A nucleophilic substitution reaction in microemulsions based on either an alcohol ethoxylate or a sugar surfactant

A nucleophilic substitution reaction between 4-tert-butylbenzyl bromide and a series of iodide salts has been performed in oil-in-water microemulsions based on either a fatty alcohol ethoxylate or a sugar surfactant. The reaction kinetics was compared with the kinetics of the same reaction performed in a microhomogeneous reaction medium, d-MeOH. Previous results showing a particularly high reactivity in the microemulsion based on the fatty alcohol ethoxylate was confirmed. It was shown that in both microemulsions the reaction rate was almost independent of the choice of counterion to iodide. This indicates that complexation of the cation with the surfactant headgroup, which, in particular, could have taken place with surfactants containing oligooxyethylene chains (a “crown ether effect”), seems not to be of importance.

¹²⁷I NMR studies, as well as quadrupole splitting experiments performed by ²H NMR, indicate that there is a certain accumulation of iodide at the oil–water interface of the microemulsions. It is difficult to draw any quantitative conclusions in this respect, however.

The results obtained in this study, combined with results from previous investigations of the same reaction, indicate that the unexpectedly high reactivity obtained in the microemulsion based on a surfactant containing an oligooxyethylene headgroup is most probably due to the nucleophile being poorly solvated when present in the headgroup layer of such a microemulsion. Poorly solvated anions are known to be highly reactive nucleophiles.     

Dirichlet forms,quasiregular functions and Brownian motion

Summary Given a quasiregular function on an open setU in ⁿ it is shown that there exists a diffusionX _t inU such that mapsX _t inton-dimensional Brownian motion. The process is constructed from a Dirichlet form which can be described explicitly. This enables us to apply stochastic methods in the investigation of quasiregular mappings. Some examples of applications are given, including boundary behaviour and value distribution.     

An adaptive kernel-split quadrature method for parameter-dependent layer potentials

Advances in Computational Mathematics - It is well known in the literature that standard hierarchical matrix ( ${\mathscr{H}}$ -matrix)-based methods, although very efficient for asymptotically...     

Data parallel large-scale molecular dynamics for liquids

An efficient data parallel computational scheme is presented for large-scale molecular dynamics (MD ) simulations of liquids with short-range interactions. The method is based on decomposition of the simulation cell into equally sized subcells, with the shortest side length equal to the cutoff radius. Inter- and intracell interactions are calculated in a coarse-grained manner. A geometric sorting procedure, based on particle distances to subcell boundaries, is used to minimize the overall computations and the nonproductive communications. Using only nearest-neighbor communications, an efficient scheme is developed for periodic updates of the contents of subcells due to the migration of particles. Special “null-particles” are introduced, which act as buffers during the periodic updates and allow for a globally uniform algorithm during the calculations. Communication cost is about 7% of the total CPU time. The method is found to be linearly scalable with the number of particles, performing better as the ratio of virtual to physical processors increases. The MD code is written in Fortran 90 and implemented on a CM-200. The overall speed is approximately 5.9 μs. per MD step and per particle for 1 million particles and 5.5 μs for 5 million particles. The method should be easily transferred to other massively parallel computers of SIMD and MIMD type. © 1993 John Wiley & Sons, Inc.     

DNA-binding of semirigid binuclear ruthenium complex delta,delta-[mu-(11,11'-bidppz)(phen)(4)ru(2)](4+): extremely slow intercalation kinetics

We here report a remarkably slow rearrangement of binding modes for a binuclear ruthenium(II) complex upon interaction with DNA. It has been previously shown that Delta,Delta-[mu-(11,11'-bidppz)(phen)4Ru2]4+ binds to DNA in one of the grooves. However, we find that this is only an initial, metastable, binding mode, which is extremely slowly reorganized into an intercalative binding geometry. The slow rearrangement and dissociation, revealed by flow linear dichroism and fluorescence spectroscopy, are concluded to be a result from the complex being threaded through the DNA, with one of the bridging aromatic dppz ligands intercalated between the base pairs of the DNA, placing one metal center in the minor groove and one in the major groove. A negative LD, a high luminescence quantum yield, and long luminescence lifetimes, similar to the intercalating complex Delta-[Ru(phen)2dppz]2+, indicate intercalation of the bidppz moiety. The unique slow dissociation of the complex in its final DNA-binding mode suggests that this class of threading, partially intercalated binuclear complexes may be interesting in the context of cancer therapy. Also, their unique optical and photophysical properties could make such complexes, either alone or scaffolded by DNA structures, of interest for the development of nanometer-sized molecular optoelectronic devices.     

Optimizing the efficiency of femtosecond-laser-written holograms

Computer-generated binary holograms are written on a polished copper surface using single 800-nm, 120-fs pulses from a 1-kHz-repetition-rate laser system. The hologram efficiency (i.e. the power in the holographic reconstructed image relative to the incoming laser power) is investigated for different laser-structuring parameters. Theoretical diffraction grating efficiencies for a binary amplitude grating show good agreement with the experimental measurements for diameters of the laser-formed holes below the pitch. Modelling based on straightforward geometrical arguments is used to find the optimal hole size. For a coverage (i.e. relative laser-structured area) of ～43 %, the efficiency reaches ～10 %, which corresponds to a relative power transferred to one reconstructed image of ～20 %. The efficiency as a function of pitch (for fixed coverage) is fairly constant from 2 to 6 μm.     

Potential solutions to improved sound performance of volume based lightweight multi-storey timber buildings

Lightweight building systems in general suffer from poor sound insulation, especially in the low frequency region. Since no reliable mathematical models that can predict the impact sound pressure level exists, the lightweight building design is to a high extent based upon previous experience and upon measurements. A special difficulty is related to experimental measurements since the variation among identical units must not be neglected. A modern volume based lightweight wooden building concept has here been tested by numerous well controlled measurements, in laboratory as well as in more field like conditions. The volume construction technique offers new possibilities and challenges to improve sound insulation in light weight timber construction. The main purpose was to investigate how different constructional solutions in the floor, like plaster board, mineral wool, elastic glue, dividing board, floating floor etc., affect the sound insulation. Many of the tested modifications resulted in only marginally changed impact sound pressure level but parameters that substantially can improve the sound insulation were found in using elastic glue to mount the floor boards, to install extra board layers and to use floating floors.     

Superfluidity of 3He in dilute solutions of 3He in liquid 4He

The possibility of superfluidity of ³He in dilute solutions of ³He in liquid ⁴He is investigated, and the corresponding critical temperature is estimated. The results indicate S-state pairing, i.e., for small concentrations of ³He, the highest transition temperature is obtained for L = 0, but the obtained critical temperatures are very low.     

Some Remarks on SLE Bubbles and Schramm’s Two-point Observable

Simmons and Cardy recently predicted a formula for the probability that the chordal SLE_8/3 path passes to the left of two points in the upper half-plane. In this paper we give a rigorous proof of their formula. Starting from this result, we derive explicit expressions for several natural connectivity functions for SLE_8/3 bubbles conditioned to be of macroscopic size. By passing to a limit with such a bubble we construct a certain chordal restriction measure and in this way obtain a proof of a formula for the probability that two given points are between two commuting SLE_8/3 paths. The one-point version of this result has been predicted by Gamsa and Cardy. Finally, we derive an integral formula for the second moment of the area of an SLE_8/3 bubble conditioned to have radius 1. We evaluate the area integral numerically and relate its value to a hypothesis that the area follows the Airy distribution.