The mobility of the amorphous phase in polyethylene as a determining factor for slow crack growth

Polyethylene (PE) pipes generally exhibit a limited lifetime, which is considerably shorter than their chemical degradation period. Slow crack growth failure occurs when pipes are used in long-distance water or gas distribution though being exposed to a pressure lower than the corresponding yield stress. This slow crack growth failure is characterized by localized craze growth and craze fibril rupture. In the literature, the lifetime of PE pipes is often considered as being determined by the density of tie chains connecting adjacent crystalline lamellae. But this consideration cannot explain the excellent durability of the recent bimodal grade PE for pipe application. We show in this paper the importance of the craze fibril length as the determining factor for the pipe lifetime. The conclusions are drawn from stress analysis. It is found that longer craze fibrils sustain lower stress and are deformed to a lesser degree. The mobility of the amorphous phase is found to control the amount of material that can be sucked in by the craze fibrils and thus the length of the craze fibrils. The mobility of the amorphous phase can be monitored by dynamic mechanical analysis measurements. Excellent agreement between the mobility thus derived and lifetimes of PE materials as derived from FNCT (full notch creep test) is given, thus providing an effective means to estimate the lifetime of PE pipes by considering well-defined physical properties.     

Kinetics of reversible surface crystallization and melting in poly(ethylene oxide): Effect of crystal thickness observed in the dynamic heat capacity

Poly(ethylene oxide) (PEO) in the semi-crystalline state shows a reversible surface crystallization and melting; a temperature decrease leads to a certain crystal thickening, a temperature increase reversely to an expansion of the amorphous intercrystallite layers. Dynamic calorimetry provides a means to investigate the kinetics of the process. The structural rearrangement in the region of the crystalline-amorphous interface can only be accomplished if the chains can slide through the crystallites. One therefore expects the associated time to change with the crystallite thickness. Variations of the crystal thickness of PEO can be achieved by choosing different crystallization temperatures. We studied the effect of the crystal thickness employing temperature-modulated differential scanning calorimetry and heat wave spectroscopy, and by carrying out small-angle X-ray scattering experiments for the structural characterization. The effect of the crystal thickness is clearly observed. Results indicate that the sliding diffusion through the crystallites takes place by helical jumps of whole stems. Data yield the activation energy per unit length of the stems. Received 20 April 2001 and Received in final form 13 August 2001     

Spinodal wrinkling in thin-film poly(ethylene oxide)/polystyrene bilayers

Optical microscopy and atomic force microscopy were used to study a novel roughness-induced wrinkling instability in thin-film bilayers of poly(ethylene oxide) (PEO) and polystyrene (PS). The observed wrinkling morphology is manifested as a periodic undulation at the surface of the samples and occurs when the bilayers are heated above the melting temperature of the semi crystalline PEO (T_m = 63 ) layer. During the wrinkling of the glassy PS capping layers the system selects a characteristic wavelength that has the largest amplitude growth rate. This initial wavelength is shown to increase monotonically with increasing thickness of the PEO layer. We also show that for a given PEO film thickness, the wavelength can be varied independently by changing the thickness of the PS capping layers. A model based upon a simple linear stability analysis was developed to analyse the data collected for the PS and PEO film thickness dependences of the fastest growing wavelength in the system. The predictions of this theory are that the strain induced in the PS layer caused by changes in the area of the PEO/PS interface during the melting of the PEO are sufficient to drive the wrinkling instability. A consideration of the mechanical response of the PEO and PS layers to the deformations caused by wrinkling then allows us to use this simple theory to predict the fastest growing wavelength in the system.     

Chain orientation in natural rubber, Part II: 2H-NMR study

Stress-induced crystallisation (SIC) and stress-induced melting (SIM) in natural rubbers (NR), unfilled and filled with carbon black (CB) have been studied by ²H-NMR measurements. Various materials have been swollen with small amount (< 2%) of deuterated alkane chains. The orientation of the amorphous chains, then the local deformation of the amorphous chains during deformation cycles and during stress relaxation, permits to clarify the SIC and SIM processes during hardening and recovery. By mechanical, WAXS and NMR measurements one determines the same critical draw ratio for appearance λ_A and disappearance λ_E of the crystallites. It is demonstrated that the hysteresis observed by the different techniques (stress σ, crystallinity χ, NMR splitting Δν) are due to the supercooling effect ( λ_A > λ_E, at constant temperature). During hardening at constant strain rate it is found that the local draw ratio remains constant and equal to λ_A, whereas the crystallinity increases linearly with the macroscopic draw ratio λ. The hardening σ ∼ (λ - λ_A)² is then interpreted as a reinforcement effect due to the crystallites, which act as new crosslinks. This confirms the prediction of Flory. In filled rubber the same effects are observed, and the stress amplification factor is determined as a function of the CB content. It is found that the fillers act as nucleation centres for the NR crystallites. The reinforcement of such materials is due principally to this nucleation effect and to the presence of a super network formed by both the NR crystallites and the CB fillers.     

Chain orientation in natural rubber,Part I: The inverse yielding effect

Inhomogeneous deformations are observed in stretched natural rubber of different crosslink density; the conditions of observation, nucleation and propagation are given in the first part of the paper. In samples of low crosslink density these inhomogeneities recall necking observed in others materials and in glassy polymers when the materials are drawn above a critical draw ratio. The difference is that in natural rubbers, NR, they nucleate and propagate at constant stress during unloading. This phenomenon, called inverse yielding appears during recovery only if the samples have been drawn previously in the hardening domain. During necking propagation the stress is constant. The mechanical and crystallinity properties of samples with and without inverse yielding are studied as a function of draw ratio, crosslink density and temperature. In the second part of the paper this transition zone (neck) of thickness 2 mm is studied by WAXS at the synchrotron source. From the orientation of NR crystallites and from the orientation of the stearic acid (2%, present in this type of rubber) we conclude that the deformation in the neck follows the flow lines. From the local crystallinity of the NR crystallites one deduces the local draw ratio across this transition zone. We suggest that in all these rubbers, which present a plateau of the recovery stress strain curve, micronecking exists. This effect is discussed in the framework of the Flory theory.-1     

Physical aging of glassy PMMA/toluene films: Influence of drying/swelling history

Gravimetry experiments in a well-controlled environment have been performed to investigate aging for a glassy PMMA/toluene film. The temperature is constant and the control parameter is the solvent vapor pressure above the film (i.e. the activity). Several experimental protocols have been used, starting from a high activity where the film is swollen and rubbery and then aging the film at different activities below the glass transition. Desorption and resorption curves have been compared for the different protocols, in particular in terms of the softening time, i.e. the time needed by the sample to recover an equilibrium state at high activity. Non-trivial behaviors have been observed, especially at small activities (deep quench). A model is proposed, extending the Leibler-Sekimoto approach to take into account the structural relaxation in the glassy state, using the Tool formalism. This model well captures some of the observed phenomena, but fails in describing the specific kinetics observed when aging is followed by a short but deep quench.     

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     

Elastic rod model of a supercoiled DNA molecule

We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod-like chain, involving two elastic constants, the bending and the twist rigidities. Writing this model in terms of Euler angles, we show that the corresponding Hamiltonian is singular and needs a small distance cut-off, which is a natural length scale giving the limit of validity of the model, of the order of the double-helix pitch. The rod-like chain in the presence of the cut-off is able to reproduce quantitatively the experimentally observed effects of supercoiling on the elongation-force characteristics, in the small supercoiling regime. An exact solution of the model, using both transfer matrix techniques and its mapping to a quantum mechanics problem, allows to extract, from the experimental data, the value of the twist rigidity. We also analyse the variation of the torque and the writhe-to-twist ratio versus supercoiling, showing analytically the existence of a rather sharp crossover regime which can be related to the excitation of plectoneme-like structures. Finally we study the extension fluctuations of a stretched and supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle, and we compare the theoretical predictions to some preliminary experimental data. Received 1 April 1999 and Received in final form 4 January 2000     

Surface glass transition in bimodal polystyrene mixtures

Using the cluster-embedding method of V. Zaporojchenko et al. (Macromolecules 34, 1125 (2000)), we measured the glass transition temperature T _g at the polystyrene/vacuum interface of bimodal mixtures of monodisperse polystyrenes of 3.5k and 1000k. Embedding of ≈ 1 nm Au clusters was monitored in situ by X-ray photoelectron spectroscopy (XPS). The clusters were formed by evaporation of Au onto the polymer surface. Only one glass transition was observed in the mixtures. The surface glass transition temperatures are correlated to but are below the bulk values of the mixtures and obey the Gordon-Taylor equation. The results suggest that the earlier reported molecular-weight dependence of the surface glass transition is not due to segregation of short chains to the surface.     

Stability of thin polymer films on a corrugated substrate

We study the wetting behaviour of thin polystyrene (PS) films on regularly corrugated silicon substrates. Below a critical film thickness the PS films are unstable and dewet the substrates. The dewetting process leads to the formation of nanoscopic PS channels filling the grooves of the corrugated substrates. Films thicker than the critical thickness appear stable and follow the underlying corrugation pattern. The critical thickness is found to scale with the radius of gyration of the unperturbed polymer chains. Received 6 April 2000 and Received in final form 24 August 2000     

Surface visco-elastic moduli of a Langmuir film of a polystyrene-polydimethyl siloxane block copolymer at the air-ethyl benzoate interface

Surface quasi-elastic light scattering has been applied to a spread film of a block copolymer of polystyrene and polydimethyl siloxane. The influence of surface concentration (surface pressure) at a fixed surface wave number has been explored. The capillary wave frequency and damping showed a similar dependence on the surface concentration as values obtained earlier, but due to a more appropriate analysis of the correlation functions, surface visco-elastic moduli obtained were distinctly different. By correlating the values obtained with the variations in solvated polystyrene layer thickness from neutron reflectometry, the maximum in dilational modulus was shown to occur at the same nominal surface concentration where the layer begins to stretch and take on brush-like behaviour. This same surface concentration is where the relaxation time of the spread film also has a maximum value, the relaxation time being calculated using the standard linear model of visco-elasticity, which was found to fit the frequency dependence of the surface tension and dilational moduli at the resonant nominal surface concentration of 3.1 mg m^-2. Received 21 August 2001 and Received in final form 11 January 2002     

Solid-like friction of a polymer chain

We propose a simple friction model for isolated polymer chains on a solid substrate. The chains are pulled at constant velocity by one end, the other end can be trapped on the solid substrate on localised sites. We focus on the energy dissipation due to the traps. This simple model leads to nontrivial friction laws, depending on the velocity and the distance between traps. Some refinements of the model such as the effect of thermal fluctuations are also reported. Received 20 March 2000     

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     

Tuneable micro- and nano-periodic structures in a free-standing flexible urethane/urea elastomer film

We have studied the control and manipulation of tuneable equilibrium structures in a free-standing urethane/urea elastomer film by means of atomic force microscopy, small-angle light scattering and polarising optical microscopy. The urethane/urea elastomer was prepared by reacting a poly(propyleneoxide)-based triisocyanate-terminated prepolymer (PU) with poly(butadienediol) (PBDO), with a weight ratio of 60% PU/40% PBDO. An elastomer film was shear-cast onto a glass plate and allowed to cure, first in an oven, then in air. Latent micro- and nano-periodic patterns are induced by ultra-violet (UV) irradiation of the film and can be “developed” by applying a plane uniaxial stress or by immersing the elastomer in an appropriate solvent and then drying it. For this elastomer we describe six pattern states, how they are related and how they can be manipulated. The morphological features of the UV-exposed film surface can be tuned, reproducibly and reversibly, by switching the direction of the applied mechanical field. Elastomers extracted in toluene exhibit different surface patterns depending upon the state in which they were developed. Stress-strain data collected for the films before and after UV irradiation reveal anisotropy induced by the shear-casting conditions and enhanced by the mechanical field. We have interpreted our results by assuming the film to consist of a thin, stiff surface layer (“skin”) lying atop a thicker, softer substrate (“bulk”). The skin's higher stiffness is hypothesised to be due to the more extensive cross-linking of chains located near the surface by the UV radiation. Patterns would thus arise as a competition between the effects of bending the skin and stretching/compressing the bulk, as in the work of Cerda and Mahadevan (Phys. Rev. Lett. 90, 074302 (2003)). We present some preliminary results of a simulation of this model using the Finite Element package ABAQUS.     

Molecular dynamics simulation of semiflexible polyampholyte brushes--The effect of charged monomers sequence

Planar brushes formed by end-grafted semiflexible polyampholyte chains, each chain containing an equal number of positively and negatively charged monomers, are studied using molecular dynamics simulations. Keeping the length of the chains fixed, the dependences of the average brush thickness and equilibrium statistics of the brush conformations on the grafting density and the salt concentration are obtained with various sequences of charged monomers. When similarly charged monomers of the chains are arranged in longer blocks, the average brush thickness is smaller and the dependence of brush properties on the grafting density and the salt concentration is stronger. With such long blocks of similarly charged monomers, the anchored chains bond to each other in the vicinity of the grafting surface at low grafting densities and buckle toward the grafting surface at high grafting densities.     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

Two-dimensional polymer networks at a mixed boundary: Surface and wedge exponents

We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary conditions on either side of the wedge. We report on a comprehensive study of a linear chain by exact enumeration, with various attachments of the walk's ends to the surface, in wedges of angles and , with general mixed boundary conditions. Received: 20 October 1997 / Accepted: 13 May 1998     

Self-organization of triblock copolymer patterns obtained by drying and dewetting

Self-organized block copolymer structures derived from dewetting of thin films are becoming important in nanotechnology because of the various spontaneous and regular sub-micrometric surface patterns that may be obtained. Here, we report on the self-organization of a poly(styrene)-b-poly(ethene-co-butene-1)-b-poly(styrene) triblock copolymer during drying of its solution over a mica substrate. Regular submicrometric arrangements with long-range order were formed at critical polymer concentrations, consisting of parallel ribbons and hexagonal arrays of dots (droplets). This variety of highly ordered structures is explained by the interplay between forming mechanisms, mainly due to “fingering instabilities” at the three-phase line of the copolymer solution during drying. The thickness of the structures was “quantized” due to the microphase separation of the block copolymer. The formation of hexagonal patterns may be attributed to Marangoni instability at the liquid film surface prior to dewetting.     

Dynamics of reorientation of a constrained nematic elastomer

A model is proposed for the reorientation dynamics of a confined nematic liquid crystal elastomer, where the effect of crosslinks is to couple the director to deformations of the elastic matrix. The model combines the (equilibrium) `neo-classical' theory of liquid crystal rubber elasticity with the simplest time evolution equations for a system described by two coupled, non-conserved order parameters. Relaxation from an orientation imposed by an electric field is studied as a function of elastic softness, starting angle, surface pretilt, and the relative mobilities of director and strain. Most importantly, the absence of a `semi-soft' elastic threshold changes the long-time behaviour of the effective refractive index of the medium from exponential to inverse power law decay. Predictions are compatible with recent experimental results by Chang, Chien and Meyer [Phys. Rev. E 56, 595 (1997)]. Received 22 June 1998     

Heterogeneous dynamics at the glass transition in van der Waals liquids: Determination of the characteristic scale

Recent experiments have demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous. The characteristic size of these heterogeneities has been measured to be a few nanometers at T _g. We extend here a recent model for describing the heterogeneous nature of the dynamics which allows both to derive this length scale and the right orders of magnitude of the heterogeneities of the dynamics close to the glass transition. Our model allows then to interpret quantitatively small probes diffusion experiments. Received 29 March 2002 and Received in final form 11 November 2002 RID="a" ID="a"e-mail: long@lps.u-psud.fr