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Mark-Houwink Relation

Empirical relationship correlating polymer intrinsic viscosity with molecular weight and solution temperature, crucial for polymer characterization.
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The statement of the theorem

Define the intrinsic viscosity [η][\eta] of a polymer solution, which is the ratio of the solution viscosity η\eta to the concentration cc and the solvent viscosity η0\eta_0: [η]=lim⁡c→0ηc[\eta] = \lim_{c \to 0} \frac{\eta}{c}. The Mark-Houwink equation provides an empirical relationship between [η][\eta] and the molecular weight MM: \begin{equation*} [\eta] = K M^a \end{equation*} where KK is the Mark-Houwink constant, and aa is the exponent, both of which are dependent on the specific solvent and temperature TT. The exponent aa characterizes the polymer chain conformation in solution (e.g., a=0.5a=0.5 for random coil, a=1.0a=1.0 for rigid rod).
Source: Wikipedia