Intrinsic viscosity is a measure of a solute's contribution to the viscosity

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

  of a solution

Solution

In chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is dissolved in another substance, known as a solvent. The solvent does the dissolving.- Types of solutions :...

. Intrinsic viscosity is frequently referred to as "Inherent Viscosity" in macromolecular literature. It is defined as


where is the viscosity in the absence of the solute and φ is the volume fraction of the solute in the solution. As defined here, the intrinsic viscosity is a dimensionless number. When the solute particles are rigid

Rigid body

In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it...

 sphere

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

s, the intrinsic viscosity equals 2.5, as shown first by Albert Einstein

Albert Einstein

Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

.

In practical settings, φ is usually solute mass concentration, and the units of intrinsic viscosity are deciliters per gram (dL/g), otherwise known as inverse concentration.

Formulae for rigid spheroids

Generalizing from spheres to spheroid

Spheroid

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters....

s with an axial semiaxis (i.e., the semiaxis of revolution) and equatorial semiaxes , the intrinsic viscosity can be written


where the constants are defined






The coefficients are the Jeffery functions

General ellipsoidal formulae

It is possible to generalize the intrinsic viscosity formula from spheroid

Spheroid

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters....

s to arbitrary ellipsoids with semiaxes , and .

Frequency dependence

The intrinsic viscosity formula may also be generalized to include a frequency dependence.

Applications

The intrinsic viscosity is very sensitive to the axial ratio

Axial ratio

Axial ratio, for any structure or shape with two or more axes, is the ratio of the length of those axes to each other - the longer axis divided by the shorter....

 of spheroids, especially of prolate spheroids. For example, the intrinsic viscosity can provide rough estimates of the number of subunits in a protein

Protein

Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

 fiber composed of a helical array of proteins such as tubulin

Tubulin

Tubulin is one of several members of a small family of globular proteins. The most common members of the tubulin family are α-tubulin and β-tubulin, the proteins that make up microtubules. Each has a molecular weight of approximately 55 kiloDaltons. Microtubules are assembled from dimers of α- and...

. More generally, intrinsic viscosity can be used to assay quaternary structure

Quaternary structure

In biochemistry, quaternary structure is the arrangement of multiple folded protein or coiling protein molecules in a multi-subunit complex.-Description and examples:...

. In polymer chemistry

Polymer chemistry

Polymer chemistry or macromolecular chemistry is a multidisciplinary science that deals with the chemical synthesis and chemical properties of polymers or macromolecules. According to IUPAC recommendations, macromolecules refer to the individual molecular chains and are the domain of chemistry...

 intrinsic viscosity is related to molar mass

Molar mass

Molar mass, symbol M, is a physical property of a given substance , namely its mass per amount of substance. The base SI unit for mass is the kilogram and that for amount of substance is the mole. Thus, the derived unit for molar mass is kg/mol...

 through the Mark-Houwink equation

Mark-Houwink equation

The Mark–Houwink equation gives a relation between intrinsic viscosity [\eta] and molecular weight M:[\eta]=KM^aFrom this equation the molecular weight of a polymer can be determined from data on the intrinsic viscosity and vice versa....

.A practical method for the determination of intrinsic viscosity is with a Ubbelohde viscometer

Ubbelohde viscometer

A Ubbelohde type viscometer or suspended-level viscometer is a measuring instrument which uses a capillary based method of measuring viscosity . It is recommended for higher viscosity cellulosic polymer solutions. The advantage of this instrument is that the values obtained are independent of the...

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