Diffusive transport along a structured surface: ratchet effect stability when changing the potential profile type

The phenomenon of the ratchet effect provides the motion a large number of molecular machines, existing in nature and artificially created nanomechanisms, capable to initiate directed diffusion movement along periodic structures. Two key factors, necessary for the ratchet effect occurrence, are the presence of asymmetry in the system and the organization of the non-equilibrium fluctuations process. Asymmetry can be created directly by the stationary potential form, in the field of which unidirectional motion is organized. Double-sine (smooth) and sawtooth (piecewise-linear) potential profile dependences are encountered most frequently when designing models. The source of such dependence can be a chain of collinearly located dipoles on the surface of a solid. The purpose of this work was to study the influence on the ratchet effect of changing the model potential class from smooth to piecewise linear. For this purpose, two methods of approximation of the double sinusoidal potential by a sawtooth were considered. The first, simple, consists in connecting the extremum points with straight-line segments, preserving the height of the potential barrier and the coordinates of the extrema. The second, the least squares method (LSM), reproduces the slopes of the smooth potential as closely as possible. A model of a stochastic Brownian motor with small fluctuations of the potential energy by a harmonic signal was chosen for the comparative analysis. This model has no limitations in the ranges of the environment temperature and fluctuation frequency parameters, so the ratchet effect can be studied in all operation modes of the motor. It is shown that at sufficiently high temperatures for any asymmetry of potentials, approximation by the simple method gives better results, and at high frequencies – the LSM method. An algorithm for determining the best approximation method in the ranges of parameters that generate the largest flux values is proposed. It has been shown that for single-well double-sine potentials the approximate LSM-potential gives identical results of temperature-frequency dependences. Contour graphs of relative flux values were plotted, demonstrating parameters regions of the greatest identity (stability) of the ratchet effect and the region of the greatest difference.