A Monte Carlo simulation of grafted poly(ethylene oxide) chains

Conformational changes of a simplified model of grafted poly(ethylene oxide) (PEO) chains were simulated using an off-lattice Monte Carlo model. A random-walk scheme was used in our simulations. The initial polymer structure was modeled with molecular mechanics and models of grafted polymer chains were built using programs developed in our laboratory. During the simulation, all bond angles and bond lengths were kept fixed while the dihedral angles of backbones were changed to search for energy-favorite conformations. Torsional energy, van der Waals interaction, and Coulombic interaction were considered. Periodic boundary conditions were implemented. In addition, the solvent quality was simulated implicitly by modifying the Lennard-Jones 12–6 van der Waals expression. Each PEO chain, 50-monomer long, was represented with a united-atom model. Eight series of simulations with varying solvent quality, simulation temperature, and Coulombic interaction were carried out. For each series, nine different initial grafting densities of grafted PEO chains were considered. Five different conformations were simulated at each grafting density. The calculated system energies, scaling properties, and atom density profiles were studied. Changes in solvent quality produced different structural behaviors. As the grafting density increased, there was a mushroom-to-brush transition, and the scaling property of average layer thickness was dependent on the grafting density.     

Isothermal kinetic study of nitric oxide adsorption and decomposition on Pd(111) surfaces: molecular beam experiments

The kinetics of NO adsorption and dissociation on Pd(111) surfaces and the NO sticking coefficient (s(NO)) were probed by isothermal kinetic measurements between 300 and 525 K using a molecular beam instrument. NO dissociation and N2 productions were observed in the transient state from 425 K and above on Pd(111) surfaces with selective nitrogen production. Maximum nitrogen production was observed between 475 and 500 K. It was found that, at low temperatures, between 300 and 350 K, molecular adsorption occurs with a constant initial s(NO) of 0.5 until the Pd(111) surface is covered to about 70-80% by NO. Then s(NO) rapidly decreases with further increasing NO coverage, indicating typical precursor kinetics. The dynamic adsorption - desorption equilibrium on Pd(111) was probed in modulated beam experiments below 500 K. CO titration experiments after NO dosing indicate the diffusion of oxygen into the subsurface regions and beginning surface oxidation at > or = 475 K. Finally, we discuss the results with respect to the rate-limiting character of the different elementary steps of the reaction system.     

A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks

The time evolution of species concentrations in biochemical reaction networks is often modeled using the stochastic simulation algorithm (SSA) [Gillespie, J. Phys. Chem. 81, 2340 (1977)]. The computational cost of the original SSA scaled linearly with the number of reactions in the network. Gibson and Bruck developed a logarithmic scaling version of the SSA which uses a priority queue or binary tree for more efficient reaction selection [Gibson and Bruck, J. Phys. Chem. A 104, 1876 (2000)]. More generally, this problem is one of dynamic discrete random variate generation which finds many uses in kinetic Monte Carlo and discrete event simulation. We present here a constant-time algorithm, whose cost is independent of the number of reactions, enabled by a slightly more complex underlying data structure. While applicable to kinetic Monte Carlo simulations in general, we describe the algorithm in the context of biochemical simulations and demonstrate its competitive performance on small- and medium-size networks, as well as its superior constant-time performance on very large networks, which are becoming necessary to represent the increasing complexity of biochemical data for pathways that mediate cell function.     

Monte Carlo simulation of properties of monolayers and metal islands adsorbed on metallic (111) surfaces

To obtain the surface stress changes deltasigma due to the adsorption of metal monolayers onto metallic surfaces, a new model derived from thermodynamic considerations is presented. Such a model is based on continuum Monte Carlo simulations with embedded atom method potentials in the canonical ensemble, and it is extended to consider the behavior on different islands adsorbed onto (111) substrate surfaces. Homoepitaxial and heteroepitaxial systems are studied. Pseudomorphic growth is not observed for small metal islands with considerable positive misfit with the substrate. Instead, the islands become compressed upon increase of their size. A simple model is proposed to interpolate between the misfits of atoms in small islands and the pseudomorphic behavior of the monolayer.     

Monte Carlo法模拟CO在Fe(100)表面的升温脱附

以类桥位的模型为基础,采用MonteCarlo算法,结合键级守恒-Morse势方法(BOC-MP),模拟了CO在Fe(100)表面上平躺式吸附,考虑了金属与吸附质(M-A)、吸附质与吸附质(A-A)之间的相互作用,以研究小分子在金属表面上的TPD谱图,分析了CO的解离过程和脱附过程对TPD谱图的影响,结果表明,理论模拟与实验相符.     

A realistic kinetic Monte Carlo simulation of the faceting of a Pt(110) surface under reaction conditions

The faceting process on Pt(110) is studied with the help of a kinetic Monte Carlo model taking into account realistic Pt-Pt, Pt-CO, and Pt-O interactions. The activation energies of the allowed atomic steps are estimated using available computational and experimental data. The model well reproduces the region in the parameter space where faceting occurs. Under kinetic instability conditions, the simulated faceted pattern forms a periodic hill and valley structure with a lateral periodicity of approximately 140-170 A, which is comparable with experimental data. The simulations reproduce the development of faceting on a realistic time scale.     

Study of oscillations and pattern formation in the NO + CO reaction on Pt(100) surfaces through dynamic Monte Carlo simulation: toward a realistic model

Oscillations and pattern formation driven by a surface reconstruction are studied for the catalytic reduction of NO by CO on Pt(100) single-crystal surfaces through dynamic Monte Carlo simulations at low pressure and relatively high temperatures conditions. This study incorporates recent experimental evidence obtained for the same reaction on a Rh(111) surface, which modifies the reaction scheme used in previous approaches. The main consequence of such experimental evidence is that the production of N(2) occurs through two parallel mechanisms: (a) the classical N + N recombination step; (b) the formation and subsequent decay of an (N-NO) intermediate species as the fastest pathway. Moreover, different factors influencing the NO dissociation rate, the key step in the whole reaction, such as the availability of neighboring vacant sites, the formation of N-islands, and the presence of other NO and CO adsorbed species in the neighborhood, are also taken into account and their effects discussed. Sustained, modulated, irregular, and damped oscillations are observed in our analysis as well as the formation of cellular structures and turbulent patterns. The effect and the importance of each elementary reaction step on the behavior of the system are discussed.     

A kinetic Monte Carlo simulation study of inositol 1,4,5-trisphosphate receptor (IP3R) calcium release channel

Most of the previously theoretical studies about the stochastic nature of the IP3R calcium release channel gating use the chemical master equation (CME) approach. Because of the limitations of this approach we have used a stochastic simulation algorithm (SSA) presented by Gillespie. A single subunit of De Young-Keizer (DYK) model was simulated using Gillespie algorithm. The model has been considered in its complete form with eight states. We investigate the conditions which affect the open state of the model. Calcium concentrations were the subject of fluctuation in the previous works while in this study the population of the states is the subject of stochastic fluctuations. We found out that decreasing open probability is a function of Ca(2+) concentration in fast time domain, while in slow time domain it is a function of IP3 concentration. Studying the population of each state shows a time dependent reaction pattern in fast and medium time domains (10(-4) and 10(-3)s). In this pattern the state of X(010) has a determinative role in selecting the open state path. Also, intensity and frequency of fluctuations and Ca(2+) inhibitions have been studied. The results indicate that Gillespie algorithm can be a better choice for studying such systems, without using any approximation or elimination while having acceptable accuracy. In comparison with the chemical master equation, Gillespie algorithm is also provides a wide area for studying biological systems from other points of view.     

Molecular beam measurements and Monte Carlo simulations of the kinetics of N2O decomposition on Rh(111) single-crystal surfaces

The kinetics of N2O decomposition on Rh(111) single-crystal surfaces were investigated both experimentally by isothermal molecular beam measurements and theoretically using a Monte Carlo algorithm. The present work was directed to the understanding of two unusual observations derived from our previous work on this system, namely, (1) the lower rates for N2O decomposition seen at higher reaction temperatures, and (2) the lower total nitrogen yields and final oxygen surface coverages that accompany that behavior. Experimentally, it was determined here that after the rhodium surface is rendered inactive by N2O decomposition at high (520 K) temperatures, significant activity is still possible at lower (350 K) temperatures. The Monte Carlo simulations explain these observations by assuming that the surface sites required for the activation of adsorbed N2O increase in size with increasing reaction temperature.     

Oxygen island formation on Pt(111) studied by dynamic Monte Carlo simulation

The formation of oxygen islands on the Pt(111) surface has been studied as a function of temperature by low energy electron diffraction (LEED) experiments and dynamic Monte Carlo (DMC) simulations. By raising the temperature, the (2 x 2) LEED spot intensity increases gradually and decays after a peak at around 255 K (T(p)) with full width of half maximum of 160 K. This behavior is interpreted by DMC simulations with the kinematical LEED analysis. In the DMC simulation, an oxygen atom hops to the neighboring site via the activation barrier of the saddle point. The potential energies at initial, saddle, and final points are changed at each hopping event depending on the surrounding oxygen atoms. By comparing the observed T(p) with the simulated one, the interaction energy E of oxygen atoms on Pt(111) was determined to be 25+/-3 meV at 2a(0). The DMC simulations visualize how the oxygen islands are formed and collapse on Pt(111) with increase of the temperature and well reproduce the surface configurations observed by scanning tunneling microscopy.     

Generation of atomistic models of periodic mesoporous silica by kinetic Monte Carlo simulation of the synthesis of the material

We have developed a molecular simulation method for the generation of realistic atomic-level models for periodic mesoporous silicas. Using simplified interaction potentials and simplified representations of the templating micelles, the simulation follows the reaction path of the hydrothermal synthesis and calcination of the silica material in a kinetic Monte Carlo (kMC) simulation. The only input to the simulation is the geometry of the micelle and the number of silicic acid monomers at the beginning of the synthesis. We simulated the adsorption properties of the PMS models using Grand Canonical Monte Carlo simulation. With use of MCM-41 materials of different pore sizes as a prototype material, experimental and simulated adsorption isotherms for nitrogen, ethane, and carbon dioxide were compared, showing good agreement between simulation and experiment.     

Monte Carlo simulations of the adsorption of CO2 on the MgO(100) surface

The adsorption of CO2 gas on the MgO (100) crystal surface is investigated using grand canonical Monte Carlo simulations. This allows us to obtain adsorption isotherms that can be compared with experiment, as well as to explore the possible formation of monolayers of different densities. Our model calculations agree reasonably well with the available experimental results. We find a "low-density" adsorbed monolayer where each CO2 molecule is bound to two Mg2+ ions on the MgO substrate. We also observe the formation of monolayers of higher density, where some of the CO2 molecules have rotated and tilted to expose additional binding sites. Low-temperature simulations of both the low- and high-density monolayers reveal that these states are very close in energy, with binding energies of approximately 7 kcal/mol at T=5 K. The high-density monolayer given by our model has a density that is significantly less than the reported experimental value. We discuss this discrepancy and offer suggestions for resolving it.     

Structural investigations of polymer electrolyte poly(propylene oxide)-LiClO4 using diffraction experiments and reverse Monte Carlo simulation

The structure of an amorphous polymer electrolyte, poly(propylene oxide) (PPO) complexed with LiClO4, has been studied using reverse Monte Carlo (RMC) simulations. The simulations require no force field but are based on experimental data only, in this case from x-ray and neutron diffraction experiments. Excellent agreement between the experimental data and the structures resulting from the RMC simulation is obtained. Samples with ether-oxygen to lithium concentrations (molar ratios) O:Li=16:1 and 5:1 were studied and compared to results of pure PPO from a previous study. We focus on the effects of the solvated salt on the structure of the polymer matrix, the spatial distribution of ions, and the correlations between the anions and the polymer chains. Analyzing the structures produced in the simulations, we find that for a concentration 16:1, the interchain distance is approximately the same as in pure PPO but more well defined. For a concentration 5:1, we find a larger and less well-defined interchain distance compared to the 16:1 concentration. This signifies that at the 16:1 salt concentration, there is enough free volume in the polymer host to accommodate the ions, and that the solvation of salt induces ordering of the polymer matrix. At the higher salt concentration 5:1, the polymer network must expand and become less ordered to host the ions. We also note, in accordance with previous studies, that the solvation of salt changes the conformation of the polymer chain towards more gauche states. The simulations furthermore reveal marked correlations between the polymer chains and the anions, which we suggest arise predominantly from an interaction mediated via cations, which can simultaneously coordinate both ether oxygens in the polymer chains and anions. Interanionic distances at 5 A, which are consistent with two or more anions being coordinated around the same cation, are also observed. On a larger scale, the RMC structure of PPO-LiClO4 16:1 clearly indicates the presence of salt-rich and salt-depleted domains having a length scale of <20 A. In view of such a heterogeneous structure of PPO-LiClO4 16:1, it is plausible that the increased ordering of the polymer matrix is due to rather well-defined structural arrangements within the salt-rich domains, and that the characteristic interchain distance in the salt-rich domains is similar to that of the pure polymer.     

Simulation of aggregating particles in complex flows by the lattice kinetic Monte Carlo method

We develop and validate an efficient lattice kinetic Monte Carlo (LKMC) method for simulating particle aggregation in laminar flows with spatially varying shear rate, such as parabolic flow or flows with standing vortices. A contact time model was developed to describe the particle-particle collision efficiency as a function of the local shear rate, G, and approach angle, θ. This model effectively accounts for the hydrodynamic interactions between approaching particles, which is not explicitly considered in the LKMC framework. For imperfect collisions, the derived collision efficiency [?=1 - ∫(0)(π/2) sinθ exp(-2cotθΓ(agg)/G)dθ] was found to depend only on Γ(agg)∕G, where Γ(agg) is the specified aggregation rate. For aggregating platelets in tube flow, Γ(agg)=0.683 s(-1) predicts the experimentally measured ε across a physiological range (G = 40-1000 s(-1)) and is consistent with α(2b)β(3)-fibrinogen bond dynamics. Aggregation in parabolic flow resulted in the largest aggregates forming near the wall where shear rate and residence time were maximal, however intermediate regions between the wall and the center exhibited the highest aggregation rate due to depletion of reactants nearest the wall. Then, motivated by stenotic or valvular flows, we employed the LKMC simulation developed here for baffled geometries that exhibit regions of squeezing flow and standing recirculation zones. In these calculations, the largest aggregates were formed within the vortices (maximal residence time), while squeezing flow regions corresponded to zones of highest aggregation rate.     

Mechanism of electrocatalytic reduction of nitric oxide on Pt(100)

The mechanism of electrocatalytic reduction of nitric oxide on Pt(100)-(1 x 1) in acidic media has been studied using voltammetry, in-situ infrared spectroscopy, and on-line mass spectroscopy, considering the effect of surface defects, NO coverage, and the nature of the supporting electrolyte (sulfate vs perchlorate). Related mechanistic aspects of hydroxylamine (HAM) transformations on the same surface have been also examined. The adsorption of nitric oxide on Pt(100) results in the formation of an adlayer with a structure similar to that formed under ultrahigh vacuum (UHV) conditions. Ammonia was shown to be the main product of NOads reduction on Pt(100). The saturation coverage of NO adsorbate on Pt(100) was found to be around 0.5 ML, in agreement with previous UHV and electrochemical studies. Two features observed in the voltammetric profile for the electrocatalytic reduction of saturated and subsaturated NO adlayers were tentatively ascribed to reactions of NO species having different reactivity. The Tafel slope analysis of these voltammetric features gives values of ca. 60 mV decade(-1). This value was interpreted in terms of an EC mechanism, in which the first electron/proton transfer is at equilibrium, resulted in formation of HNOads intermediate, while the second reaction step is a chemical rate-determining step. This chemical step is assumed to involve the N-O bond breaking in HNOads intermediate, which most probably requires a free neighboring site. From a comparison with NOads reduction on Pt(111) and Pt(110), it follows that (i) the reaction mechanism is structure sensitive and (ii) Pt(100) is the most active surface for breaking the N-O bond, which is in agreement with the trend observed under UHV conditions. As suggested in our previous studies, the electrocatalytic reduction of HAM is likely to proceed through its partial dehydrogenation. In this study, we further develop this idea, and, based on the mechanism for NOads reduction proposed here, we suggest HNOads to be the intermediate appearing both in HAM reduction/oxidation and in NOads reduction.     

Dynamic Monte Carlo simulation of the NO + CO reaction on Rh(111)

The kinetics of the catalytic reduction of NO by CO on Rh(111) surfaces was investigated by using dynamic Monte Carlo simulations. Our model takes into account recent experimental findings and introduces relevant modifications to the classical reaction scheme, including an alternative pathway to produce N2 through an (N-NO)* intermediate, the formation of atomic nitrogen islands in the adsorbed phase, and the influence of coadsorbed species on the dissociation of NO. All elementary steps are expressed as activated processes with temperature-dependent rates and realistic values dictated by experiments. Calculated steady-state phase diagrams are presented for the NO + CO reaction showing the windows for the conditions under which the reaction is viable. The model predicts variations in both production rates and adsorbate coverages with temperature consistent with experimental data. The effect of varying the individual kinetic parameters and the importance of each step in the reaction scheme were probed.     

Monte Carlo methods for polymer chains in two - dimensional geometries (polymers at surfaces and interfaces)

Coarse-grained models of polymers at interfaces can be defined such that their treatment by Monte Carlo simulation is most convenient and efficient for the problem at hand. This simulation strategy is briefly illustrated with three examples: (1) The orientational ordering of rigid rod-like polymers grafted to a surface, where “table methods” can be used, applying a fine discretization of the angles describing rod orientation. (2) Surface enrichment of one species in a polymer blend is treated by a semi-grand-canonical technique. (3) The number of configurations and structure of a star polymer attached with its center to a wall is studied by a “growth technique” generalizing simple sampling methods.     

Kinetic study of the "surface explosion" phenomenon in the NO+CO reaction on Pt(100) through dynamic Monte Carlo simulation

The extremely narrow production peak of N2 and CO2 which occurs in the reaction of NO+CO on Pt(100), a phenomenon known as "surface explosion," is studied using a dynamic Monte Carlo method on a square lattice at low pressure under isothermal conditions. This analysis incorporates recent experimental evidence obtained for the same reaction on a Rh(111) surface, which has shown that N2 production occurs either from the classical N+N recombination step or by the formation and successive decay of a (N-NO)* intermediary species. Moreover, the NO dissociation rate is inhibited by coadsorbed NO and CO molecules and is enhanced both by the presence of empty sites and adsorbed N atoms as nearest neighbors. These effects are taken into account in this study, along with the experimental adsorption, desorption, and diffusion rates of the reactants. The "explosive" phenomenon is analyzed through the evolution over time of an adsorbed NO+CO monolayer at a fixed temperature of 400 K. Furthermore, as the diffusion processes of the adsorbates are included, cellular structures are observed. Our simulations show quantitative agreement in the position of maxima with those obtained through experiments using isothermal desorption mass spectroscopy.     

Structure and dynamics of a free aquaporin (AQP1) by a coarse-grained Monte Carlo simulation

Structure and dynamics of a free aquaporin (AQP1) are studied by a coarse-grained Monte Carlo simulation as a function of temperature using a phenomenological potential with the input of a knowledge-based residue–residue interaction. Response of the radius of gyration (R _g) of the protein to the temperature (T) is found to be nonlinear: Decay of R _g at T ≤ T _c is followed by a continuous increase at T ≥ T _c before reaching its saturation. In thermo-responsive regime, the protein exhibits segmental globularization with the persistence of three regions along its sequence involving residues ¹M–²⁵V and ²⁵⁰V–²⁶⁹K toward the beginning and end segments with a narrow intermediate region around ¹⁵⁵A–¹⁶³D. A detail analysis of the structure factor S(q) shows a global random coil conformation at high temperatures with an effective dimension D _e ~ 1.74 and a globular structure (D _e ~ 3) at low temperatures. In thermo-responsive regime, the variation of S(q) with the wave vector q reveals a systematic redistribution of self-organizing residues (in globular and fibrous sections) that depends on the length scale and the temperature.