Simulation study of two-dimensional phase transitions of argon on graphite surface and in slit micropores

Molecular simulation has been increasingly used in the analysis and modeling of gas adsorption on open surfaces and in porous materials because greater insight could be gained from such a study. In case of homogeneous surfaces or pore walls the adsorption behavior is often complicated by the order–disorder transition. It is shown in our previous publications (Ustinov and Do, Langmuir 28:9543–9553, 2012a; Ustinov and Do, Adsorption 19:291–304, 2013) that once an ordered molecular layer has been formed on the surface, the lattice constant depends on the simulation box size, which requires adjusting the box dimensions parallel to the surface for each value of loading. It was shown that this can be accomplished with the Gibbs–Duhem equation, which results in decreasing lattice constant with an increase of the amount adsorbed. The same feature is expected to be valid for gas adsorption in narrow pores, but this has not been analyzed in the literature. This study aims at an extension of our approach to adsorption in slit graphitic pores using kinetic Monte Carlo method (Ustinov and Do, J Colloid Interface Sci 366:216–223, 2012b). The emphasis rests on the thermodynamic analysis of the two-dimensional (2D) ordering transition and state of the ordered phase; if the ordered phase exists in narrow slit pores, simulation with constant volume box always leads to erroneous results, for example, seemingly incompressible adsorbed phase. We proposed a new approach that allows for modeling thermodynamically consistent adsorption isotherms, which can be used as a basis for further refinement of the pore size distribution analysis of nanoporous materials.     

Effects of melting and ordering on the isosteric heat and monolayer density of argon adsorption on graphite

The aim of this paper is to study the effects of temperature on the state of the adsorbed argon on an uniform graphite surface. We applied the kinetic Monte Carlo scheme to simulate adsorption over a very wide range of temperature, which allows us to model the vapor–solid, the vapor–liquid and the order–disorder transition of the monolayer. The main distinction of our methodology is that it accounts for the lattice constant change with loading in the case of formation of an ordered molecular layer by appropriately changing the simulation box size. To do this we enforced the equality of the tangential pressures obtained by the virial and thermodynamic routes, which corresponds to the minimum Helmholtz free energy of a system at a given number of molecules and volume. This criterion is a consequence of the Gibbs–Duhem equation. A significant result obtained by application of the new simulation method was a sharp contraction of the monolayer just after its completion and the onset of the second layer. It manifests itself in an additional heat release. We re-determined the 2D-melting and 2D-critical temperatures of the molecular layer of argon. We also analyzed the order–disorder transition above the 2D-melting and showed that it could occur at some temperatures above the 2D-critical temperature. In this case, a hexagonal lattice appears at a sufficiently large tangential pressure. The effects of loading on the lattice constant, the 2D-critical temperature of the order–disorder transition and the differential heat of adsorption are thoroughly discussed.     

Two-dimensional order-disorder transition of argon monolayer adsorbed on graphitized carbon black: kinetic Monte Carlo method

We present results of application of the kinetic Monte Carlo technique to simulate argon adsorption on a graphite surface at temperatures below and above the triple point. We show that below the triple point the densification of the adsorbed layer with loading results in the rearrangement of molecules to form a hexagonal structure, which is accompanied by the release of an additional heat, associated with this disorder-order transition. This appears as a spike in the plot of the heat of adsorption versus loading at the completion of a monolayer on the surface. To describe the details of the adsorbed phase, we analyzed thermodynamic properties and the effects of temperature on the order-disorder transition of the first layer.     

Study on structure formation of short polyethylene chains via dynamic Monte Carlo simulation

Monte Carlo (MC) simulations of structure formation for short polyethylene chains at low temperature are performed based on a recent developed method that uses coarse-grained chains on a high coordination lattice. Local short-range interactions based on rotational isomeric state (RIS) model and long-range interactions obtained from Lennard–Jones (LJ) potential are introduced during the simulation. Properties evaluated from the simulations are the mean square dimensions, anisotropy of the radius of gyration tensor, local conformation determined by the occupancy of trans state and orientation correlation functions, energy of the system, and chain packing reflected by the pair correlation functions and structure factors. All of these parameters reveal an ordering process that produces an approximation to a hexagonal crystal phase. The hexagonal structure is imposed by the presence of a diamond lattice underlying the high coordination lattice on which the simulation is performed. Folding of the chains in the crystal is mandatory, because they have fully extended lengths in excess of the dimension of the simulated periodic box. Nevertheless, the simulations demonstrate that a high degree of crystallinity can be achieved in reasonable computer time. The simulation technique should be applicable to other choices of periodic boundary conditions that do not affect the results as strongly as in the present case.     

Method for the Manual Analysis of Moiré Structures in STM images

A method is presented to manually determine the lattice parameters of commensurate hexagonal moiré structures resolved by STM. It solves the problem that lattice parameters of moiré structures usually cannot be determined by inspection of an STM image, so that computer-based analyses are required. The lattice vector of a commensurate moiré structure is a sum of integer multiples both of the two basis vectors of the substrate and of the adsorbed layer. The method extracts the two factors with respect to the adsorbed layer from an analysis of the Fourier transform of an STM image. These two factors are related to the two factors with respect to the substrate layer. Using the cell augmentation method, six possible moiré structures are identified by algebra. When the orientation and lattice constant of the substrate are roughly known, this information is usually sufficient to determine a unique moiré structure and its lattice parameters.     

Molecular dynamic simulation of platinum heater and associated nano-scale liquid argon film evaporation and colloidal adsorption characteristics

A novel 'fluid-wall thermal equilibrium model' for the wall-fluid heat transfer boundary condition has been developed in this paper to capture the nano-scale physics of transient phase transition of a thin liquid argon film on a heated platinum surface and the eventual colloidal adsorption phenomenon as the evaporation is diminishing using molecular dynamics. The objective of this work is to provide microscopic characterizations of the dynamic thermal energy transport mechanisms during the liquid film evaporation and also the resulting non-evaporable colloidal adsorbed liquid layer at the end of the evaporation process. A nanochannel is constructed of platinum (Pt) wall atoms with argon as the working fluid. The proposed model is validated by heating liquid argon between two Pt walls and comparing the thermal conductivity and change in internal energy to thermodynamic properties of argon. Later on, phase change process is studied by simulating evaporation of a thin liquid argon film on a Pt wall using the proposed model. Gradual evaporation of the liquid film occurs although the film does not vaporize completely. An ultra-thin layer of liquid argon is noticed to have "adsorbed" on the platinum surface. An analysis similar to the theoretical study by Hamaker (1937) is performed for the non-evaporating film and the value of the Hamaker-type constant falls in the typical range. This analysis is done to quantify the non-evaporating film with an attempt to use molecular dynamics simulation results in continuum mechanics.     

聚乙烯六方相

评述了聚乙烯六方相的研究历史和结论，对其晶格结构，构象特征，热力学特性及形成原因，以及在聚乙烯结晶，尤其是形成伸直链晶体的过程中的动力学角色作了较详细的说明。     

Thermodynamic studies on thin liquid films. II. Foam film stabilized by decyl methyl sulfoxide

Thermodynamic equations in Part I of this series were extended so as to be applicable to electrolyte mixtures and the resultant equations were applied to the experimental results of a NaCl-decyl methyl sulfoxide (DeMS) mixture. Film thickness and contact angle of the black foam film stabilized by DeMS were measured as a function of the total molality of NaCl and DeMS at constant mole fraction of DeMS in the mixture under constant disjoining pressure. Newton black film was observed only above a certain DeMS concentration and the phase transition between common black and Newton black films took place twice as NaCl concentration increased at constant DeMS concentration. The surface densities of NaCl and DeMS at the film surface and the differences in the surface densities between the adsorbed films at the film surface and bulk one coexisting at equilibrium were numerically evaluated by applying the thermodynamic equations to the film tension obtained from the contact angle. The film states and phase transitions were clarified in terms of the film thickness and surface densities.     

A New Equation for Solute Retention in Liquid Chromatography

In consideration of the adsorption of solvent, diluent and solute molecules on the surface of a stationaryphase, a new equation for solute retention in liquid chromatography is presented. This equation includesthree parameters: the displacement equilibrium constant (Ksd) between the solvent and diluent molecules onthe surface of the stationary phase, the total number(N) of the solvent and diluent molecules released fromthe stationary phase after one solute molecule being adsorbed, and the parameter (I) related to the thermody-namic equilibrium constant for the solute adsorption on the stationary phase. Over the whole concentrationrange of the solvent in the mobile phase, the experimental retention data can be well described by this equa-tion, parameters K~, N and I can be obtained by the regression analysis of the experimental retention data,and consequently the number of the solvent and the diluent molecules displaced by one solute molecule fromthe stationary phase can also be derived at different solvent concentrations in the mobile phase,     

Unification of box shapes in molecular simulations

In molecular simulations with periodic boundary conditions the computational box may have five different shapes: triclinic; the hexagonal prism; two types of dodecahedrons; and the truncated octahedron. In this article, we show that every molecular simulation, formulated in one of these boxes, can be transformed into a simulation in one of the other ones. The transformation can be done in a preprocessing phase. The simulation in the new box is exactly identical to the simulation in the original one. This means that every molecular simulation may be done in the same type of box. Because the triclinic box is the easiest one to implement, we pay special attention to how to transform the other four box types into triclinic boxes. As a consequence, simulations in the often used truncated octahedron are superfluous; they may be done in a much simpler way in a triclinic box. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1930–1942, 1997     

Adsorption and structure of water on kaolinite surfaces: possible insight into ice nucleation from grand canonical monte carlo calculations

Grand canonical Monte Carlo calculations are used to determine water adsorption and structure on defect-free kaolinite surfaces as a function of relative humidity at 235 K. This information is then used to gain insight into ice nucleation on kaolinite surfaces. Results for both the SPC/E and TIP5P-E water models are compared and demonstrate that the Al-surface [(001) plane] and both protonated and unprotonated edges [(100) plane] strongly adsorb at atmospherically relevant relative humidities. Adsorption on the Al-surface exhibits properties of a first-order process with evidence of collective behavior, whereas adsorption on the edges is essentially continuous and appears dominated by strong water lattice interactions. For the protonated and unprotonated edges no structure that matches hexagonal ice is observed. For the Al-surface some of the water molecules formed hexagonal rings. However, the a o lattice parameter for these rings is significantly different from the corresponding constant for hexagonal ice ( Ih). A misfit strain of 14.0% is calculated between the hexagonal pattern of water adsorbed on the Al-surface and the basal plane of ice Ih. Hence, the ring structures that form on the Al-surface are not expected to be good building-blocks for ice nucleation due to the large misfit strain.     

A Grand Canonical Monte-Carlo Simulation Study of Xenon Adsorption in a Vycor-like Porous Matrix

We have performed atomistic Grand Canonical Monte-Carlo (GCMC) simulations of adsorption of xenon in a Vycor-like matrix at 195 K. The disordered mesoporous network is obtained by applying a numerical 3D off-lattice reconstruction procedure to a simulation box originally containing silicon and oxygen atoms of a non-porous silica solid. In order to reduce the computational cost, we have applied a homothetic decrease of the simulation box dimensions which preserves the morphology and the topology of the pore network (the average pore dimension is then around 30 Å). The surface chemistry is obtained in a realistic fashion by saturating all dangling bonds with hydrogen atoms. Small angle scattering spectra calculated on different numerical samples have evidenced a departure from Porod's law due to surface roughness. The simulated isotherms calculated on such disordered connected porous networks, show the capillary condensation phenomenon. The shape of the adsorption curves differs from that obtained for simple pore geometries. The analysis of the adsorbed quantity distribution indicates partial molecular-film formation depending on the local surface curvature and roughness.     

Monte Carlo Simulation of Microemulsion Phase Transitions by Solvent Accessible Surface Area

Results of lattice Monte Carlo simulation are presented for the behavior of a mixture of oil‐water‐amphiphile in different conditions. For the first time, the phase transitions between different types of microemulsion are modeled, in a qualitative manner, using the concept of solvent accessible surface area. All of the simulations are run in canonical (N, V, T) ensemble. Simple cubic lattices with the dimension of 50 have been used to avoid any size or surface effects of the boxes. Periodic boundary conditions and excluded volumes are used to mimic the box of simulation as a bulk of solution. All of the results are in good qualitative agreement with previous theoretical and experimental results.     

Grand canonical Monte Carlo simulation of argon adsorption at the surface of silica nanopores: effect of pore size, pore morphology, and surface roughness

Argon adsorption (77 K) in atomistic silica nanopores of various sizes and shapes has been studied by means of grand canonical Monte Carlo simulations (GCMC). We discuss the effects of confinement (pore size), pore morphology (ellipsoidal, hexagonal, constricted pore), and surface texture (rough/smooth) on the thickness variation of the adsorbed film with pressure onto the disordered inner surface of porous materials (usually called t-plot or t-curve). We show that no confinement effect occurs when the diameter of the regular cylindrical pore is larger than 10 nm. For pores smaller than 6 nm, we find that the film thickness increases as the pore size decreases. We show that the adsorption isotherm in the rough pore can be described as the sum of an adsorbed amount similar to that found for a smooth pore (of the same radius) and a constant contribution due to atoms "trapped" in the infractuosities of the rough surface which act as a microporous texture. Simulation snapshots for Ar adsorption in hexagonal and ellipsoidal smooth pores indicate that at low pressures the gas/adsorbate interface retains memory of the pore shape and becomes cylindrical prior to the capillary condensation of the fluid in the pore. The film thickness in the hexagonal pore is close to that obtained for a cylindrical pore having a similar dimension. By contrast, we find that the film thickness for an ellipsoidal pore is always larger than that for an equivalent cylindrical pore (having the same length and volume but a circular section). We show that this effect strengthens as the pore size decreases and/or the pore asymmetry increases. Ar adsorption in a cylindrical constricted pore shows that the presence of the narrower part considerably modifies the adsorption mechanism. Finally, we report GCMC simulations of Ar adsorption (77 K) on a plane silica reference substrate for different intermolecular potentials. We discuss the effect of the interaction on the shape of the adsorption isotherm and compare our results with experiments.     

A self-consistent field theory study on the morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers

By using a combinatorial screening method based on the self-consistent field theory, we investigate the equilibrium morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers in two dimensions. The triangle phase diagrams of both block copolymers are constructed by systematically varying the volume fractions of blocks A, B, and C. In this study, the interaction energies between species A, B, and C are set to be equal. Four different equilibrium morphologies are identified, i.e., the lamellar phase (LAM), the hexagonal lattice phase (HEX), the core-shell hexagonal lattice phase (CSH), and the two interpenetrating tetragonal lattice phase (TET2). For the linear ABCBA block copolymer, the reflection symmetry is observed in the phase diagram except for some special grid points, and most of grid points are occupied by LAM morphology. However, for the H-shaped (AB)(2)C(BA)(2) block copolymer, most of the grid points in the triangle phase diagram are occupied by CSH morphology, which is ascribed to the different chain architectures of the two block copolymers. These results may help in the design of block copolymers with different microstructures.     

Box length search algorithm for molecular simulation of systems containing periodic structures

We have developed a box length search algorithm to efficiently find the appropriate box dimensions for constant-volume molecular simulation of periodic structures. The algorithm works by finding the box lengths that equalize the pressure in each direction while maintaining constant total volume. Maintaining the volume at a fixed value ensures that quantitative comparisons can be made between simulation and experimental, theoretical or other simulation results for systems that are incompressible or nearly incompressible. We test the algorithm on a system of phase-separated block copolymers that has a preferred box length in one dimension. We also describe and test a Monte Carlo algorithm that allows the box lengths to change while maintaining constant volume. We find that the box length search algorithm converges at least two orders of magnitude more quickly than the variable box length Monte Carlo method. Although the box length search algorithm is not ergodic, it successfully finds the box length that minimizes the free energy of the system. We verify this by examining the free energy as determined by the Monte Carlo simulation.     

Classification of hexagonal adlayer arrangements by means of collective geometrical properties

Unequal-sphere packing model is applied for the simulation of large number of hexagonal adlayer structures with surface coverage between theta=13 and theta=1 on the hexagonal substrate, with atomic radius of the adsorbate and substrate atoms as the only input. Each structure is characterized with respect to collective adlayer properties: the average adlayer height and the adlayer roughness. The distribution of hexagonal arrangements is presented in a special plot, which can be used for identification and characterization of hexagonal adlayers of different surface coverages and atomic registries. The most likely structures are related to the extreme values of our model parameters. The usefulness of this methodology is successfully demonstrated by comparison with some real adsorbate-substrate systems, i.e., halogens and rare gases adsorbed on (111) surface. Besides the agreement with experimental results, our model offers new insight into the formation of atomic adlayers and detailed analysis of the atomic registry. We believe that our approach will be of use for identification of probable structures among the large number of combinatorial possibilities in theoretical studies and for better interpretation of experimental results (i.e., scanning-tunneling microscopy images of atomic adlayers).     

Thermodynamic model of quasiliquid formation on H2O ice: comparison with experiment

We have developed a new thermodynamic theory of the quasiliquid layer, which has been shown to be effective in modeling the phenomenon in a number of molecular systems. Here we extend our analysis to H(2)O ice, which has obvious implications for environmental and atmospheric chemistry. In the model, the liquid layer exists in contact with an ice defined as a two-dimensional lattice of sites. The system free energy is defined by the bulk free energies of ice I(h) and liquid water and is minimized in the grand canonical ensemble. An additional configurational entropy term arises from the occupation of the lattice sites. Furthermore, the theory predicts that the layer thickness as a function of temperature depends only on the liquid activity. Two additional models are derived, where slightly different approximations are used to define the free energy. With these two models, we illustrate the connection between the quasiliquid phenomenon and multilayer adsorption and the possibility of a two-dimensional phase transition connecting a dilute low coverage phase of adsorbed H(2)O and the quasiliquid phase. The model predictions are in agreement with a subset of the total suite of experimental measurements of the liquid thickness on H(2)O ice as a function of temperature. The theory indicates that the quasiliquid layer is actually equivalent to normal liquid water, and we discuss the impact of such an identification. In particular, observations of the liquid layer to temperatures as low as 200 K indicate the possibility that the quasiliquid is, in fact, an example of deeply supercooled normal water. Finally, we briefly discuss the obvious extension of the pure liquid theory to a thermodynamic theory of interfacial solutions on ice in the environment.     

Solvent mediated interactions close to fluid-fluid phase separation: microscopic treatment of bridging in a soft-core fluid

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed "wetting" film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a "bridging" transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein-Zernike equations.