The viscosity-radius relationship for concentrated polymer solutions

TL;DR

This paper derives a power law relationship between viscosity and chain radius in concentrated polymer solutions, challenging the extension assumption and explaining shear thinning through chain compression.

Contribution

It introduces a scaling-based viscosity-radius relationship showing chains compress in flow, contrary to the common extension assumption in polymer physics.

Findings

Viscosity is proportional to the radius to the power of 9.

Chain radius decreases with shear rate, explaining shear thinning.

The relationship aligns with observed viscosity-temperature and shear rate behaviors.

Abstract

A key assumption of polymer physics is that the random chains polymers extend in flow. Recent experimental evidence has shown that polymer chains compress in Couette flow in a manner counter to expectation. Here, scaling arguments developed previously are used to determine the relationship between the viscosity and chain radius of gyration. Scaling arguments determine the viscosity-radius of gyration relationship to be such that the viscosity is proportional to the radius to the power of 9. The viscosity is shown to be a power law function of the radius, and to decrease with decreasing radius under conditions where the chains are ideal random walks in concentrated solution. Furthermore, this relationship is consistent with both the widely observed viscosity-temperature and viscosity-shear rate behavior observed in polymer rheology. The assumption of extension is not consistent with these observations as it would require that the chains increase in size with increasing temperature. Shear thinning is thus a result of a decreasing radius with increasing shear rate as the radius is proportional to the the shear rate raised to the power law exponent divided by 9. The thermal expansion coefficient determines the variation in the power law exponents that are measured for different polymer systems. Typical values on n enable the measured reduction in coils size behavior to be fitted. Furthermore, the absurd notion that polymer chains extend to reduce the viscosity implies that an increasing chain size results in a reduced viscosity is addressed. This assumption would require that the viscosity increases with reducing coil radius which is simply unphysical.