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.     

An optimal Hardy–Morrey inequality

In this work we improve the sharp Hardy inequality in the case p?>?n by adding an optimal weighted H?lder seminorm. To achieve this we first obtain a local improvement. We also obtain a refinement of both the Sobolev inequality for p?>?n and the Hardy inequality, the latter having the best constant.     

A variational principle for adaptive approximation of ordinary differential equations

Summary A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error=local errorweight, for general approximation of functions of solutions to ordinary differential equations. This error representation is then approximated by a sum of computable error indicators, to obtain a useful global error indicator for adaptive mesh refinements. A uniqueness formulation is provided for desirable error representations of adaptive algorithms. Mathematics Subject Classification (2000):65L70, 65G50This work has been supported by the EU–TMR project HCL # ERBFMRXCT960033, the EU–TMR grant # ERBFMRX-CT98-0234 (Viscosity Solutions and their Applications), the Swedish Science Foundation, UdelaR and UdeM in Uruguay, the Swedish Network for Applied Mathematics, the Parallel and Scientific Computing Institute (PSCI) and the Swedish National Board for Industrial and Technical Development (NUTEK).     

On the large time behavior of the heat kernels of quasiperiodic differential operators

We prove an analog of the Berry-Esseen estimate for the heat kernel of second order elliptic differential operators with quasiperiodic coefficients. As an application of this result, we prove the L^p boundedness of the associated Riesz transform operators.     

Darboux Transformation for the Vector Sine-Gordon Equation and Integrable Equations on a Sphere

We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its Bäcklund transformations. We show that there is a new Lax operator canonically associated with our Darboux transformation resulting an evolutionary differential-difference system on a sphere. The latter is a generalised symmetry for the chain of Bäcklund transformations. Using the re-factorisation approach and the Bianchi permutability of the Darboux transformations, we derive new vector Yang–Baxter map and integrable discrete vector sine-Gordon equation on a sphere.     

Use of monomer fraction data in the parametrization of association theories

Association theories such as the CPA (cubic-plus-association), NRHB (non-random hydrogen bonding) equations of state and the various variants of SAFT (statistical associating fluid theory) have been extensively applied to phase equilibrium calculations. Such models can also be used for estimating the monomer fraction of hydrogen bonding compounds and their mixtures. Monomer fraction data are obtained from spectroscopic measurements and they are available for a few compounds such as pure water and alcohols as well as for some alcohol–alkane and similar mixtures. These data are useful for an understanding of the capabilities and limitations of association models. The purpose of this work is two-fold: (i) to compare the performance of three models, CPA, NRHB and sPC-SAFT, in predicting the monomer fraction of water, alcohols and mixtures of alcohol-inert compounds and (ii) to investigate whether “improved” model parameters can be obtained if monomer fraction data are included in the parameter estimation together with vapor pressures and liquid densities. The expression “improved” implies parameters which can represent several pure compound properties as well as monomer fraction data for pure compounds and mixtures. The accuracy of experimental monomer fraction data is discussed, as well as the role of monomer fraction data in clarifying which association scheme should be used in these equations of state. The results reveal that the investigated association models (CPA, sPC-SAFT and NRHB) can predict, at least qualitatively correct, monomer fractions of associating compounds and mixtures. Only, small differences are observed between the models. In addition, it has been shown that, using a suitable association scheme, a single set of parameters can describe satisfactorily vapor pressures, liquid densities and monomer fractions of water and alcohols. The 4C scheme is the best choice for water, while for methanol there is small difference between the 2B and 3B association schemes.     

Removing ruthenium residues from olefin metathesis reaction products

Olefin metathesis has revolutionized the way chemists design and synthesize molecules, mostly due to the development of well-defined ruthenium catalysts with high oxygen-, moisture-, and functional-group tolerance. However, the complete removal of residual ruthenium after the end of a metathesis reaction often imposes significant challenges. This Minireview summarizes the strategies for the sequestration of ruthenium impurities from olefin metathesis post-reaction mixtures, thus comprising a practical guide for synthetic chemists employing ruthenium-catalyzed metathesis reactions in the synthesis of organic or polymeric materials.     

Heart Failure and PAHs,OHPAHs, and Trace Elements Levels in Human Serum: Results from a Preliminary Pilot Study in Greek Population and the Possible Impact of Air Pollution

Cardiovascular diseases (CVDs) have been associated with environmental pollutants. The scope of this study is to assess any potential relation of polycyclic aromatic hydrocarbons (PAHs), their hydroxylated derivatives, and trace elements with heart failure via their direct determination in human serum of Greek citizens residing in different areas. Therefore, we analyzed 131 samples including cases (heart failure patients) and controls (healthy donors), and the respective demographic data were collected. Significantly higher concentrations (p < 0.05) were observed in cases’ serum regarding most of the examined PAHs and their derivatives with phenanthrene, fluorene, and fluoranthene being the most abundant (median of >50 μg L⁻¹). Among the examined trace elements, As, Cd, Cu, Hg, Ni, and Pb were measured at statistically higher concentrations (p < 0.05) in cases’ samples, with only Cr being significantly higher in controls. The potential impact of environmental factors such as smoking and area of residence has been evaluated. Specific PAHs and trace elements could be possibly related with heart failure development. Atmospheric degradation and smoking habit appeared to have a significant impact on the analytes’ serum concentrations. PCA–logistic regression analysis could possibly reveal common mechanisms among the analytes enhancing the hypothesis that they may pose a significant risk for CVD development.     

Fe(II) Spin Crossover/Polymer Hybrid Materials: Investigation of the SCO Behavior via Temperature-Dependent Raman Spectroscopy,Physicochemical Characterization and Migration Release Study

Polymeric composites constitute an appealing class of materials with applications in various fields. Spin crossover (SCO) coordination complexes are switchable materials with potential use in data storage and sensors. Their incorporation into polymers can be considered an effective method for their wider practical application. In this study, Fe(II) SCO/polylactic acid hybrid polymeric composites have been prepared by film casting. The mononuclear coordination complex [Fe{N(CN)₂}₂(abpt)₂] was incorporated into polylactic acid. The morphological, structural and thermoanalytical characterization of the composite films were performed via scanning electron microscopy (SEM), attenuated total reflectance (ATR/FTIR), Raman spectroscopy and differential scanning calorimetry (DSC). In addition, the migration release study (MRS) of the SCO compound from the polymeric matrix into the food simulant 50% v/v water/ethanol solution was also examined via UV/Vis absorption. Of particular interest was the investigation of the SCO behavior of the coordination complex after its incorporation into the polymer matrix; it was accomplished by temperature-dependent micro-Raman spectroscopy. The described attempt could be considered a preparatory step toward the development of SCO-based temperature sensors integrated into food packaging materials.