New effective method for quantitative analysis of diffusion jumps, applied in molecular dynamics simulations of small molecules dispersed in short chain systems

Diffusion jumps of small molecules dispersed in chain molecules or other kinds of slow-moving matrices have already been observed in many previous simulations of such systems, and their treatment led to important qualitative conclusions. In the present work, a new, very simple yet effective method is described, allowing for both identification of individual penetrant jump events and their quantitative treatment in a statistical sense. The method is applied in equilibrium Molecular Dynamics simulations for systems of gaseous alkanes, methane through n-butane, including also a mixture of methane and n-butane, dispersed in n-decane or n-eicosane. Equilibration and attainment of a linear diffusion regime is confirmed by means of various criteria, and the jumps detection method is applied to all systems studied. The results obtained clearly show the existence of distinct jump events in all cases, although the average jump length is reduced with penetrant or liquid alkane molecular weight. The method allows one to determine the average jump length and the corresponding jumps frequency. On the basis of these results, it was possible to estimate a random walk type diffusion coefficient, D(s,jumps), of the penetrants, which was found to be substantially lower compared with the overall diffusion coefficient D(s,MSD) obtained by the mean square displacement method. This finding led us to assume that the overall penetrants' diffusion in the studied systems is a combination of longer jumps with a smoother and more gradual displacement, a result that confirms assumptions suggested in previous studies.     

Quantization of Discretized Spacetimes and theCorrespondence Principle

An algebraic quantization procedure for discretized spacetime models is suggestedbased on the duality between finitary substitutes and their incidence algebras.The provided limiting procedure that yields conventional manifold characteristicsof spacetime structures is interpreted in the quantum algebraic framework as acorrespondence principle.     

Model kinetic study of TiCl4-induced ionization of polyisobutene capped with diphenylethylene application to the synthesis of block copolymers

The use of non-homopolymerizable monomers such as 1,1-diphenylethylene (DPE) in the synthesis of functional polymers and block copolymers by cationic polymerization has been recently reported. The most important parameters in this process, the kinetics and extent of ionization and capping as well as the stability of the cation, were investigated by studying the reaction with TiCl₄ of 1-methoxy-1,1-diphenyl-3,3,5,5-tetramethylhexane, a model for DPE-capped polyisobutene chain-end. This study was performed using ¹H NMR and the high-purity stopped-flow device coupled with UV-visible spectroscopy.     

Acid‐Catalyzed Cyclization of Terpenes Under Homogeneous and Heterogeneous Conditions as Probed Through Stereoisotopic Studies: A Concerted Process with Competing Preorganized Chair and Boat Transition States

Based on stereoisotopic studies and β‐secondary isotope effects, we propose that the acid‐catalyzed cyclization of geranyl acetate proceeds through a concerted mechanism. Under heterogeneous conditions (zeolite Y confinement), a preorganized chairlike transition state predominates, whereas under homogeneous conditions the boat‐ and chairlike transition states are almost isoenergetic. For the case of farnesyl acetate, we propose that under homogeneous conditions a concerted dicyclization occurs with a preorganized boat–chair transition state competing with the chair–chair transition state. Under zeolite confinement conditions, the chair–chairlike dicyclization transition state is highly favorable. The preference of chairlike transition states within the cavities of zeolite Y is attributed to a transition state shape selectivity effect.     

Eigenvalue density of the non-Hermitian Wilson Dirac operator

We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the ? domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and negative chiralities as well as an explicit analytical expression for the number of additional real modes.     

Brownian dynamics simulations of shear-thickening in dilute polymer solutions

A versatile model describing the shear thickening behaviour of dilute polymer solutions in high shear flows is presented. The polymer macromolecules are modelled as Hookean elastic dumbbells which deform affinely during flow. In addition, the dumbbells feel a retractive anisotropic hydrodynamic drag and an isotropic Brownian force. Furthermore, it is assumed that high shear rate increases the probability of molecules forming associations and this is described through expressions for the frequencies of association and dissociation, without explicitly accounting for finite extensibility, hydrodynamic interaction or excluded volume effects. Thus, a reversible kinetic process is incorporated into the model, which results in two diffusion equations for the associated and dissociated dumbbells. Numerical simulations predict shear thickening for specific range of parameters, which are physically meaningful and related to molecular characteristics of the polymer. A comparison against experimental data reported in the literature revealed very promising results, thus confirming the ability of this model to predict shear thickening under a wide range of conditions, for various polymer models.Nomenclature A A factor in the frequency of association - B Frequency of dissociation - B ₀ Reference frequency of dissociation - c Concentration of polymer solution - c _i Concentration of singlets (i = 1) and doublets (i = 2) in the solution - c ^* The overlap concentration - D _t Translation coefficient of molecule - F _i (Q) Spring force for a singlet (i = 1) and for a doublet (i = 2) - F Frequency of association - F ₀ Reference frequency of association - H _i Dumbbell spring constant for a singlet (i = 1) and for a doublet (i = 2) - k Boltzman's constant - k _H Huggins constant - MW Molecular weight - MW _c Critical molecular weight for formation of entanglements - n Number density of molecules in the polymer solution - n ₀ Number density of dumbbells at equilibrium - n _i Number density of singlets (i = 1) and doublets (i = 2) - Q Vector defining the size and orientation of a dumbbell - t Time - T Absolute temperature - x Degree of multimerization - W Interaction energy between the two components of a doublet Greek letters a Dimensionless anisotropy parameter - Shear rate - _i Friction coefficient of singlets (i = 1) and doublets (i = 2) - _i Intrinsic viscosity of singlets (i = 1) and doublets (i = 2) - _red Reduced viscosity of solution - _sp Specific viscosity - Viscosity of the polymer solution of concentration c - _s Viscosity of the solvent - (t) White noise - K ^T Velocity gradient tensor - _Hi Time constant of a singlet (i = 1) and a doublet (i = 2) - ₁ Length scale of singlets (standard deviation of singlet lengths at equilibrium) - ₂ Length scale of doublets - T _p Stress tensor - T _xy Shear Stress (xy element of T _p ) - T _pi Contributions to the stress tensor of singlets (i = 1) and doublets (i = 2) - ₀ Equilibrium configuration distribution function of Q - _i Configuration distribution function of singlets (i = 1) and doublets (i = 2)     

Preparation and certification of new thorium isotopic reference materials

Preparation of two Isotopic Reference Materials of thorium has been performed, starting from highly enriched ²³²Th (99.99%) and ²³⁰Th (99.8%). After full characterization (chemical and isotopic) of these purified base materials the thorium nitrate was transformed to thorium dioxide. Accurately weighed amounts of the two isotopes in the dioxide form were subsequently dissolved in nitric acid and resulted in solutions with amount ratios n(²³⁰Th)/n(²³²Th) close to 10^–5 (IRMM-035) and 3 · 10^–6 (IRMM-036). These gravimetrically prepared ratios were finally verified by means of Thermal Ionization Mass Spectrometry (TIMS). The purpose of the Reference Materials is to calibrate thorium isotope amount ratio measurements. Received: 7 July 1997 / Revised: 1 December 1997 / Accepted: 7 December 1997     

Synthesis,characterization and crystal structures of two 2‐naphthyl substituted pyrazoles

The synthesis, characterization and X‐ray crystal structures of two 2‐naphthyl‐substituted pyrazoles ‐ 3‐(2‐naphthyl) pyrazole ( 1 ) and 5‐(2‐naphthyl)‐3‐trifluoromethyl‐pyrazole ( 3 ) ‐ are reported. In addition, the isolation and structural characterization of 5‐hydroxy‐3‐(2‐naphthyl)‐5‐trifluoromethyl‐4,5‐dihydropyrazole ( 2 ), an intermediate of the synthesis of 3 , is included. Two simple methods of dehydration of 2 are also presented.