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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.

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Citations
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Journal ArticleDOI

Fine Golden Rings: Tunable Surface Plasmon Resonance from Assembled Nanorods in Topological Defects of Liquid Crystals.

TL;DR: Unprecedented, reversible, and dynamic control over an assembly of gold nanorods dispersed in liquid crystals (LC) is demonstrated, with shifts of 100 nm or more in the surface plasmon resonance peak, an order of magnitude greater than any previous work with AuNR composites.
Journal ArticleDOI

Hard-body models of bulk liquid crystals

TL;DR: Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter, and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments.
Journal ArticleDOI

Phase transitions in a system of hard rectangles on the square lattice

Joyjit Kundu, +1 more
- 16 May 2014 - 
TL;DR: The phase diagram of a system of monodispersed hard rectangles of size m × mk on a square lattice is generalized, showing that for k ≥ 7, the system undergoes three entropy-driven phase transitions with increasing density.
Journal ArticleDOI

Monte Carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers

TL;DR: First-order lyotropic phase transitions between isotropic and nematic phases near the concentrations predicted by a statistical thermodynamic theory, but with significantly narrower coexistence regions are found.
Journal ArticleDOI

Interfacial tension at the boundary between nematic and isotropic phases of a hard rod solution

TL;DR: In this paper, the authors generalize Onsager's theory to spatially inhomogeneous hard rod solutions and determine the excess surface free energy per unit area or interfacial tension for hard rod isotropic and nematic phases coexisting at equilibrium.
References
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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.