From random to self-avoiding walks

A brief review will be given of the current situation in the theory of self-avoiding walks (SAWs). The Domb-Joyce model first introduced in 1972 consists of a random walk on a lattice in which eachN step configuration has a weighting factor Π _i=0 ^N?2 Π_j=i+2/N(1?ωδ_ij). Herei andj are the lattice sites occupied by the ith and jth points of the walk. When ω=0 the model reduces to a standard random walk, and when ω=1 it is a self-avoiding walk. The universality hypothesis of critical phenomena will be used to conjecture the behavior of the model as a function ofω for largeN. The implications for the theory of dilute polymer solutions will be indicated.     

Charge Dispersal in the Quinuclidine Radical Cation and in the Quinuclidinium Ion,as Revealed by PE and ICR Spectroscopy

The n ionization energies I and the gas-phase basicities GB of CH₃-, Cl-, or CN-substituted quinuclidines have been measured by PE and ICR spectroscopy. The dependence of the shifts ΔI and ΔGB (relative to the values of the parent molecule) allow conclusions about the charge dispersal accompanying the n ionization or the protonation of quinuclidine in the gas phase. The agreement with the results of a minimal basis set ab initio calculation is excellent. Comparison of the solution pK_a values with either I or GB reveals that 2-substituted quinuclidines exhibit sizeable solvent-induced proximity effects, i.e. that the corresponding quinuclidinium ions are more acidic in solution than expected on the basis of the gas-phase basicities. This agrees with earlier results concerning 2-substituted pyridines.     

A route to annulated indoles via a palladium-catalyzed tandem alkylation/direct arylation reaction

A norbornene-mediated palladium-catalyzed tandem alkylation/C-H functionalization sequence is described, in which an alkyl-aryl bond and a heteroaryl-aryl bond are formed in one pot. A variety of highly substituted six- and seven-membered ring annulated indoles were synthesized in good yields from bromoalkyl indoles and aryl iodides.     

Carbon Participation in the Solvolysis of 6- and 7-Substituted 2-Norbornyl p-Toluenesulfonates. Norbornanes,Part 11

The solvolysis rates and products of several 7-anti-substituted 2-endo-norbornyl p-toluenesulfonates 11 have been determined and compared with those of the previously reported 6-exo-substituted 2-exo-norbornyl p-toluenesulfonates 1. Although the number of bonds between the substituent and the reaction site is the same in the two series, the inductive effect of the substitutents is transmitted far more strongly in the 6-exo-2-exo-series 1 than in the 7-anti-2-endo-series 11 ; i.e. their inductivities differ widely. It is concluded that through space induction involves graded bridging of the substituent-bearing C-atom to the incipient cationic center at C(2) and that this involves differential bridging strain. The different reactivities of unsubstituted 2-exo- and 2-endo-norbornyl derivatives can then be ascribed to a stereoelectronic effect.     

Conics in finite projective planes

There does not exist a general theory of conics in finite projective planes, because the many definitions of conics which are equivalent in desarguesian projective planes yield different types of conics in more general situations. Thus even the use of the word conic can lead to confusion, particularly in the finite case. This note is an attempt to clarify these various definitions and give as an example in a finite projective plane a von Staudt conic which is not an Ostrom conic. We conjecture that any finite projective plane admitting an Ostrom conic must be desarguesian.     

One-Dimensional Particle Processes with Acceleration/Braking Asymmetry

The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental Diagram of traffic and to be associated to hysteresis effects of traffic flow. We study this question in the context of exclusion and queueing processes, by including an asymmetry between deceleration and acceleration in the formulation of these processes. For exclusions processes, this corresponds to a multi-class process with transition asymmetry between different speed levels, while for queueing processes we consider non-reversible stochastic dependency of the service rate w.r.t. the number of clients. The relationship between these 2 families of models is analyzed on the ring geometry, along with their steady state properties. Spatial condensation phenomena and metastability are observed, depending on the level of the aforementioned asymmetry. In addition, we provide a large deviation formulation of the fundamental diagram which includes the level of fluctuations, in the canonical ensemble when the stationary state is expressed as a product form of such generalized queues.     

Synthesis and structure–property relationship of carbazole‐alt‐benzothiadiazole copolymers

A series of four π‐conjugated carbazole‐alt‐benzothiadiazole copolymers (PCBT) were prepared by Suzuki cross‐coupling reaction between synthesized dibromocarbazoles as electron‐rich subunits and 4,7‐bis(4,4,5,5‐tetramethyl‐1,3,2‐dioxaborolan‐2‐yl)?2,1,3‐benzothiadiazole as electron‐deficient subunits. The subunits were directly linked through 2,7‐ or 3,6‐ positions of the carbazole. In addition, the carbazole monomers have been N‐substituted by a branched or a linear side‐chain. The chemical structure of the copolymers and their precursors was confirmed by NMR and IR spectroscopies, and their molar masses were estimated by SEC. Thermal analysis under N₂ atmosphere showed no weight loss below 329°C, and no glass transition was observed in between 0 and 250°C. The band gaps of all PCBTs evaluated by optical spectroscopies and by cyclic voltammetry analysis were consistent with expectations and ranged between 2.2 and 2.3 eV. Finally, 2,7 and 3,6 linkages were shown to influence optical properties of PCBTs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2059–2068     

Characterization of polyoxometalate/polymer photo-composites: A toolbox for the photodegradation of organic pollutants

Different inorganic/organic photocomposites based on polyoxometalate (POM) nanoparticles have been developed for photocatalytic applications. Currently, polyoxometalate nanoparticles have been successfully in-situ embedded into an acrylate polymer network by photopolymerization upon mild visible light irradiation at 405 nm. The proposed POM/polymer photocomposites have been characterized using complementary techniques for a better understanding of their photocatalytic activity. Interestingly, the obtained photocomposites exhibit high rigidity, excellent thermal stability, a non-negligible porosity and new functionalities such as light reactivity and redox properties. Moreover, developed composites showed efficient catalytic activity for the color removal of aqueous solutions of erythrosine and rose Bengal under Light Emitting Diodes LED@375 nm irradiation reaching 80 and 90% as a final color removal, respectively.