Model for dynamics of inhomogeneous and bulk fluids

An accurate model for the density of states (DOS) for strongly inhomogeneous and bulk fluids has been proposed based on gamma distributions. The contribution to the density of states from the collective dynamics is modeled as an incomplete gamma distribution and the high frequency region is obtained from the solution of the memory equation using a sech memory kernel. Using only the frequency moments as input, the model parameters for the collective dynamics are obtained by matching moments of the resulting distribution. The model results in an analytical expression for the self-diffusivity of the fluid. We present results for soft sphere fluids confined in slit-shaped pores as well as bulk soft sphere liquids. Comparisons of the DOS, velocity autocorrelation functions, and memory kernels with molecular dynamics simulations reveal that the model predicts features in the DOS over the entire frequency range and is able to capture changes in the DOS as a function of fluid density and temperature. As a result the predicted VACFs, memory kernels, and self-diffusivities are accurately predicted over a wide range of conditions. Since the frequency moments for bulk liquids can be obtained from pair correlation functions, our method provides a direct route from fluid structure to dynamics. For fluids confined in slit-shaped pores, where the frequency moments are obtained from molecular dynamics simulations, the predicted self-diffusivities capture the resulting oscillations due to variations in the solvation pressure, and in the case of smooth walled pores, the predictions are superior to those obtained using kinetic theory.     

Solvation forces between molecularly rough surfaces

Surface heterogeneity affects significantly wetting and adhesion properties. However, most of the theories and simulation methods of calculating solid-fluid interactions assume a standard thermodynamic model of the Gibbs' dividing solid-fluid interface, which is molecularly smooth. This assumption gives rise to a layering of the fluid phase near the surface that is displayed in oscillating density profiles in any theories and simulation models, which account for the hard core intermolecular repulsion. This layering brings about oscillations of the solvation (or disjoining) pressure as a function of the gap distance, which are rarely observed in experiments, except for ideal monocrystal surfaces. We present a detailed study of the effects of surface roughness on the solvation pressure of Lennard-Jones (LJ) fluids confined by LJ walls based on the quenched solid density functional theory (QSDFT). In QSDFT, the surface roughness is quantified by the roughness parameter, which represents the thickness of the surface "corona" - the region of varying solid density. We show that the surface roughness of the amplitude comparable with the fluid molecular diameter effectively damps the oscillations of solvation pressure that would be observed for molecularly smooth surfaces. The calculations were done for the LJ model of nitrogen sorption at 74.4 K in slit-shaped carbon nanopores to provide an opportunity of comparing with standard adsorption experiments. In addition to a better understanding of the fundamentals of fluid adsorption on heterogeneous surfaces and inter-particle interactions, an important practical outcome is envisioned in modeling of adsorption-induced deformation of compliant porous substrates.     

Solid deformation induced by the adsorption of methane and methanol under sub- and supercritical conditions

Carbonaceous materials with some degree of flexibility in their physical structure can expand or contract under the influence of the forces exerted by adsorbed molecules. To gain insight into how adsorption of non-polar and polar fluids could deform a carbon solid, we present GCMC simulations of sub- and supercritical adsorption of methane and methanol in slit-shaped pores whose walls are made of graphene layers. Our extensive simulation study shows that there is a strong correlation between solvation pressure and solid deformation, and that the expansion or contraction of the pore strongly depends on adsorbate loading, temperature and pore size.     

Calculation of the adsorption-desorption hysteresis curves in narrow-pore systems

The gas and liquid spinodal branches for an adsorbate located in narrow slit-shaped, cylindrical, and spherocylindrical pores were calculated. The adsorbate is modeled by Lennard-Jones spherical particles. The calculation was based on the lattice gas model taking into account the intermolecular interactions of nearest neighbors in the quasichemical approximation. The density-temperature diagrams for the gas and liquid spinodal branches in the pores are similar to the equilibrium vapor-liquid phase diagrams: they have a common critical point; the dense-phase branches are shifted to lower pore fillings, while the rarefied-phase branches are shifted toward higher pore fillings. The width of adsorption-desorption hysteresis loop in the adsorption isotherms for Lennard-Jones particles was analyzed as a function of the pore size and the interaction potential of the adsorbate with the pore walls. The effect of pore wall roughness and the accuracy of isotherm calculation on the width of the adsorption-desorption hysteresis loop in cylindrical pores is discussed Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 813–823, May, 2007.     

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.     

Excluded volume effects in macromolecular forces and ion-interface interactions

A charged Yukawa liquid confined in a slit nanopore is studied in order to understand excluded volume effects in the interaction force between the pore walls. A previously developed self-consistent scheme [S. Buyukdagli, C. V. Achim, and T. Ala-Nissila, J. Stat. Mech. 2011, P05033] and a new simpler variational procedure that self-consistently couple image forces, surface charge induced electric field, and pore modified core interactions are used to this aim. For neutral pores, it is shown that with increasing pore size, the theory predicts a transition of the interplate pressure from an attractive to a strongly repulsive regime associated with an ionic packing state, an effect observed in previous Monte Carlo simulations for hard core charges. We also establish the mean-field theory of the model and show that for dielectrically homogeneous pores, the mean-field regime of the interaction between the walls corresponds to large pores of size d > 4 ?. The role of the range of core interactions in the ionic rejection and interplate pressure is thoroughly analyzed. We show that the physics of the system can be split into two screening regimes. The ionic packing effect takes place in the regime of moderately screened core interactions characterized with the bare screening parameter of the Yukawa potential b ? 3/l(B), where l(B) is the Bjerrum length. In the second regime of strongly screened core interactions b ? 3/l(B), solvation forces associated with these interactions positively contribute to the ionic rejection driven by electrostatic forces and enhance the magnitude of the attractive pressure. For weakly charged pores without a dielectric discontinuity, core interactions make a net repulsive contribution to the interplate force and also result in oscillatory pressure curves, whereas for intermediate surface charges, these interactions exclusively strengthen the external pressure, thereby reducing the magnitude of the net repulsive interplate force. The pronounced dependence of the interplate pressure and ionic partition coefficients on the magnitude and the range of core interactions indicates excluded volume effects as an important ion specificity and a non-negligible ingredient for the stability of macromolecules in electrolyte solutions.     

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.     

Spatial confinement effect on the atomic structure of solid argon

Molecules confined in nanopores show unusual behavior not seen in bulk systems. The present paper reports on molecular dynamics simulations of unusual freezing behavior in confined Ar. Similar to bulk Ar, liquid Ar confined in pores with a diameter D>15sigma (5.1 nm), where sigma is the diameter of the Ar atom, crystallizes when the cooling rate is lower than a critical value (Qc). We also find that the spatial confinement does not have significant influence on Qc when D>15sigma (5.1 nm). In the pore of 10sigma (3.4 nm) in diameter, on the other hand, the behavior is dramatically changed. Crystalline Ar does not appear inside the pore even when the system is cooled at a rate lower than the Qc in the bulk system by over two orders of magnitude. Instead, amorphous Ar characterized by local icosahedral configurations is formed in the pore. We further find that, even when crystalline Ar is formed outside the pore, it does not grow deeply into the pore. This supports that the amorphous Ar is actually the most stable phase in the pore. It is well known that Ar is a poor glass former. Our finding that even such an amorphous Ar is the most stable in the pore suggests that, in any system, it is possible to prepare amorphous structure selectively by using nano-molds.     

The fundamentals of adsorption theory for a mixture of bulky molecules in slit-shaped pores with heterogeneous wall surfaces

The fundamentals of the adsorption theory for a mixture of bulky molecules blocking more than one adsorption site on the surface in slit-shaped pores with heterogeneous wall surfaces are outlined. The adsorbate—adsorbate lateral interactions are taken into account in the quasi-chemical approximation and in the mean-field approximation. The expressions for the partial adsorption isotherms and for the binary coefficients of mixture separation and the way of isolation of the partial contributions of molecules on heterogeneous adsorption sites on pore walls are discussed. A simplified variant of adsorption theory for a binary mixture of molecules of different sizes in two-layer pores with the assumption of complete coverage of the pores is considered. The influence of the energy of binding of molecules to pore walls, lateral interactions, and the ratio of the component sizes on the shape of adsorption isotherms is analyzed. The results of calculations are compared with the experimental data for the benzene—CCl₄—microporous AC carbon adsorbent system.     

Adsorption of a binary mixture of adhesive fluids in planar pores: a Monte Carlo study

Grand canonical Monte Carlo simulation is used to study the adsorption of a binary sticky hard-sphere fluid mixture in planar pores. The wall-component 1 and wall-component 2 contact densities are determined to calculate the pressure as a function of the composition of the mixture and the separation between the walls. From these data dependence of the solvation force between the plates on pore width is estimated. The simulation results are compared with the predictions of the Percus-Yevick approximation for planar pores. The density profiles of particular components show interesting shapes stemming from the interplay between the steric effects and the competitive adhesion among all possible species pairs. It is shown that narrowing of the pore causes selective partitioning of individual components of the mixture between the bulk phase and the interior of the pore. The agreement between the two methods is better at wider pores and for the component comprised of weakly adhesive particles.     

Characteristic features of phase diagrams describing condensation of adsorbate in narrow pores

The phase diagrams describing condensation of adsorbate in micro- and mesoporous adsorbents having slit-shaped and cylindrical pores whose size varied from 1 to 20 monolayers were constructed. The study was performed using the lattice-gas model in the quasichemical approximation to take into account the intermolecular interactions. The phase diagrams for various values of the potential arising from different types of adsorbate--adsorbent interaction were analyzed for adsorption of helium, neon, methane, and carbon tetrachloride in graphite pores. Other adsorption systems are considered and the relationship between the pressure and temperature of adsorbate condensation is discussed. A nonmonotonic variation of the critical densities for pore widths from 3 to 10 molecular diameters was found. The pattern of this variation depends on the ratio of the energy of lateral interactions of the adsorbate molecules to the energy of interaction of the adsorbate molecules with pore walls. The critical temperature decreases monotonically with a decrease in the pore width. The stronger the adsorbate interaction with the pore walls, the greater the decrease in the critical temperature.     

Modeling of adsorption in pores with strongly heterogeneous walls: parametric lattice-site wall model

We present results of grand canonical Monte Carlo simulations of adsorption in cylindrical pores with rough surface modeled by a parametric lattice-site approach. The sites are randomly distributed over the pore walls. They could be attractive, neutral or repulsive with respect to the smooth pore model. Each site is characterized by two amplitudes (structural and energetic) which modify locally the structure and energetic properties of the surface. The results presented here show how different parameters of the model affect the mechanism of adsorption and, consequently, the form of the isotherm.     

Transient ordering in a quasi-two-dimensional liquid near freezing

We report the results of a theoretical study of locally ordered fluctuations in a quasi-two-dimensional colloid fluid. The fluctuations in the equilibrium state are monitored by the aperture cross-correlation function of radiation scattered by the fluid, as calculated from molecular dynamics simulations of near hard spheres with diameter sigma confined between smooth hard walls. These locally ordered fluctuations are transient; their decay can be monitored as a function of the time between the cross-correlated scattered radiation signals, but only the single-time cross-correlated signals are discussed in this paper. Systems with thicknesses less than two hard sphere diameters were studied. For wall separation H in the range 1 sigma/=1.57 sigma, hexagonal fluctuations persist in the dense liquid up to H=1.75 sigma, and fluctuations with square ordered symmetry, that of the solid to which the liquid freezes, only emerge at densities approximately 2% below freezing. For H=1.8 sigma and 1.85 sigma, hexagonal ordered flucuations are no longer found, and the square ordered fluctuations dominate the dense liquid region as the system freezes into a two layer square solid. For H=1.9 sigma and 1.95 sigma, where the liquid freezes into a two layer hexagonal solid, both square and hexagonal ordered fluctuations are observed. At lower densities, the ordered fluctuations only exhibit square symmetry. Hexagonal ordered fluctuations appear at densities approximately 7% below freezing and become more dominant as the density is increased, but the square ordered fluctuations persist until the system is converted into the solid.     

Drying of colloidal solutions of fluoroalkyl oligomers

The change in the supramolecular structure upon drying (solvent removal) of colloidal solutions of fluoroalkyl oligomers at atmospheric pressure has been studied using atomic force microscopy. In an initial colloidal solution, micrometer-sized particles of the dense phase consist of randomly oriented oligomers in the form of rigid rods of a 3–5 nm length forming a porous framework filled with solvent molecules, which solvate the oligomer chains. The drying-induced capillary pressure, which in nanosized pores is of the same order of magnitude as the solvation energy, leads to framework deformation, collapse of the pores, and the formation of lamellar and dendritic structures on a 50–100 nm scale. The ordering of these structures (formation of blocks of parallel oriented fibers typical of a fluoroplastic) increases as the heat-treatment temperature and the drying rate are increased, increasing the roughness of the surface (ratio of real to smooth surface area) and its hydrophobicity.     

Effect of Macromolecular Crowding on the Conformation of Confined Chain Polymers

Summary: The conformational behavior of flexible linear chain polymers confined in cylindrical pores and slab pores has been studied, employing a hard‐bead chain model and a modification of a recently proposed recoil‐growth bias Monte Carlo methodology, which improves the sampling efficiency in confined environments. It is found that the scaling law that correlates the unconstrained component of the radius of gyration of the polymer with the pore diameter in cylindrical pores is close but neatly different than the de Gennes mean‐field value. The results also indicate that the addition of spherical particles with sizes within the protein limit may be employed to tune the folding of the confined polymer, since in this case the depletion constraints work against the effective stretching forces induced by confinement. Remarkably, the presence of the depleting particles at sufficiently high concentration leads to appreciable changes in the exponents of the conformational scaling laws with respect to the uncrowded system.

Conformational behavior of flexible hard‐bead chain polymers confined in narrow pores.     

Freezing phenomena of lennard-jones fluid confined in jungle-gym nanospace: a monte carlo study

We performed grand canonical Monte Carlo simulations for a Lennard-Jones fluid confined in a jungle-gym (JG) nanospace of cubic structure modeled on a specific type of metal organic frameworks (MOFs) to investigate freezing phenomena. Our simulations clarified that the JG nanospace with the pore sizes from 5sigma to 11sigma strongly depresses freezing due to a geometrical hindrance effect, resulting in far lower freezing temperature than the bulk freezing point. The fluid-rod interaction is found to give little effect on the freezing temperature in the larger pore sizes. For smaller pores from 2sigma to 3sigma, on the other hand, a dominant factor is a template effect to enhance the localization of molecules into a specific configuration that matches the locations of potential minima, leading to a variety of molecular configurations. In this range of smaller pore sizes, the solidification temperatures are higher than those of the larger pores mainly due to strong influence of the fluid-rod interaction but are still lower than the bulk freezing temperature. In addition, a unique solid-to-solid transition is observed in a specific size of pore of 2.73sigma, which is caused by structural correlation between adjacent cells. On the basis of these results, a phase diagram in the JG nanospace is drawn.     

Pressure enhancement in carbon nanopores: a major confinement effect

Phenomena that occur only at high pressures in bulk phases are often observed in nanopores, suggesting that the pressure in such confined phases is large. We report a molecular simulation study of the pressure tensor of an argon nanophase within slit-shaped carbon pores and show that the tangential pressure is positive and large, while the normal pressure can be positive or negative depending on pore width. We also show that small changes in the bulk pressure have a large effect on the tangential pressure, suggesting that it should be possible to control the latter over wide ranges in laboratory experiments.     

Discrete solvation layering in confined binary liquids

The solvation force profiles of squalane/octamethylcyclotetrasiloxane (OMCTS) mixtures confined between Si3N4 tips and highly oriented pyrolytic graphite (HOPG) and hexadecane/OMCTS confined between alkanethiol-functionalized tips and freshly cleaved mica have been measured by atomic force microscopy. Measurements on HOPG reveal oscillatory behavior where discrete solvation layers of both squalane and OMCTS are observed in a single force curve. The large repulsive force of the first solvation layer (squalane) on HOPG indicates that it is strongly bound. Oscillatory behavior is also observed for hexadecane/OMCTS on mica excepting that the oscillations are found in the attractive regime. The OMCTS layers in this case are less ordered with slightly larger (approximately 1 A) periodicities. These results are in agreement with computer simulations for binary liquid mixtures but differ qualitatively from surface force apparatus experiments.     

Mesostructured gamma-Al(2)O(3) with a lathlike framework morphology

A novel three-step assembly pathway is reported for the formation of a mesostructured alumina with framework pore walls made of crystalline, lathlike gamma-Al(2)O(3) nanoparticles. In the initial supramolecular assembly step of the pathway a mesostructured alumina with a wormhole framework morphology and amorphous pore walls is assembled through the hydrolysis of Al(13) oligocations and hydrated aluminum cations in the presence of a nonionic diblock or triblock poly(ethylene oxide) surfactant as the structure-directing porogen. The walls of the initial mesostructure are then transformed in a second hydrolysis step at a higher temperature to a surfactant-boehmite mesophase, denoted MSU-S/B, with a lathlike framework made of boehmite nanoparticles. A final thermal reaction step topochemically converts the intermediate boehmitic mesophase to a mesostructure with crystalline gamma-Al(2)O(3) pore walls, denoted MSU-gamma, with retention of the lathlike framework morphology. The boehmitic MSU-S/B intermediates formed from the chloride salts of aluminum incorporate chloride anions into the mesostructure. Chloride ion incorporation tends to disorder the nanoparticle assembly process, leading to a broadening of the slit-shaped framework pores in the final MSU-gamma phases and to the introduction of intra- and interparticle textural mesopores. However, the well-ordered MSU-gamma phases made from aluminum nitrate as the preferred aluminum reagent exhibit narrow framework pore size distributions and average pore sizes that are independent of the surfactant size and packing parameter, in accord with a lathlike framework assembled from nanoparticles of regular size and connectivity. The high surface areas ( approximately 300-350 m(2)/g) and pore volumes ( approximately 0.45-0.75 cm(3)/g) provided by these mesostructured forms of gamma-Al(2)O(3) should be useful in materials and catalytic applications where the availability of surface Lewis acid sites and the dispersion of supported metal centers govern reactivity.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.