On the computational calculation of surface free energies for the disordered semihexagonal reconstructed Au(100) surface

Previously we developed a general method for calculating the free energy of any surface constrained to a distinct surface excess number/density. In this paper we show how to combine a range of such surfaces, whose free energies have been calculated, to produce an ad hoc semigrand canonical ensemble of surfaces from which ensemble surface properties can be calculated, including the ensemble surface free energy. We construct such an ensemble for the disordered Au(100) semihexagonal reconstructed surface using a Glue model potential at 1000 K and calculate the ensemble surface free energy to be 0.088 18 eVA(2). The ensemble average surface lateral density was found to be 1.375 (with respect to the bulk), which is in agreement with previous grand canonical Monte Carlo studies.     

On interfacial tension calculation from the test-area methodology in the grand canonical ensemble

We propose the extension of the test-area methodology, originally proposed to evaluate the surface tension of planar fluid-fluid interfaces along a computer simulation in the canonical ensemble, to deal with the solid-fluid interfacial tension of systems adsorbed on slitlike pores using the grand canonical ensemble. In order to check the adequacy of the proposed extension, we apply the method for determining the density profiles and interfacial tension of spherical molecules adsorbed in slitlike pore with different pore sizes and solid-fluid dispersive energy parameters along the same simulation. We also calculate the solid-fluid interfacial tension using the original test-area method in the canonical ensemble. Agreement between the results obtained from both methods indicate that both methods are fully equivalent. The advantage of the new methodology is that allows to calculate simultaneously the density profiles and the amount of molecules adsorbed onto a slitlike pore, as well as the solid-fluid interfacial tension. This ensures that the chemical potential at which all properties are evaluated during the simulation is exactly the same since simulations can be performed in the grand canonical ensemble, mimicking the conditions at which the adsorption experiments are most usually carried out in the laboratory.     

Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

A simulation method for the calculation of chemical potentials in small, inhomogeneous, and dense systems

We present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.     

Grand canonical ensemble molecular dynamics simulation of water solubility in polyamide-6,6

Grand canonical ensemble molecular dynamics simulation is employed to calculate the solubility of water in polyamide-6,6. It is shown that performing two separate simulations, one in the polymeric phase and one in the gaseous phase, is sufficient to find the phase coexistence point. In this method, the chemical potential of water in the polymer phase is expanded as a first-order Taylor series in terms of pressure. Knowing the chemical potential of water in the polymer phase in terms of pressure, another simulation for water in the gaseous phase, in the grand canonical ensemble, is done in which the target chemical potential is set in terms of pressure in the gas phase. The phase coexistence point can easily be calculated from the results of these two independent simulations. Our calculated sorption isotherms and solubility coefficients of water in polyamide-6,6, over a wide range of temperatures and pressures, agree with experimental data.     

Hydrogen-bonded layer-by-layer films of block copolymer micelles with pH-responsive cores

The structure of grafted adsorbing polymers on surfaces is described as a statistical ensemble of loops generated by an one-dimensional random walk perpendicular to the surface. The configuration of each chain is considered as a succession of closed loops ended by an open loop (a tail). The probability of formation of each individual loop is the product between the probability of first return to the surface and a Boltzmann factor containing the free energy of the Flory-Huggins kind, which is approximated by the minimum free energy of all possible configurations of that loop. At high grafting densities, the attractive interactions between monomers and surface control the fraction of polymer belonging to either closed loops or tails, hence the formation of a stretched grafted brush. At low grafting densities, the increase of that interaction above a critical value generates an abrupt collapse of the brush on the surface. Whereas for long polymers (with more than about 100 Kuhn segments), the structure of the brush can be determined, in general, only via Monte-Carlo sampling, it is argued that the two structural transitions indicated above can be well predicted by simple approximations.     

Modeling of adsorption and nucleation in infinite cylindrical pores by two-dimensional density functional theory

In this paper, we present an analysis of argon adsorption in cylindrical pores having amorphous silica structure by means of a nonlocal density functional theory (NLDFT). In the modeling, we account for the radial and longitudinal density distributions, which allow us to consider the interface between the liquidlike and vaporlike fluids separated by a hemispherical meniscus in the canonical ensemble. The Helmholtz free energy of the meniscus was determined as a function of pore diameter. The canonical NLDFT simulations show the details of density rearrangement at the vaporlike and liquidlike spinodal points. The limits of stability of the smallest bridge and the smallest bubble were also determined with the canonical NLDFT. The energy of nucleation as a function of the bulk pressure and the pore diameter was determined with the grand canonical NLDFT using an additional external potential field. It was shown that the experimentally observed reversibility of argon adsorption isotherms at its boiling point up to the pore diameter of 4 nm is possible if the potential barrier of 22kT is overcome due to density fluctuations.     

Confinement free energy of surfaces bearing end-grafted polymers in the mushroom regime and local measurement of the polymer density

End-tethered polymer chains usually adopt mushroomlike structures on the surface when their density is low. The behaviors of these surface-attached hemicoils are described by existing polymer theory. Dolan and Edwards derived the free energy of a single polymer chain confined between two planar surfaces. Their theory was used to approximate the steric interaction free energy, E, of two identical surfaces bearing polymers in the mushroom regime and to compare with experimental data obtained from surface force measurements. However, because of a mislabeled plot in the original paper, experimental force profiles did not seem to fit the free energy approximation satisfactorily. We have correctly relabeled the involved plot and derived a new simple expression for E. In order to verify this expression, we have performed experiments on PEG45 polymers incorporated in lipid bilayers using a surface force apparatus. The measured force profiles are in perfect agreement with the prediction. We show that such measurements can be used to determine the local density of grafted polymer with good precision.     

Structure of short polymers at interfaces: a combined simulation and theoretical study

The structure of polymers confined between surfaces is studied using computer simulation and a density functional approach. The simple model system considers the polymer molecule as a pearl necklace of freely jointed hard spheres, having attractions among the beads, confined between attractive surfaces. This approach uses the universality of the free-energy functional to obtain the self-consistent field required in the single chain simulation. The second-order direct correlation function for the uniform bulk fluid required as input has been calculated from the reference interaction site model integral equation theory using mean spherical approximation. The theoretical results are shown to compare well with the Monte Carlo simulation results for varying densities, chain lengths, and with different attractive interaction parameters. The simulation results on the conformational properties give important indications regarding the behavior of chains as they approach the surfaces.     

Effect of surface grafted polymers on the adsorption of different model proteins

Adsorption of a model protein to a surface with end-grafted polymers was studied by Monte Carlo simulations. In the model the effect on protein adsorption in the presence of end-grafted polymers was evaluated by calculating the change in free energy between an end-grafted surface and a surface without polymers. The change in free energy was calculated using statistical mechanical perturbation theory. Apart from ordinary athermal polymer-polymer and protein-polymer interactions we also study a broad selection of systems by varying the interaction between proteins and polymers and effective polymer-solvent interactions. The interactions between the molecules span an interval from -0.5 to +0.5 kT. Consequently, general features of protein adsorption to end-grafted surfaces is investigated by systematically changing properties like hydrophilicity/hydrophobicity of the polymer, protein and surface as well as grafting density, degree of polymerization and protein size. Increasing grafting density as well as degree of polymerization decreases the adsorption of protein except in systems with attractive polymer-protein interactions, where adsorption increases with increasing chain length and higher grafting density. At a critical polymer-protein interaction neither chain length nor grafting density affects the free energy of adsorption. Hydrophilic polymers were found to prevent adsorption better than hydrophobic polymers. Very small particles with radii comparable to the size of a polymer segment were, however, better excluded from the surface when using hydrophobic than hydrophilic polymers. For systems with attractive polymer-protein interaction not only the volume of the protein was shown to be of importance but also the size of the exposed surface.     

Surface forces between telechelic brushes revisited: the origin of a weak attraction

Telechelic polymers are useful for surface protection and stabilization of colloidal dispersions by the formation of polymer brushes. A number of theoretical investigations have been reported on a weak attraction between two telechelic brushes when they are at the classical contact, i.e., when the surface separation is approximately equal to the summation of the brush thicknesses. While recent experiments have confirmed the weak attraction between telechelic brushes, its origin remains elusive because of conflicting approximations used in the previous theoretical calculations. In this paper, we have investigated the telechelic polymer-mediated surface forces by using a polymer density functional theory (PDFT) that accounts for both the surface-adhesive energy and segment-level interactions specifically. Within a single theoretical framework, the PDFT is able to capture both the depletion-induced attraction in the presence of weakly adhesive polymers and the steric repulsion between compressed polymer brushes. In comparison of the solvation forces between telechelic brushes with those between brushes formed by surfactant-like polymers and with those between two asymmetric surfaces mediated by telechelic polymers, we conclude that the weak attraction between telechelic brushes is primarily caused by the bridging effect. Although both the surfactant-like and telechelic polymers exhibit a similar scaling behavior for the brush thickness, a significant difference has been observed in terms of the brush microstructures, in particular, the segment densities near the edges of the polymer brushes.     

Mesoscale simulation of polymer reaction equilibrium: combining dissipative particle dynamics with reaction ensemble Monte Carlo. I. Polydispersed polymer systems

We present a mesoscale simulation technique, called the reaction ensemble dissipative particle dynamics (RxDPD) method, for studying reaction equilibrium of polymer systems. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), allowing for the determination of both static and dynamical properties of a polymer system. The RxDPD method is demonstrated by considering several simple polydispersed homopolymer systems. RxDPD can be used to predict the polydispersity due to various effects, including solvents, additives, temperature, pressure, shear, and confinement. Extensions of the method to other polymer systems are straightforward, including grafted, cross-linked polymers, and block copolymers. To simulate polydispersity, the system contains full polymer chains and a single fractional polymer chain, i.e., a polymer chain with a single fractional DPD particle. The fractional particle is coupled to the system via a coupling parameter that varies between zero (no interaction between the fractional particle and the other particles in the system) and one (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the DPD equations of motion, accompanied by changes in the coupling parameter. The coupling-parameter changes are either accepted with a probability derived from the grand canonical partition function or governed by an equation of motion derived from the extended Lagrangian. The coupling-parameter changes mimic forward and reverse reaction steps, as in RxMC simulations.     

Multifunctional silane polymers for persistent surface derivatization and their antimicrobial properties

We demonstrate a versatile methodology combining both covalent surface anchoring and polymer cross-linking that is capable of forming long-lasting coatings on reactive and nonreactive surfaces. Polymers containing reactive methoxysilane groups form strong Si-O-Si links to oxide surfaces, thereby anchoring the polymer chains at multiple points. The interchain cross-linking of the methoxysilane groups provides additional durability to the coating and makes the coatings highly resistant to solvents. By tailoring the chemical structure of the polymer, we were able to control the surface energy (wetting) of a variety of surfaces over a wide range of water contact angles of 30-140 degrees . In addition, we synthesized covalently linked layer-by-layer polymeric assemblies from these novel methoxysilane polymers. Finally, antibacterial agents, such as silver bromide nanoparticles and triiodide ions, were introduced into these functional polymers to generate long-lasting and renewable antiseptic coatings on glass, metals, and textiles.     

Healing of interfacial surfaces in polymer systems

Literature data on the problems related to the healing of interfacial surfaces in polymers are revisited. Specific features and behavior of the contacting surfaces of polymer films in the rubbery and glassy states, as well as in heterophase polymer systems, are analyzed. Particular details associated with the healing of interfacial surfaces in polymers, which are capable of chemical interactions with each other, are considered. Special attention is focused on the analysis of the phenomena taking place on the newborn interfaces formed owing to the deformation of polymers in different physical states. Processes providing healing of shear bands and crazes during annealing of deformed polymer glasses are discussed. The above phenomena are shown to present evident practical interest from the viewpoint of the development of advanced nanocomposites based on polymer matrices.     

Monte Carlo molecular simulation of the hydration of K-montmorillonite at 353 K and 625 bar

Monte Carlo molecular simulations of the hydration of K-saturated Wyoming-type montmorillonite at constant stress in the NPzzT ensemble and at constant chemical potential in the grand canonical muVT ensemble, under basin-like conditions of 353 K and 625 bar, show a strong tendency of the K+ ions to adhere to the siloxane surface, forming predominant inner-sphere complexes with tetrahedral oxygen atoms and adsorbed water molecules. Simulations in the grand canonical ensemble predict that none of the K-montmorillonite hydrates, the one-, two-, and three-layer hydrates, are stable in this environment of high depth, temperature, and pressure. The most nearly stable configuration corresponds to the one-layer hydrate, characterized by a d001 spacing of 12.75 A, the adsorbed water being 60 molecules/layer or 180.83 mg of H2O/g of clay, an internal energy of -22.73 kcal/mol, an interlayer density of 0.365 g/mL, and a pressure tensor, Pzz, of 1999.9 bar. The interlayer structure consists of two close layers of water molecules 0.50 A from the midplane, with broad shoulders on the sides, the protons oriented toward the midplane and the siloxane surfaces, and the K+ ions close to the clay surfaces and on the interlayer midplane.     

Molecular dynamics simulations of polyelectrolyte adsorption

We have performed molecular dynamics simulations of polyelectrolyte adsorption at oppositely charged surfaces from dilute polyelectrolyte solutions. In our simulations, polyelectrolytes were modeled by chains of charged Lennard-Jones particles with explicit counterions. We have studied the effects of the surface charge density, surface charge distribution, solvent quality for the polymer backbone, strength of the short-range interactions between polymers and substrates on the polymer surface coverage, and the thickness of the adsorbed layer. The polymer surface coverage monotonically increases with increasing surface charge density for almost all studied systems except for the system of hydrophilic polyelectrolytes adsorbing at hydrophilic surfaces. In this case the polymer surface coverage saturates at high surface charge densities. This is due to additional monomer-monomer repulsion between adsorbed polymer chains, which becomes important in dense polymeric layers. These interactions also preclude surface overcharging by hydrophilic polyelectrolytes at high surface charge densities. The thickness of the adsorbed layer shows monotonic dependence on the surface charge density for the systems of hydrophobic polyelectrolytes for both hydrophobic and hydrophilic surfaces. Thickness is a decreasing function of the surface charge density in the case of hydrophilic surfaces while it increases with the surface charge density for hydrophobic substrates. Qualitatively different behavior is observed for the thickness of the adsorbed layer of hydrophilic polyelectrolytes at hydrophilic surfaces. In this case, thickness first decreases with increasing surface charge density, then it begins to increase.     

Local structure and thermodynamics of a core-softened potential fluid: theory and simulation.

Phase behavior and structural properties of homogeneous and inhomogeneous core-softened (CS) fluid consisting of particles interacting via the potential, which combines the hard-core repulsion and double attractive well interaction, are investigated. The vapour-liquid coexistence curves and critical points for various interaction ranges of the potential are determined by discrete molecular dynamics simulations to provide guidance for the choice of the bulk density and potential parameters for the study of homogeneous and inhomogeneous structures. Spatial correlations in the homogeneous CS system are studied by the Ornstein-Zernike integral equation in combination with the modified hypernetted chain (MHNC) approximation. The local structure of CS fluid subjected to diverse external fields maintaining the equilibrium with the bulk CS fluid are studied on the basis of a recently proposed third order+second order perturbation density functional approximation (DFA). The accuracy of DFA predictions is tested against the results of a grand canonical ensemble Monte Carlo simulation. Reasonable agreement between the results of both methods proves that the DFA theory applied in this work is a convenient theoretical tool for the investigation of the CS fluid, which is practically applicable for modeling numerous real systems.     

Dissipative particle dynamics simulations in the grand canonical ensemble: applications to polymer brushes.

We have used the dissipative particle dynamics (DPD) method in the grand canonical ensemble to study the compression of grafted polymer brushes in good solvent conditions. The force-distance profiles calculated from DPD simulations in the grand canonical ensemble are in very good agreement with the self-consistent field (SCF) theoretical models and with experimental results for two polystyrene brush layers grafted onto mica surfaces in toluene.     

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

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