A theory of diffusion controlled reactions in polyatomic molecule system

Solvation dynamics on the diffusion timescale elucidated using energy-represented dynamics theory

Photoexcitation of a solute alters the solute-solvent interaction, resulting in the nonequilibrium relaxation of the solvation structure, often called a dynamic Stokes shift or solvation dynamics. Thanks to the local nature of the solute-solvent interaction, the characteristics of the local solvent environment dissolving the solute can be captured by the observation of this process. Recently, we derived the energy-represented Smoluchowski-Vlasov (ERSV) equation, a diffusion equation for molecular liquids, which can be used to analyze the solvation dynamics on the diffusion timescale. This equation expresses the time development for the solvent distribution on the solute-solvent pair interaction energy (energy coordinate). Since the energy coordinate can effectively treat the solvent flexibility in addition to the position and orientation, the ERSV equation can be utilized in various solvent systems. Here, we apply the ERSV equation to the solvation dynamics of 6-propionyl-2-dimethylamino naphthalene (Prodan) in water and different alcohol solvents (methanol, ethanol, and 1-propanol) for clarifying the differences of the relaxation processes among these solvents. Prodan is a solvent-sensitive fluorescent probe and is thus widely utilized for investigating heterogeneous environments. On the long timescale, the ERSV equation satisfactorily reproduces the relaxation time correlation functions obtained from the molecular dynamics (MD) simulations for these solvents. We reveal that the relaxation time coefficient on the diffusion timescale linearly correlates with the inverse of the translational diffusion coefficients for the alcohol solvents because of the Prodan-solvent energy distributions among the alcohols. In the case of water, the time coefficient deviates from the linear relationship for the alcohols due to the difference in the extent of importance of the collective motion between the water and alcohol solvents.

Elucidating the Mass Transportation Behavior of Gas Diffusion Layers via a H2 Limiting Current Test

The gas diffusion layer (GDL), as a key component of proton exchange membrane fuel cells (PEMFCs), plays a crucial role in PEMFC's polarization performance, particularly in mass transport properties at high current densities. To elucidate the correlation between GDLs' structure and their mass transport properties, a limiting current test with the H2 molecular probe was established and employed to investigate three representative GDLs with and without the microporous layer (MPL). By varying humidity and back pressure, the mass transport resistance of three GDLs was measured in an operating fuel cell, and an elaborate analysis of H2 transport was conducted. The results showed that the transport resistance (RDM) of GDLs was affected by the thickness and pore size distribution of the macroporous substrate (MPS) and the MPL. In the process of gas transport, the smaller pore size and thicker MPL increase the force of gas on the pore wall, resulting in an increase in transmission resistance. Through further calculation and analysis, the total transport resistance can be divided into pressure-related resistance (RP) and pressure-independent resistance (RNP). RP mainly originates from the transport resistance in both MPLs and the substrate layers of GDLs, exhibiting a linear relationship to the pressure; RNP mainly originates from the transport resistance in the MPLs. 29BC with thick MPL shows the largest RNP, and T060 without MPL shows the RNP = 0. This methodology enables in situ measurements of mass transport resistances for gas diffusion media, which can be easily applied for developing and deploying PEMFCs.

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.

Diffusion theory of molecular liquids in the energy representation and application to solvation dynamics

The generalized Langevin equation (GLE) formalism is a useful theoretical fundament for analyzing dynamical phenomena rigorously. Despite the systematic formulation of dynamics theories with practical approximations, however, the applicability of GLE-based methods is still limited to simple polyatomic liquids due to the approximate treatment of molecular orientations involved in the static molecular liquid theory. Here, we propose an exact framework of dynamics based on the GLE formalism incorporating the energy representation theory of solution, an alternative static molecular liquid theory. A fundamental idea is the projection of the relative positions and orientations of solvents around a solute onto the solute-solvent interaction, namely the energy coordinate, enabling us to describe the dynamics on a one-dimensional coordinate. Introducing systematic approximations, such as the overdamped limit, leads to the molecular diffusion equation in the energy representation that is described in terms of the distribution function of solvents on the energy coordinate and the diffusion coefficients. The present theory is applied to the solvation dynamics triggered by the photoexcitation of benzonitrile. The long-time behavior of the solvation time correlation function is in good agreement with that obtained by the molecular dynamics simulation.

Atomistic description of molecular binding processes based on returning probability theory

The efficiency of molecular binding such as host-guest binding is commonly evaluated in terms of kinetics, such as rate coefficients. In general, to compute the coefficient of the overall binding process, we need to consider both the diffusion of reactants and barrier crossing to reach the bound state. Here, we develop a methodology of quantifying the rate coefficient of binding based on molecular dynamics simulation and returning probability (RP) theory proposed by Kim and Lee [J. Chem. Phys. 131, 014503 (2009)]. RP theory provides a tractable formula of the rate coefficient in terms of the thermodynamic stability and kinetics of the intermediate state on a predefined reaction coordinate. In this study, the interaction energy between reactants is utilized as the reaction coordinate, enabling us to effectively describe the reactants' relative position and orientation on one-dimensional space. Application of this method to the host-guest binding systems, which consist of β-cyclodextrin and small guest molecules, yields the rate coefficients consistent with the experimental results.

Solvation dynamics in electronically polarizable solvents: Theoretical treatment using solvent-polarizable three-dimensional reference interaction-site model theory combined with time-dependent density functional theory

The theory of solvation structure in an electronically polarizable solvent recently proposed by us, referred to as the "solvent-polarizable three-dimensional reference interaction-site model theory," is extended to dynamics in this study through the combination with time-dependent density functional theory. Test calculations are performed on model charge-transfer systems in water, and the effects of electronic polarizability on solvation dynamics are examined. The electronic polarizability slightly retards the solvation dynamics. This is ascribed to the decrease in the curvature of the nonequilibrium free energy profile along the solvation coordinate. The solvent relaxation is bimodal, and the faster and the slower modes are assigned to the reorientational and the translational modes, respectively, as was already reported by the surrogate theory combined with the site-site Smoluchowski-Vlasov equation. The relaxation path along the solvation coordinate is a little higher than the minimum free energy path because the translational mode is fixed in the time scale of the reorientational relaxation.

Dynamics theory for molecular liquids based on an interaction site model

Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.