The viscosity-radius relationship for concentrated polymer solutions

Dave E Dunstan

doi:10.1038/s41598-018-36596-6

Abstract

A key assumption of polymer physics is that the random chain 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 and experimental evidence from the literature are used to determine the relationship between the viscosity, η, and chain radius of gyration, RG. The viscosity-radius of gyration relationship is found to be {boldsymbol{eta }}{boldsymbol{ sim }}{{boldsymbol{R}}}_{{boldsymbol{G}}}^{{boldsymbol{m}}{boldsymbol{(}}dot{{boldsymbol{gamma }}}{boldsymbol{)}}} where m(dot{{boldsymbol{gamma }}}) is the power law exponent of the viscosity-temperature relationship that depends on the specific polymer-solvent system and the shear rate, dot{{boldsymbol{gamma }}}. 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 {{boldsymbol{R}}}_{{boldsymbol{G}}} sim {dot{{boldsymbol{gamma }}}}^{-{boldsymbol{n}}{boldsymbol{/}}{boldsymbol{m}}{boldsymbol{(}}dot{{boldsymbol{gamma }}}{boldsymbol{)}}} where n is the power law exponent. Furthermore, the thermal expansion coefficients determine the variation in the power law exponents that are measured for different polymer systems. Typical values of n enable the measured reduction in coils size behavior to be fitted. Furthermore, the 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.

Highlights

Polymers are of interest for reasons spanning wide practical application, through to the elegant theories of polymer dynamics introduced by Kuhn, Flory and de Gennes[1,2,3]
We present a brief history of the developments in polymer experiments and modelling in order to explain why the assumption that the chains extend in flow has become universally accepted and that there is little evidence for extension in simple Couette flow other than that observed for DNA and recent experimental evidence shows chain contraction in flow for random chain polymers[13,14,15,16,17,18,19,20,21,22,23,24,25]
Scaling arguments and experimental evidence are used to show that chains are predicted to compress in flow, and that variations in the observed power law exponents for shear thinning can be explained by the non-ideality embodied in the thermal compressibility of differing polymers[59,60]

Summary

Introduction

Polymers are of interest for reasons spanning wide practical application, through to the elegant theories of polymer dynamics introduced by Kuhn, Flory and de Gennes[1,2,3]. An alternative approach that assumes compression, allows the measured radius-shear rate behaviour to be predicted, and the power law behaviour observed for polymers in flow to be modelled[25]. This shows that the viscosity decreases as the radius decreases in a manner that is physically consistent with the observed behaviour for concentrated random chain polymers[25].

Results

Conclusion