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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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On lyotropic behavior of molecular bottle-brushes: A Monte Carlo computer simulation study

TL;DR: In this paper, a three dimensional continuous space Monte Carlo computer simulation study is presented to discuss the extension of flexible, linear polymer chains due to the presence of equally flexible side chains.
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Macroscopic Limits and Phase Transition in a System of Self-propelled Particles

TL;DR: This model is the space-inhomogeneous extension of (Frouvelle and Liu, Dynamics in a kinetic model of oriented particles with phase transition, 2012), in which the existence and stability of the equilibrium states were investigated.
Book ChapterDOI

Density Functional Theories of Hard Particle Systems

TL;DR: In this paper, the authors deal with the applications of the density functional formalism to the study of inhomogeneous systems with hard core interactions, including a brief tutorial on the fundamentals of the method, and the exact free energy DF for one-dimensional hard rods obtained by Percus.
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Liquid crystalline solutions of cellulose in phosphoric acid

TL;DR: In this article, it was found that anhydrous phosphoric acid is an excellent direct solvent for cellulose, and liquid crystalline solutions are formed above a cellulose concentration of 7.5% at room temperature; even solutions containing 38% (w/w) cellulose can be prepared.
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Orientationally Ordered Colloidal Co-Dispersions of Gold Nanorods and Cellulose Nanocrystals

TL;DR: Nematic-like and helicoidally orientational self-assemblies of gold nanorods co-dispersed with cellulose nanocrystals to form liquid crystalline phases are developed and polarization-sensitive extinction spectra and two-photon luminescence imaging are used to characterize orientations and spatial distributions.
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.