The Equation of State of a Gaussian Phantom Network with Defined Cross Link Functionality

TL;DR

This paper models a Gaussian phantom network's equation of state using mean field approximation and Mayer's cluster expansion, analyzing how cross link functionality affects the network's compressibility.

Contribution

It introduces a mean field approach to derive the equation of state for Gaussian phantom networks with various cross link functionalities.

Findings

Equation of state derived using Mayer's cluster expansion

Comparison of isothermal compressibility for different functionalities

Insights into the effect of cross link functionality on network properties

Abstract

A phantom network of Gaussian chains far from the point of gelation can be described as a gas of interacting particles represented by the cross links. The type of particles varies with the network functionality, whereas the type of interaction depends on the properties of the connecting chains. In a mean field approximation the Equation of State can be calculated using Mayer's cluster expansion. The resulting isothermal compressibility is compared for different cross link functionalities.