Entropy Theories

In the theory, z is later related to the total configurational entropy because s JS = z /A, where s is the entropy of the unit of minimum or critical size, z (j c cannot be less than A ln 2). Further, the relaxation time. 

In general, volume V and entropy S of the supercooled liquid can be treated as functions of P and T. We may therefore write. 

V and S in the above equations are molar volumes and entropies. At T the molar (minimum) free volume is given by N vj , where N is the Avagadro number. Therefore, N v[ = (F/ - Vg) and = (Si - Sg). In view of the fact dv = diS = 0 at Tg, it is easily seen that, the two equations yield two different equations for dTg dP  

In equations (3.16) and (3.17), AX, where X is , or Cp, is given by X(liquid) - X(glass). Indeed the two expressions (3.16 and 3.17) provide a means of experimental verification of the two theories because variation of glass transition with pressure can be experimentally determined along with other quantities, namely, Aar, Ayff and AC/.. Some of these quantities have been measured on several polymeric and non-polymeric glass-forming compounds and the data are presented in Table 3.1. It is evident that 

It may be noted that the entropy of the melt is considered as entirely configurational in AG theory. At Tm, it is equal to = dJiJT . The manner of decrease of this quantity is considered as determined by the difference between the heat capacities of melt and the crystalline phases in the supercooled region. At Tg, the frozen entropy, 5 is calculated as 

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Amadei, A., Apol, M. E. F., Di Nola, A., Berendsen, H. J. C. The quasi-Gaussian entropy theory Free energy calculations based on the potential energy distribution function. J. Chem. Phys. 104 (1996) 1560-1574... 

We have already observed that the entropy theory of elasticity predicts a modulus of the right magnitude and possessing the proper temperature coefficient. Now let us examine the suitability of Eq. (3.39) to describe experimental results in detail. 

GENERALIZED ENTROPY THEORY OE POLYMER GLASS EORMATION... 

II. Strengths and Weakness of the Original Entropy Theories of Glass Formation... 

B. Relation of Entropy Theory to Elastic Modulus Model of Structural Relaxation... 

GENERALIZED ENTROPY THEORY OF POLYMER GLASS FORMATION 127... 

Martinez and Angell [4] have recently reviewed the parallelism between the temperature dependence of the viscosity and that of S, and they have shown that this correlation is strong for the small molecule glass formers considered in their study. Since these findings are relevant to the entropy theory of glass formation. 

II. STRENGTHS AND WEAKNESSES OF THE ORIGINAL ENTROPY THEORIES OF GLASS FORMATION... 

GENERALIZED ENTROPY THEORY OF POLYMER GLASS FORMATION 149 The specific internal energy pw of Eq. (20) is given by pM= pB( b, s)-2p2c( b,Es)... 

This relation enables evaluating the fragility parameter Ks as well as the structural relaxation times r over the whole temperamre range To < T < Ta-Because T] depends on polymer microstructure and molar mass, Ap likewise exhibits the same dependence. Computations of Ks within the entropy theory have not been possible before. 

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