scispace - formally typeset
Journal ArticleDOI

The effects of shape on the interaction of colloidal particles

Lars Onsager
- 01 May 1949 - 
- Vol. 51, Iss: 4, pp 627-659
TLDR
In this article, it was shown that colloids in general are apt to exhibit considerable deviations from Raoult's law and that crystalline phases retaining a fair proportion of solvent may separate from concentrated solutions.
Abstract
Introdzution. The shapes of colloidal particles are often reasonably compact, so that no diameter greatly exceeds the cube root of the volume of the particle. On the other hand, we know many coiloids whose particles are greatly extended into sheets (bentonite), rods (tobacco virus), or flexible chains (myosin, various Iinear polymers). In some instances, a t least, solutions of such highly anisometric particles are known to exhibit remarkably great deviations from Raoult’s law, even to the extent that an anisotropic phase may separate from a solution in which the particles themselves occupy but one or two per cent of the total volume (tobacco virus, bentonite). We shall show in what follows how such results may arise from electrostatic repulsion between highly anisometric particles. Most colloids in aqueous solution owe their stability more or less to electric charges, so that each particle will repel others before they come into actual contact, and effectively claim for itself a greater volume than what it actuaily occupies. Thus, we can understand that colloids in general are apt to exhibit considerable deviations from Raoult’s law and that crystalline phases retaining a fair proportion of solvent may separate from concentrated solutions. However, if we tentatively increase the known size of the particles by the known range of the electric forces and multiply the resulting volume by four in order to compute the effective van der Waal’s co-volume, we have not nearly enough to explain why a solution of 2 per cent tobacco virus in 0.005 normal NaCZ forms two phases.

read more

Citations
More filters
Journal ArticleDOI

Excluded volume for a pair of linear chains of tangent hard spheres with an arbitrary relative orientation

TL;DR: In this article, the authors obtained analytical expressions for the excluded volume for a pair of linear homonuclear chains with an arbitrary relative orientation, and the corresponding expression for the second virial coefficient.
Journal Article

Pre-crystalline, high-entropy aggregates : A role in polymer crystallization?

TL;DR: In this paper, the authors distinguish three main modes of crystallization for polymers with a relatively flexible main-chain, i.e., (i) usual lamellar crystallization occurring by cooling from the reference state (melt or solution) above the temperature To down to T > T g ; (ii) crystallization from the glass; (iii) crystallisation from a stable thermotropic mesophase.
Journal ArticleDOI

The interaction between two cylinder shaped colloidal particles

TL;DR: In this paper, the theory of the stability of lyophobic colloids, as given by Derjaguin and by Verwey and Overbeek for the flat-plate model or the sphere model of colloidal particles, is applied to cylindershaped colloidal particle, by considering the interaction between two parallel particles and between two particles in a crossed position.
Journal ArticleDOI

A new proof on axisymmetric equilibria of a three-dimensional Smoluchowski equation

TL;DR: In this paper, the authors present a new and simplified proof of classical well-known results: (1) all equilibria are axisymmetric and (2) modulo rotational symmetry.
Journal ArticleDOI

Isotropic-nematic interfaces of hard-rod fluids

TL;DR: In this paper, the authors present a method with which interfacial biaxiality can be dealt with efficiently and systematically, and apply it to the pure hard-rod fluid and to a binary mixture of thin and thick hard rods.
References
More filters
Journal ArticleDOI

The Role of Attractive and Repulsive Forces in the Formation of Tactoids, Thixotropic Gels, Protein Crystals and Coacervates

TL;DR: In this paper, it was shown that the Coulomb attraction between the micelles and the oppositely charged ions in the solution gives an excess of attractive force which must be balanced by the dispersive action of thermal agitation and another repulsive force.