Diffusion coefficient of electrolytes

Since perchlorate ions, and more generally the majority of anions used in common electrolyte systems, are known to move rapidly in liquid solutions, it is reasonable to assume that the rate determining step in controlling the kinetics of the overall process is the ion diffusion throughout the polymer fibrils. This conclusion has been experimentally confirmed. For example, the diffusion coefficient of electrolyte counterions in bulk polyacetylene has been determined (Will, 1985) to be seven orders of magnitude lower than in liquid electrolytes, namely about 10 cm s vs 10 cm s ... 

Thermal batteries are a special class of reserve batteries which take advantage of the long-term stability intrinsic to many interfaces when both the active material and the electrolyte are solid state, at least until activation. The stability is attributable to the very low diffusion coefficients of electrolyte ions in the solid state for the chosen electrolyte systems. These batteries are fully assembled with electrolyte present, but the electrolyte remains a solid nonconductor until it is melted by rapid heating from a pyrotechnic heat source. 

On the assumption of complete dissociation in a solution containing two species of ions, the diffusion coefficients of electrolytes can be predicted very accurately at infinite dilution using the equation... 

Diffusion Coefficient of Electrolyte through Ion Exchange Membranes... 

When an ion exchange membrane is used in electrodialysis, one side of the membrane contacts a dilute solution and the other a concentrated solution. There is a diffusion flux of electrolyte and non-electrolyte of low molecular weight through the membrane. Because the diffused amount directly affects current efficiency and the purity of products, the diffusion coefficient of electrolytes through membranes is important in practical applications. The following simplified method may be used to determine the coefficient after one side of the membrane has contacted a concentrated solution and the other side a dilute solution (in some cases, pure water) for a given period, the amount of electrolytes diffused through the membrane into the dilute solution is determined, and the diffusion coefficient is calculated by the Fick equation. 

Figure 6.7 Model concentration profile at the membrane-solution interface during electrodialysis (cation exchange membrane). F is the Faraday constant, Clf C2, C3 and C4, concentrations of desalting side solution, of the membrane—solution interface desalting side, at the membrane-solution interface (the concentrated side) and of the concentrated solution, respectively <5m, is the thickness of ion exchange membrane, <5i and d2 the thickness of the diffusion boundary layer at the desalting side and concentrated side, respectively t+ and t+ are the transport numbers of the cation in the solution and in the membrane, I is the current density, D and Dm are diffusion coefficients of electrolyte in the solution and in the membrane.

Diffusion coefficients of electrolytes in water are greatly dependent on concentration variations of 100% from infinite dilution to near-saturation are not uncommon. Moreover the change is often non-linear and accurate prediction of its effect is extremely difficult. Other physical properties, such as viscosity and density, change over this concentration range but not to such an extent. 

On the other hand, the electrical conductivity information is essential for several practical applications of the hydro-thermal systems. It is well known, for instance, the use of electrical conductivity measurements on Une to prevent corrosion problems in steam generators and other applications of the steam/water cycle. Tracer diffusion coefficients of electrolytes can be calculated from limiting electrical conductivity and used to predict mass transfer in many geochemical processes and hydrothermal reactions. 

Lobo, V.M.M. Valente, A.J.M. Ribeiro. A.C.F.Differential Mutual Diffusion Coefficients of Electrolytes Measured by the Open-Ended Conductimetric Capillary Cell A Review.FocMi Chem.Biochem.Nova Science Publishers New York 15-38 2003. 

The diffusion coefficient of oxygen in solid silver was measured with a rod of silver initially containing oxygen at a conceim ation cq placed end-on in contact with a calcia-zirconia electrolyte and an Fe/FeO electrode. A constant potential was applied across dre resulting cell... 

From the value of the diffusion coefficient of Br2 in electrolyte solutions, conclu-... 

Table 9. Diffusion coefficients of Br2 in the aqueous electrolyte phase at 25 °C (taken from Ref. [68])...

The primary question is the rate at which the mobile guest species can be added to, or deleted from, the host microstructure. In many situations the critical problem is the transport within a particular phase under the influence of gradients in chemical composition, rather than kinetic phenomena at the electrolyte/electrode interface. In this case, the governing parameter is the chemical diffusion coefficient of the mobile species, which relates to transport in a chemical concentration gradient. 

FIG. 17 Diffusion coefficients of the counterions and coions of a 1 1 RPM model electrolyte in a cylindrical nanopore of i = lOd. The circles and triangles represent the results of coions and counterions, respectively. 

The influence of an interfacial kinetic barrier on the transfer process is readily illustrated by fixing the concentrations and the diffusion coefficients of Red for the two phases and examining the current response of the UME as K is varied. For illustrative purposes, we arbitrarily set and y = 1, i.e., initially the equilibrium conditions are such that there are equal concentrations of the target solute in the two phases, and the solute diffusion coefficient is phase-independent. Figure 17 shows the chronoamperometric characteristics for several K values from zero up to 1000. Under the defined conditions, these values of K reflect the ease with which the transfer process can respond to a perturbation of the local concentration of Red in phase 1, due to electrolytic depletion. 

Supporting electrolytes at sufficiently high concentration are present in both O and W phases. For the sake of simplicity, we assume that the diffusion coefficients of relevant species in the a phase (a = O, W) have the common value Z) . The W phase is well-buffered, whereas the O phase contains no buffer component. 

Experimental methods for determining diffusion coefficients are described in the following section. The diffusion coefficients of the individual ions at infinite dilution can be calculated from the ionic conductivities by using Eqs (2.3.22), (2.4.2) and (2.4.3). The individual diffusion coefficients of the ions in the presence of an excess of indifferent electrolyte are usually found by electrochemical methods such as polarography or chronopotentiometry (see Section 5.4). Examples of diffusion coefficients determined in this way are listed in Table 2.4. Table 2.5 gives examples of the diffusion coefficients of various salts in aqueous solutions in dependence on the concentration. 

Polymer gels and ionomers. Another class of polymer electrolytes are those in which the ion transport is conditioned by the presence of a low-molecular-weight solvent in the polymer. The most simple case is the so-called gel polymer electrolyte, in which the intrinsically insulating polymer (agar, poly(vinylchloride), poly(vinylidene fluoride), etc.) is swollen with an aqueous or aprotic liquid electrolyte solution. The polymer host acts here only as a passive support of the liquid electrolyte solution, i.e. ions are transported essentially in a liquid medium. Swelling of the polymer by the solvent is described by the volume fraction of the pure polymer in the gel (Fp). The diffusion coefficient of ions in the gel (Dp) is related to that in the pure solvent (D0) according to the equation ... 

Diffusion of cations in a Nation membrane can formally be treated as in other polymers swollen with an electrolyte solution (Eq. (2.6.21). Particularly illustrative here is the percolation theory, since the conductive sites can easily be identified with the electrolyte clusters, dispersed in the non-conductive environment of hydrophobic fluorocarbon chains (cf. Eq. (2.6.20)). The experimental diffusion coefficients of cations in a Nation membrane are typically 2-4 orders of magnitude lower than in aqueous solution. 

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