Huggins equation

The Huggins Equation is an empirical equation used to relate the reduced viscosity of a dilute polymer solution to the concentration of the polymer in solution. It is named after Maurice L. Huggins. The Huggins equation states:

$$\frac{\eta_s}{c}= [\eta] + k_H [\eta]^2 c $$

Where $${\eta_s}$$ is the specific viscosity of a solution at a given concentration of a polymer in solution, $$[\eta]$$ is the intrinsic viscosity of the solution, $$k_H$$ is the Huggins coefficient, and $$c$$ is the concentration of the polymer in solution. In isolation, $$n_s$$ is the specific viscosity of a solution at a given concentration.

The Huggins equation is valid when $$[\eta]c$$ is much smaller than 1, indicating that it is a dilute solution. The Huggins coefficient used in this equation is an indicator of the strength of a solvent. The coefficient typically ranges from about $$0.3$$ (for strong solvents) to $$0.5$$ (for poor solvents).

The Huggins equation is a useful tool because it can be used to determine the intrinsic viscosity, $$[\eta]$$, from experimental data by plotting $$\frac{\eta_s}{c}$$versus the concentration of the solution, $$c$$.