*From*: vkitzing &$at$& sunny.mpimf-heidelberg.mpg.de (Eberhard von Kitzing)*Subject*: Mobility paradox, summary*Date*: Tue, 2 Apr 1996 12:44:26 +0200

Dear colleges on the Computational Chemistry List, this morning I thought about an apparently simple problem where I do not know a solution jet. Consider a symmetric 1:1 electrolyte system with a single dielectric constant which is divided by a planar surface into a right hand and a left hand side. The cationic and anionic concentrations, cC and cA, on both sides are the same; to obtain global electro neutrality cC == cA is required. Exceptions from this rule are allowed only locally, e.g. within a few Debye length around the boundary. The ionic mobilities are mu1 > mu2 on the right hand side and mu2 and mu1 on the other for cations and anions, respectively. At equilibrium there is no problem. Now an external electric field E is applied and this creates the problem. On the first view one would write the individual ionic fluxes jC and jA far away from the central boundary: left hand side and right hand side cations jC(left) = + F mu1 E cC and jC(right) = + F mu2 E cC anions jA(left) = - F mu2 E cA and jA(right) = - F mu1 E cA where F is Faraday's constant. But this implies jC(left) != jC(right) and jA(left) != jA(right) which violates the particle conservation law. I would assume that such a problem has been discussed in literature. Has anybody some ideas? ========================================================================= > >I think that the current density at the cathode is > > j(K)=(mu+ + mu- )F E |Z+|(n+ - (mu-/mu+)dn- - dn-(diff)) > >and at the anode: > > j(A)=(mu+ + mu- )F E |Z-|(n- - dn- + dn-(diff)) > >and for kinetic equilibrium j(K)= j(A) obtains, because the diffusion > >current dn-(diff) will balance the unequal changes in particle density > >in the left and right parts of the cell which stem from the inequality > >of mobility values. > > This may be the situation close to the boundary. But one cannot have > a non-zero concentration gradient over macroscopic distances. I did not realize that by 'planar surface' you meant a material division which separates the cell into two compartments (that is, a membrane).In this case there will of course be no diffusion gradient over macroscopic distances, but instead a diffusion poential which influences the field strength in the left and right compartment.The faster ions will be slowed down and vice versa until the current densities are equal again. I do not think that under these conditions concentration differences between left an right part can be stationary. But if the concentrations are equal again,the diffusion potential should vanish, which gives rise to concentration differences,this again to diffusion potential, ... . I suppose therefore an oscillatory behaviour. Best Wishes, M. Mauksch, CCC uni-erlangen ------------------------------------------------------------------------- Eberhard von Kitzing Max-Planck-Institut fuer Medizinische Forschung Jahnstr. 29, D69120 Heidelberg, FRG Carl-Zuckmayer Str. 17, D69126 Heidelberg (privat) FAX : +49-6221-486 459 (work) Tel.: +49-6221-486 467 (work) Tel.: +49-6221-385 129 (home) internet: vkitzing &$at$& sunny.MPImF-Heidelberg.mpg.de http://sunny.mpimf-heidelberg.mpg.de/people/vkitzing/Eberhard.html