Polydisperse fluid

Institute of Physical Chemistry, Martin-Luther-University Halle-Wittenberg, D-06099 Halle, Germany 

In section 9.2, the polydispersity is proven to influence strongly the phase eqnilibrium. As an example the liquid + liquid equilibrium of a polymer solution is discussed. In section 9.3, the approaches to polydispersity are treated in 

Edited by A. R. H. Goodwin, J. V. Sengers and C. J. Peters International Union of Pure and Applied Chemistry 2010 Published by the Royal Society of Chemistry, www.rsc.org 

2 Influence of Polydispersity on the Liquid + Liquid Equilibrium of a Polymer Solution 

Polymers in coexisting phases have different molar-mass distributions which are also different from that of the initial homogeneous system. Obviously, the influence of polydispersity on the LLE is not only of a quantitative nature but of a qualitative nature as well. This demixing behaviour is important for some practical problems, for example, in the high-pressure synthesis of low-density polyethene [polyethylene] or of poly(but-3-enoic acid ethene) [poly(ethylene-co-vinylacetate)]. The polyethene is obtained as a solute in supercritical ethene 

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Several colloidal systems, that are of practical importance, contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size. Thus, they may be viewed as containing an infinite number of components. It has been several decades since the introduction of polydispersity as a model for molecular mixtures [73], but only recently has it received widespread attention [74-82]. Initially, work was concentrated on nearly monodisperse mixtures and the polydispersity was accounted for by the construction of perturbation expansions with a pure, monodispersive, component as the reference fluid [77,80]. Subsequently, Kofke and Glandt [79] have obtained the equation of state using a theory based on the distinction of particular species in a polydispersive mixture, not by their intermolecular potentials but by a specific form of the distribution of their chemical potentials. Quite recently, Lado [81,82] has generalized the usual OZ equation to the case of a polydispersive mixture. Recently, the latter theory has been also extended to the case of polydisperse quenched-annealed mixtures [83,84]. As this approach has not been reviewed previously, we shall consider it in some detail. 

The polydisperse fluid structure is characterized by the total, / (r, a, (j ), and the direct, c(r, a, (jy), correlation function, both being functions of the particle diameters. These functions are related via the OZ equation (17), which is rewritten in the form... 

Numerical results for the some model polydisperse systems have been reported in Refs. 81-83. It has been shown that the effect of increasing polydispersity on the number-number distribution function is that the structure decreases with increasing polydispersity. This pattern is common for the behavior of two- and three-dimensional polydisperse fluids [81] and also for three-dimensional quenched-annealed systems [83]. 

Statistical mechanics was originally formulated to describe the properties of systems of identical particles such as atoms or small molecules. However, many materials of industrial and commercial importance do not fit neatly into this framework. For example, the particles in a colloidal suspension are never strictly identical to one another, but have a range of radii (and possibly surface charges, shapes, etc.). This dependence of the particle properties on one or more continuous parameters is known as polydispersity. One can regard a polydisperse fluid as a mixture of an infinite number of distinct particle species. If we label each species according to the value of its polydisperse attribute, a, the state of a polydisperse system entails specification of a density distribution p(a), rather than a finite number of density variables. It is usual to identify two distinct types of polydispersity variable and fixed. Variable polydispersity pertains to systems such as ionic micelles or oil-water emulsions, where the degree of polydispersity (as measured by the form of p(a)) can change under the influence of external factors. A more common situation is fixed polydispersity, appropriate for the description of systems such as colloidal dispersions, liquid crystals, and polymers. Here the form of p(cr) is determined by the synthesis of the fluid. 

Thin films (Langmuir-Blodgett, etc.) Chemical equilibria Polydisperse fluids Zeolites... 

Gualtieri, J. A., Kincaid, J. M., and Morrison, G., Phase equilibria in polydisperse fluids. J. Chem. 

Schlijper, A. G., Flash calculations for polydisperse fluids A variational approach. Fluid Phase Eg. 34, 149 (1987). 

Cuesta and co-workers [263,264] have looked at the issue of demixing in several types of polydisperse fluids, but the issue of compound formation... 

Briano JG, Glandt ED (1984) Statistical thermodynamics of polydisperse fluids. J Chem Phys 80 3336-3343... 

In some cases the polydisperse fluids cannot be described by a single distribution function and these require a sum of a finite number of simple distribution functions. ... 

Browarzik D, Kehlen H (1996) Stability of polydisperse fluid mixtures. Fluid Phase Equilib... 

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