Zero-temperature properties of randomly self-interacting polymers

We study the zero-temperature behavior of several simple models for randomly self-interacting polymers in one and 1+1 dimensions. Results are based on exact enumeration and closed-form expressions.     

Enumerations of Lattice Animals and Trees

We have developed an improved algorithm that allows us to enumerate the number of site animals on the square lattice up to size 46. We also calculate the number of lattice trees up to size 44 and the radius of gyration of both lattice animals and trees up to size 42. Analysis of the resulting series yields an improved estimate, =4.062570(8), for the growth constant of lattice animals, and, ₀=3.795254(8), for the growth constant of trees, and confirms to a very high degree of certainty that both the animal and tree generating functions have a logarithmic divergence. Analysis of the radius of gyration series yields the estimate, =0.64115(5), for the size exponent.     

Similarity of Percolation Thresholds on the HCP and FCC Lattices

Extensive Monte Carlo simulations were performed in order to determine the precise values of the critical thresholds for site (p ^hcp _{c, S} =0.199 255 5±0.000 001 0) and bond (p ^hcp _{c, B} =0.120 164 0±0.000 001 0) percolation on the hcp lattice to compare with previous precise measurements on the fcc lattice. Also, exact enumeration of the hcp and fcc lattices was performed and yielded generating functions and series for the zeroth, first, and second moments of both lattices. When these series and the values of p _c are compared to those for the fcc lattice, it is apparent that the site percolation thresholds are different; however, the bond percolation thresholds are equal within error bars, and the series only differ slightly in the higher order terms, suggesting the actual values are very close to each other, if not identical.     

Location of the collapsed phase for two-dimensional,directed, interacting polymers

By mapping a model for a directed polymer onto a novel polygon problem, we give a physically appealing proof for the location of the boundary of the collapsed phase in phase space, applicable also when interactions with a surface are included.     

A microscopic model with quasicrystalline properties

A classical lattice gas model with two-body nearest neighbor interactions and without periodic ground-state configurations is presented. The main result is the existence of a decreasing sequence of temperatures for which the Gibbs states have arbitrarily long periods. It is possible that the sequence accumulates at nonzero temperature, giving rise to a quasiperiodic equilibrium state.     

Dielectric and optical properties of polymer-liquid crystal composite

Dielectric properties of polymer-liquid crystal mixture, having constituent polymer, poly-butyl methacrylate (PBMA) and liquid crystal, cholesteryl nonanoate, are reported as a function of frequency and temperature. The measurement has been done in a temperature range of 300-375 K and frequency range of 100 Hz-10 MHz. The dielectric permittivity and dielectric loss shows significant changes with the addition of polymer molecules in liquid crystal. The significant feature of composite formation is that the pure liquid crystal and polymer do not show dielectric relaxation in the frequency range covered, while the composite shows relaxation peak at a particular frequency. The optical transmittance of pure liquid crystal and composite has also been measured and compared.     

The fusion of ethylene oxide polymers

Summary Calorimetric measurements by DSC technique have been made in pure polyethylene glycol (PEG) and oxide (PEO) polymers having a very wide molecular-weight range (from 600 to 4000 000) and in PEO (MW 600 000)-NaSCN complexes. It was found that the melting temperature increases with increasing molecular weight, ranging from 293 K in the polymer with MW=600 to 340 K in that with MW=4000 000. The behaviour of the heats of fusion with increasing molecular weight reflects the trend expected in systems, in which the increase of the main chain length produces a relevant growth of the degree of crystallinity. A distinct maximum of the heat of fusion has been found at about MW=10000, this result being an evidence of the high amount of crystalline regions building up the structure of that system. The dependence of the melting temperature on molecular weight has been nicely accounted for by using the expression of Flory, deduced from the statistical theory of polymers having the most probable molecular-weight distribution. The addition of sodium thiocyanate to PEO modifies the morphology of the host polymer and, for salt concentrations higher than 0.03 molar fraction, gives rise to the formation of a PEO-salt crystalline complex characterized by a high melting temperature. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Overlap properties and adsorption transition of two Hamiltonian paths

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems. Received 4 December 1998 and Received in final form 10 March 1999     

An exact solution on the ferromagnetic face-cubic spin model on a Bethe lattice

The lattice spin model with Q-component discrete spin variables restricted to have orientations orthogonal to the faces of Q  -dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The partition function of the model with dipole–dipole and quadrupole–quadrupole interaction for arbitrary planar graph is presented in terms of double graph expansions. The latter is calculated exactly in case of trees. The system of two recurrent relations (RR) which allows to calculate all thermodynamic characteristics of the model is obtained. The correspondence between thermodynamic phases and different types of fixed points of the RR is established. Using the technique of simple iterations the plots of the zero field magnetization and quadrupolar moment are obtained. Analyzing the regions of stability of different types of fixed points of the system of recurrent relations the phase diagrams of the model are plotted. For Q?2$Q?2$ the phase diagram of the model is found to have three tricritical points, whereas for Q>2$Q>2$ there are one triple and one tricritical points.     

Low temperature magneto-conductivity properties of micro-sized Ag/HD-PE metal/polymers

A composite material of a polyethylene matrix filled by a fine silver powder was prepared with different Ag contents and physical behaviours ranging from insulator to conductor. Ac differential magnetic susceptibility χ measurements show the samples are paramagnetic up to an Ag concentration of ∼65%. At low temperatures the composite is spin-glass type, whereas the transition from insulator to conductor corresponds to an abatement of χ at zero magnetizing field. Magneto-conductivity effects have been observed in resistivity measurements at low temperatures. They can be explained in terms of an effective exchange electronic scattering mechanism between the conduction electrons and the diluted magnetic moments arising from unpaired electron spins of boundary silver particles. Moreover, the presence of a broad minimum in the resistivity curve at T = ∼ 20 K, observed in samples with an Ag concentration just above the percolation threshold, addresses to possible interference effects similar to those reported in disordered materials. Received 17 October 2000 and Received in final form 22 February 2001     

Phase Transitions of Single Semistiff Polymer Chains

We study numerically a lattice model of semiflexible homopolymers with nearest neighbor (nn) attraction and energetic preference for straight joints between bonded monomers. For this we use a new Monte Carlo algorithm, the “prunedenriched Rosenbluth Method” (PERM). It is very efficient both for relatively open configurations at high temperatures and for compact and frozen-in low-T states. This allows us to study in detail the phase diagram as a function of nn attractionε and stiffnessx. It shows aθ-collapse line with a transition from open coils (smallε) to molten compact globules (largeε) and a freezing transition toward a state with orientational global order (large stiffnessx). Qualitatively this is similar to a recently studied mean-field theory [S. Doniach, T. Garel, and H. Orland (1996),J. Chem. Phys. 105(4), 1601], but there are important differences in details. In contrast to the mean-field theory and to naive expectations, theθ-temperatureincreases with stiffnessx. The freezing temperature increases even faster, and reaches theθ-line at a finite value ofx. For even stiffer chains, the freezing transition takes place directly, without the formation of an intermediate globular state. Although being in conflict with mean-field theory, the latter had been conjectured already by Doniachet al. on the basis of heuristic arguments and of low-statistics Monte Carlo simulations. Finally, we discuss the relevance of the present model as a very crude model for protein folding.     

From equilibrium spin models to probabilistic cellular automata

The general equivalence betweenD-dimensional probabilistic cellular automata (PCA) and (D+1)-dimensional equilibrium spin models satisfying a disorder condition is first described in a pedagogical way and then used to analyze the phase diagrams, the critical behavior, and the universality classes of some automata. Diagrammatic representations of time-dependent correlation functions of PCA are introduced. Two important classes of PCA are singled out for which these correlation functions simplify: (1) Quasi-Hamiltonian automata, which have a current-carrying steady state, and for which some correlation functions are those of aD-dimensional static model. PCA satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes. (2) Linear (and more generally affine) PCA for which the diagrammatics reduces to a random walk problem closely related to (D+1)-dimensional directed SAWs: both problems display a critical behavior with mean-field exponents in any dimension. The correlation length and effective velocity of propagation of excitations can be calculated for affine PCA, as is shown on an explicitD=1 example. We conclude with some remarks on nonlinear PCA, for which the diagrammatics is related to reaction-diffusion processes, and which belong in some cases to the universality class of Reggeon field theory.     

Monte carlo study of the interacting self-avoiding walk model in three dimensions

We consider self-avoiding walks on the simple cubic lattice in which neighboring pairs of vertices of the walk (not connected by an edge) have an associated pair-wise additive energy. If the associated force is attractive, then the walk can collapse from a coil to a compact ball. We describe two Monte Carlo algorithms which we used to investigate this collapse process, and the properties of the walk as a function of the energy or temperature. We report results about the thermodynamic and configurational properties of the walks and estimate the location of the collapse transition.     

Ion track etching revisited: II. Electronic properties of aged tracks in polymers

We compile here electronic ion track etching effects, such as capacitive-type currents, current spike emission, phase shift, rectification and background currents that eventually emerge upon application of sinusoidal alternating voltages across thin, aged swift heavy ion-irradiated polymer foils during etching. Both capacitive-type currents and current spike emission occur as long as obstacles still prevent a smooth continuous charge carrier passage across the foils. In the case of sufficiently high applied electric fields, these obstacles are overcome by spike emission. These effects vanish upon etchant breakthrough. Subsequent transmitted currents are usually of Ohmic type, but shortly after breakthrough (during the track’ core etching) often still exhibit deviations such as strong positive phase shifts. They stem from very slow charge carrier mobility across the etched ion tracks due to retarding trapping/detrapping processes. Upon etching the track’s penumbra, one occasionally observes a split-up into two transmitted current components, one with positive and another one with negative phase shifts. Usually, these phase shifts vanish when bulk etching starts. Current rectification upon track etching is a very frequent phenomenon. Rectification uses to inverse when core etching ends and penumbra etching begins. When the latter ends, rectification largely vanishes. Occasionally, some residual rectification remains which we attribute to the aged polymeric bulk itself. Last not least, we still consider background currents which often emerge transiently during track etching. We could assign them clearly to differences in the electrochemical potential of the liquids on both sides of the etched polymer foils. Transient relaxation effects during the track etching cause their eventually chaotic behaviour.     

Changes in the electrical properties of pure and doped polymers under the influence of small doses of X-rays

Abstract

A study has been made of the temperature dependence of the d.c. conductivity of pure and borated low density polyethylene LDPE (4% and 8% borax). The above calculations were carried out before and after X-ray irradiation. The irradiation dose was varied from 0 to 1000 rad.

The d.c. electrical conductivity of Polyvinyl chloride (PVC) and perspex was measured as a function of temperature ranging from 20°C to 100°C. These samples were irradiated with X-rays of dose 200 rad. The variation of the d.c. conductivity of the treated samples versus temperature was investigated.

The results reveal that the d.c. conductivity of LDPE is highly affected by radiation and/or dopant. In addition, the sensitivity of the explored polymers to X-ray irradiation is strongly dependent on its chemical nature.     

Desorption of polymers: role of the stagnant layer

The desorption of polymers is studied theoretically and with Monte Carlo simulations. Two regimes can be distinguished: in one regime the detachment of the polymer from the surface is the slowest process, and in the other it is the diffusion of the polymer away from the surface. In both regimes the desorption rate depends on the thickness H of the stagnant layer, i.e. the layer in which the polymer movement is dominated by diffusion. In the diffusion-limited regime the desorption rate scales as H ^{? 2}, as expected for diffusive processes. In the detachment-limited regime the desorption rate scales as H ^{? 1}. The importance of the thickness of the stagnant layer in the detachment-limited regime is due to the fact that the polymer, after it has detached, will most likely readsorb soon after: the probability that the polymer does not readsorb, but crosses the stagnant layer, is inversely proportional to the thickness of the stagnant layer.     

Stretching dynamics of semiflexible polymers

We analyze the nonequilibrium dynamics of single inextensible semiflexible biopolymers as stretching forces are applied at the ends. Based on different (contradicting) heuristic arguments, various scaling laws have been proposed for the propagation speed of the backbone tension which is induced in response to stretching. Here, we employ a newly developed unified theory to systematically substantiate, restrict, and extend these approaches. Introducing the practically relevant scenario of a chain equilibrated under some prestretching force f _pre that is suddenly exposed to a different external force f _ext at the ends, we give a concise physical explanation of the underlying relaxation processes by means of an intuitive blob picture. We discuss the corresponding intermediate asymptotics, derive results for experimentally relevant observables, and support our conclusions by numerical solutions of the coarse-grained equations of motion for the tension.     

Living polymers in random media: a 2D Monte-Carlo investigation on a square lattice

The evolution of the mean chain length and mean end to end square radius of a two dimensional system of living polymers at constant monomer concentration is studied as a function of the obstacle density . The fact that the system adapts the mean chain length in order to reduce the entropic constraint does not lead to a different asymptotic dependence of on than what is observed for dead polymers. The change of the molecular weight distribution form in the presence of obstacles suggests that a Levy flight could appear in system of wormlike micelles in a porous medium. Received: 1 September 1997 / Received in final form: 22 January 1998 / Accepted: 30 January 1998     

Computer simulation of driven diffusive systems with exchanges

The field-driven Kawasaki model with a fractionp admixture of Glauber dynamics is studied by computer simulation:p=0 corresponds to the order-parameter-onserving driven diffusive system, whilep=1 is the equilibrium Ising model. Forp=0.1 our best estimates of critical exponents based on a system of size 4096×128 are0.22, ^RS0.45, andv v 1. These exponents differ from both the values predicted by a field-theoretic method forp=0 and those of the equilibrium Ising model. Anisotropic finite-size scaling analyses are carried out, both for subsystems of the large system and for fully periodic systems. The results of the latter, however, are inconsistent, probably due to the complexity of the size effects. This leaves open the possibility that we are in a crossover regime fromp=0 top0 and that our critical exponents are effective ones. Forp=0 our results are consistent with the predictionsv >v .     

A lattice-gas hamiltonian for micellar binary solutions

An explicit Ising-spin lattice Hamiltonian is proposed as a model for studying the phase diagrams of micellar binary solutions on the micellar length scale. Incorporating many essential features, it can be used to check the validity of a previously suggested scenario for nonuniversality at the consolute point.