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.     

Fracture and friction: Stick-slip motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first-order phase transitions we discuss a soft selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as functions of the driving velocity. The relevance of our results to recent experiments is discussed.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

Scaling of the size and temporal occurrence of burst sequences in creep rupture of fiber bundles

We present a detailed statistical analysis of the size and temporal occurrence of burst sequences in the creep rupture of a proposed linear viscoelastic fiber bundle model. According to the model, the burst sequences of fiber breaks display a power law asymptotic behavior analogous to that of the static-fracture [Kloster et al., Phys. Rev. E 56, 2615, (1997)]. Moreover, power law asymptotics apply to inter-arrival times between successive bursts with a universal exponent close to unity.     

Impact of gel balls beyond the Hertzian regime

We study experimentally the impact of spherical gel balls on a rigid substrate, where the balls largely deform like a pancake at high impact velocities. In our previous study (Y. Tanaka, Y. Yamazaki, K. Okumura, Europhys. Lett. 63, 149 (2003)), we measured the contact time τ_f and maximally deformed size versus impact velocity and explained the behaviors at the scaling level. In this study, we further measure τ_m, the time required to reach the maximum deformation (from the initial contact), and the restitution coefficient e. We also make a static experiment where we obtain the force-deformation curve of the gel balls up to fairly large deformations to explain the data on the impact. We propose two phenomenological treatments going beyond the scaling argument, one for intermediate impact velocities and the other for large velocities; the former is based on the static experiment while the latter on a Lagrangian constructed from appropriate constraints. Results from these treatments reproduce the experimental behavior of τ_m.     

Neutral color-spin-locking phase in neutron stars

We present results for the spin-1 color-spin-locking (CSL) phase using a NJL-type model in two-flavor quark matter for compact stars applications. The CSL condensate is flavor symmetric and therefore charge and color neutrality can easily be satisfied. We find small energy gaps ≃ 1MeV, which make the CSL matter composition and the EoS not very different from the normal quark matter phase. We keep finite quark masses in our calculations and obtain no gapless modes that could have strong consequences in the late cooling of neutron stars. Finally, we show that the region of the phase diagram relevant for neutron star cores, when asymmetric flavor pairing is suppressed, could be covered by the CSL phase.     

Early stages of phase separation from polydisperse polymer mixtures

We study the early stages of phase separation in a mixture of a polydisperse and a monodisperse polymer within the Cahn-Hilliard framework. We model the polydisperse component using a finite, but arbitrarily large, number of components, and show that the number of components required for convergent behaviour to be achieved is computationally undemanding. We study the growth rate of fluctuations following a quench into the two-phase region of the phase diagram. The q-dependence of the growth rate is shown to be commensurate with the behaviour of a monodisperse-monodisperse mixture, with the major difference being an effective mobility that is dependent on the quench depth. We also study the deviation of the time dependence of the scattering function from single exponential behaviour. Received 29 June 2000 and Received in final form 20 November 2000     

Prospects of ion-mobility measurements in superheavy element research

The element specific electron configuration of ions directly reflects the two quantum mechanical observables 〈r²〉 and r_max, which denote the r² expectation value of the electron density and the principle maximum of the wave function of the outermost electron orbital, respectively. Thus, the determination of these observables may present a new access to element identification of single superheavy nuclides. In this paper, we discuss how these observables are related to ionic radii deduced from ion-mobility data using the most simple hard sphere model and semi-empirical (n,6,4) model potentials for the interaction of heavy ions with noble gases. A concept for a high resolution ion-mobility spectrometer is presented. Optimum extraction efficiency of the ions will be achieved by decoupling the ion motion from the electric field drift by the friction force of the suitably shaped gas flow at the exit nozzle.     

Viscosity effects in foam drainage: Newtonian and non-newtonian foaming fluids

We have studied the drainage of foams made from Newtonian and non-Newtonian solutions of different viscosities. Forced-drainage experiments first show that the behavior of Newtonian solutions and of shear-thinning ones (foaming solutions containing either Carbopol or Xanthan) are identical, provided one considers the actual viscosity corresponding to the shear rate found inside the foam. Second, for these fluids, a drainage regime transition occurs as the bulk viscosity is increased, illustrating a coupling between surface and bulk flow in the channels between bubbles. The properties of this transition appear different from the ones observed in previous works in which the interfacial viscoelasticity was varied. Finally, we show that foams made of solutions containing long flexible PolyEthylene Oxide (PEO) molecules counter-intuitively drain faster than foams made with Newtonian solutions of the same viscosity. Complementary experiments made with fluids having all the same viscosity but different responses to elongational stresses (PEO-based Boger fluids) suggest an important role of the elastic properties of the PEO solutions on the faster drainage.     

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.     

Nucleon sigma term and quark condensate in nuclear matter

We study the bound-nucleon sigma term and the quark condensate in nuclear matter. In the quark-meson coupling (QMC) model the nuclear correction to the sigma term is small and negative, i.e., it decelerates the decrease of the quark condensate in nuclear matter. However, the quark condensate in nuclear matter is controlled primarily by the scalar-isoscalar σ field. Compared to the leading term, it moderates the decrease more than that of the nuclear sigma term alone at densities around and larger than the normal nuclear-matter density.     

The origin of the redshift in Brillouin spectra of silica films containing tin nanoparticles

The abrupt change of velocity in surface acoustic waves in thin films of amorphous SiO_x containing nanometre scale -Sn crystals is shown to be directly associated with the size-dependent melting of the nanoparticles, confirming preliminary experiments. High resolution thin film powder diffraction using synchrotron radiation shows that the abrupt redshift in the Brillouin spectra satellites occurs at the same temperature as the melting of the nanoparticles, evident for the loss of the Bragg peaks. Effective medium theory is used to explain the origin of the anomaly. A central peak in the Brillouin spectrum, the intensity of which shows a maximum at the melting temperature, can be interpreted in terms of overdamped fluctuations in the dielectric function. The melting temperature as a function of particle size is in agreement with theoretical predictions. No evidence for strain could be found on the X-ray diffraction profiles; the a- and c-axis thermal expansion coefficients are the same as those in bulk tin. Received 30 March 2000 and Received in final form 24 July 2000     

On the Mössbauer studies of harmonically bound quantum oscillators in Brownian motion

In many biological systems like whole cells, membranes or proteins and some of the polymeric systems, dynamics reveals itself in M?ssbauer spectra as a non Lorentzian behaviour above some particular temperature which is characteristic of the system. Moreover mean square displacement and line width show temperature dependence above the characteristic temperature. Brownian motion of harmonically bound oscillator has been able to explain the non-Lorentzian behaviour. In the present paper, a quantum picture of the above model is discussed and lineshape is expressed as the closed form for the extreme overdamping case. In addition to the non-Lorentzian behaviour, the present model also predicts a temperature dependence of mean square displacement and linewidth. Received 16 July 1997 and Received in final form 2 September 1998     

Plasma desorption mass spectroscopy of thiol-passivated gold nanoparticles

Plasma desorption mass spectrometry has been applied to characterization of dodecanthiol-passivated gold nanoparticles. An overview of the experimental set-up and mass analyses for the nanoparticles prepared in different conditions are shown. Mass distributions were found to shift to higher mass regions with increasing reaction temperature and reaction period. The results are consistent with those of transmission electron microscopy observations, UV-visible absorption spectra and also with a reported laser desorption mass spectrometry.     

Charge exchange collisions of H<Superscript>+</Superscript>/D<Superscript>+</Superscript> ions with alkaline Earth atoms (Ca,Mg)

The Classical Trajectory Monte Carlo (CTMC) Method has been used to calculate the differential, partial and total single electron capture cross sections for the collision of H⁺/D⁺ with Ca and Mg atoms in the energy range of 1–100 keV. The differential cross sections at angles near the diffraction limit (<0.1^○) in both systems show a forward peak followed by an asymptotic fall at higher angles. Total and partial capture cross sections are found to be in good agreement with the experimental observations. Oscillations in the partial capture cross sections have been explained due to the swapping of the field electron. Isotope effect in the electron transfer is reported to be negligible.     

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     

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     

Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength

Results on the structural and dynamical properties of aqueous solutions of NaPSS (HPSS) are reported. Most samples of previous measurements, including our own, are contaminated by the presence of (temporal) aggregates. The emphasis of this paper lies on investigations of well purified samples at very low ionic strength where interacting effects are maximum. As previously reported, this can be achieved by pumping the suspension through ion exchange resin by means of a tube-pump, using filters of pore size. Information has been extracted from static and dynamic light scattering and viscosity measurements. A second maximum is observed in the scattering curves versus wavenumber for the first time. It is discussed on the basis of two current models describing the structure of charged macromolecules. The short time dynamics reflects the measured intensity. Detailed viscosity data in comparison of those of rodlike (TMV), slightly flexible so-called fd virus particles (length 880 nm) are used to confirm the interpretation of the light scattering results. The recently observed maximum in the reduced viscosity could be confirmed. Received: 5 May 1997 / Revised: 1 September 1997 / Accepted: 10 November 1997     

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.     

Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.