Dynamical precursor of nematic order in a dense fluid of hard ellipsoids of revolution

We investigate hard ellipsoids of revolution in a parameter regime where no long range nematic order is present but already finite-size domains are formed which show orientational order. Domain formation leads to a substantial slowing down of a collective rotational mode which separates well from the usual microscopic frequency regime. A dynamic coupling of this particular mode into all other modes provides a general mechanism which explains an excess peak in spectra of molecular fluids. Using molecular dynamics simulation on up to 4096 particles and on solving the molecular mode coupling equation we investigate dynamic properties of the peak and prove its orientational origin. Received 19 September 2001 and Received in final form 19 March 2002     

Thickness of the interphase layer determined from volume changes produced by mutual diffusion in binary microheterogeneous polymer mixtures

The mutual diffusion of pairs of polymers has been studied at 160°C for two systems: isotactic polypropylene with polyethylene and poly(vinyl chloride) with polyethylene. From the assumption that Fick's law is valid and with a rhombohedral lattice model for the microheterogeneous system, it was possible to obtain from volume changes the thickness of the interphase layer after various diffusion times. It was found that the values so calculated differ considerably from the experimental values, the greatest deviations occuring after 20 min diffusion. From this it follows that non-Fickian diffusion strongly influences the distribution of concentrations in the diffuse interface, and thus affects the calculated value of the interphase layer thickness. For both polymer pairs Fickian behavior was confirmed for up to about 10 min diffusion time, in good agreement with experimental data.     

Attempt for the diffused interphase layer determination from the volume changes of microheterogeneous polymer mixtures

Summary For the experiments there have been prepared such microheterogeneous mixtures of isotactic polypropylene with polyethylene and of polyvinylchloride with polyethylene which contained maximum 60 volume per cent of dispersed phase component (iPP; PVC respectively) at 160°C for various diffusion times, whereat with sufficient exactness the tetrahedric lattice model could be applied. From the dependence of the mixture excess volume on dispersed phase volume fraction, calculated from additive and real densities, the volume fraction at the maximum dilatation ( _m ) was determined. At supposing theFickian course of the mutual diffusion, it was possible to calculate the thickness of the interphase layer.It was stated that for both polymer pairs the diffusion after 15 min had been practically stopped. This phenomenon, which could be explained by the kinetic hindrances during the interpenetration of the different nature polymer segments, is resulting in the deviation from theFickian course of diffusion.

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Zusammenfassung Zwecks Durchführung der Experimente wurden mikroheterogene Mischungen von isotaktischem Polypropylen mit Polyäthylen und von Polyvinylchlorid mit Polyäthylen vorbereitet, die höchstens 60 Vol.-% von dispergierter Phase (iPP oder PVC) bei 160°C für verschiedene Diffusionszeiten enthielten. Hierdurch konnte mit genügender Präzision mit dem Tetraeder-Gittermodell gearbeitet werden. Der Volumenbruch bei maximaler Dilatation ( _m ) wurde aus der Abhängigkeit des Exzessvolumens vom Volumenbruch der dispergierten Phase auf Grund von additiven und tatsächlichen Dichten berechnet. Unter Voraussetzung desFickschen Gesetzes für die Diffusion war es möglich, die Dicke der Zwischenphasenschicht auszurechnen.Man stellt fest, daß die Diffusion für beide Polymerpaare nach 15 min praktisch zum Stillstand kommt. Diese Erscheinung, die durch die kinetische Behinderung bei der Durchdringung von Polymersegmenten verschiedener Art erklärt werden könnte, ergibt Abweichungen vomFickschen Verlauf.

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With 2 figures and 1 table     

Influence of Na-related defects on ArF laser absorption in CaF2

ArF laser pulse transmission through commercial high purity CaF₂ is determined by measuring the energy of each pulse before and behind the sample up to an incident fluence H of 10 mJ/cm². The steady state transmission of ArF laser pulses decreases with increasing fluence. The related absorption coefficients α ^st(H) are proportional to H and rationalized by effective 1- and 2-photon absorption coefficients 2.4×10^?4 cm^?1≤α ^eff≤16.8×10^?4 cm^?1 and 1.7×10^?9 cm?W^?1≤β ^eff≤9.3×10^?9 cm?W^?1, respectively. The α ^eff and β ^eff values increase with the Na content of the CaF₂ samples as identified by the fluorescence of Na-related M _Na centers at 740 nm. This relation is simulated by a rate equation model describing the ArF laser induced M _Na generation in the dark periods between the laser pulses and their annealing during laser irradiation. M _Na generation starts with intrinsic 2-photon absorption in CaF₂, yielding self-trapped excitons (STE). These pairs of F and H centers move upon thermal activation and the F centers combine with F _Na to form M _Na centers. M _Na annealing occurs by its photo dissociation into a pair of F and F _Na centers.     

The three-band Hubbard hamiltonian with spin-orbit coupling: Canting and localization

In two dimensions the three-band Hubbard model with additional lifting of the degeneracy of the two spin directions (e.g. due to spin-orbit coupling) is investigated. The calculations are performed using self-consistent field methods. At half filling, for the nearly antiferromagnetically ordered state, the Hamiltonian can be diagnonalized analytically. A canting of the antiferromagnetically ordered copper spins can be described. This canting corresponds to the Dzialoshinskii-Moriya canting. An additional hole in an infinite layer is examined. This hole forms a self trapped localized state. The magnetic polaronremains stable over a wide range of the additional spin-orbit coupling and finally gets unstable. Such polarons are the beginning of phase-separation in the cuprates.     

Evolution operator and stable coherent states

The time evolution of a coherent state is discussed using the evolution operator of the underlying Hamiltonian.     

On the theory of light scattering in molecular liquids

The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities ρ _lm(q) with l = 0 and l = 2. l, m denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger [1] for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous phenomenological theories. We emphasize the importance of the helicity index m for the microscopic theory by showing, that only the existence of m = 1 components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived. Received 3 July 2000 and Received in final form 7 November 2000     

Diffuse interphase layer in microheterogeneous polymer mixtures

The thickness of the interphase layer as a function of time at 160°C has been determined directly in a microheterogeneous polymer mixture, and the layer thickness between two bonded sheets has also been measured by phase-contrast microscopy. Two mixtures of polymers, isotatic polypropylene with polyethylene and poly(vinyl chloride) with polyethylene, were prepared by mixing size-sorted powders in suspension, followed by evaporating the suspension medium and compacting the powdered mixtures. The mutual penetration initially obeyed Fick's second law; then diffusion was retarded and stopped after 15–20 min. An equilibrium state was reached which did not correspond to the classical thermodynamic equilibrium, at which the so-called equilibrium thickness of the interphase layer for the pair isotactic polypropylene-polyethylene was about 28,000 Å and for the pair poly(vinyl chloride)-polyethylene was about 89,600 Å. The equilibrium values can be used as a quantitative criterion for the compatibility of the polymer pairs.     

Brown representability for triangulated categories with a linear action by a graded ring

Archiv der Mathematik - In this paper we give necessary and sufficient conditions for a functor to be representable in a strongly generated triangulated category which has a linear action by a...