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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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Journal ArticleDOI

Phase behavior of binary mixtures of thick and thin hard rods

TL;DR: In this paper, a straightforward extension of the Onsager-theory for hard rods was used to study the thermodynamic stability of the isotropic (I) and nematic (N) phase of binary mixtures of thick and thin hard rods of the same length.
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Highly Ordered Carbon Nanotube Nematic Liquid Crystals

TL;DR: In this article, the orientation of single-wall nanotube liquid crystals measured by polarized Raman spectroscopy at the isotropic−nematic transition exceeds by far the value reported in previous experiments.
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Soft quasicrystals - Why are they stable?

TL;DR: In this article, the authors provide a concise review of the emerging field of soft quasicrystals, suggesting that the existence of two natural length-scales, along with three-body interactions, may constitute the underlying source of their stability.
Journal ArticleDOI

Liquid crystalline properties of solutions of persistent polymer chains

TL;DR: In this article, a synthesis of theories for the orientational entropy and excluded volume interaction for persistent chain polymers at intermediate degrees of chain flexibility, when extended to liquid-like densities, was shown to satisfactorily account for experimental data on the volume fractions of polymer at coexistence of isotropic and anisotropic phases, the concentration dependence of the order parameter within the lyotropic liquid crystal and the osmotic pressure equation of state for several extended chainpolymers.
Journal ArticleDOI

Generalized constitutive equation for polymeric liquid crystals Part 1. Model formulation using the Hamiltonian (poisson bracket) formulation

TL;DR: In this paper, the Hamiltonian formulation of equations in continuum mechanics through Poisson brackets is used to generate a constitutive equation for the stress and the order parametr tensor for a polymeric liquid crystal.
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.