Empty liquid state and re-entrant phase behavior of the patchy colloids confined in porous media.

Patchy colloids with three and four equivalent patches, confined in an attractive random porous medium, undergo re-entrant gas-liquid phase separation with the liquid phase density approaching zero at low temperatures. The (bonding) colloid-colloid interaction causes the liquid-gas phase separation, which is modulated by the presence of the randomly distributed hard-sphere obstacles, attracting the colloids via Yukawa potential. Due to this interaction, a layer of mutually bonded colloids around the obstacles is formed. The network becomes nonuniform, with colloid particles locally centered on the obstacles. Features described in this article may open possibilities to produce equilibrium gels with predefined nonuniform distribution of particles and indicate how complicated the phase behavior of biological macromolecules in a crowded environment may be.

Shielded attractive shell model again: resummed thermodynamic perturbation theory for central force potential.

The approach developed earlier to describe the dimerizing shielded attractive shell (SAS) primitive model of chemical association due to Cummings and Stell is generalized and extended to include a description of a polymerizing SAS model. Our extension is based on the combination of the resummed thermodynamic perturbation theory for central force (RTPT-CF) associating potential and self consistent scheme, which takes into account the changes in the system free volume due to association. Theoretical results for thermodynamical properties of the model at different bonding length, density and temperature are compared against newly generated computer simulation results. The theory gives very accurate predictions for the model with bonding length L (*) from the range 0 < L (*) < 0.6 at all values of the density and temperature studied, including the limit of infinitely large temperature.

Inverse patchy colloids with two and three patches. Analytical and numerical study.

We propose an analytical solution of the multi-density Ornstein-Zernike equation supplemented by the associative Percus-Yevick closure relations specifically designed to describe the equilibrium properties of the novel class of patchy colloidal particles represented by the inverse patchy colloids with arbitrary number of patches. Using Baxter's factorization method, we reduce solution of the problem to the solution of one nonlinear algebraic equation for the fraction of the particles with one non-bonded patch. We present closed-form expressions for the structure (structure factor) and thermodynamic (internal energy) properties of the system in terms of this fraction (and parameters of the model). We perform computer simulation studies and compare theoretical and computer simulation predictions for the pair distribution function, internal energy, and number of single and double bonds formed in the system, for two versions of the model, each with two and three patches. We consider the models with formation of the double bonds blocked by the patch-patch repulsion and the models without patch-patch repulsion. In general very good agreement between theoretical and computer simulation results is observed.

Phase Behavior and Percolation Properties of the Patchy Colloidal Fluids in the Random Porous Media.

The lack of a simple analytical description of the hard-sphere fluid in a matrix with hard-core obstacles is limiting progress in the development of thermodynamic perturbation theories for the fluid in random porous media. We propose a simple and highly accurate analytical scheme, which allows us to calculate thermodynamic and percolation properties of a network-forming fluid confined in the random porous media, represented by the hard-sphere fluid and overlapping hard-sphere matrices, respectively. Our scheme is based on the combination of scaled-particle theory, Wertheim's thermodynamic perturbation theory for associating fluids and extension of the Flory-Stockmayer theory for percolation. The liquid-gas phase diagram and percolation threshold line for several versions of the patchy colloidal fluid model confined in a random porous media are calculated and discussed. The method presented enables calculation of the thermodynamic and percolation properties of a large variety of polymerizing and network-forming fluids confined in random porous media.

Comparison of several classical density functional theories for the adsorption of flexible chain molecules into cylindrical nanopores.

Adsorption of flexible oligomers into narrow cylindrical pores has been studied by means of several versions of classical density functional theory (CDFT) and Monte Carlo simulation. The adsorption process is interesting to study due to the competition between the entropic depletion of oligomers from the pores and the wall-oligomer attraction. It is also challenging to describe using current CDFTs, which tend to overestimate the amount of the adsorbed fluid. From a comparison of several different CDFT approaches, we find that this is due to the assumption of ideal or freely jointed chain conformations. Moreover, it is demonstrated that it is impossible to obtain a reasonable description of the adsorption isotherms without taking into account accurate contact values in the distribution functions describing the structure of the reference monomer fluid. At low densities, more accurate result are obtained in comparison with Monte Carlo simulation data when accurate contact values are incorporated into the theory rather than the more commonly used hard-sphere contact value. However, even the CDFT with accurate contact values still overestimates the amount of the adsorbed fluid due to the ideal or freely jointed chain approximation, used for the description of chain conformations in most CDFT approaches. We find that significant improvement can achieved by employing self-consistent field theory, which samples self-avoiding chain conformations and decreases the number of possible chain conformations, and, consequently, the amount of the adsorbed fluid.

Two-patch colloidal model with re-entrant phase behaviour.

We propose a second-order thermodynamic perturbation theory for a hard-sphere patchy colloidal model with two doubly bondable patches of type A and B. AB bonding results in the formation of a three-dimensional network of the particles and AA and BB bonding promotes chain formation. The theory is applied to study the phase behaviour of the model at different values of the potential model parameters. Competition between network and chain formation gives rise to a re-entrant phase behaviour with upper and lower critical points. The model with an additional van der Waals type of interaction may have a re-entrant phase diagram with three critical points and two separate regions of the liquid-gas phase coexistence. We analyze our results in terms of the fractions of the particles in different bonding states and conclude that re-entrant phase coexistence can be seen as a coexistence between a gas phase rich in chain ends and a liquid phase rich in branch points.

Second-order resummed thermodynamic perturbation theory for central-force associating potential: multi-patch colloidal models.

We propose a second-order version of the resummed thermodynamic perturbation theory for patchy colloidal models with arbitrary number of multiply bondable patches. The model is represented by the hard-sphere fluid system with several attractive patches on the surface and resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. The theory represents an extension of the earlier proposed first order resummed thermodynamic perturbation theory for central force associating potential and takes into account formation of the rings of the particles. In the limiting case of singly bondable patches (total blockage), the theory reduces to Wertheim thermodynamic perturbation theory for associating fluids. Closed-form expressions for the Helmholtz free energy, pressure, internal energy, and chemical potential of the model with an arbitrary number of equivalent doubly bondable patches are derived. Predictions of the theory for the model with two patches appears to be in a very good agreement with predictions of new NVT and NPT Monte Carlo simulations, including the region of strong association.

An improved thermodynamic perturbation theory for square-well m-point model of the patchy colloids.

We propose an improved version of Wertheim's first order thermodynamic perturbation theory for the square-well m-point model of patchy colloids. Our version of the theory takes into account changes in the free volume of the system due to bond formation. The new theory is a significant improvement, giving good agreement with Monte Carlo simulations of the model.

Resummed thermodynamic perturbation theory for central force associating potential. Multi-patch models.

A resummed thermodynamic perturbation theory for associating fluids with multiply bondable central force associating potential is extended for the fluid with multiple number of multiply bondable associating sites. We consider a multi-patch hard-sphere model for associating fluids. The model is represented by the hard-sphere fluid system with several spherical attractive patches on the surface of each hard sphere. Resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. Closed form analytical expressions for thermodynamical properties (Helmholtz free energy, pressure, internal energy, and chemical potential) of the models with arbitrary number of doubly bondable patches at all degrees of the blockage are presented. In the limiting case of total blockage, when the patches become only singly bondable, our theory reduces to Wertheim's thermodynamic perturbation theory (TPT) for polymerizing fluids. To validate the accuracy of the theory we compare to exact values, for the thermodynamical properties of the system, as determined by Monte Carlo computer simulations. In addition we compare the fraction of multiply bonded particles at different values of the density and temperature. In general, predictions of the present theory are in good agreement with values for the model calculated using Monte Carlo simulations, i.e., the accuracy of our theory in the case of the models with multiply bondable sites is similar to that of Wertheim's TPT in the case of the models with singly bondable sites.

Investigating the quartz (1010)/water interface using classical and ab initio molecular dynamics.

Two different terminations of the (1010) surface of quartz (α and ß) interacting with water are simulated by classical (CMD) (using two different force fields) and ab initio molecular dynamics (AIMD) and compared with previously published X-ray reflectivity (XR) experiments. Radial distribution functions between hydroxyl and water show good agreement between AIMD and CMD using the ClayFF force field for both terminations. The Lopes et al. (Lopes, P. E. M.; Murashov, V.; Tazi, M.; Demchuk, E.; MacKerell, A. D. J. Phys. Chem. B2006, 110, 2782-2792) force field (LFF), however, underestimates the extent of hydroxyl-water hydrogen bonding. The ß termination is found to contain hydroxyl-hydroxyl hydrogen bonds; the quartz surface hydroxyl hydrogens and oxygens that hydrogen bond with each other exhibit greatly reduced hydrogen bonding to water. Conversely, the hydroxyl hydrogen and oxygens that are not hydrogen bonded to other surface hydroxyls but are connected to those that are show a considerable amount of hydrogen bonding to water. The electron density distribution of an annealed surface of quartz (1010) obtained by XR is in qualitative agreement with electron densities calculated by CMD and AIMD. In all simulation methods, the interfacial water peak appears farther from the surface than observed by XR. Agreement among AIMD, LFF, and XR is observed for the relaxation of the near-surface atoms; however, ClayFF shows a larger discrepancy. Overall, results show that for both terminations of (1010), LFF treats the near-surface structure more accurately whereas ClayFF treats the interfacial water structure more accurately. It is shown that the number of hydroxyl and water hydrogen bonds to the bridging Si-O-Si oxygens connecting the surface silica groups to the rest of the crystal is much greater for the α than the ß termination. It is suggested that this may play a role in the greater resistance to dissolution of the ß termination than that of the α termination.

Direct and quantitative comparison of pixelated density profiles with high-resolution X-ray reflectivity data.

A method for comparing pixelated density profiles (e.g. obtained from molecular dynamics or other computational techniques) with experimental X-ray reflectivity data both directly and quantitatively is described. The conditions under which such a comparison can be made quantitatively (e.g. with errors <1%) are determined theoretically by comparing calculated structure factors for an intrinsic continuous density profile with those obtained from density profiles that have been binned into regular spatial increments. The accuracy of the X-ray reflectivity calculations for binned density profiles is defined in terms of the inter-relationships between resolution of the X-ray reflectivity data (i.e. its range in momentum transfer), the chosen bin size and the width of the intrinsic density profile. These factors play a similar role in the application of any structure-factor calculations that involve the use of pixelated density profiles, such as those obtained from iterative phasing algorithms for inverting structures from X-ray reflectivity and coherent diffraction imaging data. Finally, it is shown how simulations of a quartz-water interface can be embedded into an exact description of the `bulk' phases (including the substrate crystal and the fluid water, below and above the actual interface) to quantitatively reproduce the experimental reflectivity data of a solid-liquid interface.

Resummed thermodynamic perturbation theory for central force associating potential: One-patch model.

A resummed thermodynamic perturbation theory for associating fluids with multiply bondable central force associating potential is proposed. We consider a simple one-patch model for associating fluids. The model is represented by the hard-sphere system with a circular attractive patch on the surface of each hard-sphere. Resummation is carried out to account for the blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. Closed form analytical expressions for thermodynamical properties (Helmholtz free energy, pressure, internal energy, and chemical potential) of the model with a doubly bondable patch at all degrees of the blockage are presented. In the limiting case of total blockage, when the particles become only singly bondable, our theory reduces to Wertheim's thermodynamic perturbation theory for dimerizing fluids. To validate the accuracy of the theory we compare to exact values, for the thermodynamical properties of the system, as determined by Monte Carlo computer simulations. In addition we compare the fraction of multiply bonded particles at different values of the density and temperature. Very good agreement between predictions of the theory, corrected for ring formation, and Monte Carlo computer simulation values was found in all cases studied. Less accurate are the original versions of the theory and Wertheim's thermodynamic perturbation theory for dimerization, especially at lower temperatures and larger sizes of the attractive patch.

Phase coexistence in polydisperse athermal polymer-colloidal mixture.

A theoretical scheme developed earlier [Y. V. Kalyuzhnyi et al., Chem. Phys. Lett. 443, 243 (2007)] is used to calculate the full phase diagram of polydisperse athermal polymer-colloidal mixture with polydispersity in both colloidal and polymeric components. In the limiting case of bidisperse polymer-colloidal mixture, theoretical results are compared against computer simulation results. We present the cloud and shadow curves, critical binodals, and distribution functions of the coexisting phases and discuss the effects of polydispersity on their behavior. According to our analysis polydispersity extends the region of the phase instability, shifting the critical point to the lower values of the pressure and density. For the high values of the pressure polydispersity causes strong fractionation effects, with the large size colloidal particles preferring the low-density shadow phase and long chain length polymeric particles preferring the high-density shadow phase.

Effect of temperature on the adsorption of water in porous carbons.

We report experimental and simulation studies to investigate the effect of temperature on the adsorption isotherms for water in carbons. Adsorption isotherms are measured by a gravimetric technique in carbon-fiber monoliths at 378 and 423 K and studied by molecular simulation in ideal carbon pores in the temperature range 298-600 K. Experimental adsorption isotherms show a gradual water uptake, as the pressure increases, and narrow adsorption-desorption hysteresis loops. In contrast, simulated adsorption isotherms at room temperature are characterized by negligible uptake at low pressures, sudden and complete pore filling once a threshold pressure is reached, and wide adsorption-desorption hysteresis loops. As the temperature increases, the relative pressure at which pore filling occurs increases and the size of the hysteresis loop decreases. Experimental adsorption-desorption hysteresis loops are narrower than those from simulation. Discrepancies between simulation and experimental results are attributed to heterogeneities in chemical composition, pore connectivity, and nonuniform pore-size distribution, which are not accounted for in the simulation model. The hysteresis phase diagram for confined water is obtained by recording the pressure-density conditions that bound the simulated hysteresis loop at each temperature. We find that the hysteresis critical temperature, i.e., the lowest temperature at which no hysteresis is detected, can be hundreds of degrees lower than the vapor-liquid critical temperature for bulk model water. The properties of confined water are discussed with the aid of simulation snapshots and by analyzing the structure of the confined fluid.

Water in carbon nanotubes: adsorption isotherms and thermodynamic properties from molecular simulation.

Grand canonical Monte Carlo simulations are performed to study the adsorption of water in single-walled (6:6), (8:8), (10:10), (12:12), and (20:20) carbon nanotubes in the 248-548 K temperature range. At room temperature the resulting adsorption isotherms in (10:10) and wider single-walled carbon nanotubes (SWCNs) are characterized by negligible water uptake at low pressures, sudden and complete pore filling once a threshold pressure is reached, and wide adsorption/desorption hysteresis loops. The width of the hysteresis loops decreases as pore diameter narrows and it becomes negligible for water adsorption in (8:8) and (6:6) SWCNs. Results for the isosteric heat of adsorption, density profiles along the pore axis and across the pore radii, order parameter across the pore radii, and x-ray diffraction patterns are presented. Layered structures are observed when the internal diameter of the nanotubes is commensurate to the establishment of a hydrogen-bonded network. The structure of water in (8:8) and (10:10) SWCNs is ordered when the temperature is 298 and 248 K, respectively. By simulating adsorption isotherms at various temperatures, the hysteresis critical temperature, e.g., the lowest temperature at which no hysteresis can be detected, is determined for water adsorbed in (20:20), (12:12), and (10:10) SWCNs. The hysteresis critical temperature is lower than the vapor-liquid critical temperature for bulk Simple Point Charge-Extended (SPCE) water model.

Ion adsorption at the rutile-water interface: linking molecular and macroscopic properties.

A comprehensive picture of the interface between aqueous solutions and the (110) surface of rutile (alpha-TiO2) is being developed by combining molecular-scale and macroscopic approaches, including experimental measurements, quantum calculations, molecular simulations, and Gouy-Chapman-Stern models. In situ X-ray reflectivity and X-ray standing-wave measurements are used to define the atomic arrangement of adsorbed ions, the coordination of interfacial water molecules, and substrate surface termination and structure. Ab initio calculations and molecular dynamics simulations, validated through direct comparison with the X-ray results, are used to predict ion distributions not measured experimentally. Potentiometric titration and ion adsorption results for rutile powders having predominant (110) surface expression provide macroscopic constraints of electrical double layer (EDL) properties (e.g., proton release) which are evaluated by comparison with a three-layer EDL model including surface oxygen proton affinities calculated using ab initio bond lengths and partial charges. These results allow a direct correlation of the three-dimensional, crystallographically controlled arrangements of various species (H2O, Na+, Rb+, Ca2+, Sr2+, Zn2+, Y3+, Nd3+) with macroscopic observables (H+ release, metal uptake, zeta potential) and thermodynamic/electrostatic constraints. All cations are found to be adsorbed as "inner sphere" species bonded directly to surface oxygen atoms, while the specific binding geometries and reaction stoichiometries are dependent on ionic radius. Ternary surface complexes of sorbed cations with electrolyte anions are not observed. Finally, surface oxygen proton affinities computed using the MUSIC model are improved by incorporation of ab initio bond lengths and hydrogen bonding information derived from MD simulations. This multitechnique and multiscale approach demonstrates the compatibility of bond-valence models of surface oxygen proton affinities and Stern-based models of the EDL structure, with the actual molecular interfacial distributions observed experimentally, revealing new insight into EDL properties including specific binding sites and hydration states of sorbed ions, interfacial solvent properties (structure, diffusivity, dielectric constant), surface protonation and hydrolysis, and the effect of solution ionic strength.

Adsorption properties of a colloid-polymer mixture confined in a slit pore.

The soft fundamental-measure theory, which was based on the additive colloid-polymer mixture [M. Schmidt, Phys. Rev. E 62, 3799 (2000)] has been employed to investigate the adsorption of a colloid-polymer mixture within a hard slit pore. The calculated results show that the adsorption for the confined colloid-polymer mixture is very different from those of the colloid-colloid and polymer-polymer mixtures. The equilibrium particle density distribution strongly depends on the softness of a star polymer. The local relative concentration oscillates with a spatial period close to the diameter of a large particle in the same way as the equilibrium particle density distribution. The size selectivity in adsorption depends both on the softness of a star polymer and on the particle size ratio in a binary mixture. In particular, the strong adsorption occurs at the ultra-soft polymer and high bulk packing fraction.

Distribution functions of a simple fluid under shear: low shear rates.

Anisotropic pair distribution functions for a simple, soft sphere fluid at moderate and high density under shear have been calculated by nonequilibrium molecular dynamics, by equilibrium molecular dynamics with a nonequilibrium potential, and by a nonequilibrium distribution function theory [H. H. Gan and B. C. Eu, Phys. Rev. A 45, 3670 (1992)] and some variants. The nonequilibrium distribution function theory consists of a nonequilibrium Ornstein-Zernike relation, a closure relation, and a nonequilibrium potential and is solved in spherical harmonics. The distortion of the fluid structure due to shear is presented as the difference between the nonequilibrium and equilibrium pair distribution functions. From comparison of the results of theory against results of equilibrium molecular dynamics with the nonequilibrium potential at low shear rates, it is concluded that, for a given nonequilibrium potential, the theory is reasonably accurate, especially with the modified hypernetted chain closure. The equilibrium molecular-dynamics results with the nonequilibrium potential are also compared against the results of nonequilibrium molecular dynamics and suggest that the nonequilibrium potential used is not very accurate. In continuing work, a nonequilibrium potential better suited to high shear rates [H. H. Gan and B. C. Eu, Phys. Rev. A 46, 6344 (1992)] is being tested.

Towards a computational chemical potential for nonequilibrium steady-state systems.

We explore an approach to derive a computable chemical potential analog for thermostatted steady-state systems arbitrarily far from equilibrium. Although our method is not rigorous, it is based on theoretical and numerical evidence and exploits analogies with Widom's method widely used in computer simulations of equilibrium fluids. We obtain two formulas, one for steady states and one for the transient region. Despite being analogous to the equilibrium expression, the steady-state formula can only be used for approximate calculations. Possessing less obvious characteristics, we present representative calculations for the transient approach and discuss its numerical feasibility.