Site model theory

The PRISM (Polymer-Reference-Interaction-Site model) theory is an extension of the Ornstein-Zernike equation to molecular systems [20-22]. It connects the total correlation function h(r)=g(r) 1, where g(r) is the pair correlation function, with the direct correlation function c(r) and intramolecular correlation functions (co r)). For a primitive model of a polyelectrolyte solution with polymer chains and counterions only, there are three different relevant correlation functions the monomer-monomer, the counterion-counterion, and the monomer-counterion correlation function [23, 24]. Neglecting chain end effects and considering all monomers as equivalent, we obtain the following three PRISM equations for a homogeneous and isotropic system in Fourier space ... 

Statistical thermodynamics is also changing in recent years. Newly developed RISM (Reference Interactions Site Model) theory has no restriction on the shape of solute species, in contrast to old theories in which spherical species are usually assumed. Ab initio calculations are being combined with molecular dynamic simulations. This combination becomes possible because of the improvement of high-speed computers. The polarization effect and multibody problem will be... 

Yield involves an irreversible deformation and takes place by a shearing mechanism in which molecules slide past one another. If molecules are to slide past each other, energy barriers have to be overcome. Raising the temperature of the polymer will make it easier for these barriers to be overcome, as diseussed already in relation to the site-model theory of mechanical relaxation in section 5.7.3 and as discussed in section 8.2.5 of the present ehapter in relation to yielding. 

Kinoshita, M. Okamoto, Y. Hirata, F. (1997) Solvation structure and stability of peptides in aqueous solutions analyzed by the reference interaction site model theory. Journal of Chemical Physics 107, 1586-1599... 

An alternative theoretical approach to determining gas solubility utilizes the reference interaction site model theory. This theory has been applied for the noble gases and is found to give reasonable agreement to experimental data... 

Kinoshita M, Hirata F (1997) Analysis of salt effects on solubility of noble gases in water using the reference interaction site model theory. J Chem Phys 106 5202-5215... 

We now take the intuitive step (to be justified below by the site model theory) that the viscoelastic behaviour can be directly related to a controlling molecular rate process with a constant activation energy. 

The site model theory is based on transition state theory, and although first developed to explain the dielectric behaviour of crystalline solids [11,12] has also been applied to mechanical relaxations in polymers [13]. 

We have so far discussed two types of theories, those based on the site model, and thosebased on the WLF equation and its ramifications, which deal with time-temperature equivalence. The site model theories predict constant activation energies and are more applicable to relaxation transitions originating from localised chain motions, whereas the WLF equation theories deal with the glass transition behaviour in amorphous polymers. 

The discussion so far considers the theoretical shear stress of a crystal in the absence of thermal fluctuations. Frank [81] considered that there are always local thermal fluctuations, which must be taken into account. At any temperature T, there is a significant chance of thermal fluctuations in the timescale of the experiments supplying an energy up to 50 kT. Furthermore, this discussion only relates the yield stress to the elastic energy whereas U is strictly the activation enthalpy. Analogous to the site model theory (see Section 7.3), we should discuss the Gibbs free energy AG, where AG — TAS and the shear strain rate is... 

T. Imai, A. Kovalenko and F. Hirata. Partial molar volume of proteins studied by the three-dimensional reference interaction site model theory. J. Phys. Ghem. B 109, 2005, 6658-6665. 

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