Estimation of the lattice heat capacity of rare-earth compounds

On the basis of the experimental data reported in literature, the contributions of cation mass (m) and molar volume (V) to lattice heat capacity (C) were analyzed. The volumetric-mass formula, C_x=(l —f)·C₁+f·C₂+C_m·(m_x — m_x′), was presented for estimating the heat capacities of rare-earth compounds. In the formula C₁ and C₂ represent the lattice heat capacities of two reference substances respectively, f = V_x—V₁/V₂—V₁ and C_m represents the lattice heat capacity variation with the variation 1 g of cation mass. The equation relating the C_m with temperatures was derived as follows: C_m = 0.084 e ?0.0074T ?0.27 e ?0.045T, and m_x and m_x′ (= (1 - f) m₁₊f m₂) represent the practical and “assumed” cation masses of the substance in question respectively.     

The spread of unicyclic graphs with given size of maximum matchings

The spread s(G) of a graph G is defined as s(G) = max _i,j |λ _i − λ _j |, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U ^*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U ^*(n,k), and the graph with the largest spread in U(n,k).      

Kinetics of the gas-phase thermal elimination of N-alkyl-pyrazoles

The kinetic study of the gas-phase thermal elimination reactions of N-ethyl-3,5 dimethyl-pyrazole (I), N-ethyl-pyrazole (II), N-sec-butyl-pyrazole (III), and N-tert-butyl-pyrazole (IV) using a flow system is reported. After obtaining activation parameters for I we carried out competitive reactions with II, III and IV using I as internal standard to obtain their E_a. The values of Δ(ΔH) calculated for II, III and IV agree with the little differences in E_a experimentally found.     

Approximation of any physicochemical constants of homologues with the use of recurrect functions

Dependencies of various physicochemical constants of organic compounds (A) versus number of carbon atoms in the molecule within different homologous series [A = f(n _C )] usually are non-linear. The simplest recurrent equation A(n + 1) = a A(n) + b, connecting A-values for homologues (n + 1 carbon atoms) with the values of the same constants for previous members of series (n carbon atoms), indicates practically “ideal” linear character for most properties of organic compounds. It is the reasonable basis for approximation (or extrapolation) any physicochemical constants within any homologous series using the standard approach without special selection of appropriate algebraic functions. Principal mathematical properties of the function A(n + 1) = aA(n) + b and some of its chemical applications are considered.     

Construction of characteristic polynomial of reciprocal graphs from the number of pendant vertices

A method for construction of the characteristic polynomial (CP) coefficients of the three classes of reciprocal graphs, viz., L_n + n(p), C_n + n(p), and K_1,n?1 + n(p), has been developed that requires only the value of n. The working formulas have been expressed in matrix product form, computer programs for which can easily be developed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Graphical representation of the state of orientation of polymer systems

The orientation distribution function for noncrystalline structural units in polymer systems cannot be determined completely from any experimental source; only the second and/or fourth moments of the distribution function, i.e., the second and/or fourth orders of the generalized orientation factors F_lm^j, can be evaluated. It is there-fore necessary to estimate the distribution function from F_2m^j and F_4m^j. In this paper, a graphical representation of the state of orientation is first discussed in terms of plots of F₄₀^j against F₂₀^j for several types of distribution functions for uniaxial orientation. These are three types of extreme concentration of the distribution at particular polar angles θ₀ given by θ₀ = 0, 0<θ₀<π/2, and θ₀ = π/2; five types of rather realistic distributions having single maxima at θ_j = 0, θ₀, π/2 and double maxima at θ_j = 0, π/2, and a single minimum at θ_j = θ₀; and four types of more realistic distributions including Kratky's floating rod model in an affine matrix. Second, estimation of the distribution function for uniaxial orientation from F₄₀^j and F₂₀^j is discussed quantitatively in terms of the mean-square error by three approximation methods: (a) expansion of the distribution function in finite series of spherical harmonics through the fourth order, (b) approximation of the distribution function as a composite of two components, random orientation and a particular orientation distribution given by N_a (cos²θ_j)^a, N_a being a constant, and (c) approximation of the distribution function by N_a (cos²θ_j)^a alone. It is concluded that when the orientation distribution is sharp, estimation by the second method of approximation gives a smaller error than the first.     

Chemical composition and antibacterial activity of methanolic extract and essential oil of Iranian Teucrium polium against some of phytobacteria

The antibacterial activity of essential oil and methanolic extract of Teucrium polium was determined against Pseudomonas aeruginosa, Pantoea agglomerans, Brenneria nigrifluens, Rhizobium radiobacter, Rhizobium vitis, Streptomyces scabies, Ralstonia solanacearum, Xanthomonas campestris and Pectobacterium cartovorum by disc diffusion method. Minimum inhibitory concentration and minimum bactericidal concentration were determined by using the serial dilution method. Chemical composition of essential oil and methanolic extract was determined by GC-MS and HPLC. α-Pinene (25.769%) and myrcene (12.507) were of the highest percentage in T. polium essential oil, and sinapic acid (15.553 mg/g) and eugenol (6.805 mg/g) were the major compounds in the methanolic extract. Our results indicate that both methanolic extract and essential oil did not show antibacterial activity against P. aeruginosa. Also the essential oil did not show antibacterial activity against P. cartovorum. In general, both methanolic extract and essential oil showed the same antibacterial activity against R. solanacearum, P. agglomerans, B. nigrifluens and S. scabies.     

Effect of length and number of interlinking molecules on the strength of adhesion

The fracture energy G of an adhesive bond appears to be a product of two terms: G = G_O [1 + f(R, T)], where G_O is the intrinsic (chemical) strength of the interface and f(R, T), usually much larger than unity, reflects energy dissipated within the adherends at a crack speed R and temperature T. Values of G_O have been determined for interlinked sheets of an SBR elastomer by measuring the peel strength at low rates and high temperatures, and in the swollen state, to minimize internal losses. Both the density ΔN and molecular length L of interlinking molecules were varied. G_O was found to increase in proportion to (ΔN)L^3/2, in accord with the molecular theory of Lake and Thomas. As the peel rate was raised and the test temperature lowered, G was considerably increased by internal dissipative processes, becoming as much as 1000 × G_O near the glass transition. The loss function f(R, T) was found to depend somewhat upon the strand length L, being about twice as large at intermediate peel rates when L was increased by 40%. It also depended on the density ΔN of interlinking molecules, being about twice as large at high peel rates when the density of interlinks was reduced by a factor of six. Thus, the loss function f(R, T) is greater when the interlinking molecules are few and long, and it is lower when they are many and short. However, it is mainly governed by two parameters: peel rate R and temperature difference (T − T_g), in accord with a viscoelastic loss mechanism. © 1996 John Wiley & Sons, Inc.     

Preparation of maleopimar adducts of polyfluoroalkyl esters of tall colophony

Maleopimar adducts of tall colophony esters with alcohols-telomers 1H,1H,5H-perfluoropentane-1-ol, 1H,1H,7H-perfluoroheptane-1-ol, and 1H,1H,9H-perfluorononane-1-ol were synthesized in conditions of Diels-Alder reaction.     

Hydrostannylation of phosphaalkenes [1]

Hydrostannylation reactions of the phosphaalkenes 9,11, and 21 with the triorganotin hydrides 1 proceed by different routes. Whereas the trior-ganotin hydrides 1a,b undergo regioselective 1,2-addition to the P/C double bond of the P-aminophosphaalkene 9 to furnish the 2-stannylphosphanes 17a,b, the 1,2-addition products to the P-halophosphaalkenes 11 and 21 can only be postulated as the reactive intermediates 20 and 23, respectively. The reactions of 11 with 1a,b proceed with cleavage of the triorganotin halide via the diphosphene 15 to furnish the cyclophosphanes 18 and 19. On the other hand, the hydrostannylation reactions of the phosphaalkene 21 are not selective, and the 1,3-diphosphetane 22 is isolated as one of the reaction products. © 1998 John Wiley & Sons, Inc. Heteroatom Chem 9:453–460, 1998     

Synthetic transformations of methylenelactones of eudesmanic type. Behavior of isoalantolactone under the conitions of heck reaction

By Heck reaction of isoalantolactone with aryl bromides or aryl iodides (3aR,4aS, 8aR,9aR,E)-3-arylmethylidene-8a-methyl-5-methylidenedecahydronaphtho[2,3-b]furan-2(3H)-ones and (4aS,8aR,9aS)-3-arylmethyl-8a-methyl-5-methylidene-4a,5,6,7,8,8a,9,9a-octahydronaphtho[2,3-b]furan-2(4H)-ones, products of the double bond shift, were synthesized. The yields of the arylation products depend on the nature of the catalytic system and on the structure of the aryl halide. The structures of (3aR,4aS,8aR,9aR,E)-3-(3,4-dimethoxybenzylidene)-8amethyl-5-methylidenedecahydronaphtho[2,3-b]furan-2(3H)-one and (4aS,8aR,9aS)-3-(2-methylsulfanylbenzyl)-8amethyl-5-methylidene-4a,5,6,7,8,8a,9,9a-octahydronaphtho[2,3-b]furan-2(4H)-one were proved by XRD analysis.     

The kinetics of the decarboxylation of n-butylmalonic acid in alkanols and amines

Rate constants and activation parameters are reported for the decarboxylation of n-butylmalonic acid in four normal alkanols (hexanol? 1, octanol? 1, decanol? 1, and dodecanol? 1) and in five amines (aniline, N-methylaniline, N-ethylaniline, N-n-propylaniline, and N-n-butylaniline). Both ΔH? and ΔS? of the reaction in both homologous series decrease regularly with increasing length of the hydrocarbon chain of solvent. If we compare data for the reaction in alkanol–amine pairs containing the same total number of carbon atoms in the molecule, we find that the ΔH? values are identical, but that the value of ΔS? is 0.8 eu/mole higher for the reaction in the amines as compared with the alcohol. The rate constant, at all temperatures, is 1.5 times as large in the amine as it is in the corresponding alcohol. Empirical equations are deduced relating the parameters ΔH? ΔS? ΔG? and k of the reaction to the parameters n and T, where n is the total number of carbon atoms in the solvent molecule and T is the absolute temperature. The results reported herein are compared with previously reported data for malonic acid.     

A method for simulation of photochemical processes and calculation of quantum yields of reactions

The possibility of construction of a semiempirical method for simulation of photochemical processes and calculation of quantum yields of reactions has been studied. The practicability of the approach was demonstrated for the o-xylene → m-xylene, m-xylene → p-xylene, m-xylene → o-xylene, and o-diethylbenzene → m-diethylbenzene photoisomerization reactions as an example. The calculated quantum yields of the reactions are in qualitative agreement with experimental data.     

Theory of polydisperse reacting polymer systems

The kinetics of irreversible reactions between polymer chains of different molecular weights are studied, with emphasis on the case of highly reactive end groups. We calculate the rate constant k(N, M) for reaction between chains of lengths N and M respectively, in dilute and semi-dilute solutions and in the melt. In all cases, k(N, M) is dominated by the shortest chain: the limit k(N) ≡ k(N, ∞) is well-defined and scales as if both chains were of length N. In dilute solutions k(N, M) obeys mean field theory, being proportional to the equilibrium reactive group contact probability. For melts and concentrated solutions, k(N, M) follows diffusion-controlled laws: k(N, M) ≈ (R/τ_N)ƒ(M/N) where R_N and τ_N are the coil size and relaxation time of the shortest chain N, and ƒ(M/N) is a cross-over function describing the approach to the asymptotic form k(N) for M/N ≫ 1. We calculate the leading contributions to this cross-over function, which has universal forms depending on the concentration regime. The implications of these results for high-conversion free-radical polymerization are discussed.     

Some aspects of the polymerization of N-vinylcarbazole by grignard reagents

The polymerization of N-vinylcarbazole (NVC) initiated by PhMgBr in benzene was studied at 32°C. R_p is second order with respect to PhMgBr concentration but increases with NVC concentration (up to 0.06 M) and falls thereafter. R_p and P _n are depressed by the addition of thiophene and water. Modifiers such as benzaldehyde, butanone, and ethylene glycol practically inhibit the polymerization. Carbon tetrachloride and carbon dioxide, when passed through the NVC solution first, enhance the R_p and P _n increases with increasing PhMgBr and NVC concentrations, respectively. R_p increases with temperature, but P _n shows a maxium at a certain temperature. A cationic mechanism has been proposed where the polymerization is initiated by RMg⁺ cations produced from the ionization of PhMgBr by the Ashby and Smith mechanism.     

Isomorphism in electron-pair densities of atoms

The spherically averaged electron-pair intracule (relative motion) h(u) and extracule (center-of-mass motion) d(R) densities are a couple of densities which characterize the motion of electron pairs in atomic systems. We study a generalized electron-pair density (q; a, b) that represents the probability density function for the magnitude of two-electron vector a r _j +b r _k of any pair of electrons j and k to be q, where a and b are nonzero real numbers. In particular, h(u)=g(u;1, −1) and d(R) = . It is shown that the scaling property of the Dirac delta function and the inversion symmetry of orbitals in atoms due to the central force field generate several isomorphic relations in the electron-pair density (q; a, b) with respect to the two parameters a and b. The approximate isomorphism d(R)≅8h(2R) known in the literature between the intracule and extracule densities is a special case of the present results. Received: 24 May 2000 / Accepted: 18 July 2000 / Published online: 27 September 2000     

Molecular Recognition of Pyranosides by a Family of Trimeric, 1,1′-Binaphthalene-Derived Cyclophane Receptors

The synthesis and carbohydrate-recognition properties of a new family of optically active cyclophane receptors, 1 – 3 , in which three 1,1′-binaphthalene-2,2′-diol spacers are interconnected by three buta-1,3-diynediyl linkers, are described. The macrocycles all contain highly preorganized cavities lined with six convergent OH groups for H-bonding and complementary in size and shape to monosaccharides. Compounds 1 – 3 differ by the functionality attached to the major groove of the 1,1′-binaphthalene-2,2′-diol spacers. The major grooves of the spacers in 2 are unsubstituted, whereas those in 1 bear benzyloxy (BnO) groups in the 7,7′-positions and those in 3 2-phenylethyl groups in the 6,6′-positions. The preparation of the more planar, D₃-symmetrical receptors (R,R,R)- 1 (Schemes 1 and 2), (S,S,S)- 1 (Scheme 4), (S,S,S)- 2 (Scheme 5), and (S,S,S)- 3 (Scheme 8) involved as key step the Glaser-Hay cyclotrimerization of the corresponding OH-protected 3,3′-diethynyl-1,1′-binaphthalene-2,2′-diol precursors, which yielded tetrameric and pentameric macrocycles in addition to the desired trimeric compounds. The synthesis of the less planar, C₂-symmetrical receptors (R,R,S)- 2 (Scheme 6) and (S,S,R)- 3 (Scheme 9) proceeded via two Glaser-Hay coupling steps. First, two monomeric precursors of identical configuration were oxidatively coupled to give a dimeric intermediate which was then subjected to macrocyclization with a third monomeric 1,1′-binaphthalene precursor of opposite configuration. The 3,3′-dialkynylation of the OH-protected 1,1′-binaphthalene-2,2′-diol precursors for the macrocyclizations was either performed by Stille (Scheme 1) or by Sonogashira (Schemes 4, 5, and 8) cross-coupling reactions. The flat D₃-symmetrical receptors (R,R,R)- 1 and (S,S,S)- 1 formed 1 : 1 cavity inclusion complexes with octyl 1-O-pyranosides in CDCl₃ (300 K) with moderate stability (ΔG⁰ ca. −3 kcal mol⁻¹) as well as moderate diastereo- (Δ(ΔG⁰) up to 0.7 kcal mol⁻¹) and enantioselectivity (Δ(ΔG⁰)=0.4 kcal mol⁻¹) (Table 1). Stoichiometric 1 : 1 complexation by (S,S,S)- 2 and (S,S,S)- 3 could not be investigated by ¹H-NMR binding titrations, due to very strong signal broadening. This broadening of the ¹H-NMR resonances is presumably indicative of higher-order associations, in which the planar macrocycles sandwich the carbohydrate guests. The less planar C₂-symmetrical receptor (S,S,R)- 3 formed stable 1 : 1 complexes with binding free enthalpies of up to ΔG⁰=−5.0 kcal mol⁻¹ (Table 2). With diastereoselectivities up to Δ(ΔG⁰)=1.3 kcal mol⁻¹ and enantioselectivities of Δ(ΔG⁰)=0.9 kcal mol⁻¹, (S,S,R)- 3 is among the most selective artificial carbohydrate receptors known.     

Relationships on the effect of water on glass transition temperature and young's modulus of nylon 6

The glass transition temperature T_g of nylon 6 decreases monotonically toward a finite value T_gl upon increase of the moisture content. The mechanism of this decrease entails the reversible replacement of intercaternary hydrogen bonds in the accessible regions of the polyamide. The limiting glass transition temperature T_gl is approached when the moisture content approaches W_l, which corresponds to the amount of water required for complete interaction with all accessible amide groups. Denoting with T_g0 the glass transition temperature of the dry polymer, the effect of water on T_g is represented by the equation, T_g = (ΔT_g)₀ exp{?[ln(ΔT_g)₀]W/_τW_l} + T_gl, where (ΔT_g)₀ = T_g0 ?T_gl, and τ = W(T_gl+1)/W_l. This equation appears to be generally applicable to hydrophilic polymers, since correspondingly calculated data are also in very good agreement with experimental data for polymers such as nylon 66, poly(vinyl alcohol), and polyN-vinylpyrrolidone. The effect of water of Young's modulus E of nylon 6 is represented by an analogous relationship, and the quantity In[(E?E_l)/(T_g?T_gl)] is a linear function of the moisture content.