Nonlinear Dynamics and Surface Diffusion of Diatomic Molecules

Abstract

The surface diffusion of single adatoms has been intensively studied over the last decades, [1][2][3] due to its importance in thin film and crystal growth. [4] Once individual atoms are adsorbed on a surface they can meet, thus forming larger clusters. However, the diffusion of even the simplest cluster, a dimer, on a surface is by far not yet understood. [5][6][7][8][9][10][11][12][13] The diffusion dynamics can be strongly affected by the coupling of the intramolecular motion to the translational motion of the centre of mass (CM) of the cluster. [12][13][14][15] Herein, we present a simple, one-dimensional model for studying the Hamiltonian and diffusive dynamics of a dimer, which is relevant to systems where quasione-dimensional motion takes place.[16] The deterministic dynamics of this model is characterized by a complex behavior, dominated by nonlinear effects, parametric resonances and chaotic features. At variance with the case of a single atom, at T ¼ 6 0 the role of the internal degrees of freedom of the dimer is responsible for deviations from activated behavior of the diffusion coefficient. In Section 1, we briefly outline our model. In Sections 2 and 3, we discuss the nonlinear deterministic and thermal dynamics, respectively, and compare the two situations in Section 4. Concluding remarks are given in Section 5. ModelWe consider the deterministic and thermal dynamics of a dimer moving on a periodic one-dimensional substrate. The particle-substrate interaction is a sinusoidal function of amplitude 2 U 0 and period a, and the interparticle interaction is given by a harmonic potential with spring constant K and equilibrium length l. We use Langevin dynamics to deal with finite temperature T. The equations of motion for the two atoms of mass m and of coordinates x 1 and x 2 composing the dimer are given by Equation (1):where the effect of finite temperature T is taken into account by the stochastically fluctuating forces f i , satisfying the conditions hf i (t)i = 0 and hf i (t)f j (0)i = 2mhk B Td ij d(t), and by the damping term mhẋ i . In the following, we will use representative[a] C.

Atomic scale friction of molecular adsorbates during diffusion

“…Hence, a number of sources contribute to the energy exchange and thus to the friction: electronic terms, 4,5 spin, 6,7 phononic degrees of freedom, 4,[8][9][10] , and the internal degrees of freedom of the adsorbate. [11][12][13] The origin and magnitude of the friction depend on the nature of the adsorbate-substrate bond and the electronic properties of the substrate. Phononic friction, for example, acts in both conducting and insulating substrates and, here, the damping of adsorbate motion arises primarily from the emission of substrate phonons.…”

Dumbbell diffusion in a spatially periodic potential

“…This is especially emphasized for stiff springs connecting the two beads. Introduction.-Investigations on the diffusion of different colloidal particles in a homogeneous solvent have a long history [1,2], while studies on the diffusion of small spheres, dimers and polymers in different potentials attract considerable interest only for a short time [3,4,5,6,7,8,9]. Laser-tweezer arrays are a new powerful tool for generating the desired spatially periodic, correlated or unstructured potentials in order to study the effects of inhomogeneous potential landscapes on the motion of colloidal particles [3,4,5,10].…”

Brownian Diffusion of Hexagonal Boron Nitride Nanosheets and Graphene in Two Dimensions

“…This observed interaction motivated us to utilize Kramers’ approach to fit our data. Kramers’ theory is one of the major approaches to describe a transition between two local energy minima, originally developed as a reaction rate theory. , This theory has been expanded to express protein folding dynamics, − the diffusion of particles between a dual optical trap, , and surface diffusion. , By following Kramers’ theory, the diffusion coefficient is expected to follow an Arrhenius type equation: D t = D 0 exp true( prefix− E normala k normalB T true) = D 0 exp true( prefix− a S k normalB T true) where D t is the translational diffusion coefficient determined with MSD analysis, D 0 is the pre-exponential factor, E a is the activation energy for a single h-BN sheet to dissociate before diffusion, a is activation energy per unit area of a single h-BN sheet, S is the area of the h-BN sheet, k B is the Boltzmann constant, and T is temperature. The hypothesis is that for h-BN to move, the sheet (which is composed of the h-BN sheet and the cationic surfactants enveloping it) has to break interactions with the glass surface (partially desorbing) and diffuse until it is adsorbed again at a different location.…”

“…41,42 This theory has been expanded to express protein folding dynamics, 43−45 the diffusion of particles between a dual optical trap, 46,47 and surface diffusion. 48,49 By following Kramers' theory, the diffusion coefficient is expected to follow an Arrhenius type equation: 49…”