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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 the depletion force due to rodlike polymers

TL;DR: In this article, Mao et al. considered a system of two parallel plates suspended in a semidilute solution of long thin rods of length L and diameter D, and numerically solved an integral equation, which is exact in the Onsager limit.
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Morphogenesis of defects and tactoids during isotropic-nematic phase transition in self-assembled lyotropic chromonic liquid crystals.

TL;DR: The complex shapes and structures of tactoids and topological defects demonstrate an important role of surface anisotropy in morphogenesis of phase transitions in liquid crystals.
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X-ray studies of regenerated cellulose fibers wet spun from cotton linter pulp in NaOH/thiourea aqueous solutions

TL;DR: In this article, the crystalline structure and morphology of regenerated cellulose fiber were investigated by synchrotron wide-angle X-ray diffraction (WAXD) and small-angle x-ray scattering (SAXS) techniques.
Journal ArticleDOI

Phase behavior of rounded hard-squares

TL;DR: In this article, Monte Carlo simulation results of rounding hard squares of varying degrees of roundness were reported, hence interpolating between disks and perfect squares, giving rise to the phases observed by Zhao et al. and further providing a roadmap for the regions of stability of different ordered phases as a function of particle roundness.
Journal ArticleDOI

Rheological properties of graphene oxide liquid crystal

TL;DR: In this article, the rheological properties of liquid crystalline graphene oxide (GO) aqueous dispersion were reported. And the authors showed that the shear viscosity exhibits sudden decrease with the increase of GO composition around a critical volume fraction, ϕ c = 0.33%.
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.