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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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Electrostatic Attraction between Two Charged Surfaces: A (N,V,T) Monte Carlo Simulation

TL;DR: In this article, the stability of two parallel charged surfaces (lamellae) neutralized by exchangeable counterions has been studied in the context of the primitive model and the phase diagram of such a system exhibits complex patterns, and 2D contour maps of the equation of state in order to localize attracto/repulsive domains and optimize adhesive properties of the interface.
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Chiral-nematic self-ordering of rodlike cellulose nanocrystals grafted with poly(styrene) in both thermotropic and lyotropic states

TL;DR: Graft copolymers of rodlike cellulose nanocrystals (CNC) with poly(styrene) (PSt) were synthesized through atom transfer radical polymerization (ATRP).
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Morphology of three lyotropic liquid crystalline biological NMR media studied by translational diffusion anisotropy.

TL;DR: The morphologies of three dilute liquid crystalline phases, which are widely used for biological NMR spectroscopy, are investigated by the study of tracer self-diffusion, and the high TMS diffusion rate observed in the bilayer plane requires extensive transient edge-to-edge contacts of such disks.
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Equilibrium order parameters of nematic liquid crystals in the Landau-De Gennes theory

TL;DR: In this article, the authors study equilibrium liquid crystal configurations in three-dimensional domains, within the continuum Landau-De Gennes theory, and obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants.
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Predicting phase equilibria in polydisperse systems

TL;DR: In this paper, a review of the theoretical prediction of phase equilibria in polydisperse systems is presented, focusing on some of the novel features of polydispersity phase behavior.
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.