Specific volume changes

In order to draw the property - composition diagram, coordinates are usually chosen so that the ideal system values correspond with the additive law regarding concentration [313]. It is known, for instance, that in an ideal system, molar volume changes additively with the concentration, and is expressed in molar fractions or molar percentages, whereas specific volume changes linearly with the concentration, and is expressed in mass fractions or mass percentages. 

The properties are evaluated at maximum allowed pressure conditions. For liquids, (3 can typically be evaluated from the specific volume change over a 5°C temperature increment. For ideal gases, Eq. (23-91) becomes... 

The physical properties, latent heat (hfg), specific volume change (vfg), and liquid specific heat capacity (Cf),-are, all required to evaluate the method. Liquid specific heat capacity can usually be measured quite easily. Data are required from the... 

Figure 1. Specific volume change vs. temperature for crystalline fractions of propylene oxide polymers from different catalysts...

By measuring the temperature change and the specific volume change accompanying a small pressure change in a reversible adiabatic process, one can evaluate the derivative... 

S(P, T) a depends on the specific volume changes with T and P. Knowing... 

Table 10-4. Enthalpies of fusion, AHm, entropies of fusion, ASm, and specific volume changes on melting, Avm, of polymers. 

A glass transition occurs for an amorphous polymer when the slope of a plot of specific volume changes abruptly with rise of temperature. The slope itself (the thermal expansion coefficient a), a = [llY] dV/dT, shows a step-change at Tg. A crystalline polymer also shows a transition at the same temperature, due to its amorphous phase. (It will be explained later that only semi-crystallinity may exist and there are almost always amorphous domains.) In the case of a crystalline polymer, however, a primary transition temperature, T, exists, signified by an abrupt change in volume. The specific volume of the crystalline polymer is always lower than that of the equivalent amorphous one because its more compact stmcture increases the density. 

A/B [60], and B/F [61]), and second-order (e.g., N/A [62-65], A/C [47,66-68], I/F [69, 70]) phase transitions, as well as singularities in the critical behavior [71], have been inferred. Lists of selected values of density and specific volume changes at different phase transitions are given in Tables 1 and 2. Collections of data and reviews have been given by Bahadur [16], Beguin et al. [72], Pisipati et al. [73], and Tsykalo [74], From the temperature dependence of volume and density, the thermal expansion coefficient a and the thermal expansivity j3... 

The terminal alloy is Li22M5, with a theoretical capacity of about 1600 mAh/g. Compared with Si-based materials, Ge exhibits a higher diffusivity for lithium ions (about 400 times greater than that in silicon at room temperature) and a lower specific volume change during the Li insertion/extraction process, which is expected to present better cycling performance at comparable capacity, and therefore shows promise as a negative electrode material for lithium-ion batteries. 

Fig. 5a - c. Molecular properties of bovine serum albumin as a function of the molar concentration, C3, of the denaturant guanidinium chloride (from [83D1]). a apparent isopotential specific volume (in cm g ) b extinction coefficient c intrinsic viscosity (in cm g ). For experimental details see the original reference. Reprinted from International Journal of Biological Macromolecules, Vol. 5, H. Durchschlag and R. Jaenicke, Partial specific volume changes of proteins ultracentrifugal and viscometric studies, pp. 143-148, 1983, with permission from Elsevier Science. 

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