Free energy configurational

Often the most important effective cluster interaction of the concentration fluctuation expansion of the configurational free energy is the EPI which is defined as... 

The configurational free energy of the chain, G, is simply equal to -kT In n. The mean number of segments bound to the confining surfaces can be obtained by differentiating the free energy with respect to 0... 

In this respect it must be recalled11 that all thermodynamic properties deduced from the crude version and the refined version II depend on the function r)(T,p) while for the other two versions it is the function f(lT, v) which is needed. As the thermodynamic properties of mixtures are usually measured in such conditions that T and p are independent variables (often with p 0), it is obviously easier to work with models involving rj(T,p) rather than (T, v). We shall therefore limit ourselves from now on to the crude version and the refined version II. Their Gibbs configurational free energies are respectively 21... 

As the DAM was described in detail elsewhere [12,13], only a brief review is accounted here. According to classical statistical mechanics, the configurational free energy is given by A, = -keT In Z where ks is Boltzmann s constant and T is the absolute temper-... 

Our goal here is to provide a simpler 2D description of the mesoscopic scale physics, consistent with Eq. (1), in a form useful for practical calculations. To that end, in analogy with density functional methods for inhomogeneous fluids we introduce an intrinsic (or configurational) free energy functional for the stepped surface. This gives the free energy of a macroscopic surface with N, steps as a functional of the positions x,(y) of all the steps. 

As noted above, the first study of the problem of partial chain flexibility has been done by Flory (1) - one more problem in polymer science which he was the first to tackle. Flory has assumed the existence of a favorable arrangement of a number of consecutive base units. The configurational free energy of this arrangement differs by an amount e from other possible sequences. Apparently, these other arrangements do not have to be all identical thus e represents an average value. Flory points out that the stiffness of the chain is involved. He places the chains and solvent molecules on a lattice, a convenient although not a necessary step. 

Now that we have an expression for the communal entropy, we can derive the probability distribution P(v). We start from the configurational free energy given by... 

A closely-related method for determining free energy differences is characterized as thermodynamic integration. The configurational free energy of an intermediate state... 

The configurational free energy resulting from the loss in conformational degrees of freedom was evaluated by means of the mean-field single-chain statistical mechanical approach. 

Feigin et al. also calculated a second extreme case, that of doublet formation. They showed that the configurational free energy change per doublet is given by an expression closely analogous to the other limiting case... 

Table 12.5. Although the basis of the comparison presented therein is slightly different (per particle vs per doublet), the results predicted by both extreme models are not too widely disparate. The configurational free energy change associated with flocculation can obviously be as large as 10 A T in systems of usual interest. Dilute dispersions are clearly more stable on this basis than more concentrated systems. What this means in terms of the effect on the critical flocculation point depends critically upon the nature of the particular system concerned.

Clark and Lai (1981), however, have simulated a polymer molecule on a tetrahedral latice using a Monte Carlo procedure. Three rotational conformational states were assumed to be accessible to each bond. The excluded volume condition was incorporated into the model by assuming that two or more segments cannot occupy the same position in space. These calculations permitted the evaluation of the change in configurational free energy of the polymer chains as a function of the interplane separation. 

The chapter contains three parts (1) evolution of the equation of state for diverse fluids, (2) formulation of the S-S hole-cell theory for the configurational free energy in single- and multicomponent systems, and (3) application of the S-S equation of state to polymeric systems at thermodynamic equilibria and under nonequilibrium conditions. 

We note that althoirgh the location of the glass transition in temperatirre-ptessure space is determined solely by the conflgurational entropy (equation lb) the zero frequency viscosity is determined solely by the configurational free energy F, (equation 7). 

The fluid is modeled as an assembly of lattice sites occupied by chain segments in contact with a fraction h of empty sites or holes. The h-function is to account for the temperature, pressure (and stress) dependent structural disorder in the system. What is required is the configurational free energy F (1)... 

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