Correlation function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations.
File(s)
Accepted version
Author(s)
Parry, Andrew
rascon, carlos
Type
Journal Article
Abstract
In a recent article, we described how the microscopic structure of density-density correlations in the fluid interfacial region, for systems with short-ranged forces, can be understood by considering the resonances of the local structure factor occurring at specific parallel wave vectors
q
[Nat. Phys. 15, 287 (2019)]. Here we investigate this further by comparing approximations for the local structure factor and pair correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the pair correlation function and structure factor across the whole spectrum of wave vectors, encapsulating the crossover from the Goldstone mode divergence (at small
q
) to bulklike behavior (at larger
q
). As shown, these approximations are exact for some square-gradient model potentials and never more than a few percent inaccurate for the others. Additionally, we show that they describe very accurately the correlation function structure for a model describing an interface near a tricritical point. In this case, there are no analytical solutions for the correlation functions, but the approximations are nearly indistinguishable from the numerical solutions of the Ornstein-Zernike equation.
q
[Nat. Phys. 15, 287 (2019)]. Here we investigate this further by comparing approximations for the local structure factor and pair correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the pair correlation function and structure factor across the whole spectrum of wave vectors, encapsulating the crossover from the Goldstone mode divergence (at small
q
) to bulklike behavior (at larger
q
). As shown, these approximations are exact for some square-gradient model potentials and never more than a few percent inaccurate for the others. Additionally, we show that they describe very accurately the correlation function structure for a model describing an interface near a tricritical point. In this case, there are no analytical solutions for the correlation functions, but the approximations are nearly indistinguishable from the numerical solutions of the Ornstein-Zernike equation.
Date Issued
2019-08-26
Date Acceptance
2019-08-16
Citation
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2019, 110, pp.022803-1-022803-12
ISSN
1539-3755
Publisher
American Physical Society
Start Page
022803-1
End Page
022803-12
Journal / Book Title
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
Volume
110
Copyright Statement
©2019 American Physical Society.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.022803
Grant Number
EP/L020564/1
Subjects
Fluids & Plasmas
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published online
Date Publish Online
2019-08-26