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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
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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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Lyotropic liquid crystalline self-assembly in dispersions of silver nanowires and nanoparticles.

TL;DR: The results of this research suggest that the nanoparticle contaminants common to many synthesis schemes facilitate liquid crystalline phase formation and that these dispersions can be processed into aligned coatings.
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Density profiles and thermodynamics of rod-like particles between parallel walls

TL;DR: In this paper, the density profile of mutually avoiding rod-like particles in the space between two parallel plates, held in equilibrium with a bulk phase of isotropic, semidilute rods, using a self-consistent integral equation which becomes exact as the rod aspect radio L/D → ∞.
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Structure of molecular liquids

TL;DR: A method for calculating the direct correlation function c(1,2) for a molecular liquid in the form of a spherical harmonic expansion is presented, by computer simulation, and predictions of the structure of molecular liquids using density functional and integral equation approaches are tested.
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Molecular Theories of Nematic Liquid Crystals

TL;DR: In this paper, the state of the art of molecular theories of nematic mesophases is reviewed, with particular emphasis on the basic assumptions and approximations, the relative strengths and weaknesses, and the most fruitful applications of each of them.
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.