Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Scaling Laws for Polymer Solutions

Mathematical relationships that describe the behavior of polymer solutions, relating concentration, viscosity, and molecular weight.
📜

The statement of the theorem

Consider the viscosity η\eta of a polymer solution as a function of the concentration cc and the molecular weight MM. For highly entangled solutions, the zero-shear viscosity η0\eta_0 exhibits a power-law dependence on molecular weight: \nη0∝Ma\eta_0 \propto M^{a} \nwhere the exponent aa is typically found to be 3.43.4 for linear polymers. Additionally, the osmotic pressure Π\Pi scales with the concentration cc and the characteristic volume V0V_0: \nΠ=kBT(c⋅V0)1/2\Pi = k_B T \left(c \cdot V_0 \right)^{1/2}
Source: Wikipedia