The statistical mechanical formalisms for dealing with mixtures containing an infinite number of components are discussed. The partition function and the thermodynamic properties can be easily generalized from the corresponding results for pure substances when the polydisperse fluid is studied in a four-dimensional space. The chemical potential field acts along the additional coordinate: the composition axis. A perturbation theory for narrow distributions is developed. A small parameter measuring the width of the chemical potential function is used within a semigrand ensemble. An equivalent, hybrid expansion expresses the results in terms of the variance of the composition distribution.

Reverse micelles prepared in the system water, sodium bis-(2-ethylhexyl) sulfoccinate (AOT), and isooctane were investigated as a templating system for the production of gold nanoparticles from Au(III) and the reducing agent sulfite. A core-shell Mie model was used to describe the optical properties of gold nanoparticles in the reverse micelles. Dynamic light scattering of gold colloids in aqueous media and in reverse micelle solution indicated agglomeration of micelles containing particles. This was verified theoretically with an analysis of the total interaction energy between pairs of particles as a function of particle size. The analysis indicated that particles larger than about 8 nm in diameter should reversibly flocculate. Transmission electron microscopy measurements of gold nanoparticles produced in our reverse micelles showed diameters of 8-10 nm. Evidence of cluster formation was also observed. Time-correlated UV-vis absorption measurements showed a red shift for the peak wavelength. This was interpreted as the result of multiple scattering and plasmon interaction between particles due to agglomeration of micelles with particles larger than 8 nm.

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