Entropy and melting

Naoki, M., and Tomomatsu, T., Analysis of melting entropy and effect of volume on the conformational entropy of frawi-polyisoprene. Macromolecules, 13, 322—327 (1980). 

Component A was assumed to be a given substance with fixed thermodynamic properties, that is, melting enthalpy, melting entropy, and (along with this) melting point. The enthalpy and entropy of crystallization of the co-crystal were set to a constant value as well, whereas the thermodynamic parameters of the co-crystal former B have been varied. 

For a more detailed discussion see Pinal, R. Effect of molecular symmetry on melting temperature and solubility, Org. Biotnol Chem. 2004,2, 2692-2599. This paper also gives the formal connection between melting entropy and ideal solubility. 

Hoover W G and Ree F H 1967 Use of computer experiments to locate the melting transition and calculate the entropy in the solid phase J. Chem. Phys. 47 4873-8... 

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

The melting temperature is a function of the melting enthalpy and entropy ... 

An attractive feature of K<)A is that it can replace the liquid or supercooled liquid vapor pressure in a correlation. K,-ja is an experimentally measurable or accessible quantity, whereas the supercooled liquid vapor pressure must be estimated from the solid vapor pressure, the melting point and the entropy of fusion. The use of KOA thus avoids the potentially erroneous estimation of the fugacity ratio, i.e., the ratio of solid and liquid vapor pressures. This is especially important for solutes with high melting points and, thus, low fugacity ratios. 

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

The variation of the phase transition temperature with pressure can be calculated from the knowledge of the volume and enthalpy change of the transition. Most often both the entropy and volume changes are positive and the transition temperature increases with pressure. In other cases, notably melting of ice, the density of the liquid phase is larger than of the solid, and the transition temperature decreases... 

The melting temperature depression or enhancement may now be expressed in terms of the melting temperature and the entropy of fusion of component A, the activity coefficients of impurity B in the liquid and solid solutions at infinite dilution, and the total concentration of the impurity B, xb [12] ... 

When we compared the viscosities of solutions of natural rubber and of guttapercha and of other elastomers and later of polyethylene vs.(poly)cis-butadiene, with such bulk properties as moduli, densities, X-ray structures, and adhesiveness, we were greatly helped in understanding these behavioral differences by the studies of Wood (6) on the temperature and stress dependent, melting and freezing,hysteresis of natural rubber, and by the work of Treloar (7) and of Flory (8) on the elasticity and crystallinity of elastomers on stretching. Molecular symmetry and stiffness among closely similar chemical structures, as they affect the enthalpy, the entropy, and phase transitions (perhaps best expressed by AHm and by Clapeyron s... 

To calculate for this transition, it is necessary to have heat capacity data for both glassy and crystaUine glycerol from near 0 K to the melting point and the heat of fusion of both glass and crystal. Such data [7] lead to a ASm for Equation (11.7) of 19.2 J K mol. Thus, glassy glycerol cannot be assigned zero entropy at OK rather, it possesses a residual entropy of 19.2 J moP. ... 

This equation shows that a high melting temperature is obtained by raising the melt enthalpy AH and/or a lowering of the melt entropy AS. Since and... 

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