Cluster ion emission in the interaction of slow highly charged ions with surfaces

Cluster ion emission from a variety of surfaces upon impact of highly charged ions is investigated by time-of-flight secondary ion mass spectrometry. The yield of cluster ions as a function of cluster size for and surface follow a power law decline with exponent approaching the -2 limit of the ”equilibrium” and ”shock wave” cluster emission models. While the decline of the cluster ion emission with cluster size is an exponential decay for highly oriented pyrolytic graphite upon impact, the decline is more gradual than for impact, such that at the relative cluster yield is 1000 times higher. Received: 22 April 1997 / Revised: 29 December 1997 / Accepted: 19 January 1998     

A neutron reflectometry study of polystyrene network interfaces

We have used neutron reflectometry to measure interfacial widths between two polystyrene films, where either one or both films are crosslinked. The observed interfacial width between two networks is larger than the size expected for “dangling ends”, which suggests motion of heterogeneous regions of the networks. In the case when one of the networks is replaced by a linear polymer, the interfacial profile can be asymmetric with a diffusion “front” of linear polymer penetrating the network to a length scale of up to 200 ?. In the case of a more densely crosslinked network and a high molecular weight linear polymer the interface is symmetric implying negligible penetration. Received: 4 December 1996 / Revised: 13 October 1997 / Accepted: 23 December 1997     

“Elastic” fluctuation-induced effects in smectic wetting films

The Li-Kardar field theory approach is generalized to wetting smectic films and the “elastic” fluctuation-induced interaction is obtained between the external flat bounding surface and distorted IA (isotropic liquid-smectic A) interface acting as an “internal” (bulk) boundary of the wetting smectic film under the assumption that the IA interface is essentially “softer” than the surface smectic layer. This field theory approach allows calculating the fluctuation-induced corrections in Hamiltonians of the so-called “correlated” liquids confined by two surfaces, in the case where one of the bounding surfaces is “rough” and with different types of surface smectic layer anchoring. We obtain that in practice, the account of thermal displacements of the smectic layers in a wetting smectic film reduces to the addition of two contributions to the IA interface Hamiltonian. The first, so-called local contribution describes the long-range thermal “elastic” repulsion of the fluctuating IA interface from the flat bounding surface. The second, so-called nonlocal contribution is connected with the occurrence of an “elastic” fluctuation-induced correction to the stiffness of the IA interface. An analytic expression for this correction is obtained.     

Elastic Green's function of icosahedral quasicrystals

The elastic theory of quasicrystals considers, in addition to the “normal” displacement field, three “phason” degrees of freedom. We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling between the phonons and phasons is small. Received: 18 December 1997 / Accepted: 6 March 1998     

Droplet suction on porous media

We study the forced aspiration of small ( mm) and large ( cm) liquid drops, deposited on prewetted porous membranes, and pumped mechanically with a constant current J. Two kinds of membranes are used where the pores are i) disconnected, cylindrical and calibrated or ii) interconnected “sponge-like”. Whatever the size of the drops and the intensity J of the current, two suction regimes are observed versus time: 1) a “locked” regime, when the drop is pinned, with a dynamic contact angle decreasing from advancing () to finite receding () contact angle; 2) an “unlocked” regime, where the contour line recedes with a constant contact angle closed to . In both regimes, the shape of the drop remains quasistatic, during the suction process, i.e. a spherical cap for small drops and a flat “gravity pancake” for large ones. Received 19 January 2000     

Micelle-smectic phase coexistence: Origin of the maximum swelling of a mixed lamellar phase

By use of a mean-field approach the spin-wave dispersion of the Cu degrees of freedom in the undoped high-T _C material Nd₂CuO₄is investigated. The experimentally observed sharp decrease of the Cu spin-wave gap with increasing temperature in the range is explained by a paramagnetic-like susceptibility of the Nd spins which couple to the Cu subsystem. The degeneracy of the “in-plane” and “out-of-plane” polarized Cu spin-wave branches is shown to be lifted by the uniaxial anisotropy of the Cu-Cu nearest-neighbor interaction. Received: 13 August 1997 / Revised: 4 December 1997 / Accepted: 11 December 1997     

Wealth distributions in asset exchange models

A model for the evolution of the wealth distribution in an economically interacting population is introduced, in which a specified amount of assets are exchanged between two individuals when they interact. The resulting wealth distributions are determined for a variety of exchange rules. For “random” exchange, either individual is equally likely to gain in a trade, while “greedy” exchange, the richer individual gains. When the amount of asset traded is fixed, random exchange leads to a Gaussian wealth distribution, while greedy exchange gives a Fermi-like scaled wealth distribution in the long-time limit. Multiplicative processes are also investigated, where the amount of asset exchanged is a finite fraction of the wealth of one of the traders. For random multiplicative exchange, a steady state occurs, while in greedy multiplicative exchange a continuously evolving power law wealth distribution arises. Received: 13 August 1997 / Revised: 31 December 1997 / Accepted: 26 January 1998     

Lubricated sliding dynamics: Flow factors and Stribeck curve

We study the fluid flow at the interface between elastic solids with randomly rough surfaces. We derive (approximate) analytical expressions for the fluid flow factors which enter in the equation describing the fluid flow, and for the frictional shear stress factors which enter in the equation for the frictional shear stress. Numerical results for a rubber cylinder with surface roughness sliding on a flat lubricated substrate, under “low” and “high” pressure conditions, are presented and discussed. Finally we discuss the role of the fluid-induced elastic deformations of the surface roughness profile.     

Nematic ordering in anisotropic elastomers: Effect of frozen anisotropy

Nematic ordering in anisotropic non-Gaussian elastomers is considered theoretically using mean field approximation. We focus on the effect of anisotropy during network cross-linking on the system elasticity and, in particular, on the so-called soft deformation mode. As the main result, we calculate the dependence of the elastomer free energy on the angle between the axis of “frozen” anisotropy and the nematic director. The dependence of the isotropic-nematic transition point on the orientational field acting on the monomers during the cross-linking process is also calculated. Received: 5 November 1997 / Revised and Accepted: 29 June 1998     

Non-commutative geometry and irreversibility

A kinetics built upon q-calculus, the calculus of discrete dilatations, is shown to describe diffusion on a hierarchical lattice. The only observable on this ultrametric space is the “quasi-position” whose eigenvalues are the levels of the hierarchy, corresponding to the volume of phase space available to the system at any given time. Motion along the lattice of quasi-positions is irreversible. Received: 24 June 1997 / Revised: 15 September 1997 / Accepted: 6 October 1997     

Heisenberg picture operators in the stochastic wave function approach to open quantum systems

A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which “unravels” the quantum Master equation can be used for the calculation of matrix elements of reduced Heisenberg picture operators, and thus for the calculation of multitime correlation functions, by extending the stochastic process to a doubled Hilbert space. The numerical performance of the stochastic simulation algorithm is investigated by means of a standard example. Received: 30 May 1997 / Revised: 4 November 1997 / Accepted: 7 November 1997     

Cubic superspace symmetry and inflation rules in metastable MgAl alloy

The diffraction properties of a quenched Al-Mg alloy which has been recently termed as a “cubic quasicrystal” are quantitatively reanalyzed. It is shown that the phase can be interpreted within the superspace formalism as an ordinary incommensurately modulated structure. The cubic six-dimensional superspace group that describes its symmetry properties has been determined. The additional inflation symmetry features exhibited by the diffraction diagram can be summed up by its invariance for the inflation factor , but this property has its origin in the specific value of the modulus of the modulation wave vectors, which is composition dependent. Other particular values of this modulus can give rise to similar scaling properties. Further experiments are required to ellucidate if the mentioned inflation symmetry is a fortuitous situation in a composition dependent wave vector, or has indeed the physical significance which would allow to describe the system as a “cubic quasicrystal”. Received: 25 June 1998 / Received in final form and Accepted: 23 September 1998     

Elastic neutron scattering and dielectric behaviour of 4% brominated betaine calcium chloride dihydrate (BCCD)

We report a combined experimental study by means of elastic neutron scattering and dielectric measurements of a partially deuterated and brominated BCCD (Betaine Calcium Chloride Dihydrate) crystal. The lowest-temperature phase is one-dimensional modulated and characterized by the coexistence of different commensurate domains (with = 1/4, 4/17, 2/9 and 1/5 on cooling), but with a clear predominance of the five-fold phase. A huge global thermal hysteresis of the wave-vector of the modulation, attaining values of about 9 K in the incommensurate phase and up to 15 K in the “harmless” low temperature part of the phase diagram, is observed up to . The role of lattice defects on this phenomenon is discussed. Similarly to the behaviour of the pure compound, the structural modulation evolves on cooling towards a soliton regime (growth of third and fifth-order satellite peaks), probably with respect to a non-stabilized non-modulated ferroelectric phase. The critical temperatures deduced from dielectric constant and pyroelectric current measurements are in very good agreement with those obtained from neutron scattering. The dielectric anomaly observed in at K, and known as the “-anomaly”, could not be related with any special feature detected in the neutron data, and in particular no correlation between this anomaly and the appearance of the soliton regime can be established. Received 26 October 1998     

Coalescence in 2 dimensions: experiments on thin copolymer films and numerical simulations

This paper presents on one hand the experimental study of the coalescence kinetics of two closed bidimensional fluid domains at the surface of a multilayered dibloc copolymer film, and on the other hand a numerical simulation of the same evolution. The latter is based on ”diffusive” phenomenological equations which are surface conservative and which neglect the 2-dimensional viscosity of the layers. The successive shapes observed in the experiments and obtained from the simulation are very close. It would not be the case if the 2D viscosity was significant. Received : 17 march 1997 / Revised : 11 september 1997 / Accepted : 2 december 1997     

Crumpling self-avoiding surfaces

Self-avoiding plaquette surfaces with a folding or bending fugacity are believed to undergo a “crumpling” transition from a flaccid phase with branched polymer characteristics (corresponding to surfaces with a high degree of folding), to a “smooth” phase (corresponding to surfaces faith a low degree of folding). I develop rigorous techniques in order to bound the free energy of this model. In particular, the limiting free energy is proven to be positive for all positive values of the folding fugacity. In addition, the existence of a nonanalyticity in the limiting free energy of a (nontrivial) subclass of surfaces is proven. This implies the existence of a phase transition in this model, which I conjecture to be from a “flaccid” to a “smooth” phase.     

Phase transitions in “small” systems

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and classified for small systems. “Small” systems are systems where the linear dimension is of the characteristic range of the interaction between the particles; i.e. also astrophysical systems are “small” in this sense. Boltzmann defines the entropy as the logarithm of the area of the surface in the mechanical N-body phase space at total energy E. The topology of S(E,N) or more precisely, of the curvature determinant allows the classification of phase transitions without taking the thermodynamic limit. Micro-canonical thermo-statistics and phase transitions will be discussed here for a system coupled by short range forces in another situation where entropy is not extensive. The first calculation of the entire entropy surface S(E,N) for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a square lattice is shown. The regions in {E,N} where D>0 correspond to pure phases, ordered resp. disordered, and D<0 represent transitions of first order with phase separation and “surface tension”. These regions are bordered by a line with D=0. A line of continuous transitions starts at the critical point of the ordinary (q=3)-Potts model and runs down to a branching point P_m. Along this line vanishes in the direction of the eigenvector of D with the largest eigen-value . It characterizes a maximum of the largest eigenvalue . This corresponds to a critical line where the transition is continuous and the surface tension disappears. Here the neighboring phases are indistinguishable. The region where two or more lines with D=0 cross is the region of the (multi)-critical point. The micro-canonical ensemble allows to put these phenomena entirely on the level of mechanics. Received 18 October 1999 and received in final form 17 November 1999     

Amphiphilic diblock copolymers with adhesive properties: I. Structure and swelling with water

We study asymmetric block copolymers with the simple diblock AB architecture, in the case where the longer block A is both hydrophobic and “soft”, whereas the shorter block B is hydrophilic and “hard”. Materials with such a particular combination of physico-chemical and mechanical properties have distinctive advantages, in particular for designing water-compatible adhesive materials. The phase diagram is established, combining NMR and SAXS characterisations of the materials. The swelling with water is monitored through gravimetry and “time-resolved” SAXS. Indications of maintained adhesive properties in a wet environment are given.     

Interface-induced dephasing of Mie plasmon polaritons

Surface and, in particular, interface effects influence all physical and chemical properties of nanostructured matter. Mie surface plasmon polaritons (MPPs) in metallic nanoparticles are excellent and sensitive sensors for optical investigation of these effects of realistic particles since their lifetimes due to dephasing (decoherence) effects and their resonance energies drastically depend upon the chemistry and topology of their surfaces/interfaces. A survey is given over some results of our own long term research on MPPs which started, in fact, as early as 1969. Theoretical models and experiments concerning the A parameter, the δ n parameter, MPP phase decoherence and static and dynamic interface charge transfer effects (“chemical interface damping”) are briefly summarized. The effect of radiation damping is disregarded throughout: we assume the particle sizes to be small enough to justify this simplification, which makes it easier to draw conclusions from the MPPs on nanomaterial properties. Obviously, there is a wide field for future research concerning particle interfaces on the basis of Mie’s theory. On the other hand, all of these effects have to be incorporated into Mie’s theory to obtain a “modern” version which is reliable on a quantitative level to describe experimental data.