Fluctuations, and Intrinsic Structure

Lennard-Jones fluid at two temperatures (reduced units). Data adapted from Ref. 131. (b) Density profile of the water/chloroform liquid/liquid interface at T = 298K. (Adapted with permission from Ref. 635. Copyright 2010 American Chemical Society.) 

The density profile is used to define the Gibbs Dividing Surface (GDS), used extensively in thermodynamic analysis of the system as well as (a somewhat crude) expression for the average location of the interface. The GDS is defined as the plane z = Zg parallel to the surface, such that the molecular deficit on the bulk side (z Zq) is balanced exactly by the surplus on the vapor side (z Zq)  

At the liquid/liquid interface, no unique GDS exists because an equation similar to Eq. [9] can be used to define a dividing surface with respect to either liquid by setting py = 0. If and Zg are locations in bulk liquid A and liquid B, respectively, the GDS with respect to liquid A is given by 

Capillary wave theory considers the density variation at the interface to be the result of the superposition of thermally excited density fluctuations on a bare intrinsic profile. Mathematically, the instantaneous local density at a 

A more direct test of the underlying assumptions of CW theory can be done by computing the spectral representation of the fluctuating surface z = C(s). This surface is represented by the superposition of capillary waves of different wave numbers q  

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