Density functional approach to the description of the structure of dimer nanoparticles at liquid-liquid interfaces.

An extension of the density functional approach from our recent work (Phys. Chem. Chem. Phys., 2019, 21, 3073-3082) is developed. It permits us to study the microscopic structure and thermodynamic properties of chain particles at the interface between two partially miscible liquids. Explicit calculations are carried out for a binary symmetric mixture of hard-sphere Yukawa fluids and dimers built of hard-sphere segments. The model is simple, but it captures the interplay between localization of dimers at the interface and their orientation and assembly into layers. The segment density profiles are combined with the site superposition approximation to interpret angle-dependent local densities of dimers. Emphasis is put on self-organization of dimers. The evolution of the interfacial structure of dimers and of fluid species with the amount of added dimers and of the supporting mixture density is explored. Preferential orientations of dimers in the outer and inner layers of the interface are discovered. Changes of the interface width upon changing the parameters of the system are discussed. Similarities and differences between the properties of the interface hosting diatomic and spherical particles are explained.

Density functional theory for the microscopic structure of nanoparticles at the liquid-liquid interface.

We propose an extension of the density functional approach to study the structure and thermodynamic properties of a system comprising a certain amount of nanoparticles at the interface between two partially miscible liquids. Model calculations have been carried out for a binary symmetric mixture of Yukawa fluids and hard-sphere nanoparticles. Despite its simplicity, the model captures the principal features of this type of system. The results indicate that nanoparticles form layers and the number of layers depends on the amount of nanoparticles and on their diameters. For the systems studied the formation of the layers evidences strong localization of the nanoparticles at the interface.

Towards the description of adsorption of water in slit-like pores with walls covered by molecular brushes.

The density profiles, adsorption isotherms, and phase behavior of a water model in a slit-like pore with walls modified by pre-adsorbed tethered chain molecules have been studied in the framework of a density functional theory. Each chain is bonded to the surface by its terminal segment, and the surface density of grafted chains is the same for each wall. The model for water taken from the work of Clark et al. [Mol. Phys. 104, 3561 (2006)] reproduces successfully a bulk equation of state. The mean field approach has been used to describe the effects of attractive interactions. The chemical association effects are taken into account by using the first-order thermodynamic perturbation theory of Wertheim. We have found that the presence of molecular brushes on the pore walls has important consequences for the adsorption and phase behavior of confined water. If the brush segments do not attract water molecules strongly, the vapor-liquid coexistence envelope shrinks upon increasing brush density, but the critical temperature is weakly affected. Alteration from capillary condensation to evaporation is observed with changes in the brush density, number of segments of tethered chains, and/or chemical identity of segments. The crossover temperature is affected by all these factors. Moreover, we have shown that affinity of water to segments of tethers is an important factor determining adsorption of water vapor and the entire phase diagram.

Adsorption and phase behavior of water-like fluid models with square-well attraction and site-site association in slit-like pores: Density functional approach.

The adsorption and phase behavior of two model fluids, both with square well inter-particle attraction and site-site associative interaction, in slit-like pores have been studied in the framework of a density functional theory. The mean field approach and the first-order mean spherical approximation have been applied to account for the attractive interactions. The chemical association effects are taken into account by using the first-order thermodynamic perturbation theory of Wertheim. A set of parameters for each fluid model has been chosen according to the work of [Clark et al., Mol. Phys. 104, 3561 (2006)], to describe successfully the vapor-liquid coexistence of water in the bulk phase. The influence of the slit-like pore width and of the strength of gas-solid interaction energy on the vapor-liquid coexistence envelope under confinement has been explored in detail. The theory and the results of the present work are valuable for further exploration of a wide set of models of associating fluids and of fluids with complex molecular architecture in different adsorbents, and to deal with activated carbon surfaces.

Phase behaviour of a continuous shouldered well model fluid. A grand canonical Monte Carlo study.

The phase behavior of the continuous shouldered well model fluid proposed by Franzese [J. Mol. Liq. 136 (2007) 267] was examined using the Monte Carlo computer simulations in the grand canonical ensemble. The essential parts of the vapour-liquid and liquid-liquid coexistence envelopes were obtained. The Widom lines departing from coexistence envelopes were calculated using maxima of the fluctuations of the number of particles as a function of chemical potential along various isotherms. The region embracing anomalies in the properties of the model was located using the approximate criterion that involves the excess pair entropy.. The temperature of maximum density line was built by performing canonical Monte Carlo simulations. Our results are consistent with previous results from molecular dynamics constant pressure-constant temperature simulations and provide wider insight into the phase behavior of the model by using the chemical potential as the external parameter.

Restricted primitive model for electrolyte solutions in slit-like pores with grafted chains: microscopic structure, thermodynamics of adsorption, and electric properties from a density functional approach.

We apply a density functional theory to describe properties of a restricted primitive model of an ionic fluid in slit-like pores. The pore walls are modified by grafted chains. The chains are built of uncharged or charged segments. We study the influence of modification of the pore walls on the structure, adsorption, ion selectivity, and the electric double layer capacitance of ionic fluid under confinement. The brush built of uncharged segments acts as a collection of obstacles in the walls vicinity. Consequently, separation of charges requires higher voltages, in comparison to the models without brushes. At high grafting densities the formation of crowding-type structure is inhibited. The double layer structure becomes more complex in various aspects, if the brushes are built of charged segments. In particular, the evolution of the brush height with the bulk fluid density and with the charge on the walls depends on the length of the blocks of charged spheres as well as on the distribution of charged species along chains. We also investigated how the dependence of the double layer capacitance on the electrostatic potential (or on the charge on the walls) changes with grafting density, the chain length, distribution of charges along the chain, the bulk fluid density, and, finally, with the pore width. The shape of the electric double layer capacitance vs. voltage changes from a camel-like to bell-like shape, if the bulk fluid density changes from low to moderate and high. If the bulk density is appropriately chosen, it is possible to alter the shape of this curve from the double hump to single hump by changing the grafting density. Moreover, in narrow pores one can observe the capacitance curve with even three humps for a certain set of parameters describing brush. This behavior illustrates how strong the influence of brushes on the electric double layer properties can be, particularly for ionic fluids in narrow pores.

Understanding the structure of aqueous cesium chloride solutions by combining diffraction experiments, molecular dynamics simulations, and reverse Monte Carlo modeling.

A detailed study of the microscopic structure of an electrolyte solution, cesium chloride (CsCl) in water, is presented. For revealing the influence of salt concentration on the structure, CsCl solutions at concentrations of 1.5, 7.5, and 15 mol % are investigated. For each concentration, we combine total scattering structure factors from neutron and X-ray diffraction and 10 partial radial distribution functions from molecular dynamics simulations in one single structural model, generated by reverse Monte Carlo modeling. This combination of computer modeling methods is capable of (a) showing the extent to which simulation results are consistent with experimental diffraction data and (b) tracking down distribution functions in computer simulation that are the least comfortable with diffraction data. For the present solutions, we show that the level of consistency between simulations that use simple pair potentials and experimental structure factors is nearly quantitative. Remaining inconsistencies seem to be caused by water-water distribution functions. Changing the pair potentials of water-water interactions from SPC/E to TIP4P-2005 has not had any effect in this respect. As a final result, we obtained particle configurations from reverse Monte Carlo modeling that were in quantitative agreement with both diffraction data and most of the molecular dynamics (MD) simulated partial radial distribution functions (prdf's). From the particle coordinates, the distribution of the number of first neighbors, as well as angular correlation functions, were calculated. The average number of water molecules around cations decreases from about 8 to about 6.5 as concentration increases from 1.5 to 15 mol %, whereas the same quantity for the anions changes from about 7 to about 5. It was also found that the average angle of Cl...H-O particle arrangements, characteristic of anion-water hydrogen bonds, is closer to 180 degrees than that found for O...H-O arrangements (water-water hydrogen bonds). The present combination of experimental and computer simulation methods appears to be promising for the study of other electrolyte solutions.

Microscopic structure and thermodynamics of a core-softened model fluid: insights from grand canonical Monte Carlo simulations and integral equations theory.

We have studied the microscopic structure and thermodynamic properties of isotropic three-dimensional core-softened model fluid by using extensive grand canonical Monte Carlo computer simulations and Ornstein-Zernike integral equations with hypernetted chain and Rogers-Young closures. Applied simulation tools permit to obtain insights into the properties of the model in addition to available molecular dynamics data of other authors. We discuss equation of state in the density-chemical potential projection and explore the temperature dependence of the chemical potential along different isochores. The limits of the region of anomalous behavior of the structural and thermodynamic properties are established by investigating derivatives resulting from the equation of state, pair contribution to excess entropy, and translational order parameter. Besides, we evaluate the dependence of the heat capacity on temperature and density. The microscopic structure is discussed in terms of the pair distribution functions and corresponding structure factors. We have established that the hypernetted chain approximation is not successful to capture the region of anomalies in contrast to Rogers-Young approximation, but is very accurate for high fluid densities. Thus we have studied the onset for crystallization transition within this theoretical framework. Moreover, using the replicated Ornstein-Zernike integral equations with hypernetted chain closure, we explore the possibility of glass transition and described it in terms of transition density and chemical potential.

Solvation force between surfaces modified by tethered chains: a density functional approach.

The behavior of Lennard-Jones fluid in slitlike pores with walls modified by tethered chain molecules is studied using density functional theory. The effects of confinement and chemical modification of pore walls on the solvation force are investigated. Two models of the pore walls are considered. According to the first model, the chain molecules are chemically bonded by their end segments to opposite walls of the pore, forming flexible pillars. In the second model the chains build up a brush at each wall due to bonding of the first segment at one wall. The nonbonded terminating segment of a molecule is strongly attracted via a short-range potential to any wall of the pore. Then a pillarlike or looplike structure of chains can be formed. In the first model the solvation force at the wall-to-wall is repulsive for narrow pores and strongly attractive for wider pores of the order of the nominal chain length. Oscillations of the solvation force are induced by adsorbed fluid structure and by ordered structure of segments on the fragment of entirely attractive force curve. In the second model, however, the solvation force decays to zero as the pore width increases. Attractive force can be induced at intermediate separation between walls due to modification of the pore walls.

Comparison of interaction potentials of liquid water with respect to their consistency with neutron diffraction data of pure heavy water.

A number of interaction potential models for liquid water are scrutinized from the point of view of their compatibility with results of neutron diffraction experiments on pure heavy water. For the quantitative assessment a protocol developed recently [L. Pusztai et al., Chem. Phys. Lett. 457, 96 (2008)] using the reverse Monte Carlo method has been applied. The approach combines the experimental total scattering structure factor (tssf) and partial radial distribution functions (prdfs) from molecular dynamics simulations in a single structural model (particle configuration). Goodness-of-fit values to the three (O-O, O-H, and H-H) simulated prdfs and to the experimental tssf provided an unbiased measure characterizing the level of consistency between various interaction potentials and diffraction experiments. Out of the sets of prdfs investigated here, corresponding to SPCE, BJH, ST2, POL3, TIP4P, TIP4P-2005, TTMF3, and ENCS interaction potentials, the ones from the TIP4P-2005 potential proved to be the most consistent with the experimental neutron-weighted tssf of heavy water. More importantly, it is shown that none of the above interaction potentials are seriously inconsistent with the measured structure factor at ambient conditions.

Phase behavior of a binary symmetric mixture in slitlike pores with opposing walls: application of density functional approach.

We study adsorption of a symmetric binary Lennard-Jones mixture, which exhibits partial mixing in a bulk phase, in slitlike pores formed by the walls having antisymmetric properties with respect to the components. The calculations are carried out by means of a density functional approach. We show that under suitable conditions the pore filling may occur as a sequence of two first-order transitions. The capillary condensation may lead to an "antisymmetric" liquidlike film, the symmetry of which follows the symmetry of the adsorbing potential, or to a "demixed" film, the symmetry of which is only weakly associated with the symmetry of the adsorption potential. The additional first-order antisymmetric-demixed film transition begins at the triple point temperature and ends at the critical end point temperature.

Capillary condensation of a binary mixture in slit-like pores.

We investigate the capillary condensation of two model fluid mixtures in slit-like pores, which exhibit different demixing properties in the bulk phase. The interactions between adsorbate particles are modeled by using Lennard-Jones (12,6) potentials and the adsorbing potentials are of the Lennard-Jones (9,3) type. The calculations are performed for different pore widths and at different concentrations of the bulk gas, by means of density functional theory. We evaluate the capillary phase diagrams and discuss their dependence on the parameters of the model. Our calculations indicate that a binary mixture confined to a slit-like pore may exhibit rich phase behavior.

Reverse Monte Carlo modeling of the structure of colloidal aggregates.

In this work we present results for the structure of aerogels coming from the diffusion-limited cluster aggregation simulation method. Pair distribution functions and structure factors, resulting from simulation, were considered as experimental input for reverse Monte Carlo modeling. The modeling yielded structural models with pair distribution functions and structure factors nearly identical to the results of the simulations. Particle configurations from both the simulations and reverse Monte Carlo modeling have been analyzed in terms of the distribution of the number of neighbors. It is suggested that the reverse Monte Carlo method, when applied to the structure factor, may be a suitable technique for the interpretation of experimental scattering data on colloidal aerogels.

Microscopic structure and properties of an interface between coexisting phases of an associating fluid adsorbed in slitlike pores.

Using density functional theory, we calculate density profiles of an associating fluid in slitlike pores. These profiles characterize an interface between two coexisting, adsorbed phases, e.g., between gaseous and liquid phases formed during capillary condensation. Our study has been carried out for weakly, as well as for strongly, associated fluids confined in pores of different widths. We also investigate the role of the fluid-wall interaction.

Capillary condensation of short-chain molecules.

A density-functional study of capillary condensation of fluids of short-chain molecules confined to slitlike pores is presented. The molecules are modeled as freely jointed tangent spherical segments with a hard core and with short-range attractive interaction between all the segments. We investigate how the critical parameters of capillary condensation of the fluid change when the pore width decreases and eventually becomes smaller than the nominal linear dimension of the single-chain molecule. We find that the dependence of critical parameters for a fluid of dimers and of tetramers on pore width is similar to that of the monomer fluid. On the other hand, for a fluid of chains consisting of a larger number of segments we observe an inversion effect. Namely, the critical temperature of capillary condensation decreases with increasing pore width for a certain interval of values of the pore width. This anomalous behavior is also influenced by the interaction between molecules and pore walls. We attribute this behavior to the effect of conformational changes of molecules upon confinement.

Capillary Condensation in Pores with Energetically Heterogeneous Walls: Density Functional versus Monte Carlo Calculations.

We investigate adsorption of a Lennard-Jones fluid in slit-like pores with energetically heterogeneous walls by using Grand Canonical Monte Carlo simulations and a density functional approach. The model of a fluid-wall potential is qualitatively similar to that invoked by Röcken et al. (J. Chem. Phys. 108, 8089, (1999); i.e., it consists of a homogeneous part that varies in the direction perpendicular to the wall and a periodic part, varying also in one direction parallel to the wall, but in contrast to the above mentioned work, both parts of the fluid-wall potential are modeled by Lennard-Jones (9, 3) type functions. The structure of the adsorbed film is characterized by local densities. We evaluate the phase diagrams for several systems characterized by different corrugation of the adsorbing potential and discuss the discrepancies between theoretical predictions and computer simulations. Copyright 2001 Academic Press.