Imre Ruff

Effect of exchange reactions on transport processes: A comparison of thermodynamic treatment with random walk on lattice points

The effect of an AX+A ⇄ A+AX exchange reaction on the transport of X is discussed for a general transport process driven by the gradient in the chemical potential of AX, as well as its special cases of isothermal diffusion and electric conductivity. This treatment based on macrodifferentials is compared with a stochastic treatment of random walk on regular lattice points in one‐, two‐ , and three‐dimensional cases. The basic equivalence is proved for the two methods which ensures the application of the latter, more simple, procedure with general validity. It is also shown that the stochastic treatment reveals some aspects that remain hidden in the thermodynamic approach.

Statistical geometry of molten alkali halides

The generalized Dirichlet–Voronoi polyhedra were used to characterize the adjacent neighborhood of the ions in computer simulated configuration set of molten RbCl and LiI as examples of binary Coulomb liquids with like and unlike size ions, respectively. The statistical distribution of various features of the DV polyhedra has been studied with the following main results: (i) radial and angular distributions of adjacent neighbors indicate traces of face‐centered‐cubic symmetry in molten RbCl and wurtzite‐like structure in LiI; (ii) the radial internal point distribution function on the DV polyhedra reveal more compact coordination spheres for Cl−, Rb+, and I− ions than for Li+ ions in the corresponding melts; (iii) the volume fluctuation of the DV polyhedra makes it possible to calculate isothermal compressibility coefficients even from (N,V,T) simulation data; (iv) identification of vacancies by seeking for the most protruding vertices of the DV polyhedra provides information on vacancy–vacancy pair correlation functions.

Grand canonical Monte Carlo simulation of liquid argon

A grand canonical Monte Carlo procedure with fixed values of the chemical potential μ, volume V, and temperature T, is described which is suitable to simulate simple fluids with only a minor increase in computer time in comparison with canonical (N,V,T) simulations and considerably faster than (N,p,T) ones. The method is rapidly convergent for rather dense systems with a reduced density of about ρσ3=0.88. The rapid convergence is attained by decreasing the vain attempts in the regime when new particles are added. The chance to find a place for an additional particle is increased by locating the cavities suitable to house a particle with the aid of the Dirichlet–Voronoi polyhedra. As an example, liquid argon is simulated with Lennard‐Jones potentials at T=86.3 K and μ=−73.4 J/mol. The simulated density has been found to be 1.468 g/cm3 which is to be compared with the experimental value of 1.425 g/cm3. The same density was obtained by starting the procedure with both 216 and 250 particles in the simulation ...

Monte Carlo simulation of the complete set of molten alkali halides

The results of Monte Carlo simulations of the complete family of molten alkali halides with a consistent set of inter-ionic potentials are reported. It is found that the structures of the melts with a common cation are isomorphous, the density scaling approximately with the sum of the ionic radii. Within groups with a common anion the local coordination varies from tetrahedral for Li+ salts to octahedral for Cs+ salts. General agreement is found with the available experimental results and with the results of other simulations using different potentials.

The rate of the electron-exchange between the tris-1,10-phenantroline complexes of iron(II) and iron(III)

Abstract The rate of the electron-exchange between ferroin and ferriin ions, unmeasurably fast for methods known so far, has been determined by the application of transfer diffusion. The second order rate constant proved to be (3·3 ± 1·4) × 10 8 /M/s. The rate constant calculated by accounting for the electrostatic repulsion only is in excellent agreement with this value, thus the inner and outer sphere rearrangement around the ions is likely less significant in the activation process of this reaction.

Effect of exchange reaction on transport processes: Fick's second law for diffusion on lattice points

Abstract The mass balance equation is derived for the lattice gas model of transfer diffusion in which the displacement of the centers of mass of particles is brought about by both common, “migrational”, motion and chemical exchange reaction of the type A + AX ⇌ AX + A. The form of Ficks second law involves a concentration-dependent diffusion coefficient. This concentration dependence must be taken into account when the c ( x , t ) functions are calculated by integrating the second law.

A Less Arbitrary Determination of Coordination Numbers in Disordered Systems

Abstract The radial distribution functions, 4πr2gij(r), of molten alkali halides, obtained by Monte Carlo simulations, have been deconvoluted into contributions from the first, second, third, etc. neighbours. These individual distribution functions indicate that in alkali halide melts the first coordination sphere of the ions contains an integral or half integral number of unlike charged ions. The shapes of the individual distribution functions show characteristic changes from first coordination shell neighbours to second shell ones and this can be utilised to make the selection of the boundary of the coordination sphere less arbitrary. Such a deconvolution reveals more of the structure in the case of the like charged ion distributions as well.

Invariants of spherical harmonics as order parameters in liquids

The application of the second- and third-order invariants of the even-l spherical harmonics for the geometrical characterization of clusters in disordered systems is discussed. Their use as sensitive order parameters is useful in the geometrical analysis of computer-simulated configurations. It is shown that the second- and third-order invariants give information on the three- and four-body angular correlations, respectively. The values of the invariants calculated for a given configuration set depend on the number of particles and their neighbours considered, i.e. on the size of the statistical sample. A renormalization is suggested to eliminate this size effect. By choosing a suitable method of averaging the spherical harmonics, they can be made characteristic either of the angular correlations within individual clusters only or also of cross-correlations between a set of clusters. Thus they can be used for the detection of traces of longer-range crystalline structures.The first five even-l invariants have been calculated for configurations of liquid argon, molten alkali-metal halides, and pure water simulated by Monte Carlo or molecular-dynamic methods. The results indicate that the structure of the first coordination spheres in liquid argon are slightly distorted hexagonal close-packed clusters which have practically no angular correlation with one another. Nearest-neighbour angular correlations in sodium, potassium, rubidium and caesium chlorides correspond to more or less distorted face-centred cubic lattices, while LiI and LiCl resemble the wurtzite and sphalerite structure, respectively. In comparison with the above cases, water is disordered to the extent that even the distorted tetrahedral clusters are barely recognizable. Peculiarly distorted tetrahedra which are in a characteristic angular correlation with one another are stabilized by a decrease in the density of water.

On the transition from the lattice-like structure of electrolytes to the Debye-Hückel limit

Charge densities around a central ion are calculated with the assumption of a slightly distorted normal distribution of point-charge ions around regular lattice sites. The conditions under which this charge distribution approaches that of the Debye–Huckel theory at infinite dilution are discussed. The lattice model in this form predicts oscillations in the charge cloud at any finite concentration, but these oscillations are very far from the central ion in dilute systems. Pair correlation functions are also reported for concentrated solutions. The shift of the first-neighbour maxima follows a concentration dependence steeper than the cube-root law for oppositely-charged pairs and less steep for like-charged pairs. The excess energy has been calculated and is in very good agreement with the HNC and MSA theory for low concentrations.

Theory of concentrated solutions of strong electrolytes. Part 1.—Some thermodynamic quantities of a lattice-like network of ions surrounded by a dielectric gradient

Calculations have been carried out on a model of electrolyte solutions with the following features: (i) the ions of the strong binary electrolyte are distributed in a lattice-like arrangement, (ii) ions are immersed in an incompressible, structure-less, continuous dielectric but this medium has a dielectric gradient in the vicinity of ions due to the polarizing effect of their electric field, (iii) coulombic interaction is calculated with respect to an average dielectric “constant” depending on the interionic separation distance, and (iv) the dielectric gradient regions around the ions result in a repulsive force between ions due to the work required to remove solvent from the dielectric gradient region when lowering the interionic separation distance. Comparison of calculated and observed data for the average dielectric constant, mean ionic activity coefficients, and partial molar enthalpy contents of several 1–1 and 1–2 electrolytes shows fairly good agreement, in some cases in the entire concentration range, with no adjustable parameters involved.