- Intrinsic viscosity
Intrinsic viscosity is a measure of a solute's contribution to the
viscosity of asolution . 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
sphere s, the intrinsic viscosity equals 2.5, as shown first byAlbert Einstein .In practical settings, φ is usually solute mass concentration, and the units of intrinsic viscosity are inverse concentration (deciliters per gram).
Formulae for rigid spheroids
Generalizing from spheres to
spheroid 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 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 of spheroids, especially of prolate spheroids. For example, the intrinsic viscosity can provide rough estimates of the number of subunits in a
protein fiber composed of a helical array of proteins such astubulin . More generally, intrinsic viscosity can be used to assayquaternary structure . Inpolymer chemistry intrinsic viscosity is related tomolar mass through theMark-Houwink equation .A practical method for the determination of intrinsic viscosity is with aUbbelohde viscometer .References
* Jeffery GB. (1922) "The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid", "Proc. Roy. Soc.", A102, 161-179.
* Simha R. (1940) "The Influence of Brownian Movement on the Viscosity of Solutions", "J. Phys. Chem.", 44, 25-34.
* Mehl JW, Oncley JL, Simha R. (1940) "Viscosity and the Shape of Protein Molecules", "Science", 92, 132-133.
* Saito N. (1951) "J. Phys. Soc. Japan", 6, 297.
* Scheraga HA. (1955) "Non-Newtonian Viscosity of Solutions of Ellipsoidal Particles", "J. Chem. Phys.", 23, 1526-1531.
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