Effective interactions between charged colloidal particles : Repulsion, attraction and phase separation

2000 ◽  
Vol 10 (PR5) ◽  
pp. Pr5-27-Pr5-38 ◽  
Author(s):  
J. P. Hansen ◽  
D. Goulding ◽  
R. van Roij
Keyword(s):  
Phase Separation ◽  
Colloidal Particles ◽  
Effective Interactions

Phase equilibria in solutions of rod-like particles

1956 ◽  
Vol 234 (1196) ◽  
pp. 73-89 ◽  
Keyword(s):  
Free Energy ◽  
Phase Separation ◽  
Partition Function ◽  
Colloidal Particles ◽  
Double Layers ◽  
Positive Energy ◽  
Isotropic Phase ◽  
Electric Double Layers ◽  
Rigid Rod ◽  
Anisotropic Phase

A partition function for a system of rigid rod-like particles with partial orientation about an axis is derived through the use of a modified lattice model. In the limit of perfect orientation the partition function reduces to the ideal mixing law ; for complete disorientation it corresponds to the polymer mixing law for rigid chains. A general expression is given for the free energy of mixing as a function of the mole numbers, the axis ratio of the solute particles, and a disorientation parameter. This function passes through a minimum followed by a maximum with increase in the disorientation parameter, provided the latter exceeds a critical value which is 2e for the pure solute and which increases with dilution. Assigning this parameter the value which minimizes the free energy, the chemical potentials display discontinuities a t the concentration a t which the minimum first appears. Separation into an isotropic phase and a some what more concentrated anisotropic phase arises because of the discontinuity, in confirmation of the theories of Onsager and Isihara, which treat only the second virial coefficient. Phase separation thus arises as a consequence of particle asymmetry, unassisted by an energy term . Whereas for a large-particle asymmetry both phases in equilibrium are predicted to be fairly dilute when mixing is athermal, a comparatively small positive energy of interaction causes the concentration in the anisotropic phase to increase sharply, while the concentration in the isotropic phase becomes vanishingly small. The theory offers a statistical mechanical basis for interpreting precipitation of rod-like colloidal particles with the formation of fibrillar structures such as are prominent in the fibrous proteins. The asymmetry of tobacco mosaic virus particles (with or without inclusion of their electric double layers) is insufficient alone to explain the well-known phase separation which occurs from their dilute solutions at very low ionic strengths. Higher-order interaction between electric double layers appears to be a major factor in bringing about dilute phase separation for these and other asymmetric colloidal particles bearing large charges, as was pointed out previously by Oster.

scholarly journals Salt-induced effective interactions and phase separation of an ultrasoft model of polyelectrolytes

2014 ◽  
Vol 112 (9-10) ◽  
pp. 1313-1319 ◽  
Author(s):  
Benjamin Rotenberg ◽  
Olivier Bernard ◽  
Jean-Pierre Hansen
Keyword(s):  
Phase Separation ◽  
Effective Interactions

Clustering and phase separation in mixtures of dipolar and active particles

Soft Matter ◽  
2020 ◽  
Vol 16 (15) ◽  
pp. 3779-3791 ◽  
Author(s):  
Ryan C. Maloney ◽  
Guo-Jun Liao ◽  
Sabine H. L. Klapp ◽  
Carol K. Hall
Keyword(s):  
Phase Separation ◽  
Colloidal Particles ◽  
Active Particles

Mixtures of dipolar and active colloidal particles display a variety of states including chains, string-fluids, and motility induced phase separation.

Effective interactions in protein–salt solutions approaching liquid–liquid phase separation

2014 ◽  
Vol 200 ◽  
pp. 20-27 ◽  
Author(s):  
Marcell Wolf ◽  
Felix Roosen-Runge ◽  
Fajun Zhang ◽  
Roland Roth ◽  
Maximilian W.A. Skoda ◽  
...  
Keyword(s):  
Phase Separation ◽  
Liquid Phase ◽  
Liquid Phase Separation ◽  
Salt Solutions ◽  
Effective Interactions ◽  
Liquid Liquid Phase Separation

scholarly journals Effective interactions between star polymers and colloidal particles

2001 ◽  
Vol 13 (28) ◽  
pp. 6177-6194 ◽  
Author(s):  
A Jusufi ◽  
J Dzubiella ◽  
C N Likos ◽  
C von Ferber ◽  
H Löwen
Keyword(s):  
Colloidal Particles ◽  
Star Polymers ◽  
Effective Interactions
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