Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

能量连续传递的超分子人工光捕获系统构筑及其在光催化反应中应用

光捕获系统在自然界光合作用过程中起着至关重要的作用.模拟自然界的光捕获体系,在生物成像、发光器件、光催化以及解决人类面临的能源问题等方面均具有重要意义[1].目前,在水相中构筑高效的人工光捕获系统已取得一系列重要进展[2].然而,为了更好地理解并模拟自然界中以多通道信息通讯为特征的捕光天线系统[3],构筑具有多步连续能量转移特征并能实现光能到化学能转化的人工光捕获体系仍然是一项具有挑战性的工作.     

Shedding Light on the Origin of Solid-State Luminescence Enhancement in Butterfly Molecules

Different molecular strategies have been carefully evaluated to produce solid-state luminescence enhancement (SLE) in compounds that show dark states in solution. A set of α-phenylstyrylarene derivatives with a butterfly shape have been designed and synthesised, for the first time, with the aim of improving the solid-state fluorescence emission of their parent styrylarene compounds. Although these butterfly molecules are not fluorescent in solution, one of them (1,2,4,5-tetra(α-phenylstyryl)benzene) exhibits a fluorescence quantum yield as high as 68 % in a drop-cast sample and 31 % in its crystalline form. In contrast, 1,3,5-tris(α-phenylstyryl)benzene and 4,6-bis(α-phenylstyryl)pyrimidine do not show SLE. A range of fluorescence spectroscopy experiments and DFT calculations were carried out to unravel the origin of different photophysical behaviour of these compounds in the solid state. The results indicate that a rational strategy to control the SLE effect in luminogens depends on a delicate balance between molecular properties and inter-/intramolecular interactions in the solid state.     

Brownian Paths Homogeneously Distributed in Space: Percolation Phase Transition and Uniqueness of the Unbounded Cluster

We consider a continuum percolation model on \(\mathbb {R}^d\), \(d\ge 1\). For \(t,\lambda \in (0,\infty )\) and \(d\in \{1,2,3\}\), the occupied set is given by the union of independent Brownian paths running up to time t whose initial points form a Poisson point process with intensity \(\lambda >0\). When \(d\ge 4\), the Brownian paths are replaced by Wiener sausages with radius \(r>0\). We establish that, for \(d=1\) and all choices of t, no percolation occurs, whereas for \(d\ge 2\), there is a non-trivial percolation transition in t, provided \(\lambda \) and r are chosen properly. The last statement means that \(\lambda \) has to be chosen to be strictly smaller than the critical percolation parameter for the occupied set at time zero (which is infinite when \(d\in \{2,3\}\), but finite and dependent on r when \(d\ge 4\)). We further show that for all \(d\ge 2\), the unbounded cluster in the supercritical phase is unique. Along the way a finite box criterion for non-percolation in the Boolean model is extended to radius distributions with an exponential tail. This may be of independent interest. The present paper settles the basic properties of the model and should be viewed as a springboard for finer results.     

Selection of Planar Chiral Conformations between Pillar[5,6]arenes Induced by Amino Acid Derivatives in Aqueous Media

Chiral α-amino acids play critical roles in the metabolic process in nearly all life forms. So far, chiral recognition of α-amino acids has mainly focused on the determination of l /d enantiomers. Herein, selection of planar chiral conformations between water-soluble pillar[5]arene WP5 and pillar[6]arene WP6 was observed due to α-side chain or ethyl ester moieties of l -α-amino acid ethyl ester hydrochlorides binding with WP5 and WP6 , respectively. Therefore, α-side chain and ethyl ester moieties of l -α-amino acid ethyl ester hydrochlorides were recognized by observing the induced CD signal and its inversion. This is a rare example of being able to detect the chiral region around α-carbon of a chiral α-amino acid molecule.     

Electrochemical characterization of core@shell CoFe2O4/Au composite

Quantum dots (QDs) have received considerable attention due to their unique optical and electrical properties. Although substantial research has focused on the potential applications and toxicological impacts of QDs, far less effort has been directed toward understanding their fate and transport in the environment. In this work, the effect of four coatings, polyethylene glycol functionalized polymer (PEGP), carboxyl derivatized polymer (COOHP), linoleic acid (LA), and polyacrylic acid-octylamine (PAA-OA), on the transport and retention of QDs in porous media were evaluated under environmentally relevant conditions. Aqueous QD suspensions (ca. 10 nM) were introduced into water-saturated columns packed with 40–50 mesh Ottawa sand at a pore-water velocity of 7.6 m/day. At an ionic strength (IS) of 3 mM and pH of 7, PEGP-coated QDs were completely retained within the column, while more than 60 % of COOHP-coated QDs were transported through a column run under identical conditions. When PAA-OA and LA were used as coatings, effluent QD recoveries increased to more than 65 and 89 % of the injected mass, respectively. Additionally, a decrease in pH from 9.5 to 5.0, or an increase of IS from 0 to 30 mM reduced the eluted mass of PAA-OA-coated QDs by more than 2 and 15 times, respectively. The relative mobility of coated QDs (LA > PAA-OA > COOHP > PEGP) was consistent with total interaction energy profiles between QDs and sand surfaces calculated based on Derjaguin–Landau–Verwey–Overbeek (DLVO) theory. At an IS of 3 mM (NaCl) and pH 7, a linear correlation was obtained between the fraction of eluted QDs and the magnitude of the primary interaction energy barrier. These findings demonstrate the strong dependence of QD transport on coating type and indicate that interaction energies based on DLVO theory can be used to predict the relative mobility of QDs in porous media.     

(Liquid + liquid) equilibrium for the ternary systems {heptane + toluene + 1-allyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide} and {heptane + toluene + 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide} ionic liquids

The (liquid + liquid) equilibrium (LLE) data for two systems containing heptane, toluene, and 1-methyl-3-propylimidazolium bis(trifluoromethylsulfonyl)imide ([mpim][Tf₂N]) or 1-allyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([amim][Tf₂N]) ionic liquids (ILs) were determined at T = 313.2 K and atmospheric pressure. The effect of a double bond in an alkyl side chain in the imidazolium cation was evaluated in terms of selectivity and extractive capacity. The results show a decrease of the amount of toluene and heptane dissolved in the IL with the allyl group. Thus, the distribution ratios of toluene and heptane of [mpim][Tf₂N] IL are higher than those of [amim][Tf₂N] IL. On the other hand, the separation factor of the [amim][Tf₂N] IL increases comparing to [mpim][Tf₂N] IL. The NRTL model was used to correlate satisfactorily the experimental LLE data for the two studied ternary systems.     

Influence of imperfect elastic contact condition on the antiplane effective properties of piezoelectric fibrous composites

A fiber-reinforced periodic piezoelectric composite, where the constituents exhibit transverse isotropic properties, is considered. The fiber cross-section is circular and the periodicity is the same in two orthogonal directions. Imperfect mechanic contact conditions at the interphase between the matrix and fibers are represented in parametric form. In order to analyze the influence of the imperfect interface effect over the behavior of the composite, the effective axial piezoelectric moduli are obtained by means of the Asymptotic Homogenization Method. Some numerical examples are given.