MarketMark–Houwink equation
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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 :

Applications
The Mark-Houwink equation can be used in size-exclusion chromatography (SEC)/gel permeation chromatography (GPC) 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 (imagine eg. the coiling of comb-like polystyrene vs. linear polystyrene). 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, [\eta]M, is proportional to the hydrodynamic radius and therefore independent of substance. It follows that :[\eta]_AM_A=[\eta]_BM_B is true at any given retention volume/time. Substitution of [\eta] using the Mark-Houwink equation gives: :K_AM_A^{a_A+1}=K_BM_B^{a_B+1} which can be used to relate the molecular weight of any two polymers using their Mark-Houwink constants (i.e. "universally" applicable for calibration). For example, if narrow molar mass distribution standards are available for polystyrene, these can be used to construct a calibration curve (typically logM vs. retention volume ) 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. ==References==
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