Supercritical fluid effect on the rates of elementary bimolecular reactions

The effect of the supercritical fluid (SCF) present in the reaction system on the rate of a bimolecular reaction has been investigated theoretically. Calculations have been carried out in the framework of the theory of nonideal reaction rates in condensed phases. The intermolecular interactions of the nearest neighbors are described in the quasi-chemical approximation taking into account the short-order correlation effects. The competing effects of raising the reaction temperature (which increases the reaction rate) and raising the pressure by increasing the amount of SCF (which hinders the meeting of the reactants) are discussed. Increasing the proportion of SCF reduces the self-diffusion coefficient and increases the viscosity of the reaction mixture.     

Approximation of contacts for calculating the velocity of the thermal motion of rodlike molecules in narrow slitlike pores

Expressions for calculating the thermal velocities of the motion of rodlike molecules in slitlike pores were obtained within the framework of a lattice gas model valid over a wide range of fluid densities (from rarefied gases to liquids) and temperatures, including the critical region. The translational and rotational motion of molecules was described using the transition-state theory for nonideal reaction systems, which takes into account the effect of the neighboring molecules on the activation barrier height. The local distributions of the components of the mixture under equilibrium conditions were calculated by describing lateral interactions in the approximation of isolated contacts. The equations of the model reflect the fact that the distributions of the components in the direction perpendicular to the pore walls (due to the effect of adsorption forces) and along the pore axis (if capillary condensation occurs) exhibit a strong anisotropy.     

Concentration dependences of the transport coefficients of rod-like molecules in narrow slit-shaped pores

The concentration dependences of the label transport and shear viscosity coefficients for rod-like molecules in slit-shaped pores were studied. The calculations were carried out using the lattice gas model, which describes a broad range of fluid concentrations (from the gaseous to the liquid state) and temperatures (including the critical region). In the calculation of the local distributions of mixture components in the equilibrium states, lateral interactions were taken into account. The translational and rotational motions of molecules were described in terms of the transition state theory for nonideal reaction systems, which took into account the influence of neighboring molecules on the height of the activation barrier. The model equations reflect the pronounced anisotropy of the distribution of system components along the normal to the pore wall surface and ordering effects of molecules along various directions. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1485–1494, September, 2006.     

A modification of the Doong-Yang model for gas mixture adsorption using the lewis relationship

The Doong-Yang model, which is used for predicting gas mixture adsorption equilibrium from pure-component isotherms of the Dubinin type, is modified by incorporating the Lewis relationship. The modified model is tested against experimental data for four binary systems, including a like-component (or nearly ideal) mixture, CH(4) + C(2)H(6), a moderately nonideal mixture, CO(2) + C(2)H(4), and two highly nonideal mixtures, CO(2) + C(3)H(8) and CO(2) + H(2)O. Comparisons are made with the ideal adsorbed solution (IAS) theory and the Bering model. Results show that the proposed model is the best for the like-component mixture and the moderately nonideal mixture. In contrast, for the highly nonideal mixtures, the original Doong-Yang model is the only one among the four models that can predict CO(2) + C(3)H(8) adsorption correctly. The IAS theory and the Bering model have similar predictions and are suitable only for like-component mixtures. The new model requires a simple numerical iteration but is easy to use; no new parameters are required. Theoretical reasons are given for the fact that the original Doong-Yang model is best for nonideal mixtures, whereas the modified Doong-Yang model is best for ideal mixtures.     

The semi-ideal solution theory for mixed ionic solutions at solid-liquid-vapor equilibrium

The semi-ideal solution theory has been presented to describe the changes in thermodynamic properties accompanying the process of mixing the nonideal electrolyte solutions M(i)X(i)-(NY)sat-H2O (i = 1 and 2) at constant activities of NY and H2O, including concentration, chemical potential, activities of all M(i)X(i), Gibbs free energy, enthalpy, entropy, thermal properties, and volumetric properties. The theory states that, under the conditions of equal activities of NY and H2O, the average hydration numbers characterizing the ion-solvent interactions have the same values in the mixture as in the subsystems and the process of mixing these nonideal electrolyte solutions is as simple as that of mixing the ideal solutions if the contributions from the ion-ion interactions to the solvent activity are assumed to be the same in the mixture as in its subsystems, which has been justified by the calculations of the Pitzer equation. Therefore, a series of novel linear equations are established for the thermodynamic properties accompanying the process of mixing these nonideal solutions as well as mixing the ideal solutions M(i)X(i)-(NY)sat-H2O (i = 1 and 2) of equal mole fractions of NY and H2O. From these equations, the widely applied empirical Zdanovskii's rule is derived theoretically, and the important constant in the McKay-Perring equation under isopiestic equilibrium is determined theoretically, which has been substantiated by comparisons with the experimental results for 18 mixtures reported in the literature. Isopiestic measurements have been made for the systems BaCl2-LaCl3-H2O, NaCl-BaCl2-LaCl3-H2O, and NaCl-LaCl3-BaCl2.2H2O(sat)-H2O at 298.15 K. The results are used to test the novel linear concentration relations, and the agreement is excellent. The novel predictive equation for the activity coefficient of M(i)X(i) in M1X1-M2X2-(NY)sat-H2O has been compared with the calculations of the Pitzer equation, and the agreement is good.     

Equilibrium fluctuations in the theory of surface processes on microparticles

The question of the role of equilibrium fluctuations in the adsorption theory and kinetics of surface processes occurring on the particles of the nanometer size range is discussed. Differences are put forward that need to be introduced to the fluctuation theory of surface processes on microparticles and that generalize Hill’s approach to describing the thermodynamic properties of small systems. We show the importance of allowing for the discrete character of adsorption centers on the surfaces and their heterogeneity when describing adsorption isotherms and the rates of adsorption processes.     

A molecular analysis of basics of the “theory of associated solutions”

The ??theory of associated solutions?? was analyzed from the point of view of its correspondence to real potential functions used to describe the equilibrium distribution of solution components. The importance of taking into account the real properties of potential functions and the necessity of the inclusion of correlation effects between interacting molecules in solution were demonstrated. Changes in equations for nonideal mixtures in the presence of associates when the volume of associates exceeds the volume of initial mixture components were considered. The accuracy of traditional methods for the determination of residual contributions in the theory of associated solutions was discussed.     

Gibbs energy minimization in gas + liquid + solid systems

An algorithm is described for the calculation of equilibrium compositions of multiple highly nonideal liquid and solid solutions, as well as pure stoichiometric phases, coexisting with a mixture of ideal gas species at fixed temperature and pressure. The total Gibbs free energy of the system is approximated as a quadratic function of the compositions of the gas phase and stable condensed phases, in an orthogonal basis set of pure elements. Only changes in thermal energy and energy related to pressure‐volume work are considered. The total Gibbs energy is minimized directly by use of both the slope and the curvature of the Gibbs energy surface with respect to the gas and condensed phase compositions in the basis elements. The algorithm described has been implemented in a computer code for the calculation of condensation sequences for cosmic nebular gases enriched in dust. Machine, compiler and library requirements for performing these calculations in the C programming language are compared. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 247–256, 2000     

Multiple rate-determining steps for nonideal and fractal kinetics

We show that the kinetic model of a single rate-determining step in a reaction mechanism can be extended to systems with multiple overall reactions for which the elementary reactions obey nonideal or fractal kinetics. The following assumptions are necessary: (1) The system studied is either closed or open, but no constraints exist preventing the evolution toward equilibrium. (2) Elementary reactions occur in pairs of forward and backward steps. (3) The kinetics of the elementary steps are either nonideal or fractal and are compatible with equilibrium thermodynamics. (4) The number of reaction routes is identical with the number of rate-determining steps. If these hypotheses are valid, then the overall reaction rates can be explicitly evaluated: they have a form similar to the kinetic equations for the elementary reactions and the apparent reaction orders and fractal coefficients can be expressed analytically in terms of the kinetic parameters of the elementary reactions. We derive a set of relationships which connect the equilibrium constants of the reaction routes, the corresponding overall rate coefficients, and the stoichiometric numbers of the rate-determining steps. We also derive a set of generalized Boreskov relations among the apparent activation energies of the forward and backward overall processes, the corresponding reaction enthalpies, and the stoichiometric coefficients of the rate-determining steps. If the elementary reactions obey fractal kinetics, the same is true for the rate-determining steps. The fractal exponents of the forward and backward overall reactions are linear combinations of the fractal exponents of the fractal elementary reactions. Similar to the theory of single rate-determining steps, our approach can be used for selecting suitable reaction mechanisms from experimental data.     

A study of the miscibility of bile components in mixed monolayers at the air-liquid interface I. Cholesterol,lecithin, and lithocholic acid

Experimental isotherms, obtained by compressing monomolecular layers formed by a number of compounds involved in gallstone formation (cholesterol, L-α-phosphatidylcholine, and lithocholic acid), are studied. Mixed monolayers consisting of pairs of these substances are also analyzed. The additivity rule for molecular areas is used for characterizing the possible interactions between such components. Applying the phase rule to the surface systems studied in conditions of extended/condensed liquid equilibrium allows the miscibility of the components in both phases to be determined. Some hypotheses are given regarding the kind of molecular rearrangements that take place when each system suffers a phase transformation. The general conclusion reached is that, at the experimental conditions used (pH=6.00 and T =298 K), significant interactions occur between the molecules of the compounds studied.     

Nonlinear chromatography Recent theoretical and experimental results

The theory of nonlinear chromatography has been advanced by the incorporation of recent results obtained by the theory of partial differential equations. The system of equations of the ideal model has been solved analytically in the case of a single component for which the equilibrium isotherm between the mobile and the stationary phases is given by a Langmuir equation. A series of computer programs has been written which permits the calculation of numerical solutions of the semi-ideal model. The properties of the solutions obtained are described and discussed for a one-component system (profile of high concentration bands of a pure compound eluted by a pure solvent), several two-component systems (elution of a pure compound band by a binary mobile phase, separation of a binary mixture eluted by a pure mobile phase), and three-component systems (separation of a binary mixture eluted by a binary solvent, displacement and separation of a binary mixture). Experimental results are reported which validate the conclusions derived from the numerical integration of the model. The conclusions of the work apply to all high-performance chromatographic procedures, i.e., to those where the kinetics of mass transfer are fast enough for the mobile and stationary phases always to be near equilibrium. More specifically, the contribution from the kinetics of the retention mechanism to the mass transfer resistance must itself be negligible. This clearly excludes affinity chromatography.     

A one-dimensional energy diffusion approach to multidimensional dynamical processes in the condensed phase

We propose a generalized one-dimensional energy diffusion approach for describing the dynamics of multidimensional dynamical processes in the condensed phase. On the basis of a formalism originally due to Zwanzig, we obtain a one-dimensional kinetic equation for a properly selected relevant dynamical quantity and derive new analytical results for the dynamics of a multidimensional electron-transfer process, nonequilibrium solvation, and diffusive escape from a potential well. The calculated results for electron-transfer reactions in solvent-separated and contact ion pair systems are found to be in good agreement with the experimental results. We are able to explain the rate of the electron-transfer reaction using much smaller and reasonable values of the solvent reorganization energy in contrast to earlier works that had to use a much larger value. The proposed theory is not only conceptually simpler than the conventional approaches but is also free from many of their limitations. More importantly, it provides a single theoretical framework for describing a wide class of dynamical phenomena.     

Ab initio calculation of proton-coupled electron transfer rates using the external-potential representation: a ubiquinol complex in solution

In quantum-mechanical/molecular-mechanical (QM/MM) treatment of chemical reactions in condensed phases, one solves the electronic Schrodinger equation for the solute (or an active site) under the electrostatic field from the environment. This Schrodinger equation depends parametrically on the solute nuclear coordinates R and the external electrostatic potential V. This fact suggests that one may use R and V as natural collective coordinates for describing the entire system, where V plays the role of collective solvent variables. In this paper such an (R,V) representation of the QM/MM canonical ensemble is described, with particular focus on how to treat charge transfer processes in this representation. As an example, the above method is applied to the proton-coupled electron transfer of a ubiquinol analog with phenoxyl radical in acetonitrile solvent. Ab initio free-energy surfaces are calculated as functions of R and V using the reference interaction site model self-consistent field method, the equilibrium points and the minimum free-energy crossing point are located in the (R,V) space, and then the kinetic isotope effects (KIEs) are evaluated approximately. The results suggest that a stiffer proton potential at the transition state may be responsible for unusual KIEs observed experimentally for related systems.     

Considering induced dipoles in a discrete model of a polar liquid

The lattice gas model is generalized to describe the equilibrium distributions of polar solution components with allowance for Lennard-Jones and dipole-dipole potential interactions with constant and induced moments. It is shown that including induced dipoles potential results in an effective many-particle interaction potential, depending on the spatial distribution of solution components. The distributions of all solution components are calculated in a quasi-chemical approximation allowing for the spatial correlation of interacting particles. A procedure for reducing the dimensionality of a set of algebraic equations is considered, and expressions for vapor-liquid equilibrium isotherms are obtained. Expressions for the rates of elementary mono- and bimolecular chemical reactions are derived using the transition state theory in systems with induced dipoles for rapidly overcoming the activation barrier in the permanent state of solvent molecules’ atomic subsystems. Ways of considering the internal motions (vibrations, rotation, and displacements) of molecules in a polar liquid are discussed.     

Theory of inhomogeneous weakly charged polyelectrolytes

A theory of inhomogeneous multicomponent systems containing weakly charged polyelectrolytes is developed. The theory treats the polymer conformation and the electrostatics simultaneously using a functional integral representation of the partition function. A mean‐field approximation to the theory leads to two sets of coupled mean‐field equations: a Poisson‐Boltzmann type equation describing the electrostatic potential, and a set of self‐consistent field equations describing the equilibrium densities. Asymptotic forms of the theory at weak and strong segregation limits are derived. The theory can be used to study the interfacial properties, microphase structures, and adsorptions of a variety of weakly charged polyelectrolyte systems. As a simple example, the interface between the polymer‐rich and polymer‐poor phases of a polyelectrolyte solution is studied.     

Salt effect on vapour-liquid equilibrium in the dimethylsulphoxide-water-0.9 m NaClO4 system at 298.15 K

Isothermal total pressure vs. liquid and vapour composition (P-x-y) equilibrium data are presented for the DMSO-H₂O and DMSO-H₂O-0.9 m NaClO₄ systems. A modified transpiration technique was used to measure the saturated vapour pressures. The compositions of the equilibrium liquid and condensed vapour phases were determined by precision refractometry. The salt appreciably affects the activity coefficients of the solvent components; the effect is discussed in terms of interactions between the DMSO and H₂O molecules and of the preferential solvation of the salt.