An Analytical Study of Molecular Transport in a Zeolite Crystallite Bed

Analytical solutions of the diffusion equations to obtain the diffusant concentrations in the macro- and micropores which constitute the pore system of a zeolite bed are presented. The parameter which determines the influence of each pore type on the evolution of the adsorbate/adsorbant system towards the equilibrium state is described. Examples are given to illustrate a qualitative and quantitative study based on the curves obtained from these equations.     

Kinetic analysis of the mechanism of plasminogen activation by streptokinase

A kinetic study is made of plasminogen activation to plasmin catalyzed by streptokinase. The goal of the present paper is the resolution of the mechanism corresponding to the activation process by a global way, considering the mechanism as a whole and under less restrictive assumptions that those used by other authors. The kinetic equations describing the evolution with time of species involved in the system have been obtained. These equations are valid for both the transient phase and the steady state of the reaction. A kinetic data analysis procedure to evaluate the kinetic parameters, based on the derived kinetic equations has been suggested, for the first time, in the present paper. The validity of the results obtained has been checked by using simulated progress curves of the species involved. Finally, we have demonstrated that the time course equations obtained can be applied directly to different mechanisms of zymogen activation that could be considered to be particular cases of the general studied mechanism.     

The equation of state for an interface during the adsorption of organic substances on an electrode

The state of the interface between a metal and a solution of an electrolyte containing a neutral surfactant was investigated using a method alternative to the traditional thermodynamic approach. The method was based on the concept that there was a stability limit of a surfactant on an electrode, and the corresponding state could be described in terms of the catastrophe theory. The surface pressure was approximated by the Whitney polynomial in powers of the de Donder parameter (completeness of adsorption) with the coefficients depending on the chemical potential and polarization of the interface. The equation of state and the equation for the stability limit were obtained from the condition of zero first and second derivatives. These equations correctly described the results of electrocapillary measurements in the spirit of the law of corresponding states. The correlation between surface pressure maxima and critical stability potentials predicted by the theory was substantiated by the electrocapillary measurements data provided that the inflexions of surface pressure curves calculated from the electrocapillary data were related to the limiting stability at which the competing forces are balanced during the adsorption of surfactants. A simple equation for surface pressure was suggested in the form of a function of the state of thermodynamic parameters and completeness of adsorption. This function described the state of a surfactant at the interface. Equilibrium equations were derived for the state of a surfactant and the spinodal.     

Thermodynamic and structural characterization of amphiphilic melamine-type monolayers

Monolayers of amphiphilic melamine derivatives are good candidates for the formation of supramolecular structures by hydrogen-bonding of nonsurface active species dissolved in the aqueous subphase by molecular recognition. In the present work, the thermodynamic and structural properties of the Langmuir monolayers of a homologous series of a selected amphiphilic melamine-type are characterized. Good candidates for such studies are the decyl, undecyl, and dodecyl homologues of the 2,4-di(n-alkylamino)-6-amino-1,3,5-triazine (2CnH(2n+1)-melamine) monolayers because of their two-phase coexistence region in the accessible temperature range. The characterization of the structural and phase behavior is performed by a combination of surface pressure studies with Brewster angle microscopy (BAM) imaging and Grazing incidence X-ray diffraction (GIXD) measurements. A comprehensive thermodynamic analysis provides good agreement between the experimental surface pressure - area (Pi-A) isotherms and the theoretical curves that were calculated on the basis of equations of state for a large region of monolayer stages developed by us in J. Phys. Chem. 1999, 103, 145. Theoretical curves calculated by application of equations of state only for the fluid monolayer state proposed recently by Rusanov (J. Chem Phys. 2004, 120, 10736) are in good agreement with the experiments in a limited temperature range. A rigorous equation is derived and applied to the experimental results for the calculation of the enthalpy of two-dimensional phase transition. The combination of BAM and GIXD illustrates that the microscopic long range ordering of the condensed monolayer phases is related to the lattice structure of the condensed monolayer.     

D.c. polarography: Current-potential curves for electrode processes involving a preceding first-order chemical reaction

An explicit equation, which is valid without any limitation in the magnitude of rate constant of the chemical reaction involved, is derived in a rigorous way, for the d.c. polarographic instantaneous (and average) current-potential curves with a c.e. mechanism accompanied by nernstian behaviour. On the basis of these equations, the range of validity of the steady state approximation is discussed.     

Thermodynamic consideration of the mixed micelle of surfactants

In conformity with the conclusion obtained previously, the mixed micelle formation of surfactants was treated thermodynamically as the appearance of a macroscopic bulk phase with the aid of the excess thermodynamic quantities similar to those used for the adsorbed film. The composition of surfactant in the mixed micelle and the thermodynamic quantities of micelle formation were found to be evaluated by applying the thermodynamic equations derived. These equations were extended so as to be applicable to any kind of surfactant mixture. It was shown that the critical micelle concentration vs. composition of surfactant curves form a diagram analogous to the phase diagram of binary mixture. Applying the equation to the published data on typical surfactant systems, this thermodynamic approach was proved to be useful to clarify the miscibility of surfactants in the micellar state.     

Joule–Thomson inversion curves of mixtures by molecular simulation in comparison to advanced equations of state: Natural gas as an example

Molecular modelling and simulation as well as four equations of state (EOS) are applied to natural gas mixtures regarding Joule–Thomson (JT) inversion. JT inversion curves are determined by molecular simulation for six different natural gas mixtures consisting of methane, nitrogen, carbon dioxide and ethane. These components are also regarded as pure fluids, leading to a total of 10 studied systems. The results are compared to four advanced mixture EOS: DDMIX, SUPERTRAPP, BACKONE and the recent GERG-2004 Wide-Range Reference EOS. It is found that molecular simulation is competitive with state-of-the-art EOS in predicting JT inversion curves. The molecular based approaches (simulation and BACKONE) are superior to DDMIX and SUPERTRAPP.     

Metastable extension of the sublimation curve and the critical contact point

Molecular dynamics methods have been employed in order to calculate the (p,rho,T)-properties and the internal energy of gas and crystal phases in stable and metastable equilibrium coexistence states for a model system consisting of 2048 Lennard-Jones particles. Thermal and caloric equations of state and the spinodal curves of the vapor and crystal phases have been determined. A new algorithm for the computation of phase equilibrium curves is suggested. Employing this method, the sublimation curve and its metastable extension to temperatures above the triple point have been calculated. It is found that the crystal-gas phase equilibrium terminates on the spinodal of the superheated crystal. The point of contact of the sublimation line and the spinodal is a singular point of the thermodynamic surface of states of a simple system considered.     

Representation of pure fluid coexistence curves by series expansion

We give a systematic recipe for constructing the coexistence curve associated with a pure fluid described by an analytical equation of state. The novelty of our result lies not in its theoretical basis, which is well known, but in the high degree of accuracy that it will routinely yield over a broad range of density and temperature for a relatively modest expenditure of computing effort. Our results are quite general: they may be applied to any analytical equation of state. The effectiveness of our method is illustrated by applying our general solution to four widely known model equations of state: van der Waals, Dieterici, Soave-Redlich-Kwong, and Carnahan-Starling with van der Waals tail term. These models show a considerable diversity of coexistence curve shapes, and our method yields accurate representations for each model. An investigation is also initiated of the representation of experimental coexistence curves that exhibit pronounced “non-classical” behavior over an appreciable range of densities.     

Dipole excitation of ions in linear radio frequency quadrupole ion traps with added multipole fields

Ion motion with auxiliary dipole excitation and collisional damping in a linear radiofrequency quadrupole ion trap incorporating small amounts of even higher order multipoles is studied analytically. The ion motion is modeled in a pseudopotential that is mostly quadratic with small amounts of higher spatial harmonics. Ion motion along x and y axes is characterized by two uncoupled forced and damped anharmonic oscillator equations. A multiple time scales method is used to solve the equations of motion of ions with a first order perturbation correction. Analytical relations between the oscillation amplitudes at steady state (the stationary amplitudes) and excitation frequency are calculated. The frequency response curves show that in some cases bistable behavior might be obtained, i.e., there are two stable stationary amplitudes for a given excitation frequency.     

Non-steady state model for free radical polymerization

The non-steady state theory for the kinetics of free radical polymerization taking no account of gel-effect is reviewed. Considering the facts that the monomer consumption in chain propagation is much higher than that in chain initiation and the rate constant of chain termination is much larger than that of chain propagation or transfer, a few very close approximations are introduced to solve the set of kinetical differential equations of free radical polymerization. The expressions for various molecular parameters, such as the molecular size function, the number- and weight-average degrees of polymerization and the dispersity, are derived. In accord with the non-steady state theory, the curves of free radical decay with reaction time or monomer conversion and the molecular parameters mentioned can be predicted from the reaction conditions. Several numerical examples are given.     

Solvation effect in thermal decomposition of 2,2′-azoisobutyronitrile

The solvation effect in the thermal decomposition of a radical initiator (AIBN) in monomer–solvent mixtures is discussed. Equations were derived which comprise the initiator decomposition constant as a function of the monomer mole fraction for chosen types of solvation. In addition, equations were deduced presenting the concentrations and partial relative decomposition rates for the solvated initiator species as a function of the monomer mole fraction. The equations obtained were compared to the experimental literature data and possible dependences of decomposition constants on monomer concentration were simulated for various solvated species. The simulated relationships were found to be straight lines, curves of saturated type (possessing a plateau), S-shaped curves, and maximum or minimum curves. © 1995 John Wiley & Sons, Inc.     

van der Waals-Tonks-type equations of state for hard-hypersphere fluids in four and five dimensions

Recently, we developed accurate van der Waals-Tonks-type equations of state for hard-disk and hard-sphere fluids by using the known virial coefficients. In this paper, we derive the van der Waals-Tonks-type equations of state. We further apply these equations of state to hard-hypersphere fluids in four and five dimensions. In the low-density fluid regime, these equations of state are in good agreement with the simulation results and existing equations of state.     

Theory of nematic networks with finite extensibility

A statistical molecular model of polymer networks, which takes into account inter-molecular orientational interaction and constancy of the chain contour length, is proposed. A simple formula for the network free energy valid for any deformations is obtained. A system of equations which describes orientational-elastic interactions in polymer networks is derived. The influence of deformation and degree of cross linking on the conditions of network phase transition into the orientationally ordered state of the nematic type is studied. The deformation curves considerably deviate from those predicted by the classical elasticity theory. A comparison of the proposed theory with experimental data for natural rubbers is carried out.     

Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems

A common assumption in the glass science community is that the entropy of a glass can be calculated by integration of measured heat capacity curves through the glass transition. Such integration assumes that glass is an equilibrium material and that the glass transition is a reversible process. However, as a nonequilibrium and nonergodic material, the equations from equilibrium thermodynamics are not directly applicable to the glassy state. Here we investigate the connection between heat capacity and configurational entropy in broken ergodic systems such as glass. We show that it is not possible, in general, to calculate the entropy of a glass from heat capacity curves alone, since additional information must be known related to the details of microscopic fluctuations. Our analysis demonstrates that a time-average formalism is essential to account correctly for the experimentally observed dependence of thermodynamic properties on observation time, e.g., in specific heat spectroscopy. This result serves as experimental and theoretical proof for the nonexistence of residual glass entropy at absolute zero temperature. Example measurements are shown for Corning code 7059 glass.     

ICP—AES分析的线性回归校准曲线

本文对ICP-AES分析中2种线性回归方法的校准曲线作了比较和讨论。对大多数元素而言,用加权法得到的校准曲线的斜率比不加权校准曲线的斜率略大,减小3校准曲线在低浓度部分的弯曲,曲线明显优于不加权校准曲线。将2种方法得到的校准曲线进行比较时,应将剩余标准偏差(或剩余变差平方和)及曲线截距等加以综合考虑。用含零标的标准系列制作校准曲线可使曲线的截距更接近原点,有利于提高在低浓度部分校准分析的准确性。     

A new methodology for the simulation of solid state phase transition kinetics by combination of nucleation and nuclei growth processes

A new methodology for the simulation of solid state phase transition kinetics has been developed by combining the influence of nucleation rate, nuclei growth rate and the power p characterizing the contact area between the growing particles. The equations used in this methodology were well known, and have been used previously for creating some of the most popular solid-state kinetic equations. The developed methodology made possible calculations of separate rate constants for two processes affecting the rate of phase transition—nucleation (described with K ₁) and nuclei growth (described with K ₂). Similar phase transitions were also approximated with the well-known single constant Avrami–Erofeev equation, but we successfully calculated both constants according to the new methodology, which allowed a separate evaluation of these two processes and explained the different induction periods. The effects of empirically adjusted constants on theoretically calculated kinetic curves were thus determined.     

A novel thermodynamic state recursion method for description of nonideal nonlinear chromatographic process of frontal analysis

A novel thermodynamic state recursion (TSR) method, which is based on nonequilibrium thermodynamic path described by the Lagrangian-Eulerian representation, is presented to simulate the whole chromatographic process of frontal analysis using the spatial distribution of solute bands in time series like as a series of images. TSR differs from the current numerical methods using the partial differential equations in Eulerian representation. The novel method is used to simulate the nonideal, nonlinear hydrophobic interaction chromatography (HIC) processes of lysozyme and myoglobin under the discrete complex boundary conditions. The results show that the simulated breakthrough curves agree well with the experimental ones. The apparent diffusion coefficient and the Langmuir isotherm parameters of the two proteins in HIC are obtained by the state recursion inverse method. Due to its the time domain and Markov characteristics, TSR is applicable to the design and online control of the nonlinear multicolumn chromatographic systems.     

Sorption and diffusion of water in poly(vinylpyrrolidone)

The effect of molecular mass, thermal prehistory, physical state, and three-dimensional chemical crosslinked structure of a polymer on dissolution and diffusion in the PVP-water system has been studied. The kinetic dependences of sorption that correspond to the Fickian or pseudonormal type have been measured. In a certain concentration range, sorption is accompanied by transition of the system to the rubbery state. In the glassy state, the negative concentration dependence of the diffusion coefficient related to the nonequilibrium state of the polymer sorbent is observed. Sorption isotherms are described by S-shaped curves. It has been shown that the thermal prehistory of the polymer sorbent has the most pronounced effect on its sorption behavior. The effect of molecular mass is insignificant, while three-dimensional chemical crosslinks in PVP manifest themselves only in the region of the rubbery state. In accordance with the double sorption model, the experimental isotherms are represented as the superposition of two isotherms described by the Langmuir and Flory-Huggins equations. For the glassy state of the polymer sorbent, the degree of the nonequilibrium state has been estimated. With due regard for the excess free volume, the detailed thermodynamic analysis of isotherms has been performed; namely, the pair interaction parameters and the free energy of mixing have been calculated. The state of water in the polymer has been examined within the framework of hydrate contributions and clusterization theory.