Entropy of self-gravitating radiation

We examine the entropy of self-gravitating radiation confined to a spherical box of radiusR in the context of general relativity. We expect that configurations (i.e., initial data) which extremize total entropy will be spherically symmetric, time symmetric distributions of radiation in local thermodynamic equilibrium. Assuming this is the case, we prove that extrema ofS coincide precisely with static equilibrium configurations of the radiation fluid. Furthermore, dynamically stable equilibrium configurations are shown to coincide with local maxima ofS. The equilibrium configurations and their entropies are calculated and their properties are discussed. However, it is shown that entropies higher than these local extrema can be achieved and, indeed, arbitrarily high entropies can be attained by configurations inside of or outside but arbitrarily near their own Schwarzschild radius. However, if we limit consideration to configurations which are outside their own Schwarzschild radius by at least one radiation wavelength, then the entropy is bounded and we find S_max MR, whereM is the total mass. This supports the validity for self-gravitating systems of the Bekenstein upper limit on the entropy to energy ratio of material bodies.     

Speciation of the new ligand di-isopropyliminodiacetoamide with Cu(II) using computational processing and graphical methods

The importance assigned to chelating agents in diverse areas has impelled studies concerning their development as related to metal ions representing a biological concern. The synthesis of di-isopropyliminodiacetoamide (D) is presented in this work. The acidity constant obtained for D was pKa = 5.79 +/- 0.04 with the aid of program SUPERQUAD. The equilibrium constants for D with Cu(II) were obtained with the aid of program SQUAD for CuD2+ and CuD2(2)+ species giving log beta1 = 4.795 +/- 0.002 and log beta2 = 8.374 +/- 0.004, respectively.     

Synthesis and characterization of Pd(II) complexes of 2‐ and 3‐thiophenecarbaldehyde immobilized on silica obtained from sepiolite

Silica obtained by acid treatment of sepiolite was used as a support for catalysts consisting of palladium complexes of 2‐ and 3‐thiophenecarbaldehyde. The support and the catalysts were characterized by X‐ray diffraction, and solid‐state ²⁹Si and ¹³C nuclear magnetic resonance spectroscopies. The supported palladium catalysts were used in the Suzuki reaction of bromobenzene with phenylboronic acid. Copyright © 2013 John Wiley & Sons, Ltd.     

Introduction: María Victoria Roux, colleague, calorimetrist, and friend

This essay is the introductory paper for a special issue of Structural Chemistry explicitly dedicated to the premier Spanish calorimetrist and thermochemist, our colleague and friend, María Victoria Roux. The studies in this issue were written on the occasion of her recent retirement from the CSIC Institute of Physical Chemistry “Rocasolano,” Madrid.     

Reductive Ring Opening of Ephedrine and Pseudo-Ephedrine-Derived Oxazolidinium Methiodides by Sodium Borohydride. A Direct Access to New Chiral Amine-Borane Adducts

Sodiun borohydride reacts with oxazolidinium methiodides derived from ephedrine and pseudoephedrine, in ethereal solvents, cleaving regioselectively the C-N bond of the ring and leading, in good yields, to chiral amine-borane adducts of know absolute configuration. The ¹HNMR data allow to predict the most stable conformation.