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Brownian motors belong to the class of nanoscale devices that use the thermal noise of the environment as one of the necessary components in the mechanism of their operation. Today, there are a lot of practical implementations of such nanomachines, both inorganic, fairly simple mechanisms produced artificially, and more complex ones created from separate biological components available at the cellular level. One of the options for implementing the mechanism of straightening the chaotic thermal noise of the environment into unidirectional motion is the presence of a motor particle in the field of action of an asymmetric periodic stationary potential, which undergoes certain small disturbances (fluctuations) periodically over time. To describe such asymmetric one-dimensional structures (for example, dipole chains or fibers of the cytoskeleton) in the theory of Brownian motors, two model potentials are most often used: piecewise linear sawtooth and double sinusoidal. In this work, within the framework of the approximation of small fluctuations, a model of a pulsating Brownian motor with a stationary double sinusoidal potential and a disturbing small harmonic signal is considered. A new method of parametrization of such a problem is proposed, which allows to separate the contributions from various factors affecting the operation of the ratchet, and the numerical procedure for calculating the average speed of the directional movement of nanoparticles for the selected type of model potentials is specified. A number of numerical dependences of the average speed on the main parameters of the system were obtained. Peculiarities of the behavior of the motor as dependent on the parameter responsible for asymmetry and the number of potential wells on the spatial period of the stationary potential have been investigated. It is shown that the direction of the generated flux of nanoparticles depends not only on the phase shift between the stationary and fluctuating components of the potential, but also on the temperature of the system and the frequency of fluctuations, i.e., a possibility of temperature-frequency control of the direction of movement in the considered model has been found. Diagrams have been constructed that allow you to choose the ratio between the parameters of the nanomotor to create a flux of particles in the desired direction. [ABSTRACT FROM AUTHOR]

It is well known that at low temperatures, the direction of motion for a quantum rocking ratchet in an asymmetric periodic potential (with a period L and an energy barrier V0), driven by an external fluctuating force F (F=0), can be opposite to the direction for the analogous classical ratchet operating at high temperature (Reimann et al, Phys. Rev. Lett. 1997, 79, 10). In the present work, within the semiclassical approximation and taking into account zero‐point fluctuations of a quantum particle in the minima of a sawtooth potential of an arbitrary asymmetry at the temperature of absolute zero, we obtain analytical expressions for the tunneling current in the rocking ratchet. These expressions allowed us to obtain the dependencies of the ratio FL/V0, at which the motion direction is reversed, on the asymmetry parameter and other parameters of the system. Similar results are obtained for a particle in a two‐sinusoidal potential. [ABSTRACT FROM AUTHOR]

We present a review of analytical approaches involved in developing the ratchet theory, which are based on the model of extremely asymmetric sawtooth potential. Analytical expressions are given for the average velocity of ratchets which operate in various motion modes, namely, motion induced by dichotomous half‐period shifts of potential profiles, adiabatic and high‐temperature modes, and motion induced by small fluctuations of an arbitrary type. The presence of jumps in the periodic extremely asymmetric sawtooth potential profile leads to a number of features of the obtained solutions which follow from the competition of the reverse sliding time tending to infinity with high fluctuation frequencies. The resulting dependences of the average velocity on the ratchet parameters clearly demonstrate that the motion direction can be controlled by tuning the frequency and temperature. The heuristic value of the presented models for controlling nanoparticle transport is discussed. [ABSTRACT FROM AUTHOR]

The operating properties of different‐type Brownian photomotors have been compared in relation to the symmetry interplay between their moving (particle/molecule) and immovable (substrate) units. As found, essentially different symmetry constraints and hence different motor behavior are characteristic of molecules if their electron density redistribution on excitation involves only odd‐order or only even‐order multipole moments. The two respective types of molecules give rise to dipole and quadrupole photomotors. Purely dipole photomotors can operate only on substrates with symmetric charge distribution and their ensemble with random molecular orientations undergoes equidirectional diffusion rather than directed motion. Contrary to this, purely quadrupole photomotors need substrates with antisymmetric charge distribution for directed motion to occur and they can move directionally in an ensemble. Also, quadrupole photomotors provide much smaller velocities of directed motion than their dipole counterparts (as a result of the much weaker interaction of quadrupoles than dipoles with an electric field). The generic distinctions between the two photomotor types are exemplified by donor‐acceptor‐substituted stilbenoids (dipole molecules) and symmetric squaraines (quadrupole molecules). The model used affords the rational design of photomotors by the selection of promising moving molecules and by the continuous wide‐range tuning of charge‐distribution symmetry in substrates. [ABSTRACT FROM AUTHOR]

Molecular devices that have an anisotropic periodic potential landscape can be operated as Brownian motors. When the potential landscape is cyclically switched with an external force, such devices can harness random Brownian fluctuations to generate a directed motion. Recently, directed Brownian motor-like rotatory movement was demonstrated with an electrically switched DNA origami rotor with designed ratchet-like obstacles. Here, we demonstrate that the intrinsic anisotropy of DNA origami rotors is also sufficient to result in motor movement. We show that for low amplitudes of an external switching field, such devices operate as Brownian motors, while at higher amplitudes, they behave deterministically as overdamped electrical motors. We characterize the amplitude and frequency dependence of the movements, showing that after an initial steep rise, the angular speed peaks and drops for excessive driving amplitudes and frequencies. The rotor movement can be well described by a simple stochastic model of the system.