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 Intrinsic viscosity \left \eta \right/math> is a measure of a solute's contribution to the viscosity \eta of a solution. It should not be confused with inherent viscosity, which is the ratio of the natural logarithm of the relative viscosity to th ...

eta Eta (uppercase , lowercase ; grc, ἦτα ''ē̂ta'' or ell, ήτα ''ita'' ) is the seventh letter of the Greek alphabet, representing the close front unrounded vowel . Originally denoting the voiceless glottal fricative in most dialects, ...

/math> and

molecular weight A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...

M

: :

KM^a From this equation the molecular weight of a

polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

can be determined from data on the intrinsic viscosity and vice versa. The values of the Mark–Houwink parameters,

a

and

K

, depend on the particular polymer-

solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...

system. For solvents, a value of

a=0.5

is indicative of a

theta solvent In a polymer solution, a theta solvent (or θ solvent) is a solvent in which polymer coils act like ideal chains, assuming exactly their random walk coil dimensions. Therefore, the Mark–Houwink equation exponent is 1/2 in a theta solvent. Ther ...

. A value of

a=0.8

is typical for good solvents. For most flexible polymers,

0.5\leq a\leq 0.8

. For semi-flexible polymers,

a\ge 0.8

. For polymers with an absolute rigid rod, such as

Tobacco mosaic virus ''Tobacco mosaic virus'' (TMV) is a positive-sense single-stranded RNA virus species in the genus ''Tobamovirus'' that infects a wide range of plants, especially tobacco and other members of the family Solanaceae. The infection causes characteri ...

a=2.0

. It is named after Herman F. Mark and

Roelof Houwink Roelof Houwink (1897–1988) was a Dutch polymer scientist, educated at the University of Delft. He worked at Phillips since 1925. From 1939 to 1956 he was director-general of the TNOs ''Rubberinstituut'' in Delft.Gary Patterson, "Polymer Science ...

Applications

size-exclusion chromatography Size-exclusion chromatography (SEC), also known as molecular sieve chromatography, is a chromatographic method in which molecules in solution are separated by their size, and in some cases molecular weight. It is usually applied to large molecules ...

, such as

gel permeation chromatography Gel permeation chromatography (GPC) is a type of size-exclusion chromatography (SEC), that separates analytes on the basis of size, typically in organic solvents. The technique is often used for the analysis of polymers. As a technique, SEC was fi ...

, the intrinsic viscosity of a polymer is directly related to the

elution In analytical and organic chemistry, elution is the process of extracting one material from another by washing with a solvent; as in washing of loaded ion-exchange resins to remove captured ions. In a liquid chromatography experiment, for exam ...

volume of the polymer. Therefore, by running several monodisperse samples of polymer in a gel permeation chromatograph (GPC), the values of

K

and

a

can be determined graphically using a

line of best fit Line fitting is the process of constructing a straight line that has the best fit to a series of data points. Several methods exist, considering: *Vertical distance: Simple linear regression **Resistance to outliers: Robust simple linear regre ...

. 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: :

K_1M_1^=K_2M_2^

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

calibration curve In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration. ...

is known for polystyrene in

toluene Toluene (), also known as toluol (), is a substituted aromatic hydrocarbon. It is a colorless, water-insoluble liquid with the smell associated with paint thinners. It is a mono-substituted benzene derivative, consisting of a methyl group (CH3) a ...

polyethylene Polyethylene or polythene (abbreviated PE; IUPAC name polyethene or poly(methylene)) is the most commonly produced plastic. It is a polymer, primarily used for packaging ( plastic bags, plastic films, geomembranes and containers including b ...

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."Gel Permeation Chromatography"
California Polytechnic State University. 11 Dec. 2007

References

{{DEFAULTSORT:Mark-Houwink equation Polymer chemistry