Quasi-isothermal experiments

The experiments described above for the cure studies of epoxy resins (a typical three-dimensional network) were restricted to isothermal experiments (or quasi-isothermal experiments in the case of MDSC). As discussed later, these are the most reliable methods for generating kinetic information, but suffer from the length of time taken to generate data and, furthermore, in some systems the heat flow may be vanishingly small. 

FIGURE 4.10 Quasi-isothermal experiments showing the apparent heat capacity of a 75/25 poly(oxyethylene)/poly(ether sulfone) blend at two temperatures as a function of demixing time. (From Dreezen, G., Groeninckx, G., Swier, S., and Van Mele, B., Polymer, 42, 1449, 2001. With permission.)... 

Quasi-isothermal experiments at 298 K with an amplitude of 0.5 K using different numbers of Al lids as samples without the use of a reference pan. The last 10 min of the 20 min runs were used for analysis. 

Figure 4.131 shows the integrated Eq. (2) at steady state of quasi-isothermal experiments such as in Fig. 4.130. The parameters and A represent the amplitude...

Figure 6.118 shows the integrated Eq. (3) for the steady state of quasi-isothermal experiments (A). The measurements needed for this analysis are displayed for polystyrene in Figs. 6.14 and 6.15 and for poly(ethylene terephthalate) in Figs. 4.129 and 4.130. The parameters in Fig. 6.118 were arbitrarily chosen to clarify the three different contributions to the approximation shown in the figure. For a solution fitted to the experiments for poly(ethylene terephthalate), see Fig. 4.131. The parameters A and A represent the amplitude contributions due to the change in x and N with temperature, and P and y are phase shifts. The plotted (N - No)/N is proportional to the heat flow (and thus to ACp). The curve (A), however, is not a sinusoidal response.

The cold crystallization of PET was analyzed by running the series of quasi-isothermal experiments at 388 K and evaluated as shown in Fig. A.13.3. The reversing Cp ( ) decreases, as expected from the lower Cp of the crystallized sample. The same decrease can be calculated from the integral of the total heat-flow rate over... 

Quasi-isothermal experiments in the melt region can often reveal a wealth of information and this is dealt with in detail in Chapter 4. 

Figure 2.2c shows the evolution of the corrected heat flow phase, (p. The fully-cured glass state is always used as a reference (zero value) for the instrument correction [68, 69]. The phase angle corrected in this way has a small negative value, tending to more positive values due to the chemical reactions. Indeed, in Figure 2.2c the corrected heat flow phase, (p, initially amounts to —2.0° and then slowly evolves toward zero as the reaction proceeds. Relaxation phenomena are superimposed as local (downward) extremes. Thus, the (downward) local extreme in (p observed at 83 min confirms the vitrification process observed in Cp in Figure 2.2b. At the end of the quasi-isothermal experiment, (p equals —0.6°.

Tft)> — T t) is identical to the result expected from a quasi-isothermal experiment = 0, see Section 3.3) and is called pseudo-isothermal. The quasi-isothermal analysis has been described in detail and yields for the heat capacity the following expression which also holds for the pseudo-isothermal case [31] where is the modulation amplitude of AT which is proportional to the heat-flow rate, HF (A oc Ahf) -... 

Figure 4.80. Apparent heat capaeity measured by DSC and MTDSC for PE035000 crystallised by cooling from the melt at 10 K min T The solid curve was obtained by DSC at 10 K min , and the open circles represent the apparent reversing heat capacity, obtained by a series of quasi-isothermal experiments [52].

If, as shown in figure 12.9a, the whole transformation strictly occurs in the interval (Te—(), IK —> 7 c, then the corresponding enthalpy change// can be calculated from equation 12.37 by using the areas of two peaks only (i) the large peak recorded in the main experiment between Te—0.1K and Te, and (ii) the corresponding peak for the zero line. In this case, the process is quasi-isothermic because the initial and final temperatures differ by only 0.1 K. Therefore, unless... 

The next important step in the study of the regularities of the autowave modes of cryochemical conversion was to perform a series of experiments with thin-film samples of reactants. The changeover to such objects, characterized by the most intense heat absorption, allowed the realization of quasi-isothermal conditions of the process development and thus favored the manifestation of the abovementioned isothermal mechanism of wave excitation, which involves autodispersing the sample layer by layer due to the density difference between the initial and final reaction products. The new conditions not only not suppressed the phenomenon, but made it possible to reveal some details of the traveling-wave-front structure, which will be discussed here and also in Section X. 

There are quasi-static and dynamic experimental techniques. The first are mostly isothermal, the second usually adiabatic. Because of the thermodynamic work done in volume expansion in isothermal experiments, the values of the bulk moduli are somewhat different from those obtained in adiabatic determinations ... 

In cases where only one temperature-dependent constant appears, it can be calculated in real-time from TS-BR data and, if the reaction is carried out at quasi-isothermal conditions, can also be calculated in real-time from TS-PFR data (see Chapter 11). In all other cases TS-PFR data processing must be done after the experiment is completed. 

A more general method of using integrated forms involves using the standard procedure where one waits until the TSR experiment is completed and then proceeds to smooth the (X, T, t) surface as described in previous discussion. On the smoothed surface one identifies the operating lines for the system and uses them in an integral method of data interpretation. This removes the restriction employed in the hydrolysis study, that the system be at quasi-isothermal conditions, and makes the method more general. 

Typical run parameters are maximum modulation amplitudes A of 0.5 to 1.5 K and modulation frequencies of 0.06 to 0.2 radians s (p = 100-30 s). For quasi-isothermal run , < > is zero (5), so that the modulation is about a fixed Tq. Separate experiments are done at different values of to cover the glass-transition range. At each sufficient time is spent to reach steady state and collect statistically significant data for an additional 10 min. Data for fully amorphous PET and PS are reported in (73), and a wide range of partially crystallized and drawn films of PET in (4). Standard TMDSC runs have heating... 

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