动力学参数数目与法方程条件数的关系

多相催化反应动力学研究的基本问题是动力学方程中的参数估计，它一直是动力学研究中的活跃领域·在参数估计中最常用的方法是最小二乘法．早在1947年［刘开始用线性最小二乘法处理动力学模型的数据．1958年在线性最小二乘法中应用置信区间问题［21．1959年MarguardM出非线性最小二乘法问．前人提出如何求非线性最小二乘法的初值［4］，及加权最小二乘法的重要性问，并对最小二乘法在动力学中的应用做了综述卜］．在多相催化动力学研究中，关干线性最小二乘法遇到根本性困难的问题前人未涉及．我们曾在动力学研究中发现线性最小二乘法的法…     

On the Kinetics of Nonisothermal Nucleation

The kinetics of supersaturated vapor nucleation is considered with allowance for the possible difference between the temperature of the clusters and that of the gaseous phase. The resultant equation for the steady-state nucleation rate has the same form as the equation of the classical theory but contains the work of the thermodynamically irreversible droplet formation. This equation relates the nucleation rate to the cluster temperatures. It is transformed into the equation of the classical theory if the clusters have the same temperature as the gaseous phase. On the basis of the thermal balance for the clusters, an equation relating their temperature and concentration to the nucleation rate is derived. The form of this equation is similar to the equation of heat propagation in a moving medium in the presence of heat sources and sinks.     

An empirical correlation for the calculation of vapour pressures of pure compounds

A four-parameter equation for vapour pressure is derived by integrating the Clapeyron equation with the aid of an empirical expression for the ΔH/Δ a wide range of reduced temperatures for 21 liquids which are representative of different classes of compounds: polar compounds, non-polar compounds, hThree methods for the application of the new equation are discussed. The best of these is more accurate than the Thek-Stiel equation although it does nAn equation for calculating vaporization enthalpies is also derived.     

A new equation for correlation of vapour-liquid equilibrium data of strongly non-ideal mixtures

A new equation for correlation of the thermodynamic excess functions of mixing, based on considerations of geometrical shape is proposed. Use of this equation for the correlation of heat of mixing data and vapour-liquid equilibrium data is proposed. The possibility of predicting multicomponent vapour-liquid equilibrium from binary data by using the proposed equation is shown. The equation is especially useful for correlating the excess functions of strongly non-ideal systems and for checking thermodynamic consistency of vapour-liquid equilibrium data.     

The Perturbed-Soft-Chain Theory: an equation of state based on the Lennard-Jones potential

Perturbed-Soft-Chain theory is a perturbation theory for chain-like molecules which uses a soft-core (Lennard-Jones) intermolecular potential energy function. Three pure-component parameters are required for the PSCT equation of state. These parameters are reported for 13 normal alkanes and 25 other compounds. The PSCT equation of state does very well in predicting the thermodynamic properties of molecules over a wide range of fluid densities and molecular complexities. The PSCT equation of state is tested against the PHCT and Peng-Robinson equation of state by determining the errors in calculated liquid-densities and vapor pressures for normal alkanes. The PSCT equation of state predicts these properties slightly better than the PHCT equation of state and much better than the Peng-Robinson equation of state.     

Application of the Quartic Hard Chain equation of state to polymer mixtures

The Quartic Hard Chain equation of state proposed by Kubic is a simple model for chain-like molecules. This study considers the application of this equation to polymer solutions. The equation was not found to be a useful predictive model because polymer parameters could not be reliably predicted from pure component properties. However, the equation was found to be a useful empirical form for representing polymer solution data. Because the Quartic Hard Chain equation is applicable to the vapour—liquid equilibria of normal fluids, this method is potentially useful for representing high pressure vapour—liquid equilibria in systems with dissolved polymer.     

New theory of equation of state for surface monolayer

A novel statistical-thermodynamic approach to deriving an equation of state for a surface monolayer has been elaborated on the basis of excluded area. A master differential equation relating surface (two-dimensional) pressure to excluded area has been derived to generate equations of state for a surface monolayer. The crudest solution (the zero approximation) of the master equation reproduces the known van Laar and Frumkin equations of state. The first approximation yields the two-dimensional van der Waals equation. The second, third, and fourth approximations lead to new and more accurate equations of state. The particular result of the fourth approximation is a precise equation of state for hard disks with deviation not more than 0.46% from data obtained by Monte Carlo and molecular-dynamics simulations within the whole range of surface density. The role of the third dimension for surface equations of state is discussed. An orientation equation of state has been proposed for monolayers containing anisometric particles. It follows from the orientation equation obtained that the orientation effect creates possibility for a two-dimensional phase transition.     

Principles of classifying diagrams for different types of biazeotropic ternary mixtures

A new equation for two-phase systems in integer units is obtained by transformations of the Serafimov equation. The total number of types of phase portraits for biazeotropic ternary mixtures is determined on the basis of this equation.     

A quartic hard chain equation of state for normal fluids

A new empirical equation of state is proposed which is applicable to mixtures of chain-like molecules. The equation is based on a simple model which uses an approximate chain theory and an approximation of the Carnahan—Starling equation. The results for pure component properties of normal fluids are comparable to the common cubic equations of state. For mixtures of chain-like molecules, the new equation is as good or better than the Peng—Robinson equation.     

Phenomenological description of transport properties of three-phase composites

The possibility is discussed of estimating the values of conductivity and dielectric permeability of three-phase composites using the modified mixing equation similar to the equation suggested earlier for two-phase systems. It is shown that the choice of theoretical mixing equation parameters for three-phase composites of the conductor–electrolyte–insulator type can be controversial; variants of solving this problem are suggested. According to the equation, three percolation thresholds can exist in this three-phase system; their position can be estimated on the basis of the maximum of dielectric permeability. The value of the maximum is determined by the ratio of conductivities of the conducting and dielectric phases. The equation can be extended to the case when interaction exists between the individual phases of the composite and a highly conducting layer is formed at the interface between these phases. The calculation of three-phase composites of the conductor–composite solid electrolyte–insulator type is calculated for the first time. It is shown that the mixing equation also allows calculating electric properties of composites in this case.     

A cubic perturbed hard-chain equation of state

A cubic equation of state is developed on the basis of perturbation theory. The equation is an association of three segments: the hard-sphere, the hard-chain, and the attraction. The expression for each segment was invoked from approximations of computer simulations of rigorous molecular theories of fluids, but compromised to some extent accuracy and theory for simplicity. This model equation is shown to be potentially capable of describing the PVT behavior of real fluids. As limiting cases, the new equation is reduced to expressions for the hard-sphere and the hard-body fluids. It also represents square-well fluids when the hard-chain contribution is eliminated. The square-well equation was found satisfactory in conforming with the molecular simulation results for square-well fluids and their mixtures.     

高分子溶液特性粘度测定的新方法

提出了一个新的一点法测定高分子溶液的特性粘度的经验公式, 并根据文献的一些数据将该公式和常用的程镕时公式进行了比较研究. 结果表明, 该公式具有比程氏公式更高的准确性和广谱性, 还有简单易于操作的优点.     

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.     

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.     

An analytic solution of capillary rise restrained by gravity

We derive an analytic solution for the capillary rise of liquids in a cylindrical tube or a porous medium in terms of height h as a function of time t. The implicit t(h) solution by Washburn is the basis for these calculations and the Lambert W function is used for its mathematical rearrangement. The original equation is derived out of the 1D momentum conservation equation and features viscous and gravity terms. Thus our h(t) solution, as it includes the gravity term (hydrostatic pressure), enables the calculation of the liquid rise behavior for longer times than the classical Lucas-Washburn equation. Based on the new equation several parameters like the steady state time and the validity of the Lucas-Washburn equation are examined. The results are also discussed in dimensionless form.     

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.     

Transcorrelated calculations of homogeneous electron gases

We have constructed the complete transcorrelated equation for homogeneous electron gases and investigated this equation on two- and three-dimensional systems. Correct asymptotic behaviours of the correlation factors can be easily obtained from the transcorrelated equation, both the long-range RPA type decay and the short-range spin dependent cusp conditions. The complete transcorrelated equation is solved numerically and the outcome correlation energies agree very well with variational quantum Monte Carlo results. Possible simplifications of the transcorrelated calculations are discussed, where we find that the RPA equation for the correlation factor can be considerably improved by adding one more term in the equation.     

Correlation of Adsorption Equilibrium Data for Water Vapor on F-200 Activated Alumina

Single component adsorption equilibrium data for water vapor on commercially available activated alumina F-200 measured in a previous study (Serbezov, 2003) is correlated by two adsorption isotherm equations, both of which are based on the adsorption potential theory. The first equation is the well known Dubinin-Astakhov (D-A) equation. The second equation is obtained from a methodology proposed by Kotoh et al. (1993). It is referred to as a dual mechanism adsorption potential (DMAP) equation because it is a linear combination of two D-A terms with n = 1 where each term accounts for a specific mechanism of water retention. The D-A equation has two fitting parameters; the DMAP equation has three fitting parameters. The DMAP model provides a better fit for the adsorption data than the D-A model, while neither model describes the desorption data well. Analysis of the DMAP equation parameters shows that most of the water is retained by virtue of capillary condensation. In addition to fitting the experimental data, the heat of adsorption was calculated as function of the relative humidity and adsorbent loading. When capillary condensation is present, the heat of adsorption is only slightly higher than the latent heat of vaporization.     

The viscosity of aqueous electrolyte solutions and the TTG model

An equation covering the dynamic viscosity from zero to high concentrations has been derived on the basis of the TTG model. The equation is compatible with the Eyring andNMR theories and has a similar form to the Othmer-rule equation. A component of the limiting viscosity slope is shown to be proportional to the Falkenhagen slope. The TTG equation was tested for 20 electrolytes of diverse charge type and found to fit the data within the experimental errors. The equation is simply extended to cover pressure, temperature, and component changes. The viscosities of three multicomponent systems are predicted to within the experimental errors. The derived parameters of the equation were found to be simply related to the TTG volume of the solute.     

Nonlinear variation of sorption parameters of n-alkane homologsl in temperature-programmed gas chromatography (tpgc) and new equation for calculation of retention indixces

It has been demonstated that the considaerable difference in temperature increments of sorption parameters of n-alkanes under isothermal conditions is the main reason for nonlinear dependence of sorption parameters on molecular mass of homolog in temperaturre programmed gas chromatography (TPGC). A new nonlinear 4th parameter equation has been given for calculation of the retention indices. Coefficients of the equation are calculated from n-alkanes. The equation allows extrapolation and interpolation calculations of retention indices under TPGC conditions with experimental precision. The results obtained; for fatty acidkl methyl esters demonstrate the advantage of ovr equation in comparison with van den Dool and Kratz's equation.