Fundamental Measure Density Functional Theory Research Articles

First-order layering and critical wetting transitions in nonadditive hard-sphere mixtures

Using fundamental-measure density functional theory we investigate entropic wetting in an asymmetric binary mixture of hard spheres with positive nonadditivity. We consider a general planar hard wall, where preferential adsorption is induced by a difference in closest approach of the different species and the wall. Close to bulk fluid-fluid coexistence, the phase rich in the minority component adsorbs either through a series of first-order layering transitions, where an increasing number of liquid layers adsorbs sequentially, or via a critical wetting transition, where a thick film grows continuously.

Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an externalmagnetic field

Using fundamental measure density functional theory we investigate paranematic–nematic andnematic–nematic phase coexistence in binary mixtures of circular platelets with vanishingthicknesses. An external magnetic field induces uniaxial alignment and acts on the plateletswith a strength that is taken to scale with the platelet area. At particle diameter ratioλ = 1.5 the system displays paranematic–nematic coexistence. Forλ = 2, demixing into two nematic states with different compositions also occurs, between anupper critical point and a paranematic–nematic–nematic triple point. Increasing thefield strength leads to shrinking of the coexistence regions. At high enough fieldstrength a closed loop of immiscibility is induced and phase coexistence vanishes ata double critical point above which the system is homogeneously nematic. Forλ = 2.5, besides paranematic–nematic coexistence, there is nematic–nematic coexistence whichpersists and hence does not end in a critical point. The partial orientational orderparameters along the binodals vary strongly with composition and connect smoothly foreach species when closed loops of immiscibility are present in the corresponding phasediagram.

Binary non-additive hard sphere mixtures: fluid demixing, asymptotic decay of correlationsand free fluid interfaces

Using a fundamental measure density functional theory we investigate both bulk andinhomogeneous systems of the binary non-additive hard sphere model. For sufficiently large(positive) non-additivity the mixture phase separates into two fluid phases with differentcompositions. We calculate bulk fluid–fluid coexistence curves for a range of size ratios andnon-additivity parameters and find that they compare well to simulation results from theliterature. Using the Ornstein–Zernike equation, we investigate the asymptotic, , decay of the partial pair correlation functions,gij(r). At low densities a structural crossover occurs in the asymptotic decay between two differentdamped oscillatory modes with different wavelengths corresponding to the two intra-specieshard-core diameters. On approaching the fluid–fluid critical point there is a Fisher–Widomcrossover from exponentially damped oscillatory to monotonic asymptotic decay. Using thedensity functional we calculate the density profiles for the planar free fluid–fluid interfacebetween coexisting fluid phases. We show that the type of asymptotic decay ofgij(r) not only determines the asymptotic decay of the interface profiles, but is also relevant forintermediate and even short-ranged behaviour. We also determine the surface tension of thefree fluid interface, finding that it increases with non-additivity, and that on approachingthe critical point mean-field scaling holds.

Towing, breathing, splitting, and overtaking in driven colloidal liquid crystals

The nonequilibrium response of a colloidal liquid-crystalline nematic phase to an external aligning field, which rotates in a plane, is explored by dynamical fundamental measure density-functional theory. Depending on the drive frequency, different dynamical states are found, which are characterized by towing and overtaking of the nematic director by the field as well as by breathing and dynamical splitting of the orientational distribution peak. This complex response can be exploited for smart optical switching and mixing devices.

Bulk phase behavior of binary hard platelet mixtures from density functional theory

We investigate isotropic-isotropic, isotropic-nematic, and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom, and radial size ratios lambda up to 5. A fundamental measure density functional theory, previously used for the one-component model, is presented and results are compared against those from Onsager theory as a benchmark. For lambda<or=1.7 the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of lambda . For size ratios lambda>or=2, we find that demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of lambda than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles.

Fundamental measure density functional theory for hard spherocylinders in static andtime-dependent aligning fields

The recently developed fundamental measure density functional theory (Hansen-Goos andMecke 2009 Phys. Rev. Lett. 102 018302) for an inhomogeneous anisotropic hard bodyfluid is used as a basic ingredient in treating the Brownian dynamics of hardspherocylinders. After discussing the relevance of a free parameter in the fundamentalmeasure density functional for the isotropic–nematic transition in equilibrium,we discuss the equilibrium phase behaviour of hard spherocylinders in a staticexternal potential which couples only to the orientations. For external potentialsfavouring rod orientations along the poles of the unit sphere, there is a well-knownparanematic–nematic transition which ceases to exist above a threshold of the strengthV0 of the external potential. However, when orientations along theequator are more favoured, in the plane of the potential energyV0 and density, there is a phase transition from paranematic to nematic forany strength, which becomes second order above a critical threshold ofV0. The full equilibriumphase diagram in the V0–density plane is computed for a fixed rod aspect ratio of 5. For the equatorial cases, strengthV0 is then oscillating in time and dynamical density functional theory isused to compute the evolution of the orientational distribution. A subtleresonance for increasing oscillation frequencies is detected if the oscillatingV0 crosses the paranematic–nematic phase transition.

Phase diagram of colloid-rod system

The semigrand ensemble theory [H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, and P. B. Warren, Europhys. Lett. 20, 559 (1992)] in conjunction with the fundamental measure density functional theory [V. B. Warshavsky and X. Song, Phys. Rev. E 69, 061113 (2004)] are used to construct the Helmholtz free energy densities of a mixture of uncharged colloidal hard spheres and colloidal rods in its solid and liquid phases. Given these free energy density functions, we apply the free energy density minimization method [G. F. Wang and S. K. Lai, Phys. Rev. E 70, 051402 (2004)] to crosshatch the system's regions of phases in coexistence. The calculated results show that the triangular area bounded by gas-liquid, gas-solid, and liquid-solid coexisting two phases which has been called the coexistence region of gas-liquid-solid corresponds in fact to sets of two phases in coexistence. The phase boundaries which define our calculated coexistence domains compare very well with previous theoretical calculations. The relevance of the phase-diagram domains to three phases in coexistence will be discussed.

Hard-sphere fluids in annular wedges: Density distributions and depletion potentials

We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density-functional theory, anisotropic integral equations, and simulations. We find that the main features of the density distribution in the slit are described by an effective two-dimensional system of disks in the vicinity of a central obstacle. This has an immediate consequence for the depletion force between the solutes (or the wall and the solute) since the latter receives a strong line-tension contribution due to the adsorption of the effective disks at the circumference of the central obstacle. For large solute-solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios of 5-10 and high solvent packing fractions larger than 0.4, the explicit density-functional results show a deep attractive well for the depletion potential at solute contact, possibly indicating demixing in a binary mixture at low solute and high solvent packing fraction besides the occurrence of gelation and freezing.

Energy Effects on the Structure and Thermodynamic Properties of Nanoconfined Fluids (A Density Functional Theory Study)

The structure and properties of fluids confined in nanopores may show a dramatic departure from macroscopic bulk fluids. The main reason for this difference lies in the influence of system walls. In addition to the entropic wall effect, system walls can significantly change the energy of the confined fluid compared to macroscopic bulk fluids. The energy effect of the walls on a nanoconfined fluid appears in two forms. The first effect is the cutting off of the intermolecular interactions by the walls, which appears for example in the integrals for calculation of the thermodynamic properties. The second wall effect involves the wall-molecule interactions. In such confined fluids, the introduction of wall forces and the competition between fluid-wall and fluid-fluid forces could lead to interesting thermodynamic properties, including new kinds of phase transitions not observed in the macroscopic fluid systems. In this article, we use the perturbative fundamental measure density functional theory to study energy effects on the structure and properties of a hard core two-Yukawa fluid confined in a nanoslit. Our results show the changes undergone by the structure and phase transition of the nanoconfined fluids as a result of energy effects.

Phase diagrams of binary alloys calculated from a density functional theory

Phase behaviors of binary alloys with an embedded atom model potential are investigated using the thermodynamic perturbation theory. The free energies of the liquid and solid phases are computed using the fundamental measure density functional theory and accurate approximations to the hard-sphere mixture correlation functions. The method is applied to calculate the Au-Cu alloy phase diagram. To improve the accuracy of the computed phase diagram, we developed a systematic approach to optimize the model potential of Au-Cu by adjusting the melting temperature of the pure Au to its experimental one. With such an optimized potential the computed Au-Cu alloy phase diagram is in good agreement with the experimental one for the whole composition range.

Structure and stability of isotropic states of hard platelet fluids

We study the thermodynamics and the pair structure of hard, infinitely thin, circular platelets in the isotropic phase. Monte Carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function, including nonmonotonical variation of some of the components with density. Integral equation theory is shown to reproduce the main features observed in simulations. The hypernetted chain closure, as well as its extended versions that include the bridge function up to second and third order in density, perform better than both the Percus-Yevick closure and Verlet bridge function approximation. Using a recent fundamental measure density functional theory, an analytic expression for the direct correlation function is obtained as the sum of the Mayer bond and a term proportional to the density and the intersection length of two platelets. This is shown to give a reasonable estimate of the structure found in simulations, but to fail to capture the nonmonotonic variation with density. We also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the Kerr coefficient vanishes. As a reference system, we compare to simulation results for hard oblate spheroids with small, but nonzero elongations, demonstrating that the case of vanishingly thin platelets is approached smoothly.

BEHAVIOR OF THE CONFINED HARD-SPHERE FLUID WITHIN NANOSLITS: A FUNDAMENTAL-MEASURE DENSITY-FUNCTIONAL THEORY STUDY

A property of central interest for theoretical study of nanoconfined fluids is the density distribution of molecules. The density profile of the hard-sphere fluids confined within nanoslit pores is a key quantity for understanding the configurational behavior of confined real molecules. In this report, we produce the density profile of the hard-sphere fluid confined within nanoslit pores using the fundamental-measure density-functional theory (FM-DFT). FM-DFT is a powerful approach to studying the structure and the phase behavior of nanoconfined fluids. We report the computational procedure and the calculated data for nanoslits with different widths and for a wide range of hard-sphere fluid densities. The high accuracy of the resulting density profiles and optimum grid-size values in numerical integration are verified. The data reveal a number of interesting features of hard spheres in nanoslits, which are different from the bulk hard-sphere systems. These data are also useful for a variety of purposes, including obtaining the shear stress, thermal conductivity, adsorption, solvation forces, free volume and prediction of phase transitions.

Fundamental measure density functional theory studies on the freezing of binary hard-sphere and Lennard-Jones mixtures

Free energies and correlation functions of liquid and solid hard-sphere (HS) mixtures are calculated using the fundamental measure density functional theory. Using the thermodynamic perturbation theory the free energies of solid and liquid Lennard-Jones (LJ) mixtures are obtained from correlation functions of HS systems within a single theoretical approach. The resulting azeotrope- and spindle-type solid-liquid phase diagrams of HS and LJ binary mixtures are in good agreement with the corresponding ones from computer simulations.

Density profiles and solvation forces for a Yukawa fluid in a slit pore

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.

Theoretical studies of the correlations in moderately asymmetric binary hard-sphere solid mixtures

A theoretical approach to calculate the correlation functions in binary hard-sphere (HS) solid mixtures is developed. The method is motivated by the theory of correlations in one-component HS solids [Rascon, Phys. Rev. E 54, 1261 (1996)] and the Kirkwood-Buff theory for solutions. Combined with the fundamental measure density functional theory the approach provides correlation functions in good agreement with the numerical simulations results for the moderately asymmetric mixtures.

Exact bulk correlation functions in one-dimensional nonadditive hard-core mixtures

In a recent paper [Phys. Rev. E 76, 031202 (2007)], Schmidt proposed a fundamental measure density functional theory for one-dimensional nonadditive hard-rod fluid mixtures and compared its predictions for the bulk structural properties with Monte Carlo simulations. The aim of this Brief Report is to recall that the problem admits an exact solution in the bulk, which is briefly summarized in a self-contained way.

Peel or coat spheres by convolution, repeatedly

A convolution transformation is presented that maps the four fundamental measures (Minkowski functionals) of a three-dimensional sphere to those of a sphere with a different radius. It is shown that the set of all these transformations, parametrized by the induced change in radius, forms an Abelian (commutative) group and hence constitutes a flexible framework for the manipulation of spheres. The corresponding one-dimensional case is laid out and the relationship to fundamental measure density functional theory is discussed briefly.

Hydration Structure and Interfacial Properties of Water near a Hydrophobic Solute from a Fundamental Measure Density Functional Theory

Using a density functional theory (DFT) based on Rosenfeld's formalism for hard spheres, we investigate the influence of model solutes of different sizes on the structure and interfacial properties...

Fundamental measure density functional theory for nonadditive hard-core mixtures: The one-dimensional case

We treat a one-dimensional binary mixture of hard-core particles that possess nonadditive diameters. For this model, a density functional theory is constructed following similar principles as an earlier extension of Rosenfeld's fundamental measure theory to three-dimensional nonadditive hard-sphere mixtures. The theory applies to arbitrary positive and moderate negative nonadditivity and reduces to Percus' exact functional in the additive case. Bulk direct correlation functions are obtained as functional derivatives of the excess free energy functional. Results for the partial pair correlation functions in bulk, as calculated via the Ornstein-Zernike route and using the direct correlation functions as input, show very good agreement with results from our Monte Carlo computer simulations of the mixture.

Fundamental-measure density functional theory study of the crystal-melt interface of the hard sphere system

Two versions of the fundamental measure density functionals together with a new interfacial density profile parametrization were used to study the hard-sphere crystal-melt interface in the framework of the fundamental measure density functional theory. The equilibrium interfacial density profiles and interfacial free energies were found as a result of minimization of grand canonical potential of system with respect to parameters of density profile. We found that the average interfacial free energy is about 0.78, which is in reasonable agreement with simulation results.