Mean Distance Of Closest Approach Research Articles

Coupled mutual diffusion in aqueous calcium sulphate + sulphuric acid solutions

Taylor dispersion method was used to measure binary mutual diffusion coefficients of calcium sulphate in water at concentrations ranging 0.0000 to 0.0100 mol dm−3 and at 298.15 K. Experimental results are discussed based on the Onsager-Fuoss and Pikal models and compared with theoretical diffusion coefficients, calculated using different values of the mean distance of closest approach of ions, a. The influence parameter a on the diffusion of this system is also discussed.Ternary mutual diffusion coefficients (Dik) measured by the same technique are reported for aqueous CaSO4 + H2SO4 solutions at 298.15 K and concentrations up to 0.0100 mol dm−3. The coupled diffusion of CaSO4 (1) and H2SO4 (2) is significant, as indicated by the large negative cross-diffusion coefficients. Nernst equations are used to predict transport coefficients from limiting ionic conductivities and help to interpret both concentration dependence of the diffusion coefficients and the electrostatic mechanism for the coupled diffusion of the solutes.

Effect of the mean distance of closest approach of ions on the diffusion coefficient calculations in aqueous solutions of silver salts

Abstract Diffusion coefficients of silver salts in aqueous solutions are estimated from Onsager-Fuoss and Pikal models, using different values of the mean distance of closest approach of ions, a, determined from different theoretical procedures. The influence of this parameter on the diffusion of these systems is discussed.

Estimation of the mean distance of closest approach of some heavy metal ions in aqueous solutions: some experimental and theoretical calculations

The estimation of numerical values of the mean distance of closest approach of ions, a, of heavy metal ion salts in aqueous solutions, determined from activity coefficients, as well as from different theoretical approaches, is presented and discussed.

Mean distance of closest approach of alkaline-earth metals ions in aqueous solutions: Experimental and theoretical calculations

The estimation of numerical values of the mean distance of closest approach of ions, a, of alkaline-earth metal ion salts in aqueous solutions, determined from activity coefficients, as well as from different theoretical approaches, is presented and discussed.

Mean distance of closest approach of ions: Lithium salts in aqueous solutions

Numerical values for the mean distance of closest approach of ions, “ a”, for lithium salts in aqueous solutions are presented and discussed. These values were obtained from both experimental activity and diffusion coefficients, and estimated by using different theoretical approaches.

Mean distance of closest approach of ions: Sodium salts in aqueous solutions

The estimation of numerical values for the mean distance of closest approach of ions, a, of sodium salts in aqueous solutions, determined from activity and diffusion coefficients, and also from different theoretical approaches, is presented and discussed.

Factors Influencing Blind Conflict Risk in En Route Sectors Under Free-Flight Conditions

We develop a simulation model of the flight of aircraft through an en route sector. The model is used in two experiments. The first studies the effect of directional clumping on risk. The second is a full factorial design with replication, which simulates a large number of scenarios to assess the impact of key input factors on free-flight risk measures. We measure risk for a given flight by the mean distance of closest approach to other aircraft and the mean number of approaches closer than a specified distance. Using analysis of variance and regression analysis, we determine that the most important influences on blind collision risk are time of entry into the sector and number of aircraft. Also influential are certain orientations of flight paths and the distribution of airspeeds. The least important factor is altitude. The relationship between number of aircraft and the two risk measures can be quantified in regression relationships.

Conformational transitions of duplex and triplex nucleic acid helices: thermodynamic analysis of effects of salt concentration on stability using preferential interaction coefficients

For order-disorder transitions of double- and triple-stranded nucleic acid helices, the midpoint temperatures Tm depend strongly on a +/-, the mean ionic activity of uniunivalent salt. Experimental determinations of dTm/d ln a +/- and of the enthalpy change (delta H(o)) accompanying the transition in excess salt permit evaluation of delta gamma, the stoichiometrically weighted combination of preferential interaction coefficients, each of which reflects thermodynamic effects of interactions of salt ions with a reactant or product of the conformational transition (formula; see text) Here delta H(o) is defined per mole of nucleotide by analogy to delta gamma. Application of Eq. 1 to experimental values of delta H(o) and Tm yields values of delta gamma for the denaturation of B-DNA over the range of NaCl concentrations 0.01-0.20 M (Privalov et al. (1969), Biopolymers 8,559) and for each of four order-disorder transitions of poly rA.(poly rU)n, n = 1, 2 over the range of NaCl concentrations 0.01-1.0 M (Krakauer and Sturtevant (1968), Biopolymers 6, 491). For denaturation of duplexes and triplexes, delta gamma is negative and not significantly dependent on a +/-, but delta gamma is positive and dependent on a +/- for the disproportionation transition of poly rA.poly rU duplexes. Quantitative interpretations of these trends and magnitudes of delta gamma in terms of coulombic and excluded volume effects are obtained by fitting separately each of the two sets of thermodynamic data using Eq. 1 with delta gamma PB evaluated from the cylindrically symmetric Poisson-Boltzmann (PB) equation for a standard model of salt-polyelectrolyte solutions. The only structural parameters required by this model are: b, the mean axial distance between the projections of adjacent polyion charges onto the cylindrical axis; and a, the mean distance of closest approach between a salt ion center and the cylindrical axis. Fixing bMS and aMS for the multi-stranded (ordered) conformations, we determined the corresponding best fitted values of bSS and aSS for single-stranded RNA and DNA. The resulting best fitted values of aSS are systematically less than aDS by 2-4 A. Uncertainty in the best-fitted values of bSS is significantly lower than in the aSS, because bMS is known with relatively high precision and because the larger uncertainty in aMS has a relatively small effect on the best-fitted values of bSS:bSS = 3.2 +/- 0.6 A for single-stranded poly rA and poly rU; and bSS = 3.4 +/- 0.2 A for single-stranded DNA. These values are approximately one-halt of those expected for a fully extended single-stranded conformation. With the best fitted values of ass and bss, our calculations of delta gamma PB are in close quantitative agreement with experimental observations on each of five nucleic acid order-disorder transitions.

Effect of the boundary condition at distance of closest approach on Wien dissociation of a weak electrolyte: A singular perturbation solution

A singular perturbation technique is developed in order to examine the effect of plausible variations in the boundary condition of the ion-pair distribution function f at the distance of closest approach of the oppositely charged ions in a weakly dissociated electrolyte. Such variations from the point-ion model may arise in practice where the ions are weakly solvated or in ion-exchange resins or soluble polyelectrolytes. The relative increase K(X)/K(0) in the dissociation constant of the weak electrolyte to which a uniform electric field X is applied is calculated to third order in the field-dependent parameter ε, assuming that the mean distance of closest approach between the charge centers of oppositely charged ions, a, is nonzero. A novel feature of this problem is that the boundary condition on f at distance a depends on the dissociation constant itself. It is found that the constant of proportionality in Onsager’s linear law, derived for the idealized case of a weakly dissociated electrolyte of point ions, remains unchanged when a≠0 but the second- and third-order terms in the expansion for K(X)/K(0) in powers of ε are each increased by an additional term which is proportional to exp (−1/a).

The mean distance of closest approach in the theory of liquids

Abstract The mean distance of closest approach, for two colliding particles, is defined as an average over their relative kinetic energies. It is shown that the mean distance of closest approach thus defined, is formally identical to the effective hard-sphere diameter in the Barker and Henderson perturbation theory of liquids.

Magnetic field dependence of plasma relaxation times

A previously derived Fokker-Planck collision integral for an electron plasma in a dc magnetic field is examined in the limit in which the Debye length is greater than the thermal gyroradius, which is in turn greater than the mean distance of closest approach. It is demonstrated that the collision integral can be satisfactorily approximated by the classical Landau value (which ignores the presence of a dc magnetic field) if the following replacement is made: In the Coulomb logarithm, the Debye length is replaced by the gyroradius. This induces a fundamental logarithmic dependence on magnetic field in the relaxation times. Numerical comparison of the asymptotic approximations with the previously derived exact results is made, and good agreement is found. The simplification this introduces into the description of collision processes in magnetized plasmas is considerable.

Dependence of micelle aggregation number on polar head structure: II. Light scattering by aqueous solutions of decyldiethylammonium bromide and related heterocyclic surfactants

Aggregation numbers of decyldiethylammonium, decylpyrrolidinium, decylmethylpyrrolidinium, decylmethylpiperidinium, decylmorpholinium, decylmethylmorpholinium, and decylpiperazinium bromide were determined in 0.5 m NaBr and in 0.5 m NaCl. The aggregation number of decylpiperidinium bromide in 0.5 m NaCl was also determined. The smallest micelles were formed by decylmethylpiperidinium bromide and decylmethylmorpholinium bromide (about 36 surfactant ions per micelle in 0.5 m NaCl) and the largest by decylpyrrolidinium bromide (over 159 surfactant ions per micelle in 0.5 m NaBr). Surfactant ions for which the mean distance of closest approach of the counterion to the charge center is small form relatively large micelles. Charge location and hydrogen bonding are other factors which can affect the polar head's role in micelle formation.