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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

Modeling of long-range electrostatic interactions in DNA.

TL;DR: A Monte Carlo approach was used to compute the statistical properties of closed DNA chains with different descriptions of the electrostatic interactions, and found clear but relatively small differences between the two potentials for the conformational properties of supercoiled DNA.
Journal ArticleDOI

Biaxial Nematic Order in the Hard-boomerang Fluid

TL;DR: In this article, a fluid of hard boomerangs, each composed of two hard spherocylinders joined at their ends at an angle ψ, has been investigated using Straley's theory, which is a simplification of Onsager's second-virial treatment of long hard rods.
Journal ArticleDOI

Membrane-Mediated Aggregation of Curvature-Inducing Nematogens and Membrane Tubulation

TL;DR: It is demonstrated that for a large group of elongated membrane inclusions, where the two spontaneous curvatures have equal sign, the tubular conformation and sometimes the sheet conformation of the membrane are the common equilibrium shapes.
Journal ArticleDOI

Ferroelectric phase in Stockmayer fluids

TL;DR: In this paper, the existence of a ferroelectric nematic phase in fluids consisting of spherical particles which interact with Lennard-Jones and dipolar forces was established by using a density-functional theory.
Journal ArticleDOI

Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics

TL;DR: In this article, the authors provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment, and show that the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment.
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.