Mark–Houwink equation

The Mark–Houwink equation, also known as the Mark–Houwink–Sakurada equation or the Kuhn–Mark–Houwink–Sakurada equation or the Landau-Kuhn-Mark-Houwink-Sakurada equation gives a relation between intrinsic viscosity [ η ] {displaystyle } and molecular weight M {displaystyle M} : The Mark–Houwink equation, also known as the Mark–Houwink–Sakurada equation or the Kuhn–Mark–Houwink–Sakurada equation or the Landau-Kuhn-Mark-Houwink-Sakurada equation gives a relation between intrinsic viscosity [ η ] {displaystyle } and molecular weight M {displaystyle M} : From this equation the molecular weight of a polymer can be determined from data on the intrinsic viscosity and vice versa. The values of the Mark–Houwink parameters, a {displaystyle a} and K {displaystyle K} , depend on the particular polymer-solvent system. For solvents, a value of a = 0.5 {displaystyle a=0.5} is indicative of a theta solvent. A value of a = 0.8 {displaystyle a=0.8} is typical for good solvents. For most flexible polymers, 0.5 ≤ a ≤ 0.8 {displaystyle 0.5leq aleq 0.8} . For semi-flexible polymers, a ≥ 0.8 {displaystyle ageq 0.8} . For polymers with an absolute rigid rod, such as Tobacco mosaic virus, a = 2.0 {displaystyle a=2.0} . It is named after Herman F. Mark and Roelof Houwink. In size-exclusion chromatography, such as gel permeation chromatography, the intrinsic viscosity of a polymer is directly related to the elution volume of the polymer. Therefore, by running several monodisperse samples of polymer in a gel permeation chromatograph (GPC), the values of K {displaystyle K} and a {displaystyle a} can be determined graphically using a line of best fit. Then the molecular weight and intrinsic viscosity relationship is defined.