Diffusion of adsorbates on random alloy surfaces

In this work the diffusion of non-interacting adsorbates on a random AB alloy surface is considered. For this purpose a simple cubic (sc), body-centered cubic (bcc) or face-centered cubic (fcc) auxiliary metal lattice is introduced. The auxiliary lattice is truncated parallel to its (100) plane in such a way that the fourfold hollow positions of the metal surface form a regular net of adsorption sites with square symmetry. The adsorption energy of each adsorption site is determined by its own environment, i.e. by the numbers of direct A or B neighbors. The Monte-Carlo method has been utilized to simulate surface diffusion of adsorbates on such energetically heterogeneous alloy surfaces and to calculate the tracer, jump and chemical diffusion coefficients. The chemical diffusion coefficient was calculated via two different approaches: the fluctuation and the Kubo-Green method. The influence of energetical heterogeneities on the surface diffusion is largely pronounced at low temperatures and low surface coverages, where most of the adatoms are trapped by deep adsorption sites. It was found that at low temperatures the sequential occupation of the different types of adsorption sites can be observed. Received: 24 October 1997 / Accepted: 17 December 1997     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

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     

Copolymer at a selective interface and two-dimensional wetting: a grand canonical approach

We consider two different problems involving the localization of a single polymer chain: (i) a periodic AB copolymer at a selective fluid-fluid interface, with the upper (resp. lower) fluid attracting A (resp. B) monomers (ii) a homopolymer chain attracted to a hard wall (wetting). Self avoidance is neglected in both models, which enables us to study their localization transition in a grand canonical approach. We recover the results obtained in previous studies via transfer matrix methods. Moreover, we calculate in this way the loop length distribution functions in the localized phase. Some finite size effects are also determined and tested numerically. Received 13 April 2000     

On the number of intersections of self-repelling polymer chains

We give a detailed analysis of the intersection properties of polymers. Using the renormalization group we provide a full crossover function for the dependence of the number of intersections in a single polymer on chain length and excluded volume strength. We compare our results with Monte-Carlo data and with exact calculations for a random walk, finding good agreement in all respects. Restricting to the vicinity of the eight ternary fixed points we also calculate the number of intersections between two chains placed at a fixed distance, including the two halves of a block-copolymer. The analysis of these systems confirms the interpretation of the different contributions to the number of intersections in a single chain. Due to the highly nontrivial character of the correlations in a polymer chain the correction exponents in both cases however are different. None of the results can be extracted from any Flory-type estimate. Received: 1 April 1997 / Revised: 24 October 1997 / Accepted: 29 January 1998     

Adsorption and spreading of polymers at plane interfaces; theory and molecular dynamics simulations

Nonequilibrium processes play a key role in the adsorption kinetics of macromolecules. It is expected that the competition between transport of polymer towards an interface and its subsequent spreading has a significant influence on the adsorbed amount. An increase of the transport rate can lead to an increase of the adsorbed amount, especially when the polymer has too little time to spread at the interface. In this study we present both molecular dynamics simulations and analytical calculations to describe some aspects of the adsorption kinetics. From MD simulations on a poly(ethylene oxide) chain in vacuum near a graphite surface, we conclude that the spreading process can, in first approximation, be described by either a simple exponential function or by first-order reaction kinetics. Combining these spreading models with the transport equations for two different geometries (stagnation-point flow and overflowing cylinder) we are able to derive analytical equations for the adsorption kinetics of polymers at solid-liquid and at liquid-fluid interfaces. Received: 18 July 1997 / Received in final form: 27 October 1997 / Accepted: 6 November 1997     

Anomalous adhesion in adsorbed polymer layers

Anomalous adhesion behaviour observed in the polydimethylsiloxane/heptane/silica system is reported. This behaviour is characterised by the infrequent appearance of one or more elastic minima which occur in addition to the ever-present primary adhesion. The resulting elastic force is attributed to loops connecting the tip to the substrate and can be described by two models; a worm-like chain, and a freely jointed chain. Both models give similar values for the characteristic segment length of around 0.24 nm and indicate that the chains have been extended by between 90 to 95% of their chain contour length before desorption. In some cases multiple adhesions were observed between tip and substrate and have been used to suggest a method for determining the distribution of adsorbed polymer loops. Received: 12 November 1997 / Accepted: 6 March 1998     

The effect of stiffness in wormlike micelles

The effect of stiffness in a 2D living polymer system is investigated by Monte-Carlo simulation in a canonical ensemble. As the flexibility decreases, the mean chain contour length decreases and goes through a local maximum. The mean end to end square distance shows a non-monotonic behaviour due to the coil-to-rod transition and the decrease in chain contour length. Near the maximum of chain ordering in the bulk, the chain length distribution adapts itself to increase the configurational entropy. With the parameters used in this simulation, it seems that the effect of the stiffness for high stiffness is to decrease as in the isotropic case, since the ordering decreases again. Received: 16 September 1997 / Revised: 27 June 1998 / Accepted: 29 June 1998     

Dynamical properties of low-dimensional and spin-Peierls systems

Properties of low-dimensional spin-Peierls systems are described by using a one-dimensional S =1/2 antiferromagnetic Heisenberg chain linearly coupled to a single phonon mode of wave vector (whose contribution is expected to be dominant). By exact diagonalizations of small rings with up to 24 sites supplemented by a finite size scaling analysis, static and dynamical properties are investigated. Numerical evidences are given for a spontaneous discrete symmetry breaking towards a spin gapped phase with a frozen lattice dimerization. Special emphasis is put on the comparative study of the two inorganic spin-Peierls compounds CuGeO₃ and NaV₂O₅ and the model parameters are determined from a fit of the experimental spin gaps. We predict that the spin-phonon coupling is 2 or 3 times larger in NaV₂O₅ than in CuGeO₃. Inelastic neutron scattering spectra are calculated and similar results are found in the single phonon mode approximation and in the model including a static dimerization. In particular, the magnon S =1 branch is clearly separated from the continuum of triplet excitations by a finite gap. Received: 30 July 1997 / Revised: 16 September 1997 / Accepted: 10 October 1997     

From molecular flexibility to shape, curvature and thermotropic transitions in pure surfaces

A material surface of pure constituents with a flexible molecular chain (amphiphilics) is considered; thermodynamic behaviour is studied in the chain length-temperature plane. The Hamiltonian of the system is modelled as the sum of a formation term which refers to the polymer nature of the chain, and of a fluctuation term with a specific elastic form. For closed systems the model exhibits phases with uniform curvature and conformational order/disorder or, alternatively, modulated phases; a critical chain length is found for the existence of modulated phases; the dependence of transition temperature on energy parameters is determined. A critical region is found for open systems, where conformational disorder drives spontaneous generation of curvature; this lies above a characteristic chain length and around the shape transition temperature. Received: 13 November 1996 / Revised: 9 May 1997 / Received in final form: 4 November 1997 / Accepted: 10 November 1997     

Microgels and fractal structures at interfaces and surfaces

The behavior of microgels near surfaces and their adsorption is studied by simple scaling theory. Two different types of microgels can be studied, i.e., fractal type microgels and randomly crosslinked polymer chains. In the first case the gel can be described mainly by introducing a spectral dimension. The second type requires more attention and uses the number of crosslinks as parameter. The main result is that soft gels with weakly coupled crosslinks and a low number of crosslinks adsorb much better than hard gels, with many crosslinks. Similar results for fractal gels and branched polymer are presented. Fractal gels with low connectivity adsorb easier than gels with a large connectivity dimension. We discuss also consequences on surface protection by microgels. Received: 11 August 1997 / Received in final form: 20 November 1997 / Accepted 22 January 1998     

Field-induced winding of chiral polymers

We propose a microscopic model of a chiral polymer chain with permanent transverse dipoles interacting with an external electric field. Its behaviour has been investigated by computer simulation in the limit of weak chirality. Large-scale (tertiary) helical winding induced along the field direction has been found above a threshold field E_c, and the helix parameters have been calculated as functions of the field strength. Below E_c there is no coherent helical structure of the chain conformation. We find a characteristic scaling of the threshold and the winding radius a with the chain bending modulus , and . Received: 15 November 1997 / Accepted: 16 February 1998     

Extensive stretch of polysiloxane network chains with random- and super-coiled conformations

The stress-elongation relations at large deformations for the polymer network chains with randomcoiled and supercoiled conformations are investigated using the polysiloxane networks with high elongations at break far over 10. Supercoil is the conformation of network chains in deswollen polymer networks which are made by removing solvent from the networks crosslinked in solutions at low polymer concentrations. The validity of the scaling concept of Pincus blob for the mechanical response of a polymer chain is experimentally confirmed for the network composed of randomcoiled chains. The analysis of the stress- relations for the deswollen networks comprised of supercoiled chains on the basis of the Pincus blob concept suggests that supercoil is a much more contracted conformation relative to randomcoil. Received: 25 August 1997 / Received in final form: 13 October 1997 / Accepted: 22 January 1998     

Competition of disorder and interchain hopping in a two-chain Hubbard model

We study the interplay of Anderson localization and interaction in a two chain Hubbard ladder allowing for arbitrary ratio of disorder strength to interchain coupling. We obtain three different types of spin gapped localized phases depending on the strength of disorder: a pinned 4k _F Charge Density Wave (CDW) for weak disorder, a pinned 2k _F CDW^π for intermediate disorder and two independently pinned single chain 2k _F CDW for strong disorder. Confinement of electrons can be obtained as a result of strong disorder or strong attraction. We give the full phase diagram as a function of disorder, interaction strength and interchain hopping. We also study the influence of interchain hopping on localization length and show that localization is enhanced by a small interchain hopping but suppressed by a large interchain hopping. Received 6 April 2001     

Mn-site doping induced CMR properties in calcium rich manganites Pr1‒xCaxMnO3(0.6 ≤ x ≤ 0.7)

Doping of Mn-site by chromium, cobalt and nickel has been investigated in the calcium rich manganites and . Whatever the nature of the doping element, a rapid disappearance of the charge ordered (CO) state is observed, decreasing as the doping rate increases. But the most important result concerns the Cr-doped compounds for which a re-entrant insulator to metal transition at 90-120 K is observed for x =0.10-0.12, in a zero magnetic field. The possibility to induce colossal magnetoresistance (CMR) properties for high (IV) contents ((IV)/) for x =0.07-0.12 is shown for the first time, the resistance ratios reaching at 30 K. This study also shows differently that the small size of the A-site cation (Pr, Ca) is not a redhibitory obstacle to the appearance of CMR properties in manganites, in contrast with previously established phase diagrams. Received: 18 June 1997 / Revised: 4 August 1997 / Accepted: 10 November 1997     

Simulation of the Critical Adsorption of Semi-Flexible Polymers

The critical adsorption of semi-flexible pol.ymer chains on attractive surfaces is studied using Monte Carlo simulations.The results reveal that the critical adsorption point of a free polymer chain is the same as that of an end-grafted one.For the end-grafted polymer,we find that the finite-size scaling relation and the maximum fluctuation of adsorbed monomers are equivalent in estimating the critical adsorption point.The effect of chain stiffness on the critical adsorption is also investigated.The surface attraction strength for the critical adsorption of semi-flexible polymer chain decreases exponentially with an increase in the chain stiffness;In other words,lower adsorption energy is needed to adsorb a stiffer polymer chain.The result is explained from the viewpoint of the free energy profile for the adsorption.     

Physical adsorption on heterogeneous surfaces: The effect of the topography of surfaces on the evaluated adsorption energy distribution

It has been known for a long time that the topography of surfaces is a very important factor governing the adsorption on heterogeneous solid surfaces. In spite of this, all methods to evaluate the adsorption energy distribution, developed so far were based on the patchwise model of heterogeneous surfaces. The purpose of this paper is to show how the well-known Condensation Approximation method can be applied to determine the adsorption energy distribution on the heterogeneous surfaces with a fully random topographical distribution of sites. The method is developed for the case of localized adsorption with nearest-neighbour interaction between admolecules.     

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics. Received: 22 May 1998 / Received in final form: 24 August 1998 / Accepted: 4 September 1998     

Dynamics of strongly entangled polymer systems: activated reptation

The effect of excluded-volume interactions on the reptation dynamics of long polymer chains is considered theoretically. It is shown that interactions give rise to an exponential increase of the reptation time, , if polymer chains are long enough: , where is the number of monomers per entanglement. We propose a novel dynamical mechanism of activated reptation implying that neighboring chains exchange conformations of their terminal fragments. It is shown that the exchange mechanism is compatible with the equilibrium polymer chain statistics and that it provides a bridge between the previous theories. Received: 25 July 1997 / Accepted: 8 October 1997