Low-Shear Polymer Viscosity

Quick Start

At low shear values we can readily estimate the viscosity of a polymer solution.

Concentration Dependence

ηsolv cP
CEntangled g/l
CMax g/l
Bond length nm
Rg nm

We need to know what sorts of things happen when we change the concentration of a polymer in our coating/printing solution. The approach here is comparatively user friendly. A more sophisticated version is in Polymer Viscosity app in Practical Solubility.

The complicated behaviour is simplified in the app. You have the viscosity of the base solvent. You then set a concentration, CE at which the polymer chains become fully entangled - at this point the viscosity increases rapidly. You select a concentration range of interest. Finally, you need to provide Rg, the radius of gyration of your polymer which you can estimate from a number, N, of pseudo bonds and a pseudo bond length (Kuhn length), b.

The viscosity increase depends on a pseudo viscosity which in turn depends on Rg³, then there is a Rousean-like 1.3 power dependency on concentration, C, along with a cubic dependency on C/CE. With fudge factors A and B we have the inelegant formula:

η = η0A(B.C.Rg³)1.3(C/CE

The point of the app is to get a feel for what happens as you change your polymer, its concentration and the solvent used (good solvents give larger Rg values than bad ones).

If your polymer concentration is relatively small and you "only" increase the viscosity to a few 10's of cP this might seem harmless. But if you also have a dispersion then the effect of this "harmless" increase might be disasterous, as discussed below the Dispersion Viscosity app.