Quantum statistical theory of chemical reactions

Exact rate equations for chemical reactions taking place in a closed homogeneous system arbitrarily far from equilibrium are derived by use of a recently developed method. The possibly different kinetic temperatures of the species are taken into account. The diagram expansion of the integral kernels of the rate equations is given and the renormalization of the interaction carried out. In lowest order non-linear non-markovian equations are obtained which reduce after suitable approximations to the usual collision theory results.     

Stochastic models of firstorder nonequilibrium phase transitions in chemical reactions

The steady states of a simple nonlinear chemical system kept far from equilibrium are analyzed. A standard macroscopic analysis shows that the nonlinearity introduces an instability causing a transition analogous to a thermodynamic first-order phase transition. Near this transition the system exhibits hysteresis between two alternative steady states. Fluctuations are introduced into this model using a stochastic master equation. The solution of this master equation is unique, preventing two alternative exactly stable states. However, a quasi-hysteresis occurs involving transitions between alternative metastable steady states on a time scale that is longer than that of the fluctuations around the mean steady state values by a factor of the forme , where ø is the height of a generalized thermodynamic potential barrier between the two states. In the thermodynamic limit this time scale tends to infinity and we have essentially two alternative stable steady states.     

Determination of the rate constants of excited-complex formation and the diffusion rate constants for triplet-triplet annihilation kinetics for tetrapyrrole molecules in liquid solutions

With the flash-photolysis method, the kinetis of triplet-triplet annihilation (TTA) is investigated for a number of tetrapyrrole molecules in liquid solutions. Based on the analysis of the kinetic scheme of TTA through the formation of excited complexes (TT) a procedure for determining the constant of the rate of (TT) formation from two molecules in the triplet state (k₁) is proposed. The k₁ values obtained are equal to the rate constants for the processes controlled by molecular diffusion in the solution (K_d), which are calculated by a modified Vavilov-Debye formula. The values of K_d can be determined experimentally by the proposed procedure for processing the data on TTA. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 4, pp. 521–527, July–August, 1998.     

Relative rate constants for the formation of muonic radicals in liquid aromatic systems

The distribution of muon polarization between different radicals observed in neat p-di-fluorobenzene, aniline and bromobenzene and their binary mixtures with benzene has been measured and is interpreted in terms of relative rate constants for Mu addition. Mu shows the same intramolecular and intermolecular selectivity pattern as the heavier hydrogen isotopes, but its selectivity is smaller.Support by the Swiss National Foundation for Scientific Research, by the Swiss Institute for Nuclear Research (SIN), the Netherlands Organisation for the Advancement of Pure Research (Z.W.O.) and the Foundation for Fundamental Research on Matter (F.O.M.) are gratefully acknowledged.     

Elastic constants and the continuum theory of liquid crystals

Exact expressions for the elastic constants of arbitrary director fields are derived by expanding the free energy density in terms of the relevant invariants. It is shown that the anisotropic terms in the expansion can be dealt with completely, i.e. knowledge of the isotropic terms in the expansion suffices in order to obtain nunerical values for these constants. Some simple examples are given.     

Statistical theory of angular momentum polarization in chemical reactions

A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directions [kcirc] and [kcirc]′ and the product rotational angular momentum j′ are treated in detail, including both pairwise and triple correlations. Explicit formulae are given for three choices of the quantization axis: along [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.     

Statistical theory of the elastic constants of nematic liquid crystals

A statistical mechanical theory of the Frank elastic constants is formulated. The free energy functional is constructed for the deformed sample and the free energy density is defined for the case of small spatial gradients. The Frank constants are expressed in terms of the direct correlation function c(1, 2) and the orientational single particle distribution function. For the example of Onsager spherocylinders three constants K ₁, K ₂ and K ₃ are calculated. The results of these calculations are similar to those given by Priest and by Straley.     

Statistical theory of angular momentum polarization in chemical reactions

A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directions [kcirc] and [kcirc]′ and the product rotational angular momentum j′ are treated in detail, including both pairwise and triple correlations. Explicit formulae are given for three choices of the quantization axis : along [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.     

Visualizing chemical reactions in solution by picosecond x-ray diffraction

We present a time-resolved x-ray diffraction study to monitor the recombination of laser-dissociated iodine molecules dissolved in CCl4. The change in structure of iodine is followed during the whole recombination process. The deexcitation of solute molecules produces a heating of the solvent and induces tiny changes in its structure. The variations in the distance between pairs of chlorine atoms in adjacent CCl4 molecules are probed on the mA length scale. However, the most striking outcome of the present work is the experimental determination of temporally varying atom-atom pair distribution functions. Variations of the mean density of the solution during thermal expansion are also followed in real time. One concludes that not only time-resolved optical spectroscopy but also time-resolved x-ray diffraction can be used to monitor atomic motions in liquids.     

Stochastic theory of nonlinear rate processes with multiple stationary states

A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of $\text{O}$(N⁰) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is $\text{O}$(e^N). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.     

Thermodynamics of isothermal vitrification by chemical reactions in a liquid

Summary We report here first observations of the decrease in heat capacity during isothermal vitrification of a thermosetting polymer. A new experimental method has been developed for this study which allows simultaneous measurements of both the heat capacity and the enthalpy released as chemical reactions occur in quasi-isothermal conditions. During the curing the heat capacity of a thermoset first increases slightly, undergoes an abrupt decrease in a narrow range of time and thereafter slowly decreases. The abrupt decrease represents the irreversible transition of the liquid to a vitreous solid which is equivalent to the reversible glass transition appearing in a supercooled liquid when the temperature is lowered.     

Quantum cluster equilibrium theory of liquids: temperature dependent chemical shifts,quadrupole coupling constants and vibrational frequencies in liquid ethanol

Temperature dependent NMR chemical shifts for hydrogen and oxygen, NMR quadrupole coupling constants for deuterium and vibrational frequencies for the OH bond of liquid ethanol are calculated for the temperature range 250 to 350 K using the ab initio quantum cluster equilibrium method and compared with experimental measurements. The calculated NMR chemical shifts, quadrupole coupling constants and infrared vibrational frequencies are in good agreement with experimental measurements. The results indicate that cyclic tetramer and pentamer structures rather than linear structures are the principal components of liquid ethanol.     

Features of the kinetics of chemical reactions in a nanostructured liquid

A review of the literature on the supramolecular structure of a liquid medium and the kinetics of formation of the structure has been presented. The models that relate the kinetics of chemical reactions to the liquid medium structure have been discussed. It has been shown that the results of the mathematical modeling of the kinetics of reactions in a nanostructured liquid medium taking into account the difference in the reactivity of molecules of the reagents and associates are consistent with the experimental data; in particular, they can be used to explain the cause of the observed kinetic anomalies.     

Perturbation theory for large coupling constants

The perturbation technique for large coupling constantsg ² is used for obtaining the solutions of Schrödinger equation for a double exponential potential. In particular the solution valid forg ² e ^-r/2 g²e^-r/2 ? 1, is obtained int erms of confluent hypergeometric functions. A noteworthy aspect of this application is that the procedure developed can also be used for solving certain singular potentials.     

α，β— 蒎烯气相臭氧化速率常数的测定

对α-蒎烯、β-蒎烯和O3的大气反应进行了初步实验室模拟,利用长光程傅里叶变换红外光谱技术结合相对速率法测得在1.0×105Pa,296±3K条件下,α-蒎烯、β-蒎烯和O3气相反应的速率常数分别为2.83×1017cm3@molecule-1@s-1和1.48×1017cm3@molecule-1@s.     

Stochastic theory of nonequilibrium steady states. Part II: Applications in chemical biophysics

The mathematical theory of nonequilibrium steady state (NESS) has a natural application in open biochemical systems which have sustained source(s) and sink(s) in terms of a difference in their chemical potentials. After a brief introduction in Section 1, in Part II of this review, we present the widely studied biochemical enzyme kinetics, the workhorse of biochemical dynamic modeling, in terms of the theory of NESS (Section 2.1). We then show that several phenomena in enzyme kinetics, including a newly discovered activation-inhibition switching (Section 2.2) and the well-known non-Michaelis-Menten-cooperativity (Section 2.3) and kinetic proofreading (Section 2.4), are all consequences of the NESS of driven biochemical systems with associated cycle fluxes. Section 3 is focused on nonlinear and nonequilibrium systems of biochemical reactions. We use the phosphorylation-dephosphorylation cycle (PdPC), one of the most important biochemical signaling networks, as an example (Section 3.1). It starts with a brief introduction of the Delbrück-Gillespie process approach to mesoscopic biochemical kinetics (Sections 3.2 and 3.3). We shall discuss the zeroth-order ultrasensitivity of PdPC in terms of a new concept — the temporal cooperativity (Sections 3.4 and 3.5), as well as PdPC with feedback which leads to biochemical nonlinear bistability (Section 3.6). Also, both are nonequilibrium phenomena. PdPC with a nonlinear feedback is kinetically isomorphic to a self-regulating gene expression network, hence the theory of NESS discussed here could have wide applications to many other biochemical systems.     

Fundamental constants in effective theory

In the discussion between L.B. Okun, G. Veneziano, and M.J. Duff concerning the number of fundamental dimensionful constants in physics [9], they advocated, respectively, 3, 2, and 0 fundamental constants. Here, we consider this problem with an example of effective relativistic quantum field theory, which emerges in the low-energy corner of quantum liquids and which reproduces many features of our physics, including Lorentz invariance, chiral fermions, gauge fields, and dynamical gravity.     

利用溶液理论计算饱和甲烷中二氧化碳溶解度

求取二氧化碳在饱和液态甲烷中的溶解度,对于在较高温度下实现液化天然气至关重要。文中在理想溶液基础上,采用正规溶液关系式和改进的Scatchard-H ildebrand关系式进行二氧化碳的溶解度计算,并且在临界点附近采用经验公式对其进行修正。将上述计算结果与Davis实验数据进行比较后表明,改进的正规溶液理论计算方法在低于140K温区时可推荐用于此项溶解度计算,经验公式可用于接近临界温度区域的溶解度计算。