Fluid Density Functional Theory Research Articles

The method of collective variables: a link with the density functional theory

Recently, based on the method of collective variables the statistical field theory for multicomponent inhomogeneous systems was formulated [O. Patsahan, I. Mryglod, J.-M. Caillol, Journal of Physical Studies, 2007, 11, 133]. In this letter we establish a link between this approach and the classical density functional theory for inhomogeneous fluids.

Density functional theory for the ground state of spherically confined dusty plasma

The spatial structure of dusty plasma confined in a spherical microcavity has been investigated by use of the density functional theory for classical fluids, in which all particles undergo an isotropic harmonic potential and the interparticle interaction is described by the hard-core Yukawa potential. The fundamental measure theory of Rosenfeld and its modified versions have been used in the energy functional to incorporate hard-core interactions between particles. Based on the variational principle, the equilibrium density profile can be obtained by use of an iteration calculation with the average density of particles as an input. In terms of density profiles presented under various conditions, the roles of the trapped parameter, coupling parameter, screening parameter, and the average number density of particles are discussed, and significant influences of these factors on the structure of confined dusty plasma are found.

Surface-induced phase behavior of polymer/nanoparticle blends with attractions

In an athermal blend of nanoparticles and homopolymer near a hard wall, there is a first order phase transition in which the nanoparticles segregate to the wall and form a densely packed monolayer above a certain nanoparticle density. Previous investigations of this phase transition employed a fluids density functional theory (DFT) at constant packing fraction. Here we report further DFT calculations to probe the robustness of this phase transition. We find that the phase transition also occurs in athermal systems at constant pressure, the more natural experimental condition than constant packing fraction. Adding nanoparticle-polymer attractions increases the nanoparticle transition density, while sufficiently strong attractions suppress the first-order transition entirely. In this case the systems display a continuous transition to a bulk layered state. Adding attractions between the polymers and the wall has a similar effect of delaying and then suppressing the first-order nanoparticle segregation transition, but does not lead to any continuous phase transitions.

Toward Quantitative Coarse-Grained Models of Lipids with Fluids Density Functional Theory.

We describe methods to determine optimal coarse-grained models of lipid bilayers for use in fluids density functional theory (fluids-DFT) calculations. Both coarse-grained lipid architecture and optimal parametrizations of the models based on experimental measures are discussed in the context of dipalmitoylphosphatidylcholine (DPPC) lipid bilayers in water. The calculations are based on a combination of the modified-iSAFT theory for bonded systems and an accurate fundamental measures theory (FMT) for hard sphere reference fluids. We furthermore discuss a novel approach for pressure control in the fluids-DFT calculations that facilitates both partitioning studies and zero tension control for the bilayer studies. A detailed discussion of the numerical implementations for both solvers and pressure control capabilities are provided. We show that it is possible to develop a coarse-grained lipid bilayer model that is consistent with experimental properties (thickness and area per lipid) of DPPC provided that the coarse-graining is not too extreme. As a final test of the model, we find that the predicted area compressibility moduli and lateral pressure profiles of the optimized models are in reasonable agreement with prior results.

A tug-of-war between electronic excitation and confinement in a dynamical context

Quantum fluid density functional theory has been used to study the time evolution of various reactivity parameters such as hardness, electrophilicity, entropy, chemical potential, polarizability, electronegativity etc. in a confined environment during time dependent processes like atom-ion collision and atom-field interaction. Responses in the reactivity parameters of the helium atom, in the dynamical context, for ground state as well as in excited state, have been reported. The confinement is incorporated through a Dirichlet type boundary condition. With a decrease in the size of the cylindrical box, the system gets harder and less polarizable. Simultaneous excitation and confinement may bring back the ground state behavior.

Extension of the Steele 10-4-3 potential for adsorption calculations in cylindrical, spherical, and other pore geometries

Simplified fluid-substrate interaction models derived from the Lennard-Jones potential are widely used in the simulation of gas physisorption phenomena. In this paper, we reinterpret the well known Steele 10-4-3 potential for a gas molecule interacting with a planar surface, and use the resultant scheme to derive new potentials for cylindrical and spherical pore geometries. These new potentials correctly recover the Steele result in the limit of infinite pore radius, a useful improvement over existing models. We demonstrate the new cylindrical Steele 10-4-3 potential in calculations of argon adsorption via fluid density functional theory. This potential yields markedly different adsorption behavior than existing cylindrical potentials, which follow from small but significant differences in both the strength and the shape of the fluid-surface interaction. These differences cannot be fully reconciled simply by reparameterizing (scaling) the existing models; the new potential is more realistic in design, and is especially to be preferred in studies where comparison with planar substrates is made. Finally, we discuss extensions of this approach to more complicated pore geometries, yielding a family of Steele-like potentials that all satisfy the correct planar limit.

Nanodrop of an Ising Magnetic Fluid on a Solid Surface

The density functional theory of inhomogeneous simple fluids is extended to an Ising magnetic fluid in contact with a solid surface, which is subjected to an external uniform or nonuniform magnetic field. The system is described by two coupled integral equations regarding the magnetic moment and fluid density distributions. The dependence of the contact angle that a nanodrop makes with the solid surface on the parameters involved in the magnetic interactions between the molecules of fluid and between the molecules of fluid and an external magnetic field is calculated. For the uniform magnetic field, the contact angle increases with increasing magnetic field, approaching an asymptotic value that depends on the strength of the fluid-fluid magnetic interactions. In the nonuniform field generated by a permanent magnet, the contact angle first increases with increasing magnetic field B(M) and then decreases, with the decrease being almost linear for large values of B(M). The obtained results are in qualitative agreement with the experimental data on the contact angle of magnetic drops on a solid surface available in the literature.

Renormalized Kinetic Theory of Classical Fluids in and out of Equilibrium

We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distribution function $f$, the correlation function $C=<\delta f\delta f >$, the retarded and advanced density response functions $\chi^{R,A}=\delta f/\delta\phi$ to an external potential $\phi$, and the associated memory functions $\Sigma^{R,A,C}$. The basis of the theory is an effective action functional $\Omega$ of external potentials $\phi$ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density $f$ and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques are then used to perform the closure of the hierarchy through memory functions. The latter satisfy functional equations that can be used to devise systematic approximations. The present formulation can be equally regarded as (i) a generalization to dynamical problems of the density functional theory of fluids in equilibrium and (ii) as the classical mechanical counterpart of the theory of non-equilibrium Green's functions in quantum field theory. It unifies and encompasses previous results for classical Hamiltonian systems with any initial conditions. For equilibrium states, the theory reduces to the equilibrium memory function approach. For non-equilibrium fluids, popular closures (e.g. Landau, Boltzmann, Lenard-Balescu) are simply recovered and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.

A perturbative density functional theory for square-well fluids

We report a perturbative density functional theory for quantitative description of the structural and thermodynamic properties of square-well fluids in the bulk or at inhomogeneous conditions. The free-energy functional combines a modified fundamental measure theory to account for the short-range repulsion and a quadratic density expansion for the long-range attraction. The long-correlation effects are taken into account by using analytical expressions of the direct correlation functions of bulk fluids recently obtained from the first-order mean-spherical approximation. The density functional theory has been calibrated by extensive comparison with simulation data from this work and from the literature. The theory yields good agreement with simulation results for the radial distribution function of bulk systems and for the density profiles of square-well fluids near the surfaces of spherical cavities or in slit pores over a broad range of the parameter space and thermodynamic conditions.

Free-Energy Density Functional of Ions at a Dielectric Interface.

Ions at dielectric interfaces are found in a wide range of applications including biology, nanofluidics, and fuel cells. Often, the excluded volume of the ions has first-order effects on measured properties. Here, density functional theory of fluids is used to develop a statistical mechanical theory of how ions (charged hard spheres of different sizes) arrange around a dielectric interface.

Fluids density functional theory studies of supramolecular polymers at a hard surface

We have applied a fluids density functional theory based on that of Yu and Wu [J. Chem. Phys. 116, 7094 (2002)] to treat reversible supramolecular polymers near a hard surface. This approach combines a hard-sphere fluids density functional theory with the first-order thermodynamic perturbation theory of Wertheim. The supramolecular polymers are represented in the theory by hard-spheres with two associating sites. We explore the effects of the bonding scheme, monomer concentration, and association energy upon the equilibrium chain sizes and the depletion lengths. This study is performed on simple systems containing two-site monomers and binary mixtures of two-site monomers combined with end stopper monomers which have only a single association site. Our model has correct behavior in the dilute and overlap regimes and the bulk results can be easily connected to simpler random-flight models. We find that there is a nonmonotonic behavior of the depletion length of the polymers as a function of concentration and that this depletion length can be controlled through the concentration of end stoppers. These results are applicable to the study of colloidal dispersions in supramolecular polymer solutions.

Dynamic density functional theory versus kinetic theory of simple fluids

By combining methods of kinetic and density functional theory, we present a description ofmolecular fluids which accounts for their microscopic structure and thermodynamicproperties as well as their hydrodynamic behavior. We focus on the evolution ofthe one-particle phase space distribution, rather than on the evolution of theaverage particle density which features in dynamic density functional theory. Theresulting equation can be studied in two different physical limits: diffusive dynamics,typical of colloidal fluids without hydrodynamic interaction where particles aresubject to overdamped motion resulting from coupling with a solvent at rest, andinertial dynamics, typical of molecular fluids. Finally, we propose an algorithmto solve numerically and efficiently the resulting kinetic equation by employinga discretization procedure analogous to the one used in the lattice Boltzmannmethod.

Binary fluid with attractions near a planar wall

It is well known that a mixture of big and small hard spheres next to a planar wall will exhibit segregation based on their size difference. The larger spheres will tend to locate next to the substrate because the overall system entropy loss per unit area is less. In the present study we determine the role of attraction between the small particles and the wall to displace the larger particles. Both fluids density-functional theory and discontinuous molecular dynamics simulations demonstrate that at a certain attractive potential, which is on the order of the thermal energy, the large particles can indeed be dislodged from the surface layer so the small particles are now the major surface component. Exploration of a range of parameters, including relative sphere size and concentration, as well as attractions between the small spheres in the bulk, shows that the phenomenon is quite robust.

A density functional theory for Yukawa chain fluids in a nanoslit

A weighted density functional theory is developed for Yukawa chain fluids confined in a nanoslit. The excess free-energy functional is separated into repulsive and attractive contributions. A simple Heaviside function is used as the weighting function to calculate the weighted density in both contributions. The excess free-energy functional of repulsive interaction is calculated by the equation of state developed by Liu et al., while the contribution to excess free-energy functional by attractive interaction is calculated using the statistical associating fluids theory for chain molecules with attractive potentials of variable range. For pure fluids, the predicted density profiles near the nanoslit wall are in good agreement with simulations. The effect of cut-off introduced in the weighting function for the attractive part is examined; in addition, the surface excess and partition coefficient are calculated. The density profiles are also predicted for mixtures of two Yukawa chain fluids with different chain lengths, hard-core diameters, fluid–fluid and wall–fluid interactions. This work reveals that it is important to decompose the excess free-energy functional into repulsive and attractive contributions, and a simple weighting function can be used for both contributions.

An efficient algorithm for classical density functional theory in three dimensions: Ionic solutions

Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses O(N log N) operations and O(N) memory, where N is the number of grid points. This system-size scaling is significant because of the very large N required for three-dimensional systems. The algorithm uses fast Fourier transforms (FFTs) to evaluate the convolutions of the DFT Euler-Lagrange equations and Picard (iterative substitution) iteration with line search to solve the equations. The pros and cons of this FFT/Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT, we use fundamental measure theory. For the electrostatic DFT, we present two algorithms. One is for the "bulk-fluid" functional of Rosenfeld [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)] that uses O(N log N) operations. The other is for the "reference fluid density" (RFD) functional [D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)]. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires O(N(2)) operations.

Equilibrium behaviour of a novel gas separation process, with application to carbon capture

A novel gas separation process is described and analysed in the context of carbon capture. It involves a highly selective absorbent fluid below its saturation pressure pre-mixed with the gas to be separated and adsorbed into a porous solid. This fluid mixture simultaneously forms gas-like and liquid-like regions within the porous solid depending on the pore size. The gas component to be separated is selectively absorbed by the liquid-like regions, and a novel ‘pressure-swing wetting layer absorption’ process is used to recover the absorbed gas. This work examines the equilibrium behaviour of this process in the context of carbon capture using the density functional theory (DFT) of classical fluids. The DFT model employed represents the porous solid in terms of ideal graphitic slit-pores, and a ternary fluid model is calibrated to represent mixtures of tetrahydrofuran (the absorbent fluid), carbon dioxide and nitrogen. Under the conditions investigated here we find that the equilibrium behaviour of this system is superior to the analogous pressure-swing adsorption process without solvent. This result motivates further experimental and dynamical process modelling studies of this system.

Analytic Theory for Dilute Colloids in a Charged Slit

Nanofluidic devices can now be manufactured with a slit-like geometry whose charged walls are 50-1000 nm wide. Through these slits, large charged macromolecules at very low concentration suspended in electrolytes can flow and be analyzed and separated based on their charge and other properties. To study such a system and to compute the flow of these colloidal macromolecules, the equilibrium distribution across the slit (perpendicular to the flow) is needed. Here, an analytic theory for such a concentration distribution of dilute colloid particles in a charged slit is presented. The theory is based on classical density functional theory (DFT) of fluids with the colloid particles described as large, charged, hard spheres and the background electrolyte described as point charges. In the limit of a very dilute colloid, low surface charge on the slit walls, and noninteracting electrical double layers at these walls, the approximate theory is quantitatively correct when compared to numerical solutions of the DFT equations. Outside of this regime of parameters, the approximate theory is generally qualitatively correct, especially when the colloid particles and the slit have the same sign charge.

Microscopic density functional theory of wetting and drying of a solid substrate by an explicit solvent model of ionic solutions

Classical density functional theory (DFT) of inhomogeneous fluids is applied to an explicit solvent ‘semi-primitive’ model (SPM) of ionic solutions to investigate the influence of ionic solutes on the wetting behaviour of a solvent in contact with a neutral or charged planar substrate. The SPM is made up of three species of hard sphere particles with different diameters, interacting via an attractive Yukawa potential to model excluded volume and cohesion. The solvent particles are neutral, while the monovalent anions and cations are oppositely charged. The polar nature of the solvent is modelled by a continuum dielectric permittivity linked to the local solvent density. All three species interact with the impenetrable substrate via an attractive external potential. While excluded volume effects are accurately described by a Rosenfeld ‘fundamental measure’ free energy functional, the short range Yukawa attraction and Coulombic interactions are treated within the mean-field approximation. The ionic solutes are found to have a significant impact on the wetting behaviour of the solvent, in particular on the wetting temperature. Strong electric fields, or long-ranged (weakly screened) Coulombic forces are shown to have the propensity to change the wetting transition from second to first order. The cation–anion size asymmetry leads to charge separation on the liquid–vapour interface of the solution, which in turn can induce a drying transition on the liquid side of liquid–vapour coexistence.

Density Functional Theory Approach for Charged Hard Sphere Fluids Confined in Spherical Micro-Cavity

Within the framework of the density functional theory for classical fluids, the equilibrium density profiles of charged hard sphere fluid confined in micro-cavity are studied by means of the modified fundamental measure theory. The dimension of micro-cavity, the charge of hard sphere and the applied electric field are found to have significant effects on the density profiles. In particular, it is shown that Coulomb interaction, excluded volume interaction and applied electric field play the central role in controlling the aggregated structure of the system.

Interactions between Surfaces in Polydisperse Semiflexible Polymer Solutions

We generalize a recently developed polymer density functional theory (PDFT) for polydisperse polymer fluids to the case of semiflexible (stiff) polymers. As with our earlier work on flexible polymers, we show here that the generalization of the PDFT to polydisperse mixtures of semiflexible chains allows us to obtain a remarkable simplification of the solution algorithm, compared to the monodispersed case. The number of required equations for complete solution of the (polydisperse) PDFT scales inveresly with the width of the polydispersity profile. This reflects the fact that more information is required, the narrower is the polydispersity. We apply the theory to a number of model scenarios, including repulsive and adsorbing surfaces. We find that polydispersity effects on the depletion interaction are larger for dilute solutions and when the surfaces are adsorbing. We also investigate short, stiff chains and find rather dramatic effects in the presence of adsorbing surfaces.