Influence of the linking chain length on the recombination kinetics of covalently bonded triplet radical pairs and magnetic field effects

Nanosecond laser flash photolysis technique is used to study the formation and decay kinetics of covalently linked triplet radical pairs (RP) formed after photoinduced electron transfer in the series of 21 zinc porphyrin—chain—viologen (Pph—Sp_n—Vi²⁺) dyads, where the number of atoms (n) in the chain increases from 2 to 138. In poorly viscous polar solvents (acetone, CHCl₃—CH₃OH (1 : 1) mixture), the dependence of the rate constant of RP formation on n can be described by the equation k _e = k _e ⁰ n ^–a at k _e ⁰ = 2.95·10⁸ s^–1 anda = 0.8. In the zero magnetic field, the RP recombination rate constant (k _r(B = 0)) is significantly lower than k _e and ranges from 0.7·10⁶ to 8·10⁶ s^–1. The dependence of k _r(B = 0) on n is extreme. The dependence k _r(B = 0) reaches a maximum at n = 20. In the strong magnetic field (B = 0.21 T), the significant retardation of triplet RP recombination is observed. The chain length has an insignificant effect on k _r(B = 0.21 T), which ranges from 0.3·10⁶ to 0.9·10⁶ s^–1. The regularities found are discussed in terms of the interplay of molecular and spin dynamics.     

Phase-transition studies of 5O.5 and 9O.4

As part of our detailed comparative studies of groups of liquid-crystalline compounds that belong to a homologous series, we present phase-transition studies of the compounds N-(4-n-pentyloxybenzylidene)4′-n-pentylaniline (5O.5) and N-(4-n-nonyloxybenzylidene)4′-n-butylaniline (9O.4) using different experimental techniques. The compound 5O.5 is reported to exhibit a phase sequence N, S_A, S_C, S_B and S_G, while 90.4 shows the sequence S_A, S_F and S_G. The salient features of our work on 5O.5 are (i) a new smectic F phase is found in place of the reported smectic B phase, which is confirmed by both miscibility and X-ray studies; (ii) the formation of smectic-C-like short-range order in the nematic phase well above the S_A-N transition; and (iii) a large tilt-angle variation in the smectic C phase (0–23·5°C) in a small temperature range (4·1°C). The phase changes across the S_A-I transition, and for the first time across S_F-S_A transition, are carried out by volumetric studies. The detailed inferences of these are also presented.     

Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties

We apply our recently proposed proper quantization rule, ò_xA^x_Bk(x) dx -ò_x0A^x_0Bk₀(x) dx=np{\int_{x_A}^{x_B}k(x) dx -\int_{x_{0A}}^{x_{0B}}k_0(x) dx=n\pi} , where _boxclose_boxclose_boxclose_boxclose_boxclose_boxclose_boxclose_boxclose/{k(x)=\sqrt{2 M [E-V(x) ]}/\hbar} to obtain the energy spectrum of the modified Rosen-Morse potential. The beauty and symmetry of this proper rule come from its meaning—whenever the number of the nodes of f(x){\phi(x)} or the number of the nodes of the wave function ψ(x) increases by one, the momentum integral ò_xA^x_B k(x)dx{\int_{x_A}^{x_B} k(x)dx} will increase by π. Based on this new approach, we present a vibrational high temperature partition function in order to study thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F and entropy S. It is surprising to note that the specific heat C (k = 1) first increases with β and arrives to the maximum value and then decreases with it. However, it is shown that the entropy S (k = 1) first increases with the deepness of potential well λ and then decreases with it.     

Darstellung und Schwingungsspektren von Chloro-Bromo-Dirhodaten(III), [Rh2ClnBr9−n]3−, n = 0–9

Preparation and Vibrational Spectra of Nonahalogenodirhodates(III), [Rh₂Cl_nBr_9-n]^3?, n = 0–9 The pure nonahalogenodirhodates(III), A₃[Rh₂Cl_nBr_9-n], A = K, Cs, (TBA); n = 0–4, 9, have been prepared. They are formed from the monomer chlorobromorhodates(III), [RhCl_nBr_6-n]^3?, n = 0–6, which are bridged to confacial bioctahedral complexes by ligand abstraction in less polar organic solvents. From the mixtures the complexions are separated by ion exchange chromatography on DEAE-cellulose. The solid, air-stable, air-stable, K-, Cs- and (TBA)-salts of [Rh₂Cl_nBr_9-n]^3?, n = 0–4, are green, of [Rh₂Cl₉]^3? are brown. The IR and Raman spectra of [Rh₂Br₉]^3? and [Rh₂Cl₉]^3? are assigned according to the point group D_3h. The chlorobromodirhodates exist as mixtures of geometrical and structural isomers, which belong to different point groups. The vibrational spectra exhibit bands in characteristic regions; at high wavenumbers stretching vibrations with terminal ligands v(Rh—Cl_t): 360–320, v(Rh—Br_t): 280–250; in a middle region with bridging ligands v(Rh—Cl_b): 300–270, v(Rh—Br_b): 210–170 cm^?1; the deformation bands are observed at distinct lower frequencies. The terminal ligands are fixed very strong, and the distance between v(Rh—X_t) and v(Rh—X_b) increases with decreasing size of the cations.     

What,Methane Again?!

A combination of an error discovered in the Multiwell code and some more recent examinations of the system CH₃ + H = CH₄ prompted a reexamination of earlier work by this author. Values of the energy transfer parameter, 〈ΔE_d〉, are considerably different from the previous study. It is suggested that the Baulch et al. parameters for this system can be improved by replacing the values for k_rec,₀ and k_rec,_∞ with values suggested by Troe and Ushakov. k_rec,₀ = [Ar] 10^?26.19 exp[–(T/21.22 K)^0.5] cm⁶ molecule^?2 s^?1, k_rec,_∞ = 3.34 × 10^?10 (T/25200 K)^0.186 cm³ molecule^?1 s^?1 while keeping their value for F_c = 0.63 exp(–T/3315) + 0.37 exp(–T/61).     

Extremal hexagonal chains concerning k-matchings and k-independent sets

Denote by _n the set of the hexagonal chains with n hexagons. For any B _{n n} , let m _k (B _n ) and i _k (B _n ) be the numbers of k-matchings and k-independent sets of B _n , respectively. In the paper, we show that for any hexagonal chain B _{n n} and for any k0, m _k (L _n )m _k (B _n )m _k (Z _n ) and i _k (L _n )i _k (B _n )i _k (Z _n ), with left equalities holding for all k only if B _n =L _n , and the right equalities holding for all k only if B _n =Z _n , where L _n and Z _n are the linear chain and the zig-zag chain, respectively. These generalize some related results known before.     

Robustness Screen in Enantioselective Catalysis Enabled Generation of Enantioenriched Heterocyclic Scaffolds in One Pot

Enantioselective catalysis has emerged as a powerful synthetic paradigm and has accelerated the development of new methods to make diverse chiral molecules. Generally, these reactions are very sensitive to the steric and electronic environment present in the catalyst as well as the substrates. With this scenario, the presence of an additional component in the reaction mixture is expected to add complexity in achieving the enantioselective variants. Herein, we report that various enantioenriched molecules could be obtained from multiple starting materials in one pot. The reaction of aminoaromatics A with alkynols B₁, B₂, B₃…?B_n with a Au^I/chiral Brønsted acid catalyst afforded AB₁*, AB₂*, AB₃*…AB_n*; while, the reaction of alkynols B with aminoaromatics A₁, A₂, A₃…A_n under the same reaction conditions gave A₁B*, A₂B*, A₃B*…A_nB * .     

Hosoya index of unicyclic graphs with prescribed pendent vertices

The Hosoya index z(G) of a (molecular) graph G is defined as the total number of subsets of the edge set, in which any two edges are mutually independent, i.e., the total number of independent-edge sets of G. By G(n, l, k) we denote the set of unicyclic graphs on n vertices with girth and pendent vertices being resp. l and k. Let be the graph obtained by identifying the center of the star S _n-l+1 with any vertex of C _l . By we denote the graph obtained by identifying one pendent vertex of the path P _n-l-k+1 with one pendent vertex of . In this paper, we show that is the unique unicyclic graph with minimal Hosoya index among all graphs in G(n, l, k).      

Dielectric relaxation of a short molecule in a liquid-crystalline solvent

Abstract

Dielectric relaxation measurements of 5 mole % 4-n-hexyloxycyanobenzene (I) dissolved in 4-n-pentyloxyphenyl-trans-4-n-octylcyclohexylcarboxylate (II) were carried out from 1 kHz to 10 MHz in the nematic, smectic A and smectic B phases. The relaxation frequency of I parallel to the director is about 05 MHz in the S_Bphase and increases rapidly at the transition from S_B to S_A.     

Solubility and Enhanced Tension of Solute in Solution

Abstract

In solution, solute molecules B are coupled by attractive forces between them and all other molecules present; and these other molecules enhance the tension in the coupling force between solute molecules an amount π_B, the osmotic pressure of the solution solute. Two equilibria determine the n ^o _B moles of pure solute which dissolve in n ¹⁰ _A moles of pure liquid solvent. If at T the solute is solid and in excess, then 1) the n _B ^lsat moles of B in the n^l _A moles of A in a solution saturated with B are in thermodynamic equilibrium with the solid solute at the same T and p and 2) the n _B ^lsat moles of B and n^l _A moles of A may also be in chemical equilibrium with the moles of new molecular or ionic species formed in the solution. Solute molecules dissolve until the chemical potential of the solution solute, p^l _B(T p, x_B ^lsat), equals the chemical potential of pure solid solute at the same T and p, μ _B ^so(T, p). When the solution is saturated with B and the mole fraction of B is x_B ^lsat = n _B ^lsat/σj n ¹ _j, then the vapor pressures of the solid solute at T and p, the solution solute at T and p, and the pure undercooled liquid solute at T and p-π _B ^lsat are identical. If at T the n _B ^lo moles of pure solute and the n^l _A moles of pure solvent are liquids, then if molecules of B are allowed to dissolve in A while molecules of A are dissolved in B, the resulting solutions may 1) contain only molecules of A and B or 2) contain A and B which also react to form other ionic and molecular species. The two solutions may be identical or they may differ. In all cases, however, the mole ratio of n^l _Bn^l _A in both solutions must be identical.     

The crystal and magnetic structures of Ca2NdRuO6, Ca2HoRuO6, and Sr2ErRuO6

The crystal structure of Sr₂ErRuO₆ has been refined from neutron powder diffraction data collected at room temperature; space group P2₁/n, A = 5.7626(2), B = 5.7681(2), C = 8.1489(2) Å, β = 90.19(1)°. The structure is that of a distorted perovskite with a 1:1 ordered arrangement of Ru⁵⁺ and Er³⁺ over the 6-coordinate sites. Data collected at 4.2 K show the presence of long range antiferromagnetic order involving both Ru⁵⁺ and Er³⁺. The temperature dependence of the sublattice magnetizations is described. The crystal structure of Ca₂NdRuO₆ is also that of a distored perovskite (P2₁/n, A = 5.5564(1), B = 5.8296(1), C = 8.0085(1) β = 90.19(1)°. The β = 90.07(1)°) with a random distribution of Ca²⁺ and Nd³⁺ on the A site and a 1:1 ordered arrangement of Ca²⁺ and Ru⁵⁺ on the 6-coordinate B sites. The Ru⁵⁺ sublattice is antiferromagnetic at 4.2 K but there is no evidence for magnetic ordering of the Nd³⁺ ions. Ca₂HoRuO₆ is also a distorted perovskite (P2₁/n, A = 5.4991(1), B = 5.7725(1), C = 7.9381(2), β = 90.18(1)° at 4.2 K) with a cation distribution best represented as Ca_1.46Ho_0.54[Ca_0.54Ho_0.46Ru]O₆. There is no ordering among the Ca³⁺ or Ho³⁺ ions on either the A or the B sites, but the Ca/Ho ions form a 1:1 ordered arrangement with Ru⁵⁺ on the B sites. At 4.2 K the Ru⁵⁺ ions adopt a Type I antiferromagnetic arrangement but there is no evidence of long range magnetic ordering among the Ho³⁺ ions.     

Testing the capability of a polynomial‐modified gaussian model in the description and simulation of chromatographic peaks of amlodipine and its impurity in ion‐interaction chromatography

In this paper, the capability of a polynomial‐modified Gaussian model to relate the peak shape of basic analytes, amlodipine, and its impurity A, with the change of chromatographic conditions was tested. For the accurate simulation of real chromatographic peaks the authors proposed the three‐step procedure based on indirect modeling of peak width at 10% of peak height (W_0.1), individual values of left‐half width (A) and right‐half width (B), number of theoretical plates (N), and tailing factor (Tf). The values of retention factors corresponding to the peak beginning (k_B), peak apex (k_A), peak ending (k_E), and peak heights (H₀) of the analytes were directly modeled. Then, the investigated experimental domain was divided to acquire a grid of appropriate density, which allowed the subsequent calculation of W_0.1, A, B, N, and Tf. On the basis of the predicted results for Tf and N, as well as the defined criteria for the simulation the following conditions were selected: 33% acetonitrile/67% aqueous phase (55 mM perchloric acid, pH 2.2) at 40°C column temperature. Perfect agreement between predicted and experimental values was obtained confirming the ability of polynomial modified Gaussian model and three‐step procedure to successfully simulate the real chromatograms in ion‐interaction chromatography.     

The analytical resolution of parallel first‐ and second‐order reaction mechanisms

Given the species A₁ and A₂, the competition among the three different elementary processes (1) (2) (3) is frequently found in thermal and photochemical reaction systems. In the present paper, an analytical resolution of the system (1)–(3), performed under plausible contour conditions, namely, finite initial molar concentrations for both reactants, [A₂]₀ and [A₁]₀, and nonzero reaction rate coefficients k₁, k₂, and k₃, leads to the equation [A₁] = ((δ[A₂]^γ ? [A₂])/β) ? α, where α = k₁/2k₃, γ = β + 1 = 2k₃/k₂, and δ = ([A₂]₀ + β[A₁]₀ + β α))/[A₂]₀^γ. The comparison with a numerical integration employing the fourth‐order Runge–Kutta algorithm for the well‐known case of the oxidation of organic compounds by ferrate ion is performed. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 562–566, 2010     

The electronic structures of pyridine-N-oxide and related compounds

The electronic structures of pyridinen-oxide, 2- and 4-methoxypyridinen-oxide, their conjugate acids, and 2- and 4-pyridone are calculated using the Pariser-Parr-Pople SCF-CI approximation. The results indicate that the¹ B ₁¹ A ₁ transition of pyridinen-oxide lies in the same energy region as the transition previously assigned as beingn -*. The strong electronic transitions in the 250–280 m region of pyridine-n-oxide, 4-methoxypyridinen-oxide, and 4-pyridone are assigned as being¹ A ₁¹ A ₁.

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Zusammenfassung Die elektronischen Strukturen von Pyridin-N-Oxyd, 2- und 4-Methoxypyridin-N-Oxyd, ihrer Kationen, und von 2- und 4-Pyridon wurden nach der Methode von Pariser-Parr-Popple SCF-CI berechnet. Es ergibt sich, daß der¹ B ₁¹ A ₁ Übergang des Pyridin-N-Oxyds etwa die gleiche Energie besitzt, wie die bisher einemn -* Übergang zugeordnete Bande. Der intensitätsstarke Übergang des Pyridin-N-oxyds, 4-Methoxypyridin-N-oxyds und 4-Pyridons im Bereich von 250–280 m wird einem¹A₁¹ A ₁ Übergang zugeordnet.

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Résumé Les structures électroniques de l'oxyde de pyridine, desn-oxydes de 2- et 4-methoxypyridine, leurs cations, et les 2- et 4-pyridone sont calculés par l'approximation Pariser-Parr-Pople SCF-CI. Les résultats obtenus indiquent que la transition¹ B ₁¹ A ₁ dun-oxyde de pyridine est située dans la même région d'énergie que la transition assignée auparavant comme étantn -*. Les transitions électroniques fortes dans la région de 250–280 m dun-oxyde de pyridine, dun-oxyde de 4-methoxypyridine et du 4-pyridone sont assignées comme étant¹ A ₁¹ A ₁.

     

Investigations of the sodium and lithium D-lines in strong magnetic fields

Experimental and theoretical investigations of the splitting of the hyperfine structure of the sodium and lithium-D-lines in magnetic fields between 0 and 1 T were performed. In this magnetic field region the fine structure levelsJ=1/2 andJ=3/2 of the excited term² P begin to influence each other. In case of lithium crossings and anticrossings of hyperfine states stemming from different fine structure energy levelsJ=1/2 andJ=3/2 can be observed. The measurements were performed by laseratomic-beam spectroscopy in dependence on the applied external magnetic field strength. The experimental spectra were compared with computed spectra. Spectra were simulated by calculations using for the hyperfine hamiltonian two hyperfine constantsA andB in case of sodium and four hyperfine constantsa _c ,a _d ,a ₀ andb in case of lithium. Values for this constants could be derived by fitting the theoretical splittings to the experimental ones. For the first time theg _I — factor of sodium could be determined in a purely optical way.     

Avoided-crossing molecular-beam spectroscopy of CH3SiF3

The avoided-crossing molecular-beam method has been applied to CH₃SiF₃ in the ground torsional state. Stark and hyperfine rotational anticrossings have been studied, along with barrier anticrossings in which the zero-field energy differences depend only on the torsionial splittings. For υ = 0, pure rotational spectra were measured forJ = 13 ← 12 and 14 ← 13 with a mm-wave spectrometer and for J = 1 ← 0 with the molecular-beam spectrometer. Stark and Zeeman studies have been carried out with conventional beam techniques. From a simultaneous analysis of existing microwave data for υ ? 2 and the current measurements, it was found that the moment of inertia of the methyl top I_α = 3.170(2) amu A², the effective rotational constants A^eff = 4059.522(22) Mhz, and the effective height of the barrier V₃^eff = 413.979(14) cm^?1. The true values of A and V₃ have been obtained within certain approximations. The rotational constant B and several distortion constants including D_K were evaluated. In addition to determining the electric dipole moment μ 2.33938(14) D, the data yielded values for the distortion dipole constants μ_D and μ_J, and the molecular g-factors g_| and g_⊥.     

Calculation of activation volumes of thermal conversions of trimethylsilyl(cumyl) peroxide by the spline approximation method

The overall rate constants k_s of thermal conversions of trimethylsilyl(cumyl) peroxide (TMSCP) at pressures P up to 10 kbar are separated into components taking into account the ratios of the corresponding products: the rate constants of radical decomposition k_d and the rate constant of rearrangement k _r. Spline approximation of experimental dependences of lnk on P is used to determine the continuous dependence of the activation volume V^# on P in the solvents cyclohexane, anisole, toluene, n-nonane, isopropylbenzene, and tert-butylbenzene. The dependences of V_s^#, V_d^#, V_r^# on P are synchronous and nonordinary, and their nature significantly depends on the choice of a solvent. Spline approximation of experimental dependences of the TMSCP concentrations on the reaction time in isopropylbenzene at various P is used to find differential constants k_s , which generally increase with the reaction time, especially in the pressure interval 5–10 kbar.Translated from Kinetika i Kataliz, Vol. 45, No. 6, 2004, pp. 836–841.Original Russian Text Copyright © 2004 by Zhulin, Rudakov, Antonovskii.     

Spectral moments of polymer graphs

Summary It is shown that for anyk, thekth spectral moment of a polymer graph composed ofn monomer units is an exact linear function of the parametern. This linear relation holds for all values ofn, greater than a critical value ₀=₀(k).on leave from Faculty of Science, University of Kragujevac     

Small-angle neutron scattering study on the miscibility and concentration fluctuation of hydrogen-bonded polymer blends

Thermal concentration fluctuation in the blends of deuterated poly(ethylene oxide) (dPEO) and poly(vinyl acetate-co-vinyl alcohol) [P(VAc-VOH)] with various VOH contents f_OH were examined by small angle neutron scattering techniques at a fixed blend composition, dPEO/P(VAc-VOH) = 20/80 which is close to the critical composition. Blends at the highest f_OH (=0.35) showed a non-Lorentzian scattering profile: specifically the scattering intensities at the low q (angle) region were suppressed compared to those expected from the random phase approximation (RPA) theory. However, for the blends at lower f_OH (≤0.28), the profiles could be represented by the RPA. Using the RPA we determined effective values of the Flory-Huggins interaction parameter χ_eff as a function of f_OH (=0–0.28). The χ_eff showed the minimum around f_OH = 0.1–0.18 meaning the highest miscibility of the blend at these f_OH. On the basis of the random copolymer theory, we evaluated the three interaction parameters χ_Ac–EO, χ_EO–OH, and χ_Ac–OH separately from the χ_eff(f_OH) and found the order of magnitude; χ_Ac–EO < 0 < χ_EO–OH < χ_Ac–OH. The largest positive χ_Ac–OH showing intrachain interaction in the P(VAc-VOH) copolymer was concluded to be the origin of the enhanced miscibility at around f_OH = 0.1–0.18. On the basis of the Coleman and Painter's theory, the effects of hydrogen bonding on these three χ_A-B were discussed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2556–2565, 2008