Analytical Calculation of Viscosity in Rouse Networks Below Gelation Transition

TL;DR

This paper derives an exact relationship between zero-shear viscosity and radius of gyration in Rouse networks, and develops a graph-based analytical approach to characterize viscosity in subcritical regimes.

Contribution

It introduces a novel analytical framework linking viscosity and network structure in Rouse models, including a random graph approach for mean-field systems.

Findings

Exact viscosity-radius relationship established

Analytical expressions derived for mean-field network viscosity

Asymptotic behavior characterized in dilute and pre-gelation limits

Abstract

This work establishes an exact relationship between the zero-shear viscosity and the radius of gyration for generalized Rouse model with arbitrary network configurations. Building on this fundamental relationship, we develop a random graph approach to derive analytical expressions for network viscosity in mean-field connected systems through coarse-grained graph viscosity relations. The theory fully characterizes the subcritical regime, determining precise asymptotic behavior in both dilute and pre-gelation limits.