Impact of Particle Shape on the Physics of Colloidal Suspensions

Lars Onsager wrote only one full-length paper on colloidal suspensions [31], yet he clearly had a keen interest in such systems for a considerable length of time. Apparently, he was the first to coin the phrase "potential of average force" in a lucid reassessment [12] of the work of Gibbs, Smoluchowski and Einstein on the application of statistical mechanics to mesoscopic particles. Kirkwood¹ was inspired in part by Onsager's presentation to develop a theory of liquids a few years later. The potential of mean force, of course, figures heavily in the modern theory of solutions, often starting with McMillan and Mayer's² formal analysis of 1945. For instance, Zimm's³ application to isotropic solutions of rods appeared only one year later. Actually, Mayer was already aware of the structure of a full formal theory at about the same time that Onsager published a very short preview of his virial theory and phase behaviour of rodlike colloids in 1942 [24]. Still, then and later [31], Onsager never did write a formal solution theory, rigorous beyond the second virial term.

Onsager's abstract [11] on colloid dynamics is tantalizing for it was never expanded into a publication proper. As early as 1932, he had figured out the correct Brownian component of the viscosity of a dilute suspension of ellipsoids, at least in a slender body approximation. Moreover, he shrewdly realized the implication of the theory for polymer physics, namely that chainlike molecules could not be perfectly straight if the experimental viscosities were to be understood. Around the same time, W. Kuhn⁴ reached similar conclusions in what are regarded as seminal papers although his computations are less exacting. Onsager's form for the viscosity was later rederived by Simha⁵ who gave an expression valid for less restricted aspect ratios. The precise mathematical physics of the dynamics of suspensions of anisometric particles has taxed the skills of a number of outstanding theoreticians. It continues to weigh heavily both in the craft of particle characterization and in the explanation of fascinating rheological phenomena witnessed in the laboratory…