Distinct Diffusion Coefficients Research Articles

Inferences on dynamic water structure in aqueous solutions from diffusion measurements

The dynamic, hydrogen-bonded structure of water can be profoundly affected by addition of solutes as reflected by the resulting solute—solvent interactions. Measurements of diffusion coefficients for the solute species and for water are a useful probe for studying those interactions and changes in the dynamic water structure. The analysis of transport properties of electrolyte solutions is presently approached both theoretically and experimentally by the use of generalised transport coefficients such as Onsager phenomenological coefficients, velocity correlation coefficients or the closely related distinct diffusion coefficients of Friedman. However, two of these approaches generally use a solvent-fixed frame of reference and thereby exclude the information available from studying the diffusion of the solvent. The velocity correlation coefficient approach is used here to examine hydrogen-bonding effects in binary solution containing water as one component. We discuss also examples where intra-diffusion data for water in aqueous solutions give important insights into the dynamic structure of aqueous solutions.

Droplet ignition with variable properties and distinct binary diffusion coefficients

The effects of variable thermophysical properties on the ignitability of a single-component fuel droplet in a hot oxidizing environment were investigated by a matched asymptotic analysis of large activation energy. It is shown that the effects of variable thermophysical properties on the ignition are partly via the mass evaporation rate and partly through the thermal driving force for droplet evaporation, beta, which directly influences the ignition Damkoehler number. It was found that the ignition Damkoehler number increased both with an increase of beta and with a decrease in the fuel reaction order. 17 refs.

Distinct and self-terms of mass-current correlation functions of binary atomic liquids.

Recently defined distinct diffusion coefficients and distinct time-correlation functions (TCF's) related to them have been calculated by molecular dynamics in the ordinary NVEp ensemble, where N is the number of particles, V the total volume of the system, E the total energy, and p the total momentum. Lennard-Jones mixtures of simple structure were considered. For the ideal system, the theoretical predictions for the distinct TCF's were found to be in complete agreement with the molecular-dynamics results. For nonideal systems, the distinct functions are very suitable for indicating phase separation or the inverse phenomena, particularly when the corresponding self-TCF is added. The results show furthermore that the proposed separation of the mass current in self- and distinct terms is completely equivalent to that given in earlier work using one-particle and collective diffusive processes.

Velocity correlations in the molecular dynamics ensemble: Computation of the distinct diffusion coefficients

The theory of the correction for the difference in the fluctuations among the different ensembles is applied to derive the time correlation function formula required to compute the distinct diffusion coefficients in the barycentric reference frame by molecular dynamics. In the process it is found that the dynamical variables in the time correlation function of any mass transport coefficient of any reference frame are the same in the canonical as in the molecular dynamics ensemble. The result agrees with the accepted formulas for computing the kinetic part of the mutual diffusion coefficient in a binary mixture of nonelectrolytes and for computing the electrical conductivity in molten salts and electrolyte solutions. The static velocity correlations in the molecular dynamics ensemble are analyzed without recourse to the other ensembles. In sharp contrast with the ensembles which are not constrained with respect to the total momentum, the laboratory-frame velocities of two different particles at the same time are found to be correlated. The result obtained is equivalent to the initial value of the canonical time correlation function of the barycentric distinct diffusion coefficients derived in the preceding paper.

The role of reference frames in the molecular theory of diffusive transport in solutions

Starting with the Green–Kubo formulas for the phenomenological coefficients of irreversible thermodynamics, the molecular expression for the distinct diffusion coefficient Dd[R],αβ in any internal reference frame R is derived. It follows that Dd[R],αβ is given by the time integral of a time correlation function (tcf) Λd[R],αβ(t) whose dynamical variables are the velocities of two different particles of species α and β, each relative to a microscopic reference velocity ŵR . These relative dynamic variables have the welcome feature of being orthogonal to the total momentum of the system so that Λd[R],αβ(t) vanishes at long times. Hence the divergence of the barycentric distinct diffusion coefficients, suggested by their usual interpretation in terms of a time correlation function that lacks an explicit dependence on the reference frame, is resolved. The influence of the reference frame on the behavior of the barycentric distinct tcf ’s is analyzed. In great measure this influence is exposed by considering initial values of the tcf ’s; in turn the initial values are decisive in establishing the sign of the distinct diffusion coefficients in ideal or nearly ideal mixtures. Finally, by applying new linear relations connecting the self and distinct tcf ’s, a complete description of some of the barycentric distinct tcf ’s may be given in the limiting cases of a pure fluid and a tracer in a host liquid.

R. A. Robinson Memorial Lecture. Hydration of cation–cation and anion–anion pairs

Electrolyte mixture thermodynamics is strongly affected by close interactions between ions with the same sign of charge. Also in suitable cases spin relaxation, electron-transfer kinetics and distinct diffusion coefficients are sensitive to configurations in which the ions in such pairs are so close that their hydration shells interpenetrate or rearrange. Many such close pairs are surprisingly stable.

A thermodynamic approximation for the estimation of velocity correlation coefficients in binary liquid mixtures

An equation is derived using the relations of equilibrium thermodynamics to estimate limiting distinct diffusion coefficients, (or velocity cross-correlation coefficients) in binary non-electrolyte mixtures. It is tested against 13 mixtures. Good agreement is obtained with distinct diffusion coefficients derived experimentally in the case of near deal systems. For non-ideal mixtures the calculated values appear to follow the experimental coefficients to some extent. For this reason, the thermodynamic approximation is not as suitable for a reference equation as a structural approximation previously derived.

Limiting law for distinct diffusion coefficients in ionic solutions

The limiting laws for the distinct diffusion coefficient and the corresponding Onsager phenomenological coefficient are obtained from the cluster theory of electrolyte conductance. Results are given for single electrolytes and common-ion mixtures with unrestricted charges and friction coefficients in both cases.

Hydrodynamic approximation for distinct diffusion coefficients

The distinct diffusion coefficient is a measure of the coupling of the diffusive motions of two particles. It is given as the integral over a velocity cross correlation rather than the velocity self correlation that determines the self-diffusion coefficient. A hydrodynamic approximation for the distinct diffusion coefficient is proposed and then tested by comparison with data for a wide range of non-ionic binary mixtures. The hydrodynamic approximation gives negative distinct diffusion coefficients and is in qualitative agreement with most of the data. In many cases, deviations from the model results can be explained in terms of interactions which are not accurately treated by the model.

Theory of quasi-steady one-dimensional diffusional combustion with variable properties including distinct binary diffusion coefficients

A previously formulated variable-property theory for a class of heat and mass transfer problems, exemplified by droplet vaporization and combustion, is generalized herein such that in addition to the previous features that the specific heats C, the thermal conductivity k, and the binary diffusion coefficient D ij are temperature dependent whereas C and k are further concentration-weighted, in the present formulation the D ij 's are also distinct for all species pairs. Explicit expressions are derived for the temperature and species profiles, the mass vaporization rate, and the flame-front standoff ratio. It is shown that oxidizer mass diffusion in the outer region and heat transport in the inner region are the dominant transport processes. A simplified model is recommended to obtain estimates of the various vaporization characteristics.

Shape studies on macromolecules in aqueous and detergent solvents by transient electric birefringence

Transient electric birefringence of macromolecules is described by two exponential decay times, which are functions of two distinct rotary diffusion coefficients for their equivalent ellipsoids. The dimensions of the ellipsoid are calculated from these decay times. This method has been applied to hydrophilic and hydrophobic proteins in distilled water and in anionic and nonionic detergents. BSA and human transferrin in H 2O yield dimensions in agreement with published values. Helix pomatia hemocyanin (Hph) in H 2O, yields dimensions that are used to calculate values for s and [η], which agree with published values. Hph has been shown to be a circular cylinder of spherical subunits. The s value for this model, calculated according to Kirkwood's theory, agrees with the measured value. This agreement in s values supports the dimensions obtained by transient birefringence. The dimensions for seven proteins (11 700–72 000 mol wt) in SDS, obtained by this method, are in agreement with values reported by Reynolds and Tanford for mol wt < 26 000. Larger proteins show flexibility by this method, evidenced by shorter lengths than those reported by Reynolds and Tanford. However, in the two ranges of molecular weight, this method yields values of protein molecular weight, in agreement with the model of Reynolds and Tanford for proteins in SDS. The membrane protein, rhodopsin, dissolved in Ammonyx LO and digitonin, yields dimensions whose axial ratio is 6.8 in both detergents. This structure supports the model for rhodopsin proposed by Wald. Finally, this method is shown to be applicable to the study of detergent micelle structure, when the micelles resemble ellipsoids are shown for Triton X-100.