Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model

The effect of solvent fluctuations on the rate of electron transfer reactions is considered using linear response theory and a second-order cumulant expansion. An expression is obtained for the rate constant in terms of the dielectric response function of the solvent. It is shown thereby that this expression, which is usually derived using a molecular harmonic oscillator ("spin-boson") model, is valid not only for approximately harmonic systems such as solids but also for strongly molecularly anharmonic systems such as polar solvents. The derivation is a relatively simple alternative to one based on quantum field theoretic techniques. The effect of system inhomogeneity due to the presence of the solute molecule is also now included. An expression is given generalizing to frequency space and quantum mechanically the analogue of an electrostatic result relating the reorganization free energy to the free energy difference of two hypothetical systems [J. Chem. Phys. 39, 1734 (1963)]. The latter expression has been useful in adapting specific electrostatic models in the literature to electron transfer problems, and the present extension can be expected to have a similar utility

Thin‐layer inertial effects in plasticity and dynamics in the Prandtl problem

Especially in metal forming, large plastic deformation occurs in thin plates. The problem of compressing dies is analyzed to evaluate the spreading of a thin layer in between. The velocity of dies is a given function in time so that the kinematics of the process is known. This problem can be considered as a generalization of the classical Prandtl problem by taking inertial effects into account and introducing dimensionless parameters as internal variables depending on time. The first parameter is purely geometric corresponding to the thin‐layer approximation; the second and the third parameters are dimensionless velocity and acceleration during the dies getting pressed. We use singular asymptotic expansions of unknown functions and study how these parameters vary preceding the dies of moment. Depending on this relation, the dynamic corrections to the quasistatic solution is a part of various terms of the asymptotic series. The corresponding analytical investigation both for general case and for particular typical regimes of plates motion is carried out.TU Berlin, Open-Access-Mittel - 201

Rate theory for correlated processes: Double-jumps in adatom diffusion

We study the rate of activated motion over multiple barriers, in particular the correlated double-jump of an adatom diffusing on a missing-row reconstructed Platinum (110) surface. We develop a Transition Path Theory, showing that the activation energy is given by the minimum-energy trajectory which succeeds in the double-jump. We explicitly calculate this trajectory within an effective-medium molecular dynamics simulation. A cusp in the acceptance region leads to a sqrt{T} prefactor for the activated rate of double-jumps. Theory and numerical results agree

AC Driven Jumps Distribution on a Periodic Substrate

A driven Brownian particle (e.g. an adatom on a surface) diffusing on a low-viscosity, periodic substrate may execute multiple jumps. In the presence of an additional periodic drive, the jump lengths and time durations become statistically modulated according to a syncronyzation mechanism reminiscent of asymmetric stochastic resonance. Here, too, bistability plays a key role, but in a dynamical sense, inasmuch as a particle switches between locked and running states.Comment: 4 pages, 4 figures, RevTeX, to be published in Surface Science Letter

О роли двух термодинамических постулатов в феноменологическом построении механики сплошной среды

A general integral form of representation of five postulates in continuum mechanics, possible noncontradictory axiomatics of phenomenological construction of the fourth and fifth of them (namely, the laws of change of the internal energy and entropy) as well as the role of the Fourier law or its hyperbolic generalization in definition of temperature, are discussed. It is shown that in contrast to the statistical and molecular approaches, in this case, the internal energy and entropy of an individual (liquid) volume can be completely defined by specifying its source, flow through the surface, and production. Thus two thermodynamic postulates serve as definitions. The energy conjugate pairs of quantities of different physical nature and the possibility of expanding the table of postulates are discussed.Обсуждаются единая интегральная форма записи пяти постулатов механики сплошной среды, возможная непротиворечивая аксиоматика феноменологического построения четвёртого и пятого из них — законов об изменении внутренней энергии и энтропии, а также роль закона Фурье или его гиперболического обобщения в определении температуры. Показывается, что в отличие от статистического и молекулярного подходов в данном случае внутренняя энергия и энтропия индивидуального (жидкого) объёма могут быть полностью определены посредством задания своих источника, потока через границу и производства. Тем самым два термодинамических постулата выполняют роль определений. Обсуждаются энергетические сопряжённые пары величин различной физической природы и возможности расширения таблицы постулатов

Dynamic Stokes shift in solution: Effect of finite pump pulse duration

The time-evolution of the fluorescence spectrum of a dissolved chromophore excited by an ultrafast pump pulse is considered. The average value of the energy difference of the solute in its excited and ground states is used to describe the relaxation of the maximum of the transient fluorescence spectrum to its equilibrium value (dynamic Stokes shift, DSS). A simple formula for the normalized DSS is obtained which generalizes an earlier standard classical expression and includes the effect of a pump pulse of finite duration. As an example, dielectric dispersion data are used for a dipolar solute in water to estimate the quantum correction to the standard DSS expression. The correction is negligible when the frequency of the pump pulse is close to the maximum in the absorption spectrum, but a deviation from the standard formula can be expected for the pump pulse tuned to a far wing of the absorption band of the chromophore. An expression is given for this deviation

Low-temperature reactions: Tunnelling in space.

International audienceChemical reactions with activation barriers generally slow to a halt in the extreme cold of dense interstellar clouds. Low-temperature experiments on the reaction of OH with methanol have now shown that below 200 K there is a major acceleration in the rate that can only be explained by enhanced quantum mechanical tunnelling through the barrier