The mean spherical model in a random external field and the replica method

We provide a quick elementary solution of the mean spherical model in a random external field. This also allows an immediate proof of the self-averaging property of the free energy. We calculate the free energy by means of the replica method, i.e., for any (not necessarily integer) replica numbern, and show that when a phase transition occurs the limits andn 0 are not interchangeable.     

RELATIONSHIPS BETWEEN X—H STRETCHING OVERTONE FREQUENCIES AND BOND LENGTHS/BOND ANGLES

A relationship between the X-H (X = N, O, C, and so on) equilibrium bond length in a Morse oscillator and the X-H stretching overtone frequency shifts is obtained theoretically. We use the equation to discuss the empirical linear relationships that have been proposed for heterocyclics, alkanes and fluorinated benzenes. On the other hand, a unified relationship between the X-H bond angles and the experimental quantities (ω(?) and the coupling strength λ) is also presented for XH2, XH, and XH4 molecules or molecular fragments. Calculations of X-H bond angles for a number of molecules show that the results from our equations are in excellent agreement with the experimental values. Also we can extract the information of relative magnitude of bond coupling force field.     

Thermodynamics of phenylated polyphenylene between 0 and 340 K

In an adiabatic vacuum calorimeter, the temperature dependence of the heat capacity C _p of phenylated polyphenylene and initial comonomer 1,4-bis(2,4,5-triphenylcyclopentadienone-3-yl)benzene was studied between 6 and 340 K with an uncertainty of about 0.2%. In a calorimeter with a static bomb and an isothermal shield their energies of combustion DUcomb were measured. From the experimental data, the thermodynamic functions C _p ⁰ (T), H ⁰(T)-H ⁰(0), S ⁰(T)-S⁰(0), G ⁰(T)-H ⁰(0) were calculated from 0 to 340 K, and standard enthalpies of combustion ΔH _comb ⁰ and thermodynamic parameters of formation-enthalpies ΔH _f ⁰, entropies ΔH _f ⁰, Gibbs functions ΔG _f ⁰ - of the substances studied were estimated at T=298.15 K at standard pressure. The results were used to calculate the thermodynamic characteristics (ΔH _f ⁰ ,ΔS _f ⁰, ΔG _f ⁰) of phenylated polyphenylene synthesis in the range from 0 to 340 K. This revised version was published online in July 2006 with corrections to the Cover Date.     

An equilibrium and calorimetric investigation of the hydrolysis of L-tryptophan to (indole + pyruvate + ammonia)

Apparent equilibrium constants and calorimetric enthalpies of reaction have been measured for the reaction L-tryptophan(aq) + H₂O(l) = indole(aq) + pyruvate(aq) + ammonia(aq) which is catalyzed by L-tryptophanase. High-pressure liquid-chromatography and microcalorimetery were used to perform these measurements. The equilibrium measurements were performed as a function of pH, temperature, and ionic strength. The results have been interpreted with a chemical equilibrium model to obtain thermodynamic quantities for the reference reaction: L-tryptophan(aq) + H₂O(l) = indole(aq) + pyruvate^–(aq) + NH ₄ ⁺ (aq). At T=25°C and I_m=O the results for this reaction are: K^o=(1.05±0.13)×10^–4, G°=(22.71±0.33) kJ-mol^–1, H°=(62.0±2.3) kJ-mol^–1, and S°=(132±8) J-K^–1-mol^–1. These results have been used together with thermodynamic results from the literature to calculate standard Gibbs energies of formation, standard enthalpies of formation, standard molar entropies, standard molar heat capacities, and standard transformed formation properties for the substances participating in this reaction.Presented at the Symposium, 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.     

Melt‐state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉_o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉_o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np³ (MPa), and the entanglement molecular weight, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002     

四唑及其衍生物的理论研究Ⅷ: 硝氨四唑衍生物的从头算

运用从头计算法,在HF/6-31G^*水平下,全优化计算了7种硝氨四唑衍生物的分子几何和电子结构。结果表明,标题物的四唑环近似为平面构型;2H式中性分子的芳香性大于相应的1H式异构体。5-硝氨-1H四唑分子内氢键使硝氨基与环共面;其余标题物中硝氨基与环垂直。不同水平下的总能量计算表明,标题物中电子相关效应显著;1H式中性分子较2H式的能量高,5-硝氨四唑负离子在三个负离子中最稳定。根据电荷分布阐明了四唑环质子化位置和标题物与金属的配位方式。此外还计算了各标题物的红外光谱及热力学性质。     

A conductance study of the association of alkali cations with 1,13-dibenzo-24-crown-8 in acetonitrile

A conductance study concerning the association of Na⁺, K⁺, Rb⁺, and Cs⁺ with 1,13-dibenzo-24-crown-8 in acetonitrile has been carried out at 35, 30, 25, 20, and 15°C. The observed molar conductivities were found to decrease significantly for mole ratios less than unity. A model involving 11 stoichiometry has been used to analyze the conductivity data. The stability constant, K, and the molar conductivity _C for each 11 complex were determined from the conductivity data by using a nonlinear least squares curve fitting procedure. The binding sequence, based on the value of log K at 25°C, is found to be Rb⁺>Cs⁺>K⁺>Na⁺. Values of H^o and S^o are reported and their significance is discussed.     

Cure behavior of epoxy resin/MMT/DETA nanocomposite

The Flory's gelation theory, non-equilibrium thermodynamic fluctuation theory and Avrami equation have been used to predict the gel time t _g and the cure behavior of epoxy resin/organo-montmorillonite/diethylenetriamine intercalated nanocomposites at various temperatures and organo-montmorillonite loadings. The theoretical prediction is in good agreement with the experimental results obtained by dynamic torsional vibration method, and the results show that the addition of organo-montmorillonite reduces the gelation time t _gand increases the rate of curing reaction, the value of k, and half-time of cure after gelation point t_1/2 decreases with the increasing of cure temperature, and the value of n is ~2 at the lower temperatures (<60°C) and decreases to ~1.5 as the temperature increases, and the addition of organo-montmorillonite decreases the apparent activation energy of the cure reaction before gelation point, but has no apparent effect on the apparent activation energy of the cure reaction after gelation point. There is no special curing process required for the formation of epoxy resin/organo-montmorillonite/diethylenetriamine intercalated nanocomposite. This revised version was published online in July 2006 with corrections to the Cover Date.     

Correlation analysis of quantum chemical data and the polarizability effect in H-complexes

The study is concerned with analysis of the energies of formation (E), frequency shifts (Δν) in IR spectra, ionization potentials (IP) of H-complexes, hydrogen bond lengths (r), and spin densities (sd) in H-complexes involving radical cations, obtained from quantum chemical calculations for 20 series of H-complexes. It was for the first time established that the E, IP, r, and sd values and the changes in enthalpy (δH) depend not only on the inductive and resonance effects but also on the polarizability effect of the substituents bound to the donor and acceptor centers in the H-complexes. Interrelations between the polarizability effect and the molecular structure of H-complexes are considered. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 602–608, April, 2006.     

Application of a chemical equilibrium model to thermodynamic functions of transfer of alcohols from water to aqueous surfactants

In ternary aqueous solutions, hydrophobic solutes such as alcohols tend to aggregate with surfactants to form mixed micelles. These systems can be studied by meas of the functions of transfer of hydrophobic solutes from water to aqueous solutions of surfactant. These thermodynamic functions often go through extrema in the critical micellar concentration (CMC) region of the surfactant. A simple model based on interactions between surfactant and hydrophobic solute monomers, on the distribution of the hydrophobic solute between water and the micelles and on the shift in the CMC induced by the hydrophobic solute, can simulate the magnitude and trends of the transfer functions using parameters which are mostly derived from the binary systems. In order to check the model more quantitatively, volumes and heat capacities of transfer of alcohols from water to aqueous solutions of a nonionic surfactant, octyldimethylamine oxide, were measured. A quantitative agreement was achieved with three adjustable parameters. Good fits are also obtained for the transfers to the ionic surfactants, octylamine hydrobromide and sodium dodecylsulfate. When the equilibrium displacement contribution is small, the distribution constants and the partial molar properties of the alcohols in the micellar phase agree well with the parameters obtained with similar models.