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).      

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.     

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.     

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.     

Synthesis of Phenyl- and Benzyl-Substituted Pyrrolidines and of a Piperidine by Intramolecular C-Alkylation. Synthons for tricyclic skeletons

The construction of new or novelly functionalized annulated and bridged tricylic compounds by two consecutive C,C-bond formations (a and b in la , Scheme 1) is described. In a first step, chloroalkyl-substituted aminonitriles yielded pyrrolidines 8 , 15a , 15b , 23 , 25 and piperidine 18 by carbanionic ring closure (Schemes 5, 6, 7 and 8). Subsequent Friedel-Crafts cyclization transformed the β-aminonitriles 8 , 15a , 15b , and 18 either directly or via their carboxylic acid derivatives to the indeno [1, 2-c]pyrrole, 2, 5-methano-3-benzazocine, benz [f]isoindoline and 1, 4-ethano-2-benzazapine skeletons 11 , 16a , 16b and 21 , respectively (Schemes 5, 6 and 7). By classical ring expansion reactions the pyrrolo [3, 4-c]isoquinoline and benzopyrano-[3, 4-c]pyrrole skeletons 28 resp. 31 were obtained from 11 (Scheme 9).     

Analysis of the melt viscosity and glass transition of polystyrene

The melt viscosity, the glass transition, and the effect of pressure on these are analyzed for polystyrene on the basis of the Tammann-Hesse viscosity equation: log η = log A + B/(T ? T₀). Evidence that the glass transition is an isoviscosity state (log η_g ? 13) for lower molecular weight fractions (M < M_c) is reviewed. For a polystyrene fraction of intermediate molecular weight (M ? 19,000; t_g = 89°C.), it is shown that B is independent of the p–v–T state of the polymer liquid and that dT₀/dP = dT_g/dP. This is consistent with the postulate that B is determined by the internal barriers to rotation in the isolated polymer chain. Relationships are derived for flow “activation energies” at constant pressure and at constant volume, and for the “activation volume.” Values for polystyrene along the zero-pressure isobar and along the constant viscosity, glasstransition line are reported. For the latter, ΔV_g* is constant and corresponds to about 10 styrene units. The “free volume” viscosity equation: log η = log A + b/2.3?, is reexamined. For polystyrene and polyisobutylene, ?_g/b = 0.03, but ?_g and b themselves differ appreciably in these polymers. The parameter b is the product of an equilibrium term Δα and the kinetic term B, and none of these is a “universal” constant for different polymers. The physical significance of the free volume parameter ?, particularly with regard to the “excess” liquid volume, remains undefined. Two new relationships for dT_g/dP, one an exact derivation and the other an empirical correlation, are presented.     

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.     

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.     

Enumeration of the isomers of phenylenes

Summary The [h]phenylene C_6h H_2h+4 isomers are enumerated up toh=12. The numbers are compared with old and new data for C _n H₅ isomers of benzenoids, fluoranthenoids and biphenylenoids.

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Anzahl möglicher Isomerer von Phenylenen

Zusammenfassung Die Anzahl der [h]Phenylen-Isomeren C_6h H_2h+4 wurde bish=12 ausgewertet. Die Zahlen wurden mit alten und neuen Daten für C _n H _s -Isomere von Benzenoiden, Fluoranthenoiden und Biphenyloiden verglichen.

     

Phenomenological theory of the kinetics of ultrasonic emulsification

Summary A working model is given for the rate of ultrasonic emulsification, considering the dispersion at the interface (areaA) and the coagulations in the volumeV of the emulsion. A bimolecular coagulation leads to the equationc=c _∞tanhbt;c _∞=(Aα/Vβ)^1/2;b=(Aαβ/V)^1/2 while a monomolecular coagulation givesc=c _∞{1−exp (−at)};c _∞=Aα/Vβ;a=β. The experiments on the dependence of c_∞,a andb uponA andV favour the bimolecular coagulation. The results are satisfactorily explained on general theoretical grounds.

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Zusammenfassung Ein Arbeitsmodell für die Geschwindigkeit der Ultraschallemulgierung wird entwickelt, das Dispersion in der Grenzfl?che (Fl?cheA) und Koagulation im Volumen (V) der Emulsion annimmt. Eine bimolekulare Koagulation führt zu der Gleichung:c=c _∞ tanhbt;c _∞=(Aα/Vβ)^1/2;b=(Aαβ/V)^1/2, eine monomolekulare dagegen zu:c=c _∞{1−exp (at−)};c _∞=Aα/Vβ;α=β. Die Versuche über die Abh?ngigkeit vonc _∞,a undb vonA undV scheinen für bimolekulare Koagulation zu sprechen. Die Ergebnisse werden auf der Basis dieser einfachen theoretischen Grundlagen befriedigend erkl?rt.

     

Synthesis of Optically Active P‐Chiral and Optically Inactive Oligophosphines

A series of optically active P‐chiral oligophosphines (S,R,R,S)‐ 2 , (S,R,S,S,R,S)‐ 3 , (S,R,S,R,R,S,R,S)‐ 4 , and (S,R,S,R,S,R,R,S,R,S,R,S)‐ 5 with four, six, eight, and 12 chiral phosphorus atoms, respectively, were successfully synthesized by a step‐by‐step oxidative‐coupling reaction from (S,S)‐ 1 . The corresponding optically inactive oligophosphines 1′ – 5′ were also prepared. Their properties were characterized by DSC, XRD, and optical‐rotation analyses. While optically active bisphosphine (S,S)‐ 1 and tetraphosphine (S,R,R,S)‐ 2 behaved as small molecules, octaphosphine (S,R,S,R,R,S,R,S)‐ 4 and dodecaphosphine (S,R,S,R,S,R,R,S,R,S,R,S)‐ 5 exhibited the features of a polymer. Furthermore, DSC and XRD analyses showed that hexaphosphine (S,R,S,S,R,S)‐ 3 is an intermediate between a small molecule and a polymer. Comparison of optically active oligophosphines 1 – 5 with the corresponding optically inactive oligophosphines 1′ – 5′ revealed that the optically active phosphines have higher crystallinity than the optically inactive counterparts. It is considered that the properties of oligophosphines depend on the enantiomeric purity as well as the oligomer chain length.     

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.     

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.     

Rigidity percolation model of polymer fracture

A theory of the fracture of polymers with network microstructure was developed that was based on the vector, or rigidity percolation (RP) model of Kantor and Webman, in which the modulus, E, is related to the lattice bond fraction p, via E ～ [p ? p_c]^τ. The Hamiltonian for the lattice was replaced by the strain energy density function of the bulk polymer, U = σ²/2E, where σ is the applied stress and p was expressed in terms of the lattice perfection via the bond density ν, with the entanglement molecular weight, ν = ρ/M_e and appropriate measures of crosslink density for rubber, thermosets, and carbon nanotubes. The stored mechanical energy, U, was released by the random fracture of νD_o[p ? p_c] over stressed hot bonds of energy D_o ≈ 330 kJ/mol. The polymer fractured critically when p approached the percolation threshold p_c, and the net solution was obtained as σ = (2EνD_o [p ? p_c])^1/2 with a fracture energy, G_1c ～ [p ? p_c]. The fracture strength of amorphous and semicrystalline polymers in the bulk was well described by, σ = [ED_oρ/16 M_e]^1/2, or σ ≈ 4.6 GPa/M_e^1/2. Fracture by disentanglement was found to occur in a finite molecular weight range, M_c < M < M*, where M*/M_c ≈ 8, such that the critical draw ratio, λ_c = (M/M_c)^1/2, gave the molecular weight dependence of the fracture as G_1c ～ [(M/M_c)^1/2 ? 1]². The critical entanglement molecular weight, M_c, is related to the percolation threshold, p_c, via M_c = M_e/(1 ? p_c). Fracture by bond rupture was in accord with Flory's suggestion, G/G* = [1 ? M_c/M], where G* is the maximum fracture energy. Fracture of an ideal rubber with p = 1 was determined not to occur without strain hardening at λ > 4, such that the maximum stress, σ = E (λ ? 1/λ) = 3.75E. The fracture properties of rubber were found to behave as σ ～ ν, σ ～ E, and G_1c ～ ν. For highly crosslinked thermosets, it was predicted that σ ～ (Eν)^1/2, σ ～ (X ? X_c)^1/2, and G_1c ～ ν^?1/2, where X is the degree of reaction of the crosslinking groups and X_c defines the gelation point. When applied to carbon nanotubes (SWNT and MWNT) of diameter d and hexagonal bond density ν = j/b², the nominal stress as a function of diameter is σ(d) = [16 ED_o(p ? p_c) j/b]^1/2/d ≈ 211/d (GPa.nm) and the critical force, F_c(d) ≈ 166 d (nN/nm), in which j = 1.15, b = 0.142 nm, E ≈ 1 Tpa, and D_o = 518 kJ/mol. For polymer interfaces with Σ chains per unit area of length L and width X ～ L^1/2, G_1c is then ～ [p ? p_c], where p ～ ΣL/X. The results predicted by the RP fracture model were in good agreement with a considerable body of fracture data for linear polymers, rubbers, thermosets, and carbon nanotubes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 168–183, 2005     

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.     

Calculation of the Grüneisen constant of glassy polymers from thermoelastic data

Thermoelastic measurements on a glassy polymer make it possible to measure directly the quantity αV/C_p where α is the coefficient of linear expansion, V the specific volume, and C_p the specific heat at constant pressure. By further measuring the bulk modulus (B_T) it is possible to derive a relatively accurate value of the thermodynamic Gruneisen constant (γ_T) where γ_T = 3B_TαV/C_v. The values obtained decrease only slightly with temperature.