Aqueous solutions of ionic liquids: study of the solution/vapor interface using molecular dynamics simulations

We performed a detailed molecular dynamics study of the interfacial structure of aqueous solutions of 1-butyl-3-methylimidazolium tetrafluoroborate in order to explain the anomalous dependence of the surface tension on concentration. At low concentrations the surface tension decreases with concentration. At higher concentrations the surface becomes saturated; a plateau is observed in simulations with a non-polarizable force field while a possible increase is detected in simulations with a polarizable force field. The structure is characterized by a surplus of cations at the surface (with hydrophobic butyl chains pointing toward vacuum) which at low concentrations is only partly compensated by the anions because of asymmetric solvation. A more hydrophobic 1-butyl-3-methylimidazolium hexafluorophosphate is also simulated for comparison.     

All-optical wavelength converter based on fiber cross-phase modulation and fiber Bragg grating

I present new method of phase modulation to amplitude modulation conversion (PM/AM conversion) that utilizes integrating capabilities of fiber Bragg grating (FBG). I found that the wavelength converter based on fiber cross-phase modulation (XPM) and new method of PM/AM conversion have an order of magnitude higher conversion efficiency then the wavelength converter based on sideband filtration method and up to 6 dB higher conversion efficiency then the converter based on the nonlinear optical loop mirror. Numerical analysis and experimental results are provided for bit rates up to 40 Gb/s.     

Small-angle X-ray scattering and light scattering on lysozyme and sodium glycocholate micelles

Small-angle X-ray scattering (SAXS) together with static (SLS) and dynamic light scattering (DLS) measurements were carried out on aqueous solutions of lysozyme (LY) and of the ionic biological detergent sodium glycocholate (NaGC). Apparent diffusion coefficients (D app), excess Rayleigh ratio, and SAXS spectra were measured for 0.1 M NaGC solutions at different ionic strengths (0.05-0.30 M NaCl). The same data were collected for LY in sodium acetate buffer 50 mM without and with 92 mM NaCl as a function of protein concentration (10-80 g L(-1)). A correlated analysis of SLS data and SAXS spectra was first tested on the LY samples and then extended to the interpretation of the NaGC data to infer information on particle structure and interaction potential. A hard-core (HC) interaction shell of uniform thickness, a screened Coulomb potential of the electric double layer (EDL) or the complete DLVO potential were alternatively used to represent the long-range tail of the interaction potential. Whenever an essentially repulsive tail is expected, all the representations give reasonable results, but the data analysis does not allow the discrimination between the oblate and the prolate symmetries of the NaGC aggregates. The DLVO model allows the interpretation of the data even when the attractive component determines the tail character. With this model an overall fit of the micelle data at all the NaCl concentrations was successfully performed by assuming a simple spherical symmetry of the micelles and invariant values of their ionization degree and Hamaker constant, thus considering just the screening effect of the added electrolyte. Whatever model is used, the results point out that the aggregates are quite hydrated (26-38 water molecules per monomer) and very slightly grow by increasing the NaCl concentration. When spherical symmetry is assumed the aggregate radii for all the samples fall in the range 15-16 A. From the SAXS and SLS, best fitting geometrical parameters, and interparticle structure factor, a D app value was calculated for each sample. An excellent consistence is achieved for LY results. On the contrary, calculated D app values systematically lower than the experimental values are always obtained for the NaGC micelles. Micelle polydispersity and internal dynamics seem to be the most probable reasons of the bad agreement.     

On Groups Admitting a Fixed-Point-Free Elementary 2-Group of Automorphisms

We give a short proof that if G is a finite group of derived length k and if G admits a fixed-point-free action of the elementary group of order 2 ⁿ , then G has a normal series of length n all of whose quotients are nilpotent of class bounded in terms of k and n only.     

Optimal Control Problems for a Class of Semilinear Multisolution Elliptic Equations

We study the optimal control problem for a class of elliptic problems that may possess multiple solutions. We obtain necessary conditions for optimal control by constructing a related parabolic problem and using known results for the parabolic problem.     

An experimental and theoretical study of stereoselectivity of furan-maleic anhydride and furan-maleimide diels-alder reactions

The stereoselectivity of the reaction of furan (1) with maleic anhydride (2) and maleimide (3) was studied experimentally and theoretically. Although the two reactions are highly similar with regard to their preference for endo and exo steroisomers, notable differences were experimentally observed and explained on the basis of calculated reaction-free energies and transition-state barriers. The experimental values of rate constants (k(1+2endo) = (1.75 +/- 0.48) x 10(-5); mol(-1) l s(-1); k(1+2exo) = (3.10 +/- 0.55) x 10(-5); mol(-1) l s(-1); k(1+3endo) = (1.93 +/- 0.082) x 10(-5); mol(-1) l s(-1), k(1+3exo) = (1.38 +/- 0.055) x 10(-5); mol(-1) l s(-1) all at 300 K) and the observed reaction course clearly confirm that neither of these reactions are prototypical examples of Diels-Alder [4 + 2] cycloadditions, whose dominant preference is for endo isomers. However, only by comparing their energetics-calculated at the CCSD(T) level of theory-with the analogous reactions involving cyclopentadiene (8) as a diene can these observations be understood. The low thermodynamic stability of furan [4 + 2] adducts opens retro-Diels-Alder reaction channels and overrules the very small kinetic preference (calculated and measured here) of initial formation for endo stereoisomers. On a macroscopic scale "an irregular"-thermodynamically more stable-exo stereoisomer was consequently observed as a dominant species.     

Mathematical modeling of volumetric material growth

Growth (resp. atrophy) describes the physical processes by which a material of solid body increases (resp. decreases) its size by addition (resp. removal) of mass. In the present contribution, we propose a sound mathematical analysis of growth, relying on the decomposition of the geometric deformation tensor into the product of a growth tensor describing the local addition of material and an elastic tensor, which is characterizing the reorganization of the body. The Blatz-Co hyperelastic constitutive model is adopted for an isotropic body, satisfying convexity conditions (resp. concavity conditions) with respect to the transformation gradient (resp. temperature). The evolution law for the transplant is obtained from the natural assumption that the evolution of the material is independent of the reference frame. It involves a modified Eshelby tensor based on the specific free energy density. The heat flux is dependent upon the transplant. The model consists of the constitutive equation, the energy balance, and the evolution law for the transplant. It is completed by suitable boundary conditions for the displacement, temperature and transplant tensor. The existence of locally unique solutions is obtained, for sufficiently smooth data close to the stable equilibrium. The question of the global existence is examined in the simplified situation of quasistatic isothermal equations of linear elasticity under the assumption of isotropic growth.     

Comparison of mild extraction procedures for determination of plant-available arsenic compounds in soil

In this work three mild extraction agents for determination of plant-available fractions of elements in soil were evaluated for arsenic speciation in soil samples. Pepper (Capsicum annum, L.) var. California Wonder was cultivated in pots, and aqueous solutions of arsenite, arsenate, methylarsonic acid, and dimethylarsinic acid, at a concentration of 15 mg As kg^–1 soil, were added at the beginning of the experiment. Control pots (untreated) were also included. Deionized water, 0.01 mol L^–1 CaCl₂, and 0.05 mol L^–1 (NH₄)₂SO₄ were used to extract the plant-available fraction of the arsenic compounds in soil samples collected during the vegetation period of the plants. Whereas in control samples the extractable arsenic fraction did not exceed 1% of total arsenic content, soil amendment by arsenic compounds resulted in extraction of larger amounts, which varied between 1.4 and 8.1% of total arsenic content, depending on soil treatment and on the extracting agent applied. Among arsenic compounds determined by HPLC–ICPMS arsenate was predominant, followed by small amounts of arsenite, methylarsonic acid, and dimethylarsinic acid, depending on the individual soil treatment. In all the experiments in which methylarsonic acid was added to the soil methylarsonous acid was detected in the extracts, suggesting that the soil bacteria are capable of reducing methylarsonic acid before a further methylation occurs. No significant differences were observed between analytical data obtained by using different extraction procedures.     

The Influence of Heat Pre-Treatment on the Sorption of Water Vapour on Bentonite

Sorption isotherms of water vapour on bentonite from the Rokle locality of northwest Bohemia in the Czech Republic were measured and analysed after being treated with heat. Protracted sorption measurements were performed at 30∘C in the range of water vapour relative pressures between 0.12 and 0.94. Prior to sorption measurements, the bentonite samples were exposed to flowing dry nitrogen for 18 hours at 115, 220 and 300∘C. Compared to the sample heated at 115∘C, the bentonite samples that were treated at 220 and 300∘C exhibited a decrease in water vapour sorption capacity. This decrease in sorption capacity was accompanied by structural changes that were confirmed by X-ray diffraction analysis.     

Topological Expansion in the Complex Cubic Log–Gas Model: One-Cut Case

We prove the topological expansion for the cubic log–gas partition function

$$\begin{aligned} Z_N(t)= \int _\Gamma \cdots \int _\Gamma \prod _{1\le j<k\le N}(z_j-z_k)^2 \prod _{k=1}^Ne^{-N\left( -\frac{z^3}{3}+tz\right) }\mathrm{dz}_1\cdots \mathrm{dz}_N, \end{aligned}$$

where t is a complex parameter and \(\Gamma \) is an unbounded contour on the complex plane extending from \(e^{\pi \mathrm{i}}\infty \) to \(e^{\pi \mathrm{i}/3}\infty \). The complex cubic log–gas model exhibits two phase regions on the complex t-plane, with one cut and two cuts, separated by analytic critical arcs of the two types of phase transition: split of a cut and birth of a cut. The common point of the critical arcs is a tricritical point of the Painlevé I type. In the present paper we prove the topological expansion for \(\log Z_N(t)\) in the one-cut phase region. The proof is based on the Riemann–Hilbert approach to semiclassical asymptotic expansions for the associated orthogonal polynomials and the theory of S-curves and quadratic differentials.