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.
Briano et al. (Sun,) studied this question.
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