Journal of Luminescence 94–95 (2001) 137–142 Motors on the molecular scale Markus Porto a, *, Michael Urbakh b , Joseph Klafter b a Max-Planck-Institut f . ur Physik komplexer Systeme, N . othnitzer Straße 38, D-01187 Dresden, Germany b School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel Abstract An approach which has been recently introduced to construct microscopic engines is investigated. The main characteristic of the approach is the possibility to determine dynamically the direction of motion of the engines. The engines, which are moving objects on a substrate, are able to move translationally or rotationally and simultaneously perform useful functions such as pulling of a cargo. We discuss an example in which the energy is fed into the engine by changing locally the intrinsic lengths of the moving object. The local changes might be obtained by externally exciting the system. The transformation of the supplied energy into directed motion is through dynamical competition between the intrinsic lengths given by the moving object and the characteristic lengths of the substrate. r 2001 Elsevier Science B.V. All rights reserved. Keywords: Molecular motors; Molecular machinery; Directed transport 1. Introduction As predicted by Feynman almost 40 years ago [1], the handling of individual atoms and molecules has become widespread in many fields of science [2]. However, one still faces the challenge to further ‘tame’ atoms and molecules and make nanoscale objects perform useful functions. Although first steps in this direction have already been made experimentally [3] and despite the growing interest in molecular scale machinery which has been partly driven by studies of biological motors [4], real progress concerning the construction of a man-made nanoscale coun- terpart of the ‘steam locomotive’ and its corre- sponding ‘railway system’ has not occurred yet. This is mainly due to missing concepts of how to transform the supplied energy in an efficient and controllable way to a specific function on the molecular scale. Most theoretical studies in this area rely on the idea of particles moving in spatially asymmetric potentials which can over- come simple diffusion under non-equilibrium conditions and gain directionality [5]. New alter- native concepts have been proposed recently [6,7], in which directed motion of molecular engines is obtained dynamically and no static asymmetry is required which is built into in the system. The main advantages of this newly proposed engine [6] are: (a) the directionality in the motion is determined dynamically and does not require any spatial asymmetry of the moving object or of the substrate, (b) the engine is powerful enough to allow for the transportation of a cargo, (c) the same concept applies for both translational and rotational motions as well as for motion in two *Corresponding author. Tel.: +49-351-871-2213; fax: +49- 351-871-1999. E-mail address: porto@mpipks-dresden.mpg.de (M. Porto). 0022-2313/01/$-see front matter r 2001 Elsevier Science B.V. All rights reserved. PII:S0022-2313(01)00245-9