Diffusion‐controlled reactions. II. An approach based on a generalized diffusion equation

Accurate analytical calculation of the rate coefficient for the diffusion-controlled reactions due to hyperbolic diffusion

Using an approach based on the diffusion analog of the Cattaneo-Vernotte differential model, we find the exact analytical solution to the corresponding time-dependent linear hyperbolic initial boundary value problem, describing irreversible diffusion-controlled reactions under Smoluchowski's boundary condition on a spherical sink. By means of this solution, we extend exact analytical calculations for the time-dependent classical Smoluchowski rate coefficient to the case that includes the so-called inertial effects, occurring in the host media with finite relaxation times. We also present a brief survey of Smoluchowski's theory and its various subsequent refinements, including works devoted to the description of the short-time behavior of Brownian particles. In this paper, we managed to show that a known Rice's formula, commonly recognized earlier as an exact reaction rate coefficient for the case of hyperbolic diffusion, turned out to be only its approximation being a uniform upper bound of the exact value. Here, the obtained formula seems to be of great significance for bridging a known gap between an analytically estimated rate coefficient on the one hand and molecular dynamics simulations together with experimentally observed results for the short times regime on the other hand. A particular emphasis has been placed on the rigorous mathematical treatment and important properties of the relevant initial boundary value problems in parabolic and hyperbolic diffusion theories.

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.

Transition path times reveal memory effects and anomalous diffusion in the dynamics of protein folding

Recent single-molecule experiments probed transition paths of biomolecular folding and, in particular, measured the time biomolecules spend while crossing their free energy barriers. A surprising finding from these studies is that the transition barriers crossed by transition paths, as inferred from experimentally observed transition path times, are often lower than the independently determined free energy barriers. Here we explore memory effects leading to anomalous diffusion as a possible origin of this discrepancy. Our analysis of several molecular dynamics trajectories shows that the dynamics of common reaction coordinates used to describe protein folding is subdiffusive, at least at sufficiently short times. We capture this effect using a one-dimensional fractional Brownian motion (FBM) model, in which the system undergoes a subdiffusive process in the presence of a potential of mean force, and show that this model yields much broader distributions of transition path times with stretched exponential long-time tails. Without any adjustable parameters, these distributions agree well with the transition path times computed directly from protein trajectories. We further discuss how the FBM model can be tested experimentally.

Long-distance energy transfer photosensitizers arising in hybrid nanoparticles leading to fluorescence emission and singlet oxygen luminescence quenching

This paper presents energy transfer occurring in small organically modified core-shell nanoparticles (core lanthanide oxide, shell polysiloxane) (diameter < 10 nm) conjugated with photosensitizers designed for photodynamic therapy applications. These nanoparticles covalently encapsulate a photosensitizing PDT drug in different concentrations. Stable dispersions of the nanoparticles were prepared and the photophysical properties of the photosensitizers were studied and compared to those of the photosensitizers in solution. Increasing the photosensitizer concentration in the nanoparticles was not found to cause any changes in the absorption properties while fluorescence and singlet oxygen quantum yields decreased. As a possible explanation, we have suggested that both long distance energy transfer such as FRET and self-quenching could occur into the nanoparticles. A simple "trend" model of this kind of energy transfer complies with results of experiments on steady state fluorescence and singlet oxygen luminescence.

An efficient molecular dynamics simulation method for calculating the diffusion-influenced reaction rates

We present a molecular dynamics (MD) simulation method for calculating the diffusion-influenced reaction rates in the limit of low reactant concentrations. To calculate the reaction rate coefficient, we use MD trajectories of a nonreactive equilibrium system that are initiated with a pair of reactant molecules in reactive configuration. Hence reaction systems involving complicated reactant molecules with geometrically restricted reactivities can be treated with comparable efficiency as the simple hard-sphere reaction system. Compared to the similar MD method proposed by Van Beijeren, Dong, and Bocquet [J. Chem. Phys. 114, 6265 (2001)], the present method has a couple of advantages. First, reactions involving more general sink functions can be treated. Second, more accurate results can be obtained when the reaction probability upon collision is less than unity. As an application, we investigate the effects of nondiffusive dynamics and hydrodynamic interaction of reactants on the reaction rate.

Solvation dynamics in supercritical fluids: Equilibrium versus nonequilibrium solvent response functions

We present a theoretical study of solvation dynamics in supercritical fluids. Molecular dynamics simulations show a significant difference between equilibrium and nonequilibrium solvent response functions, especially pronounced at medium and low solvent densities. We propose an analytical theory for the nonequilibrium solvation function based on the generalized nonlinear Smoluchowski-Vlasov equation. The theory is shown to be in good agreement with simulation, providing an accurate description of the nonequilibrium time-dependent solvent density profile around the solute over a wide range of supercritical solvent densities. The nonequilibrium solvent response function is shown to reflect gradual solvent clustering around the excited solute.

Ion solvation dynamics in supercritical fluids

We present a theoretical study of ion solvation dynamics in a supercritical solvent. Molecular dynamics simulations show a significant difference between equilibrium and nonequilibrium solvent response functions, especially pronounced at medium and low solvent densities. We propose a simple analytical theory for the nonequilibrium solvation function based on the generalized nonlinear Smoluchowski-Vlasov equation. The theory is shown to be in excellent agreement with simulation over a wide range of supercritical solvent densities.

Rapid fluorescence quenching of S2-xanthione by 3,3-diethylpentane in perfluorohydrocarbons

Rapid fluorescence quenching of S2-xanthione by 3,3-diethylpentane has been studied in three perfluorohydrocarbons of different viscosities. The donor fluorescence decay in the presence of a quencher was fitted using the Smoluchowski-Collins-Kimball (SCK) model. The molecular parameters, R (the sum of the molecular radii), D (the sum of diffusion coefficients), and the specific rate constant of the process, kappa, were determined. The values of parameter D for all systems studied differed from the sum of the macroscopic diffusion coefficients Dx measured independently. This behavior is explained by the dependence of the molecular diffusion coefficient (as determined from the SCK model) on the distance traveled by the donor and quencher molecules during the excited donor lifetime.