Viscosity

Measurement of Viscosity for Polymer Solutions

The most common method measures the time for draining of a specific volume of a solution through a capillary in response to gravity. This phenomenon is described by Poiseuille's equation.

v = pi Pr⁴/ 8 eta l

• v is the rate of flow, in terms of volume
• P is the pressure difference that produces the flow
• r and l are the radius and length of the capillary
• eta is the viscosity of the liquid

eta_rel = eta / eta₀ = l rho / l₀ rho₀

Often the solutions are so dilute that the ratio of the densities can be taken to be 1. The concentration dependence of eta_rel is

eta_rel = 1 + [eta]c + kc² + ...

For sufficiently dilute solutions, the intrinsic viscosity, [eta], of polymers without strong interactions is obtained via linear extrapolation, PC Fig. 10.12, suggested by

(eta_rel - 1)/c = eta_sp/c = [eta] + kc

where eta_sp is the specific viscosity. (This plot is decidedly nonlinear when a strongly ionized polyelectrolyte is diluted with water, F Fig. 146, due to expansion of the polymer as the counterions are diluted.) Somewhat different forms were suggested by Huggins

eta_sp/c = [eta] + k'[eta]²c

and Kraemer

(ln eta_rel)/c = [eta] + k"[eta]²c

The constants in the last two equations are related by k" = k' - 1/2.

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