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A weighted correlation approach of the density functional theory for an inhomogeneous fluid at an interface
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering. (Kemisk apparatteknik)
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This doctoral thesis presents a newly developed density functional theory (DFT), i.e., the weighted correlation approach (WCA), to study the structural and thermodynamic properties of an inhomogeneous fluid at an interface. The WCA approach provides a generic formulation to evaluate the change of the single-particle direct correlation function in terms of a series of pair direct correlation functions weighted by different correlation-weight functions with adjustable correlation-weight factors. When applied practically, however, an approximation of the pair direct correlation function has to be made, together with appropriate definitions of the weighted densities and the choices of the correlation-weight functions. Despite this seeming complexity, it is shown that the WCA approach can be regarded as a generalization of the classic density functional approaches and this enables us to develop and apply DFT methods in different ways. For demonstration purposes, several implementations of the WCA approach are proposed and applied to predict the density distribution of an inhomogeneous fluid at an interface. The WCA approach is also employed with a novel pressure expression to investigate the inhomogeneous fluid-mediated interaction pressure for different cases. The WCA calculations from the above applications suggest that it is a successful approach for describing the structural and thermodynamic properties of an inhomogeneous fluid at an interface, as compared to the published results of the Monte Carlo simulations, density functional methods and experimental data.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , viii, 62 p.
Series
Trita-CHE-Report, ISSN 1654-1081 ; 2013:9
Keyword [en]
inhomogeneous fluid, interface, density functional theory
National Category
Chemical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-119776ISBN: 978-91-7501-668-9 (print)OAI: oai:DiVA.org:kth-119776DiVA: diva2:612339
Public defence
2013-05-16, Sal D3, Lindstedtsvägen 5, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Projects
Bentonite Erosion project, Svensk kärnbränslehantering AB (SKB)EC project BELBaR (Bentonite Erosion: effects on the Long term performance of the engineered Barrier and Radionuclide Transport)
Note

QC 20130409

Available from: 2013-04-09 Created: 2013-03-21 Last updated: 2013-04-09Bibliographically approved
List of papers
1. The weighted correlation approach for density functional theory: a study on the structure of the electric double layer
Open this publication in new window or tab >>The weighted correlation approach for density functional theory: a study on the structure of the electric double layer
2011 (English)In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 23, no 17, 175002- p.Article in journal (Refereed) Published
Abstract [en]

Within the framework of density functional theory, a weighted correlation approach is developed in order to obtain the density distributions of an inhomogeneous fluid. It results in a formally exact expression, by means of the concept of a weighted pair correlation function, used to evaluate the change of the single-particle direct correlation function of the system relative to that of a reference state. When applying the approach for practical use, however, an approximation of the pair correlation function has to be made, along with an appropriate definition of a weight function. Noticeably, combining this approach with fundamental measure theory gives rise to a new method, which we call the FMT/WCA-k(2) approach, for studying the structural and thermodynamic properties of a charged hard-sphere fluid subjected to a spatially varying external potential. Application of the FMT/WCA-k(2) approach in a range of electrolyte concentrations and surface charge densities, against the Monte Carlo simulations, shows that it is superior to the typical approaches of density functional theory in predicting the ionic density profiles of both counter-ions and co-ions near a highly charged surface. It is capable of capturing the fine features of the structural properties of the electric double layers, to well reproduce the layering effect and the charge inversion phenomenon, also in strongly coupled cases where divalent counter-ions are involved. In addition, it is found that the FMT/WCA-k(2) approach even has an advantage over the anisotropic, hyper-netted chain approaches in giving better agreement with the Monte Carlo results.

National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-33218 (URN)10.1088/0953-8984/23/17/175002 (DOI)000289555700004 ()2-s2.0-79955033089 (Scopus ID)
Funder
ICT - The Next Generation
Note
QC 20110530Available from: 2011-05-30 Created: 2011-05-02 Last updated: 2017-12-11Bibliographically approved
2. Weighted correlation approach: An extended version with applications to the hard-sphere fluid
Open this publication in new window or tab >>Weighted correlation approach: An extended version with applications to the hard-sphere fluid
2012 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 86, no 3, 031115- p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this study is to extend the weighted correlation approach (WCA) for inhomogeneous fluids. It now introduces a generic expression to evaluate the single-particle direct correlation function in terms of a series of pair direct correlation functions weighted by different correlation-weight functions and adjustable weight factors. When applied for practical use, however, approximations of the pair direct correlation functions have to be made, together with appropriate definitions of the weighted densities and the choices of the correlation-weight functions. The WCA approach would, then, not only help us to connect and compare different strategies and their underlying assumptions in the density functional approaches, but also enable us to propose and apply density functional theory methods to predict the density profile of, e. g., the hard-sphere fluid confined between a pair of parallel planar hard walls. Numerical results of the extended WCA approach, against the Monte Carlo (MC) simulations in a range of surface separations and bulk densities, suggest that it is capable of representing the fine features of the hard-sphere density distributions. The WCA results also agree well with the calculations from the fundamental measure theory. In addition, the thermodynamic self-consistency of the WCA approach is confirmed by its fairly good agreement with the MC fitted data for the surface tension of a hard-sphere fluid at a planar hard wall. All these tests show that a pure WCA approach can be constructed to investigate the states of ionic hard-sphere fluids.

Keyword
Density-Functional Theory, Electric Double-Layers, Integral-Equation, Primitive-Model, Wall, Simulations, Adsorption, Particles, Interface, Mixtures
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-103125 (URN)10.1103/PhysRevE.86.031115 (DOI)000308587900002 ()2-s2.0-84866403125 (Scopus ID)
Funder
ICT - The Next Generation
Note

QC 20121008

Available from: 2012-10-08 Created: 2012-10-04 Last updated: 2017-12-07Bibliographically approved
3. A novel method to describe the interaction pressure between charged plates with application of the weighted correlation approach
Open this publication in new window or tab >>A novel method to describe the interaction pressure between charged plates with application of the weighted correlation approach
2011 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 135, no 24, 244107- p.Article in journal (Refereed) Published
Abstract [en]

Based on the Euler-Lagrange equation for ion density distribution in an inhomogeneous, charged, and hard-sphere fluid, a novel method is proposed to determine the interaction pressure between charged plates. The resulting expression is a sum of distinct physical contributions to the pressure, which involves different contributions to the single-particle direct correlation function. It can, therefore, be conveniently used in any density functional approach to facilitate analysis of the pressure components. In this study, the so-called fundamental measure theory (FMT)/weighted correlation approach (WCA) approach is applied to estimate both the hard-sphere and the electric residual contributions to the single-particle direct correlation function, upon the calculation of the ionic density profiles between charged plates. The results, against the Monte Carlo simulations, show that the FMT/WCA approach is superior to the typical FMT/mean spherical approximation approach of the density functional theory in predicting the interaction pressure between charged plates immersed in an electrolyte solution upon various conditions in the primitive model. The FMT/WCA approach can well capture the fine features of the pressure-separation dependence, to reproduce not only the shoulder shape and the weak attractions in monovalent electrolytes but also the strongly oscillatory behavior of pressure in divalent electrolytes where pronounced attractions are observed. In addition, it is found that the FMT/WCA approach even has an advantage over the anisotropic, hyper-netted chain approach in that it agrees with the Monte Carlo results to a very good extent with, however, much less computational effort.

National Category
Physical Sciences Chemical Sciences
Identifiers
urn:nbn:se:kth:diva-75541 (URN)10.1063/1.3672001 (DOI)000298640500010 ()2-s2.0-84855271477 (Scopus ID)
Note
QC 20120206Available from: 2012-02-06 Created: 2012-02-06 Last updated: 2017-12-08Bibliographically approved
4. Hard-sphere fluid-mediated interaction: a novel pressure expression with application of the weighted correlation approach
Open this publication in new window or tab >>Hard-sphere fluid-mediated interaction: a novel pressure expression with application of the weighted correlation approach
(English)Article in journal (Other academic) Submitted
National Category
Chemical Sciences
Identifiers
urn:nbn:se:kth:diva-120467 (URN)
Note

QS 2013

Available from: 2013-04-09 Created: 2013-04-09 Last updated: 2013-04-09Bibliographically approved
5. The swelling pressure of Na-bentonite: Study with a density functional approach
Open this publication in new window or tab >>The swelling pressure of Na-bentonite: Study with a density functional approach
2012 (English)In: Chemistry Letters, ISSN 0366-7022, E-ISSN 1348-0715, Vol. 41, no 10, 1346-1348 p.Article in journal (Refereed) Published
Abstract [en]

The combination of the fundamental measure theory (FMT) and the weighted correlation approach (WCA) within the framework of the density functional theory, i.e., the FMT/ WCA approach, is applied to study the swelling pressure of Nabentonite at different salt conditions. Good agreement between the FMT/WCA simulations and the results from both experiments and a Donnan-equilibrium-based DLVO model suggests that the hydration repulsion between charged surfaces can be well accounted by the ionion correlations effect.

Keyword
Bentonite, Swelling Pressure, Density Functional Theory, Ion-Ion Correlation, Hydration
National Category
Chemical Sciences
Identifiers
urn:nbn:se:kth:diva-105704 (URN)10.1246/cl.2012.1346 (DOI)000310931600115 ()2-s2.0-84868287438 (Scopus ID)
Funder
ICT - The Next Generation
Note

QC 20121212

Available from: 2012-11-23 Created: 2012-11-23 Last updated: 2017-12-07Bibliographically approved

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