The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transform ) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z= and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover, may be expressed by a Laurent series expansion in positive and negative powers ofz, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions of as obtained from the application of conventional many-body techniques to the calculation of . The expressions are formulated as time scale expansions, which should rapidly converge if macroscopic and microscopic time scales are sufficiently well separated, i.e., if lifetime (memory) effects are not too large.     

Effect of NaOH and NaCl on the disodiumn-decane phosphonate micellar aggregation number

The diffusion coefficient of disodiumn-decane phosphonate micelles was studied by polarography at 25°C in NaCl and in NaOH solutions, and the size and aggregation number of the micelles was computed as a function of Na⁺ concentration. All other conditions being equal, the addition of NaCl produces micelles with an aggregation number one order of magnitude larger than the NaOH addition. This is due to the increase of the effective charge per micellized head group produced by the reaction of OH- with the hydrolized head groups which are mainly present as-PO₃H- in the micellar Stern layer.     

Drift tube investigations on the reactions of O 2 + with CH4 and of CO 2 + with NO in various buffer gases

The influence of internal excitation on the reactions of O ₂ ⁺ + CH₄ and of CO ₂ ⁺ + NO has been investigated using a slow flow drift tube. The rate coefficients for these reactions obtained as a function of relative kinetic energy in various buffer gases like He, Ne, Ar, and Kr showed higher values under conditions where the internal excitation of the reactant ions was enhanced. For both reactions the lowest reactivity at all kinetic energies was observed to occur in He, indicating that He is the least effective buffer for collisionally inducing internal excitation of molecular ions.     

Solubility of gases in liquids. 18. High-precision determination of Henry fugacities for argon in liquid water at 2 to 40°C

The solubility of argon in pure liquid water was measured at ca. 100 kPa and from 2 to 40°C using an analytical method characterized by an imprecision of about ±0.05%. From the experimental results, Henry fugacities H _2,1 (T,P _s,1 ) (also known as Henry's Law constants or Henry coefficients) at the vapor pressure P _s,1 of water as well as Ostwald coefficients L _2,1 at infinite dilution were obtained. Measurements were made at roughly 0.5°C and/or 1° intervals between 2 and 8°C (region I), and at 5°C intervals above 10°C (region II). A difference plot lnH _2,1 /T suggests an unusual temperature dependence in region I, i.e., between 2 and 8°C. Because of this, the data were treated separately in two parts corresponding to these two regions. Our results are compared with the recent high-precision data of Krause and Benson (Henry fugacities), and with calorimetrically determined quantities (enthalpies and heat capacities of solution). Finally, experimental results are compared with values calculated via scaled particle theory.Communicated in part at the 2^nd International Symposium on Solubility Phenomena in Newark, New Jersey, August 12–15, 1986, and at the 4^th ISSP in Troy, New York, July 20–August 3, 1990.     

Ionization of carbonic acid in sodium chloride solutions at 25°C

The stoichiometric pK ₁ ^* and pK ₂ ^* for the ionization of carbonic acid has been determined from emf measurements in NaCl soluions to 6.0m at 25°C. Our results at low concentrations are in good agreement with the results of Harned and Bonner, of Dyrssen and Hansson and of Roy et al. The calculated values of pK ₁ ^* using Pitzer's equations agree with the measured values to ±0.01 pK units provided higher order terms are used. It was necessary to use a triplet interaction parameter () and higher order electrostatic terms (^E) to calculate reliable values of pK ₂ ^* (±0.03 pK units) over the entire concentration range. These results demonstrate the reliability of the Pitzer equations to estimate activity coefficients in concentrated salt solutions.     

COSMO-RS: A novel view to physiological solvation and partition questions

Both, dielectric continuum solvation models as well as surface or group based methods using polarity and lipophilicity parameters have been proven to be useful tools for the analysis of solvation and partition questions. For the first time, COSMO-RS provides an integrated theory, which combines the aspects of continuum solvation and surface interactions, and which ends up with chemical potentials of molecules in almost arbitrary solvents and mixtures. Due to its sound theoretical basis, COSMO-RS does not only provide a new quantitative access to solvation and partition properties in well defined solvents, but it also opens a novel view and gives a better understanding of the general problem of solvation. Finally, this allows for a generalisation of COSMO-RS to sophisticatedphysiological partition problems involving as complex phases as blood, brain, or cell membranes. The use of COSMO-RS for drug discovery and design is demonstrated by applications to blood-brain partition coefficients, and water solubility.     

Enthalpies of solution and of crystallization of lithium nitrate and of lithium nitrate trihydrate in water at 25°C

The enthalpies of crystallization of LiNO₃ and LiNO₃–3H₂O from aqueous solutions at 25°C, measured by a calorimetric method and determined from the previously published data on the concentration dependence of the enthalpy of solution, are reported. The results are compared with the values obtained from the concentration dependences of the activity coefficients and from the temperature dependences of the solubilities. The enthalpy of solution at infinite dilution and the enthalpy of hydration are given.     

Equations for calculation of the pH of buffer solutions containing sodium or potassium dihydrogen phosphate, sodium hydrogen phosphate, and sodium chloride at 25°C

Published thermodynamic data measured in aqueous mixtures of sodium or potassium dihydrogen phosphate with hydrogen phosphate and chloride at 25°C were used to test recently developed methods for calculation of the pH of phosphate buffer solutions. Equations for ionic activity coefficients are used in these methods. It is shown that all data used in the tests up to an ionic strength of about 0.5 mol-kg^-1 can be accurately predicted by the two methods recommended. In one of these methods, equations of the Hückel type are used for ionic activity coefficients and in the other equations of the Pitzer type. Several sets of phosphate buffer solutions are recommended,e.g., for calibrations of glass electrode cells. In the recommended sets, the pH of the buffer solutions can be calculated either by the Hückel or Pitzer method, and the pH predictions of these methods agree in most cases within 0.005 at least up to ionic strengths of about 0.2 mol-kg^-1. The pH values of the two primary pH standards endorsed by IUPAC based on aqueous mixtures of KH₂PO₄ and Na₂HPO₄,i.e., pH values of 6.865 and 7.413, can also be accurately predicted by the equations recommended in this study.     

The ion product of H2O,dissociation constants of H2CO3 and pitzer parameters in the system Na+/H+/OH−/HCO 3 − /CO 3 2- /ClO 4 − /H2O at 25°C

The ion product of water and the dissociation constants of carbonic acid have been determined in 0.1, 1.0, 3.0, and 5.0M NaClO₄ at 25°C. The ion product of water K _w ^' has been evaluated by emf measurements with a combined glass electrode in NaClO₄ solutions containing 0.001–0.1M HCLO₄ or NaOH. The product K _H ^' K _l ^' K ₂ ^' of the Henry constant for CO₂ and the dissociation constants for H₂CO₃ have been determined by titration of carbonate solutions equilibrated with pCO₂ =10^–3.52 atm, and K ₂ ^' has been evaluated by potentiometric titration and by measuring the H⁺ concentration at fixed HCO ₃ ^– and CO ₃ ^2- concentrations. The ion interaction (Pitzer) equations are applied to describe the constants K _w ^' , K ₂ ^' and K _H ^' H ₁ ^' K ₂ ^' as a function of the NaClO₄ concentration. The experimental data are used to evaluate the mixing parameters _{i/ClO 4} and _{i/ClO 4} ^-/Na⁺ fori = OH ^-,HCO ₃ ^- andCO ₃ ^2-     

Thermodynamic properties of electrolyte solutions: An EMF study of the activity coefficients of KCl in the system KCl−KNO3−H2O at 25, 35 and 45°C

Electromotive force measurements were carried out on the system KCl–KNO₃–H₂O at constant total ionic strengths of 0.5, 1.0, 2.0 and 3.0 mol-kg^–1 and at 25, 35 and 45°C using a cell consisting of a potassium ionselective electrode and a Ag/AgCl electrode. The Harned coefficients and the Pitzer binary and ternary interaction parameters for the system have been evaluated at each temperature. The osmotic coefficients, excess free energies of mixing and heats of mixing of the system have been predicted at each of the experimental temperatures and ionic strengths. The solubility data at 25°C are also interpreted.