Density functional theory model of adsorption on amorphous and microporous silica materials

We present a novel quenched solid density functional theory (QSDFT) model of adsorption on heterogeneous surfaces and porous solids, which accounts for the effects of surface roughness and microporosity. Within QSDFT, solid atoms are considered as quenched component(s) of the solid-fluid system with given density distribution(s). Solid-fluid intermolecular interactions are split into hard-sphere repulsive and mean-field attractive parts. The former are treated with the multicomponent fundamental measure density functional. Capabilities of QSDFT are demonstrated by drawing on the example of adsorption on amorphous silica materials. We show that, using established intermolecular potentials and a realistic model for silica surfaces, QSDFT quantitatively describes adsorption/desorption isotherms of Ar and Kr on reference MCM-41, SBA-15, and LiChrosphere materials in a wide range of relative pressures. QSDFT offers a systematic approach to the practical problems of characterization of microporous, mesoporous, and amorphous silica materials, including an assessment of microporosity, surface roughness, and adsorption deformation. Predictions for the pore diameter and the extent of pore surface roughness in MCM-41 and SBA-15 materials are in very good agreement with recent X-ray diffraction studies.     

Adsorption of chain molecules into a thin film structure and solvation interaction versus molecular flexibility

The influence of molecular flexibility on the properties of thin fluid films formed by linear chain molecules is studied by means of a singlet level of inhomogeneous integral equation theory. The considered m-mer chain molecules are formed through the polymerization of m hard-sphere beads with two sticky bonds randomly placed inside each bead core. Different molecular flexibility, from totally flexible up to almost completely rigid is reached by varying the interbead bonding length. The homogeneous properties of the same model that is necessary input to the singlet approach are extracted from the Wertheim’s theory of polymerization. The adsorption, local density distribution, disjoining pressure and solvation force of the chain molecule films confined by attractive and repulsive surfaces are analyzed. The obtained results indicate significant influence of the molecular flexibility on the film layering that is the origin of oscillations of solvation interaction arising between film surfaces. The oscillations of solvation pressure and force become more pronounced with restriction of molecular flexibility and with increase of bulk volume fraction of chain molecules. The decay of the oscillations across the film depends on the chain length and on the physical nature of the film surfaces, i.e. whether they are lyophilic or lyophobic. The partitioning of chain molecules from the bulk into the film strongly depends on the chain flexibility and this effect is more pronounced for the lyophilic surfaces.     

Molecular dynamics study of the effect of atomic roughness on the slip length at the fluid-solid boundary during shear flow

A systematic study into the effect of solid roughness on the slip boundary condition during shear flow is presented. Atomic roughness is modeled by varying the size and spacing between solid atoms at constant packing fraction while the interaction parameters and the thermodynamic state of the fluid are kept constant. It is shown that the fluid structure as manifest in the amplitude of the density oscillations increases with increasing smoothness of the surfaces. The fluid-solid slip length is shown to exhibit nonmonotonic behavior as the solid structure is varied from smooth to rough. Slip occurs for both smooth and rough surfaces, and stick occurs only for surfaces commensurate with the fluid.     

The impact of surface area,volume, curvature,and Lennard–Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard–Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent–solute interfaces, and define a generalized Poisson–Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature‐based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.     

Density functional approach to adsorption of simple fluids on surfaces modified with a brush-like chain structure

A density functional theory to describe adsorption of a simple fluid from a gas phase on a surface modified with pre-adsorbed chains is proposed. The chains are bonded to the surface by one of their ends, so they can form a brush-like structure. Two models are investigated. According to the first model all but the terminating segment of a chain can change the configuration during the adsorption of fluid species. The second model assumes that the chains remain "frozen", and the system is considered as a nonuniform quenched-annealed mixture. We apply simple form of interactions to study adsorption phenomena, microscopic structure, and layering transitions. Our principal findings show that new layering phase transitions can occur because of a chemical modification of the substrate under certain conditions, in comparison with nonmodified surfaces. However, opposite trends, that is, smoothing the adsorption isotherms, can also be observed, depending on the surface density of the grafted chains.     

Features of nitrogen adsorption on nonporous carbon and silica surfaces in the framework of classical density functional theory

Equilibrium adsorption data of nitrogen on a series of nongraphitized carbon blacks and nonporous silica at 77 K were analyzed by means of classical density functional theory to determine the solid-fluid potential. The behavior of this potential profile at large distance is particularly considered. The analysis of nitrogen adsorption isotherms seems to indicate that the adsorption in the first molecular layer is localized and controlled mainly by short-range forces due to the surface roughness, crystalline defects, and functional groups. At distances larger than approximately 1.3-1.5 molecular diameters, the adsorption is nonlocalized and appears as a thickening of the adsorbed film with increasing bulk pressure in a relatively weak adsorption potential field. It has been found that the asymptotic decay of the potential obeys the power law with the exponent being -3 for carbon blacks and -4 for silica surface, which signifies that in the latter case the adsorption potential is mainly exerted by surface oxygen atoms. In all cases, the absolute value of the solid-fluid potential is much smaller than that predicted by the Lennard-Jones pair potential with commonly used solid-fluid molecular parameters. The effect of surface heterogeneity on the heat of adsorption is also discussed.     

Solvation forces between silica bodies in supercritical carbon dioxide

We report Monte Carlo simulations of the solvation pressure between two planar surfaces, which represent the interface of spherical silica nanoparticles in supercritical carbon dioxide. Carbon dioxide (CO2) was modeled as an atomistic dumbbell or a spherical Lennard-Jones particle. The interaction between CO2 molecules and silica surfaces was characterized by the standard Steele potential with energetic heterogeneities representing the hydrogen bonds. The parameters for the solid-fluid interaction potentials were obtained by fitting our simulations to the experimental isotherms of CO2 sorption on mesoporous siliceous materials. We studied the dependence of the solvation force on the distance between planar silica surfaces at T = 318 K, at equilibrium bulk pressures p(bulk) ranging from 69 to 200 atm. At 69 atm, we observed a long-range attraction between the two surfaces, and it vanished when the pressure was increased to 102 and then 200 atm. The results obtained with different fluid models were consistent with each other. According to our observations, energetic heterogeneities of the surface have negligible influence on the solvation pressure. Using the Derjaguin approximation, we calculated the solvation forces between spherical silica nanoparticles in supercritical CO2 from the solvation pressures between the planar surfaces.     

Forces between surfaces in liquids

The results and implications of direct force measurements between molecularly smooth mica surfaces in liquids are reviewed. These discussions include four interactions fundamental to colloid science: van der Waals forces, double layer forces, adhesion forces and structural or solvation forces (e.g. hydration forces). Also considered are the effects of preferential surface adsorption of solute molecules on these interactions, e.g. surfactant adsorptions from aqueous solutions and water condensation from non-aqueous solvents.In aqueous media it is apparent that the DLVO theory is valid at all surface separations down to the “force barrier”, but that under certain conditions hydration forces can become significant at distances below 30 Å.The measured adhesion force between two solid surfaces can be simply related to their surface energies and where meniscus forces are also present due to “capillary condensation” from vapor solvent, their effect on adhesion can be understood in terms of straightforward bulk thermodynamic principles. Here, too, it is concluded that structural forces cannot be ignored.Our results suggest that structural forces may either very monotonically with distance or be oscillatory with a periodicity equal to the molecular size. Their origin, nature, mode of action and importance for particle interactions will no doubt take many years to sort out.     

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.     

Comparison of nitrogen adsorption at 77 K on non-porous silica and pore wall of MCM-41 materials by means of density functional theory

Nitrogen adsorption on a surface of a non-porous reference material is widely used in the characterization. Traditionally, the enhancement of solid-fluid potential in a porous solid is accounted for by incorporating the surface curvature into the solid-fluid potential of the flat reference surface. However, this calculation procedure has not been justified experimentally. In this paper, we derive the solid-fluid potential of mesoporous MCM-41 solid by using solely the adsorption isotherm of that solid. This solid-fluid potential is then compared with that of the non-porous reference surface. In derivation of the solid-fluid potential for both reference surface and mesoporous MCM-41 silica (diameter ranging from 3 to 6.5 nm) we employ the nonlocal density functional theory developed for amorphous solids. It is found that, to our surprise, the solid-fluid potential of a porous solid is practically the same as that for the reference surface, indicating that there is no enhancement due to surface curvature. This requires further investigations to explain this unusual departure from our conventional wisdom of curvature-induced enhancement. Accepting the curvature-independent solid-fluid potential derived from the non-porous reference surface, we analyze the hysteresis features of a series of MCM-41 samples.     

Solvent reorganization in electron and ion transfer reactions near a smooth electrified surface: a molecular dynamics study

Molecular dynamics simulations of electron and ion transfer reactions near a smooth surface are presented, analyzing the effect of the geometrical constraint of the surface and the interfacial electric field on the relevant solvation properties of both a monovalent negative ion and a neutral atom. The simulations show that, from the solvation point of view, ion adsorption is an uphill process due to the need to shed off the ion's solvation shell and displace water from the surface. Atom adsorption, on the other hand, has only a small barrier, related to the molecularity of the solvent. Both the electrostatic interaction of the ion with the solvent and the ion's solvent reorganization energy (the relevant parameter in the Marcus electron transfer theory) decrease as the surface is approached, whereas these parameters are not sensitive to the distance from the surface for the atom. This is a consequence of the importance of long-range electrostatic interactions for ion solvation and the importance of short-range interactions for atom solvation. The electric field either attracts or repels an ion to or from the surface, but the field has no influence on the solvent reorganization energy. By including the quantum-mechanical electron transfer between the metal surface and the ion/atom in solution in the MD simulation by using a model Hamiltonian, we calculated two-dimensional free energy surfaces for ion adsorption allowing for partial charge transfer, based on a fully molecular picture of ion solvation near the surface.     

Structure of Lennard-Jones fluids confined in square nanoscale channels from density functional theory

The density distribution of Lennard-Jones fluids confined in square nanoscale channels with Lennard-Jones walls has been studied using the nonlocal density functional theory (DFT) based on the Tarazona model. The effect of channel lengths on the density profiles with various chemical potentials was discussed. It was found that there is an apparent layering phenomenon for the confined fluids due to the combining influences of the enhancing solid-fluid interaction and the excluded volume effect. The pronounced density peaks were observed at the corners of square channels due to the strong fluid-solid interactions. The grand canonical ensemble Monte Carlo simulation (GCEMC) was applied to test the nonlocal DFT results. The DFT calculations are in relatively good agreement with the GCEMC simulations. The adsorption isotherms in a series of square channels were evaluated based on the obtained density distributions. The adsorption mechanism within the square pores was investigated. A comparison between the adsorptions of the square pores with those of the corresponding slit-size pores has been given.     

Direct measurement of forces due to solvent structure

Forces measured between two molecularly smooth solid surfaces separated by inert organic liquids exhibit spatial oscillations with periodicity equal to the size of the liquid molecules. Between five and ten oscillations are measurable, and their amplitude is large compared with the conventional van der Waals force.     

Phase transition of short linear molecules adsorbed on solid surfaces from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on strongly attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the layering transitions change with the change of the chain length and with relative strength of the fluid-solid interaction. The critical temperature of the first layering transition, rescaled by the bulk critical temperature, increases slightly with an increase of the chain length. We have found that for longer chains the layering transitions within consecutive layers are shifted toward very low temperatures and that their sequence is finally replaced by a single transition.     

Nano-scale superhydrophobicity: suppression of protein adsorption and promotion of flow-induced detachment

Wall adsorption is a common problem in microfluidic devices, particularly when proteins are used. Here we show how superhydrophobic surfaces can be used to reduce protein adsorption and to promote desorption. Hydrophobic surfaces, both smooth and having high surface roughness of varying length scales (to generate superhydrophobicity), were incubated in protein solution. The samples were then exposed to flow shear in a device designed to simulate a microfluidic environment. Results show that a similar amount of protein adsorbed onto smooth and nanometer-scale rough surfaces, although a greater amount was found to adsorb onto superhydrophobic surfaces with micrometer scale roughness. Exposure to flow shear removed a considerably larger proportion of adsorbed protein from the superhydrophobic surfaces than from the smooth ones, with almost all of the protein being removed from some nanoscale surfaces. This type of surface may therefore be useful in environments, such as microfluidics, where protein sticking is a problem and fluid flow is present. Possible mechanisms that explain the behaviour are discussed, including decreased contact between protein and surface and greater shear stress due to interfacial slip between the superhydrophobic surface and the liquid.     

Adsorption isoterms and capillary condensation in a nanoslit with rough walls: a density functional theory

Adsorption isoterms and capillary condensation in an open slit with walls decorated with arrays of pillars are examined using the density functional theory. Compared with the main substrate, the pillars can have the same or different parameters in the Lennard-Jones interaction potential between them and the fluid in the slit. The roughness of the solid surface, defined as the ratio between the area of the actual surface and the area of the surface free of pillars, is controlled by the height of the pillars. It is shown that the capillary condensation pressure first increases with increasing roughness, passes through a maximum, and then decreases. The amount of adsorbed fluid at constant volume of the slit has, in general, a nonmonotonic dependence on roughness. These features of adsorption and capillary condensation are results of increased surface area and changes in the fluid-solid potential energy due to changes in roughness.     

Description of self-diffusion coefficients of gases,liquids and fluids at high pressure based on molecular simulation data

The purpose of this work is to evaluate the potential of modeling the self-diffusion coefficient (SDC) of real fluids in all fluid states based on Lennard–Jones analytical relationships involving the SDC, the temperature, the density and the pressure. For that, we generated an equation of state (EOS) that interrelates the self-diffusion coefficient, the temperature and the density of the Lennard–Jones (LJ) fluid. We fit the parameters of such LJ–SDC–EOS using recent wide ranging molecular simulation data for the LJ fluid. We also used in this work a LJ pressure–density–temperature EOS that we combined with the LJ–SDC–EOS to make possible the calculation of LJ–SDC values from given temperature and pressure. Both EOSs are written in terms of LJ dimensionless variables, which are defined in terms of the LJ parameters ɛ and σ. These parameters are meaningful at molecular level. By combining both EOSs, we generated LJ corresponding states charts which make possible to conclude that the LJ fluid captures the observed behavioral patterns of the self-diffusion coefficient of real fluids over a wide range of conditions. In this work, we also performed predictions of the SDC of real fluids in all fluid states. For that, we assumed that a given real fluid behaves as a Lennard–Jones fluid which exactly matches the experimental critical temperature T_c and the experimental critical pressure P_c of the real fluid. Such an assumption implies average true prediction errors of the order of 10% for vapors, light supercritical fluids, some dense supercritical fluids and some liquids. These results make possible to conclude that it is worthwhile to use the LJ fluid reference as a basis to model the self-diffusion coefficient of real fluids, over a wide range of conditions, without resorting to non-LJ correlations for the density–temperature–pressure relationship. The database considered here contains more than 1000 experimental data points. The database practical reduced temperature range is from 0.53 to 2.4, and the practical reduced pressure range is from 0 to 68.4.     

Molecular simulation of condensation process of Lennard-Jones fluids confined in nanospace with jungle-gym structure

We report grand canonical Monte Carlo simulations for a Lennard-Jones (LJ) fluid modeled on methane confined in nanospace with jungle-gym-like (JG) cubic structure, which is typically found in porous coordination polymers. Pillars composing the cubic structure were modeled as structureless smooth solid rods made of LJ carbon. We examined the effects of pore size, pore geometry, rod thickness, and rod potential onto the condensation phenomena in the JG pore structure. The simulations clarified that the condensation pressure and adsorption amount in the JG structure were influenced by pore size and rod potential, while the transition type was determined by rod thickness. The characteristics of the JG structure lie in the sensitivity to the slight changes in pore size, rod thickness, and rod potential owing to the combination of the packing effect of molecules and the superposition effect of rod potentials.