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     

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.     

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.     

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.     

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.     

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.     

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).      

The stability of silver iodide sols in the presence of polyacrylic acids of various molecular weights

Summary The effect of a series of polyacrylic acids, ranging in molecular weight from 1.67×10⁴ to 2.36×10⁶, on the stability of positively charged silver iodide particles has been examined. Flocculation of the sol occurred at a well defined concentration of polyacrylic acid,c _f , and a further increase in concentration of the polyelectrolyte caused restabilization of the sol. Over the range examinedc _f appeared to be related to the viscosity average molecular weight of the acid,M _v , by an equation of the form,c _f =a ·M _v ^{– b} wherea andb are constants.     

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.     

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.     

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     

Spectral Study of the Reaction of Functionally Substituted Enehydrazides with Proton Donors

Reactions of new enehydrazides, N',N'-dimethyl-N-vinylpropenohydrazide and N',N'-dimethyl-N-vinylbenzohydrazide with chloroform, phenol, and hydrogen chloride in carbon tetrachloride were studied by IR spectroscopy. In the first two cases, molecular complexes are formed between the hydrazide and proton donor. The reaction of N',N'-dimethyl-N-vinylpropenohydrazide with HCl results in formation of dihydropyrazole derivative which exists as a tautomeric mixture of the major lactam and minor lactim forms. N',N'-dimethyl-N-vinylbenzohydrazide reacts with hydrogen chloride to give protonated form in which proton is localized on the amino nitrogen atom. The structure of the initial compounds and the products was analyzed in terms of AM1 quantum-chemical calculations.     

An ab initio study of the geometry and energy of six planar conformers of β-hydroxyacrolein

Ab initio calculations with full geometry optimization have been carried out on the planar cCc, cTc, tTc, tCt, tTt, and cCt conformers of β-hydroxyacrolein using the 4-21G basis set, and on the cCc and cCt conformers using the 4-31G basis set. The hydrogen-bonded cCc conformer is the most stable and the cCt conformer the least stable, with the other conformers following the above sequence. β-Hydroxy substitution has scarcely any influence on the geometry of the trans-acrolein structure, whereas the geometry of the cis-acrolein structure shows significant changes which depend on whether the O? H group is cis or trans with respect to the CHO group about the C?C bond. The ΔE_T values for cis → trans isomerization about the C? C bond in cCt and cTc support the hypothesis that these changes in geometry are the result of a destabilizing interaction in cCt and a stabilizing interaction in cTc. The geometry of the hydrogen-bonded structure cCc sets it apart from all the other conformers: it has by far the longest C?C, the longest C?O, the longest O? H, the shortest C? C, and the shortest C? O. Its formation from cCt involves a lengthening of C?C, C?O, and O? H and a shortening of C? C and C? O, indicating a delocalization of charge within the ring. 4-21G calculations have also been made for a distorted cCt structure that has the same bond lengths and angles as the equilibrium cCc structure, and the distortion energy, cCt (equm. geom.) → cCt (distorted geom.), is found to be +13.1 kJ mole^?1. Taking the energy of this distorted cCt structure as the baseline, the hydrogen-bonding energy in cCc is found to be —80.3 kJ mole^?1.     

Theoretical calculation of vertical ionization potentials of B2H6 by means of ΔESCF procedures

The vertical ionization potentials (IPS ) of B₂H₆ are calculated by means of the ΔE_SCF procedure, within the scheme of ab initio LCAO-MO-HF-SCF . The basis set used is LEMAO -3G. The scaling factors of the various atomic orbitals for the ground state and for the various hole states are optimized independently. The iteration procedure is specially designed to avoid the changes of the symmetry of the remaining occupied orbitals. The 1 ag (B1s) hole is found to be localized. The vertical IP of the 1 ag electron is calculated to be 196.5 eV, in fair agreement with experimental value. The D_2h symmetry is thereby broken and reduced to C_2V symmetry. The valence holes are found to be delocalized. The calculated vertical IPS are: 21.781, 16.974, 14.842, 14.389, 13.599, and 12.380 eV for the 2ag, 2b1u, 1b3u, 1b2u, 3ag, and 1b3g electrons, respectively. The agreement with experimental values is much better than the Koopmans' values. All these results are in favor of the concept that the nature of the convelent bond should be considered as a result of the mutual interactions and mutual conditioning between the wave nature of the electronic motion on the one side and the various attractive and repulsive factors on the other side.     

Grafting onto wool. V. Kinetics of graft copolymerization of methyl methacrylate in the viscous media of wool fibers

The graft copolymerization of methyl methacrylate in S-carboxymethylated wool fibers was investigated in the aqueous LiBr-K₂S₂O₈ system. The rate of grafting, the degree of polymerization of graft polymer, and the number of grafting sites were determined on varying the thiol content at a constant concentration of monomer. Kinetic considerations lead to the following expression in agreement with the experimental results: Z/DP = {(k_td + k_tc)/k_p²[M]²} R_p, where Z is the number of DNP endgroups of polymer; DP is the average degree of polymerization; k_p, k_td, and k_tc are the rate constants of propagation, termination by disproportionation, and termination by recombination, respectively; [M] is the concentration of monomer in fibers, and R_p is the overall rate of grafting. For wool fibers in media sufficiently high viscosity, the rate constants k_td and k_tc of diffusion-controlled termination are approximately equal and not affected by the change in cross-link density, provided that the thiol and disulfide interchange occurs. The possibility of occurrence of mechanical bond scission through a radical mechanism is involved in systems with extremely small amounts of thiol groups.     

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.     

Copolymerization characteristics of S-vinyl-O-tert-butylthiocarbonate

Poly-S-vinyl-O-tert-butylthiocarbonate is an excellent precursor to poly(vinyl mercaptan) because the tert-butyloxycarbonyl blocking group can be removed by either acid hydrolysis or thermolysis under conditions which minimize the oxidation of the liberated mercaptan to disulfide. Dilatometric studies of the homopolymerization of S-vinyl-O-tert-butylthiocarbonate demonstrated that the polymerization rate was directly proportional to the concentration of free-radical initiator; no thermal initiation was observed. The molecular weight of the homopolymers and copolymers ranged from 30,000 to 50,000 (GPC). Copolymerization of S-vinyl-O-tert-butylthiocarbonate (M₂) with styrene, (r₁ = 3.0, r₂ = 0.2), methyl methacrylate (r₁ = 1.40, r₂ = 0.17) and vinyl acetate (r₁ = 0.04, r₂ = 11.0) indicated that a sulfur atom adjacent to the vinyl group increases the resonance stability (Q₂ = 0.5) and the electron density (e₂ = ?1.4) of the double bond and the corresponding radical. Water-soluble copolymers could be prépared by incorporating either N-vinylpyrrolidone (r₁ = 0.12, r₂ = 3.94) or N-isopropylacrylamide (r₁ = 1.17, r₂ = 0.3) with M₂. The water solubility of the copolymers decreased markedly when the tert-butyloxycarbonyl group was removed. Copolymers of M₂ with N-vinyl-O-tert-butylcarbamate (r₁ = 0.13, r₂ = 5.10) were utilized to prepare crosslinked poly(vinyl amine–vinyl mercaptan); the crosslinking resulted from urea linkages formed during thermolysis of the copolymer.