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     

Chain radius dependence on concentration in a 2D living polymer system

A living polymer system is used to study the effect of concentration on a broad, polydisperse two-dimensional polymer system. It is found that the mean squared end-to-end radius of a chain of L monomers does not decrease by following a simple power law of the concentration but by a function of the form . An origin for such a behaviour is proposed. Received: 21 November 1997 / Received in final form: 21 April 1998 / Accepted: 24 April 1998     

Polymer adsorption on heterogeneous surfaces

The adsorption of a single ideal polymer chain on energetically heterogeneous and rough surfaces is investigated using a variational procedure introduced by Garel and Orland (Phys. Rev. B 55, 226 (1997)). The mean polymer size is calculated perpendicular and parallel to the surface and is compared to the Gaussian conformation and to the results for polymers at flat and energetically homogeneous surfaces. The disorder-induced enhancement of adsorption is confirmed and is shown to be much more significant for a heterogeneous interaction strength than for spatial roughness. This difference also applies to the localization transition, where the polymer size becomes independent of the chain length. The localization criterion can be quantified, depending on an effective interaction strength and the length of the polymer chain. Received: 29 October 1997 / Revised: 19 December 1997 / Accepted: 6 March 1998     

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. Received 22 October 1998 and Received in final form 12 April 1999     

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     

Deformation of globular polysoaps: extension, confinement and extensional flow

A theoretical model of the extension and confinement of globular polysoaps predicts novel force laws. Polysoaps are polymers comprising of a flexible hydrophilic backbone incorporating, at intervals, amphiphilic monomers. The equilibrium configuration of long polysoaps, that form numerous spherical intrachain micelles, is a spherical globule of close packed micelles. The coupling of the deformation to the hierarchical self organization of the chain gives rise to a distinctive force law involving, for extension, two plateau regimes. When the chain is stretched by extensional flow the two regimes merge and the polysoap exhibits a single globule-stretch transition. Received 16 June 1998 and Received in final form 19 November 1998     

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     

Secondary super-structures in random copolymers

Secondary domain superstructures in correlated random block copolymers are considered theoretically using the concept of the second order parameter related to fluctuations of the local mean block length. It is shown that the size of secondary domains, , is much larger than the primary domain size, L: , while , where is a small parameter defining the composition asymmetry. Different secondary morphologies are characterized. It is also shown that separation of the system in two macroscopic phases with different primary morphologies predicted earlier using the free energy expansion up to ( is the usual order parameter related to local composition) is an artifact of this widely accepted theoretical model. Received 15 July 1998 and Received in final form 18 January 1999     

Fractal dimension of Siegel disc boundaries

Using renormalization techniques, we provide rigorous computer-assisted bounds on the Hausdorff dimension of the boundary of Siegel discs. Specifically, for Siegel discs with golden mean rotation number and quadratic critical points we show that the Hausdorff dimension is less than 1.08523. This is done by exploiting a previously found renormalization fixed point and expressing the Siegel disc boundary as the attractor of an associated Iterated Function System. Received: 26 January 1998 / Received in final form: 5 June 1998 / Accepted: 11 June 1998     

The segregation of poly(styrene-b-isoprene) diblock copolymers to the surface of a polystyrene melt: the effect of the ratio of block lengths

The effect of the ratio of block lengths on the interfacial partitioning of poly(styrene-block-1,4 isoprene) diblock copolymers from their mixtures with polystyrene homopolymer melt is investigated utilizing a series of copolymers with almost constant molecular weight but different compositions. The concentration profile of the copolymer is measured directly using the nuclear reaction analysis technique; a segregation of the diblock is found at both the air/polymer surface, due to the lower surface energy of polyisoprene, and at the substrate/polymer interface. No significant effect of the block length ratio on the free-surface excess was observed. The block molecular weights have apparently led to dangling chain conformations in the non-overlapping mushroom and in the overlapping mushroom regimes whereas the brush regime was not accessible; no indications of a real border between the two former regimes was found. Received: 20 July 1998 / Received in final form and Accepted: 11 September 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     

Scattering from solutions of star polymers

We study the scattering intensity of dilute and semi-dilute solutions of star polymers. The star conformation is described by a model introduced by Daoud and Cotton. In this model, a single star is regarded as a spherical region of a semi-dilute polymer solution with a local, position dependent screening length. For high enough concentrations, the outer sections of the arms overlap and build a semi-dilute solution (a sea of blobs) where the inner parts of the actual stars are embedded. The scattering function is evaluated following a method introduced by Auvray and de Gennes. In the dilute regime there are three regions in the scattering function: the Guinier region (low wave vectors, ) from where the radius of the star can be extracted; the intermediate region () that carries the signature of the form factor of a star with f arms: ; and a high wavevector zone () where the local swollen structure of the polymers gives rise to the usual q ^-5/3 decay. In the semi-dilute regime the different stars interact strongly, and the scattered intensity acquires two new features: a liquid peak that develops at a reciprocal position corresponding to the star-star distances; and a new large wavevector contribution of the form q ^-5/3 originating from the sea of blobs. Received: 3 September 1997 / Revised: 13 January 1988 / Accepted: 31 March 1998     

The topological structure of 2D disordered cellular systems

We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged concentrically around a germ cell. We single out the most significant parameters that characterize statistically the organization of these patterns. Universality and specificity in disordered cellular structures are discussed. Received: 23 September 1997 / Received in final form: 14 January 1998 / Accepted: 29 January 1998     

Quantum scattering in the strip: From ballistic to localized regimes

Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined. Received: 28 January 1998 / Revised: 16 June 1998 / Accepted: 6 July 1998     

Anomalous viscosity exponent in a discretized model for a chain diffusion in one dimension

We present a one-dimensional Monte Carlo simulation for the diffusion motion of a chain of N beads. We found that the scaling exponent for the viscosity can be smaller or greater than 3. This anomalous behavior cannot be attributed to the diffusivity scaling or the length fluctuations but is due to the chain dynamics details during diffusion in which the end beads play the key role. The viscosity exponent 3 and its expected relation with the diffusivity exponent are recovered in the asymptotic regime (N ↦∞). Received 24 September 2001 and Received in final form 28 January 2002     

Frequency up-converted radiation from a cavity moving in vacuum

We calculate the photon emission of a high finesse cavity moving in vacuum. The cavity is treated as an open system. The field initially in the vacuum state accumulates a dephasing depending on the mirrors motion when bouncing back and forth inside the cavity. The dephasing is not linearized in our calculation, so that qualitatively new effects like pulse shaping in the time domain and frequency up-conversion in the spectrum are found. Furthermore we predict the existence of a threshold above which the system should show self-sustained oscillations. Received: 10 December 1997 / Received in final form: 27 March 1998 / Accepted: 27 March 1998     

Chain length dependence of anomalous swelling in multilamellar lipid vesicles

Using small-angle X-ray scattering, the repeat distance vs. temperature is measured for a homologous series of multilamellar vesicles of lecithins with varying acyl chain length in excess water condition around the lipid main transition. A systematic chain length dependence is found which is in accordance with a bending rigidity renormalization and critical unbinding of the lamellae close to the transition, as previously suggested in H?nger et al. [Phys. Rev. Lett. 72, 3911 (1994)]. Received 13 January 1999 and Received in final form 6 September 1999     

Pulsed polarization gradient cooling in an optical dipole trap with a Laguerre-Gaussian laser beam

We utilized a blue-detuned Laguerre-Gaussian (doughnut) laser beam to trap cold rubidium atoms by optical dipole force. ”Pulsed” polarization gradient cooling was applied to the trapped atoms to suppress the trap loss due to heating caused by random photon scattering of the trapping light. In this trap about 10⁸ atoms were initially captured and the trap lifetime was 1.5 s, which was consistent with losses due to background gas collisions. This trap can readily be applied to atom guiding, compression, and evaporative cooling. Received: 10 July 1997 / Received in final form: 5 January 1998 / Accepted: 16 January 1998     

Change of the scaling behavior of the end-to-end square distance in a two-dimensional polydisperse system

The simulation of a two-dimensional, broadly polydisperse, living polymers system at high concentration reveals an unusual conformational behaviour for the longer chains. Unlike in three dimensions, the longer chains are not swollen but are squeezed by the smaller chains. This observation is discussed in terms of a two dimensional solvent- polymer mixture whose solvent particules are larger than the polymer monomers. Received: 13 December 1996 / Revised: 16 March 1998 / Accepted: 27 March 1998     

Spontaneous SU(2) symmetry breaking in one-dimensional quantum antiferromagnet

We present a Bethe Ansatz based investigation of a one-dimensional (1D) Heisenberg spin chain in a real 3D crystal lattice. We have shown that due to an influence of the lattice distortion on a crystalline field of ligands of magnetic ions, a Heisenberg antiferromagnetic spin chain is unstable under the appearance of a magnetic anisotropy of the “easy-plane” type. The effects of an external magnetic field and nonzero temperature onto such a phase transition are studied. Received: 19 January 1998 / Revised: 16 March 1998 / Accepted: 17 March 1998