Thermal stability of brominated poly(isobutylene‐co‐isoprene)

The thermal stability of brominated isobutylene–isoprene rubber (BIIR) was investigated through studies of the elastomer and a model compound that accurately represented the reactive functionality within the polymer. An analysis of commercial BIIR and reaction products of brominated 2,2,4,8,8‐pentamethyl‐4‐nonene (BPMN) by NMR demonstrated that bromination of isobutylene–isoprene rubber by 1,3‐dibromo‐5,5‐dimethylhydantoin yielded a kinetically favored exomethylene substitution product, 3‐bromo‐6,6‐dimethyl‐2‐(2,2‐dimethylpropyl)‐1‐heptene ( 2 ), as opposed to the more stable endo‐isomer, (E,Z)‐4‐(bromomethyl)‐2,2,8,8‐tetramethyl‐4‐nonene ( 3 ). The exposure of BIIR and the brominated model compound BPMN to vulcanization temperatures led to the isomerization of 2 to 3 at a rate strongly dependent on HBr concentration. The elimination of HBr from these allylic bromides to produce exo‐ and endo‐conjugated dienes proceeded concurrently with isomerization, and the kinetics of these processes could be rationalized on the basis of a polar reaction mechanism. The product distributions obtained from both the model system and BIIR were consistent, thereby justifying an extension of the model compound approach to an analysis of BIIR vulcanization chemistry. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2019–2026, 2001     

Stability and analyticity in maximum-norm for simplicial Lagrange finite element semidiscretizations of parabolic equations with Dirichlet boundary conditions

Stability and analyticity estimates in maximum-norm are shown for spatially discrete finite element approximations based on simplicial Lagrange elements for the model heat equation with Dirichlet boundary conditions. The bounds are logarithm free and valid in arbitrary dimension and for arbitrary polynomial degree. The work continues an earlier study by Schatz et al. [5] in which Neumann boundary conditions were considered. Received November 1998 / Revised version received August 11, 1999 / Published online July 12, 2000     

Time discretization via Laplace transformation of an integro-differential equation of parabolic type

We consider the discretization in time of an inhomogeneous parabolic integro-differential equation, with a memory term of convolution type, in a Banach space setting. The method is based on representing the solution as an integral along a smooth curve in the complex plane which is evaluated to high accuracy by quadrature, using the approach in recent work of López-Fernández and Palencia. This reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. The method is combined with finite element discretization in the spatial variables to yield a fully discrete method. The paper is a further development of earlier work by the authors, which on the one hand treated purely parabolic equations and, on the other, an evolution equation with a positive type memory term. The authors acknowledge the support of the Australian Research Council.     

Normal incidence X-ray standing wave analysis of thin gold films

Normal incidence X-ray standing wave (NIXSW) analysis has been successfully performed on epitaxial gold films on mica substrates using reflection from the (1 1 1) planes parallel to the surface. We show that NIXSW can be used to monitor the decrease in order within the gold film caused by annealing, and the position of sulfur within a monolayer of methyl thiolate (CH₃S-) on the surface. The Au-S layer spacing was found to be 2.54 ± 0.05 Å, in close agreement with previous work on a single crystal system.     

Formation of metallic nanophases in silica by ion beam mixing. Part II: cluster formation

2 matrix by ion-beam mixing of SiO₂/Ag multilayers is studied via Rutherford backscattering spectrometry, optical absorption, and transmission electron microscopy experiments. In a first step, irradiation with MeV heavy ions transforms the continuous Ag layers into a string of micrometer-sized Ag inclusions. This mechanism can be attributed to lateral segregation of metallic atoms induced by irradiation. In a second step, the Ag inclusions are broken up by incoming ions and Ag nanoclusters are formed by agglomeration of mobile Ag atoms. The latter mechanism is likely due to a combination of ballistic mixing and radiation-induced segregation or radiation-enhanced diffusion processes. The size of the metallic nanoclusters formed depends also on the irradiation temperature. Received: 27 October 1997/Accepted: 3 February 1998     

Generating the tame and wild kernels by Dennis-Stein symbols

For many number fieldsF, it is proved that the tame kernel, K₂( ), and the wild kernel, W(F), ofF are generated by Dennis-Stein symbols. For some real quadratic number fields, generators for the tame kernel are given.     

A combinatorial approach to the electron correlation problem

Starting from a path-integral formulation of quantum statistical mechanics expressed in a space of Slater determinants, we develop a method for the Monte Carlo evaluation of the energy of a correlated electronic system. The path-integral expression for the partition function is written as a contracted sum over graphs. A graph is a set of distinct connected determinants on which paths can be represented. The weight of a graph is given by the sum over exponentially large numbers of paths which visit the vertices of the graph. We show that these weights are analytically computable using combinatorial techniques, and they turn out to be sufficiently well behaved to allow stable Monte Carlo simulations in which graphs are stochastically sampled according to a Metropolis algorithm. In the present formulation, graphs of up to four vertices have been included. In a Hartree-Fock basis, this allows for paths which include up to sixfold excitations relative to the Hartree-Fock determinant. As an illustration, we have studied the dissociation curve of the N(2) molecule in a VDZ basis, which allows comparison with full configuration-interaction calculations.     

Theoretical study of the SN2 reaction of Cl−(H2O)+CH3Cl using our own N-layered integrated molecular orbital and molecular mechanics polarizable continuum model method (ONIOM, PCM)

The effects of solvation in the S_N2 reaction Cl^–(H₂O)+CH₃Cl were investigated using our own N-layered integrated molecular orbital and molecular mechanics (ONIOM) polarizable continuum model (PCM) method [Vreven T, Mennucci B, da Silva CO, Morokuma K, Tomasi J (2001) J Chem Phys 115:62–72], which surrounds the microsolvated ONIOM system with a polarizable continuum. The microsolvating water molecule tends to stay in the vicinity of the original chloride ion. In the ONIOM calculations, Cl^–+CH₃Cl was considered as the model system and was handled with the high-level method, while the explicit water molecule in the microsolvated complex was treated at the low-level. The molecular orbital (MO) and ONIOM(MO:MO) calculations allow us to assess the errors introduced by the ONIOM extrapolation, as well as the effects of microsolvation on the potential-energy surfaces. We find that ONIOM[B3LYP/6-31+G(d,p):HF/6-31+G(d,p)] and ONIOM[B3LYP/6-31+G(d,p):HF/6-31+G(d,p)]-PCM methods are good approximations to the target B3LYP/6-31+G(d,p) and B3LYP/6-31+G(d,p)-PCM methods. In addition, several approximate (computationally less expensive) schemes in the ONIOM-PCM method have been compared to the exact scheme, and all are shown to perform well.Contribution to the Jacopo Tomasi Honorary Issue