Mark-Houwink equation
Encyclopedia
The Mark–Houwink 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. 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
,
.
, such as gel permeation chromatography
, the intrinsic viscosity of a polymer is directly related to the elution
time of the polymer. Therefore, by running several monodisperse
samples of polymer in a gel permeation chromatograph (GPC), the values of
and 
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–Houwinck equation when the polymer-solvent systems have the same intrinsic viscosity:
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
is known for polystyrene
in toluene
, 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.
Intrinsic viscosity
Intrinsic viscosity \left[ \eta \right] is a measure of a solute's contribution to the viscosity \eta of a solution. Intrinsic viscosity is frequently referred to as "Inherent Viscosity" in macromolecular literature...
and molecular weight :From this equation the molecular weight of a polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
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-solventSolvent
A solvent is a liquid, solid, or gas that dissolves another solid, liquid, or gaseous solute, resulting in a solution that is soluble in a certain volume of solvent at a specified temperature...
system. For solvents, a value of
is indicative of a theta solventTheta solvent
In a polymer solution, a theta solvent is a solvent in which polymer coils act like ideal chains, assuming exactly their random walk coil dimensions...
. 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 virusTobacco mosaic virus
Tobacco mosaic virus is a positive-sense single stranded RNA virus that infects plants, especially tobacco and other members of the family Solanaceae. The infection causes characteristic patterns on the leaves . TMV was the first virus to be discovered...
,
.Applications
In size exclusion chromatographySize exclusion chromatography
Size-exclusion 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 or macromolecular complexes such as proteins and industrial polymers...
, such as gel permeation chromatography
Gel Permeation Chromatography
Gel permeation chromatography is a type of size exclusion chromatography , that separates analytes on the basis of size. The technique is often used for the analysis of polymers. As a technique, SEC was first developed in 1955 by Lathe and Ruthven. The term gel permeation chromatography can be...
, the intrinsic viscosity of a polymer is directly related to the elution
Elution
Elution is a term used in analytical and organic chemistry to describe the process of extracting one material from another by washing with a solvent ....
time of the polymer. Therefore, by running several monodisperse
Monodisperse
A collection of objects are called monodisperse, or monosized, if they have the same size and shape when discussing particles, and the same mass when discussing polymers...
samples of polymer in a gel permeation chromatograph (GPC), the values of
and 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–Houwinck equation when the polymer-solvent systems have the same intrinsic viscosity:
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
Calibration curve
In analytical chemistry, a calibration 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
Polystyrene
Polystyrene ) also known as Thermocole, abbreviated following ISO Standard PS, is an aromatic polymer made from the monomer styrene, a liquid hydrocarbon that is manufactured from petroleum by the chemical industry...
in toluene
Toluene
Toluene, formerly known as toluol, is a clear, water-insoluble liquid with the typical smell of paint thinners. It is a mono-substituted benzene derivative, i.e., one in which a single hydrogen atom from the benzene molecule has been replaced by a univalent group, in this case CH3.It is an aromatic...
, polyethylene
Polyethylene
Polyethylene or polythene is the most widely used plastic, with an annual production of approximately 80 million metric tons...
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.