Configurational entropy temperature dependence

A. Milchev, I. Gutzow. Temperature dependence of the configurational entropy of undercooled melts and the nature of the glass transition. J Macromol Sci B 22 583-615, 1982. 

The expression derived for the wet glass transition, Tgw, assuming the configurational entropy as the temperature dependent function30) ist ... 

Let us now turn to a discussion of the relation of the temperature dependence of the polymer melt s configurational entropy with its glass transition and address the famous paradox of the Kauzmann temperature of glass-forming systems.90 It had been found experimentally that the excess entropy of super-cooled liquids, compared with the crystalline state, seemed... 

Fig. 19, where the exponential tail is restricted to the region Q < 0. Why are spontaneous events not observed for 2 > 0 The reason is that spontaneous events can only release and not absorb energy from the environment see Eq. (215). This is in line with the argumentation put forward in Section VI.A, where the first time that cooperative regions release the stress energy, it gets irreversibly lost as heat in the environment. As the number of stressed regions monotonically decreases as a function of time, the weight of the heat exponential tails decreases with the age of the system as observed in Fig. 19. The idea that only energy decreasing events contribute to the effective temperature (Eq. (215)) makes it possible to define a time-dependent configurational entropy [189].

Free Volume Versus Configurational Entropy Descriptions of Glass Formation Isothermal Compressibility, Specific Volume, Shear Modulus, and Jamming Influence of Side Group Size on Glass Formation Temperature Dependence of Structural Relaxation Times Influence of Pressure on Glass Formation... 

Unfortunately, reliable experimental estimates of the configurational entropy are unavailable to enable explicit application of the AG model for polymer fluids. Instead, the temperature dependence of t in polymer melts is often analyzed in terms of the empirical Vogel-Fulcher-Tammann-Hesse (VFTH) equation [103],... 

Figure 21. LCT computations for the reduced configurational entropy 5ic defined by Eq. (53) as a function of the reciprocal of the reduced pressure SP = P — Po /P (where P denotes the Vogel pressure) for high molar mass (M = 40001) F-S polymer fluid at fixed temperature T = 388 K. The inset illustrates the temperature dependence of P (symbols) and the line represents a fit to the data points, using P = a + bT with a = —378.6 MPa and b = 1.0825 MPa/K. (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Chemical Physics 123, 111102 (2005). Copyright 2005 American Institute of Physics.)...

Figure 23 presents the computed temperature dependence of the dimensionless configurational entropy (for the TA) model) defined as... 

Figure 23. Temperature dependence of the reduced configurational entropy per unit site (defined by Eq. (70)) for the free association equilibrium polymerization model in the infinite pressure limit. The values of the enthalpy Afip = -35 KJ/mol and entropy Aip = -105 J/(mol K) of polymerization are identical to those used iu our extensive studies of equilibrium polymeriza-tiou, and the initial monomer concentration 4)° is taken as 4)° = 0.1. The crossover...

The thermodynamic functions of fc-mers adsorbed in a simple model of quasi-one-dimensional nanotubes s adsorption potential are exactly evaluated. The adsorption sites are assumed to lie in a regular one-dimensional space, and calculations are carried out in the lattice-gas approximation. The coverage and temperature dependance of the free energy, chemical potential and entropy are given. The collective relaxation of density fluctuations is addressed the dependence of chemical diffusion coefficient on coverage and adsorbate size is calculated rigorously and related to features of the configurational entropy. 

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