Gaussian density fluctuation theories

The final ingredient in this theory is an assumption permitting averaging with respect to the density fluctuations to eliminate the condition here on the densities. The simplest such assumption is that these coordinates obey a gaussian functional distribution built on the information [py(r) X ) and [8py r)8p r ) X )f, this... 

This is the general expression for Gaussian composition fluctuations in incompressible polymer blends derived from EP theory. The original derivation of Shi, Noolandi and coworkers [66,67] uses as a starting point the density functional (Eq. 53) and gives the identical result. A generalization for compressible blends can be found in [13]. 

In the Gaussian thread limit analytic results have been derived for copolymer fluids using the molecular closures. " The analytic results provide insights to several key questions and behaviors that emerge from the numerical PRISM studies. These Include (1) the role of nonzero monomer hard-core diameter, density fluctuations, and concentration fluctuations on dlblock liquid-phase behavior and structure (2) relationship between phenomenological field-theoretic approachesand the molecular closure-based versions of PRISM theory and (3) the influence of molecular weight, composition, solution density, and chemical and conformational asymmetries of the blocks on copolymer microphase separation temperatures. 

We have briefly reviewed methods which extend the self-consistent mean-field theory in order to investigate the statics and dynamics of collective composition fluctuations in polymer blends. Within the standard model of the self-consistent field theory, the blend is described as an ensemble of Gaussian threads of extension Rg. There are two types of interactions zero-ranged repulsions between threads of different species with strength /AT and an incompressibility constraint for the local density. 

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