Glass transition cooperativity from broad band heat capacity spectroscopy

Molecular dynamics is often studied by broad band dielectric spectroscopy (BDS) because of the wide dynamic range available and the large number of processes resulting in electrical dipole fluctuations and with that in a dielectrically detectable relaxation process. Calorimetry on the other hand is an effective analytical tool to characterize phase and glass transitions by its signatures in heat capacity. In the linear response scheme, heat capacity is considered as entropy compliance. Consequently, only processes significantly contributing to entropy fluctuations appear in calorimetric curves. The glass relaxation is a prominent example for such a process. Here, we present complex heat capacity at the dynamic glass transition (segmental relaxation) of polystyrene (PS) and poly(methyl methacrylate) (PMMA) in a dynamic range of 11 orders of magnitude, which is comparable to BDS. As one of the results, we determined the characteristic length scale of the corresponding fluctuations. The dynamic glass transition measured by calorimetry is finally compared to the cooling rate dependence of fictive temperature and BDS data. For PS, dielectric and calorimetric data are similar but for PMMA with its very strong secondary relaxation process some peculiarities are observed.     

Inverse problem and the trace formula for the Hill operator, II

Consider the Hill operator on where is a 1-periodic real potential and The spectrum of T is absolutely continuous and consists of intervals separated by gaps . Let be the Dirichlet eigenvalue of the equation on the interval [0,1]. Introduce the vector with components and where the sign or for all . Using nonlinear functional analysis in Hilbert spaces we show, that the mapping is a real analytic isomorphism. In the second part a trace formula for is proved. Received December 22, 1997; in final form July 7, 1998     

Whispering gallery modes in nanosized dielectric resonators with hexagonal cross section

The size dependence of whispering gallery modes in dielectric resonators with hexagonal cross section has been observed within the visible spectral range for cavity diameters comparable to the light wavelength. As a model system single, tapered, high aspect ratio zinc oxide nanoneedles were analyzed. They enable systematic investigations as a function of the resonator diameter down to the nanometer regime. A simple plane wave interference model without free parameter describes the spectral positions and the linewidths of the modes in good agreement with the experiment.     

Superfluid interfaces in quantum solids

One scenario for the nonclassical moment of inertia of solid 4He discovered by Kim and Chan [Nature (London) 427, 225 (2004)] is the superfluidity of microcrystallite interfaces. On the basis of the most simple model of a quantum crystal--the checkerboard lattice solid--we show that the superfluidity of interfaces between solid domains can exist in a wide range of parameters. At strong enough interparticle interaction, a superfluid interface becomes an insulator via a quantum phase transition. Under the conditions of particle-hole symmetry, the transition is of the standard U(1) universality class in 3D, while in 2D the onset of superfluidity is accompanied by the interface roughening, driven by fractionally charged topological excitations.     

Alkylaminophosphanyl substituted half-sandwich complexes of vanadium(III) and chromium(III): preparation and reactivity in ethylene polymerisation

[Cp^R(RPNEt₂)]M (Cp^R=t-BuC₅H₃, C₅(CH₃)₄, indenyl, fluorenyl; M=Li, K) smoothly react with VCl₃(Me₃P)₂ and CrCl₃(THF)₃ systems giving paramagnetic complexes [Cp^R(R¹PNEt₂)]MCl₂ (M=V(Me₃P)₂, Cr). After reaction with MAO these complexes are active in the polymerisation of ethylene yielding highly crystalline, high-density products of high molecular weight (M_w ranging from 100 000 to 4.5×10⁶ g mol⁻¹, 20≤T_p≤100 °C). Polymerisation with chromium complexes leads to the formation of polyethylenes with broad molecular weight distribution.     

Adsorption characteristics of bottle-brush polymers on silica: effect of side chain and charge density

The adsorption behavior of bottle-brush polymers with different charge/PEO ratio on silica was studied using optical reflectometry and QCM-D. The results obtained under different solution conditions clearly demonstrate the existence of two distinct adsorption mechanisms depending on the ratio of charge/PEO. In the case of low-charge density brush polymers (0-10 mol %), the adsorption occurs predominantly through the PEO side chains. However, the presence of a small amount of charge along the backbone (as low as 2 mol %) increases the adsorption significantly above that of the uncharged bottle-brush polymer in pure water. As the charge density of the brush polymers is increased to 25 mol % or larger the adsorption occurs predominantly through electrostatic interactions. The adsorbed layer structure was studied by measuring the layer dissipation using QCM-D. The adsorbed layer formed by the uncharged brush polymer dissipates only a small amount of energy that indicates that the brush lie along the surface, the scenario in which the maximum number of PEO side chains interact with the surface. The adsorbed layers formed by the low-charge density brush polymers (2-10 mol %) in water are more extended, which results in large energy dissipation, whereas those formed by the high-charge density brush polymers (50-100 mol %) have their backbone relatively flat on the surface and the energy dissipation is again low.