View source for Chemistry: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 [[Physics:Intrinsic viscosity|intrinsic viscosity]] <math>[\eta]</math> and [[Physics:Molecular weight|molecular weight]] <math>M</math>:<ref>Paul, Hiemenz C., and Lodge P. Timothy. ''Polymer Chemistry''. Second ed. Boca Raton: CRC P, 2007. 336, 338–339.</ref><ref>Rubinstein, Michael, and Colby, Ralph H.. ''Polymer Physics''. Oxford University Press, 2003.</ref>
:<math>[\eta]=KM^a</math>
From this equation the molecular weight of a [[Chemistry:Polymer|polymer]] can be determined from data on the intrinsic viscosity and vice versa.

The values of the Mark–Houwink parameters, <math>a</math> and <math>K</math>, depend on the particular polymer-[[Physics:Solvent|solvent]] system. For solvents, a value of <math>a=0.5</math> is indicative of a [[Physics:Theta solvent|theta solvent]]. A value of <math>a=0.8</math> is typical for good solvents. For most flexible polymers, <math>0.5\leq a\leq 0.8</math>. For semi-flexible polymers, <math>a\ge 0.8</math>. For polymers with an absolute rigid rod, such as [[Biology:Tobacco mosaic virus|Tobacco mosaic virus]], <math>a=2.0</math>.

It is named after Herman F. Mark and Roelof Houwink.

==Applications==
In [[Biology:Size-exclusion chromatography|size-exclusion chromatography]], such as [[Physics:Gel permeation chromatography|gel permeation chromatography]], the intrinsic viscosity of a polymer is directly related to the [[Chemistry:Elution|elution]] volume of the polymer. Therefore, by running several monodisperse samples of polymer in a gel permeation chromatograph (GPC), the values of <math>K</math> and <math>a</math> can be determined graphically using a line of best fit. Then the molecular weight and intrinsic viscosity relationship is defined.

Also, the molecular weights of two different polymers in a particular solvent can be related using the Mark–Houwink equation when the polymer-solvent systems have the same intrinsic viscosity:
:<math>K_1M_1^{a_1}=K_2M_2^{a_2}</math>
Knowing the Mark–Houwink parameters and the molecular weight of one of the polymers allows one to find the molecular weight of the other polymer using a GPC. The GPC sorts the polymer chains by volume and as intrinsic viscosity is related to the volume of the polymer chain, the GPC data is the same for the two different polymers. For example, if the GPC [[Biology:Calibration curve|calibration curve]] is known for [[Chemistry:Polystyrene|polystyrene]] in [[Chemistry:Toluene|toluene]], [[Chemistry:Polyethylene|polyethylene]] in toluene can be run in a GPC and the molecular weight of polyethylene can be found according to the polystyrene calibration curve via the above equation.<ref>[http://chemweb.calpoly.edu/djones/chem444/GPC.pdf "Gel Permeation Chromatography"] {{webarchive|url=https://web.archive.org/web/20090902124125/http://chemweb.calpoly.edu/djones/chem444/GPC.pdf |date=2009-09-02 }} California Polytechnic State University. 11 Dec. 2007</ref>

==References==
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[[Category:Polymer chemistry]]

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