Anomalous behaviour of the diffusion coefficient in interacting adsorbates

Langevin simulations provide an effective way to study collective effects of Brownian particles immersed in a two-dimensional periodic potential. In this paper, we concentrate essentially on the behaviour of the tracer (D_Tr) and collective diffusion coefficients (D_C) as function of friction (Γ). Our simulations show that in the high friction limit, the two physical quantities D_Tr and D_C present qualitatively the same behaviour, for both coupled and decoupled substrate potentials. However, for the low friction regime, and especially for the coupled potential case, an anomalous diffusion behaviour is found where D_Tr∼Γ^-σ_Tr and D_C∼Γ^-σ_C, with σ_Tr<σ_C<1. We also found that in the case of weak dynamical coupling between the adparticles and the substrate, the exponents are not universal and rather depend on the potentials. Moreover, changes in the inter-particle potentials may reverse the behaviour to a normal one.     

The velocity autocorrelation function and self-diffusion coefficient of fluids with steeply repulsive potentials

We consider the velocity autocorrelation function, vacf, or C_v(t) and self-diffusion coefficients, D, of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, ? (r) = ?(σ/r)ⁿ. The C_v(t) are calculated numerically by molecular dynamics simulations. Accurate expressions for the short time expansion of C_v(t) to order O(t⁴) for n large are derived for this fluid. We propose novel expressions for C_v (t) that, for n large, spans the transition from the short time regime (expandable in even powers of time) and the longer time exponential-like regime characteristic of hard spheres. Inter alia we introduce relaxation times that characterize the duration of a collision and the decay of the velocity correlation within the mean-collision or Enskog-like relaxation time, T_E.     

Theory of light scattering from a system of interacting Brownian particles

Starting from a N-particle diffusion equation for a system of N interacting spherical Brownian particles, a non-linear transport equation for concentration fluctuations δc(r, t) of the particles is derived. This dynamic equation is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations. A cluster expansion to lowest order in the average concentration results in a set of two coupled equations. The spectrum of light scattered by the interacting particles is in general not a Lorentzian, due to the non-linear term in the transport equation. For small scattering wave vectors k the width is D(ω)k², where ω is the transferred frequency. It is shown that D(0) = D_e, the effective diffusion coefficient. For a hardcore interaction potential the spectrum is Lorentzian and it is found that D_e = D₀(1 + φ), where D₀ is the diffusion constant for independent particles and φ the volume concentration of Brownian particles.     

Dynamical properties of colloidal systems: III. Collective and self-diffusion of interacting charged particles

The formalism, developed in two earlier papers, for the dynamics of interacting Brownian particles is applied to a system of charged spherical particles in solution. Memory-type transport equations are derived for the propagators of collective and self-diffusion. The memory function for collective diffusion can be related, in the hydrodynamic limit, to the viscosity of the “fluid” of Brownian particles. The memory functions are calculated for a Debye-Hückel system, from an experimentally determined static structure factor S(k), and for an overdamped one-component plasma (OCP). In the two latter cases satisfactory agreement is found with dynamical light scattering results on solutions of polystyrene spheres; in particular, the deviation of the dynamical structure factor from a simple exponential decay can be related to memory effects. With regard to self-diffusion the velocity autocorrelation function, the mean square displacement of one particle and from it the self-diffusion coefficient D_s are calculated. Using S(k) for an actual system, $\text{D}{}_{\mathrm{s}}\text{≈}\text{1}\text{3}\text{D}{}_0$ is obtained, where D₀ is the free diffusion constant. The calculations on the basis of the overdamped OCP-model show that the dynamical properties of the experimentally investigated systems of charged polystyrene spheres can be described by this model for a wide range of scattering angles.     

Dynamics and sedimentation velocity in charge-stabilized colloidal suspensions

Summary Charge-stabilized suspensions are characterized by the strong electrostatic interactions between the particles so that rather dilute systems may exhibit strong correlation resulting in a well-developed short-range order. This microstructure, quantitatively described by the pair distribution functiong(r), is rather different from that of (uncharged) hard spheres. It is shown how this difference affects the ?hydrodynamic function?H(k), which appears in the expression for the first cumulant Γ(k)=k ² D _eff(k)=k ² H(k)/S(k) of the dynamic autocorrelation function. Without hydrodynamic interaction,H(k)=D ⁰, which is the free-diffusion coefficient. Using pairwise additive hydrodynamic interaction and the lowest-order many-body theory of hydrodynamic interaction, it is found thatH(k) can deviate considerably fromD ⁰ even for systems of volume fractions ϕ as low as 10⁻³. These effects are more pronounced for collective diffusion than for self-diffusion. SinceH(k=0) is closely related to the sedimentation velocity, we have studied this quantity as a function of volume fraction. It is found that (H(0)/D ⁰) −1 scales asφ ^1/3 at low ϕ in salt-free suspensions. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Theoretical studies of chemisorbed oxygen on Ag(110)

The interaction of an oxygen atom with a 26-atom cluster model of the (110) face of Ag has been investigated with ab initio self-consistent-field and configuration-interaction theory. The SCF results for the bridge site (C_2v) predict $\text{r = 0.3}\text{A}\text{?}$ and ω_e = 327 cm^?1, in good agreement with the available experimental evidence. The calculated binding energy (D_e = 9 kcal/mole) is roughly an order of magnitude too small. The inclusion of electron correlation increases r_e and ω_e only slightly, but should have a dramatic effect on D_e. The ground state corresponds to a “surface oxide” state. The theoretical projected density-of-states curves exhibit “bonding” and “anti-bonding” O(2p) peaks, separated by ~ 6 eV, in good agreement with recent angle-resolved photoemission data.     

On the solid-like phase transition in crystals of polystyrene spheres in aqueous suspensions

We present results of calculations for the fractional energy difference between the bcc and fcc phases present in ordered systems of polystyrene spheres in aqueous suspensions. The theoretical model developed for those systems is an extension of the concept of a Wigner lattice. The interaction between the particles is assumed to be a screened coulomb potential. We conclude that the phase transition occurs when λr₅ = 1.05 where λ^-1 is the Debye screening length and r_s is the radius of the spherical volume of the unitary cell.     

Viscous compressible hydrodynamics at planes,spheres and cylinders with finite surface slip

We consider the linearized time-dependent Navier-Stokes equation including finite compressibility and viscosity. We first constitute the Green's function, from which we derive the flow profiles and response functions for a plane, a sphere and a cylinder for arbitrary surface slip length. For high driving frequency the flow pattern is dominated by the diffusion of vorticity and compression, for low frequency compression propagates in the form of sound waves which are exponentially damped at a screening length larger than the sound wave length. The crossover between the diffusive and propagative compression regimes occurs at the fluid's intrinsic frequency w \omega ∼ c ² r₀ \rho_{0}^{}/h \eta , with c the speed of sound, r₀ \rho_{0}^{} the fluid density and h \eta the viscosity. In the propagative regime the hydrodynamic response function of spheres and cylinders exhibits a high-frequency resonance when the particle size is of the order of the sound wave length. A distinct low-frequency resonance occurs at the boundary between the propagative and diffusive regimes. Those resonant features should be detectable experimentally by tracking the diffusion of particles, as well as by measuring the fluctuation spectrum or the response spectrum of trapped particles. Since the response function depends sensitively on the slip length, in principle the slip length can be deduced from an experimentally measured response function.     

Quantum-statistical conductance theory of nonideal plasmas by use of the force-force correlation function method

Using the formalism of force-force correlation functions developed recently, the Spitzer formula for the conductance is generalized by taking into account the following effects: (1) dynamical screening; (2) ion-ion correlations by the ion structure factor; (3) deviations from Coulomb's interaction law; (4) influence of the Debye-Onsager relaxation effect; (5) quantum effects.It is shown that all these effects decrease the conductance in comparison with the values predicted by the Spitzer theory and lead to a more reasonable agreement with the experimental data in the region μ = e²/r_DkT ? 1 (r_D - Debye radius).Electron-electron interactions are treated by a systematic perturbative expansion of the force-force correlation function with the help of the Matsubara Green's function technique.     

Viscoelastic behaviour of fluids with steeply repulsive potentials

We analyse the shear stress, C _s(t) and pressure or ‘bulk’, C _b(t) time-correlation functions for steeply repulsive inverse power fluids (SRP) in which the particles interact via a pair potential with the analytic form, φ(r) = ε(σ/r) ⁿ , in a new approach to the understanding of their viscoelastic properties. We show analytically, and confirm by molecular dynamics simulations, that close to the hard-sphere limit both these time-correlation functions have the analytic form, C _s(t)/C _s(0) and C _b(t)/C _b(0) = 1 – T*(nt*)²+ O((nt*)⁴), where T* = k _B T/ε, is the reduced temperature, k _B is Boltzmann's constant and t* = (ε/mσ²)^½ t is the reduced time. This leads to an alternative and much simpler derivation of formulae for the shear and bulk viscosities which for the limiting case of hard spheres are numerically very close to the traditional Enskog relations. These simple relations for the finite and continuous SRP interaction are in satisfactory agreement with the essentially exact molecular dynamics simulation results for ca. n ≥ 18.     

Ethylene adsorption on the Pt-Cu bimetallic catalysts. Density functional theory cluster study

The adsorption of ethylene on Cu₁₂Pt₂ clusters has been studied within the density functional theory (DFT) approach to understand the high ethylene selectivity of Cu-rich Pt-Cu catalyst particles in the reaction of hydrogen-assisted 1,2-dichloroethane dechlorination. The structural parameters for Cu₁₂Pt₂ clusters with D_4h, D_2d, and C_3v symmetry have been calculated. The relative stability of the isomeric Cu₁₂Pt₂ clusters follows the order: C_3v > D_2d > D_4h. Each isomer has an active site for ethylene adsorption that consists of a single Pt atom surrounded by Cu atoms. The interaction of ethylene with the active site yields a π-C₂H₄ adsorption complex. The strongest π-C₂H₄ complex forms with the cluster of C_3v symmetry; the bonding energy, ΔE_π(C₂H₄), is −15.6 kcal mol⁻¹. The bonding energies for the π-C₂H₄ complex with Cu₁₄ and Pt₁₄ clusters are −6.5 and −18.8 kcal mol⁻¹, respectively.The addition of Pt to Cu modifies the valence spd-band of the cluster as compared to a Cu₁₄ cluster. The DOS near the Fermi level increases when C₂H₄ adsorbs on the Cu₁₂Pt₂ cluster. As well, the center of the d-band shifts toward lower binding energies. Ethylene adsorption also induces a number of states below the d-band. These states correspond to those of gas-phase C₂H₄.The vibrational frequencies of C₂H₄ adsorbed on the clusters of D_4h and C_3v symmetry have been calculated. The phonon vibrations occur below 250 cm⁻¹. The intense bands around 200 cm⁻¹ are attributed to stretching vibrations of the Pt-Cu bonds normal to the cluster surface. The stretching vibrations of the Pt-C bonds depend on the local structure of the active site: ν_s(Pt-C) = 268 cm⁻¹ and ν_as(Pt-C) = 357 cm⁻¹ for the cluster of the D_4h symmetry; ν_s(Pt-C) = 335 cm⁻¹ and ν_as(Pt-C) = 397 cm⁻¹ for the cluster of the C_3v symmetry. Bands in the range of 800-3100 cm⁻¹ are attributed to vibrations of the adsorbed C₂H₄ molecule. The signature frequencies of the π-C₂H₄ adsorption complex are the δ_s(CH₂) deformation vibration at ∼1200 cm⁻¹ and the ν(C-C) stretching vibration at ∼1500 cm⁻¹. These vibration are absent for di-σ-C₂H₄ adsorption complexes.     

Thermal conductivity of fluids with steeply repulsive potentials

We consider the thermal conductivity of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, φ(r) = ε(σ/r)ⁿ. The time correlation function for the heat flux, C_λ(t), and the time average, C_λ(0) are calculated numerically by molecular dynamics simulations, and accurate expressions for these are also derived for the SRP fluid. We show, by molecular dynamics simulations, that close to the hard-sphere limit this time correlation function has the same analytic form as for the shear and pressure correlation functions for the shear and bulk viscosity, i.e. C_λ(t)/C_λ(0) = 1 ?T* (nt*)² + 0((nt*)⁴), where T* = k _B T/ε, is the reduced temperature, k _B is Boltzmann's constant and t* = (ε/σ²)^1/2 t is the reduced time. The thermal conductivity for the limiting case of hard spheres is numerically very close to that given by the traditional Enskog relation. At low densities the normalized relaxation times are typically largest for the thermal conductivity, followed by shear and then bulk viscosity. Close to the maximum fluid density, the latter two increase rapidly with density (especially for the shear) but continue a monotonic decline for the thermal conductivity. This reflects the relative insensitivity of the thermal conductivity to the approach to the fluid-solid phase boundary.     

Semiinclusive two-particle correlations and independent cluster emission at ISR energies

Semiinclusive two-particle correlations are calculated in the independent cluster emission model. The resulting semi-inclusive correlation functions ?₂ⁿ(y₁ = y₂ = 0) agree rather than well experimental data, esp. with respect to the multiplicity dependence. The average number of charged particles per cluster found from comparison with semiinclusive data is 2.5 charged particles per cluster, a value found earlier also from analysis of inclusive correlations.     

Dust acoustic wave oscillations in C60 molecule

In this letter, dispersion properties of low-frequency electrostatic waves in a C₆₀ molecule are investigated. It is assumed that C₆₀ molecule is charged due to the field emission, and hence the C₆₀ molecule can be regarded as charged dust spheres surrounded by degenerate electrons and ions. We obtain the dispersion relation for the low-frequency electrostatic oscillations in the C₆₀ molecule by using the quantum hydrodynamic model in conjunction with the Poisson equation.     

Statistical dynamics of conserved densities for the hard-sphere Lorentz gas

The statistical dynamics of a particle scattered by randomly positioned stationary hard spheres are investigated. We examine the somewhat unusual long-wavelength, low-frequency fluctuation spectra resulting from the existence of an infinite set of mutually coupled conserved densities of which the number density and energy density are two members. The analytically soluble infinite-mode correlation functions are compared with the corresponding functions obtained by truncating the set of slow modes at successively increasing orders. Furthermore, we evaluate the long-wavelenght number density autocorrelation function for a fixed speed, υ₀, in terms of a frequency-dependent diffusivity D(ω;υ₀) and obtain the fluctuation spectra of all conserved densities by an additional velocity average with the appropriate canonical weights. The effect of the frequency-dependent diffusivity D(ω;υ₀) on the density fluctuation spectra at frequencies small compared to the mean collision frequency is elucidated.     

A phase cell cluster expansion for Euclidean field theories

We adapt the cluster expansion first used to treat infrared problems for lattice models (a mass zero cluster expansion) to the usual field theory situation. The field is expanded in terms of special block spin functions and the cluster expansion given in terms of the expansion coefficients (phase cell variables); the cluster expansion expresses correlation functions in terms of contributions from finite coupled subsets of these variables. Most of the present work is carried through in d space time dimensions (for φ₂⁴ the details of the cluster expansion are pursued and convergence is proven). Thus most of the results in the present work will apply to a treatment of φ₃⁴ to which we hope to return in a succeeding paper. Of particular interest in this paper is a substitute for the stability of the vacuum bound appropriate to this cluster expansion (for d = 2 and d = 3), and a new method for performing estimates with tree graphs. The phase cell cluster expansions have the renormalization group incorporated intimately into their structure. We hope they will be useful ultimately in treating four dimensional field theories.     

The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the ??extrinsic?? characteristics of the oscillator (amplitudes of ??classical?? oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|_max ?? 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|_max ?? 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|_max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|_max ?? 0. The influence of the CCS formation on the averaged probability ??D?? of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value ??D _r=0?? = 10^?80 to ??D?? ?? 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.     

Wavefunctions of helium-like systems in limiting regions

We find an approximate analytic form for the solution ψ(r ₁, r ₂, r ₁₂) of the Schrödinger equation for a system of two electrons bound to a nucleus in the spatial regions r ₁ = r ₂ = 0 and r ₁₂ = 0, which are of great importance for a number of physical processes. The forms are based on the well-known behavior of ψ(r ₁, r ₂, r ₁₂) near the singular triple coalescence point. The approximate functions are compared to the locally exact ones obtained earlier by the correlation function hyperspherical harmonic (CFHH) method for the helium atom, light helium-like ions, and the negative ion of hydrogen H^?. The functions are shown to determine a natural basis for the expansion of CFHH functions in the considered spatial region. We demonstrate how these approximate functions simplify calculations of high-energy ionization processes.     

Sum rules for Sαβ(k,ω) for two diffusing species

Starting from the Smoluchowski equation without hydrodynamic interactions for two species of spherical diffusing particles, sum rules are derived here for the first three moments of S_αβ(k,ω), i.e., for the initial value of the first, second and third time-derivatives of F_αβ(k, t) (the time-dependent correlations between the fluctuations in the local concentration of diffusing particles of species α and β). These sum rules are written in terms of the potential of interaction u_αβ(r) between the diffusing particles and the two- and three-particles distribution functions. This derivation is motivated by its potential use in the study of counterion effects on the diffusion of highly charged colloidal particles. Thus, we propose to approximate the memory function involved in the time evolution equation for F_αβ(k, t by a two-parameter model, with its (k-dependent) parameters being determined by the sum rules derived here. This procedure, along with Kirkwood's superposition approximation, reduces the dynamical problem to the knowledge of the radial distribution functions g_αβ(r).     

Formation and application of correlated states in nonstationary systems at low energies of interacting particles

We consider prerequisites and investigate some optimal methods for the formation of a correlated coherent state of interacting particles in nonstationary systems. We study the influence of the degree of particle correlation on the probability of their passage through the Coulomb barrier for the realization of nuclear reactions at low energies. For such processes, the tunneling probability and, accordingly, the probability of nuclear reactions can grow by many orders of magnitude (in particular, the barrier transparency increases from D _{r = 0} ≈ 10⁻⁴² for an uncorrelated state to D _{|r| = 0.98} ≈ 0.1 at a correlation coefficient |r| ≈ 0.98). The formation of a correlated particle state is considered in detail for different types of monotonic decrease in the frequency of a harmonic oscillator with the particle located in its parabolic field. For the first time, we have considered the peculiarities and investigated the efficiency of the creation of a correlated state under a periodic action on a harmonic oscillator. This method is shown to lead to rapid formation of a strongly correlated particle state that provides an almost complete clearing of the potential barrier even for a narrow range of oscillator frequency variations.