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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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Statistics of Orientation Effects in Linear Polymer Molecules

TL;DR: In this paper, the effects of orientation on the combinatorial term g for the number of ways to pack together Nx linear polymers (x mers) were evaluated as a function of the molecules in each permitted direction for the case of straight rigid rods.
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Piezoresistive response of epoxy composites with carbon nanoparticles under tensile load

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Carbon nanotube-filled polymer composites. Numerical simulation of electrical conductivity in three-dimensional entangled fibrous networks

TL;DR: In this article, a new modeling approach is presented to simulate direct current electrical conductivity in entangled fibrous networks using a spline calculation; the corresponding volume conductivity is determined by integration using finite element software.
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Understanding shape entropy through local dense packing

TL;DR: It is shown quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs, and the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing.
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Liquid-crystalline ordering in the solution of partially flexible macromolecules

TL;DR: In this article, the liquid-crystalline ordering in the solution of persistent chains which length, L, is comparable with the length of the effective Kuhn segment, l, is considered by means of a generalization of the Onsager method.
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.