A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Absolutely indecomposable symmetric matrices

Let A be a symmetric matrix of size n×n with entries in some (commutative) field K. We study the possibility of decomposing A into two blocks by conjugation by an orthogonal matrix T∈Mat_n(K). We say that A is absolutely indecomposable if it is indecomposable over every extension of the base field. If K is formally real then every symmetric matrix A diagonalizes orthogonally over the real closure of K. Assume that K is a not formally real and of level s. We prove that in Mat_n(K) there exist symmetric, absolutely indecomposable matrices iff n is congruent to 0, 1 or −1 modulo 2s.     

Determination of coumarins by voltammetric techniques in micellar and emulsified media

An electroanalytical study of the oxidation processes of umbelliferone and hymecromone at a glassy carbon electrode in micellar solution and emulsified medium by different voltammetric techniques is described. The non-ionic surfactant Triton X-405 in acetate-buffered medium at pH 4.8 was found to be the most suitable. Different ranges of linearity were obtained in the micellar solutions, depending on the technique used; the limits of determination for differential pulse voltammetry (DPV) at a stationary electrode were 2.9×10^?6 mol l^?1 and 3.3×10^?6 mol l^?1 for umbelliferone and hymecromone, respectively. In the emulsified medium formed with a mixture of toluene and ethyl acetate (3:2), the oxidation processes yielded similar results. With DPV, linear calibration plots were obtained in the ranges 1.0×10^?5–9.0×10^?7 mol l^?1 umbelliferone and 1.0×10^?5–2.0×10^?6 mol l^?1 hymecromone. The media used are predominantly aqueous so that special reference electrodes and solvent purification are not needed.     

Synthesis of Some C‐3,4,5‐Substituted 2,6‐Dimethyl‐1,4‐dihydropyridines (4‐DHPs)

A series of C‐3,4,5‐substituted 2,6‐dimethyl‐1,4‐dihydropyridines (1,4‐DHPs) with pharmacological properties were prepared by a variation from the classical Hantzsch synthesis. The procedure involves treatment of the respective aldehyde with either ethyl‐3‐aminocrotonate or 3‐aminocrotonitrile in anhydrous acetic acid at temperatures not exceeding 60°C, thus minimizing by‐product formation. The structures of title compounds were elucidated by ¹H NMR, ¹³C NMR, FTIR, and elemental analysis.     

New chiral Schiff's bases with a 1,3,4‐thiadiazole ring in the mesogenic core: synthesis,mesomorphic and ferroelectric properties

Two new homologous series of chiral esters derived from Schiff's bases containing a 1,3,4‐thiadiazole unit (series 6 and 7) were synthesized and their liquid crystalline and ferroelectric properties investigated. All the compounds of series 6 exhibit SmC*–SmA dimorphism and the compounds of series 7 exhibit a SmC* phase. All the compounds of these series are ferroelectric liquid crystals.     

Columnar liquid crystalline benzenetrisamides with pendant 1,3,4-oxadiazole groups

Novel liquid crystal materials based on 1,3,5-benzenetrisamide derivatives with three pendant 2-phenyl-5-(mono-, di-, and/or tri-n-alkoxyphenyl)-1,3,4-oxadiazole arms (Ia–c, IIa–c) were prepared. The mesomorphic properties of these compounds were characterised and studied by differential scanning calorimetry, polarising optical microscopy and X-ray diffraction. The formation of a columnar mesophase was found to be dependent on the number of alkoxy side chains. The compounds Ib and IIb, with a total of six alkoxy chains, and compounds Ic and IIc, with nine alkoxy chains, exhibited an enantiotropic hexagonal columnar (Col_h ) phase with high isotropisation temperatures; however, compounds Ia and IIa with a total of three alkoxy chains formed a crystalline phase. Compounds IIb and c were room temperature liquid crystals.     

Columnar liquid crystals based on amino-1,3,4-thiadiazole derivatives

Novel liquid crystal materials base on amino-thiadiazoles, specifically 5-(3,4-di-, and/or 3,4,5-tri-n-alkoxy)phenyl-2-amino-1,3,4-thiadiazoles (3a–f, n?=?10, 12, 14) and 5-(3,4-di- and/or 3,4,5-tri-n-alkoxy)phenyl-2-(4-amino)phenyl-1,3,4-thiadiazoles (6a–f, n?=?10, 12, 14) were synthesised. The mesomorphic properties of these compounds were studied by differential scanning calorimetry and polarising optical microscopy. All the compounds in series 3a–f and series 6a–f display an enantiotropic columnar phase. The mesomorphic properties were found to be dependent on the number of the side alkoxy chains, and on the length of the rigid core, and on the position of the thiadiazole ring. The best results were obtained with compounds of series 3a–f.     

Stability bands for moving solitons in uniform and inhomogeneous damped ac-driven circular Toda lattices

By means of systematic simulations, we study the motion of discrete solitons in weakly dissipative Toda lattices (TLs) with periodic boundary conditions, resonantly driven by a spatially staggered time-periodic (ac) force. A complex set of alternating stability bands and instability gaps, including scattered isolated stability points, is revealed in the parametric plane of the soliton’s velocity and forcing amplitude for a given size of the circular lattice. The analysis is also reported for the circular TL including a single light- or heavymass defect. The stability chart as a whole shrinks and eventually disappears with the increase of the lattice’s size and strength of the mass defect. Qualitative explanations to these findings are proposed. We also report the dependence of the stability area on the initial position of the soliton, finding that the area is largest for some intersite position. For a pair of solitons traveling in opposite directions, there exist regimes where both solitons survive periodic collisions in small-size lattices.     

Bilevel multiplicative problems: A penalty approach to optimality and a cutting plane based algorithm

Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure. They are characterised by the existence of two optimisation problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimisation problem. In this paper we focus on the class of bilevel problems in which the upper level objective function is linear multiplicative, the lower level one is linear and the common constraint region is a bounded polyhedron. After replacing the lower level problem by its Karush–Kuhn–Tucker conditions, the existence of an extreme point which solves the problem is proved by using a penalty function approach. Besides, an algorithm based on the successive introduction of valid cutting planes is developed obtaining a global optimal solution. Finally, we generalise the problem by including upper level constraints which involve both level variables.