Topological Constraints at the Theta Point: Closed Loops at Two Loops

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-induced first-order transition.Comment: 5 pages, RevTeX, typo

Pseudo-Casimir force in confined nematic polymers

We investigate the pseudo-Casimir force in a slab of material composed of nematically ordered long polymers. We write the total mesoscopic energy together with the constraint connecting the local density and director fluctuations and evaluate the corresponding fluctuation free energy by standard methods. It leads to a pseudo-Casimir force of a different type than in the case of standard, short molecule nematic. We investigate its separation dependence and its magnitude and explicitly derive the relevant limiting cases.Comment: 7 pages, 2 figure

Solution of a model of SAW's with multiple monomers per site on the Husimi lattice

We solve a model of self-avoiding walks which allows for a site to be visited up to two times by the walk on the Husimi lattice. This model is inspired in the Domb-Joyce model and was proposed to describe the collapse transition of polymers with one-site interactions only. We consider the version in which immediate self-reversals of the walk are forbidden (RF model). The phase diagram we obtain for the grand-canonical version of the model is similar to the one found in the solution of the Bethe lattice, with two distinct polymerized phases, a tricritical point and a critical endpoint.Comment: 16 pages, including 6 figure

Thermodynamic approach to the dewetting instability in ultrathin films

The fluid dynamics of the classical dewetting instability in ultrathin films is a non-linear process. However, the physical manifestation of the instability in terms of characteristic length and time scales can be described by a linearized form of the initial conditions of the films's dynamics. Alternately, the thermodynamic approach based on equating the rate of free energy decrease to the viscous dissipation [de Gennes, C. R. Acad. Paris.v298, 1984] can give similar information. Here we have evaluated dewetting in the presence of thermocapillary forces arising from a film-thickness (h) dependent temperature. Such a situation can be found during pulsed laser melting of ultrathin metal films where nanoscale effects lead to a local h-dependent temperature. The thermodynamic approach provides an analytical description of this thermocapillary dewetting. The results of this approach agree with those from linear theory and experimental observations provided the minimum value of viscous dissipation is equated to the rate of free energy decrease. The flow boundary condition that produces this minimum viscous dissipation is when the film-substrate tangential stress is zero. The physical implication of this finding is that the spontaneous dewetting instability follows the path of minimum rate of energy loss.Comment: 8 pages, 3 figures. Under revie

Long-range Casimir interactions between impurities in nematic liquid crystals and the collapse of polymer chains in such solvents

The elastic interactions between objects embedded in a nematic liquid crystal are usually caused by the average distorsion-rather than by the fluctuations-of the nematic orientational field. We argue that for sufficiently small particles, the nematic-mediated interaction originates purely from the fluctuations of the nematic director. This Casimir interaction decays as d^(-6), d being the distance between the particles, and it dominates van der Waals interactions close to the isotropic-to-nematic transition. Considering the nematic as a polymer solvent, we show that the onset of this Casimir interaction at the isotropic-to-nematic transition can discontinuously induce the collapse of a flexible polymer chain from the swollen state to the globular state, without crossing the Theta-point.Comment: 6 pages, 1 figur

Non-Equilibrium in Adsorbed Polymer Layers

High molecular weight polymer solutions have a powerful tendency to deposit adsorbed layers when exposed to even mildly attractive surfaces. The equilibrium properties of these dense interfacial layers have been extensively studied theoretically. A large body of experimental evidence, however, indicates that non-equilibrium effects are dominant whenever monomer-surface sticking energies are somewhat larger than kT, a common case. Polymer relaxation kinetics within the layer are then severely retarded, leading to non-equilibrium layers whose structure and dynamics depend on adsorption kinetics and layer ageing. Here we review experimental and theoretical work exploring these non-equilibrium effects, with emphasis on recent developments. The discussion addresses the structure and dynamics in non-equilibrium polymer layers adsorbed from dilute polymer solutions and from polymer melts and more concentrated solutions. Two distinct classes of behaviour arise, depending on whether physisorption or chemisorption is involved. A given adsorbed chain belonging to the layer has a certain fraction of its monomers bound to the surface, f, and the remainder belonging to loops making bulk excursions. A natural classification scheme for layers adsorbed from solution is the distribution of single chain f values, P(f), which may hold the key to quantifying the degree of irreversibility in adsorbed polymer layers. Here we calculate P(f) for equilibrium layers; we find its form is very different to the theoretical P(f) for non-equilibrium layers which are predicted to have infinitely many statistical classes of chain. Experimental measurements of P(f) are compared to these theoretical predictions.Comment: 29 pages, Submitted to J. Phys.: Condens. Matte

Identification of a polymer growth process with an equilibrium multi-critical collapse phase transition: the meeting point of swollen, collapsed and crystalline polymers

We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behaviour of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail model (ISAT) on that lattice, the process on the triangular lattice model does not map to the canonical equilibrium model. On the other hand, we show that the collapse transition of the canonical ISAT model on the triangular lattice behaves in a way reminiscent of the $\theta$-point of the interacting self-avoiding walk model (ISAW), which is the standard model of polymer collapse. This implies an unusual lattice dependency of the ISAT collapse transition in two dimensions. By studying an extended ISAT model, we demonstrate that the growth process maps to a multi-critical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either $\theta$-point-like (second-order) or first-order, and these two are separated by a multi-critical point. It is this multi-critical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gas-like swollen polymer phase (coil) and the low-temperature liquid drop-like collapse phase (globule) there is also a maximally dense crystal-like phase (crystal) at low temperatures dependent on the parameter values. The multi-critical point is the meeting point of these three phases. Our hypothesised phase diagram resolves the mystery of the seemingly differing behaviours of the ISAW and ISAT models in two dimensions as well as the behaviour of the trail growth process

Collision of Polymers in a Vacuum

In a number of experimental situations, single polymer molecules can be suspended in a vacuum. Here collisions between such molecules are considered. The limit of high collision velocity is investigated numerically for a variety of conditions. The distribution of contact times, scattering angles, and final velocities are analyzed. In this limit, self avoiding chains are found to become highly stretched as they collide with each other, and have a distribution of scattering times that depends on the scattering angle. The velocity of the molecules after the collisions is similar to predictions of a model assuming thermal equilibration of molecules during the collision. The most important difference is a significant subset of molecules that inelastically scatter but do not substantially change direction.Comment: 7 pages, 6 figure

Continuum theory of tilted chiral smectic phases

We demonstrate that the sequence of distorted commensurate phases observed in tilted chiral smectics is explained by the gain in electrostatic energy due to the lock-in of the unit cell to a number of layers which is the integer closest to the ratio pitch over thickness of the subjacent Sm-C$^*_\alpha$ phase. We also explain the sign change of the helicity in the middle of the sequence by a balance between two twist sources one intrinsic and another due to the distortion of the Sm-C$^*_\alpha$

Density profiles and surface tensions of polymers near colloidal surfaces

The surface tension of interacting polymers in a good solvent is calculated theoretically and by computer simulations for a planar wall geometry and for the insertion of a single colloidal hard-sphere. This is achieved for the planar wall and for the larger spheres by an adsorption method, and for smaller spheres by a direct insertion technique. Results for the dilute and semi-dilute regimes are compared to results for ideal polymers, the Asakura-Oosawa penetrable-sphere model, and to integral equations, scaling and renormalization group theories. The largest relative changes with density are found in the dilute regime, so that theories based on non-interacting polymers rapidly break down. A recently developed ``soft colloid'' approach to polymer-colloid mixtures is shown to correctly describe the one-body insertion free-energy and the related surface tension