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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
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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Monte Carlo simulation of a lyotropic first-order isotropic-nematic phase transition in a lattice polymer model

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Graphene-based chiral liquid crystal materials for optical applications

TL;DR: In this article, a review of the latest research progress on graphene-based chiral liquid crystal (GBCLC) materials is presented, where the theoretical basis, synthesis route and applications of GBCLCs as well as the stabilizing effect of graphene on the blue phase are discussed.
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Isotropic-liquid crystalline phase diagram of a CdSe nanorod solution.

TL;DR: The coexistence concentrations of both phases are found to be lower and the biphasic region wider than the results predicted by the hard rod model, indicating that the attractive interaction between the nanorods may be important in the formation of the liquid crystalline phase in this system.
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Sterically Engineered Perylene Dyes for High Efficiency Oriented Fluorophore Luminescent Solar Concentrators

TL;DR: In this paper, a new family of perylenebisimide (PBI) dyes designed for oriented fluorophore solar concentrators is presented, which can reduce waveguide escape cone (EC) losses.
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Entropy-driven crystallization in dense systems of athermal chain molecules.

TL;DR: The direct observation of entropy-driven crystallization in simulations of dense packings of linear hard-sphere chains is described, showing the ordering transition is driven by the increase in translational entropy: ordered sites exhibit enhanced mobility as their local free volume becomes more spherical and symmetric.
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.