Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.     

Modulation of electron transfer kinetics by protein conformational fluctuations during early-stage photosynthesis

The kinetics of electron transfer during the early stages of the photosynthetic reaction cycle has recently been shown in transient absorption experiments carried out by Wang et al. [Science 316, 747 (2007)] to be strongly influenced by fluctuations in the conformation of the surrounding protein. A model of electron transfer rates in polar solvents developed by Sumi and Marcus using a reaction-diffusion formalism [J. Chem. Phys. 84, 4894 (1986)] was found to be successful in fitting the experimental absorption curves over a roughly 200 ps time interval. The fits were achieved using an empirically determined time-dependent function that described protein conformational relaxation. In the present paper, a microscopic model of this function is suggested, and it is shown that the function can be identified with the dynamic autocorrelation function of intersegment distance fluctuations that occur in a harmonic potential of mean force under the action of fractional Gaussian noise.     

Concentration fluctuations in nonisothermal reaction-diffusion systems

In this paper a simple reaction-diffusion system, namely a binary fluid mixture with an association-dissociation reaction between the two components, is considered. Fluctuations at hydrodynamic spatiotemporal scales when a temperature gradient is present in this chemically reacting system are studied. First, fluctuating hydrodynamics when the system is in global equilibrium (isothermal) is reviewed. Comparing the two cases, an enhancement of the intensity of concentration fluctuations in the presence of a temperature gradient is predicted. The nonequilibrium concentration fluctuations are spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a proportional, variantq(-4) to a proportional, variantq(-2) behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion- or activation-controlled regimes of the reaction by measuring these fluctuations. In addition, the possible observation of these fluctuations in nonequilibrium molecular dynamics simulations is considered.     

SBS/Pani · DBSA mixture plasticized with DOP and NCLS - Effect of the plasticizers on the probability density of volume resistivity measurements

Plasticized mixtures of styrene-butadiene-styrene block copolymer (SBS) and Polyaniline (Pani) were prepared in a Haake internal mixer. Two different plasticizers were used: dioctyl phthalate (DOP) and cashew nut shell liquid (CNSL). Pani and plasticizers were characterized by FTIR and the resistive behavior of plasticized mixtures was investigated along the electrification time. It is shown that obtained experimental data are subject to deterministic dynamic fluctuations that cannot be described by single normal probability distribution functions (PDF) along the time. The PDF analysis shows that obtained PDFs must be described as sums of at least three distinct Gaussian distributions with different areas. It is also shown that the Gaussian component with larger area may provide better representation of the measured volume resistivity values.     

Computer simulation of a binary polymer mixture in three dimensions

The behavior of a binary polymer mixture was simulated on a cubic lattice over both the miscibility and immiscibility regions. The number and distribution of interactions in the mixture were found to be different from the mean-field picture; however, the observed phase behavior agrees with that predicted by the mean-field theory and is not affected by the observed concentration fluctuations. The relationship between the phenomenological χ parameter and the heterosegmental interaction energy was investigated. Polymer chains show nearly ideal behavior, even for strongly interacting mixtures; this simplifies the theoretical treatment of polymer mixtures analogous to homopolymer melts.     

Mesoscopic dynamics of diffusion-influenced enzyme kinetics

A particle-based mesoscopic model for enzyme kinetics is constructed and used to investigate the influence of diffusion on the reactive dynamics. Enzymes and enzyme-substrate complexes are modeled as finite-size soft spherical particles, while substrate, product, and solvent molecules are point particles. The system is evolved using a hybrid molecular dynamics-multiparticle collision dynamics scheme. Both the nonreactive and reactive dynamics are constructed to satisfy mass, momentum, and energy conservation laws, and reversible reaction steps satisfy detailed balance. Hydrodynamic interactions among the enzymes and complexes are automatically accounted for in the dynamics. Diffusion manifests itself in various ways, notably in power-law behavior in the evolution of the species concentrations. In accord with earlier investigations, regimes where the product production rate exhibits either monotonic or nonmonotonic behavior as a function of time are found. In addition, the species concentrations display both t(-1/2) and t(-3/2) power-law behavior, depending on the dynamical regime under investigation. For high enzyme volume fractions, cooperative effects influence the enzyme kinetics. The time dependent rate coefficient determined from the mass action rate law is computed and shown to depend on the enzyme concentration. Lifetime distributions of substrate molecules newly released in complex dissociation events are determined and shown to have either a power-law form for rebinding to the same enzyme from which they were released or an exponential form for rebinding to different enzymes. The model can be used and extended to explore a variety of issues related concentration effects and diffusion on enzyme kinetics.     

CO oxidation on Ir(111) surfaces under large non-Gaussian noise

In this article we consider the CO oxidation on Ir(111) surfaces under large external noise with large autocorrelation imposed on the composition of the feed gas, both in experiments and in theory. We report new experimental results that show how the fluctuations force the reaction rate to jump between two well defined states. The statistics of the reaction rate depend on those of the external noise, and neither of them have a Gaussian distribution, and thus they cannot be modeled by white or colored noise. A continuous-time discrete-state Markov process is proposed as a suitable model for the observed phenomena. The model captures the main features of the observed fluctuations and can be modified to accommodate other surface reactions and other systems under non-Gaussian external noise.     

Hydrogen motions in the alpha-relaxation regime of poly(vinyl ethylene): a molecular dynamics simulation and neutron scattering study

The hydrogen motion in poly(vinyl ethylene) (1,2-polybutadiene) in the alpha-relaxation regime has been studied by combining neutron spin echo (NSE) measurements on a fully protonated sample and fully atomistic molecular dynamics simulations. The almost perfect agreement between experiment and simulation results validates the simulated cell. A crossover from Gaussian to non-Gaussian behavior is observed for the intermediate scattering function obtained from both NSE measurements and simulations. This crossover takes place at unusually low Q values, well below the first maximum of the static structure factor. Such anomalous deviation from Gaussian behavior can be explained by the intrinsic dynamic heterogeneity arising from the differences in the dynamics of the different protons in this system. Side group hydrogens show a markedly higher mobility than main chain protons. Taking advantage of the simulations we have investigated the dynamic features of all different types of hydrogens in the sample. Considering each kind of proton in an isolated way, deviations from Gaussian behavior are also found. These can be rationalized in the framework of a simple picture based on the existence of a distribution of discrete jumps underlying the atomic motions in the alpha process.     

Electric field versus surface alignment in confined films of a diblock copolymer melt

The dynamics of alignment of microstructure in confined films of diblock copolymer melts in the presence of an external electric field was studied numerically. We consider in detail a symmetric diblock copolymer melt, exhibiting a lamellar morphology. The method used is a dynamic mean-field density functional method, derived from the generalized time-dependent Ginzburg-Landau theory. The time evolution of concentration variables and therefore the alignment kinetics of the morphologies are described by a set of stochastic equations of a diffusion form with Gaussian noise. We investigated the effect of an electric field on block copolymers under the assumption that the long-range dipolar interaction induced by the fluctuations of composition pattern is a dominant mechanism of electric-field-induced domain alignment. The interactions with bounding electrode surfaces were taken into account as short-range interactions resulting in an additional term in the free energy of the sample. This term contributes only in the vicinity of the surfaces. The surfaces and the electric field compete with each other and align the microstructure in perpendicular directions. Depending on the ratio between electric field and interfacial interactions, parallel or perpendicular lamellar orientations were observed. The time scale of the electric-field-induced alignment is much larger than the time scale of the surface-induced alignment and microphase separation.     

Complex chemical kinetics in single enzyme molecules: Kramers's model with fractional Gaussian noise

A model of barrier crossing dynamics governed by fractional Gaussian noise and the generalized Langevin equation is used to study the reaction kinetics of single enzymes subject to conformational fluctuations. The direct application of Kramers's flux-over-population method to this model yields analytic expressions for the time-dependent transmission coefficient and the distribution of waiting times for barrier crossing. These expressions are found to reproduce the observed trends in recent simulations and experiments.     

Diffusion-limited many-body reactions in one dimension and the method of interparticle distribuion functions

The method of interparticle distribution functions (IPDF) has yielded several exact solutions of the kinetics of diffusion-limited reaction processes in one dimension. We generalize the IPDF method to the case where lattice sites may be occupied by more than one particle and apply it to the reaction processes v → μ (v>μ). We briefly review the case of v = 2, for which the kinetics is anomalous, that is, does not agree with the predictions of classical rate equations. The case lf v = 3 is marginal. We compute the exact leading time behavior of the concentration decay, and the distribution of distances between nearest particles in the long time asymptotic limit. From the results of extensive simulations, we observe the previously postulated logarithmic corrections to the concentration power-law-decay. The case of v > 3 is well decribed by classical rate equations. We show how this is expressed in the IPDF approach.     

Slow dynamics of the high density Gaussian core model

We numerically study crystal nucleation and glassy slow dynamics of the one-component Gaussian core model (GCM) at high densities. The nucleation rate at a fixed supercooling is found to decrease as the density increases. At very high densities, the nucleation is not observed at all in the time window accessed by long molecular dynamics (MD) simulation. Concomitantly, the system exhibits typical slow dynamics of the supercooled fluids near the glass transition point. We compare the simulation results of the supercooled GCM with the predictions of mode-coupling theory (MCT) and find that the agreement between them is better than any other model glassformers studied numerically in the past. Furthermore, we find that a violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than canonical glassformers. Analysis of the probability distribution of the particle displacement clearly reveals that the hopping effect is strongly suppressed in the high density GCM. We conclude from these observations that the GCM is more amenable to the mean-field picture of the glass transition than other models. This is attributed to the long-ranged nature of the interaction potential of the GCM in the high density regime. Finally, the intermediate scattering function at small wavevectors is found to decay much faster than its self part, indicating that dynamics of the large-scale density fluctuations decouples with the shorter-ranged caging motion.