On the Wang–Uhlenbeck Problem in Discrete Velocity Space

The arguably simplest model for dynamics in phase space is the one where the velocity can jump between only two discrete values, ±v with rate constant k. For this model, which is the continuous-space version of a persistent random walk, analytic expressions are found for the first passage time distributions to the origin. Since the evolution equation of this model can be regarded as the two-state finite-difference approximation in velocity space of the Kramers–Klein equation, this work constitutes a solution of the simplest version of the Wang–Uhlenbeck problem. Formal solution (in Laplace space) of generalizations where the velocity can assume an arbitrary number of discrete states that mimic the Maxwell distribution is also provided.     

Monte Carlo simulation of the two-dimensional Potts model using nonextensive statistics

The standard Potts model is investigated in the framework of nonextensive statistical mechanics. We performed Monte Carlo simulations on two-dimensional lattices with linear sizes ranging from 16 to 64 using the Metropolis algorithm, where the classical Boltzmann–Gibbs transition probabilities were modified for the nonextensive case. We found that the Potts model undergoes a phase transition in the nonextensive scenario. We established the order of the phase transition and we computed the critical temperature for different values of the Tsallis entropic index.     

Convenient synthesis of 1-alkoxy-di- and tetrahydrophosphinine 1-oxides by ring enlargement

The double bond of the P-alkoxy 3,4-dimethyl-2,5-dihydro-1H-phosphole 1-oxides reacts easily with dichlorocarbene to give two diastereomers of an unstable adduct useful in the synthesis of ring expanded products, such as 1,2-dihydrophosphinine oxides or 1,2,3,6-tetrahydrophosphinine oxides. The former can be prepared by thermolysis of the adducts, while the latter are obtained by cyclopropane ring opening effected by silver nitrate in an alcoholic solvent. The preparation of the double-bond isomers of 1-alkoxy-tetrahydrophosphinine oxides containing only one methyl substituent in the ring is also described. The reaction of dihydro-1H-phosphole oxides with dichlorocarbene can be modified to give P-alkoxy 1,4-dihydrophosphinine oxides in an unexpected reaction.     

ChemInform Abstract: Equilibrium Structure and Torsional Barrier of BH3NH3.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

Unexpected condensation reaction of two units of 1,2‐dihydrophosphinine 1‐oxides in the presence of tetracyanoethylene

In the presence of tetracyanoethylene, the reaction of two molecules of dihydrophosphinine oxide 2B followed an unexpected route to afford diphosphatricyclododecatrienes 4 instead of the corresponding Diels–Alder cycloadducts ( 3 ). Structures of the products ( 4 ) have been elucidated by a joint application of spectroscopy and quantum chemical calculations. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:29–35, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10062     

ChemInform Abstract: Chemical Vapor Deposition of Gallium Nitride from the GaCl3 + NH3 System. Theoretical Study of the Structure and Thermodynamics of Potential Intermediates Formed in the Gaseous Phase.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

P-Substituted 3-phosphabicyclo [3.1.0] hexane 3-oxides from diastereoselective substitution at phosphorus

Preparation of P-amino-3-phosphabicyclo[3.1.0]-hexane 3-oxides either by addition of dichlorocarbene to the double bond of 1-amino-2,5-dihydro-1H-phosphole 1-oxides or by substitution of the P-chloro derivative of the bicyclic system was accomplished. Two different diastereomers are obtained by the two approaches; their ¹³C NMR spectra were interpreted on the basis of the P-ethoxy isomers, whose structures were confirmed by X-ray analysis. The P-hydroxy adduct was also prepared, and it was found that intermolecular O H … O hydrogen bonding connects the molecules together in the solid phase. This effect eliminates the possibility of diastereoisomerism, as was also observed in the case of P-hydroxy tetrahydrophosphinine oxides. Thermolysis of the P-hydroxy adduct is a better way to synthesize 1-hydroxy-1,2-dihydrophosphinine oxides than by hydrolysis of the phosphinic chlorides.     

Liquid-liquid phase equilibria in polymer solutions and polymer mixtures

The pressure dependence of liquid-liquid equilibria in weakly interacting binary macromolecular systems (homopolymer solutions and blends) will be discussed. The common origin of the separate high-temperature/low-temperature and high-pressure/low-pressure branches of demixing curves will be demonstrated by extending the study into the region of metastable liquid states including the undercooled, overheated and stretched states (i.e. states at negative pressures). The seemingly different response of the UCST-branch of solutions and blends when pressurized (pressure induced mixing for most polymer solutions, pressure induced demixing for most blends) will be explained in terms of the location of a hypercritical point found either at positive (most solutions) or negative pressure (most blends). Further, it is shown that the pressure dependence of demixing of homopolymer solutions and blends may be described using a ‘master-curve’ which, however, is sometimes partly masked by degradation or by vapour-liquid and/or solid-liquid phase transitions. Experimental results demonstrating the extension of liquid-liquid phase boundary curves into the metastable regions will be presented, and the existence of solubility islands in the vicinity of the hypercritical points discussed.