Radon measure-valued solutions of nonlinear strongly degenerate parabolic equations

We prove the existence of suitably defined weak Radon measure-valued solutions of the homogeneous Dirichlet initial-boundary value problem for a class of strongly degenerate quasilinear parabolic equations. We also prove that: \((i)\) the concentrated part of the solution with respect to the Newtonian capacity is constant; \((ii)\) the total variation of the singular part of the solution (with respect to the Lebesgue measure) is nonincreasing in time. Conditions under which Radon measure-valued solutions of problem \((P)\) are in fact function-valued (depending both on the initial data and on the strength of degeneracy) are also given.     

Existence, uniqueness and behavior of solutions for a class of nonlinear parabolic problems

We prove existence, uniqueness, regularity results and estimates describing the behavior (both for large and small times) of a solution u of some nonlinear parabolic equations of Leray-Lions type including the p-Laplacian. In particular we show how the summability of the initial datum u₀ and the value of p influence the behavior of the solution u, producing ultracontractive or supercontractive estimates or extinction in finite time or different kinds of decay estimates.     

Depth-resolved molecular structure and orientation of polymer thin films by synchrotron X-ray diffraction

An exemplary system suitable for optoelectronics applications, i.e. poly(3-hexylthiophene), hereinafter P3HT, deposited by spin casting onto silicon substrates functionalised by three selected molecules and then properly annealed, has been examined. Grazing Incidence X-ray Scattering (GIXS) measurements have been performed with 4-circle diffractometer, allowing for a fine control of sample axes movement.By choosing different grazing incident angles, diffraction patterns from different layers of polymeric thin films have been recorded. Both in-plane and out-of-plane geometries have been combined in order to obtain complementary structural information. In this way structural and orientational differences of the polymer along with the film thickness (?50 nm) have been highlighted. For all P3HT films spun on functionalized Si wafer, macromolecular layers close to the substrate surface give some evidence of higher order and orientation than those outmost the surface, and this behaviour is pronounced to a different extent depending on the functionalized molecules used. Contrariwise P3HT layers deposited onto bare Si wafer display reduced orientation and decreased crystallite size, especially at buried interface.     

Quasilinear elliptic equations with subquadratic growth

In this paper we consider nonlinear boundary value problems whose simplest model is the following:

(0.1)     

Field effect transistors with organic semiconductor layers assembled from aqueous colloidal nanocomposites

We demonstrate field effect transistors based on organic semiconductor molecules dispersed in a self-organized polystyrene (PS) latex bead matrix. An aqueous colloidal composite made of PS and tetrahexylsexithiophene (H4T6) is deposited with a micropipet into the channel of a bottom-contact field effect transistor. The beads self-organize into a network whose characteristic distances are governed by their packing. The semiconductor molecules crystallize in the interstitial voids, leading to the growth of large interconnected domains. Depending on the bead size and the ratio between H4T6 and PS, the fraction of the different phases in the polymorph can be controlled. In the transistors where the H4T6 metastable "red phase" is the largest, the device response and the charge mobility are comparable to those of sexithienyl thin films grown by high-vacuum sublimation.     

On the physical relevance of max- and log-max-selfsimilar distributions

This work emphasizes the special role played by max-semistable and log-max-semistable distributions as relevant statistical models of various observable and “internal” variables in Physics. Some of their remarkable properties (chiefly self-similarity) are displayed in some detail. One of their characteristic features is a log-periodic variation of the scale parameter which appears in the stable extreme value distributions. Received 29 November 1999 and Received in final form 24 March 2000     

Application of molecular mechanics to refine and understand the crystal structure of polythiophene and its oligomers

A molecular mechanics computational procedure, previously used for the refinement and the analysis of several crystalline polymers, was applied to investigate the crystal structures of the tetramer (T4) and hexamer (T6) of thiophene, as well as the crystal structure of polythiophene (PT). Simultaneous minimization of intra- and intermolecular energies of the T4 and T6 structures, obtained by Rietveld analysis of powder X-ray diffraction profiles, leads to molecular conformations showing smaller deviations from the ring co-planarity than the original models. For both oligomers the calculations confirm that the molecular centre of inversion is not a crystallographic centre of symmetry, as also revealed by X-ray diffraction of the T6 single crystal. This surprising effect appears to arise from intermolecular interactions between the terminal residues, hence is not relevant with respect to the PT polymer structure. The small energy cost for constraining the molecules at the crystallographic centre of symmetry is in agreement with experimental findings that reveal the existence of polymorphs for both T4 and T6. The calculations on the T6 single crystal were used to upgrade the MM2-like force field, which was then used to determine the minimum-energy model of the monoclinic crystal structure of polythiophene.     

Highly Regioregular Poly-3-alkylthiophenes: Influence of the Structure on Photoluminescence

Summary.   A class of regioregular poly-3-alkylthiophenes was synthesized via a new and simple synthetic procedure. These polymers exhibit a regioregularity as high as 95–100% and show different thermal behaviour depending on the length of the side chain. The high conjugation length reached is responsible for a red-orange emission with photoluminescence (PL) quantum efficiencies of about 45% in solution. The study of the PL of spin coated films at different temperatures allows to correlate the PL spectra with the structure of the polymers as detected by XRD. Received June 23, 2000. Accepted (revised) August 21, 2000     

Synthesis of intramolecularly cyclized poly(phenylene sulfide)s of the thianthrene-type

Oligomers containing thianthrene units in the chain are synthesized by AlCl₃-catalyzed reaction of diphenylsulfide, thianthrene, poly(p-phenylene sulfide), and poly(m-phenylene disulfide) with sulfur at 80°C. The products are compared with that obtained by the reaction of diphenylsulfide with AlCl₃ at 225°C. IR spectra and elemental analyses are consistent with cyclic chain structures and show a higher cyclization for CHCl₃-insoluble fractions. X-ray diffraction analysis indicates the same structure for the samples obtained with the different methods of synthesis. A possible structural model is tentatively proposed.