论化学平衡中的独立等量关系

物料平衡等式(MBE)、电荷平衡等式(CBE)和质子平衡等式(PBE)是化学平衡定量解析中的常用等量关系。本文从理论上证明了CBE可以由MBE导出,因此在计算中不是一个必不可少的独立条件。由于H~+来源的多样性,在涉及酸碱的化学平衡中,CBE比MBE的计算效率更高。这些结论与计算实践相一致,即在配位平衡、氧化还原平衡和沉淀平衡的计算中,MBE为主,CBE起辅助作用;在酸碱平衡计算中,CBE为主,MBE为辅。PBE也不是一个独立等量关系,而且仅适用于酸碱平衡,可以完全被效率更高的CBE代替。本研究明确了化学平衡中的独立等量关系,不仅有助于提高化学平衡定量解析的效率,而且使其理论结构更加简洁明晰。     

Self-memorization Equation in Atmospheric Motion

In view of the fact that the atmospheric motion isan irreversible process, a memory function which can recall observational data in the past is suggested. In terms of defining an inner product in Hilbert space, a new concept of self-memorization in the atmospheric motion is proposed, thus the traditional atmospheric motion equation is generalized to a self-memorization equation in inclusion of multi-time observations. Self-memorization equations of a barotropic nondivergent model and a barotropic primitive equation model are exemplified.It is proved that some existing difference schemes can be derived from the self-memorization equation by giving particular values to memory function. However, it demonstrates that multi-time numerical prediction models can be unified into a framework of self-memorization equation. If a stochastic method in solving the memory function is taken, the selfmemorization equation will be transformed to a sort of dynamic-stochastic prediction model.     

Shape factors in equations of state. Part II. Repulsion phenomena in multicomponent chain fluids

An equation of state for the multicomponent fluid phase of nonattracting rigid particles of arbitrary shape is presented. The equation is a generalization of a previously presented equation of state for pure fluids of rigid particles; the approach describes the volumetric properties of a pure fluid in terms of a shape factor, zeta, which can be back calculated by scaling the volumetric properties of pure fluids to that of a hard sphere. The performance of the proposed equation is tested against mixtures of chain fluids immersed in a "monomeric" solvent of hard spheres of equal and different sizes. Extensive new Monte Carlo simulation data are presented for 19 binary mixtures of hard homonuclear tangent freely-jointed hard sphere chains (pearl-necklace) of various lengths (three to five segments), with spheres of several size ratios and at various compositions. The performance of the proposed equation is compared to the hard-sphere SAFT approach and found to be of comparable accuracy. The equation proposed is further tested for mixtures of spheres with spherocylinders. In all cases, the equation proved to be accurate and simple to use.     

Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the Fokker-Planck equation

The problem of the derivation of the diffusion equation exactly following from the Fokker-Planck (or Klein-Kramers) equation for heavy (or large) particles in a fluid in an external force field is solved in the case in which the particles are ions subject to a uniform (but in general time-varying) electric field. It is found that such a diffusion equation maintains memory of the initial ion velocity distribution, unless sufficiently large values of time are considered. In such temporal asymptotic limit, the diffusion equation exactly becomes (i) the Smoluchowski equation when the electric field is constant in time, and (ii) a new equation generalizing the Smoluchowski equation, when the electric field is arbitrarily time varying. Finally, it is shown that the obtained exact (or asymptotic) results make questionable the procedures and the results of approximate theories developed in the past to get a "corrected" Smoluchowski equation when the external force can also be, in general, position dependent.     

Retention model of protein for mixedmode interaction mechanism in ion exchange and hydrophobic interaction chromatography

A unified retention equation of proteins was proved to be valid for a mixed-mode interaction mechanism in ion exchange chromatography (IEC) and hydrophobia interaction chro-matography (HIC). The reason to form a "U" shape retention curve of proteins hi both HIC and IEC was explained and the concentration range of the strongest elution ability for the mobile phase was determined with this equation. The parameters in this equation could be used to characterize the difference for either HIC or IEC adsorbents and the changes in the molecular conformation of proteins. With the parameters in this equation, the contributions of salt and water in the mobile phase to the protein retention in HIC and IEC were discussed, respectively. In addition, the comparison between the unified equation and Melander' s three-parameter equation for mixed-mode interaction chromatography was also investigated and better results were obtained in former equation.     

Calculation of interparticle spacing in colloidal systems

Interparticle spacing (IPS) is a very important parameter for estimation of the viscosity of a suspension. A new equation for calculating IPS was derived on the assumption that each particle is surrounded by a virtual cell, which is the free volume that each particle can occupy. This idea was originated by Kuwabara and widely used for calculating electrophoretic mobility in concentrated suspensions. Our new IPS equation was evaluated and compared with a pre-existing IPS equation proposed by Dinger and Funk using experimental data from three commercial sources of titania. Our equation was found to give reasonable values, including cases where the equation of Dinger and Funk gave anomalous values.     

Method of kinetic analysis of photodegradation: nifedipine in solutions

A rate equation for photodegradation was derived from Lambert-Beer's law and Grotthus-Draper's law: -dc/dt=k1(1-exp(-(k2c+k3(c0-c))))k2c/(k2c+k3(c0-c)) where c is the concentration of reactant, c0 is the initial concentration of reactant, t is time, k1 is the rate constant, and k2 and k3 are the absorption coefficient of reactant and its photodegradation product, respectively. In a case where the photodegradation products have no photoabsorption, k3 assumes the value of zero in the above general equation. In a case where the photodegradation products have the same spectrum and molar absorptivity as that of the reactant, k3 assumes the value of k2, and hence the photodegradation is not a first-order reaction; however, the equation itself gives the pseudo-first-order reaction rate equation. In a case where the concentration of reactant is high enough, the equation approaches a zero-order reaction rate equation. The photodegradation rate of nifedipine in solutions under a germicidal lamp, near an ultraviolet fluorescent lamp and a fluorescent lamp was analyzed using the above equation. The photodegradation rate was directly proportional to the amount of light absorbed, and fitted well with the equation. The above theoretical equation was substantiated by the photodegradation of nifedipine, and hence is expected to apply to other photosensitive drugs.     

Specific interactions in mixed electrolyte solutions from solubility measurements

The solubility of thallium I chloride in a wide range of dilute electrolyte solutions is interpreted using a new specific-interaction equation for activity coefficients. This equation is shown to be consistent with the solubility data, but the Guggenheim specific-interaction equation is not. The relation of interaction coefficients to ion association is discussed.     

Comparison of the Nernst-Planck model and the Poisson-Boltzmann model for electroosmotic flows in microchannels

In the analysis of electroosmotic flows, the internal electric potential is usually modeled by the Poisson-Boltzmann equation. The Poisson-Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distributions are not affected by fluid flows. Although this is a reasonable assumption for steady electroosmotic flows through straight microchannels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst-Planck equation instead of the Poisson-Boltzmann equation to model the internal electric field. In the present work, the predictions of the Nernst-Planck equation are compared with those of the Poisson-Boltzmann equation for electroosmotic flows in various microchannels where the convective transport of ions is not negligible.     

Stochastic simulation of catalytic surface reactions in the fast diffusion limit

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit. This derivation justifies the widely used assumption that the adlayer is in equilibrium for the current coverages and temperature when all reactants are highly mobile. Given the reduced master equation, two novel and efficient simulation methods of lattice gas reactions in the infinite diffusion limit are derived. The first method involves solving the reduced master equation directly for small lattices, which is intractable in configuration space. The second method involves reducing the master equation further in the large lattice limit to a set of differential equations that tracks only the species coverages. Solution of the reduced master equation and differential equations requires information that can be obtained through short, diffusion-only kinetic Monte Carlo simulation runs at each coverage. These simulations need to be run only once because the data can be stored and used for simulations with any set of kinetic parameters, gas-phase concentrations, and initial conditions. An idealized CO oxidation reaction mechanism with strong lateral interactions is used as an example system for demonstrating the reduced master equation and deterministic simulation techniques.     

Evaluation of Excess Molar Polarization in Binary Mixtures of Amines in Nonpolar Solvents

Abstract

A new expression for the excess molar polarization in binary mixture of polar and nonpolar liquids has been proposed. An experimental assessment of the proposed equation has been made by comparison with an earlier equation in the binary mixtures of amines in nonpolar liquids. The proposed equation for excess molar polarization is found to be more appropriate for detailed study of molecular association in the liquid mixtures.     

Determination and correlation of solubility of tylosin tartrate in alcohol mixtures

Data on (solid + liquid) equilibrium of tylosin tartrate in {methanol + (ethanol, 1-propanol or 2-propanol)} solvents will provide essential support for industrial design and further theoretical studies. In this study, the solubility of tylosin tartrate in alcohol mixtures was measured over temperature range from (278.15 to 323.15) K under atmospheric pressure by a gravimetric method. From the experimental results, the solubility of tylosin tartrate in selected solvents noted above was found to increase with increasing temperature and mass fraction of methanol. The solubility data were correlated with the modified Apelblat equation, the λh equation and van’t Hoff equation. The results showed that the three equations agreed well with the experimental values, and that the modified Apelblat equation was more accurate than the λh equation and van’t Hoff equation. Further, the standard enthalpy, standard entropy and standard Gibbs free energy of solution of tylosin tartrate in mixed solvents were calculated according to solubility results, model parameters with modified Apelblat equation and van’t Hoff equation.     

Hypevirial theorem for open dynamical assemblies in the density matrix representation

The concepts of “open assembly” is defined, and the hypervirial theorem is derived in three steps: (i) An equation of motion of the reduced density matrix of the first order is derived. (ii) This equation is utilized to derive a general equation of continuity for single-particle properties. (iii) The hypervirial equation for open assemblies is obtained as a long-time average of the continuity equation. The hypervirial theorem is shown to be equivalent to a simple postulate: no physical property can keep on accumulating for ever in a limited volume. Finally, the hypervirial theorem is applied to the problems of force, torque, and virial balance in open dynamical assemblies, and the results are compared with the corresponding classical results.     

The kinetics of free radical chain reactions in solutions of trichlorofluorethylene in cyclohexane

The kinetics of the gamma-radiation-induced free radical chain reaction in solutions of C₂Cl₃F in cyclohexane (RH) was investigated over a temperature range of 87.5–200°C. The following rate constants and rate constant ratios were determined for the reactions: In competitive experiments in ternary solutions of C₂Cl₄ and C₂Cl₃F in cyclohexane the rate constant ratio k_2c/k_2a was determined By comparing with previous data for the addition of cyclohexyl radicals to other chloroethylenes it is shown that in certain cases the trends in activation energies for cyclohexyl radical addition can be correlated with the C? Cl bond dissociation energies in the adduct radicals.     

Adsorption Equilibrium Equation of Carboxylic Acids on Anion-Exchange Resins in Water

The adsorption of propionic acid and benzoic acid on anion-exchange resins was analyzed, and an adsorption equilibrium equation of carboxylic acids was proposed. The adsorption of carboxylic acids on the anion-exchange resins was considered to be the sum of the physical adsorption of the molecule and the ion-exchange adsorption of the ion, which were independent of each other. For the physical adsorption of carboxylic acids, it was conformed to the Freundlich equation. For the ion-exchange adsorption of carboxylate ions, the equilibrium equation corresponded well with the experimental results for wide ranges of concentration and pH. The equation contains a selectivity coefficient S(A)(Cl) for the chloride ion versus the carboxylate ion, which was considered essentially a constant. The influent of the bicarbonate ion from carbon dioxide in air could also be expressed by the additional equilibrium equation with the selectivity coefficient S(HCO(3))(Cl) for the chloride ion versus the bicarbonate ion. Consequently, an adsorption equilibrium equation can estimate the equilibrium adsorption amounts. Even the effect of a coexisting bicarbonate ion is inconsequential when the parameters of the Freundlich isotherm equation and the selectivity coefficients of the carboxylate ion and the bicarbonate ion in each resin are determined in advance. Copyright 2001 Academic Press.     

Energy migration in one-dimensional structures with resonance interaction

A new approach is proposed to derive the equation of elementary excitation motion along chains and it is used to obtain an important correction of the equation.     

On the relaxation theory of glass transition in liquids

A method for calculating the constant in the main equation of glass transition (which relates the relxation time and the cooling rate near the glass transition temperature) with consideration given to the temperature dependence of the activation energy in this region is proposed. A modification of the main glass transition equation is considered. Application of this equation to the relaxation spectrometry of amorphous polymers and inorganic glasses is discussed.     

CO2与2-丁醇二元系统的高压相平衡模型

采用固定体积可视观察法测定了在323.2~353.2 K温度范围内2-丁醇在CO₂中高压相平衡数据. 运用Peng-Robinson状态方程(PR)和van der Waals-2混合规则建立了相平衡模型, 并运用Chrastil半经验方程建立了溶解度方程. 通过优化计算得到了状态方程中的模型参数, 同时得到的Chrastil溶解度方程为c=ρ^3.3617·exp(-2198.8193/T+6.5545). 二元体系的溶解热为-18.2809 kJ/mol.