Density Profiles Of Fluid Research Articles

On the interplay between sedimentation and phase separation phenomena in two-dimensional colloidal fluids

Colloidal particles that are confined to an interface effectively form a two-dimensional fluid. We examine the dynamics of such colloids when they are subject to a constant external force, which drives them in a particular direction over the surface. Such a situation occurs, for example, for colloidal particles that have settled to the bottom of their container, when the container is tilted at an angle, so that they ‘sediment’ to the lower edge of the surface. We focus in particular on the case when there are attractive forces between the colloids which causes them to phase separate into regions of high density and low density and we study the influence of this phase separation on the sedimentation process. We model the colloids as Brownian particles and use both Brownian dynamics computer simulations and dynamical density functional theory (DDFT) to obtain the time evolution of the ensemble average one-body density profiles of the colloids. We consider situations where the external potential varies only in one direction so that the ensemble average density profiles vary only in this direction. We solve the DDFT in one-dimension, by assuming that the density profile only varies in one direction. However, we also solve the DDFT in two dimensions, allowing the fluid density profile to vary in both the x- and y-directions. We find that in certain situations the two-dimensional DDFT is clearly superior to its one-dimensional counterpart when compared with the simulations and we discuss this issue.

Effect of critical fluctuations on adsorption of van der Waals fluid in a spherical cavity

A recently proposed non-uniform fifth-order thermodynamic perturbation theory (TPT) is employed to investigate the adsorption of a hard core attractive Yukawa (HCAY) fluid in a spherical cavity. Extensive comparison with available simulation data indicate that the non-uniform fifth-order TPT is sufficiently reliable in calculating the density profiles of the HCAY fluid in the highly confining geometry, and generally is more accurate than a previous third-order + second-order perturbation density functional theory. The non-uniform fifth-order TPT is free from numerically solving an Ornstein–Zernike integral equation, and also free of any adjustable parameter; consequently, it can be applied to both supercritical and subcritical temperature regions. The non-uniform fifth-order TPT is employed to investigate critical adsorption of the HCYA fluid in a single spherical cavity – it is disclosed that the critical fluctuations near the critical point induce depletion adsorption – quantitative theoretical calculation on relationship between the critical depletion adsorption, parameters of coexistence bulk phase and the responsible external field is in agreement with qualitative physical analysis.

Density Profile and Solvation Force for Hyperbranched Polymerization Fluids Confined in Parallel Plates

Within the framework of density functional theory(DFT),a free energy function was formulated in terms of modified fundamental measure theory(MFMT) for hard sphere repulsion and statistical mechanic theory with the weighted density approximation(WDA) for polymerization.A chemical potential for ABg hyperbranched polymerization fluids was determined and an expression of the density profiles of the polymerization fluids confined in parallel plates was derived.The influence of the reaction conversion,the volume fraction,and the number of B-kind functional groups on density profiles was discussed.Furthermore,the relationship between the reaction conversion or the plate width and solvation forces was also analyzed in terms of density profiles.

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.

Grating-based holographic X-ray diffraction: theory and application to confined fluids

A grating-based holographic X-ray diffraction technique has been developed for reconstructing density profiles of nano-scale fluids confined in channel arrays. Within this approach, the reference wave is due to diffraction from the fabricated channel array, whereas the object wave is generated by the confinement-induced ordering of the fluid. The ensemble-averaged density profile of the fluid across the confining channel, which constitutes a weak phase object, is then determined in a model-independent manner from the interference between the reference and object waves by direct Fourier inversion. The validity of the linear holographic approach and its connection to the autocorrelation function, the inclusion of channel tapering, and volume-diffraction effects are discussed in detail.

Interfacial properties of the Mie n−6 fluid: Molecular simulations and gradient theory results

In a first part, interfacial properties of a pure monoatomic fluid interacting through the Mie n-6 potential (n=8, 10, 12, and 20) have been studied using extensive molecular simulations. Monte Carlo and molecular dynamics simulations have been employed, using, respectively, the test area approach and the mechanic route. In order to yield reference values, simulations have been performed with a cutoff radius equal to 10sigma, which is shown to be sufficient to avoid long range corrections. It is shown that both approaches provide results consistent with each other. Using the molecular simulations results, it is demonstrated that a unique scaling law is able to provide an accurate estimation of the surface tension whatever the repulsive exponent n, even far from the critical point. Furthermore, it is shown that the surface tension of the Mie n-6 fluid is as well accurately described by a unique Parachor's law. Density profiles are shown to be well represented by the tanh mean field profile, with slight deviations for the lowest temperatures and the smallest n. In addition, the interfacial width is shown to increase when n decreases (for a given reduced temperature) and to follow the usual scaling behavior for not too low temperature. In a second part, interfacial properties of the Mie n-6 fluid computed by the gradient theory, coupled with an equation of state based on the Barker-Henderson perturbation theory, have been compared with those obtained by molecular simulations. It is demonstrated that, even far from the critical point, the gradient theory is efficient to compute surface tensions and density profiles of this model fluid, provided the equation of state accurately model the phase behavior of the fluid involved (which is not the case for n=8 in this study).

STRUCTURE OF CONFINED HARD ELLIPSES USING MOLECULAR DENSITY FUNCTIONAL THEORY

Density functional (DF) theory is used to study confined two-dimensional molecular fluids. The approximate DF used here is based upon a functional Taylor series expansion of the excess grand potential about the density of a uniform molecular liquid. This formalism is applied to obtain the density profiles of the hard-ellipse fluid confined between two parallel hard walls. The required direct correlation function is obtained using Percus–Yevick and hypernetted chain approximations for low- and high-number density, respectively. Both the restricted orientation model and the extension of this model are used. Generally, we obtained that the number density of the hard ellipses with the major axes parallel to the wall is larger near the walls than the other directions. To check the results, we show that for isotropic hard-ellipse fluids the average number density in the middle of the wall is almost equal to the bulk density and as we expect the average number density of the ellipses at the wall is nearly equal to the amount of the reduced pressure, βP. We also perform Monte Carlo simulation and find reasonable agreement with our results.

Dynamical density functional theory for molecular and colloidal fluids: A microscopic approach to fluid mechanics

In recent years, a number of dynamical density functional theories (DDFTs) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is overdamped and also in the regime where inertial effects are relevant. In this paper, we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation, which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalization of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium density functional theory (DFT). For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.

Interfacial and wetting properties of a binary point Yukawa fluid

We investigate the interfacial phase behavior of a binary fluid mixture composed of repulsive point Yukawa particles. Using a simple approximation for the Helmholtz free energy functional, which yields the random phase approximation for the pair direct correlation functions, we calculate the equilibrium fluid density profiles of the two species of particles adsorbed at a planar wall. We show that for a particular choice (repulsive exponential) of the wall potentials and the fluid pair-potential parameters, the Euler-Lagrange equations for the equilibrium fluid density profiles may be transformed into a single ordinary differential equation and the profiles obtained by a simple quadrature. For certain other choices of the fluid pair-potential parameters fluid-fluid phase separation of the bulk fluid is observed. We find that when such a mixture is exposed to a planar hard wall, the fluid exhibits complete wetting on the species 2 poor side of the binodal, i.e., we observe a thick film of fluid rich in species 2 adsorbed at the hard wall. The thickness of the wetting film grows logarithmically with the concentration difference between the fluid state point and the binodal and is proportional to the bulk correlation length of the intruding (wetting) fluid phase. However, for state points on the binodal that are further from the critical point, we find there is no thick wetting film. We determine the accompanying line of first-order (prewetting) surface phase transitions which separate a thin and thick adsorbed film. We show that for some other choices of repulsive wall potentials the prewetting line is still present, but its location and extent in the phase diagram is strongly dependent on the wall-fluid interaction parameters.

Nonmonotonic crossover from adsorption to desorption in supercritical fluid near a weakly attractive surface

The density profiles of a supercritical Lennard-Jones fluid near a weakly attractive surface are used to study the excess adsorption Gamma of supercritical fluid in a wide density range. We report the observation of two extrema of Gamma along the isotherm as a function of density. The attractive fluid-wall interaction potential tends to make Gamma positive, whereas the missing neighbor effect tends to make Gamma negative. The latter effect enhances with increasing fluid density due to the growth of the fluid-fluid attraction that results in the crossover from adsorption to depletion (Gamma=0) at some particular fluid density. With approaching the critical point, Gamma decreases as the bulk correlation length and passes through a minimum when the average density of confined fluid is close to the bulk critical density. Variation of Gamma with temperature and density is determined by the monotonic trend from adsorption to desorption upon increasing fluid density and by the increase of the absolute value of Gamma when approaching the critical point. Interplay of these trends results in two extrema of Gamma in the temperature-density plane. This effect may be responsible for the crossover from adsorption to desorption with approaching the critical temperature observed experimentally along the isotherms and along the critical isochore. The density profiles of a supercritical fluid are found to be exponential and the power law behavior predicted theoretically was not detected even when the bulk correlation length xi achieves 11 molecular diameters.

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.

Effect of Fluid-Solid Interactions on Symmetry Breaking in Closed Nanoslits

The possibility of symmetry breaking of the fluid (argon) density distribution across a long closed slit with identical walls composed of solid carbon dioxide was noted in previous papers by the authors. The main conclusion was that there is a range of average densities in which symmetry breaking occurs and that outside that range the fluid density profile is symmetrical. A critical temperature T(sb) was also identified below which symmetry breaking can occur. In this paper, symmetry breaking is examined for walls made of other materials and it is shown that it occurs only when the energy parameter epsilon(fw) of the fluid-wall interaction in the Lennard-Jones potential satisfies the inequalities epsilon(fw1) < or = epsilon(fw) < or = epsilon(fw2), where epsilon(fw1) and epsilon(fw2) are temperature-dependent critical values of epsilon(fw). The value of epsilon(fw1) increases and that of epsilon(fw2) decreases with increasing temperature. The comparison of the theory with Monte Carlo simulations confirms the existence of symmetry breaking across the slit. The possibility of symmetry breaking along the slit is also noted.

Interfacial properties of Morse fluids

The interfacial properties as reflected in the interfacial tension values and the density profile of Morse fluids has been studied. The parameter range is chosen to coincide with that describing the behaviour of solid metals. The interfacial tension has been found to follow Guggenheim's and MacLeod's relations. However, the constants, while independent of temperature for each metal, are not the universal values predicted; with the exception of Macleod's exponent p. The density profile illustrates the change in densities across the interface dividing the coexisting vapour and liquid phases. The correlation length is also found to follow the universal relation with temperature, but again the constants, while independent of temperature, are dependent on the type of metal. The value of constant ν is found to be different for all five metals considered and is found to differ from the three-dimensional Ising model value of ν = 0.630, which is also predicted by applying the Lennard–Jones model.

Symmetry breaking of the fluid density profiles in closed nanoslits

The density profiles in a fluid interacting with the two identical solid walls of a closed long slit were calculated for wide ranges of the number of fluid molecules in the slit and temperature by employing a nonlocal density functional theory. Using argon as the sample fluid and considering the walls composed of solid carbon dioxide, it is shown that the density profile corresponding to the stable state of the fluid considerably changes its shape with increasing average density rho(av) of the fluid inside the slit. Temperature dependent critical values rho(sb1) and rho(sb2) of rho(av) were identified, such that for rho(sb1)<or=rho(av)<or=rho(sb2) the stable state of the system is described by an asymmetric density profile whereas outside this range it is described by a symmetric one. Hence a spontaneous symmetry breaking of the fluid density distribution in a closed slit with identical walls can take place. On the basis of the results obtained for closed slits, the symmetry breaking in open slits was also examined.

Fluid Density Profile Transitions and Symmetry Breaking in a Closed Nanoslit

The density profiles in a fluid interacting with the two identical solid walls of a closed long slit were calculated for wide ranges of the number of fluid molecules in the slit and temperature by employing density functional theory in the local density approximation. Two potentials, the van der Waals and the Lennard-Jones, were considered for the fluid-fluid and the fluid-walls interactions. It was shown that the density profile corresponding to the stable state of the fluid considerably changes its shape with increasing average density (rhoav) of the fluid inside the slit, the details of changes being dependent on the selected potential. For the van der Waals potential, a single temperature-dependent critical value rhosb of rhoav was identified, such that for rhoav < rhosb the stable state of the system is described by a symmetric density profile, whereas for rhoav >/= rhosb it is described by an asymmetric one. This transition constitutes a spontaneous symmetry breaking of the fluid density distribution in a closed slit with identical walls. For rhoav >/= rhosb, a metastable state, described by a symmetric density profile, was present in addition to the stable asymmetric one. The shape of the symmetric profile changed suddenly at a value rhoc-h > rhosb of the average density, the density rhoc-h being almost independent of temperature. Because of the shapes of the profiles before and after the transformation, this transition was named cup-hill transformation. At the transition point, the density of the fluid near the walls decreased suddenly from a liquid-like value becoming comparable with the density of a gaseous phase, and the density in the middle of the slit increased suddenly from a gaseous-like value becoming on the order of the density of a liquid phase. For the Lennard-Jones potential, there are two temperature-dependent critical densities, rhosb1 and rhosb2, such that the stable density profile is asymmetric (symmetry breaking occurs) for rhosb1 </= rhoav </= rhosb2 and symmetric for rhoav outside of the latter interval. These critical densities occur only for temperatures lower than a certain temperature, Tsb,0. The cup-hill transition is similar to that for the van der Waals potential at low temperatures but becomes smoother with increasing temperature.

Confinement-induced liquid ordering investigated by x-ray phase retrieval

Using synchrotron x-ray diffraction, we have determined the ensemble-averaged density profile of colloidal fluids within confining channels of different widths. We observe an oscillatory ordering-disordering behavior of the colloidal particles as a function of the channel width, while the colloidal solution remains in the liquid state. This phenomenon has been suggested by surface force studies of hard-sphere fluids and also theoretically predicted, but here we see it by direct measurements of the structure for comparable systems.

Thermodynamic perturbation theory in fluid statistical mechanics

A methodology is proposed that pushes the thermodynamic perturbation theory (TPT) from first order to higher order. The second-order correction is superior to a macroscopic compressibility (MC) approximation of Barker and Henderson. The present third-order TPT performs far better than the original first-order TPT and second-order TPT based on the MC approximation for many subfields in fluid statistical mechanics, such as predicting excess Helmholtz free energy, excess chemical potential, bulk pressure, gas-liquid coexistence, and solid-liquid equilibrium of very short-range potential fluids. A nonuniform version of the TPT is proposed; it is also shown that the nonuniform third-order TPT performs far better than the nonuniform first-order TPT in predicting density profile of fluids in critical region. The present report indicates that the TPT still can be a "universal" and accurate theoretical tool that has general applicability in fluid statistical mechanics, especially in soft-matter physics.

Dynamical density functional theory for dense atomic liquids

Starting from Newton’s equations of motion, we derive a dynamical density functionaltheory (DDFT) applicable to atomic liquids. The theory has the feature that it requires asinput the Helmholtz free energy functional from equilibrium density functionaltheory. This means that, given a reliable equilibrium free energy functional, thecorrect equilibrium fluid density profile is guaranteed. We show that when theisothermal compressibility is small, the DDFT generates the correct value for thespeed of sound in a dense liquid. We also interpret the theory as a dynamicalequation for a coarse grained fluid density and show that the theory can be used(making further approximations) to derive the standard mode coupling theorythat is used to describe the glass transition. The present theory should provide auseful starting point for describing the dynamics of inhomogeneous atomic fluids.

Further Test of Third Order + Second-Order Perturbation DFT Approach: Hard Core Repulsive Yukawa Fluid Subjected to Diverse External Fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.

DENSITY FUNCTIONAL APPROXIMATION FOR NON-HARD SPHERE FLUIDS SUBJECTED TO EXTERNAL FIELDS

A theoretical way is proposed, by which any hard sphere density functional approximation (DFA) can be applied to non-hard sphere fluids for the calculation of density profile in the framework of density functional theory (DFT). Used as examples, the present formalism is combined respectively with two recently proposed hard sphere DFAs to predict the density profile of Lennard–Jones (LJ) fluid, hard core square well (SW) fluid and penetrable potenial fluid subjected to diverse external fields. Extensive comparison between theoretical predictions and corresponding simulation results shows that the present theoretical way, when combined with an accurate hard sphere DFA, can perform well for calculating the density profile of the non-uniform fluids of the above mentioned potentials. Concretely speaking, for LJ and hard core SW fluid, even a less accurate FEDFA is sufficient, while for extreme potential such as the penetrable potenial, a more accurate adjustable parameter free version of LTDFA is needed to combine with the present theoretical way to predict density profile satisfactorily. The advantage of the proposed theoretical way is that the resultant DFA is applicable to both subcritical and supercritical temperature cases, thereby overcoming the disadvantages of previous two categories of DFT approach.