Effects of excluded volume interaction and dimensionality on diffusion-mediated reactions

Bimolecular photo-induced electron transfer enlightened by diffusion

Photochemical electron transfer between freely diffusing molecules has been studied extensively. Here, we try to elucidate how much these works have contributed to the understanding of electron transfer. To this end, we have revisited the work performed in the experimental and theoretical areas of concern from the beginning of the 20th century up to the present day. We present a critical look at the major contributions and compile the current picture of a variety of phenomena around electron transfer in solution. This is based on two main developments, besides the theory of Marcus: encounter theories of diffusion and laser techniques in time-resolved spectroscopy.

Interplay of reactive interference and crowding effects in the diffusion-influenced reaction kinetics

We investigate the interplay of reactive interference and crowding effects in the irreversible diffusion-influenced bimolecular reactions of the type A+B→P+B by using the Brownian dynamics simulation method. It is known that the presence of nonreactive crowding agents retards the reaction rate when the volume fraction of the crowding agents is large enough. On the other hand, a high concentration of B is known to increase the reaction rate more than expected from the mass action law, although the B's may also act as crowders. Therefore, it would be interesting to see which effect dominates when the number density of B as well as the number density of the crowders increases. We will present an approximate theory that provides a reasonable account for the Brownian dynamics simulation results.

Concentration effects on the rates of irreversible diffusion-influenced reactions

We formulate a new theory of the effects of like-particle interactions on the irreversible diffusion-influenced bimolecular reactions of the type A + B → P + B by considering the evolution equation of the triplet ABB number density field explicitly. The solution to the evolution equation is aided by a recently proposed method for solving the Fredholm integral equation of the second kind. We evaluate the theory by comparing its predictions with the results of extensive computer simulations. The present theory provides a reasonable explanation of the simulation results.

Survival of a static target in a gas of diffusing particles with exclusion

Let a lattice gas of constant density, described by the symmetric simple exclusion process, be brought in contact with a "target": a spherical absorber of radius R. Employing the macroscopic fluctuation theory (MFT), we evaluate the probability P(T) that no gas particle hits the target until a long but finite time T. We also find the most likely gas density history conditional on the nonhitting. The results depend on the dimension of space d and on the rescaled parameter ℓ=R/√[D(0)T], where D(0) is the gas diffusivity. For small ℓ and d>2, P(T) is determined by an exact stationary solution of the MFT equations that we find. For large ℓ, and for any ℓ in one dimension, the relevant MFT solutions are nonstationary. In this case, lnP(T) scales differently with relevant parameters, and it also depends on whether the initial condition is random or deterministic. The latter effects also occur if the lattice gas is composed of noninteracting random walkers. Finally, we extend the formalism to a whole class of diffusive gases of interacting particles.

Tracer dynamics in a single-file system with absorbing boundary

The paper addresses the single-file diffusion in the presence of an absorbing boundary. The emphasis is on an interplay between the hard-core interparticle interaction and the absorption process. The resulting dynamics exhibits several qualitatively new features. First, starting with the exact probability density function for a given particle (a tracer), we study the long-time asymptotics of its moments. Both the mean position and the mean-square displacement are controlled by dynamical exponents which depend on the initial order of the particle in the file. Second, conditioning on nonabsorption, we study the distribution of long-living particles. In the conditioned framework, the dynamical exponents are the same for all particles, however, a given particle possesses an effective diffusion coefficient which depends on its initial order. After performing the thermodynamic limit, the conditioned dynamics of the tracer is subdiffusive, the generalized diffusion coefficient D(1/2) being different from that reported for the system without absorbing boundary.

Roles of nucleation, denucleation, coarsening, and aggregation kinetics in nanoparticle preparations and neurological disease

Kinetic models for nucleation, denucleation, Ostwald ripening (OR), and nanoparticle (NP) aggregation are presented and discussed from a physicochemical standpoint, in terms of their role in current NP preparations. Each of the four solid-state mechanisms discussed predict a distinct time dependence for the evolution of the mean particle radius over time. Additionally, they each predict visually different particle size distributions (PSDs) under limiting steady-state (time-independent) conditions. While nucleation and denucleation represent phase transformation mechanisms, OR and NP aggregation do not. Thus, when modeling solid-state kinetics relevant to NP processing, either the time evolution of the mean particle radius or the fractional conversion data should be fit using appropriate models (discussed herein), without confusing/combining the two classes of models. Experimental data taken from the recent literature are used to demonstrate the usefulness of the models in real-world applications. Specifically, the following examples are discussed: the preparation of bismuth NPs, the synthesis of copper indium sulfide nanocrystals, and the aggregation of neurological proteins. Because the last process is found to obey reaction-limited colloid aggregation (RLCA) kinetics, potential connections between protein aggregation rates, the onset of neurological disease, and population lifespan dynamics are suggested by drawing a parallel between RLCA kinetics and Gompertz kinetics. The physical chemistry underpinning NP aggregation is investigated, and a detailed definition of the rate constant of aggregation, k(a), is put forth that provides insight into the origin of the activation energy barrier of aggregation. For the two nanocrystal preparations investigated, the initial kinetics are found to be well-described by the author's dispersive kinetic model for nucleation-and-growth, while the late-stage NP size evolution is dominated by OR. At intermediate times, it is thought that the two mechanisms both contribute to the NP growth, resulting in PSD focusing as discussed in a previous work [Skrdla, P. J. J. Phys. Chem. C2012, 116, 214-225]. On the basis of these two mechanisms, a synthetic procedure for obtaining monodisperse NP PSDs, of small and/or systematically targeted mean sizes, is proposed.

Diffusion-mediated geminate reactions under excluded volume interactions

In this paper, influence of crowding by inert particles on the geminate reaction kinetics is theoretically investigated. Time evolution equations for the survival probability of a geminate pair are derived from the master equation taking into account the correlation among all diffusing particles, and the results are compared with those obtained by Monte Carlo simulations. In general, excluded volume interactions by the inert particles slow down the diffusive motion of reactants. However, when the initial concentration of the inert particles is uniform and high, we show that additional influence of interference between reaction and correlated diffusion accelerates the transient decay of the survival probability in the diffusion-controlled limit. We also study the escape probability for a nonuniform initial distribution of the inert particles by taking the continuous limit in space. We show that reaction yield is increased when the reaction proceeds in the presence of a positive density gradient of the inert particles which inhibits the escape of reactants. The effect can be interpreted as a cage effect.

Effects of excluded volume interaction on diffusion-reaction processes in crowded environments

In nonequilibrium phase transitions of reaction-diffusion processes, the irrelevance of excluded volume interaction for the critical properties generally has been accepted due to the rare probability of multiple occupancy at criticality. Moreover, this belief is common sense in scale-free (SF) networks, which correspond to infinite dimensional irregular structures. However, the conventional belief is not satisfied in crowded environments in which the total number of particles is preserved in time. In this paper, we show, by investigating a typical process for epidemic spreading in crowded environments, that excluded volume interaction indeed changes critical behaviors in one dimension and surprisingly even mean-field behaviors in SF networks.