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.     

On the stereochemistry of the Horner—Emmons reaction between 3-functionally substituted 2-methyl-2-propenylphosphonates and aliphatic aldehydes

The reaction of diethyl 3-ethoxycarbonyl-2-methyl-2-propenylphosphonate (1a) with 3-methylbutanal (2) in heterogeneous MOH (solid)-benzene systems in the presence of 5–10 mol.% of benzyltriethylammonium chloride (BTEAC) gives the reaction product (3) with a higher, for M=K, or lower, for M=Li, ratio of 2E,4E and 2Z,4E-stereoisomers than that observed in the absence of BTEAC. Tetrabutylammonium bromide (TBAB) as a catalyst of the reaction1a + 2 3 in the system KOH (solid)-wet benzene leads to a higher [2E,4E-3][2Z,4E-3] ratio than BTEAC; this ratio grows from 4456 without TBAB to 8020 at 100 mol.% of TBAB. In the latter case the stereochemical outcome of the reaction is similar to that obtained when tetrabutylammonium hydroxide in dry benzene is used as the deprotonating agent. The corresponding diisopropyl phosphonate (1b) and 3,7-dimethyloctanal (4a) interact in the system KOH (solid)-wet benzene-TBAB to give hydroprene (5) containing 88 % of the 2E,4E-isomer (5a) while in the case of 1 equiv. of [(n-Bu₄)N]OH in dry benzene the content of5a is 92 %. Diisopropyl 3-isopropoxycarbonyl-2-methyl-2-propenylphosphonate (1c) and 7-methoxy-3,7-dimethyloctanal (4b) under either of these conditions afford methoprene (6) containing 93 % of the 2E,4E-isomer.Part 6, see ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1094–1098, June, 1993.     

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.     

The aqueous cationic system sodium undecenoate-dodecyltrimethylammonium bromide at low concentration

The aqueous sodium undecenoate (SUD) –dodecyltrimethylammonium bromide (DTAB) catanionic system was studied at low concentration. The system did not precipitate, even at a 1:1 SUD:DTAB proportion, but showed the formation of a coacervate in a range of surfactant mixture compositions. Micelles have a preferential composition of 0.37 mole fraction of SUD. This behavior is attributed to the presence of the double bond at the distal extreme of the SUD molecule, which can form hydrogen bonds with water. Consequently, the –CH=CH₂ group is situated at the interface between the hydrocarbon micelle core and water, reducing the interfacial free energy. Structural computations demonstrate that the mentioned SUD proportion produces complete coverage of the micelle surface by the double bonds.     

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.     

Isoperichoric focusing field-flow fractionation and thin layer isoperichoric focusing based on coupling of gradient generated by primary field with secondary field action: general principles and performances

The primary field forces can generate spatially oriented gradient of the effective property of a continuum or pseudo-continuum fluid (carrier liquid). When this gradient is coupled with the action of a secondary field of identical or different nature the isoperichoric focused zones of the dispersed species can appear. Consequently, they can be separated according to differences responding to the property gradient of the carrier liquid. This concept can be applied under static (non-flow) conditions in thin layer focusing as well as under dynamic conditions with the elution due to the carrier liquid flow in focusing field-flow fractionation. The gradient established by the action of the primary field and the concentration distribution of the isoperichoric focused zone formed by the coupled effect of the gradient and of the primary or secondary field are described theoretically. The rigorous relationship describing the shape of the focused zone is compared with the approximate solutions. The performances of the proposed principle were evaluated by model calculations. Potential experimental configurations considering the implementation of the static and dynamic conditions are discussed. The generalized isoperichoric focusing theory can be applied to describe the particular processes operating in analytical and preparative focusing separations of the particles of various, but especially of biological origin.     

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.