Low-Shear Polymer Viscosity

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, C_E 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 R_g, 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 R_g³, then there is a Rousean-like 1.3 power dependency on concentration, C, along with a cubic dependency on C/C_E. With fudge factors A and B we have the inelegant formula:

η = η₀A(B.C.R_g³)^1.3(C/C_E)³

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 R_g 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.