Algorithm for simulation of transient and alternating current electrical properties of conducting membranes, junctions, and one-dimensional, finite galvanic cells

Abstract

Publication costs assisted by the National Science FoundationAn algorithm for computer simulation of transient concentration profiles and both transient and ac electrical properties of conducting membranes has been developed and described. Applications include transport by several ions with different mobilities and valences in permselective membranes, totally blocked cells, and finite galvanic cells. The algorithm is based on the Nernst-Planck system of equations coupled with Poisson's equation, introduced via the displacement current; therefore, electroneutrality is not assumed and migration effects are included automatically. Simulations of transient and steady-state properties as well as ac impedances are compared with solutions obtained analytically. Conventional linearization of field equations is not required to obtain transient responses. However, conversion from time to frequency using the Fourier transform to obtain impedances is theoretically limited to dimensionless currents and voltages less than unity. We have demonstrated versatility of the algorithm by simulating a case of biological interest-the inductive behavior of the squid giant axon.

Computer simulation of ion-selective membrane electrodes and related systems by finite-difference procedures

“…Early studies of this type were restricted to ion-exchanger systems with one kind of mobile ionic site or ligand [18,19]. Later, valinomycin membranes with tetraphenylborate sites were also treated [20] when ionophore-based membranes with ionic additives became a focus of interest [45][46][47].…”

“…The current density was chosen as 4.488 μA cm -2 , which results in a total membrane potential of -500 mV (and an internal potential difference of -438.21 mV) for the final steady state. Evidently, this current flow induces an enrichment of mobile sites on one side of the membrane, and a depletion on the other side [18][19][20]50]. The numerical results obtained for the final state can directly be compared with exact data since a theoretical description of the steady state is available [50].…”

“…A series of numerical simulations have been reported in the past for membranes of ion-selective electrodes [18][19][20][21][22][23][24][25], for liquid junctions of reference electrodes [22,24] and for diffusion layers of other electrode systems [26][27][28][29]. In an early contribution, Buck's group introduced digital simulations for investigating the electrical behavior of membranes based on liquid ionexchangers [18,19].…”

“…In an early contribution, Buck's group introduced digital simulations for investigating the electrical behavior of membranes based on liquid ionexchangers [18,19]. The work was later extended to ionophore membranes with mobile ionexchanger sites [30].…”

Influence of cationic and anionic additives on the electrical properties of ionophore-based ion-selective membranes

“…Most of these treatments were restricted to potentiometric systems at zero current, however. Actually, the basic problem for membranes with an amperometric current flow is that the mobile ionic sites, other than the fixed ones, tend to establish a concentration polarization [46,47]. The reason is that these species are driven by the applied electric field to one side of the membrane but, at the same time, they are strictly confined to the organic phase.…”