Intrinsic viscosity

Intrinsic viscosity ${\displaystyle \left[\eta \right]}$ is a measure of a solute's contribution to the viscosity ${\displaystyle \eta }$ of a solution. If ${\displaystyle \eta _{0}}$ is the viscosity in the absence of the solute, ${\displaystyle \eta }$ is (dynamic or kinematic) viscosity of the solution and ${\displaystyle \phi }$ is the volume fraction of the solute in the solution, then intrinsic viscosity is defined as the dimensionless number $${\displaystyle \left[\eta \right]=\lim _{\phi \rightarrow 0}{\frac {\eta -\eta _{0}}{\eta _{0}\phi }}}$$ It should not be confused with inherent viscosity, which is the ratio of the natural logarithm of the relative viscosity to the mass concentration of the polymer.

When the solute particles are rigid spheres at infinite dilution, the intrinsic viscosity equals ${\displaystyle {\frac {5}{2}}}$, as shown first by Albert Einstein.

In practical settings, ${\displaystyle \phi }$ is usually solute mass concentration (c, g/dL), and the units of intrinsic viscosity ${\displaystyle \left[\eta \right]}$ are deciliters per gram (dL/g), otherwise known as inverse concentration.