Thermodynamics of d-dimensional hard sphere fluids confined to micropores

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss' interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of both approaches is to evaluate either the surface area or the volume of the d-dimensional exclusion sphere confined to a slit pore. We, further, present an analytical form of thermodynamic functions such as entropy and pressure tensor as a function of the size of the slit pore. Molecular dynamics simulations are performed for d = 2 and d = 3, and the results are compared with analytically obtained equations of state. They agree satisfactorily in the low density regime, and, for given density, the agreement of the results becomes excellent as the width of the slit pore gets smaller, because the higher order virial coefficients become unimportant.     

Density inhomogeneity and diffusion behavior of fluids in micropores by molecular-dynamics simulation

The density profiles and the diffusion behavior of fluid argon confined in micropores were studied by molecular-dynamics simulations. The effects of pore size (width), temperature and number density on the density profiles and the self-diffusion coefficients in micropores were simulated with pore widths from 0.6 to 4.0 nm. The density profiles are greatly affected by the pore size. Strong inhomogeneities in the channel direction and vapor-liquid phase separation in the micropores were observed when initial conditions were chosen in the coexistence region of the fluid. The self-diffusion coefficient in the channel direction in the pores was found to be much lower than in the bulk, and decreasing with decreasing pore size, decreasing temperature, and increasing density.     

Probing memory effects in confined fluids via diffusion measurements

Confinement of fluids in porous materials is widely exploited in a variety of technologies, including chemical conversion by heterogeneous catalysis and adsorption separations. Important fundamental phenomena associated with many-molecule interactions occur in such systems, including a remarkably long "memory" of the past when the actual amount of molecules in the pores dramatically depends on the history of how the external conditions have been changed. We demonstrate that the intrinsic diffusivity as measured by NMR serves as an excellent probe of the history-dependent states of the confined fluid. A remarkable feature of our results are differences in diffusivity between out-of-equilibrium states with the same density within the hysteresis loop. This reflects different spatial distributions of the confined fluid that accompany the arrested equilibration of the system in this region.     

Impact of surface roughness on diffusion of confined fluids

Using event-driven molecular dynamics simulations, we quantify how the self diffusivity of confined hard-sphere fluids depends on the nature of the confining boundaries. We explore systems with featureless confining boundaries that treat particle-boundary collisions in different ways and also various types of physically (i.e., geometrically) rough boundaries. We show that, for moderately dense fluids, the ratio of the self diffusivity of a rough wall system to that of an appropriate smooth-wall reference system is a linear function of the reciprocal wall separation, with the slope depending on the nature of the roughness. We also discuss some simple practical ways to use this information to predict confined hard-sphere fluid behavior in different rough-wall systems.     

Effect of micropores on the effective diffusion coefficient

The effective diffusion coefficient for catalysts differing in their porous structure has been derived from experimental data on H₂S conversion in the Claus reaction. The effective diffusion coefficient increases under conditions of catalyst deactivation due to sulfur condensation in micropores. A mathematical model is suggested to describe the micropore effect on the effective diffusion coefficient.     

Time-resolved photoluminescence characteristics of subnanometer ZnO clusters confined in the micropores of zeolites

Subnanometric ZnO clusters confined in different micropore zeolites are studied by steady-state and nanosecond time-resolved photoluminescence (PL) spectroscopy. The microsecond-scale lifetime is observed at room temperature for ZnO clusters confined in zeolites, which is significantly different from that of macrocrystalline ZnO on the external surface of zeolites. The dependence of luminescence lifetime on the amount of ZnO in zeolites indicates that the electron-phonon interactions between the ZnO clusters and the zeolite host significantly affect the dynamic relaxation process of ZnO clusters. The long lifetime luminescence of ZnO clusters can be achieved by weakening the coupling of electronic transition to zeolites host phonons. The similar long-lived luminescence is obtained when dispersing ZnO clusters into the porous SiO2. It is suggested that encapsulating the semiconductor cluster in the porous support is a possible way to inhibit or to retard the electron-hole recombination.     

Mean field kinetic theory for a lattice gas model of fluids confined in porous materials

We consider the mean field kinetic equations describing the relaxation dynamics of a lattice model of a fluid confined in a porous material. The dynamical theory embodied in these equations can be viewed as a mean field approximation to a Kawasaki dynamics Monte Carlo simulation of the system, as a theory of diffusion, or as a dynamical density functional theory. The solutions of the kinetic equations for long times coincide with the solutions of the static mean field equations for the inhomogeneous lattice gas. The approach is applied to a lattice gas model of a fluid confined in a finite length slit pore open at both ends and is in contact with the bulk fluid at a temperature where capillary condensation and hysteresis occur. The states emerging dynamically during irreversible changes in the chemical potential are compared with those obtained from the static mean field equations for states associated with a quasistatic progression up and down the adsorption/desorption isotherm. In the capillary transition region, the dynamics involves the appearance of undulates (adsorption) and liquid bridges (adsorption and desorption) which are unstable in the static mean field theory in the grand ensemble for the open pore but which are stable in the static mean field theory in the canonical ensemble for an infinite pore.     

Phase behavior of model confined fluids. Influence of substrate-fluid interaction strength

We examine the relationship between the macroscopic phase behavior of nanoconfined fluids and the nature of microscopic interactions between a confining substrate and fluid. Two model slit-pore systems are explored using grand canonical transition-matrix Monte Carlo simulation. One system consists of a square-well fluid interacting with a square-well substrate, and the other contains an embedded point charge model of lysozyme interacting with a mica surface. Fluid phase diagrams are constructed for a broad range of substrate conditions. Our results indicate that one observes a maximum in the critical temperature of the fluid phase envelope upon variation of substrate strength for a given slit width. Both systems studied exhibit such maxima at intermediate wall strength. The physical rationale for this observation suggests that this behavior should be generally expected. We introduce two metrics that enable one to predict conditions that produce maxima in critical temperature. The first is related to the contact angle a fluid develops at a single confining substrate. The second is based upon virial coefficient information and requires knowledge of the substrate-fluid and fluid-fluid interaction potentials only.     

Local linear viscoelasticity of confined fluids

In this paper the authors propose a novel method to study the local linear viscoelasticity of fluids confined between two walls. The method is based on the linear constitutive equation and provides details about the real and imaginary parts of the local complex viscosity. They apply the method to a simple atomic fluid undergoing zero mean oscillatory flow using nonequilibrium molecular dynamics simulations. The method shows that the viscoelastic properties of the fluid exhibit dramatic spatial changes near the wall-fluid boundary due to the high density in this region. It is also shown that the real part of the viscosity converges to the frequency dependent local shear viscosity sufficiently far away from the wall. This also provides valuable information about the transport properties in the fluid, in general. The viscosity is compared with predictions from the local average density model. The two methods disagree in that the local average density model predicts larger viscosity variations near the wall-fluid boundary than what is observed through the method presented here.     

Viscosity of confined inhomogeneous nonequilibrium fluids

We use the nonlocal linear hydrodynamic constitutive model, proposed by Evans and Morriss [Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)], for computing an effective spatially dependent shear viscosity of inhomogeneous nonequilibrium fluids. The model is applied to a simple atomic fluid undergoing planar Poiseuille flow in a confined channel of several atomic diameters width. We compare the spatially dependent viscosity with a local generalization of Newton's law of viscosity and the Navier-Stokes viscosity, both of which are known to suffer extreme inaccuracies for highly inhomogeneous systems. The nonlocal constitutive model calculates effective position dependent viscosities that are free from the notorious singularities experienced by applying the commonly used local constitutive model. It is simple, general, and has widespread applicability in nanofluidics where experimental measurement of position dependent transport coefficients is currently inaccessible. In principle the method can be used to predict approximate flow profiles of any arbitrary inhomogeneous system. We demonstrate this by predicting the flow profile for a simple fluid undergoing planar Couette flow in a confined channel of several atomic diameters width.     

Local structure and density fluctuations in confined fluids

Spatial confinement modifies the microscopic structure of dense fluids, thereby inducing for example structural forces between the confining walls. However, confinement also modifies the fluids' density fluctuations, resulting in more elusive but equally important effects. In this brief review it is shown that both of these phenomena are naturally analyzed using the confined fluid's pair densities, which have recently become also experimentally accessible. Two particular topics are discussed, namely, the mechanisms of oscillatory density profiles and ensuing solvation forces in dense confined fluids as well as the behavior of liquids in solvophobic confinement.     

Modeling velocity autocorrelation functions for confined fluids using gamma distributions

We propose a model for the short-time dynamics of fluids confined in slit-shaped pores. The model has been developed from the observation that the real lobe of the instantaneous normal mode density of states (INM DOS) closely follows a gamma distribution. By proposing that the density of states of the confined fluid can be represented by a gamma distribution, the resulting velocity autocorrelation function (VACF) is constructed such that it is accurate upto the fourth frequency moment. The proposed model results in an analytical expression for the VACF and relaxation times. The VACFs obtained from the model have been compared with the VACFs obtained from molecular dynamic simulations and INM analysis for fluids confined in slit-shaped pores over a wide range of confinement and temperatures. The model is seen to capture the short-time behavior of the VACF extremely accurately and in this region is superior to the predictions of the VACF obtained from the real lobe of the INM DOS. Although the model predicts a zero self-diffusivity, the predicted relaxation times are in better agreement with the molecular dynamics results when compared with those obtained from the INM theory.     

Freezing of fluids confined between mica surfaces

Using grand ensemble simulations, we show that octamethyl-cyclo-tetra-siloxane (OMCTS) confined between two mica surfaces can form a variety of frozen phases which undergo solid-solid transitions as a function of the separation between the surfaces. For atomically smooth mica surfaces, the following sequence of transitions 1[triangle up] --> 1[triangle up]b --> 2B --> 2 square --> 2[triangle up] are observed in the one- and two-layered regimes, where n[triangle up], n[square], and nB denote triangular, square, and buckled phases, respectively, with the prefix n denoting the number of confined layers. The presence of potassium on mica is seen to have a strong influence on the degree of order induced in the fluid. The sequence of solid-solid transitions that occurs with the smooth mica surface is no longer observed. When equilibrated with a state point near the liquid-solid transition, a counterintuitive freezing scenario is observed in the presence of potassium. Potassium disrupts in-plane ordering in the fluid in contact with the mica surface, and freezing is observed only in the inner confined layers. The largest mica separations at which frozen phases were observed ranged from separations that could accommodate six to seven fluid layers. The extent of freezing and the square-to-triangular lattice transition was found to be sensitive to the presence of potassium as well as the thermodynamic conditions of the bulk fluid. The implications of our results on interpretation of surface force experiments as well as the generic phase behavior of confined soft spheres is discussed.     

Dielectric permittivity profiles of confined polar fluids

The dielectric response of a simple model of a polar fluid near neutral interfaces is examined by a combination of linear response theory and extensive molecular dynamics simulations. Fluctuation expressions for a local permittivity tensor epsilon(r) are derived for planar and spherical geometries, based on the assumption of a purely local relationship between polarization and electric field. While the longitudinal component of epsilon exhibits strong oscillations on the molecular scale near interfaces, the transverse component becomes ill defined and unphysical, indicating nonlocality in the dielectric response. Both components go over to the correct bulk permittivity beyond a few molecular diameters. Upon approaching interfaces from the bulk, the permittivity tends to increase, rather than decrease as commonly assumed, and this behavior is confirmed for a simple model of water near a hydrophobic surface. An unexpected finding of the present analysis is the formation of "electrostatic double layers" signaled by a dramatic overscreening of an externally applied field inside the polar fluid close to an interface. The local electric field is of opposite sign to the external field and of significantly larger amplitude within the first layer of polar molecules.     

A mathematical model for stress-driven diffusion in polymers

A model for case II diffusion into polymers is presented. The addition of stress terms to the Fickian flux is used to produce the characteristics progressive front. The stress in turn obeys a concentration-dependent evolution equation. The model equations are analyzed in the limit of small diffusivity for the problem of penetration into a semiinfinite medium. Provided that the coefficient functions obey two monotonicity conditions, the solvent concentration profile is shown to have a steep front that progresses into the medium. The formulas governing the progression of the front are developed. After the front decays away, the long time behavior of the solution is shown to be a similarity solution as in Fickian diffusion. Two techniques for approximating the solvent concentration and the front position are presented. The first approximation method is a series expansion; formulas are given for the initial speed and deceleration of the front. The second approximation method uses a portion of the long time similarity solution to represent the short time solution behind the front.     

Longitudinal and volume viscosities of fluids confined in nanochannel

Longitudinal and volume viscosities of Lennard-Jones fluid, argon–krypton binary mixture and isotopic fluid mixture confined to nanochannels of different widths are calculated by employing theoretical technique based on Green–Kubo formula. A significant enhancement is observed in longitudinal and volume viscosities when width of the nanochannel is less than 10 nm. Effect of mass ratio of two species on longitudinal and volume viscosities is also studied for equimolar isotopic fluid mixture. It is found that enhancement in viscosity is more for larger mass ratios. It is also noted that enhancement in longitudinal and shear viscosities is more than volume viscosity.     

Anisotropic diffusion in confined colloidal dispersions: the evanescent diffusivity

We employ an analogy to traditional dynamic light scattering to describe the inhomogeneous and anisotropic diffusion of colloid particles near a solid boundary measured via evanescent wave dynamic light scattering. Following this approach, we generate new expressions for the short-time self- and collective diffusivities of colloidal dispersions with arbitrary volume fraction. We use these expressions in combination with accelerated Stokesian dynamics simulations to calculate the diffusivities in the limit of large and small scattering wave numbers for evanescent penetration depths ranging from four particle radii to one-fifth of a particle radius and volume fractions from 10% to 40%. We show that at high volume fractions, and larger penetration depths, the boundaries have little effect on the dynamics of the suspension parallel to the wall since, to a first approximation, the boundary acts hydrodynamically much as another nearby particle. However, near and normal to the wall, the diffusivity shows a strong dependence on penetration depth for all volume fractions. This is due to the lubrication interactions between the particles and the boundary as the particle moves relative to the wall. These results are novel and comprehensive with respect to the range of penetration depth and volume fraction and provide a complete determination of the effect of hydrodynamic interactions on colloidal diffusion adjacent to a rigid boundary.     

Thermodynamic and structural properties of confined discrete-potential fluids

The thermodynamic and structural behaviors of confined discrete-potential fluids are analyzed by computer simulations, studying in a systematic way the effects observed by varying the density, temperature, and parameters of the potentials that characterize the molecule-molecule interactions. The Gibbs ensemble simulation technique for confined fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is applied to a fluid confined between two parallel hard walls. Two different systems have been considered, both formed by spherical particles that differ by the interparticle pair potential: a square well plus square shoulder or a square shoulder plus square well interaction. These model interactions can describe in an effective way pair potentials of real molecular and colloidal systems. Results are compared with the simpler reference systems of square-shoulder and square-well fluids, both under confinement. From the adsorption characterization through the use of density profiles, it is possible to obtain specific values of the interparticle potential parameters that result in a positive to negative adsorption transition.     

Equivalence of nonequilibrium algorithms for simulations of planar Couette flow in confined fluids

Shear flow in fluids confined between planar solid walls is conventionally simulated by moving the walls past each other at constant relative velocity. In infinite fluids (in periodic boundary conditions), it is simulated using one of the "synthetic" nonequilibrium algorithms (the so-called Sllod and Dolls algorithms). Here I formulate the boundary conditions for the motion of confining walls that make these three algorithms equivalent in the weak-field limit.