Silanols cured by borates as lubricants in extrusion of LLDPE. Impact of elasticity of the lubricant on sliding friction

Addition of a viscoelastic material based on silanols cured by boron oxide was used to delay sharkskin and stick–slip instabilities in extrusion of linear low-density polyethylene (LLDPE). Delay of flow instabilities to rates of extrusion 25–35 times higher than without additive and about 40% less extrusion pressure at the same throughput are achieved by the use of this material as an additive (∼0.1%) to LLDPE or as a coating of the extrusion die. Mechanical properties of the lubricant were changed by small variations of composition to investigate the impact of elasticity on lubrication and sharkskin delay. Both lubrication and sharkskin delay were considerably improved when more elastic lubricants were used while the chemical composition of the lubricants was nearly the same. Filling the lubricants with powders of metal oxides or especially particulates having plate-like particles (kaolin, mica, BN) helped to delay the flow instabilities further to even higher throughputs. Together with experimental results, we present a tentative explanation for the importance of elasticity of polymer processing aids in the delay of sharkskin and the stabilization of slip. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Non-local continuum mechanics and fractional calculus

The present work introduces fractional calculus into the continuum mechanics area describing non-local constitutive relations. Considering a one-dimensional body and assuming total stored energy depending not only upon the local strain but also upon a fractional derivative of the stain, an elastic model with non-local stress–strain behavior is introduced. Fractional calculus provides a natural framework for describing non-local constitutive relations and requires no assumptions for the interval of non-local influence. Furthermore, the proposed method works in finite intervals contrary to the existing theories requiring infinite domains.     

High Pressure Instrumentation: Low and Negative Pressures

Much work on semiconductors, soft solids and biological materials does not require the megabar capability of the diamond anvil cell; a few accurate kbar being all that may be required. Work in this range poses its own challenges, to make the experiments routine, safe and reliable, and well-calibrated. We contrast diamond anvil cells working at what for them is very low pressure, with traditional bombs working at what for them is dangerously high pressure. We describe our preferred solution, a single-diamond cell, and demonstrate its use with Raman data from ethanol under low pressure. Negative hydrostatic pressure cannot be obtained by traditional methods. However, we present data showing the Raman spectrum of ethanol apparently at the negative pressure of m 3 kbar.     

On the problem of the relation between phason elasticity and phason dynamics in quasicrystals

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals [S. Francoual et al. Phys. Rev. Lett. 91, 225501 (2003); A. Létoublon et al. 54, 753 (2001)]. We will show that the data reported call for a more detailed development of the elasticity theory of Jarić and Nelsson [M.V. Jarić and D.R. Nelsson, Phys. Rev. B 37, 4458 (1988)] in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a “satellite position” at a distance q from each Bragg peak; that (2) has an intensity that scales with the intensity of the corresponding Bragg peak; (3) falls off as 1/q²; and (4) has a time decay constant that is proportional to 1/Dq². It is thus superfluous to call for a picture of “phason waves” in order to explain such data, especially as such “waves” violate many physical principles.     

Mechanical spectra measurement to probe the magnetolattice coupling in cupric oxide

Mechanical spectra (complex Young's modulus Y*=Y′+iY″ versus frequency and temperature) of polycrystalline cupric oxide CuO were measured by vibrating reed method from liquid nitrogen temperature to room temperature at the kilohertz frequency. The abnormal behavior of internal friction and the change of slope of the real part of the complex Young's modulus versus temperature are observed around 213 and 230 K, where two successive magnetic transitions were established. At low temperatures, below 130 K, a higher internal friction platform with the decrease of temperature was clearly observed which might show a phase transition. Our study indicates that mechanical spectrum is an effective tool to detect subtle phase transitions and there is a strong magnetolattice coupling in CuO.     

A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.     

Spin-Hall effect: Back to the beginning at a higher level

The phenomena of the spin-Hall effect, initially proposed over three decades ago in the context of asymmetric Mott skew scattering, was revived recently by the proposal of a possible intrinsic spin-Hall effect originating from a strongly spin-orbit coupled band structures. This new proposal has generated an extensive debate and controversy over the past 2 years. On August 2006 the first workshop on the spin-Hall effect was held at the Asian Pacific Center for Theoretical Physics. Its purpose was to bring together many of the leading groups in this field to resolve such issues and identify future challenges. We offer this short summary to clarify formerly controversial issues now settled and help refocus the research efforts in new and important avenues.     

Stability of an hexagonal array of coherently strained conical islands against Ostwald ripening

We present a linear stability analysis of an hexagonal array of coherently strained islands against the exchange of material between islands. Surprisingly, ultra-dense arrays are found to be metastable due to the short-range stabilizing effect of elastic interactions which overcome the destabilizing contribution of surface energy. Mean-field simulations are used to investigate the ripening kinetics of local volume defects in arrays which are found to equilibrate through island volume oscillations. Simulations of global perturbations directly verify the existence of the metastable regime and confirm the nature of the most unstable mode as derived from the stability analysis for sub-critical island coverage.     

Superelements for the finite element solution of two-dimensional elliptic problems with boundary singularities

A novel singular superelement (SSE) formulation has been developed to overcome the loss of accuracy encountered when applying the standard finite element schemes to two-dimensional elliptic problems possessing a singularity on the boundary arising from an abrupt change of boundary conditions or a reentrant corner. The SSE consists of an inner region over which the known analytic form of the solution in the vicinity of the singular point is utilized, and a transition region in which blending functions are used to provide a smooth transition to the usual linear or quadratic isoparametric elements used over the remainder of the domain. Solution of the finite element equations yield directly the coefficients of the asymptotic series, known as the flux/stress intensity factors in linear heat transfer or elasticity theories, respectively. Numerical examples using the SSE for the Laplace equation and for computing the stress intensity factors in the linear theory of elasticity are given, demonstrating that accurate results can be attained for a moderate computational effort.     

On Variational Approaches to Plate Modes

The three basic functionals of potential energy, complementary energy and Hellinger–Prange–Reissner are usedto obtain a rational derivation of Reissner–Mindlinplate models, starting from the three-dimensional theory.We show that the models so obtained are instances of the same plate theory; nevertheless, due to the different constitutive relations governing their response, they mimic the three-dimensional behaviour in three different manners.