Brownian dipole rotator in alternating electric field V. M. Rozenbaum, * O. Ye. Vovchenko, and T. Ye. Korochkova Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova Street 17, Kiev 03164, Ukraine Received 25 February 2008; published 10 June 2008 The study addresses the azimuthal jumping motion of an adsorbed polar molecule in a periodic n-well potential under the action of an external alternating electric field. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment as well as the frequency dependences of polarizability and the average angular velocity, the three quantities exhibiting conspicuous stochastic resonance. As shown, unidi- rectional rotation can arise only provided simultaneous modulation of the minima and maxima of the potential by an external alternating field. For a symmetric potential of hindered rotation, the average angular velocity, if calculated by the second-order perturbation theory with respect to the field intensity, has a nonzero value only at n = 2, i.e., when two azimuthal wells specify a selected axis in the system. Particular consideration is given to the effect caused by the asymmetry of the two-well potential on the dielectric loss spectrum and other Brownian motion parameters. When the asymmetric potential in a system of dipole rotators arises from the average local fields induced by an orientational phase transition, the characteristics concerned show certain peculiarities which enable detection of the phase transition and determination of its parameters. DOI: 10.1103/PhysRevE.77.061111 PACS numbers: 05.40.a, 05.60.Cd, 82.20.w, 45.20.dc I. INTRODUCTION Being relatively loosely bound to the surface, physisorbed molecules are rather motile and exhibit, in particular, high rotational mobility. Hindered rotational movement is also typical of chemisorbed polyatomic molecules or polyatomic groups tightly bound to a surface through one atom, whereas other atoms can have several equilibrium positions in the potential induced by the nearest substrate atoms 1,2. Much recent interest has been attracted by so-called molecular ro- tors artificially formed on surfaces 3,4. These molecular engines provide an insight into the physical principles of controlled mechanical movement and friction on the nano- scale as well as the effects of random thermal movement which are inherent in nanodevices as opposed to conven- tional macromachinery. Rotational movement of molecules and atomic groups on a solid surface manifests itself in a variety of experiments. Vibrational spectroscopy detects characteristic absorption in the frequency regions of both stretching and deformation angular vibrations, the former also giving rise to the spec- tral lines at combined frequencies, i.e., at sums and differ- ences of the frequencies of original lines. In addition, rota- tional movement causes specific broadening of spectral lines, with its temperature dependence governed by the rotational reorientation frequencies. For instance, rotations of hydroxyl groups on oxide surfaces become possible due to relatively small reorientation barriers U   55 meV, which are comparable to the characteristic thermal energy k B T  26 meV at T =300 K. As a result, characteristic IR ab- sorption arises in the frequency region 100- 200 cm -1 and a typical temperature dependence of the Arrhenius type is observed for the spectral bands of the valent OH vibrations 1. Dielectric measurements offer another promising method to detect rotational movement of polar surface species. To exemplify, the temperature dependence of the dielectric loss tangent reflects the stochastic resonance 5 which arises when the frequency of the applied electric field approaches that of thermally activated molecular reorientations between the equilibrium angular positions. Experiments of this kind are very sensitive to the local environment of a surface center thus being structurally informative. This motivates the devel- opment of models which depict the frequency dependence of polarizability for rotationally mobile polar surface centers. The origin of unidirectional rotation in a linearly polarized alternating electric field is also of great interest: it has much in common with Brownian motors in which directed motion arises from the ratchet effects governed by an asymmetric fluctuating potential 6–9. The present paper addresses the angular Brownian motion of a particle in a periodic n-well potential under the action of the external alternating electric field Sec. II. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment and the frequency dependences of polarizability and the average angular velocity of a dipole rotator. The general prerequisites for the initiation of unidirectional rotation have been analyzed Sec. III. As found by the second-order per- turbation theory with respect to the field intensity, unidirec- tional rotation in a symmetric potential is only possible at n = 2, i.e., when two azimuthal wells specify a selected axis in the system Sec. IV. Therefore, the case of a two-well potential is considered in detail and we also include the ef- fect of asymmetry induced by local fields, which result both from environmental inhomogeneities and from orientational ordering in the low-temperature region Sec. V. The results obtained demonstrate that stochastic resonance clearly mani- fests itself in temperature dependences of experimentally ob- servable characteristics of dipole rotators; this phenomenon gives valuable structural evidence about the local environ- * vrozen@mail.kar.net PHYSICAL REVIEW E 77, 061111 2008 1539-3755/2008/776/0611119 ©2008 The American Physical Society 061111-1