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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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Theory of wormlike polymer chains in confinement

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Liquid crystalline suspensions of poly(tetrafluoroethylene) 'whiskers'

TL;DR: In this paper, the formation of liquid crystalline order in suspensions of (extended chain) crystalline whiskers of the flexible macro molecule poly(tetrafluoroethylene) (PTFE).
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Self-assembly of short DNA duplexes: from a coarse-grained model to experiments through a theoretical link

TL;DR: In this paper, the authors investigate the self-assembly of short blunt-ended double-helical duplexes with a combined numerical and theoretical approach and evaluate the input quantities for the theoretical framework directly from the DNA model.
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Modeling the phase behavior of polydisperse rigid rods with attractive interactions, with applications to SWNTs in super acids

TL;DR: The phase behavior of rodlike molecules with polydisperse length and solvent-mediated attraction and repulsion is described by an extension of the Onsager theory for rigid rods, and the model is used to compute phase separation and length fractionation as a function of well depth and rod concentration.
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Chain statistics in micelles and bilayers: Effects of surface roughness and internal energy

TL;DR: In this article, a mean field theory for amphiphile chain organization and thermodynamics in micellar aggregates is applied to rotational isomeric state, model chains.
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.