Heat flow phase

Recently, a (semi-)quantitative use of the heat flow phase was discussed. From the contribution of the temperature dependence of the reaction rate to the heat flow phase signal, an overall activation energy was estimated for an epoxy cine without vitrification [77]. If vitrification occurs, one obtains the phase shift due to thermal relaxation only by removing the contributions of the temperature dependence of the reaction rate and of the heat transfer conditions from the heat flow phase signal [78]. 

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The simultaneous measurement of the amplitude (modulus) of the complex heat capacity, the heat flow and the phase angle between heat flow and heating rate (termed heat flow phase) enables a more detailed study of complicated material systems, both in quasi-isothermal and non-isothermal conditions. The extraction of the signals is briefly summarised below. More details on theory and applications are given in dedicated special issues of Thermochimica Acta [6,7] wid Journal of Thermal Analysis and Calorime-try [8] and in other chapters of this book. 

Using the corrected heat flow phase (material contribution) and the modulus of the complex heat capacity, Cp, the components in-phase (Cp and out-of-phase (Cp ) with the modulated heating rate can be calculated using Eq. (4) (for more detailed approaches see Refs. [3,9,10]) ... 

It should be noted that the corrected heat flow phase is very small in most cases, so that the difference in value between C and Cp is negligible. For isothermal experiments, the reversing heat flow equals zero because of a zero underlying heating rate and consequently the non-reversing heat flow equals the total heat flow. 

Figure 2.2. Quasi-isothermal cure of an epoxy-anhydride at 100°C (a) comparison of the non-reversing heat flow obtained in MTDSC to the heat flow obtained in conventional DSC (arrow), (b) heat capacity and (c) corrected heat flow phase.

Figure 2.2c shows the corrected heat flow phase for the epoxy-anhydride system cured at 100°C the heat flow phase measured quasi-isothermally at 100° C for the fully cured resin was used as a reference point. The evolutions will be discussed in detail in the following section. In this paragraph, the magnitude of the signal is considered. 

The experiment of Figure 2.2 will now be considered in more detail as a typical example of isothermal cure with vitrification. It shows the nonreversing heat flow (Figure 2.2a), the heat capacity (Figure 2.2b) and the heat flow phase (Figure 2.2c) as a function of reaction time for the quasi-isothermal cure of an epoxy-anhydride resin at 100°C for 200 min. The reaction exotherm obeys an auto-catalytic behaviour the heat flow increases at... 

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°.

Figure 2.3. Quasi-isothermal cure of an unsaturated polyester at 30°C (a) non-reversing heat flow and complex viseosity (logarithmie seale) (b) heat capacity and heat flow phase the symbol (o) denotes the point at maximum auto-aeeeleration in the non-reversing heat flow...

Figure 2.5. Quasi-isothermal cure of a melamine-formaldehyde (MF) resin (pH 9.5 F/M = 1.7) at 119°C in closed high-pressure steel (HPS) and open A1 pans (a) non-reversing heat flow and heat capacity (b) heat flow phase.

As observed in the previous sections, relaxation phenomena are superimposed as local (downward) extremes in the heat flow phase. Thus, the heat flow phase gives an indication of a vitrification or devitrification process during the thermal treatment. In non-isothermal experiments, conditions of partial vitrification—a zone where the material is in between the liquid/ rubbery and the glassy state—can occur depending on the heating rate and the reactivity of the curing system (section 5.4). 

Partial vitrification is also observed in isothermally cured epoxy systems. However, the effect is less pronounced since the glass transition domain at goo is narrower for these networks [80]. An example is given in Figure 2.14 for the system DGEBA-MDA T oo = 102°C). At 80°C, a stepwise decrease in Cp and a relaxation peak are observed. At 100°C, the system is partially vitrifjdng and the phase angle remains in the relaxation regime at the end of cure. At 120°C, no vitrification effect is noticed anymore, neither in Cp, nor in heat flow phase. 

Figure 2.14. Quasi-isothermal cure of an epoxy(/ = 2)-amine(/ = 4) at 80, 100, and 120°C (a) heat capacity (b) heat flow phase (shifted for clarity).

Note that the measurements of ACp,react at full conversion can be disturbed by vitrification, as already illustrated with the heat capacity and the heat flow phase signals of the system DGEBA-MDA in Figure 2,14,... 

The information available in the heat capacity evolution is a key factor for the correct interpretation of the heat flow signal. The results indicate that the heat flow phase angle contains interesting information regarding the rheological state of the reacting material and especially about the occurrence of relaxation phenomena. 

Figure 2.112. Nonreversing (NR) heat flow (a), heat capacity change (ACp) (b), and heat flow phase (( )) (c) for the isothermal cure of stoichiometric diglycidyl ether of bisphenol A (DGEBA) and methylenedianilme (MDA) mixture at 70/80/100 °C the increase in ACp due to reaction and the stepwise decrease due to vitrification are indicated on the graph (1 °C/60s) [data reproduced fromSwier et al. (2004) with permission of John Wiley Sons, Inc.].

Figure 2.116. Nonreversing heat flow, change in heat capacity, and heat flow phase signal from MTDSC and percent of hght transmittance from optical microscopy (OM) for the reactive blend DGEBA + aniline (r = l)/20 wt% PES cnred at 100/90/80°C the cloud point from OM (A), onset of heat flow phase relaxation corresponding to vitrification of PES-rich phase (O) and epoxy-amine-rich phase ( ) are shown and also indicated in the heat flow and heat capacity signals [reprinted from Swier and Van Mele (2003a) with permission of Elsevier Ltd.].

When the cure temperature is below the full cure glass transition of the epoxy-amine (Tg = 95 C), vitrification of the epoxy-amine-rich phase also takes place. This clearly occurs in Hg. 2.116 for the reaction at 80°C.The heat flow phase angle is important in this respect, showing a second relaxation peak. Partial vitrification is seen at 90 C, and it is again most obvious in the heat flow phase or phase angle. 

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