Measurements of the complex shear modulus of polymers under hydrostatic pressure usina the quartz resonator method

Abstract

The quartz resonator method measures the complex shear modulus or compliance of viscoelastic materials in the frequency range from 50 kHz to 140 MHz at temperatures between ?150°C and 300°C and pressures up to 1 GPa. This method can be applied to viscous fluids or polymer melts -even in their glassy or seminystalline regime.

The phase diagram of poly(diethylsiloxane) PDES (a mesophase polymer) was determined for two samples with different molecular weight at pressures up to 400 MPa and temperatures between 20°C and 100°C. Phase transitions are indicated by a sharp bend in the shear compliance although the volume effect of the mesophase-isotropic transition vanishes around 80 MPa.

The pressure dependence of the glass relaxation process (in PVAc), was studied by measuring the change of the complex shear modulus with pressure at constant temperatures between 95°C and 145°C and pressures up to 600 MPa. Additionally to the relaxation process, also the pressure dependence of the real part of the shear modulus in the glassy region can be determined for testing the dislocation concept in the meandermodell by W. Pechhold.     

A Banach space-valued ergodic theorem for amenable groups and applications

In this paper, we study unimodular amenable groups. The first part of the paper is devoted to results on the existence of uniform families of ε-quasi tilings for these groups. First we extend constructions of Ornstein and Weiss by quantitative estimates for the covering properties of the corresponding decompositions. Then we apply the methods developed to obtain an abstract ergodic theorem for a class of functions mapping subsets of a countable amenable group into some Banach space. This result extends significantly and complements related results found in the literature. Further, using the Lindenstrauss ergodic theorem, we link our results to classical ergodic theory. We conclude with two important applications: uniform approximation of the integrated density of states on amenable Cayley graphs and almost-sure convergence of cluster densities in an amenable bond percolation model.     

Uniform Approximation of the Integrated Density of States for Long-Range Percolation Hamiltonians

In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (IDS) or spectral distribution function can be approximated uniformly in the energy variable. This result is already new for percolation on ℤ ^d . Using this, we are able to characterize the set of discontinuities of the IDS.     

Uniform Existence of the Integrated Density of States for Randomly Weighted Hamiltonians on Long-Range Percolation Graphs

We consider random Hamiltonians defined on long-range percolation graphs over $\mathbb {Z}^{d}$ . The Hamiltonian consists of a randomly weighted Laplacian plus a random potential. We prove uniform existence of the integrated density of states and express the IDS using a Pastur-Shubin trace formula.     

Uniform Existence of the Integrated Density of States on Metric Cayley Graphs

Given an arbitrary, finitely generated, amenable group we consider ergodic Schrödinger operators on a metric Cayley graph with random potentials and random boundary conditions. We show that the normalised eigenvalue counting functions of finite volume parts converge uniformly. The integrated density of states (IDS) as the limit can be expressed by a Pastur-Shubin formula. The spectrum supports the corresponding measure and discontinuities correspond to the existence of compactly supported eigenfunctions. In this context, the present work generalises the hitherto known uniform IDS approximation results for operators on the d-dimensional metric lattice to a very large class of geometries.     

A functional equation related to symmetry of operators

In this note we determine the unique solution to the functional equation \(f(x + y) ( x- y) = \left( f(x) -f (y) \right) (x + y)\). We require no additional assumptions on the function \(f\). Moreover we solve this functional equation if \(f\) is only defined on a finite interval. The interest in this type of functional equation is motivated by the study of symmetrizing measures for (the generator of) a Lévy-driven Ornstein–Uhlenbeck process.     

Solutal Marangoni convection in a Hele–Shaw geometry: Impact of orientation and gap width

The European Physical Journal Special Topics - We study Marangoni roll cell convection in a ternary mass transfer system composed of cyclohexanol, water and butanol (transferred species) placed in...     

On the transition from cellular to wavelike patterns during solutal Marangoni convection

We study characteristic convection patterns emerging during the mass transfer of acetic acid from a glycerol-water layer to a superposed acetone layer by means of experiments and numerical simulations. The patterns form as a result of the stationary Marangoni instability. The initial phase of the pattern evolution is studied using high-resolution simulations. They show hierarchically ordered cellular structures which closely resemble experimental observations. In the later stages presently accessible to the experiments, the cells are locally replaced by relaxation oscillation waves. The emergence of these structures is favored when the experiment is performed in narrow cuvettes.