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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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Journal ArticleDOI

Optical characterization of the nematic lyotropic chromonic liquid crystals: light absorption, birefringence, and scalar order parameter.

TL;DR: The scalar order parameter of the phase of Blue 27 is determined to be relatively high, in the range 0.72-0.79, which puts the finding into the domain of general validity of the Onsager model, however, the observed temperature dependence of the scalar Order parameter points to the importance of factors not accounted for in the athermal Onsagersager model.
Journal ArticleDOI

Chiral symmetry breaking by spatial confinement in tactoidal droplets of lyotropic chromonic liquid crystals.

TL;DR: This work reports on chiral symmetry breaking in the nematic tactoids formed in molecularly nonchiral polymer-crowded aqueous solutions of low-molecular weight disodium cromoglycate and explains the chirality induction as a replacement of energetically costly splay packing of the aggregates within the curved bipolar tactoidal shape with twisted packing.
Book ChapterDOI

Shear-Induced Transitions and Instabilities in Surfactant Wormlike Micelles

TL;DR: In this paper, the authors report recent developments on the shear-induced transitions and instabilities found in surfactant wormlike micelles, and describe three types of transitions and/or instabilities: shearthickening, shearbanding, and flow-aligning and tumbling instabilities characteristic of nematic structures.
Journal ArticleDOI

Architectural transitions in Vibrio cholerae biofilms at single-cell resolution

TL;DR: High-resolution optical microscopy is used to image all individual cells in Vibrio cholerae biofilms at different stages of development and extracted the precise 3D cellular arrangements, cell shapes, sizes, and global morphological features during biofilm growth on submerged glass substrates under flow.
Journal ArticleDOI

Dynamics of individual single-walled carbon nanotubes in water by real-time visualization.

TL;DR: It is determined that commonly available SWNTs in liquids can be considered as rigid Brownian rods in the absence of imposed external fields or self-attractive forces, in agreement with theoretical estimates.
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.