Superposition principle, intermolecular

Since we are interested in this chapter in analyzing the T- and P-dependences of polymer viscoelasticity, our emphasis is on dielectric relaxation results. We focus on the means to extrapolate data measured at low strain rates and ambient pressures to higher rates and pressures. The usual practice is to invoke the time-temperature superposition principle with a similar approach for extrapolation to elevated pressures [22]. The limitations of conventional t-T superpositioning will be discussed. A newly developed thermodynamic scaling procedure, based on consideration of the intermolecular repulsive potential, is presented. Applications and limitations of this scaling procedure are described. 

Finally, we mention that very recently three other integral equation approaches to treating polymer systems have been proposed. Chiew [104] has used the particle-particle perspective to develop theories of the intermolecular structure and thermodynamics of short chain fluids and mixtures. Lipson [105] has employed the Born-Green-Yvon (BGY) integral equation approach with the Kirkwood superposition approximation to treat compressible fluids and blends. Initial work with the BGY-based theory has considered lattice models and only thermodynamics, but in principle this approach can be applied to compute structural properties and treat continuum fluid models. Most recently, Gan and Eu employed a Kirkwood hierarchy approximation to construct a self-consistent integral equation theory of intramolecular and intermolecular correlations [106]. There are many differences between these integral equation approaches and PRISM theory which will be discussed in a future review [107]. 

The electric field intensity from a given molecule is the same regardless of the species with which it interacts. The principle of superposition says the total electric field in the system is given by the vector sum of the individual electric fields of all the species in a system. Therefore, if we understand the behavior of a single molecule, we can quantify its contribution to the energy of the macroscopic system as a whole. Equation (4.4) relates the electric field, E, to the intermolecular forces, F, and to the intermolecular potential ener, F. In the discussion that follows, we will refer to all of these quantities, as appropriate, to characterize the intermolecular interactions that cause the system to deviate from ideal gas behavior. ... 

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