Poly heat capacity changes

Table II extends the values given originally by Pitzer and now encompasses all the n-alkanes of interest to us. The model used can be typified by that shown in Figure 5 for one octyl side chain in poly(di-n-octyl itaconate). It has been calculated O that the rotational barriers for the (>C-CO) and (O-Cj) bonds will be too high to allow free rotation at the temperature, and so this section of the chain is considered to be immobile. Rotation of the terminal methyl unit is a low energy process and will already be occurring, so one can restrict consideration to the six remaining (C-C) bonds for poly(di-/i-octyl itaconate). All of these will contribute to the heat capacity change and as there are two side chains per monomer unit, twelve bonds must be considered in the calculation. The variation of Cy as a function of temperature is shown for the homologous series of n-alkanes in Figure 6, but only the n-octyl will be considered here.

In order to compare experimental and theoretical heat capacity changes at Tg, a baseline heat capacity - temperature curve below Tg must be constructed. This was accomplished by measuring the Cp - T behavior for poly(dimethyl itaconate). That for the octyl derivative was then estimated by adding a contribution from each additional methylene unit measured from the vibrational frequencies for this unit and the acoustical frequencies used by Dole for polyethylene. It was then... 

Changing a heat capacity, Cp, in above-mentioned equations into the residual electrical resistivity, p, they can be reduced to the corresponding kinetics models as applied to describe the results of residual resistivity measurements [5] for LuHo.igo and LuHo.254- Experimental [5] and theoretical [7], [8] results of investigation of the short-range order relaxation in LuHq.iso and LuHo.254 poly crystals were obtained from data about measurements of residual-resistivity-time dependence and are presented in Fig. 1 (b). These results we described within the framework of the first- and second-order kinetics models as well (see Fig. 1(b)). Migration energies for LuHq.iso and LuHo.254 solid solutions were evaluated and are listed in Table 1. 

Improvements beyond the empirical, direct additivity of heat capacities is needed at low temperatures, where skeletal vibrations govern the heat capacities. With only few measured points it is possible to establish the functional relationship of the 0, and 3 temperatures with concentration for the inter- and intramolecular vibrations (see Sect. 2.3). The group-vibration frequencies are strictiy additive, so that heat capacities of complete copolymer systems can be calculated using the ATHAS, as discussed in Sect. 2.3.7. hi Fig. 2.70 the glass transition changes with concentration, to reach 373 K for the pure polystyrene, as for the previously discussed copolymer systems with polystyrene. Below T, the solid Cp of both components needs to be added for the heat capacity of the copolymer, above, the liquid Cp must be used. The glass transition retains the same shape and width as seen in Fig. 7.68 on the example of brominated poly(oxy-2,6-dimethyl-l,4-phenylene) [29]. 

Figure 3.25 shows the changes of heat capacity with temperature for the polyepichlorohydrin (PECH)/poly(vinyl acetate) (PVAc) combination at different diffusion times. In the glass transition region, the heat capacity traces are different for the different diffusion times.However, it is difficult to draw out more detailed information from these traces. The dCp/dT curves, however, clearly showed that an interface is formed by thermal diffusion, (see Figure 3.26). This is shown by the increase in the dCp/dT signal between the two glass transitions. With increasing diffusion time, the concentration of the interface will change and its thickness will increase.

Figures 5.24 and 5.25 present as examples the results of a volumetric and a calorimetric measurement on poly (vinylacetate). The glass transition has a characteristic signature which shows up in the curves. As we can see, the transition is associated with steps in the expansion coefficient dp /dT and the heat capacity d H/dT, i.e. changes in the slope of the functions p T) and H T). The transition extends over a finite temperature range with typical widths in the order of 10 degrees. The calorimetric experiment also exhibits another characteristic feature. One can see that the location of the step depends on the heating rate T, showing a shift to higher temperatures on increasing the rate.

Figure 9.8 Plot of changes in heat capacity at glass transition temperature versus heat of fusion of semicrystalline poly(lactic acid) (PLA) with different thermal history (marked circle shows the estimated heat of fusion for 100% crystal) [22].

---