Optimization of the facet structure of transition-metal catalysts applied to the oxygen reduction reaction.

Predicting the optimal structure for a catalytic material has been a long-standing goal, but typically an arbitrary active site on a uniform surface is modelled. Identification of the most-active facet structure for structure-sensitive chemistries, such as the oxygen reduction reaction, is lacking. Here we develop an approach to predict the optimal structure of a catalytic material by identifying the active site and identifying the density and spatial arrangement of such sites while minimizing the surface energy. We find that the theoretical peak performance predicted by linear scaling relations is unattainable because of the lack of suitable active sites on low-index planes, as well as geometric and stability constraints. A random array of vacancies results in a modest performance enhancement compared to ideal facets, whereas defect sites with a maximum density in disordered structures significantly increase the catalyst performance. We applied this methodology to the oxygen reduction reaction on defected Pt(111), Pt(100), Au(111) and Au(100) surfaces.

Acceleration and sensitivity analysis of lattice kinetic Monte Carlo simulations using parallel processing and rate constant rescaling.

Kinetic Monte Carlo (KMC) simulation provides insights into catalytic reactions unobtainable with either experiments or mean-field microkinetic models. Sensitivity analysis of KMC models assesses the robustness of the predictions to parametric perturbations and identifies rate determining steps in a chemical reaction network. Stiffness in the chemical reaction network, a ubiquitous feature, demands lengthy run times for KMC models and renders efficient sensitivity analysis based on the likelihood ratio method unusable. We address the challenge of efficiently conducting KMC simulations and performing accurate sensitivity analysis in systems with unknown time scales by employing two acceleration techniques: rate constant rescaling and parallel processing. We develop statistical criteria that ensure sufficient sampling of non-equilibrium steady state conditions. Our approach provides the twofold benefit of accelerating the simulation itself and enabling likelihood ratio sensitivity analysis, which provides further speedup relative to finite difference sensitivity analysis. As a result, the likelihood ratio method can be applied to real chemistry. We apply our methodology to the water-gas shift reaction on Pt(111).

Steady state likelihood ratio sensitivity analysis for stiff kinetic Monte Carlo simulations.

Kinetic Monte Carlo simulation is an integral tool in the study of complex physical phenomena present in applications ranging from heterogeneous catalysis to biological systems to crystal growth and atmospheric sciences. Sensitivity analysis is useful for identifying important parameters and rate-determining steps, but the finite-difference application of sensitivity analysis is computationally demanding. Techniques based on the likelihood ratio method reduce the computational cost of sensitivity analysis by obtaining all gradient information in a single run. However, we show that disparity in time scales of microscopic events, which is ubiquitous in real systems, introduces drastic statistical noise into derivative estimates for parameters affecting the fast events. In this work, the steady-state likelihood ratio sensitivity analysis is extended to singularly perturbed systems by invoking partial equilibration for fast reactions, that is, by working on the fast and slow manifolds of the chemistry. Derivatives on each time scale are computed independently and combined to the desired sensitivity coefficients to considerably reduce the noise in derivative estimates for stiff systems. The approach is demonstrated in an analytically solvable linear system.

Stochastic simulations of ErbB homo and heterodimerisation: potential impacts of receptor conformational state and spatial segregation.

ErbB overexpression is linked to carcinogenesis. It is hypothesised that this is due to increased receptor density and receptor clustering, leading to increased receptor dimerisation and activation. Herein, spatial stochastic simulations have been performed to shed light receptor dimerisation processes. First, ligand-independent homodimerisation, is considered, based upon constitutive oligomerisation estimates (14%) in A431 cells that overexpress epidermal growth factor receptor (EGFR). When autocrine stimulation is blocked, ligand-independent EGFR activation is demonstrated by persistent, low levels of phosphorylation. The possibility that ligand-independent signalling is due to the fluctuation of EGFR conformation is considered. The agent-based model predicts the frequency (expressed as a probability) that uniformly distributed receptors would need to flux to the open conformation to reach 14% EGFR dimers at high receptor density. Simulations suggest that ligand-independent EGFR homodimerisation is highly density dependent, since collisions between 'open', dimerisation-competent receptors are a rare event at low receptor levels. Simulations that incorporate receptor clustering lower the threshold for homodimerisation of unoccupied receptors as well as the estimate of the probability for fluxing to the dimer-competent conformation. The impact of ErbB receptor clustering patterns on hetero and homodimerisation rates is also considered, using immunoelectron microscopy data derived from SKBR3 breast cancer cells that express ErbB2>>EGFR>ErbB3. Partial spatial segregation of ErbB receptors has a profound effect on simulated heterodimerisation rates. Despite the general assumption that ErbB2 is a preferred heterodimerising partner for other ErbBs, it is predicted that most ErbB2 will form homodimers. Overall, it is proposed that both receptor density and membrane spatial organisation contribute to the carcinogenesis process.

Temporal coarse-graining of microscopic-lattice kinetic Monte Carlo simulations via tau leaping.

A coarse-time-step method is presented that enables the execution of multiple events at each time increment of microscopic-lattice kinetic Monte Carlo simulations. The method employs the n-fold method to create groups of reactions in which the tau-leap algorithm of Gillespie, originally proposed for well-mixed systems, is applied. Creation of groups of reactions is an essential step to avoid violation of the leap condition that arises when the tau-leap algorithm is applied to a single site. The method is general, very easy to implement, and can result in substantial computational savings when global updating is employed. An illustrative example from crystal growth of a simple cubic lattice with the solid-on-solid approximation is presented.

Molecular dynamics study of the stabilization of the silica hexamer Si6O15(6-) in aqueous and methanolic solutions.

We use molecular dynamics simulations to study the stabilization of the hexameric, cagelike silicate with double three-ring structure in aqueous and methanolic solutions. We find that in purely aqueous environments its stabilization requires the presence of both tetramethylammonium and tetraethylammonium (TEA) cations and involves the formation of a stable TMA layer which leads to a water-silicate heteronetwork clathrate. We also find that TEA alone can facilely stabilize the hexamer when methanol cosolvent is added, in accordance with experiment. The mechanism of this stabilization, however, differs from that in purely aqueous environments. Because of the unique properties of water-methanol mixtures, the organosilicate complex does not participate in heteronetwork clathrates but resides in a large solvent cavity; that is, it is forced out of true solution.

Potential of mean force for tetramethylammonium binding to cagelike oligosilicates in aqueous solution.

We have carried out free energy calculations to compute the potential of mean force for the cagelike silicate polyion-TMA+ cation ion pair interaction in aqueous solution. We also have studied solvent reorganization-related entropic effects. We conclude that the organocations, as opposed to, for example, alkali-metal ions, play a pivotal role in reorganizing the solvent around the cagelike silicates in a manner conducive to the formation of heteronetwork clathrates that are stable both thermodynamically and kinetically. In the case of stable cagelike polysilicate anions, this solvent reorganization correlates with entropic losses. We also infer that transient cagelike polysilicate species, that may indeed form but participate in floppy clathrates, eventually have to give way to cagelike polysilicates that lead to more rigid structures.

The role of molecular interactions and interfaces in diffusion: transport diffusivity and evaluation of the Darken approximation.

Kinetic Monte Carlo (KMC) simulations are carried out to directly study diffusion of benzene through thin (37-100 nm) NaX zeolite membranes under a gradient in chemical potential. Nonlinearities in adsorbate loading near the membrane boundaries are shown to arise from the difference in adsorbate density between the zeolite and adjacent fluid phase. Direct extraction of the transport diffusivity from gradient KMC simulations enables testing of the Darken approximation. This rigorous approach reveals limitations of the Darken approximation and, for the first time, the potentially complex nonunique functionality and multiplicity of the transport diffusivity for strongly interacting adsorbates. In the companion paper we explore these nonlinear interfacial effects in the context of permeation through both single-crystal and polycrystalline membranes.

The role of molecular interactions and interfaces in diffusion: permeation through single-crystal and polycrystalline microporous membranes.

In this second paper of a two part series, we investigate the implications of the interfacial phenomenon, caused by adsorbate-adsorbate interactions coupled with the difference in adsorbate density between the zeolite and the gas phase, upon benzene permeation through single-crystal and polycrystalline microporous NaX membranes. The high flux predicted for thin single-crystal membranes reveals that substantially enhanced flux should be expected in submicron films. Simulations also indicate that the standard local equilibrium assumption made for larger scale membranes is inapplicable at the submicron scale associated with nanometer size grains of thin and/or polycrystalline membranes. Apparent activation energies predicted for benzene permeation through NaX membranes via kinetic Monte Carlo (KMC) simulations are in good agreement with laboratory experiments. The simulations also uncover temperature-dependent flux pathways leading to non-Arrhenius behavior observed experimentally. The failure of the Darken approximation, especially in the presence of the interfacial phenomenon, leads to a substantial overprediction of the flux. Simulations of polycrystalline membranes suggest that this same interfacial phenomenon leads to resistance that can reduce flux by an order of a magnitude with only moderate polycrystallinity.

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.

Molecular valves actuated by intermolecular forces.

Phase behavior in nanostructured thin films under a gradient in chemical potential is studied via kinetic Monte Carlo simulation. Switching between saturated, partially saturated, and unsaturated states drives precipitous changes in permeation. This phenomenon could render nanostructured thin films as molecular valves, where adsorbate-adsorbate forces actuate the flow of molecules.

Molecular sieve valves driven by adsorbate-adsorbate interactions: hysteresis in permeation of microporous membranes.

A recently derived mesoscopic framework describing activated micropore diffusion is employed to explore system criticality in microporous membranes under nonequilibrium conditions. Rapid exploration of parameter space, possible with this continuum framework, elucidates a novel temperature-induced ignition and extinction of the molecular flux under a macroscopic gradient in pressure (chemical potential). Deviation from equilibrium like phase behavior (i.e., shifting and narrowing of phase envelopes and double hysteresis) derives from asymmetry of the coupled boundaries of the nonequilibrium membrane. We confirm this new phase behavior, akin to "opening" and "closing" of a molecular valve, via gradient kinetic Monte Carlo simulations of thin one-dimensional and three-dimensional systems. The heat of adsorption, strength of adsorbate-adsorbate intermolecular forces, and chemical potential gradient are all shown to control 'valve' actuation, suggesting potential implications in chemical sensing and novel diffusion control.

Spatially adaptive grand canonical ensemble Monte Carlo simulations.

A spatially adaptive Monte Carlo method is introduced directly from the underlying microscopic mechanisms, which satisfies detailed balance, gives the correct noise, and describes accurately dynamic and equilibrium states for adsorption-desorption (grand canonical ensemble) processes. It enables simulations of large scales while capturing sharp gradients with molecular resolution at significantly reduced computational cost. A posteriori estimates, in the sense used in finite-elements methods, are developed for assessing errors (information loss) in coarse-graining and guiding mesh generation.

Molecular dynamics studies on the role of tetramethylammonium cations in the stability of the silica octamers Si8O20(8-) in solution.

The stability of silica octamers, Si(8) observed in tetramethylammonium (TMA) solutions by Kinrade et al. is investigated in connection with the TMA concentration by performing equilibrium molecular dynamics simulations of Si(8)-TMA-water mixture at two concentrations. At the experimental concentration at which the silica octamers have been observed spectroscopically, we find that, on the average, six TMA molecules surround the silica octamer, coordinated so that each cation occupies a face of the cubic octamer. We also find that upon TMA adsorption, water molecules associated with the siloxane oxygens leave the silica surface, whereas the hydrogen-bond network of the silanol oxygens with water molecules remains intact. No TMA adsorption is observed at the concentration at which the octamers have not been observed.

Hierarchical multiscale mechanism development for methane partial oxidation and reforming and for thermal decomposition of oxygenates on Rh.

A thermodynamically consistent C1 microkinetic model is developed for methane partial oxidation and reforming and for oxygenate (methanol and formaldehyde) decomposition on Rh via a hierarchical multiscale methodology. Sensitivity analysis is employed to identify the important parameters of the semiempirical unity bond index quadratic exponential potential (UBI-QEP) method and these parameters are refined using quantum mechanical density functional theory. With adjustment of only two pre-exponentials in the CH4 oxidation subset, the C1 mechanism captures a multitude of catalytic partial oxidation (CPOX) and reforming experimental data as well as thermal decomposition of methanol and formaldehyde. We validate the microkinetic model against high-pressure, spatially resolved CPOX experimental data. Distinct oxidation and reforming zones are predicted to exist, in agreement with experiments, suggesting that hydrogen is produced from reforming of methane by H2O formed in the oxidation zone. CO is produced catalytically by partial oxidation up to moderately high pressures, with water-gas shift taking place in the gas-phase at sufficiently high pressures resulting in reduction of CO selectivity.

Bifurcation analysis of Liesegang ring pattern formation.

Bifurcation analysis is introduced to a prototype Liesegang ring (LR) model to explain pattern formation as an instability of a propagating plane reaction front. A theoretical criterion for the onset of patterning is derived and numerically tested. The uneven spacing law of LR bands is explained as a consequence of the time varying velocity of the moving reaction front. Suggestions for controlling pattern formation are provided.

Reaction network reduction for distributed systems by model training in lumped reactors: Application to bifurcations in combustion.

A new methodology is presented to derive reduced reaction mechanisms for distributed reacting flows by model training in a lumped parameter system (a continuous-stirred tank reactor). The method identifies the relevant transport time scales in the reaction zone of a distributed system along with the local composition vector, over a range of operation conditions. A training box in the parameter space of pressure-transport time scale-composition is then identified. Sensitivity and principal component analyses are subsequently performed at bifurcation points in a lumped parameter system at representative conditions of the training box. The most inclusive chemistry derived in the lumped system captures the proper transport-chemistry coupling and is suitable for the distributed reactor. Application to ignition of hydrogen/air and methane/air mixtures is presented and validated for premixed and diffusion flames in a stagnation flow geometry. (c) 1999 American Institute of Physics.