Configurational entropy equation

The critical size of the stable nucleus at any degree of under cooling can be calculated widr an equation derived similarly to that obtained earlier for the concentration of defects in a solid. The configurational entropy of a mixture of nuclei containing n atoms widr o atoms of the liquid per unit volume, is given by the Boltzmann equation... 

Flocculation into a minimum of the type depicted in figure 7 will be opposed by the loss in configurational entropy of the particles. We may formally express this by the equation (30,31),... 

As a first approximation, assume that the total entropy change, ASy, is made up solely of configurational entropy. This can be determined by using the Boltzmann equation for the entropy of a disordered system ... 

Because the configurational entropy of interstitial defects has the same form as that of vacancies, a population of self-interstitial atoms is also thermodynamically stable. The creation of these defects can then also be treated as a pseudochemical equilibrium, and an equation for the relationship between the number of self-interstitials and the appropriate equilibrium constant for interstitial generation, Kv is readily... 

The configurational entropy evaluated above omits all mention of electron spin. Because there are two spin directions, a spin degeneracy of 2, these must be included in the possible configurations. When this term is included, the Heikes equation becomes the Chaikin-Beni equation ... 

The configurational entropy change, A.Sf, due to the distribution of the defects over the available positions, can be determined by using the Boltzmann equation. The number of ways of distributing the nP vacancies that have been created over the N available positions in the atom array affected by Frenkel defects is... 

The configurational entropy on the b lattice is given by an identical equation. For the perfect long-range ordered modification the configurational entropy is zero, and the entropy change due to disorder is thus... 

The configurational entropy model describes transport properties which are in agreement with VTF and WLF equations. It can, however, predict correctly the pressure dependences, for example, where the free volume models cannot. The advantages of this model over free volume interpretations of the VTF equation are numerous but it lacks the simplicity of the latter, and, bearing in mind that neither takes account of microscopic motion mechanisms, there are many arguments for using the simpler approach. 

Application of Stirling s formula to equation 5.191 and comparison with the configurational state of pure components lead to the definition of a configurational entropy of mixing term in the form... 

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],... 

Substituting Equation (53) into Equation (45) gives a statistical expression for the solute contribution to the configurational entropy of the mixture ... 

The summation replaces the product in going from Equation (53) to Equation (54) since we are dealing with logarithms in the latter. Note that the configurational entropy refers explicitly to the entropy associated with the mixture itself the internal entropy of the molecules themselves is clearly not included. Next a series of mathematical manipulations will transform Equation (54) into a more useful form ... 

The entropy of the mixture is calculated from this by the Boltzmann entropy equation, Equation (45). By separately letting TV2 and TV, equal zero, the configurational entropies of the solvent and the solute, respectively, are obtained from Sm,x. Finally, by subtracting S, and S2 from S,mx, an expression is obtained for ASm. 

It is now generally accepted that the viscous flow of polymeric liquids is connected with chain segment rotation, i.e. with configurational entropy. From this point of view Miller concluded that the Simha-Boyer equation was not correct since the relative free-volume in SB theory equals zero at 0 K, not at T = T0. If the latter... 

According to the glass-transition occurs when the system readies a certain minimum value of the configurational entropy ASc at Fg, which can be calculated according to the equation... 

Ensembles 600 Enterokinase 480 Enthalpy 55 activation 56, 545-547 protein folding 509 -512 specific heat effects 511, 545 - 547 Enthalpy-entropy compensation 346 Enthalpy versus entropy in protein folding 509-512, 587, 599 Entropy 55, 68-72 activation 56, 545 -547 binding 324, 345 Boltzmann equation 510 chelate effect 345 configurational 510 configurational entropy of loops 535 effective concentration 68-72 equilibria on enzyme surface 118 hydrogen bond 338 hydrophobic bond 332, 510 importance in enzyme catalysis 72 importance in enzyme-substrate binding 72... 

The change in configurational entropy, AS g, on forming a loop of n residues from an open random coil has been estimated from simple polymer theory and the probability that the two points where the loop in the random coil is linked lie simultaneously within a defined volume element V. Thus, equations of the form... 

This equation has a formal analogy to (17). Instead of the Langmuir configurational entropy —2RT In [(1 — 8)/8], we now find the term... 

If the configurational entropy ASM is assumed to represent the total entropy change ASm on mixing, the free energy of mixing is obtained by combining equations... 

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