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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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The effect of direct interactions on Brownian diffusion

TL;DR: In this paper, the effect of direct interactions between suspended particles on their diffusion coefficient was investigated starting from the generalized Einstein relation, and it was shown that an attractive potential added to the hard core repulsion leads to a decrease of the diffusion coefficient, whereas a repulsive term has the opposite effect.
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Isotropic-nematic phase separation in asymmetrical rod-plate mixtures

TL;DR: In this article, a theoretical underpinning for the observed phase behavior starting from the Onsager discrepancy was presented, in which higher virial terms were incorporated by rescaling the second virial term using an extension of the Carnahan-Starling excess free energy for hard spheres (Parsons’ method).
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Nematic droplets in aqueous dispersions of carbon nanotubes

TL;DR: From the scatter in the data, it is deduced that the surface tension of the coexisting isotropic and nematic phases must be extremely low, that is, of the order of nN/m.
Journal ArticleDOI

Selecting a common direction: I. How orientational order can arise from simple contact responses between interacting cells

TL;DR: It is found that individuals tend to cluster together in one direction of alignment, and how nonhomogeneous pattern evolves close to the bifurcation point is investigated.
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Cholesteric order in aqueous solutions of the polysaccharide Xanthan

TL;DR: In this paper, aqueous solutions of the polyelectrolytic polysaccharide Xanthan at a concentration of 7.5 % (vol/vol) have long range order very similar to cholesteric liquid crystals.
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.