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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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Liquid crystal formation in suspensions of hard rodlike colloidal particles: direct observation of particle arrangement and self-ordering behavior.

TL;DR: Monodisperse, hard rodlike colloidal particles with a wide range of length-to-width ratios (L/W) and liquid crystals, or nematic and smectic phases, spontaneously appeared in their suspensions.
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Energy filtered electron tomography of ice-embedded actin and vesicles

TL;DR: In spite of the missing-wedge effect that is especially obvious in the study of membrane-filament interaction, single-axis tilt tomography was found to be an appropriate (in fact the only available) method for this kind of investigation.
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Structural polymorphism of the cytoskeleton: a model of linker-assisted filament aggregation.

TL;DR: T theoretical understanding of the classification of linker proteins as bundling proteins or crosslinking proteins is provided and possible mechanisms by which the cell may control cytoskeletal morphology are suggested.
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Axial Symmetry and Classification of Stationary Solutions of Doi-Onsager Equation on the Sphere with Maier-Saupe Potential

TL;DR: In this article, the structure of stationary solutions to the Doi-Onsager equation with Maier-Saupe potential on the sphere was studied in the modelling of rigid rod-like molecules of polymers.
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A Review on Polymer Crystallization Theories

TL;DR: In this paper, the major theories of polymer crystallization are reviewed and a detailed comparison of various theories is made in a logical and self-contained fashion, aiming to inspire further open discussions.
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.