Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids

Abstract

Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined. C 2015 AIP Publishing LLC. [http://dx

Gaussian and non-Gaussian fluctuations in pure classical fluids

“…Indeed, previous studies have shown that the GCE distributions are not Gaussian (or symmetric) and therefore this assumption is not justified for the present purposes. 14,20 This point will also be discussed further in Sec. III.…”

“…4,11,12 Nevertheless, there is interest in the properties of the resulting non-Gaussian distributions. 4,[12][13][14] The third and higher moments of these distributions are finite and have been developed by Greene and Callen. 15 They are important for understanding higher thermodynamic derivatives, especially close to the critical point, which characterize the behavior of fluids and their mixtures.…”

“…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.…”

“…14,[18][19][20] FST provides an alternative view of the commonly studied closed system thermodynamic properties in terms of fluctuating quantities occurring in an equivalent Grand Canonical Ensemble (GCE) system. FST represents a generalization of the Kirkwood-Buff theory of solutions, [21][22][23] to include energy fluctuations.…”

“…Nevertheless, the third moments of the bivariate particle-energy joint distribution in the GCE can be useful and quantify the non-Gaussian behavior of the underlying probability distribution. 14 Here, we use FST to help provide the second and third derivatives of the entropy for use in the usual entropy expansion to provide a general non-Gaussian particle, volume, and energy probability distribution that is applicable to any ensemble. The initial steps essentially follow previous entropy expansion approaches, 9,15 although here we start from the probability distributions for a series of ensembles.…”