Conformational properties of polymers

We discuss exact enumeration technique and its application to polymers and biopolymers. Using this method one can obtain phase diagram in thermodynamic limit. The method works quite well in describing the outcomes of single molecule force spectroscopy results where finite size effects play a crucial role.      

Statistics of ideal randomly branched polymers in a semi-space

We investigate the statistical properties of a randomly branched 3-functional N-link polymer chain without excluded volume, whose one point is fixed at the distance d from the impenetrable surface in a 3-dimensional space. Exactly solving the Dyson-type equation for the partition function Z(N, d )= N^-θe^γN in 3D, we find the “surface” critical exponent θ = , as well as the density profiles of 3-functional units and of dead ends. Our approach enables to compute also the pairwise correlation function of a randomly branched polymer in a 3D semi-space.     

Main-chain smectic liquid-crystalline polymers as randomly disordered systems

We report a high-resolution X-ray lineshape study of main-chain smectic polymers. The results indicate that the layer ordering differs fundamentally from the algebraic decay typical for other smectic liquid-crystalline systems. The lineshapes are best described by broad squared Lorentzians indicating some form of short-range correlations. However, several higher harmonics are observed, which excludes simple liquid-like short-range order. This behaviour is tentatively attributed to a random field of defects associated with entangled hairpins in the main-chain polymer structure.     

The tricritical behavior of self-interacting partially directed walks

We present the thermodynamics of two variations of the interacting partially directed self-avoiding walk problem by discussing versions where the length of the walks assume real as well as a integral values. While the discrete model has been considered previously to varying degrees of success, the continuous model we now define has not. The examination of the continuous model leads to theexact derivation of several exponents. For the discrete model some of these exponents can be calculated using a continued-fraction representation. For both models the crossover exponent is found to be 2/3. Moreover, we confirm the tricritical nature of the collapse transition in the generalized ensemble and calculate the full scaling form of the generating function. Additionally, the similarities noticed previously to other models, but left unexplored, are explained with the aid of necklacing arguments.     

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.     

Rooted Spiral Trees on Hyper-Cubic Lattices

We study rooted spiral trees in 2,3 and 4 dimensions on a hyper cubic lattice using exact enumeration and Monte-Carlo techniques. On the square lattice, we also obtain exact lower bound of 1.93565 on the growth constant λ. Series expansions give θ= −1.3667±0.0010 and ν = 0.6574±0.0010 on a square lattice. With Monte-Carlo simulations we get the estimates as θ= −1.364±0.010, and ν = 0.656±0.010. These results are numerical evidence against earlier proposed dimensional reduction by four in this problem. In dimensions higher than two, the spiral constraint can be implemented in two ways. In either case, our series expansion results do not support the proposed dimensional reduction.     

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.     

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.     

Delocalized radiation damage in polymers

We present and discuss measurements of electron-irradiation damage in polystyrene and other polymers, based on fading of the 7-eV energy-loss peak. These measurements suggest a large increase in characteristic dose as the electron-beam diameter is reduced from 1 μm to below 1 nm. This finding is discussed in terms of secondary-electron production and delocalization of the inelastic scattering, both as it affects the volume of specimen in which the energy is deposited and the volume giving rise to the inelastic signal used to assess the damage.     

Positron decay in polymers: Molecular weight dependence in polystyrene

The decay time τ_l ofo-Ps by the electron pickoff process has been measured in polystyrene as a function of molecular weight. For samples below their glass transition temperature τ_l is essentially independent of . In the low molecular weight region, , τ_l increased with decreasing in line with earlier theoretical predictions. The overall behaviour reflects closely the dependence of free volume on . The effects of molecular motion on τ_l are examined and it is concluded that the decay time is insensitive to such motions in polystyrene below the melting point, in contrast to what is observed in polytetrafluoroethylene.     

First-passage times in a critical stochastic model

Average first-passage times for a single-variable stochastic model with a critical fixed point at the origin are computed by exact enumeration. The numerical measurements show excellent agreement with analytical results. The scaling function approaches the predicted asymptotic dependence.     

Localisation in disordered systems—I: The disordered spectrum

Starting from a definition of the localisation-delocalisation of electronic, wavefunctions in disordered systems based on the nature of the disordered spectrum, a delocalisation criterion identical to that of Abou-Chacraet al is recovered. The new derivation on provides a very clear picture of the mechanism of delocalisation and brings out its incompatibility with the normalisability of wavefunctions at the transition.     

Expectation-based approach for one-dimensional randomly disordered phononic crystals

An expectation-based approach to the statistical theorem is proposed for the one-dimensional randomly disordered phononic crystal. In the proposed approach, the expectations of the random eigenstates of randomly disordered phononic crystals are investigated. In terms of the expectations of the random eigenstates, the wave propagation and localization phenomenon in the random phononic crystal could be understood in a statistical perspective. Using the proposed approach, it is proved that for a randomly disordered phononic crystal, the Bloch theorem holds in the perspective of expectation. A one-dimensional randomly disordered binary phononic crystal consisting of two materials with the random geometry size or random physical parameter is addressed by using the proposed approach. From the result, it can be observed that with the increase of the disorder degree, the localization of the expectations of the eigenstates is strengthened. The effect of the random disorder on the eigenstates at higher frequencies is more significant than that at lower frequencies. Furthermore, after introducing the random disorder into phononic crystals, some random divergent eigenstates are changed to localized eigenstates in expectation sense.     

Decay to equilibrium in random spin systems on a lattice. II

We study the continuous spin systems on ad3-dimensional lattice with random ferromagnetic interactions of finite range. We show that, if the temperature is sufficiently high and the probability of interaction to be large is small enough, the almost sure decay to equilibrium has a subexponential upper bound.     

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     

Classical ultraviolet photoelectron spectroscopy of polymers

Although X-ray photoelectron spectroscopy of polymers was well established by Clark and coworkers in the 1970s, ultraviolet photoelectron spectroscopy of polymer films, was developed later. Previous to the 1970s, the first attempts to use ultraviolet light on polymer films took the form of appearance potential (valence band edge) measurements. Only some years later could the full valence band region of thin polymer films, including insulating polymers, semiconducting polymers and electrically conducting polymers. The development of what might be termed “classical ultraviolet photoelectron spectroscopy” of polymer films may be loosely based upon a variety of issues, including adapting thin polymer film technology to ultra high vacuum studies, the widespread use of helium resonance lamps for studies of solid surfaces, the combined advent of practical and sufficient theoretical–computational methods. The advent of, and the use of, easily available synchrotron radiation for multi-photon spectroscopies, nominally in the area of the near UV, is not included in the term “classical”. At the same time, electrically conducting polymers were discovered, leading to applications of the corresponding semiconducting polymers, which added technologically driven emphasis to this development of ultraviolet photoelectron spectroscopy for polymer materials. This paper traces a limited number of highlights in the evolution of ultraviolet photoelectron spectroscopy of polymers, from the 1970s through to 2008. Also, since this issue is dedicated to Prof. Kazuhiko Seki, who has been a friend and competitor for over two decades, the author relies on some of Prof. Seki's earlier research, unpublished, on who-did-what-first. Prof. Seki's own contributions to the field, however, are discussed in other articles in this issue.     

Low-temperature specific heats of lanthanum and yttrium phosphate glasses

Summary The specific heats of (R₂O₃) _x (P₂O₅)_1−x glasses containing high concentrations of La³⁺ and Y³⁺ ions have been measured between 1.5K and 30K. It is shown that, in addition to the usual Debye contribution, there is an excess specific heat arising from localized vibrational states which has been discussed in terms of two distinct models. The first predicts a maximum in the temperature dependence of the excess specific heat associated with the crossover frequency from phonon to fracton behaviour. The phonon-fracton density of states used to fit the excess specific heat gives rise to model parameters having the same magnitudes as those found previously for other glasses including samarium phosphates. The second model, formulated on the basis of soft vibrations in glasses, predicts a minimum in the excess specific heat, which is also observed. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Capanello, Italy, July 4–8, 1994.     

Semianalytical calculation of the Rouse dynamics of randomly branched polymers

We present a semianalytical approach to the determination of the dynamic properties of randomly branched polymers under the Rouse approximation. The principal procedure is based on examining an eigenvalue spectrum which represents the average dynamic behavior of various structures. The calculated spectra show that the eigenvalue distribution is random even within a single structure, which in turn produces a continuous spectrum of values for the entire class. The autocorrelation function for the square of the radius of gyration was calculated based on these spectra, which confirms that the dynamics are nonexponential as earlier reported. A universal stretched exponent is also found in this study.