Thermal Thermogram

Thermogravimetry The products of a thermal decomposition can be deduced by monitoring the sample s mass as a function of applied temperature. (Figure 8.9). The loss of a volatile gas on thermal decomposition is indicated by a step in the thermogram. As shown in Example 8.4, the change in mass at each step in a thermogram can be used to identify both the volatilized species and the solid residue. 

In a testing context, it refers to the first detection of exothermic-activity on the thermogram. The differential scanning calorimeter (DSC) has a scan rate of I0°C/min, whereas the accelerating rate calorimeter (ARC) has a sensitivity of 0.02°C/min. Consequently, the temperature at which thermal activity is detected by the DSC can be as much as 50°C different from ARC data. 

Differential Scanning Calorimeter (DSC) thermograms were obtained on a Perkin Elmer DSC-2 run at 10°C per minutes. Dynamic Mechanical Thermal Analysis (DMTA) spectra were obtained on a Polymer Labs DMTA at a frequency of 1Hz with a temperature range from -150°C to +150°C at a scan rate of 5°C per minute. 

Fig. 6 DSC thermograms showing representative thermal transitions in frozen solutions. The top thermogram is for a mannitol solution and is characteristic of a metastable glass-forming system.

In the broadest sense, thermal analysis (TA) measures physical changes in a material as a function of temperature. TA instruments measure variables in a sample such as heat flow, weight, dimensions, etc. A typical fingerprint of a compound might be the endothermic peak on a thermogram indicating a sample s crystalline melt. 

We use differential scanning calorimetry - which we invariably shorten to DSC - to analyze the thermal properties of polymer samples as a function of temperature. We encapsulate a small sample of polymer, typically weighing a few milligrams, in an aluminum pan that we place on top of a small heater within an insulated cell. We place an empty sample pan atop the heater of an identical reference cell. The temperature of the two cells is ramped at a precise rate and the difference in heat required to maintain the two cells at the same temperature is recorded. A computer provides the results as a thermogram, in which heat flow is plotted as a function of temperature, a schematic example of which is shown in Fig. 7.13. 

The differential scanning calorimetry (DSC) thermogram of miconazole was obtained using a DuPont 2100 thermal analyzer system. The thermogram shown in Fig. 2 was obtained at a heating rate of 10°C/min and was run over the range 50—300 °C. Miconazole was found to melt at 186.55 °C. 

The basic principle of heat-flow calorimetry is certainly to be found in the linear equations of Onsager which relate the temperature or potential gradients across the thermoelements to the resulting flux of heat or electricity (16). Experimental verifications have been made (89-41) and they have shown that the Calvet microcalorimeter, for instance, behaves, within 0.2%, as a linear system at 25°C (41)-A. heat-flow calorimeter may be therefore considered as a transducer which produces the linear transformation of any function of time f(t), the input, i.e., the thermal phenomenon under investigation]] into another function of time ig(t), the response, i.e., the thermogram]. The problem is evidently to define the corresponding linear operator. 

The combination of Eqs. (28) and (22) gives the Laplace transform of the impulse response H(p) which allows us to solve Eq. (21). By the inverse transformation, the relation which gives the output of the linear system g(t) (the thermogram) to any input/(0 (the thermal phenomenon under investigation) is obtained. This general equation for the heat transfer in a heat-flow calorimeter may be written (40, 46) ... 

This simplified equation is equivalent to Tian s equation [Eq. (16)], and it appears that n is indeed the time constant r of the calorimeter. Thence, the successive coefficients n in Eq. (29) may be called the calorimeter time constants of 1st, 2nd,. .., ith order. When the Tian equation applies correctly, all time constants r, except the first r may be neglected. Since the value of the coefficients n of successive order decreases sharply [the following values, for instance, have been reported (40) n = 144 sec, r2 = 38.5 sec, r3 = 8.6 sec, ri 1 sec], this approximation is often valid, and the linear transformation of many thermal phenomena produced by the thermal lag in the calorimeter may actually be represented correctly by Eqs. (16) or (30). It has already been shown (Section IV.A) that the total heat produced in the calorimeter cell is then proportional to the area limited by the thermogram. 

In the range of linearity, Eq. (29) correctly represents the heat transfer within the calorimeter. It should be possible, then, by means of this equation to achieve the deconvolution of the thermogram, i.e., knowing g(l) (the thermogram) and the parameters in Eq. (29), to define f(t) (the input). This is evidently the final objective of the analysis of the calorimeter data, since the determination of the input f(t) not only yields the total amount of heat produced, but also defines completely the kinetics of the thermal phenomenon under investigation. 

The differential equations Eqs. (10) and (29)3, which represent the heat transfer in a heat-flow calorimeter, indicate explicitly that the data obtained with calorimeters of this type are related to the kinetics of the thermal phenomenon under investigation. A thermogram is the representation, as a function of time, of the heat evolution in the calorimeter cell, but this representation is distorted by the thermal inertia of the calorimeter (48). It could be concluded from this observation that in order to improve heat-flow calorimeters, one should construct instruments, with a small... 

In any case, thermal inertia may be decreased but never completely removed (48). Data from heat-flow calorimeters must therefore be recorded in such a way that (1) the total amount of heat produced by the phenomenon under investigation is measured with precision, and (2) the correction of the thermograms is easily performed. 

From Tian s equation [Eq. (30)3, it appears that in order to transform the calorimeter response g(t) into a curve proportional to the thermal input f(t), it is sufficient to add, algebraically, to the ordinate of each point on the thermogram g(t), a correction term which is the product of the calorimeter time constant n, by the slope of the tangent to the thermogram at this particular point. This may be achieved manually by the geometrical construction presented on Fig. 10. 

It has been shown recently, however, that these equations may be solved 62), by means of the state functions theory (64) and/or the time-domain matrix methods 63). Figure 14 shows, for instance, that the computer calculations allow us to determine, with a good approximation, the time-dependence of thermal phenomena taking place in the calorimeter, although all significant details of their kinetics are completely blurred on the thermogram 62). This method has been recently used to correct... 

All heat evolutions which occur simultaneously, in a similar manner, in both twin calorimetric elements connected differentially, are evidently not recorded. This particularity of twin or differential systems is particularly useful to eliminate, at least partially, from the thermograms, secondary thermal phenomena which would otherwise complicate the analysis of the calorimetric data. The introduction of a dose of gas into a single adsorption cell, containing no adsorbent, appears, for instance, on the calorimetric record as a sharp peak because it is not possible to preheat the gas at the exact temperature of the calorimeter. However, when the dose of gas is introduced simultaneously in both adsorption cells, containing no adsorbent, the corresponding calorimetric curve is considerably reduced. Its area (0.5-3 mm2, at 200°C) is then much smaller than the area of most thermograms of adsorption ( 300 mm2), and no correction for the gas-temperature effect is usually needed (65). 

Measurements of thermal analysis are conducted for the purpose of evaluating the physical and chemical changes that may take place in a heated sample. This requires that the operator interpret the observed events in a thermogram in terms of plausible reaction processes. The reactions normally monitored can be endothermic (melting, boiling, sublimation, vaporization, desolvation, solid-solid phase transitions, chemical degradation, etc.) or exothermic (crystallization, oxidative decomposition, etc.) in nature. 

Differential thermal analysis proved to be a powerful tool in the study of compound polymorphism, and in the characterization of solvate species of drug compounds. In addition, it can be used to deduce the ability of polymorphs to thermally interconvert, thus establishing the system to be monotropic or enantiotropic in nature. For instance, form I of chloroquine diphosphate melts at 216°C, while form II melts at 196°C [18]. The DTA thermogram of form I consists of a simple endotherm, while the thermogram of form II is complicated (see Fig. 4). The first endotherm at 196°C is associated with the melting of form II, but this is immediately followed by an exotherm corresponding to the crystallization of form I. This species is then observed to melt at 216°C, establishing it as the thermodynamically more stable form at the elevated temperature. 

In order for maleimide/vinyl ether photoinitiator free photopolymerization to be useful, it is important that the cured films have good thermal/UV stability. Since there are no small molecule photoinitiators added to the uncured mixture initially, there is no residual small molecule photo initiator present in the final crosslinked film. This accounts for the enhanced UV stability we have observed for cured maleimide/vinyl ether films. In addition, TGA thermograms of photocured films of the MPBM/CHVE mixture (Figure 8) exhibit excellent thermal stability, with decomposition occurring at higher temperatures than for a simple UV cured HDDA film with 3 weight percent DMAP photoinitiator. (Such thermal stability would be... 

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