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 or the Mark-Chrystian equation gives a relation between intrinsic viscosity and molecular weight :
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, and, depend on the particular polymer-solvent system as well as temperature. For solvents, a value of is indicative of a theta solvent. A value of is typical for good solvents. For most flexible polymers,. For semi-flexible polymers,. For polymers with an absolute rigid rod, such as Tobacco mosaic virus,.
It is named after Herman F. Mark and Roelof Houwink.
Applications
The Mark-Houwink equation can be used in size-exclusion chromatography /gel permeation chromatography to construct the so called universal calibration curve which can be used to determine the molecular weight of a polymer A using a calibration done with polymer B.In SEC molecules are separated based on hydrodynamic volume, i.e. the size of the coil a given polymer forms in solution. The hydrodynamic volume, however, cannot simply be related to molecular weight. This means that the molecular weight associated with a given retention time/volume is substance specific and that in order to determine the molecular weight of a given polymer a molecular-weight size marker of the same substance must be available.
However, the product of the intrinsic viscosity and the molecular weight,, is proportional to the hydrodynamic radius and therefore independent of substance. It follows that
is true at any given retention volume/time. Substitution of using the Mark-Houwink equation gives:
which can be used to relate the molecular weight of any two polymers using their Mark-Houwink constants.
For example, if narrow molar mass distribution standards are available for polystyrene, these can be used to construct a calibration curve in eg. toluene at 40 °C. This calibration can then be used to determine the "polystyrene equivalent" molecular weight of eg. a polyethylene sample or any other polymer for which standards might not be available if the Mark-Houwink parameters for both substances are known in this solvent and at this temperature.