Defining Ideal Phantom Polymer Networks

Abstract

Elastomers are modeled as networks with $\ddot{I}•$-functional junctions containing $N$ ideal, $n$-segment, freely jointed chains (FJCs) per unit volume (p.u.v.). Our compact model of the exact FJC length probability density (Treloar, 1975), accurately yields their exact distribution moments (Flory, 1969). The governing geometry of fluctuations of $N_X=2N/\ddot{I}•$ junctions p.u.v., parametrically maps their $\hat{I}»$(elongation ratio)-dependent distribution to an equivalent FJC consisting of $n_{f\ddot{I}•}=(n/\ddot{I}•)(1-\hat{I}›)$ segments, where $\hat{I}›=(1/3n)(\hat{I}{»}^2+2/\hat{I}»))$. The resulting elastic pre-factor, $N_{\text{eff}}kT=(N-\hat{I}\cdot N_X)kT$, with junction effectiveness $\hat{I}\cdot =\ddot{I}•(1-\hat{I}›)/(\ddot{I}•-\hat{I}›)$, defines ideal phantom networks

47 Pages (Including 14 Pages for Main Text (including title/abstract page and references), 33 Pages (including title page and references) for Supplementary Information), 28 Figures (including 22 in Supplementary Information, 1 table in Supplementary Information)