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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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Journal ArticleDOI

Statistical theory of the elastic constants of nematic liquid crystals

TL;DR: In this article, a statistical mechanical theory of the Frank elastic constants is formulated and a free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients.
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Connectivity percolation of polydisperse anisotropic nanofillers

TL;DR: It is shown that for a given average length, a length distribution that is strongly skewed to shorter lengths produces the lowest threshold relative to the equivalent monodisperse one, and if the lengths and diameters of the particles are linearly correlated, polydispersity raises the percolation threshold and more so for a more skewed distribution toward smaller lengths.
Journal ArticleDOI

The isotropic–nematic phase transition in uniaxial hard ellipsoid fluids: Coexistence data and the approach to the Onsager limit

TL;DR: In this paper, the Onsager-Parsons-Lee theory has been applied to the I−N phase transition for aspect ratios up to x=1000, affording an accurate investigation of the approach to the onsager limit for this model.
Journal ArticleDOI

Mesoscopic properties of semiflexible amyloid fibrils.

TL;DR: The contour length, persistence length, bending rigidity, and critical percolation concentration for semiflexible amyloid fibrils formed from the globular proteins beta-lactoglobulin, bovine serum albumin, and ovalbumin are determined.
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.