Chapter 5
Rotation of a Dipole
Here we consider a dipole in a viscous medium under the influence of an oscillating
electric field and thermal noise, then we add an extra ratchet field. We analyze the
properties of rotation of both cases. Because of the very low Reynolds numbers
involved with molecular processes, we considered overdamped Langevin dynamics,
as a consequence the inertia term becomes negligible. We observed rotation for
some values of the parameters.
5.1 Introduction
In recent years, with the advance of the nanotechnology, new techniques have
evolve to visualize single-molecules, as scanning tunneling [1] and atomic force
microscopies [2]. In Ref. [3] was observed rotation of a single molecule within a
supramolecular bearing. After the first examples of unidirectional rotating molecular
motors based on simple organic molecules [4, 5], several works were reported
on this subject as [6–14]. Also great theoretical efforts have been devoted to
understand and to propose nanoscale rotors and stators as molecular motors capable
to transform efficiently a driven random rotation into a directed translational motion
[15–17]. As a biological example of a molecular motor consisting of rotor and
stator is the rotatory motor of bacterial flagella which is driven by a transmembrane
electrochemical gradient of protons, [18], also is the ATP synthase which has been
very well studied: [19–21]. Most of these motors are called Brownian motors, for
an excellent review on this subject see Ref. [22] and references within.
Although ‘brownian motors’ are known to permit thermally activated motion
in one direction only, the concept of channelling random thermal energy into
controlled motion has not yet been very extended to the molecular level and the
basic principles are not very well understood. Experiments suggest that dynamics is
inescapable and may play a decisive role in the evolution of nanotechnology, [23].
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. A. Fornés, Principles of Brownian and Molecular Motors, Springer Series in
Biophysics 21, https://doi.org/10.1007/978-3-030-64957-9_5
65
Rotation of a Dipole
Here we consider a dipole in a viscous medium under the influence of an oscillating
electric field and thermal noise, then we add an extra ratchet field. We analyze the
properties of rotation of both cases. Because of the very low Reynolds numbers
involved with molecular processes, we considered overdamped Langevin dynamics,
as a consequence the inertia term becomes negligible. We observed rotation for
some values of the parameters.
5.1 Introduction
In recent years, with the advance of the nanotechnology, new techniques have
evolve to visualize single-molecules, as scanning tunneling [1] and atomic force
microscopies [2]. In Ref. [3] was observed rotation of a single molecule within a
supramolecular bearing. After the first examples of unidirectional rotating molecular
motors based on simple organic molecules [4, 5], several works were reported
on this subject as [6–14]. Also great theoretical efforts have been devoted to
understand and to propose nanoscale rotors and stators as molecular motors capable
to transform efficiently a driven random rotation into a directed translational motion
[15–17]. As a biological example of a molecular motor consisting of rotor and
stator is the rotatory motor of bacterial flagella which is driven by a transmembrane
electrochemical gradient of protons, [18], also is the ATP synthase which has been
very well studied: [19–21]. Most of these motors are called Brownian motors, for
an excellent review on this subject see Ref. [22] and references within.
Although ‘brownian motors’ are known to permit thermally activated motion
in one direction only, the concept of channelling random thermal energy into
controlled motion has not yet been very extended to the molecular level and the
basic principles are not very well understood. Experiments suggest that dynamics is
inescapable and may play a decisive role in the evolution of nanotechnology, [23].
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. A. Fornés, Principles of Brownian and Molecular Motors, Springer Series in
Biophysics 21, https://doi.org/10.1007/978-3-030-64957-9_5
65