Analysis of First-Order Reactions with Distributed Parameters

Simple methods of analysis of first-order kinetic processes controlled by distributions of parameters (activation energies and/or frequency factors) are presented. Both the isothermal and nonisothermal regimes are considered. The procedures make use of numerically calculated time derivatives of the concentrations of decaying species (reactants in the case of chemical reactions). They do not require any adjustable initial or boundary values of parameters (like concentration at the infinite time) being thus more accurate and reliable than earlier methods in which kinetic parameters were determined from the concentration, and not from its time derivative. The methods were successfully employed in analysis of the thermally driven cis–trans isomerization of a photochromic crown ether containing the azobenzene moiety incorporated in the crown.     

Synthesis of mesoporous carbons using ordered and disordered mesoporous silica templates and polyacrylonitrile as carbon precursor

Mesoporous carbons were synthesized from polyacrylonitrile (PAN) using ordered and disordered mesoporous silica templates and were characterized using transmission electron microscopy (TEM), powder X-ray diffraction, nitrogen adsorption, and thermogravimetry. The pores of the silica templates were infiltrated with carbon precursor (PAN) via polymerization of acrylonitrile from initiation sites chemically bonded to the silica surface. This polymerization method is expected to allow for a uniform filling of the template with PAN and to minimize the introduction of nontemplated PAN, thus mitigating the formation of nontemplated carbon. PAN was stabilized by heating to 573 K under air and carbonized under N2 at 1073 K. The resulting carbons exhibited high total pore volumes (1.5-1.8 cm3 g(-1)), with a primary contribution of the mesopore volume and with relatively low microporosity. The carbons synthesized using mesoporous templates with a 2-dimensional hexagonal structure (SBA-15 silica) and a face-centered cubic structure (FDU-1 silica) exhibited narrow pore size distributions (PSDs), whereas the carbon synthesized using disordered silica gel template had broader PSD. TEM showed that the SBA-15-templated carbon was composed of arrays of long, straight, or curved nanorods aligned in 2-D hexagonal arrays. The carbon replica of FDU-1 silica appeared to be composed of ordered arrays of spheres. XRD provided evidence of some degree of ordering of graphene sheets in the carbon frameworks. Elemental analysis showed that the carbons contain an appreciable amount of nitrogen. The use of our novel infiltration method and PAN as a carbon precursor allowed us to obtain ordered mesoporous carbons (OMCs) with (i) very high mesopore volume, (ii) low microporosity, (iii) low secondary mesoporosity, (iv) large pore diameter (8-12 nm), and (v) semi-graphitic framework, which represent a desirable combination of features that has not been realized before for OMCs.     

Cationic polymerization of 1,4,6-trioxaspiro [4,4]-nonane

Cationic polymerization of 1,4,6-trioxaspiro [4,4]-nonane ( 1 ) with (CH₃)₃O⁺SbF₆^?(2) and CH₃OSO₂CF₃(3) initiators has been investigated. Although the observed rates of initiation and propagation are relatively slow, they consist of rapid reversible elementary reactions. In ¹H-NMR spectra, a broadening of the monomer signal was observed, indicating a fast exchange between “free” monomer and monomer engaged in the active species. The variety of orthoester bonds were observed in the polymer formed at the early stages of monomer conversion. The final polymer has, however, structure of a linear poly(ester–ether) including two subsequent ester or ether linkages. To account for these new facts, the mechanism of polymerization was proposed, consisting of a rapid reversible opening of one of the rings in the monomer molecule involved in the growing species, followed by the slower opening of the second ring with formation of the ester linkages. It appears that the rings originally present in the chains rearrange into the linear units intramolecularly.     

Ordinary and strong density continuity of complex analytic functions

In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:²²,G(x,y)=(x,y ³ ), is not density continuous [1]. We will also characterize those analytic functions which are strongly density continuous at the given pointa . From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b andb is either real or imaginary.     

Some remarks on the theorem of Möbius

H.S.M. Coxeter in his book Introduction to Geometry quotes a theorem of Möbius. In the paper two counterexamples are given. A corrected version of the theorem is stated and proved.     

Simple formula for nuclear charge radius

A new formula for the nuclear charge radius is proposed, dependent on the mass numberA and neutron excessN-Z in the nucleus. It is simple and it reproduces all the experimentally available mean square radii and their isotopic shifts of even-even nuclei much better than other frequently used relations.This work is partly supported by the Polish Committee of Scientific Research under contract No. 203119101     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solutions. IX. The Mixed Tetragonal Distorted Bis(Salicylato)Cobalt(II) Complex in Various Solvents

Mixed cobalt(II) complexes with the monodentate ligands: 2-hydroxybenzoic acid deprotonated (sal^–, the salicylate ion) and water, have been investigated. The combined results of the spectrophotometric and conductance measurements, as well as known the X-ray structure for solids, were used to determine the structure of the studied complexes in solution. The electronic absorption spectra in aqueous acid (0.01M HClO₄), ethylene glycol (glycol), formamide (FM), N,N-dimethylformamide (DMF), and dimethyl sulfoxide (DMSO) solutions have been recorded. The d-d electronic spectra have been treated by the crystal-field model (CFM) and angular overlap model (AOM). Low-symmetry splittings of the broad asymmetric bands in the experimental spectra (solutions at room temperature) were found by Gaussian analysis. The effect of the and bonding of the monodentate ligands (with oxygen-donor ligators) on the central metal ion was described in the ligand–field framework. A comparison of the stereochemistry of the complex species in various solutions was made.     

On Calderón-Toeplitz operators

We discuss boundedness and Schatten ideal criteria for a class of Toeplitz style operators based on the Calderón reproducing formula. These operators are a variation on Calderón-Zygmund operators but our results also apply to classical Toeplitz operators acting on the weighted Bergman space of the upper half plane.     

Symmetry-adapted perturbation-theory calculations of intermolecular forces employing density-functional description of monomers

A symmetry-adapted perturbation theory based on Kohn-Sham determinants [SAPT(KS)] and utilizing asymptotically corrected exchange-correlation potentials has been applied to the He2, Ne2, (H2O)2, and (CO2)2 dimers. It is shown that SAPT(KS) is able to recover the electrostatic, first-order exchange, second-order induction, and exchange-induction energies with an accuracy approaching and occasionally surpassing that of regular SAPT at the currently programmed theory level. The use of the asymptotic corrections is critical to achieve this accuracy. The SAPT(KS) results can be obtained at a small fraction of the time needed for regular SAPT calculations. The robustness of the SAPT(KS) method with respect to the basis set size is also demonstrated. A theoretical justification for high accuracy of SAPT(KS) predictions for the electrostatic, first-order exchange, and second-order induction energies has been provided.     

Modifying the thermosensitivity of copolymers of sodium styrene sulfonate and<Emphasis Type="Italic"> N</Emphasis>-isopropylacrylamide with dodecyltrimethylammonium chloride

The interactions between copolymers of sodium styrene sulfonate (SSS) and N-isopropylacrylamide (NIPAM), anionic polyelectrolytes, and dodecyltrimethylammonium chloride (DTAC), a cationic surfactant, were studied in aqueous solutions of various ionic strengths. The copolymers were found to be thermoresponsive, showing a lower critical solution temperature (LCST). The influence of the polymer composition, the surfactant concentration, and the ionic strength on the LCST was studied. The surfactant was found to interact strongly with the polymer, forming mixed polymer-surfactant micelles. The critical aggregation concentration (cac) of the polymer-surfactant system was found from fluorescence spectroscopy using pyrene as a fluorescent probe. A strong dependence of the anionic polyelectrolyte-cationic surfactant interactions on the structure of the ionic comonomer was observed.