Fluctuation solution theory of pure fluids

Abstract

Fluctuation Solution Theory (FST) provides an alternative view of fluid thermodynamics in terms of pair fluctuations in the particle number and excess energy observed for an equivalent open system. Here we extend the FST approach to provide a series of triplet and quadruplet particle and excess energy fluctuations that can also be used to help understand the behavior of fluids. The fluctuations for the gas, liquid, and supercritical regions of three fluids (H2O, CO2, and SF6) are then determined from accurate equations of state. Many of the fluctuating quantities change sign on moving from the gas to liquid phase and, therefore, we argue that the fluctuations can be used to characterize gas and liquid behavior. Further analysis provides an approach to isolate contributions to the excess energy fluctuations arising from just the intermolecular interactions and also indicates that the triplet and quadruplet particle fluctuations are related to the pair particle fluctuations by a simple power law for large regions of the phase diagram away from the critical point.

Gaussian and non-Gaussian fluctuations in pure classical fluids

“…The main reason for adopting the above combinations is to negate the fact that the energy fluctuations in the GCE are sensitive to the zero of energy. 24 The above pair fluctuation densities can be converted to a set of corresponding dimensionless counterparts (indicated by lower case letters) by…”

“…24 Note that, in the above volume derivatives of the entropy, there is an additional term involving pair fluctuations that will only contribute for isobaric ensembles.…”

“…Furthermore, the excess enthalpy definition avoids the zero of energy problem for open systems. 24 Before using the above quantities to develop the entropy expansion, we note that the corresponding quantities, ρ 1 δV = δV E + δN 1 and βδE = δH E − Z δV E + βE 1 δN 1 , when used in Equation (6) give…”

“…The other F's simplify considerably to give (24) all of which involve quantities that are available experimentally. Therefore, the FST based Gaussian probability distribution is then…”

“…19 By examining the corresponding fluctuations, one can obtain further insight into the properties of mixtures and simple fluids. 14,24 It is well known that particle and energy pair fluctuations in the GCE can be related to the response functions. However, it is less common to use the particle-energy triplet (or higher) fluctuations to investigate higher derivatives of the response functions.…”