Controlling the preferential motion of chiral molecular walkers on a surface

Abstract

Chiral molecular walkers, standing on their ‘feet’ on an anisotropic surface, perform preferential unidirectional Brownian motion under the influence of an external oscillating field according to their orientation, conformation and chirality.

Externally driven molecular ratchets on a periodic potential surface: a rate equations approach

“…Note that a spatially asymmetric waveform requires, within the HTST, at least two peaks to be present. Such a PES corresponds, e.g., to a bipedal molecule diffusing along a single direction by means of the inchworm mechanism, 16,19 so that the first peak (to the right from A to B) corresponds to the molecule stepping with its back 'foot' to the right, while the second peak corresponds to the front 'foot' stepping in the same direction, thereby displacing the molecule by one lattice constant.…”

“…Two types of such stimuli can be easily simulated: (i) an electrostatic field and (ii) a temperature gradient. 16 In the first case the molecule is to be charged and then a spatially uniform electric field E(t) (in units of energy over distance) would create an additional electrostatic potential, DU(x,t) = ÀE(t)x, changing linearly with the coordinate x along our 1D system. This extra potential will affect the energy barriers in a certain way, as it would tilt the PES one way or another, depending on the field direction.…”

“…where p A (0) = 1, and then taking the results over long times (the stationary limit). Even though our treatment is general, in order to be specific, the results of the analytical and numerical calculations described below are given having a realistic molecule in mind, 1,3-bis(imidazol-1-ylmethyl)-5(1-phenylethyl)benzene (or BIPEB for short), 16 see the inset in Fig. 2, where its R enantiomer is shown.…”

“…1 with the calculated energy barriers D 0 1 = 0.339 eV, D 0 2 = 0.316 eV, D 0 3 = 0.170 eV and D 0 4 = 0.147 eV. 16 The lattice constant of the Cu row is a = 2.52 Å. Let us first consider our system with a constant external field being applied.…”

“…Apart from some simple examples, investigations of specific external fields require numerical solutions of this partial differential equation. Recently we proposed a kinetic Monte Carlo approach to study Brownian molecular ratchets on surfaces 16 which has the advantage of considering realistic molecules and surfaces at a reasonable computational time. In this paper we propose an alternative approach, a simple method based on rate equations, which is numerically even more advantageous.…”