Relationship between dynamic mechanical property and thermodynamic interaction parameter of concentrated polymer solutions

The use of concentrated polymer solutions is one of the basic techniques in the application of polymers. They may be coating materials, plasticized polymers, and oil-extended rubber. In these applications the solubility relation is one of the key requirements. The polymer-solvent interaction is expected to influence the mechanical property of the mixture. It is the intent of this study to explore how the dynamic mechanical property is affected by the change of thermodynamic interaction parameter in concentrated polymer solutions. The theoretical development is based on several assumptions: (1) a polymer chain in the amorphous state and in its own environment assumes unperturbed configuration; (2) a polymer chain in a good solvent (poor) is expanded (contracted) relative to the unperturbed dimension; (3) the expanded (contracted) chain configuration results in the higher (lower) entanglement density; (4) both expanded and contracted chains store an elastic energy, the magnitude of which may be estimated; (5) the elastic energy of the deformed chain is balanced by the thermodynamic energy of interaction. The paper focuses on the development of a theory. Also, limited examples of the application of the theory are presented.     

Critical dynamic approach to stationary states in complex systems

A dynamic scaling Ansatz for the approach to stationary states in complex systems is proposed and tested by means of extensive simulations applied to both the Bak-Sneppen (BS) model, which exhibits robust Self-Organised Critical (SOC) behaviour, and the Game of Life (GOL) of J. Conway, whose critical behaviour is under debate. Considering the dynamic scaling behaviour of the density of sites (ρ(t)), it is shown that i) by starting the dynamic measurements with configurations such that ρ(t=0) →0, one observes an initial increase of the density with exponents θ= 0.12(2) and θ= 0.11(2) for the BS and GOL models, respectively; ii) by using initial configurations with ρ(t=0) →1, the density decays with exponents δ= 0.47(2) and δ= 0.28(2) for the BS and GOL models, respectively. It is also shown that the temporal autocorrelation decays with exponents C_a = 0.35(2) (C_a = 0.35(5)) for the BS (GOL) model. By using these dynamically determined critical exponents and suitable scaling relationships, we also obtain the dynamic exponents z = 2.10(5) (z = 2.10(5)) for the BS (GOL) model. Based on this evidence we conclude that the dynamic approach to stationary states of the investigated models can be described by suitable power-law functions of time with well-defined exponents.     

Universality in lattice models of dynamic arrest: introduction of an order parameter

We introduce an order parameter for dynamical arrest. Dynamically available volume (unoccupied space that is available to the motion of particles) is expressed as holes for the simple lattice models we study. Near the arrest transition the system is dilute in holes, so we expand dynamical quantities in a series of hole density. Unlike the situation when presented in particle density, all cases of simple models that we examine have a quadratic dependence of the diffusion constant on hole density. This observation implies that in certain regimes ideal dynamical arrest transitions may possess a hitherto unnoticed degree of universality.     

Evidence of distributed interstitialcy-like relaxation of the shear modulus due to structural relaxation of metallic glasses

The interstitialcy theory is used to calculate the kinetics of shear modulus relaxation induced by structural relaxation of metallic glasses. A continuous distribution of activation energies is shown to be a salient feature of the relaxation. High precision in situ contactless electromagnetic acoustic-transformation shear modulus (600- kHz) measurements performed on a Zr-based bulk metallic glass are found to strongly support the approach under consideration. It is revealed that the activation energy spectra derived from isothermal and isochronal shear modulus measurements are in good agreement with each other. It is concluded that the increase of the shear modulus during structural relaxation can be understood as a decrease of the concentration of structural defects similar to dumbbell interstitials in simple crystalline metals.     

Suppression of superconductivity in high-T c cuprates due to nonmagnetic impurities: Implications for the order parameter symmetry

We show explicitly that the broad histogram single-spin-flip random walk dynamics does not give correct microcanonical average even in one dimension. The dynamics violates the detailed balance condition by an amount proportional to the inverse system size. As a result, in distribution different configurations with the same energy can have different probabilities. We propose a modified dynamics which ensures detailed balance and the histogram obtained from this dynamics is exactly flat. The broad histogram equation relating the average number of potential moves to density of states is generally valid. Received 2 October 1998 and Received in final form 13 October 1998     

Critical behavior of higher cumulants of order parameter in the 3D-Ising universality class

QCD deconfinement phase transition is supposed to be the same universality class as the 3D-Ising model. According to the universality of critical behavior, the Binder-like ratios and ratios of higher cumulants of order parameter near the critical temperature in the 3D-Ising model are studied. The Binder-like ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. The normalized cumulant ratios, like the Skewness and Kurtosis, do not diverge with correlation length, contrary to the corresponding cumulants. Possible applications of these characters in locating critical point in relativistic heavy ion collisions are discussed.     

AdS solutions in gauge supergravities and the global anomaly for the product of complex two-cycles

Cohomological methods are applied for the special set of solutions corresponding to rotating branes in arbitrary dimensions, AdS black holes (which can be embedded in ten or eleven dimensions), and gauge supergravities. A new class of solutions is proposed, the Hilbert modular varieties, which consist of the 2n-fold product of the two-spaces H ⁿ /Γ (where H ⁿ denotes the product of n upper half-planes, H ², equipped with the co-compact action of Γ⊂SL(2,ℝ) ⁿ ) and (H ⁿ )^∗/Γ (where (H ²)^∗=H ²∪{cusp of Γ} and Γ is a congruence subgroup of SL(2,ℝ) ⁿ ). The cohomology groups of the Hilbert variety, which inherit a Hodge structure (in the sense of Deligne), are analyzed, as well as bifiltered sequences, weight and Hodge filtrations, and it is argued that the torsion part of the cuspidal cohomology is involved in the global anomaly condition. Indeed, in the presence of the cuspidal part, all cohomology classes can be mapped to the boundary of the space and the cuspidal contribution can be involved in the global anomaly condition.     

Dispersion of nanoparticles: From organic solvents to polymer solutions

This work is devoted to a systematic study of nanoparticle dispersion by ultrasonication in different solutions: from organic solvents to polymer solutions. The cluster size of nanoparticles at different concentrations in both organic solvents and polymer solutions were directly characterized by Dynamic Light Scattering to study the effect of solid concentration, surfactant and polymer on the dispersion. It reveals that in stabilized suspensions, the smallest attainable size or aggregate size of nanoparticles is independent of solvent type and solid content over the tested range. Furthermore, nanoparticles in simple solvent and in polymer solutions had the similar evolution of cluster size and almost the same final size, which could be very helpful to optimize the dispersion of nanofillers in polymer solutions and nanocomposites. It is also shown that, with appropriate sonication amplitudes, the dispersion procedure developed for very dilute suspensions could be transferred to higher concentration suspensions or even to polymer suspensions.     

Inhomogeneous microscopic shear strains in a complex crystal lattice subjected to large macroscopic strains (exact solutions)

Nonlinear theory of microscopic and macroscopic strains is developed for the case of large inhomogeneous relative displacements of two sublattices making up a complex crystal lattice; in this case, in addition to an acoustic mode, a pseudooptical, strongly nonlinear mode is excited. The equation of relative motion of the sublattices can be solved exactly for the specific case of a centrosymmetric crystal. The corresponding equilibrium equation is the sine-Helmholtz equation and has a doubly periodic solution. This solution describes fragmentation of the lattice, more specifically, the appearance of a domain superstructure with large periods, whose building blocks contain oppositely sensed rotons separated by topological defects that are opposite in sign. Purely elastic microscopic strains are followed by elastoplastic ones. Both types of strain arise as a result of bifurcation, which causes a change from the initially homogeneous strain field to an inhomogeneous one. The domain sizes take on optimal values when the external homogeneous macroscopic strains reach a certain threshold magnitude.     

Thermal expansion of boehmite: An anomaly near 560 K due to non-stoichiometric water

The thermal expansion of boehmite, A1OOH, has been investigated between 78 and 650 K. The results show a contraction of all lattice parameters around 560 K.A differential scanning calorimetric study reveals that two successive thermal effects exist around this temperature. The first effect is an exotherm related to a structural reorganization characterized by a contraction of one lattice parameter: c. The second effect is an endotherm, which is associated with a loss of non-stoichiometric water, characterized by a contraction perpendicular to the layers, along b axis.     

Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system

We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system.     

Landau-type pressure dependence of the order parameter: application to the ferroelectric-paraelectric pressure-induced transition in KNbO3

Following the Landau model, the pressure–temperature dependence of the order parameter is derived. Using the Lyddane–Sachs–Teller (LST) relationship, the model is applied to ferroelectricity to deduce the pressure behaviour of the soft mode driving the transition. Comparison with experiment is made using recent data obtained on KNbO₃ under pressure over a large temperature range. The results indicate that the ferroelectric–paraelectric (FE–PE) transition observed in KNbO₃ at high pressure from ～4 to ～25?GPa is of the second-order type.     

Universal behavior of entrainment due to coherent structures in turbulent shear flow

A solution is suggested for a persistent mystery in the physics of turbulent flows: cumulus clouds rise to towering heights, practically without entraining the ambient medium, while apparently similar turbulent jets quickly lose their identity through entrainment and mixing. Dynamical system computations on a model vortical flow show that entrainment due to coherent structures depends sensitively on relative speeds of fluid parcels. Local heating, for example, can alter drastically the sizes of Kolmogorov-Arnol'd-Moser tori and chaotic mixing regions. The entrainment rate and, hence, the lifetime of a turbulent shear flow show a universal, nonmonotone dependence on the heating.     

Acoustoelasticity in soft solids: assessment of the nonlinear shear modulus with the acoustic radiation force

The assessment of viscoelastic properties of soft tissues is enjoying a growing interest in the field of medical imaging as pathologies are often correlated with a local change of stiffness. To date, advanced techniques in that field have been concentrating on the estimation of the second order elastic modulus (mu). In this paper, the nonlinear behavior of quasi-incompressible soft solids is investigated using the supersonic shear imaging technique based on the remote generation of polarized plane shear waves in tissues induced by the acoustic radiation force. Applying a theoretical approach of the strain energy in soft solid [Hamilton et al., J. Acoust. Soc. Am. 116, 41-44 (2004)], it is shown that the well-known acoustoelasticity experiment allowing the recovery of higher order elastic moduli can be greatly simplified. Experimentally, it requires measurements of the local speed of polarized plane shear waves in a statically and uniaxially stressed isotropic medium. These shear wave speed estimates are obtained by imaging the shear wave propagation in soft media with an ultrafast echographic scanner. In this situation, the uniaxial static stress induces anisotropy due to the nonlinear effects and results in a change of shear wave speed. Then the third order elastic modulus (A) is measured in agar-gelatin-based phantoms and polyvinyl alcohol based phantoms.