V. M. Rozenbaum

Origin of states connected with twisted intramolecular charge shift in polymethine cations: a simple analytical treatment

Abstract Based on the Hueckel method and simple model of long-range interelectron repulsion, the tendency for polymethine cations to form twisted structures in the excited state is elucidated. Changes in energy level positions and populations as well as the intramolecular charge transfer occurring on twisting are simulated in terms of π-decoupling of the corresponding conjugated system. The charge transfer between the fragments formed is shown to depend on the end-group nature and to alternate in direction for rotations of successive bonds in the polymethine chain. It is also reversed on switching from the ground to the excited state. The energy advantage of certain excited-state twistings over the planar form can be understood by taking into account the long-range Coulomb interaction of electrons in a quasi-one-dimensional system. On this basis, electron density transfer from the longer to shorter fragment is preferable and can compensate the general energetic disadvantage of π-decoupling upon twisting. Using the [Me2N–(CH)13–NMe2]+ cation as an example, it is inferred that the rotation around the 2–3 bond in the excited state is highly probable for long streptopolymethines, whereas twisting the 1–2 bond is improbable. The reverse predictions are found for boron-containing polymethines.

Nonequilibrium molecular transport photoinduced by potential energy fluctuations

The mechanism of directed substrate-parallel motion of molecules caused by photoinduced potential energy fluctuations is investigated. Unlike simplistic models (e.g., an on-off ratchet), the approach suggested implies that the necessary asymmetry of the potential energy can arise not only from the asymmetry of the substrate potential but also from an asymmetric distribution of the fluctuating charge density in the molecule. The thus induced asymmetry of the potential energy governs the direction motion and enables, under certain conditions, its reversal at some frequencies of resonant laser pulses or temperature. These inferences are exemplified by the model charge distributions in the molecule and substrate, and the charge density fluctuations which are obtained by quantum chemical calculations for the realistic molecule of a substituted phenylpyrene compound on a model substrate.

Orientations of linear nonpolar molecules in a regular chain

Energetically preferable orientational states for linear nonpolar molecules are determined which result from the competition of quadrupole–quadrupole and Van der Waals dipole–dipole interactions. It is shown that with the decreasing intermolecular distance a and hence with the increasing Van der Waals contribution to the total energy, the system concerned successively passes through the following orientational phases: alternating longitudinal and transverse molecular orientations relative to the chain axis (phase I), planar arrangement of molecules inclined to the chain axis at some angle which tends to diminish with decrease in a (phase II), molecules aligned parallel to the chain axis (phase III). In contrast to the continuous transition between phases II and III, the nature of the transition I→II depends on the radius of the interactions taken into account. In the approximation of short-range interactions, the phase transition represents a jump, whereas long-range interactions, if included, lead the sy...

Photoinduced diffusion molecular transport

We consider a Brownian photomotor, namely, the directed motion of a nanoparticle in an asymmetric periodic potential under the action of periodic rectangular resonant laser pulses which cause charge redistribution in the particle. Based on the kinetics for the photoinduced electron redistribution between two or three energy levels of the particle, the time dependence of its potential energy is derived and the average directed velocity is calculated in the high-temperature approximation (when the spatial amplitude of potential energy fluctuations is small relative to the thermal energy). The thus developed theory of photoinduced molecular transport appears applicable not only to conventional dichotomous Brownian motors (with only two possible potential profiles) but also to a much wider variety of molecular nanomachines. The distinction between the realistic time dependence of the potential energy and that for a dichotomous process (a step function) is represented in terms of relaxation times (they can differ on the time intervals of the dichotomous process). As shown, a Brownian photomotor has the maximum average directed velocity at (i) large laser pulse intensities (resulting in short relaxation times on laser-on intervals) and (ii) excited state lifetimes long enough to permit efficient photoexcitation but still much shorter than laser-off intervals. A Brownian photomotor with optimized parameters is exemplified by a cylindrically shaped semiconductor nanocluster which moves directly along a polar substrate due to periodically photoinduced dipole moment (caused by the repetitive excited electron transitions to a non-resonant level of the nanocylinder surface impurity).

Analytical representation of the relations of inertial diffusion transport

A generalized approach has been proposed to describe the diffusive transport of inertial particles at which the known inertialess relations (in particular, between the concentration of particles and the corresponding flux) are supplemented by a factor allowing the calculation of inertial effects in terms of the matrix continued fraction method. The advantage of this approach, which is in the analytical representation of the results, is illustrated by solving the problem of the determination of the effective diffusion coefficient of an inertial particle in a sawtooth potential and the average velocity of the adiabatic inertial ratchet. The character of the nonanalytic behavior of these quantities in the presence of large gradients of the potential has been established.

Net transport due to noise-induced internal reciprocating motion

We consider a system of two coupled Brownian particles fluctuating between two states. The fluctuations are produced by both equilibrium thermal and external nonthermal noise, the transition rates depending on the interparticle distance. An externally induced modulation of the transition rates acts on the internal degree of freedom (the interparticle distance) and generates reciprocating motion along this coordinate. The system moves unidirectionally due to rectification of the internal motion by asymmetric friction fluctuations and thus operates as a dimeric motor that converts input energy into net movement. The properties of the motor are primarily determined by the properties of the reciprocating engine, represented by the interparticle distance dynamics. Two main mechanisms are recognized by which the engine operates: energetic and informational. In the physically important cases where only one of the motion-inducing mechanisms is operative, exact solutions can be found for the model with linearly coupled particles. We focus on the informational mechanism, in which thermal noise is involved as a vital component and the reciprocating velocity exhibits a rich behavior as a function of the model parameters. An efficient rectification method for the reciprocating motion is also discussed.

Near-surface transport of semiconductor nanoclusters upon cyclic photoexcitation

A mechanism for the directed motion of a semiconductor nanocluster along a polar substrate upon cyclic photoexcitation that alters the electron density distribution inside the particle is studied. A model that allows us to estimate the average velocity and optimize the system parameters (particle size, distance between the particle and the substrate, the average cycle duration, and charge distribution in the substrate) so as to ensure the maximum velocity is proposed. At the optimum parameters, the average velocity of directed motion can be quite high (~3 mm/s).

DIFFUSION OF A MASSIVE PARTICLE IN A PERIODIC POTENTIAL: APPLICATION TO ADIABATIC RATCHETS

We generalize a theory of diffusion of a massive particle by the way in which transport characteristics are described by analytical expressions that formally coincide with those for the overdamped massless case but contain a factor comprising the particle mass which can be calculated in terms of Riskens matrix continued fraction method (MCFM). Using this generalization, we aim to elucidate how large gradients of a periodic potential affect the current in a tilted periodic potential and the average current of adiabatically driven on-off flashing ratchets. For this reason, we perform calculations for a sawtooth potential of the period L with an arbitrary sawtooth length (l<L) instead of the smooth potentials typically considered in MCFM-solvable problems. We find nonanalytic behavior of the transport characteristics calculated for the sharp extremely asymmetric sawtooth potential at l→0 which appears due to the inertial effect. Analysis of the temperature dependences of the quantities under study reveals the dominant role of inertia in the high-temperature region. In particular, we show, by the analytical strong-inertia approach developed for this region, that the temperature-dependent contribution to the mobility at zero force and to the related effective diffusion coefficient are proportional to T(-3/2) and T(-1/2), respectively, and have a logarithmic singularity at l→0.

Fluctuation-induced transport of two coupled particles: Effect of the interparticle interaction

We consider a system of two coupled particles fluctuating between two states, with different interparticle interaction potentials and particle friction coefficients. An external action drives the interstate transitions that induces reciprocating motion along the internal coordinate x (the interparticle distance). The system moves unidirectionally due to rectification of the internal motion by asymmetric friction fluctuations and thus operates as a dimeric motor that converts input energy into net movement. We focus on how the law of interaction between the particles affects the dimer transport and, in particular, the role of thermal noise in the motion inducing mechanism. It is argued that if the interaction potential behaves at large distances as x(α), depending on the value of the exponent α, the thermal noise plays a constructive (α > 2), neutral (α = 2), or destructive (α < 2) role. In the case of α = 1, corresponding piecewise linear potential profiles, an exact solution is obtained and discussed in detail.

Adiabatic Brownian ratchets with the inclusion of inertia

Inertial corrections to the drift velocity of a Brownian particle have been calculated for two main classes of Brownian ratchets operating in the adiabatic regime of fluctuations of the potential energy: first, the stationary periodic potential and dichotomic fluctuations of an external force with zero average value (rocking ratchet) and, second, dichotomic fluctuations of the periodic potential itself. It has been shown that, in contrast to passive transport at which the inertial correction always reduces the effective mobility and diffusion coefficients, inertial corrections for Brownian ratchets can play a constructive role, increasing the drift velocity at least at high temperatures.