Moments of Ramanujan?s generalized elliptic integrals and extensions of Catalan?s constant

We undertake a thorough investigation of the moments of Ramanujan?s alternative elliptic integrals and of related hypergeometric functions. Along the way we are able to give some surprising closed forms for Catalan-related constants and various new hypergeometric identities.     

The Infinite Square Well with a Singular Perturbation

We study the influence of a singular potential on an infinite square well. Two cases are considered. In the first, the singular potential is centered in the potential well, in the second case it is off-center. We also present a discussion on the self adjointness of the Hamiltonian of some exactly solvable potentials perturbed with singular potentials.     

Quantum mechanics of a simulated trihydrogen dication

The Schroedinger equation is solved exactly within the Born–Oppenheimer approximation for a simulacrum of the \(H_3^{2+}\) -ion. The ion is assumed to form an isosceles triangle and the ground state energy is obtained over its geometrical parameter space. No multi-center molecular integrations are required. We indicate how the approximation to the actual molecule can be improved systematically.     

About the structure of cellulose: debating the Lindman hypothesis

The hypothesis advanced in this issue of CELLULOSE [Springer] by Bjorn Lindman, which asserts that the solubility or insolubility characteristics of cellulose are significantly based upon amphiphilic and hydrophobic molecular interactions, is debated by cellulose scientists with a wide range of experiences representing a variety of scientific disciplines. The hypothesis is based on the consideration of some fundamental polymer physicochemical principles and some widely recognized inconsistencies in behavior. The assertion that little-recognized (or under-estimated) hydrophobic interactions have been the reason for a tardy development of cellulose solvents provides the platform for a debate in the hope that new scientific endeavors are stimulated on this important topic.     

Solid-state energetics and electrostatics: Madelung constants and Madelung energies

The Madelung constants of ionic solids relate to their geometry and electrostatic interactions. Furthermore, because of issues in their evaluation, they are also of considerable mathematical interest. The corresponding Madelung (electrostatic, coulomb) energy is the principal contributor to the lattice energies of ionic systems, and these energies largely influence many of their physical properties. The Madelung constants are here defined and their properties considered. A difficulty with their application is that they may be defined relative to various lattice distances, and with various conventions for inclusion of the charges, leading to possible confusion in their use. Instead, the unambiguous Madelung energy, E(M), is to be preferred in chemistry. An extensive list of Madelung energies is presented. From this data set, it is observed that there is a strong linear correlation between the lattice energies of ionic solids, U(POT), and their Madelung energies: U(POT)/kJ mol(-1) = 0.8519E(M) + 293.9. This correlation establishes that the lattice energy, U(POT), for ionic solids is about 15% smaller than the attractive Madelung energy, the difference arising from the repulsions unaccounted for by the solely coulombic Madelung energy calculation. Correlations of U(POT) against E(M) for alkali metal hydrides and transition metal compounds, each having considerable covalency, show much reduced Madelung contributions to the lattice energy. These correlations permit ready estimation of lattice energies, and are the first to be based on actual data rather than a broad analysis. The independent volume-based thermodynamic (VBT) method, which relies on a separate correlation with the formula unit volume of the ionic material, complements these correlations.     

Stuck in traffic: Patterns of powder adhesion

The adhesion of fine particles to surfaces is important for applications ranging from drug delivery to fouling of solar cells. In this letter, we show that powder adhesion can occur in unexpected patterns, concentrating particular grain types in some locations and clearing them from others, and we propose a straightforward traffic model that appears to reproduce many of the behaviors seen. The model predicts different patterns depending on inter-particle cohesion, and we find in both experiment and model that adhesion occurs in three distinct stages.      

ChemInform Abstract: Relationships Among Ionic Lattice Energies,Molecular (Formula Unit) Volumes,and Thermochemical Radii

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