A Global Method for Relaxation in W1,p and in SBVp

 An integral representation formula for a class of functionals defined on and in (the space of special functions of bounded variation) is obtained without requiring the regularity conditions usually imposed in the literature. The approach is based on the general results of [10] and on a Poincaré-Wirtinger type inequality introduced by DE GIORGI, CARRIERO & LEACI [25]. Applications to relaxation problems and dimension-reduction problems in brittle thin films are presented. (Accepted May 8, 2002) Published online October 18, 2002 Communicated by L. Ambrosio     

Unusual Oxidative Dealkylation of Certain 4-Alkyl-1,4-Dihydropyridines With MnO2/Bentonite Using Microwave Irradiation,in the Absence of Solvent (II)

Several Hantzsch 4-alkyl-1,4- dihydropyridines have been oxidized to the corresponding aromatic systems. An unexpected mixture of 4-alkyl pyridines and/or dealkylated pyridines are formed.     

Novel Deep Cavity Calix[4]pyrroles Derived from Steroidal Ketones

Novel steroidal calix[4]pyrroles were prepared in excellent yields from commercially available cholic acid derivatives using an efficient synthetic sequence. Once in hand, it was found that these calix[4]pyrroles exist in the form of four different configurational isomers. Separation of these isomers was achieved readily using normal phase HPLC techniques. Once purified, the steroidal calix[4]pyrroles were screened via -FABMS analyses to judge their utility in effecting the enantioselective recognition of appropriate organic anions. Results that provided support for antipodal R > S selectivity were obtained in the case of both tartaric acid and mandelic acid. Direct extraction studies were then carried out and these confirmed the pattern of R > S selectivity observed by -FABMS.     

Single-particle electrophoresis for studying the adsorption of cationic polymers onto anionic particles

Understanding the adsorption of polymers onto particles is crucial for many technological and biomedical applications. Even though polymer adsorption on particles is a dynamic process, most experimental techniques can only study the adsorption indirectly, in equilibrium and on the ensemble level. New analysis methods are required to overcome these limitations. We investigated the use of single-particle electrophoresis to study the adsorption kinetics of cationic polymers onto anionic particles and compared the resulting data to a theoretical model. In this approach, the electrophoretic mobility of single polystyrene (PS) particles, exposed to different concentrations of poly(2-guanidinoethyl methacrylate), was measured as a function of time. The polymer adsorption leads to an electrophoretic mobility change of the PS particle over time, from the initial negative value to a positive value at equilibrium. By fitting the kinetics data to the Langmuir model, the adsorption rate, desorption rate and equilibrium constant were determined. Finally, the adsorption kinetics of several other polymers was investigated. This showed that the presented technique enables direct analysis and comparison of the kinetics of polymer adsorption on the single-particle level.     

Systems of oblate molecules. Monte Carlo study

Monte Carlo (MC) simulations were performed for systems of hard oblate spherocylinders with breadth-to-height ratios φ = 0.5–3.5 and packing fractions y = 0.25–0.45 and for Kihara oblate molecule systems of φ = 1 at reduced temperatures T* = 0.75 and 1.0 and y = 0.05–0.45. The compression factors and the dependence of the average correlation functions on the shortest surface-to-surface distance were determined for the case of hard oblate spherocylinders and the compression factors, residual internal energies and average correlation functions for the case of the generalized Kihara molecule systems. In addition, values of the third virial coefficient of the hard oblate spherocylinders were evaluated in the range of φ = 1–3. Results of the MC simulations for the hard oblate spherocylinders compare well with the available data in the literature and theoretical values; thermodynamic functions of the Kihara molecule systems were determined from the second-order perturbation theory. They agree well with our MC values at lower densities and higher reduced temperatures.     

Study of the ferromagnetic transition in a positionally frozen Heisenberg spin system

Using extensive Monte Carlo simulations with both particle and cluster orientational moves, in conjunction with finite size scaling and histogram reweighting techniques, we have determined the Curie temperature for two models of positionally frozen Heisenberg spin systems: a system with spatial correlations corresponding to a hard sphere fluid and a spatially random system. We find that the results for the positionally frozen hard sphere Heisenberg system are fairly similar to those previously obtained for the Heisenberg spin fluid and quantitatively agree with the mean field theory estimates. The random system undergoes the ferromagnetic transition at a higher temperature since the lack of core repulsion increases the spin correlations. In this case however the mean field theory overestimates by far the critical temperature.     

Solvent effects on model telechelic polymers

A theory to predict the competition between intermolecular and intramolecular hydrogen bonding is extended to mixtures and applied to a model telechelic mixture. The theory is tested by comparing with simulation results for a mixture of fully flexible linear chains that can associate in a hydrogen bonding solvent. The simulation model for the telechelic is a flexible linear tetramer hard sphere chain with two hydrogen bonding sites, one on each terminal segment. The solvent is modelled as a hard sphere with four tetrahedrally arranged hydrogen bonding sites. The solvent is seen to affect the ability of the solute to bond intermolecularly and intramolecularly. The extent of hydrogen bonding and thermodynamic properties of the system were studied using Monte Carlo simulation and compared with predictions from a new statistical mechanics based theory for mixtures. Agreement of simulation and theory is good over the range of densities, temperatures and compositions studied.     

Gibbs ensemble simulation of the vapour-liquid equilibrium of square well spherocylinders

Gibbs ensemble Monte Carlo simulations have been performed for systems of square-well spherocylinders of different length-to-breadth ratio. The results are used to test a recent perturbation theory proposed for this kind of system. In addition, the results are compared to similar simulations performed for a Kihara fluid of elongated molecules. An unexpected good agreement is found for the coexistence thermodynamic and structural properties of both model fluids, hence suggesting that the hard spherocylinder plus square-well interaction should be considered as a reference potential for a perturbative treatment of more complex fluid models.