Effect of low molecular weight compounds on the relaxation behavior of poly(2-hydroxyethyl methacrylate) in the glassy state and in the transition region from the glassy to the rubberlike state

The method of free torsional vibrations was used to determine the temperature dependence of the storage and loss shear modulus of poly(2-hydroxyethyl methacrylate) samples swollen with ethylene glycol, formamide, n-propanol, and water. The measurements included the glassy region (starting with temperatures from ?130 to ?190°C) and the main (α) transition from the glassy to the rubberlike state. At a volume fraction of the low molecular weight compound v_d > 0.2, the above systems exhibit, besides the α dispersion, only the secondary (β_SW) dispersion, which is generally attributed to the relaxation motions of the hydroxyethyl groups of the side chains interacting with molecules of the diluent. If no separation of the diluent in a second phase occurs at the measurement temperatures, the temperatures of both dispersions decrease with increasing v_d and approach the glass transition temperature of the low molecular weight compound. The concentration dependences of the dispersion temperatures were described by an equation derived elsewhere for the concentration dependence of the glass transition temperature. The results indicate that molecules of the diluent contribute significantly to the intensity of the β_SW transition and simultaneously affect its limiting temperatures (for v_d = 1 and v_d = 0). Specific differences among the systems described above appear only at those temperatures where same of the low molecular weight compound separates into a crystalline or glassy phase.     

Hosoya polynomials of TUC4C8(R) nanotubes

For a connected graph G, the Hosoya polynomial of G is defined as H(G, x) = ∑_{u,v}?V(G)x^{d(u, v)}, where V(G) is the set of all vertices of G and d(u,v) is the distance between vertices u and v. In this article, we obtain analytical expressions for Hosoya polynomials of TUC₄C₈(R) nanotubes. Furthermore, the Wiener index and the hyper‐Wiener index can be calculated. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Use of Wheeler–Jonas equation to explain xenon dynamic adsorption breakthrough curve on granular activated carbon

The Wheeler–Jonas equation (WJ equation) is widely used to predict breakthrough of volatile organic compounds on granular activated carbon (GAC) and the most important criteria is to calculate the overall adsorption rate constant (k _v ) and amount adsorbed based on breakthrough curve. The operational factors, including temperatures, concentrations and flow rates, for packed bed, can affect the values of k _v more or less and to what degree has not yet been systematically investigated. What’s more, the relation between the dynamic adsorption coefficient (k _d) or Henry constant, which is used for the design of packed bed, and WJ equation is not clear. In order to solve these problems, we performed xenon dynamic adsorption on GAC adsorber experiments under different values of xenon concentrations, flow rates and temperatures, obtained the breakthrough curves for elution times versus xenon concentrations, and then employed WJ equation to explain breakthrough curves. The experimental results indicate that the WJ equation can fit the breakthrough curve very well and k _d be integrated into the WJ equation. The values of k _v are proportional to the values of flow rates and k _d, but independent of that of temperatures and xenon concentrations.     

Monte carlo simulation of diffusion-limited drug release from finite fractal matrices

How fast can drug molecules escape from a controlled matrix-type release system? This important question is of both scientific and practical importance, as increasing emphasis is placed on design considerations that can be addressed only if the physical chemistry of drug release is better understood. In this work, this problem is studied via Monte Carlo computer simulations. The drug release is simulated as a diffusion-controlled process. Six types of Menger sponges (all having the same fractal dimension, d _f = 2.727, but with different values of random walk dimension, d _w ∈ [2.028, 2.998]) are employed as models of drug delivery devices with the aim of studying the consequences of matrix structural properties (characterized by d _f and d _w ) on drug release performance. The results obtained show that, in all cases, drug release from Menger sponges follows an anomalous behavior. Finally, the influence of the matrix structural properties on the drug release profile is quantified.     

Ordering chemical unicyclic graphs by Wiener polarity index

Suppose G is a chemical graph with vertex set V(G). Define D(G) = {{u, v} ⊆ V (G) | d _G (u, v) = 3}, where d _G (u, v) denotes the length of the shortest path between u and v. The Wiener polarity index of G, W _p (G), is defined as the size of D(G). In this article, an ordering of chemical unicyclic graphs of order n with respect to the Wiener polarity index is given.     

Hydrolyzed Vinyl Acetate–Divinylbenzene Copolymer Microspheres Containing L -Proline for Chiral Separation of Amino Acids

A new packing material for ligand-exchange chromatography, L -proline-modified hydrolyzed vinyl acetate-divinylbenzene copolymer microspheres, has been prepared and evaluated. The microspheres, prepared by a one-step swelling and polymerization method, have a narrow bead size (as determined by scanning electron microscopy, SEM), a broad pore-size distribution (by nitrogen adsorption) and, especially, inhomogeneous structural composition (by differential scanning calorimetry). The support, which has an L -proline content of 0.35 mmol g^–1 (nitrogen analysis), provides good enantioselectivity and column efficiency. Twenty-three of the twenty-four common D ,L -amino acids tested were resolved on a 250 mm × 4.6 mm i.d. column and mixtures of up to seven racemic amino acids were easily separated into their enantiomers. Two average pore diameters, volume-average (d_v) and surface-average (d_s) pore diameters, are defined. The ratio d_v/d_s is used to characterize the broadness of the pore-size distribution. It is shown that the widely used formula d=4V_p/S for cylindrical pores, where V_p is pore volume and S the specific surface area, gives the surface-average pore diameter.     

On Unicycle Graphs with Maximum and Minimum Zeroth-order Genenal Randić Index

Let G be a graph and d _v denote the degree of the vertex v in G. The zeroth-order general Randić index of a graph is defined as R _α⁰(G) = ∑ _v∈V(G) d _v ^α where α is an arbitrary real number. In this paper, we obtained the lower and upper bounds for the zeroth-order general Randić index R _α⁰(G) among all unicycle graphs G of order n. We give a clear picture for R _α⁰(G) of unicycle graphs according to real number α in different intervals.     

Orientational preference of two ethylene ligands bound to a nickel atom

CASSCF and CCI calculations have been performed to analyze the bonding in Ni(C₂H₄)₂. Three different relative orientations of the two olefins have been studied. It is found that a structure with D_2d symmetry, where the C-C bonds in the two olefins make a 90 degree angle to each other, gives the lowest energy. A D_2h form, with the two C-C bonds and Ni in the same plane, is 10.3 kcal/ mol higher in energy. The reason for the preference of the D_2d form is analyzed in terms of valence bond theory, and is found to be due to a d ⁸ structure with two simultaneous d bonds. A C _2v form, for which the two nickel olefin bonds make a 103 degree angle to each other and the C-C bonds are parallel to each other, is 32 kcal/mol higher in energy than the D_2d form. The low binding energy of the C _2v form is due to a poor interaction with inefficient sd hybridization.     

Interaction between two double layers for Na3PO4 types electrolytes at y0 > yd > 0

Interaction between two double layers for the Na₃PO₄ type electrolytes at y ₀ > y _d > 0 were investigated with the aid of λ parameter methods and the accurate numeral results were given. The maximum of the interaction energies between two double layers for A_v+ B_v- A_{v_ + } B_{v_ - } type electrolytes at y ₀ > y _d > 0 is independent of y ₀, but increases with y _d . The interaction energies between two double layers for NaCl, CaCl₂, FeCl₃, Na₂SO₄ and Na₃PO₄ type electrolytes at y ₀ = 5 and y _d = 2 were compared. If the negative or positive ions for A_v+ B_v- A_{v_ + } B_{v_ - } type electrolytes have the same charge number, the maximum of their interaction energies increases with the charge number of the ions of opposite charge. If the negative or positive ions of the electrolytes have different charge numbers, the relative heights of the maxima of their interaction energies are indefinite. For the in pairs conjugate type electrolytes like CaCl₂ and Na₂SO₄ or FeCl₃ and Na₃PO₄, the larger the charge number of the negative ions of the electrolytes is, the higher the maximum of their interaction energies is. The results for Na₃PO₄ type electrolytes at y ₀ > y _d > 0 can also be applied to FeCl₃ type electrolytes at y ₀ > y _d > 0.     

The splitting of d-orbitals in less symmetrical molecules containing a cyclopentadienyl ligand

The splitting of d orbitals in an electrostatic field due to a cyclopentadienyl ring and four ligands arranged at the corners of a square is investigated. It is shown that, although the symmetry of the molecule is C _s, the effective symmetry for the d ¹ and d ² systems is G _4v. The linear combinations for the d ² system in C _1v symmetry are given and the matrix elements for the secular determinant are listed. The results may be applied to a discussion of the bonding in tricarbonyl--cyclopentadienylethyl-molybdenum, whose structure is related to the idealized model considered.

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Zusammenfassung Bei der Aufspaltung der d-ZustÄnde in einem elektrostatischen Feld, welches erstens von einem Cyclopentadienyl-Ring und zweitens von vier an den Ecken eines Quadrates angeordneten Liganden hervorgerufen wird, ist die effektive Symmetrie D _4v — trotz der C _s-Symmetrie des Moleküls. Für das d ²-System werden die Linearkombinationen der Slaterdeterminanten und die Elemente der Störmatrix angegeben. Das Ganze lÄ\t sich z. B. auf die Diskussion von Tricarbonyl--cyclopentadienylÄthylmolybdÄn anwenden, dessen Struktur der des behandelten Modells sehr Ähnlich ist.

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Résumé La décomposition des orbitales d dans le champ d'un groupe cyclopentadiényl et de quatre ligandes arrangés en carré est étudiée. Pour les systèmes d ¹ et d ², la symétrie effective est C _4v , celle de la molécule n'étant que C _s. Pour d ², on donne les combinaisons linéaires adapté à la symétrie C _4v , et la matrice des énergie perturbatrices. Les résultats s'appliquent à la discussion du cyclopentadiényl-éthyl-molybdène tricarbonyle dont la structure ressemble le modèle étudié.

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On leave from: Institut Rudjer Bokovi, Zagreb, Yugoslavia     

Inverting the external-potential-to-electron density map in systems of electrons by minimization of a least-squares fit functional for analytic potentials

In a system of electrons, there is a map connecting any external potential v with its electron density ρ _v. In this work, we describe a procedure for inverting this potential-to-density map, so that potentials (if any) corresponding to a target density ρ_t can be obtained. We give the trial external potential v _α , an analytic expression depending on a number of parameters α = (α₁, …) and then minimize the least-squares integral ∫(ρ _α − ρ_t)² d r by the conjugate gradient method, where ρ _α is the density corresponding to v _α . The implementation takes advantage of the analytic nature of v _α . The procedure can be applied to any system and quantum chemistry model, and works both for ground and excited states, as well as for ensembles of states. The method is tested with some excited states of the particle-in-a-box model, confirming the lack of a Hohenberg–Kohn theorem for excited states. It is also applied to the first singlet excited state of the helium atom, where, apart from the nucleus–electron attraction potential, some generalized external potentials are found.     

Symmetry adapted formulation of the generalized Brillouin theorem

The singly excited functions satisfying Brillouin theorem are expressed as linear combinations of configuration-state functions for any spin and spatial symmetries (atomic or molecular) and for any reference wave function. The generality of the formulation is ensured by the use of the irreducible tensor method that can be adapted to any symmetry point group of interest. The expansion coefficients are simply written as products of fractional parentage coefficients, spin- and orbit-recoupling coefficients, and phase factors. The formalism is illustrated for some atomic (K_h) and molecular (C_∞v, C_3v, and T_d) configurations. Group theoretical techniques are also used to correlate the Brillouin conditions within a chain of groups.     

Preferential Formation of Mono-Metallofullerenes Governed by the Encapsulation Energy of the Metal Elements: A Case Study on Eu@C2n (2n=74–84) Revealing a General Rule

Encapsulating one to three metal atoms or a metallic cluster inside fullerene cages affords endohedral metallofullerenes (EMFs) classified as mono-, di-, tri-, and cluster-EMFs, respectively. Although the coexistence of various EMF species in soot is common for rare-earth metals, we herein report that europium tends to prefer the formation of mono-EMFs. Mass spectroscopy reveals that mono-EMFs (Eu@C_2n) prevail in the Eu-containing soot. Theoretical calculations demonstrate that the encapsulation energy of the endohedral metal accounts for the selective formation of mono-EMFs and rationalize similar observations for EMFs containing other metals like Ca, Sr, Ba, or Yb. Consistently, all isolated Eu-EMFs are mono-EMFs, including Eu@D_3h(1)-C₇₄, Eu@C_2v(19138)-C₇₆, Eu@C_2v(3)-C₇₈, Eu@C_2v(3)-C₈₀, and Eu@D_3d(19)-C₈₄, which are identified by crystallography. Remarkably, Eu@C_2v(19138)-C₇₆ represents the first Eu-containing EMF with a cage that violates the isolated-pentagon-rule, and Eu@C_2v(3)-C₇₈ is the first C₇₈-based EMF stabilized by merely one metal atom.     

Relaxation dispersion and zero-field spectroscopy of thermotropic and lyotropic liquid crystals by fast field-cycling N.M.R.

Abstract

Systematic field-cycling measurements of the T ₁ relaxation dispersion in numerous nematic liquid crystals (azoxybenzenes, Schiff's bases, biphenyls, phenyl-cyclohexanes, cyclo-cyclo-hexanes) confirm our previous observations obtained for PAA and MBBA that order fluctuations of the nematic director are a significant relaxation contribution only at low Lamor frequencies v, i.e. far below the usual megahertz range. Their significance is demonstrated most convincingly by the characteristic square-root dispersion law, T ₁ ～ v ^1/2, which occurs in the kilohertz range and which completely disappears above the nematic–isotropic phase transition. The strength of the collective relaxation mechanism varies by more than two orders of magnitude in the sequence (selection) PAA-d ₈ PAA, PAA-d ₆ PAB, OCB7, MBBA, CB7, PCH7, MBBA-d ₆ MBBA-d ₁₃ and CCH7. This finding can be understood almost quantitatively by the widely differing separations and orientations of proton pairs on the molecules, together with the different viscoelastic parameters of the nematogens. In addition, the underlying slow molecular reorientations have been observed in MBBA and PAA by intensity changes of the zero-field spectra, which are absent for high-field measurements. Similarly, smectic type order fluctuations in layered liquid crystal structures prove to be an effective relaxation mechanism only at low Lamor frequencies. This has been verified by the related linear relaxation dispersion profile, T ₁ ～ v ¹, for both thermotropic systems (TBBA, C₁₂-AA) and lamellar lyotropic mixtures (e.g. potassium laurate in water and phospholipids in water). Our results concerning the time scale of the T ₁ ～ v ^1/2 and T ₁ ~ v ¹ regime do not agree with conclusions drawn from conventional high-field techniques.     

Preferential Formation of Mono‐Metallofullerenes Governed by the Encapsulation Energy of the Metal Elements: A Case Study on Eu@C2n (2n=74–84) Revealing a General Rule

Encapsulating one to three metal atoms or a metallic cluster inside fullerene cages affords endohedral metallofullerenes (EMFs) classified as mono‐, di‐, tri‐, and cluster‐EMFs, respectively. Although the coexistence of various EMF species in soot is common for rare‐earth metals, we herein report that europium tends to prefer the formation of mono‐EMFs. Mass spectroscopy reveals that mono‐EMFs (Eu@C_2n) prevail in the Eu‐containing soot. Theoretical calculations demonstrate that the encapsulation energy of the endohedral metal accounts for the selective formation of mono‐EMFs and rationalize similar observations for EMFs containing other metals like Ca, Sr, Ba, or Yb. Consistently, all isolated Eu‐EMFs are mono‐EMFs, including Eu@D_3h(1)‐C₇₄, Eu@C_2v(19138)‐C₇₆, Eu@C_2v(3)‐C₇₈, Eu@C_2v(3)‐C₈₀, and Eu@D_3d(19)‐C₈₄, which are identified by crystallography. Remarkably, Eu@C_2v(19138)‐C₇₆ represents the first Eu‐containing EMF with a cage that violates the isolated‐pentagon‐rule, and Eu@C_2v(3)‐C₇₈ is the first C₇₈‐based EMF stabilized by merely one metal atom.     

Graphs with maximum connectivity index

Let G be a graph and d_v the degree (=number of first neighbors) of its vertex v. The connectivity index of G is χ=∑ (d_ud_v)^−1/2, with the summation ranging over all pairs of adjacent vertices of G. In a previous paper (Comput. Chem. 23 (1999) 469), by applying a heuristic combinatorial optimization algorithm, the structure of chemical trees possessing extremal (maximum and minimum) values of χ was determined. It was demonstrated that the path P_n is the n-vertex tree with maximum χ-value. We now offer an alternative approach to finding (molecular) graphs with maximum χ, from which the extremality of P_n follows as a special case. By eliminating a flaw in the earlier proof, we demonstrate that there exist cases when χ does not provide a correct measure of branching: we find pairs of trees T, T′, such that T is more branched than T′, but χ(T)>χ(T′). The smallest such examples are trees with 36 vertices in which one vertex has degree 31.     

Favorable performance of the DFT methods in predicting the minimum‐energy structure of the lowest triplet state of WF4

The tetrahedral structure of the lowest triplet state of the WF₄ complex was examined using different variants of the density functional theory (DFT) and conventional ab initio methods. The low‐level, conventional, ab initio methods, such as SCF, MP2, MP3, and CISD, predict the tetrahedral structure to be a minimum, whereas the DFT schemes predict an imaginary frequency for the e vibrational mode. Only after recovering electron correlation effects at the MP4 and higher levels, the conventional electronic structure methods also predict the T_d structure to be a second‐order stationary point. This is not the correlation but the exchange part of the DFT functionals which is responsible for the discrepancy between the DFT and low‐level, conventional, ab initio predictions. The lowering of symmetry to C_2v leads to a minimum on the lowest triplet potential energy surface and the electronic energy difference between the T_d and C_2v stationary points amounts to 0.85 and 0.96 kcal/mol at the B3LYP and CCSD(T) levels, respectively. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 369–375, 1999     

Electrochemical Characterization and Determination of Mercury Using Carbon Paste Electrodes Modified with Cyclodextrins

In this work the characterization and determination of mercury in HClO₄ media using carbon paste electrodes modified with α‐ and β‐cyclodextrins (CPE_α‐CD and CPE_β‐CD) at E_d=?0.7 V with a t_d = 20 s and a potential scan v=20 mV s^?1 is studied‥ The statistical results obtained indicate that the modified electrodes displayed a better analytical performance as compared to that obtained with the unmodified CPE. The detection limits for the CPE_α‐CD and for the CPE_β‐CD were 0.05 and 0.09 μM, respectively, while for the CPE it was 0.41 μM. The CPE_β‐CD exhibited greater sensitivity as compared to that of the CPE_α‐CD.     

The structure of astatine azide, AtN3—A theoretical study

For the first time theoretical evidence for the experimentally hitherto unknown astatine azide, AtN₃, the heaviest of all halogen azides, is presented. The structure and the vibrational data of AtN₃ were computedab initio at RHF and electron-correlated MP2 levels of theory using a quasirelativistic (MWB) pseudopotential for astatine, where the basis functions for the valences andp electrons consist of the standard double- basis set. For nitrogen a standard 6-31G(d) basis was used. The molecule represents a true minimum (NIMAG=0) at all levels of theory applied and is predicted to exist in a planartrans bentC _s structure. Since hybrid functionals, which define the exchange functional as a linear combination of Hartree-Fock, local, and gradient-corrected exchange terms, are known to predict the experimental parameters best, we also computed astatine azide (At-N1-N2-N3) at the B3-LYP level; the results are as follows:d(At-N1)=2.267,d(N1–N2)=1.239,d(N2–N3)=1.146 å; (A1-N1-N2)=111.6, (N1-N2-N3)=171.9;v ₁,=157.4,v ₂=366.6,v ₃=559.0,v ₄=659.6,v ₅=1264.7,v ₆=2165.1 cm^–1 (unscaled). The heat of formation was computed at B3-LYP level to be H _f ^o (AtN₃)=+80 kcal mol^–1.