Clustering and Micellization in a Janus Fluid
Recent Monte Carlo simulations on the Kern and Frenkel model of a Janus fluid have revealed that in the vapour phase there is the formation of preferred clusters made up of a well-defined number of particles: the micelles and the vesicles. A cluster theor
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Clustering and Micellization in a Janus Fluid
All truths are easy to understand once they are discovered; the point is to discover them. [Galileo Galilei (1564–1642)]
Abstract Recent Monte Carlo simulations on the Kern and Frenkel model of a Janus fluid have revealed that in the vapour phase there is the formation of preferred clusters made up of a well-defined number of particles: the micelles and the vesicles. A cluster theory is developed to approximate the exact clustering properties stemming from the simulations. It is shown that the theory is able to reproduce semi-quantitatively the micellisation phenomenon. Keywords Janus fluid · Janus particles · Kern-Frenkel model · Monte Carlo simulation · Cluster theory · Micelle · Vesicle.
2.1 Introduction In the statistical mechanics of fluids the liquid state is a particularly fascinating one [1, 49]. A liquid is the state where correlations really play an important role. The pioneering work of Berni J. Alder [50] showed that, because of the absence of attractive forces, the hard-sphere fluid admits only a single fluid phase. In order to find the liquid phase it is sufficient to add an attractive square-well to the pairpotential of the hard-spheres. The resulting hard-sphere square-well fluid admits a bell-shaped gas-liquid coexistence curve [51, 52] with the critical point moving at low temperatures and high densities as the attractive well width diminishes. Recently N. Kern and D. Frenkel [22] studied, through computer experiments, a new fluid model made of hard-spheres with patchy square-well attractions. In its simplest version, the single patch case, the model only depends on the surface coverage χ of the patch and the attraction range. Between the two extreme cases χ = 0, the hard-sphere model,
R. Fantoni, The Janus Fluid, SpringerBriefs in Physics, DOI: 10.1007/978-3-319-00407-5_2, © The Author(s) 2013
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2 Clustering and Micellization in a Janus Fluid
and χ = 1, the hard-sphere square-well model, where the particles pair-potential is isotropic, the particles interaction is directional. The χ = 1/2 model is known as the Janus limit, as the particle, like the roman God, has two faces of different functionalities. Another important process, which may lead to the manifestation of macroscopic phenomena, in certain fluids, is the clustering or association. In 1956, for example, Leon N. Cooper [53] found that the stable state of the degenerate electron fluid in a metal is one in which particles of opposite spin and opposite momentum form pairs. It was then understood that whereas the electrons in a metal form pairs with relative angular momentum zero, in 3 He this would be prevented by the hard core repulsion, and that therefore Cooper pairing had to occur in a state of finite angular momentum. In 1961 A. Lenard [54] proved analytically that a two-component plasma living in one dimension undergoes a transition from the conducting to the insulating state by the formation of neutral dimers made of a positive and a negative charge. A two-component plasma li
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