed in Fig. 4.80, below. 4.3 Differential Scanning Calorimetry ___________________________________________________________________ 349 4.3.7 Applications Heat Capacity. To make an actual heat capacity measurement, one must first do a calibration of the constant K. The procedure has been illustrated in Sect. 2.3.1 with Fig. 2.30. Three consecutive runs should be made. These allow to calculate the calibration constant K as given in Eq. (3) of Fig. 2.30: The three runs must agree within experimental error in their absolute amplitude of the initial and final isotherms. A deviation signals that the heat-loss characteristics of the calorimeters have changed. The only solution is then to start over. Such mishap occurs from time to time even with the greatest of care. Another important precaution is to keep the temperature-range for calibration sufficiently short to have a linear baseline, i.e., when halving the temperature range, the baseline change must be half. A well-kept DSC may permit temperature-ranges as wide as 100 K. The amplitudes, a, should be taken at intervals of 10 K, leading to a calibration table that agrees with typical heat capacity steps in data tables. Another hint for good quality DSC measurements is to adjust sample and calibrant amplitudes to similar levels and to choose the sample mass sufficiently high to minimize errors. Note, however, that too high amplitudes lead to instrument lags that may limit precision. This is even more important for TMDSC where the lag may become so large that the modulation is not experienced by the whole sample. Figure 2.46 is an example of a heat capacity measurement of polyethylene. The data were first extrapolated to full and zero crystallinity, as discussed in Sect. 2.3.6, to characterize the limiting states of solid polyethylene (orthorhombic crystals and amorphous). The low-temperature data, below about 130 K, were measured by adiabatic calorimetry as described in Sect. 4.2. Besides the experimental data, the computed heat capacities from theAdvanced THermal AnalysisSystem, ATHAS, can also be derived, as shown in Fig. 2.51 and summarized for many polymers in Appendix 1. This system makes use of an approximate frequency spectrum of the vibrations in the crystal. At sufficiently low temperature only vibrations contribute to the heat capacity and missing frequency information can be derived by fitting to the heat capacity. The skeletal vibrations are vibrations that involve the backbone of the molecule (torsional and accordion-like motion). Their heat capacity contribution is most important up to room temperature. The group vibrations are more localized (C C and CH stretching and CH bending vibrations) and contribute mainly at higher temperature. A comparison of the computed and the measured heat capacity indicates deviations that start at about 250 K and signal other contributions to the heat capacity. For polyethylene this motion is conformational and of importance to understand the mechanical properties. Thisexample illustrates the importance ofgood experimental heat capacity data. Only if C p is known, is a sample well characterized. Besides interpretation of the heat capacity by itself, the heat capacity, C p, can also be used to derive the integral thermodynamic functions, enthalpy, H, entropy, S, and free enthalpy, G, also called Gibbs function: 4 Thermal Analysis Tools ___________________________________________________________________ 350 Fig. 4.73 Polyethylene data are shown in Fig. 2.23. At the equilibrium melting temperature of 416.4 K, the heat of fusion and entropy of fusion are indicated as a step increase. The free enthalpy shows only a change in slopes, characteristic of a first-order transition. Actual measurements are available to 600 K. The further data are extrapolated. This summary allows a close connection between quantitative DSC measurement and the derivation of thermodynamic data for the limiting phases, as well as a connection to the molecular motion. In Chaps. 5 to 7 it will be shown that this information is basic to undertake the final quantitative step, the analysis of nonequilibrium states as are common in polymeric systems. Fingerprinting of Materials. Changing toa less quantitative application, materials are characterized by their phase transition or chemical reactions in what has become known as fingerprinting. The measurements can be done by DTA with quantitative information on the transition temperature and made quantitative with respect to the thermodynamic functions by using DSC. The DSC is furthermore also able to measure kinetics parameters as shown in Fig. 3.98. The DTA curve of Fig. 4.73, taken as an unknown, is easily identified as belonging to amyl alcohol (DSC cell A of Fig. A.9.2, 2 l in air). At least two events are available for identification, the melting (2) and the boiling (3). It helps the interpretation to look at the sample and know that it is liquid between (2) and (3) and has evaporated after (3). It is always of importance to verify transitions observed by DTA by visual inspection. The small exotherm (1) at about 153 K is due to some crystallization. It occurs on incomplete crystallization on the initial cooling, a typical behavior of alcohols. The curve Fig. 4.74 represents a DTA trace, easily identified as belonging to poly(ethylene terephthalate) which was quenched rapidly from the melt to very low temperatures before analysis (DTA cell D of Fig. A.9.2, 10 mg of sample in N 2 ). 4.3 Differential Scanning Calorimetry ___________________________________________________________________ 351 Fig. 4.74 Under such conditions, poly(ethylene terephthalate) remains amorphous on cooling; i.e., it does not have enough time to crystallize, and thus it freezes to a glass. At point (1) the increase in heat capacity due to the glass transition can be detected. At point (2), crystallization occurs with an exotherm. Note that after crystallization the baseline drops towards the crystalline level. Endotherm (3) indicates the melting, and finally, there is a broad, exotherm with two peaks (4) due to decomposition. Optical observation to recognize glass and melt by their clear appearances is helpful. Microscopy between crossed polarizers is even more definitive for the identification of an isotropic liquid or glass. More details about this DSC trace will be discussed in Sect. 5.4. Figure 4.75 refers to iron analyzed with a high-temperature DTA as sketched H in Fig. A.9.3. About 30 mg of sample were analyzed in helium. In this case several solid–solid transitions can be used for the characterization of the sample in addition to the fusion which is represented by endotherm four. As a group, these solid-solid transitions are characteristic of iron and can be usable for its identification. A more quantitative analysis may also allow to distinguish between the many variations of commercial irons. The diagram in Fig. 4.76 is a DTA curve of barium chloride with two molecules of crystal water measured by high-temperature DTA (10 mg sample, in air). The crystal water is lost in two stages. Identification of these transitions is best through the weight loss and analysis of the chemical nature of the evolved molecules. Endotherm (3) is a solid-state transition. Either X-ray diffraction or polarizing microscopy can characterize it. Finally, anhydrous barium chloride melts at (4), proven by a loss of the particle character on opening the sample pan after cooling. Figure 4.77 shows two qualitative DTA traces which can be used to interpret a chemical reaction between the two compounds. The chemical reaction can be 4 Thermal Analysis Tools ___________________________________________________________________ 352 Fig. 4.76 Fig. 4.75 performed either to identify the starting materials or to study the reaction between the substances. The top curve is a DTA trace of pure acetone (DSC type A of Fig. A.9.2, 1 5 mg of sample, static nitrogen). A simple boiling point is visible. The bottom trace is of pure p-nitrophenylhydrazine with a melting point, followed by an exothermic decomposition. The top of Fig. 4.78 is the DTA curve after mixing of both components in the sample cell. The chemical reaction leading to the product is: 4.3 Differential Scanning Calorimetry ___________________________________________________________________ 353 Fig. 4.78 Fig. 4.77 CH 3 HCH 3 H \| \| C=O + H 2 N NphenyleneNO 2  C=NNphenyleneNO 2 +H 2 O // CH 3 CH 3 acetone + p-nitrophenylhydrazine  p-nitrophenylhydrazone + water 4 Thermal Analysis Tools ___________________________________________________________________ 354 Fig. 4.79 The p-nitrophenylhydrazone has a different thermal behavior. It does not decompose in the range of temperature used for analysis and does not show the low boiling point of acetone. To date, little use has been made of this powerful DTA technique in organic chemical analyses and syntheses. In Fig. 4.79 the DTA curves for the pyrosynthesis of barium zincate out of barium carbonate and zinc oxide are shown. The experiment was done by simultaneous DTA and thermogravimetry on 0.1 cm 3 samples in an oxygen atmosphere. Curve A is the heating trace of the mixture of barium carbonate and zinc oxide. The DTA curve is rather complicated because of the BaCO 3 solid–solid transitions. The loss of CO 2 has already started at 1190 K. The main loss is seen between 1350 and 1500 K. On cooling after heating to 1750 K, however, a single crystallization peak occurs at 1340 K (curve B). On reheating the mixture, which is shown as curve C, the new material can be identified as barium zincate by its 1423 K melting temperature. Unfortunately no explanation is given for the two small peaks at 1450 and 1575 K in the original research. Quantitative Analysis of the Glass Transition. Cooling through the glass transition changes a liquid to a glassy solid. The transition occurs whenever crystallization is not possible under the given conditions. It is a much more subtle transition than crystallization, melting, evaporation or chemical reaction in that it has no enthalpy or entropy of transition. Only its heat capacity changes, as shown in Fig. 2.117. Characterization of the glass transition requires DSC data of high quality. At the glass transition, large-amplitude motion becomes possible on heating (devitrification), and freezes on cooling (vitrification). In contrast to the small- amplitude vibrational motion in solids,the large-amplitude motion involvestranslation and rotation, and for polymers, internal rotation (conformational motion). For more details on the glass transition, see also Chaps. 2 and 5 7. For characterization, one 4.3 Differential Scanning Calorimetry ___________________________________________________________________ 355 finds first the glass-transition temperature, T g , defined as the temperature of half- vitrification or devitrification. For homopolymers and other pure materials, the breadth of the transition, given by T 2  T 1 , and is typically 35 K. For polymers, blends, and semicrystalline polymers this breadth can increase to more than 100 K. The beginning, at T b , and the end of the transition, at T e , are also characteristically different from sample to sample. All five temperatures of Fig. 2.117 should thus be recorded together with the change in heat capacity, C p ,atT g . Since the change into and out-of the glassy state follows a special, cooperative kinetics, the time-scale in terms of the heating or cooling rate needs to be recorded also (see Sects. 2.5.6 and 4.4.6). A sample cooled more slowly vitrifies at lower temperature and stores in this way information on its thermal history. Reheating the sample gives rise to enthalpy relaxation or hysteresis as is described in Sect. 6.3. Only when cooling and heating rates are about equal is there only little hysteresis. Quantitative analysis of the intrinsic properties of a material and its thermal history is thus possible. Finally, it is remarked in Fig. 2.117 that it is possible to estimate from C p how many units of the material analyzed become mobile at T g . The DSC of the glass transition is thus a major source for characterization of materials. Quantitative Analysis of the Heat of Fusion. The melting transition with its various characteristic temperatures and the enthalpy of fusion is discussed in Fig. 4.62 as a calibration standard for DSC. In Fig. 4.80 the case is treated where the simple baseline method of Fig. 4.71–72 is not applicable because of a broad melting range and a large shift in the baseline. In this case, the baseline must be apportioned properly to the already absorbed heat of fusion. This change in the baseline can be estimated by eye, as marked in the figure. The points marked 1/4, 1/2, 3/4, and the completion of melting are connected as the corrected baseline, if needed with a small correction for the time needed to reach steady state (lagcorrection). More quantitative is to use a computer program involving correction of the peak for lags (desmearing to the true progress of melting [26]) and quantitative deconvolution of the peak as indicated in the figure by Eq. (2) [27]. The recorded heat capacity that follows the peak is called the apparent heat capacity, C p # . It is made up of parts of the crystal heat capacity, amorphous heat capacity, and the latent heat of fusion. In the case of polymers, the crystallinity is not 100% at low temperature, the samples are semi- crystalline (see Chap. 5). The total measured heat of fusion is then also only a fraction of the expected equilibrium value. Without measuring the heat capacity of the crystalline or semicrystalline sample, the change of crystallinity can be extracted by solving Eq. (3) [28]. The change of the heat of fusion with temperature needed for the solution is given in Eq. (1) and is available from the ATHAS Data Bank as summarized in Appendix 1. The needed quantity C p #  C p a , represents the difference between the measured curve and C p a available from the DSC trace. Figure 4.81 illustrates the change in crystallinity of a complex block copolymer with two crystallizing species which is discussed in more detail in Sect. 7.3.3. At low temperature the sample which is phase-separated into a lamellar structure of the two components consists of glassy and crystalline phases in each lamella. Next, the oligoether goes through its glass transition without change in crystallinity. This is followed by the melting of the oligoether crystals, seen by the [...]... The DSC of the glass transition is thus a major source for characterization of materials Quantitative Analysis of the Heat of Fusion The melting transition with its various characteristic temperatures and the enthalpy of fusion is discussed in Fig 4.62 as a calibration standard for DSC In Fig 4.80 the case is treated where the simple baseline method of Fig 4 .71 72 is not applicable because of a broad... top of Fig 4 .78 is the DTA curve after mixing of both components in the sample cell The chemical reaction leading to the product is: Fig 4 .76 4.3 Differential Scanning Calorimetry 353 _ Fig 4 .77 CH3 H CH3 H \ | \ | C=O + H2N N phenylene NO2  C=N N phenylene NO2 + H2O / / CH3 CH3 acetone + p-nitrophenylhydrazine  p-nitrophenylhydrazone + water Fig 4 .78 354 4 Thermal Analysis. .. difference is Ti At the end of melting, when steady state has again been attained, it is Tf, reaching the peak of the DSC curve The general integration of Cp to enthalpy goes over temperature, as shown in the top equation in Fig 4 .71 The second part of the top equation illustrates the insertion of the expression for mcp from Eq (3) of Fig 4.69, changed to the variable time and partially integrated The... measurement and the derivation of thermodynamic data for the limiting phases, as well as a connection to the molecular motion In Chaps 5 to 7 it will be shown that this information is basic to undertake the final quantitative step, the analysis of nonequilibrium states as are common in polymeric systems Fingerprinting of Materials Changing to a less quantitative application, materials are characterized... The p-nitrophenylhydrazone has a different thermal behavior It does not decompose in the range of temperature used for analysis and does not show the low boiling point of acetone To date, little use has been made of this powerful DTA technique in organic chemical analyses and syntheses In Fig 4 .79 the DTA curves for the pyrosynthesis of barium zincate out of barium carbonate and zinc oxide are shown... compounds The chemical reaction can be 352 4 Thermal Analysis Tools _ Fig 4 .75 performed either to identify the starting materials or to study the reaction between the substances The top curve is a DTA trace of pure acetone (DSC type A of Fig A.9.2, 1 5 mg of sample, static nitrogen) A simple boiling point is visible The bottom trace is of pure p-nitrophenylhydrazine with a... peak for lags (desmearing to the true progress of melting [26]) and quantitative deconvolution of the peak as indicated in the figure by Eq (2) [ 27] The recorded heat capacity that follows the peak is called the apparent heat capacity, Cp# It is made up of parts of the crystal heat capacity, amorphous heat capacity, and the latent heat of fusion In the case of polymers, the crystallinity is not 100% at... isotropizations of liquid crystals or by seeding using TMDSC (see Sect 4.4 .7) Figure 4.83 shows a similar experiment on Fig 4.82 Fig 4.83 358 4 Thermal Analysis Tools _ a heat-flux DSC as shown in the sketch A of Fig A.9.2, using different purge gases The magnitude of change in the onset temperature of melting is similar to Fig 4.82 The rounding in the vicinity of heating... with the operating system of the power-compensated DSC in Fig 4.82 When controlling the furnace temperature as in the heat-flux DSC of Fig 4. 57, there is a mass dependence of the onset of melting as illustrated in Fig 4.84 Fig 4.84 Note, that some DSCs have a lag correction incorporated in their analysis software Such corrections are, however, only approximations because of the changes with sample... environment as is pointed out on pg 340, above More applications of the DSC to the analysis of materials are presented in Sect 4.4 as well as in Chaps 6 and 7, below 4.4 Temperature-modulated Calorimetry A major advance in differential scanning calorimetry is the application of temperature modulation, the topic of this section The principle of measurement with temperature modulation is not new, the differential . equation in Fig. 4 .71 . The second part of the top equation illustrates the insertion of the expression for mc p from Eq. (3) of Fig. 4.69, changed to the variable time and partially integrated final quantitative step, the analysis of nonequilibrium states as are common in polymeric systems. Fingerprinting of Materials. Changing toa less quantitative application, materials are characterized. Quantitative analysis of the intrinsic properties of a material and its thermal history is thus possible. Finally, it is remarked in Fig. 2.1 17 that it is possible to estimate from C p how many units of