Monte Carlo simulation of equilibrium reactions at modified vapor-liquid interfaces

The equilibrium conversion of a chemical reaction is known to be affected by its local environment. Various factors may alter reaction equilibria, including shifts in pressure or temperature, solvation, adsorption within porous materials, or the presence of an interface. Previously, reactive Monte Carlo simulations have been used to predict the equilibrium behavior of chemical reactions at vapor-liquid interfaces. Here, a route is tested for tuning the interfacial conversion of a Lennard-Jones dimerization reaction by adding surfactants to the vapor-liquid interface. Several temperatures are explored as well as several different surfactant models. Even with the addition of a small concentration of surfactants, the simulations predict significant shifts in the conversion at the interface. In general, the shifts in the conversion tend to be related to the values of the interfacial tension.     

Monte Carlo simulation of vapor-liquid equilibrium and critical asymmetry of square-well dimer fluid

The critical behavior of square-well dimer fluid has been investigated using grand canonical ensemble Monte Carlo simulations combined with a histogram reweighting technique, hyper-parallel tempering and finite-size scaling. The critical temperature and density obtained are T(c)*=1.5495±0.0009 and ρ(c)*=0.1473±0.0007, which are 2.5% lower and 5.2% higher than previous results. Coexistence curves both near to and far from the critical point were obtained. The vapor-liquid equilibrium data far from the critical point are consistent with previous results. Simulation results show that the contribution of |t|(1-α) to the coexistence diameter of square-well dimer fluid dominates the critical behavior and the contribution of |t|(2β) is larger than for a hard-core square-well fluid.     

A Monte Carlo simulation of diffusion-controlled reactions in inhomogeneous systems

A random-walk model has been developed to treat the kinetics of reactions taking place in spurs at different solute concentrations. The dependence of the molecular yields on solute concentration has been studied using Monte Carlo techniques for simulation of the formation of spurs and of the random movement of the reactive species.     

Monte Carlo simulation of electron-ion recombination at high pressure

The Monte Carlo method is applied to the study of electron-ion recombination in CO₂, CH₄ and NH₃ over a wide range of pressures. Dissociative recombination is enhanced by energy transfer to the ambient gas molecules and the recombination rates peak at 11, 2 and 9 × 10⁵ CM³ s^?1, respectively. At very high pressures, the rate approaches the Langevin limit.     

Monte Carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers

Grand canonical Monte Carlo simulations of a simple model semiflexible equilibrium polymer system, consisting of hard sphere monomers reversibly self-assembling into chains of arbitrary length, have been performed using a novel sampling method to add or remove multiple monomers during a single MC move. Systems with two different persistence lengths and a range of bond association constants have been studied. We find first-order lyotropic phase transitions between isotropic and nematic phases near the concentrations predicted by a statistical thermodynamic theory, but with significantly narrower coexistence regions. A possible contribution to the discrepancy between theory and simulation is that the length distribution of chains in the nematic phase is bi-exponential, differing from the simple exponential distribution found in the isotropic phase and predicted from a mean-field treatment of the nematic. The additional short length-scale characterizing the distribution appears to arise from the lower orientational order of short chains. The dependence of this length-scale on chemical potential, bond association constant, and total monomer concentration has been examined.     

Monte Carlo adiabatic simulation of equilibrium reacting systems: The ammonia synthesis reaction

We present an application of the recently developed Monte Carlo method for simulations at fixed total enthalpy [W. R. Smith, M. Lísal, Phys. Rev. E 66 (2002) 01114-1–01114-3], combined with the reaction ensemble Monte Carlo method, for the direct prediction of equilibrium reactive adiabatic processes. For the industrially important ammonia synthesis reaction in an adiabatic plug-flow reactor, we perform direct simulations of the equilibrium reaction temperature and the composition of the exit stream as a function of the temperature and pressure of the inlet stream. The chemical species of the system are represented by all-atom potentials with interaction parameters taken from the literature. The accuracy of the molecular model is validated by comparing simulation results with experimental data. We also compare the simulation results with a macroscopic thermodynamic model based on the Soave–Redlich–Kwong equation of state. The simulation results for the reaction conversion show very good agreement with available experimental data over a wide range of temperatures and pressures, whereas the corresponding results from the macroscopic thermodynamic model slightly deteriorate with increasing pressure. Based on these comparisons, the predicted values of the reaction temperature and composition of the exit stream from the simulations are more accurate than the corresponding predicted values from the macroscopic thermodynamic model.     

Monte Carlo simulation of diffusion effects on chain‐extension reactions

The diffusion effects on chain‐extension reactions using carboxyl‐terminated polyamide‐12 as a model reactant with bisoxazolines were investigated by the stochastic Monte Carlo method. Thus, complicated direct modeling and numerical calculations were avoided. The chain‐length dependence and detailed diffusive behavior were discussed in depth. The diffusion effects retarded the progress of chain‐extension reactions and led to lower coupling efficiency. The simulated results indicated that the diffusion effects could make the final molecular weight distributions wider. In the presence of diffusion and with the progress of the coupling efficiency, peaks in the evolution curves of the weight‐average molecular weight and valleys in the evolution curves of the polydispersity index were observed, respectively, when the coupling efficiency was low enough. These phenomena were different from those without diffusion effects and were analyzed in detail. The critical entanglement chain length had strong effects on the simulated results of the diffusion effects, especially when its value was near the average chain length. The results also showed that the effects of the reactant degradation made the molecular weight distribution of the reaction system wider and weakened the diffusion effects on the coupling reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2902–2911, 2006     

Nonlinear response of the surface electrostatic potential formed at metal oxide/electrolyte interfaces. A Monte Carlo simulation study

An analysis of surface potential nonlinearity (ψ₀) at metal oxide/electrolyte interfaces is presented. By using grand canonical Monte Carlo simulations of a simple lattice model of an interface, we show that a correlation exists between ionic strength, as well as surface site densities, and the non-Nernstian response of a metal-oxide electrode. We propose two approaches to deal with the ψ₀-nonlinearity: one based on perturbative expansion of the Gibbs free energy and another based on the assumption of the pH dependence of surface potential slope. The theoretical analysis based on our new potential form gives excellent performance in extreme pH regions, where classical formulae for ψ₀ are unjustified. The new formula is general and independent of any underlying assumptions. For this reason, it can be directly applied to experimental surface potential measurements, including those for individual surfaces of single crystals, as we present for data reported by Kallay and Preo?anin [6].     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

Simulations of vapor water clusters at vapor-liquid equilibrium

The Gibbs-ensemble Monte Carlo methods based on the extended single point charge [H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. 91, 6269 (1987)] potential-energy surface have been used to study the clustering of vapor phase water under vapor-liquid equilibrium conditions between 300 and 600 K. It is seen that the number of clusters, as well as the cluster size, increase with temperature. This is primarily due to the increase in vapor density that accompanies the temperature increase at equilibrium. In addition, due to entropic effects, the percentage of clusters that have linear (or open) topologies increases with temperature and dominates over the minimum-energy cyclic topologies at the temperatures studied here. These results are insensitive to the number of molecules used in the simulations and the criterion used to define a water cluster.     

Order-parameter-based Monte Carlo simulation of crystallization

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.     

Monte Carlo simulation of hard spheroids

We present Monte Carlo simulations of the equation of state and radial distribution function for a model fluid composed of hard spheroids.     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Overcoming stiffness in stochastic simulation stemming from partial equilibrium: a multiscale Monte Carlo algorithm

In this paper the problem of stiffness in stochastic simulation of singularly perturbed systems is discussed. Such stiffness arises often from partial equilibrium or quasi-steady-state type of conditions. A multiscale Monte Carlo method is discussed that first assesses whether partial equilibrium is established using a simple criterion. The exact stochastic simulation algorithm (SSA) is next employed to sample among fast reactions over short time intervals (microscopic time steps) in order to compute numerically the proper probability distribution function for sampling the slow reactions. Subsequently, the SSA is used to sample among slow reactions and advance the time by large (macroscopic) time steps. Numerical examples indicate that not only long times can be simulated but also fluctuations are properly captured and substantial computational savings result.