Kirkwood-Alder transition

Kose A and Hachisu S 1974 Kirkwood-Alder transition in monodisperse latexes. I. Nonaqueous systems J. Coiioid interface Sc/. 46 460-9... 

Flachisu S and Kobayashi Y 1974 Kirkwood-Alder transition in monodisperse latexes. II. Aqueous latexes of high electrolyte concentration J. Colloid Interface Sol. 46 470-6... 

Takano, K. and Hachisu, S., Pressure of kirkwood-alder transition in monodisperse latex, J. Chem. Phys., 67, 2604, 1977. 

In a series of papers Hachisu. Kobayasi, and Kose (375-379) reviewed the literature and investigated the subject in further detail. The particles can form ordered arrays without being in actual contact. In these arrays particles are all the same size and other sizes are excluded. The phenomenon involves a phase transition when the concentration exceeds a certain volume fraction, usually 0.5 . 0.1, whereby a second more concentrated phase is formed within which the particles are in an ordered arrangment. This is known as the Kirkwood-Alder transition (380-382) and is a purely statistical effect that does not require an attractive potential for its explanation. It is inhibited when ionic repulsion forces exceed a low level. The transition can occur in suspensions in aqueous and nonaqueous liquids. In aqueous systems it will not occur even when the particles are very uniform, unless the system is low in electrolytes. 

Although the thermodynamic analysis of weak flocculation and colloidal phase separation, given above, illustrates the basic principles, some of the details are incorrect, in particular for more concentrated dispersions. One missing feature is the prediction of an order/disorder transition in hard sphere dispersions (for which Vmin is 0), where, at equilibrium, a colloidal crystal phase is predicted to coexist with a disordered phase over a narrow range of particle volume fractions (ip), that is, 0.50 < tp < 0.55 (Dickinson, 1983). In molecular hard-sphere fluids this is known as the Kirkwood-Alder transition , and is an entropy-driven effect. 

The correspondence between a concentrated dispersion and an assembly of hard spheres has been pursued by several authors. " The Kirkwood-Alder hard-sphere transition is in qualitative agreement with experiment, but the coexistence region is in general too narrow. Introduction of attractive forces, in the Monte Carlo simulations and approximate perturbation-cell theories, leads to iijiprovement at high salt concentrations and large volume fractions. But at low salt concentrations there remains the fundamental problem that the particles are not in proper thermodynamic equilibrium with bulk electrolyte as Ninham and coauthors put it the diffuse double-layers of the particles fill up the entire volume of the system, and there is no place to be regarded as bulk . 

The possibility of a fluid-to-solid transition in the hard-sphere model was first predicted by Kirkwood and his co-workers [17-19]. This prediction was part of the stimulus for the celebrated studies of hard spheres by Alder and Wainwright [20] at the Lawrence-Livermore National Laboratory using the molecular dynamics (MD) method and by Wood and Jacobson [21] at the... 

The phase behaviour of such colloidal suspensions should be nearly the same as those of the hypothetical hard-sphere atomic system. Kirkwood [6] stated that when a hard sphere system is gradually compressed, the system will show a transition towards a state of long-range order long before close-packing is reached. In 1957, Wood and Jacobson [7] and Alder and Wainwright [8] showed by computer simulations that systems of purely repulsive hard spheres indeed exhibit a well-defined fluid-crystal transition. It has taken some time before the fluid-crystal transition of hard spheres became widely accepted. There is no exact proof that the transition occurs. Its existence has been inferred from numerical simulations or from approximate theories as treated in this chapter. However, this transition has been observed in hard-sphere-Uke colloidal suspensions [9]. 

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