The capillary-wave Hamiltonian for an interface in the presence of a weakly corrugated substrate

We derive within the mean-field version of the Landau-Ginzburg -Wilson theory the expression for the capillary-wave Hamiltonian of the interface between twophases of an uniaxial ferromagnet fluctuating in the presence of a weakly corrugated, asymptotically flat substrate. The coefficients of interfacial stiffness as well as the coefficient multiplying the coupling between the ondulations of the interface and the corrugation of the substrate are shown to depend on the local distance l between the interface and the substrate. This distance dependence goes via the exponentially decaying terms which are multiplied by polynomials in l. Using this capillary-wave Hamiltonian we show that the weak corrugation of the substrate does not lead to a shift of the critical wetting temperature as compared to the flat substrate case.     

Kinetic theory of dense fluids. IV. Entropy balance equation and irreversible thermodynamics

The viscosity coefficient obtained in a previous paper of this series is calculated as a function of density by developing the N-particle collision operator into a dynamic cluster expansion. The excess transport coefficient Δη is given in an exponential form, where η₀ is the two-body Chapman-Enskog result for the transport coefficient, n is the density, and β_l is a density-independent quantity consisting of connected cluster contributions of (l + 2) particles. Therefore, the leading term β₁ consists of connected three-body cluster contributions. The excess shear viscosity coefficient is calculated for a monatomic hard-sphere fluid by computing β_l up to the three-body contributions and the result is compared with the molecular dynamics result by Ashurst and Hoover and also with the experimental data on Ar at 75°C. In spite of the crudity of the potential model used and the approximations made the agreement is good. The result can be improved if l-body clusters (l 4) are included in the calculation. The thermal conductivity coefficient can be obtained in a similar form by using exactly the same procedure used for the viscosity coefficient.     

Effective potentials and the onset of quantization in ultrasmall MOSFETs

The connection between the minimum size of an electron wavepacket, and the introduction of an effective potential is discussed. The effective potential approach has a long history of use in trying to transition the gap between classical mechanics and quantum mechanics. An effective potential is one in which the quasi-classical regime is approximated through a density which arises from the effective potential W(x) through exp[ − βW(x)]. The generation of the effective potentialW (x) gives the effects of the onset of quantization in the system. In this paper, we study the use of the effective potential in a triangular well formed between the oxide and the depletion field of the semiconductor. We determine the quantization energy of the carriers in the potential well and their mean set-back from the interface. Finally, we show the connection between the effective potential and the Bohm-derived quantum potentials that have become of interest in simulations.     

Classical charged fluids at equilibrium near an interface: Exact analytical density profiles and surface tension

The structure of equilibrium density profiles in an electrolyte in the vicinity of an interface with an insulating or conductive medium is of crucial importance in chemical physics and colloidal science. The Coulomb interaction is responsible for screening effects, and in dilute solutions the latter effects give rise to universal leading corrections to nonideality, which distinguish electrolyte from nonelectrolyte solutions. An example is provided by the excess surface tension for an air-water interface, which is determined by the excess particle density, and which was first calculated by Onsager and Samaras. Because of the discrepancy between the dielectric constants on both sides of the interface, every charge in the electrolyte interacts with an electrostatic image, and the Boltzmann factor associated with the corresponding self-energy has an essential singularity over the length scalel from the wall. Besides Coulomb interactions, short-range repulsions must be taken into account in order to prevent the collapse between charges with opposite signs or between each charge and its image when the solvent dielectric constant is lower than that of the continuous medium on the other side of the interface. For a dilute and weaklycoupled electrolyte,l is negligible with respect to the bulk Debye screening length ξ_D. In the framework of the grand-canonical ensemble, systematic partial resummations in Mayer diagrammatics allow one to exhibit that, in this regime, the exact density profiles at leading order are the same as if they were calculated in a partially-linearized mean-field theory, where the screened pair interaction obeys an inhomogeneous Debye equation. In the latter equation the effective screening length depends on the distancex from the interface: it varies very fast over the lengthl and tends to its bulk value over a few ξDs. The equation can be solved iteratively at any distancex, and the exact density profiles are calculated analytically up to first order in the coupling parameter l/ξ_D. They show the interplay between three effects: (1) the geometric repulsion from the interface associated with the deformation of screening clouds, (2) the polarization effects described by the images on the other side of the interface, (3) the interaction between each charge and the potential drop created by the electric layer which appears as soon as the fluid has not a charge-symmetric composition. Moreover, the expressions allow us to go beyond Onsager-Samaras theory: the surface tension is calculated for charge-asymmetric electrolytes and for any value of the ratio between the dielectric constants on both sides of the interface. Similar diagrammatic techniques also allow one to investigate the charge renormalization in the dipolar effective pair interaction along the interface with an insulating medium.     

The role of heat-conducting walls in the measurement of heat and mass transport in transient grating experiments

We present a two-dimensional model to account for the role of heat-conducting walls in the measurement of heat transport and Soret-effect-driven mass transport in transient holographic grating experiments. Heat diffusion into the walls leads to non-exponential decay of the temperature grating. Under certain experimental conditions it can be approximated by an exponential function and assigned an apparent thermal diffusivity D_{th, app} < D_{th, s}, where D_th,s is the true thermal diffusivity of the sample. The ratio D_{th, app}/D_{th, s} depends on only three dimensionless parameters, d /l_s, κ_s/κ_w, and D_{th, s}/D_{th, w}. d is the grating period, l_s the sample thickness, κ_s and κ_w the thermal conductivities of sample and wall, respectively, and D_th,w the thermal diffusivity of the wall. If at least two measurements are performed at different d /l_s, both D_th,s and κ_s can be determined. Instead of costly solving PDEs, D_th,s can be obtained by finding the zero of an analytic function. For thin samples and large grating periods, heat conduction into the walls plays a predominant role and the concentration grating in binary mixtures is no longer one-dimensional. Nevertheless, the normalized heterodyne diffraction efficiency of the concentration grating remains unaffected and the true thermal and collective diffusion coefficient and the correct Soret coefficient are still obtained from a simple one-dimensional model.     

Algebraic expressions for effective potential characteristic parameters in heavy ion scattering

In this paper, we obtain reliable expressions to calculate the barrier and pocket positions of the real part of the effective phenomenological optical potential having Woods-Saxon form factor, for different partial waves. The comparison of the results obtained from these formulae, when compared with the numerical results obtained using Newton-Raphson iterative procedure are found to be quite accurate, with error less than 1%. We also obtain algebraic expressions for estimatingl _poc, the angular momentum at which the potential pocket vanishes, the accuracy of which is tested with the exact calculations, using self-consistent iterative procedures. These and other expressions deduced in this paper provide simple and useful methods for calculating critical parameters of heavy ion effective potentials like barrier and pocket positions, curvatures at the barrier and pocket positions,l _poc and the grazing angular momentuml _g to carry out the analysis of heavy ion scattering.     

Kinetics of the formation of Fe2B layers in gray cast iron: Effects of boron concentration and boride incubation time

The growth kinetics of Fe₂B layers formed at the surface of gray cast iron were evaluated in this study. The pack-boriding process was applied to produce the Fe₂B phase at the material surface, and the variables included three temperatures (1173, 1223 and 1273 K) and four exposure times (2, 4, 6 and 8 h). Taking into account the growth fronts obtained at the surface of the material and the mass balance equation at the Fe₂B/substrate interface, the boron diffusion coefficient on the borided phase was estimated for the range of treatment temperatures. Likewise the parabolic growth constant, the instantaneous velocity of the Fe₂B/substrate interface, and the weight gain in the borided samples were established as a function of the parameters τ(t) and α(C), which are related to the boride incubation time (t₀(T)) and boron concentration at the Fe₂B phase, respectively. Observation of the growth kinetics of the Fe₂B layers in gray cast irons suggest an optimum value of boron concentration that is in good agreement with the set of boriding experimental conditions used in this work.     

Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

The double-layer contribution to the single-particle thermal diffusion coefficient of charged, spherical colloids with arbitrary double-layer thickness is calculated and compared to experiments. The calculation is based on an extension of the Debye-Hückel theory for the double-layer structure that includes a small temperature gradient. There are three forces that constitute the total thermophoretic force on a charged colloidal sphere due to the presence of its double layer: i) the force F _W that results from the temperature dependence of the internal electrostatic energy W of the double layer, ii) the electric force F _el with which the temperature-induced non-spherically symmetric double-layer potential acts on the surface charges of the colloidal sphere and iii) the solvent-friction force F _sol on the surface of the colloidal sphere due to the solvent flow that is induced in the double layer because of its asymmetry. The force F _W will be shown to reproduce predictions based on irreversible-thermodynamics considerations. The other two forces F _el and F _sol depend on the details of the temperature-gradient-induced asymmetry of the double-layer structure which cannot be included in an irreversible-thermodynamics treatment. Explicit expressions for the thermal diffusion coefficient are derived for arbitrary double-layer thickness, which complement the irreversible-thermodynamics result through the inclusion of the thermophoretic velocity resulting from the electric- and solvent-friction force.     

Compression properties of finite nuclei in a semi-classical relativistic approach

Skyrme type potentials are known to lead — in the framework of the scaling model — to a finite-nucleus incompressibility valueK _A where the volume coefficientK _v equals roughly the negative surface coefficient K_s. This is found for Skyrme interactions with K_v between 200 and 360 MeV. In a semi-classical relativistic approach on the basis of the — model (linear as well as non-linear) using in addition local density approximations, we findK _s to depend in particular on the surface energy coefficienta _s , and not so much on the value ofK _v . For a realistic value of a_s, both the linear and the non-linear — model (with NL1 parameter set) yield a ratio ¦K _s K _v ¦ of approximately 1. We discuss implications of this finding with a particular view on recent empirical results onK _v andK _s .Dedicated to Prof. Dr. H. J. Mang on the occasion of his 60th birthday     

Mean First-Passage Time in a Bistable Kinetic Model with Stochastic Potentials

The transient properties of a bistable system with the stochastic potentials are investigated. The explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The results show that the MFPT of the system increases with the amplitude Δ of the stochastic potential, decreases with the noise intensity D and the correlation length l. The stochastic potential makes against the particle moving towards the destination.     

The vicinity of an equilibrium three-phase contact line using density-functional theory: density profiles normal to the fluid interface

The paper by Nold et al. [Phys. Fluids 26 (7), 072001 (2014)] examined density profiles and the micro-scale structure of an equilibrium three-phase (liquid–vapour–solid) contact line in the immediate vicinity of the wall using elements from the statistical mechanics of classical fluids, namely density-functional theory. The present research note, building on the above work, further contributes to our understanding of the nanoscale structure of a contact line by quantifying the strong dependence of the liquid–vapour density profile on the normal distance to the interface, when compared to the dependence on the vertical distance to the substrate. A recent study by Benet et al. [J. Phys. Chem. C 118 (38), 22079 (2014)] has shown that this could explain the emergence of a film-height-dependent surface tension close to the wall, with implications for the Frumkin–Derjaguin theory.     

Effect of oxygen segregation on the surface structure of single-crystalline niobium films on sapphire

Single-crystalline Nb films are grown on (1120) oriented sapphire substrates by electron-beam evaporation in ultra-high vacuum. The films are studied in-situ by RHEED and Auger analysis. At a substrate temperature T _S=750° C the RHEED pattern shows a smooth growth of bcc-Nb in the [110] direction. In addition to the fundamental streaks, we observe superlattice streaks of fractional order in several azimuthal directions. The reciprocal lattice of the surface is determined. The basic vectors of the superlattice in real space are given by b ₁=2a ₁, b ₂=–a ₁+3a ₂ where a ₁ and a ₂ are the basic vectors of the Nb (110) surface. Auger analysis shows that the surface of these films is contaminated with oxygen. Therefore, the superstructure is attributed to a modified surface structure due to segregated oxygen, possibly having diffused from the sapphire to the film surface. The superstructure dissappears during further evaporation of Nb at T _S<450° C with a concomitant decrease of the oxygen signal. Nb films on sapphire with a clean, oxygen-free surface can only be prepared at lower temperatures in an island-growth mode.     

Helicity amplitudes and crossing relations for one-photon exchange antiproton proton reactions

Antiproton proton annihilation reactions allow unique access to the moduli and phases of nucleon electromagnetic form factors in the time-like region. We present the helicity amplitudes for the unequal-mass single-photon reaction pˉ → l ⁺ l ^- in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for one-photon exchange annihilation reaction pˉ → Bˉ are also given, where B is any spin-one-half particle with structure. Crossing relations between the ep → ep scattering and the pˉ → l ⁺ l ^- annihilation channels are discussed and the crossing matrix for the helicity amplitudes is given. This matrix may be used to verify known expressions for the space-like helicity amplitudes due to one-photon exchange.     

Effects of finite thickness on interfacial widths in confined thin films of coexisting phases

The capillary broadening of a 2-phase interface is investigated both experimentally and theoretically. When a binary mixture in a thin film with thickness D segregates into two coexisting phases the interface between the two phases may form parallel to the substrate due to preferential surface attraction of one of the components. We show that the interfacial profile (of intrinsic width w₀) is broadened due to capillary waves, which lead to fluctuations, of correlation length of the local interface positions in the directions parallel to the confining walls. We postulate that acts as an upper cutoff for the spectrum of capillary waves on the interface, so that the effective mean square interfacial width w varies as . In the limit of large D this yields or respectively for the case of short- or long-range forces between walls and the interface. We used the Nuclear Reaction Analysis depth profiling technique, to investigate this broadening effect directly in two binary polymer mixtures. Our results reveal that the interfacial width indeed increases with film thickness D, though the observed interfacial width is lower than the predicted w. This is probably due to surface tension effects imposed by the confining surfaces which are not taken into account in our model. Received: 19 February 1998 / Received in final form: 2 September 1998 / Accepted: 8 September 1998     

Wide- and narrow-band saturated fluorescence measurements of hydroxyl concentration in premixed flames from 1 bar to 10 bar

We have studied the use of wide-band detection in conjunction with saturation of a rovibronic transition of OH within itsA ^{2 +}–X ²(0,0) band. For wide-band detection, in which fluorescence is detected from the entire excited rotational manifold, the fluorescence yield is sensitive to collisions in two ways. First, it is sensitive to the ratio of rate coefficients describing rotational energy transfer and electronic quenching; this ratio determines the number of neighboring rotational levels that are populated during the laser pulse. Second, the fluorescence yield can vary with the total collisional rate coefficient; only after a sufficient number of collisions, corresponding to 2.5 ns in an atmospheric flame, does the rotational manifold reach steady state. We also compare measurements employing wide-band (detecting theR ₁ andR ₂ branches) and narrow-band (detecting a single transition) saturated fluorescence of OH. Over a wide range of conditions — obtained by varying the equivalence ratio, temperature, N₂ dilution, and pressure — the wide- and narrow-band fluorescence techniques compare well. Given this good agreement, wide-band saturated fluorescence could be especially useful for analyzing atmospheric flames with XeCl-excimer lasers; one can potentially obtain 2—D images of OH which have a high signal-to-noise ratio and a reduced sensitivity to laser irradiance and quenching.     

Intrusion of fluids into nanogrooves

We study the shape of gas-liquid interfaces forming inside rectangular nanogrooves (i.e., slit-pores capped on one end). On account of purely repulsive fluid-substrate interactions the confining walls are dry (i.e., wet by vapor) and a liquid-vapor interface intrudes into the nanogrooves to a distance determined by the pressure (i.e., chemical potential). By means of Monte Carlo simulations in the grand-canonical ensemble (GCEMC) we obtain the density ρ(z) along the midline (x = 0 of the nanogroove for various geometries (i.e., depths D and widths L of the nanogroove. We analyze the density profiles with the aid of an analytic expression which we obtain through a transfer-matrix treatment of a one-dimensional effective interface Hamiltonian. Besides geometrical parameters such as D and L , the resulting analytic expression depends on temperature T , densities of coexisting gas and liquid phases in the bulk ρ^g,l _x and the interfacial tension γ . The latter three quantities are determined in independent molecular dynamics simulations of planar gas-liquid interfaces. Our results indicate that the analytic formula provides an excellent representation of ρ(z) as long as L is sufficiently small. At larger L the meniscus of the intruding liquid flattens. Under these conditions the transfer-matrix analysis is no longer adequate and the agreement between GCEMC data and the analytic treatment is less satisfactory.     

Any l-state solutions of the Klein-Gordon equation with the generalized Hulthén potential

We present analytical solutions of the Klein-Gordon equation with non-zero l values for the general Hulthén potential within the framework of an approximation to the centrifugal potential for any l-states. The explicit expressions of bound state energy eigenvalues and eigenfunctions are derived. Three special cases, s-wave, standard Hulthén potential and ground state are discussed.     

Nucleon electromagnetic form factors and polarization observables in space-like and time-like regions

We perform a global analysis of the experimental data of the electromagnetic nucleon form factors, in space-like and time-like regions. We give the expressions of the observables in annihilation processes, such as p + ¯↦ℓ⁺ + ℓ^-, ℓ = e or μ, in terms of form factors. We discuss some of the phenomenological models proposed in the literature for the space-like region, and consider their analytical continuation to the time-like region. After determining the parameters through a fit on the available data, we give predictions for the observables which will be experimentally accessible with large statistics, polarized annihilation reactions     

Adsorption of a semiflexible wormlike chain

Adsorption of ideal polymers with stiff backbone onto a flat surface is considered theoretically. Both scaling approach and quantitative theory are developed. We predict a self-similar monomer concentration profile c(x) ∼ x ^-4/3 near the surface (when the distance to the surface x is much smaller than the chain persistence length l /2). The typical conformation of a weakly adsorbed chain can be viewed as a sequence of alternating flat (2-dimensional) trains of wormlike short loops (flat blobs) and coil-like (3-dimensional) loops forming a triple-layer structure: contact layer (x < Δ) of adsorbed fragments virtually laid on the surface, proximal layer (Δ < x < l) of flat blobs, and more dilute distal corona layer (x > l). Here Δ defines the range of monomer/surface attraction, Δ ≪ l. The adsorption transition is continuous. However, its relative width is small (T ^* is the adsorption temperature, ΔT is the relevant temperature interval): ∼ , i.e. a discontinuous transition in the limit Δ/l↦ 0. Received 10 October 2002 and Received in final form 22 November 2002 RID="a" ID="a"Permanent address: Physics Department, Moscow State University, Moscow 119992, Russia. e-mail: semenov@polly.phys.msu.ru     

Incorporation of Sn into epitaxial GaAs grown from the liquid phase

The incorporation of Sn into LPE GaAs was studied as a function of the atomic fractionx _Sn ^l of Sn in the liquid (1.6×10⁻⁴≤x _Sn ^l ≤0.54), the growth temperatureT _K and the cooling rate α. The diffusion coefficient of As in Ga for moderate Sn-doping was deduced from the growth velocities to beD _As (760° C)=(3.3±1.0)×10⁻⁵ cm²/s. The epitaxial layers were analyzed after van der Pauw with special emphasis on the sources of experimental error. With the aid of current mobility theories the concentrations of the ionized donors and acceptors were derived. From their dependence onx _Sn ^l , on α and onT _K combined with the Schottky-barrier model of Sn incorporation it can be concluded that the melt and the growing crystal surface were in thermal equilibrium. The diffusion coefficient of Sn in GaAs is about 8×10⁻¹⁴ cm²/s at 760° C. The distribution coefficient for Sn increases from 4.4×10⁻⁵ to 12.3×10⁻⁵ in the temperature range from 690 to 800° C. The total Sn incorporationx _Sn ^s was measured using the atomic absorption spectroscopy for the first time down tox _Sn ^s =10¹⁷/cm³. From these data it can be concluded that up tox _Sn ^l =0.54 the dopant Sn is incorporated as donor and as acceptor only and that within the experimental scatter there is no indication of incorporation as a neutral species.