Perfluorocarbon-Hydrocarbon Discrete Intermolecular Aggregates: An Exceptionally Short N⋯I Contact

1-Iodoperfluoroheptane ( 1a ) and tetramethylethylenediamine ( 2 , TMEDA) form the 2:1 ratio stable aggregate 3a and a similar behaviour is shown by 1-iodoperfluoroalkanes 1b-e and iodopentafluorobenzene 1f . These aggregates have been characterised in solution by 1 H/ 19 F-NMR spectroscopy and in the solid state through IR and single crystal X-ray diffraction. The determined structure of 3a (triclinic, a =6.2283(10), b =9.250(2), c =15.098(3) Å, f =81.369(5), g =81.397(5), n = 86.010(5), V =849.3(3) A m 3 , T =175(3) K, space group P-1 (No. 2), Z =1; d (calc)=2.167 g cm m 3 ; 4121 independent reflections, 3665 with I o >2( I o ); final refinement gave R1=0.0400, wR2=0.0901) showed the second shortest N > I interaction found in the crystallographic literature [2.762(3) Å] and the interdigitation of perfluorocarbon and hydrocarbon modules due to co-operative -C-H > F-C- interactions. Calculations to quantify these latter interactions have been also performed.     

Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property

We provide results allowing to state, by the simple inspection of suitable classes of posets (propositional Kripke frames), that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2^No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. Mathematics Subject Classification: 03B55, 03C90.     

The L-L estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media

We first obtain the L^p-L^q estimates of solutions to the Cauchy problem for one-dimensional damped wave equation

     

Relaxation dynamics in tert-butylpyridine/tristyrene mixture investigated by broadband dielectric spectroscopy

We investigated, by means of dielectric spectroscopy, the relaxation dynamics of glass forming binary mixtures composed by the quite rigid polar molecules tert-butylpyridine dissolved in the apolar solvent tristyrene. By changing the relative concentration of the components we observed a transition from a relaxation scenario with a structural process and an excess wing to that with a structural process and a well resolved secondary process. Another relaxation process, slower than the latter, was observed, well below Tg. Our detailed analysis evidenced that the secondary relaxation with shorter relaxation time can be identified as the Johari-Goldstein relaxation for all the mixtures, whereas the new relaxation process was attributed to a different type of motion of tert-butylpyridine needing a larger amount of free volume for the molecular rotation.     

Influence of a reduced mobility layer on the structural relaxation dynamics of aluminum capped ultrathin films of poly(ethylene terephthalate)

The structural dynamics of ultrathin polymer films of poly(ethylene terephthalate) capped between aluminum electrodes have been investigated by dielectric relaxation spectroscopy. A deviation from bulk behavior, appearing as an increase of the relaxation time at a fixed temperature, is observed for films of thickness below 35 nm. The slowing down acts as a constant shift factor independent from the temperature, and the fragility is constant. The interfacial energy between aluminum and poly(ethylene terephthalate) is calculated to be 3 mJ/m2, confirming a strong interaction between polymer and substrate, which leads to the presence of a layer characterized by a reduced mobility at their interfaces. We proposed a mathematical schematization of a multylayer model that allowed qualitative reproduction of the observed thickness dependences of the static and dynamic properties. In terms of such a model, the upper limit for the thickness of the reduced mobility layer was estimated as 20 nm. The conditions to extend the proposed model to different observables are finally suggested.     

Evolution of hypersurfaces in $ {\Bbb R}^N$ by Gaussian curvature

In this paper we first prove short time existence of a classical solution for the problem which describes the evolution by Gaussian curvature of a strictly convex hypersurface in . Then we give a proof of the existence of a viscosity solution for this problem in such a way as to define a generalized motion existing for each time. Received November 24, 1997     

The combined relaxation and vanishing Debye length limit in the hydrodynamic model for semiconductors

The combined relaxation and vanishing Debye length limit for the hydrodynamic model for semiconductors is considered in both the unipolar and the bipolar case. The resulting limit problems are non‐linear drift driven hyperbolic equations. We make use of non‐standard entropy functions and the related entropy productions in order to obtain uniform estimates. In the bipolar case additional time‐dependent L^∞‐type estimates, available from the existence theory, are needed in order to control the entropy production terms. Finally, strong convergence of the electric field allows the limit towards the limiting problem. Copyright © 2001 John Wiley & Sons, Ltd.