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.     

Relaxation and short time dynamics of bulk liquids and fluids confined in spherical cavities and slit pores

The density of states for bulk and confined fluids have been modeled using a recently proposed gamma distribution (Krishnan, S. H.; Ayappa, K. G. J. Chem. Phys. 2004, 121, 3197). The gamma distribution results in a closed form analytical expression for the velocity autocorrelation function and the relaxation time of the fluid. The two parameters of the gamma distribution are related analytically to the second and fourth frequency moments of the fluid using short time expansions. The predictions by the proposed gamma model are compared with the velocity autocorrelation functions obtained using the theory of instantaneous normal modes (INMs) and from molecular dynamics simulations. The model is applied to a bulk soft sphere liquid and fluids confined in a spherical cavity and slit-shaped pores. The gamma model is able to capture the resulting changes in relaxation time due to changes in density and temperature extremely well for both the bulk liquid and confined inhomogeneous fluid situations. In all cases, the predictions by the gamma model are superior to those obtained from the INM theory. In the case of the fluid confined in a slit pore, the loadings were obtained from a grand canonical Monte Carlo simulation where the pore is equilibrated with a bulk fluid. This is similar to a confinement situation in a surface force apparatus. The predicted relaxation times vs pore widths from the gamma model are seen to accurately capture the oscillations due to formation and disruption of layers within the slit pore.     

Using gamma distributions to predict self-diffusivities and density of states of fluids confined in carbon nanotubes

The density of states of rare gas atoms confined in carbon nanotubes is analyzed using a recently proposed model based on gamma distributions [Krishnan and Ayappa, J. Chem. Phys., 124 144503 (2006)]. The inputs into the model are the 2nd and 4th frequency moments that are obtained from molecular dynamics simulations. The predicted density of states, velocity autocorrelation functions and self-diffusivities are compared with those obtained from molecular dynamics simulations, for different nanotube loadings and temperatures. All results are reported for argon confined in a (16,16) carbon nanotube. The model predictions are extremely accurate at intermediate reduced densities of rhosigma(3) = 0.3, 0.4, where the majority of the self-diffusivity predictions lie within 10% of the simulation results. Since the frequency moments can be also obtained from Monte Carlo simulations, the study suggests an alternate route to the system dynamics of strongly confined fluids.     

Relationships between self-diffusivity, packing fraction, and excess entropy in simple bulk and confined fluids

Static measures such as density and entropy, which are intimately connected to structure, have featured prominently in modern thinking about the dynamics of the liquid state. Here, we explore the connections between self-diffusivity, density, and excess entropy for two of the most widely used model "simple" liquids, the equilibrium Lennard-Jones and square-well fluids, in both bulk and confined environments. We find that the self-diffusivity data of the Lennard-Jones fluid can be approximately collapsed onto a single curve (i) versus effective packing fraction and (ii) in appropriately reduced form versus excess entropy, as suggested by two well-known scaling laws. Similar data collapse does not occur for the square-well fluid, a fact that can be understood on the basis of the nontrivial effects that temperature has on its static structure. Nonetheless, we show that the implications of confinement for the self-diffusivity of both of these model fluids, over a broad range of equilibrium conditions, can be predicted on the basis of knowledge of the bulk fluid behavior and either the effective packing fraction or the excess entropy of the confined fluid. Excess entropy is perhaps the most preferable route due to its superior predictive ability and because it is a standard, unambiguous thermodynamic quantity that can be readily predicted via classical density functional theories of inhomogeneous fluids.     

Solvation force, structure and thermodynamics of fluids confined in geometrically rough pores

The effect of periodic surface roughness on the behavior of confined soft sphere fluids is investigated using grand canonical Monte Carlo simulations. Rough pores are constructed by taking the prototypical slit-shaped pore and introducing unidirectional sinusoidal undulations on one wall. For the above geometry our study reveals that the solvation force response can be phase shifted in a controlled manner by varying the amplitude of roughness. At a fixed amplitude of roughness, a, the solvation force for pores with structured walls was relatively insensitive to the wavelength of the undulation, lambda for 2.3/=0.5. The predictions of the superposition approximation, where the solvation force response for the rough pores is deduced from the solvation force response of the slit-shaped pores, was in excellent agreement with simulation results for the structured pores and for lambda/sigma(ff)>/=7 in the case of smooth walled pores. Grand potential computations illustrate that interactions between the walls of the pore can alter the pore width corresponding to the thermodynamically stable state, with wall-wall interactions playing an important role at smaller pore widths and higher amplitudes of roughness.     

Sublimation phenomena of Lennard-Jones fluids in slit nanopores

Using molecular dynamics simulations, The authors studied the solid-vapor coexistence states of Lennard-Jones methane confined in slit-shaped graphite nanopores. Both the intrapore solid and extrapore vapor were simulated using a unit cell which they previously developed. Frozen critical condensates in the pores were cooled stepwise, and the equilibrium vapor pressure was determined at each temperature. The obtained solid-vapor coexistence curves were remarkably lower than that of the bulk phase. Their thermodynamic model successfully predicts the simulation results without the need to introduce any adjustable parameter, and thus proves its reliability.     

Phase equilibria and plate-fluid interfacial tensions for associating hard sphere fluids confined in slit pores

The excess Helmholtz free energy functional for associating hard sphere fluid is formulated by using a modified fundamental measure theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 10156 (2002)]. Within the framework of density functional theory, the thermodynamic properties including phase equilibria for both molecules and monomers, equilibrium plate-fluid interfacial tensions and isotherms of excess adsorption, average molecule density, average monomer density, and plate-fluid interfacial tension for four-site associating hard sphere fluids confined in slit pores are investigated. The phase equilibria inside the hard slit pores and attractive slit pores are determined according to the requirement that temperature, chemical potential, and grand potential in coexistence phases should be equal and the plate-fluid interfacial tensions at equilibrium states are predicted consequently. The influences of association energy, fluid-solid interaction, and pore width on phase equilibria and equilibrium plate-fluid interfacial tensions are discussed.     

Anisotropic dynamics of dipolar liquids in narrow slit pores

We report molecular dynamics simulation results for Stockmayer fluids confined to narrow slitlike pores with structureless, nonconducting walls. The translational and rotational dynamics of the dipolar particles have been investigated by calculating autocorrelation functions, diffusion coefficients, and relaxation times for various pore widths (five or less particle diameters) and directions parallel and perpendicular to the walls. The dynamic properties of the confined systems are compared to bulk properties, where corresponding bulk and pore states at the same temperature and chemical potential are determined in parallel grand canonical Monte Carlo simulations. We find that the dynamic behavior inside the pore depends on the distance from the walls and can be strongly anisotropic even in globally isotropic systems. This concerns especially the particles in the surface layers close to the walls, where the single particle and collective dipolar relaxation resemble that of true two-dimensional dipolar fluids with different in-plane and out-of-plane relaxations. On the other hand, bulklike relaxation is observed in the pore center of sufficiently wide pores.     

Thermodynamic pressure of simple fluids confined in cylindrical nanopores by isothermal-isobaric Monte Carlo: influence of fluid/substrate interactions

The thermodynamic pressure or grand potential density is calculated by isobaric-isothermal Monte Carlo algorithm for simple Lennard-Jones fluid confined in cylindrical pores presenting chemical heterogeneities along their axis. Heuristic arguments and simulation results show that the thermodynamic pressure of the confined fluid contains two contributions. The first term is the usual pressure of the bulk fluid for a density equal to the confined fluid density defined as the total number of confined particles divided by the accessible volume due to thermal agitation. A second term has to be added, which is empirically shown to be proportional to the fluid/wall interface area and almost constant along the adsorption and desorption branches. This interfacial contribution, calculated for various pore models, has small variations reminiscent of the fluid adsorption/desorption properties calculated in the various pores. In particular, it is shown that this interfacial quantity is maximum for a fluid/substrate interaction intensity of the same order as the fluid/fluid one, while the thermodynamic pressure at which rapid desorption occurs presents a minimum. Stronger or weaker fluid/wall affinity favors gas state nucleation on the desorption of confined fluids.     

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.     

Dielectric response of polar liquids in narrow slit pores

Based on molecular dynamics (MD) simulations and a simple (Stockmayer) model we investigate the static and dynamic dielectric response of polar liquids confined to narrow slit pores. The MD simulations are used to calculate the time-dependent polarization fluctuations along directions parallel and perpendicular to the walls, from which the components of the frequency-dependent dielectric tensor can be derived via linear response theory. Our numerical results reveal that the system's response is strongly anisotropic. The parallel dielectric function, epsilonparallel(omega), has Debye-like character very similar to the corresponding isotropic bulk function, epsilonbulk(omega), at the same chemical potential. Indeed, the main confinement effect on epsilonparallel(omega) consists in a shift toward smaller values relative to the bulk function. On the other hand, in the perpendicular direction we observe a characteristic peak in the absorption part of the dielectric function, epsilonperpendicular(omega). This peak is absent in the bulk system and reflects strongly pronounced, damped oscillations in the polarization fluctuations normal to the walls. We discuss two possible origins of the oscillations (and the resulting absorption peak), that is collective oscillations of dipoles in clusters formed parallel to the walls, and the existence of a "dipolaron mode" previously observed in MD simulations of bulk polar fluids.     

Local density augmentation and dynamic properties of hydrogen-and non-hydrogen-bonded supercritical fluids: a molecular dynamics study

The local density inhomogeneities in neat supercritical fluids were investigated via canonical molecular dynamics simulations. The selected systems under investigation were the polar and hydrogen-bonded fluid methanol as well as the quadrupolar non-hydrogen-bonded carbon dioxide one. Effective local densities, local density augmentation, and enhancement factors were calculated at state points along an isotherm close to the critical temperature of each system (T(r)=1.03). The results obtained reveal strong influence of the polarity and hydrogen bonding upon the intensity of the local density augmentation. It is found that this effect is sufficiently larger in the case of the polar and associated methanol in comparison to those predicted for carbon dioxide. For both fluids the local density augmentation values are maximized in the bulk density region near 0.7rho(c), a result that is in agreement with experiment. In addition, the local density dynamics of each fluid were investigated in terms of the appropriate time correlation functions. The behavior of these functions reveals that the bulk density dependence of the local density reorganization times is very sensitive to the specific intermolecular interactions and to the size of the local region. Also, the estimated local density reorganization time as a function of bulk density of each fluid was further analyzed and successfully related to two different time-scale relaxation mechanisms. Finally, the results obtained indicate a possible relationship between the single-molecule reorientational dynamics and the local density reorganization ones.     

Freezing of Lennard-Jones fluid in cylindrical nanopores under tensile conditions

We have shown the Lennard-Jones (LJ) phase diagram for a slit-shaped nanopore by molecular simulations and thermodynamically predicted the results with no adjustable parameter. With this success, LJ phase diagrams are predictable. In this study, the freezing of an LJ CH₄ capillary condensate under a tensile condition in a nonstructural carbon nanopore with a cylindrical geometry was examined using molecular dynamics (MD) simulation. We employ a unit cell in contact with a bulk vapor phase, which is useful for the determination of the bulk vapor pressure in equilibrium with the molecules in a pore. The MD simulation results show liquid-solid (amorphous) phase transitions with a variation in the bulk vapor pressure. The frozen particles are arranged in concentric circular regions along the wall similar to those reported by Maddox and Gubbins. The freezing points are determined from the variations in density, enthalpy, arrangement, and structural functions. The obtained liquid-solid coexistence points are found to exhibit a significant dependence of the freezing point on the equilibrium bulk vapor pressure, forming an extraordinarily skewed curve on the p-T diagram, in contrast to the bulk phase coexistence that is represented by an almost vertical line. The origin of the significant dependence is considered to be the Laplace effect on the capillary condensate similar to the case with a slit-shaped pore. A simple model, which the authors earlier presented for slit-shaped nanopores, successfully predicted the p-T relation of the freezing point for cylindrical nanopores as well.     

A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. IV. The short time behavior of the memory function

Using a recently developed diagrammatic formulation of the kinetic theory of fluctuations in liquids, we investigate the short time behavior of the memory function for density fluctuations in a classical atomic fluid. At short times, the memory function has a large contribution that is generated by the repulsive part of the interatomic potential. We introduce a small parameter that is a measure of the softness of the repulsive part of the potential. The diagrams in the memory function that contribute to lowest order in that small parameter are identified and summed to give an explicit expression for the dominant contribution to the memory function at short times. The result leads to a theory for fluids with continuous potentials that is similar to the Enskog theory for hard sphere fluids.     

Vibrational dynamics of a glass forming liquid in nanoscopic confinement as probed by inelastic neutron scattering

In this article we present incoherent inelastic neutron scattering results, as a function of temperature, on the vibrational dynamics of a glass-forming liquid, namely propylene glycol, confined to the 26 Å pores of a controlled porous glass. The aim is to elucidate the effects induced by surface interactions (chemical traps) and geometrical restrictions (physical traps) on the fast microscopic dynamics of hydrogen-bonded liquids. The most prominent effect is the appearance of the ‘boson peak’ in the vibrational spectra. It is ascribed to an excess density of vibrational states due to quasilocalized collective atomic vibrations induced by confinement. A destructuring effect on the transient aggregates with the highest degree of connectivity, promoted by PG in the bulk phase, is hypothesized under confinement as a consequence of interactions, via hydrogen bond, between the hydroxyl groups (OH) of the PG molecule and the active silanol groups (Si–OH) on the surface of the porous glass.

Interfacial and/or finite-size effects are also found to give rise to a destructuring effect, under confinement, of the disordered Longitudinal Acoustic Mode, together with a broadening of the highest frequency torsional vibration and a stabilization, vs. T, of the internal CCO bending vibration.     

Constant-NTμ simulations: Free energy difference method for excess adsorption

We describe a new method to simulate confined fluids in equilibrium with a bulk. The equilibrium is first located at a low density, where conventional methods relying upon real or virtual particle exchanges are reliable. Thereafter, the chemical potential of the fluid is increased by the same amount in both systems using a variation of a recently developed free energy difference method in an isobaric (isotension) ensemble. The method, illustrated here for a simple fluid in a planar slit, is shown to be reliable up to high densities. As the method does not rely upon particle exchanges it is ideally suited to the simulation of equilibria in complex fluids, e.g., molecular liquids and polymers. © 1996 by John Wiley & Sons, Inc.     

Liquid-liquid phase separation of binary Lennard-Jones fluid in slit nanopores

The capillary phase separation of a binary mixture of two truncated and shifted Lennard-Jones (LJ) Ar liquids in slit-shaped oxygen nanopores is examined. The LJ parameters—ε(Ar(A)–Ar(A))=ε(Ar(B)–Ar(B))=0.8ε(Ar(A)–Ar(B)) and 0.5ε(Ar(A)–O)?=?ε(Ar(B)–O)—were used to distinguish the two Ar liquids. The cut off distance for Ar was 3.5σ. We employed a molecular dynamics (MD) technique in which a pore space was connected with a bulk solution to easily determine the equilibrium bulk concentration. Liquid phase isotherms were obtained for pores with widths ranging from 5.5σ to 9.5σ, and the relation between the pore width and the phase separation concentration was determined. Each simulation was run until the bulk concentration attained equilibrium (1–2 μs). The MD results show that the Patrick model overestimates the bulk concentration for a given pore size. We proposed a modified Patrick model in which the pore wall potential is considered. In our model, the Gibbs-Tolman-Koenig-Buff effect is not considered for the interfacial tension since two surfaces of tension exist on both sides of the equimolar dividing surface of the two-Ar liquid phase. The two surfaces of tension neutralized Gibbs-Tolman-Koenig-Buff effect each other. The present simple model successfully describes the relation to prove its reliability.     

微孔中简单流体扩散行为的分子动力学模拟研究

用分子动力学模拟方法研究了受限在微孔中的简单流体氩的扩散行为,考察了微孔类型、孔径、温度和密度对微孔中流体扩散系数的影响.研究发现,微孔中流体的扩散系数均小于体相流体,并且随孔径的减小而减小,同时沿孔道或狭缝方向的扩散系数分量远大于沿孔径方向的分量,并且流体在通道型微孔中的扩散系数小于在狭缝型微孔中的扩散系数,温度和密度也是影响微孔中扩散的重要因素.     

Behavior of ethylene and ethane within single-walled carbon nanotubes, 2: dynamical properties

The dynamical behavior of ethylene and ethane confined inside single-walled carbon nanotubes has been studied using Molecular Dynamics and a fully atomistic force field. Simulations were conducted at 300 K in a broad range of molecular densities, 0.026 mol⋅L⁻¹<ρ<15.751 mol⋅L⁻¹(C₂H₄) and 0.011 mol⋅L⁻¹<ρ<14.055 mol⋅L⁻¹(C₂H₆), and were oriented towards the determination of bulk and confined phase self-diffusion coefficients. In the infinite time limit, Fickian self-diffusion is the dominant mode of transport for the bulk fluids. Upon confinement, there is a density threshold (ρ=5.5 mol⋅L⁻¹) below which we observe a mixed mode of transport, with contributions from Fickian and ballistic diffusion. Nanotube topology seems to have only a small influence on the confined fluids’ dynamical properties; instead density (loading capacity) assumes the dominant role. In all cases studied and at a given density, the diffusivities of ethylene are larger than those of ethane, although the difference is relatively minor. We note the collapse of self-diffusivities obtained from the bulk fluids and confined phases into a unique single trend. These results suggest that it might be possible to infer dynamical properties of confined fluids from the knowledge of their bulk phase densities. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Ultrafast optical Kerr effect spectroscopy of water confined in nanopores of the gelatin gel

We report on the investigation of a short-time collective dynamics of water confined in the pores of the gelatin gel, using the femtosecond optical Kerr effect spectroscopy. The ultrafast responses of water molecules obtained in bulk liquid and in three concentrations of gelatin gels are explained theoretically, both in a long time and in a short time regime, taking into account all molecular motions. We prove that the contribution of molecules involved in tetrahedral, strongly H-bonded structures stabilizing the gel network increases with the gel concentration. On the other hand the long-time relaxation of water molecules is significantly slowed down in the gel pores.