Cation flux coupling

Electroneutrality is maintained by having the counterdiffusing cation fluxes coupled. Note that for this to happen, the system must be predominantly an ionic conductor, that is, t < // — if not, decoupling of the fluxes will occur (see below). 

According to the second law, the dissipation function must be positive if not zero, which of course is to be expected here, since we are dealing with a spontaneously occurring passive process. The thermodynamic force A/x+, which contains both a concentration-dependent component and an electrical component, is the sole cause of the flow J+. In a system in which more than one process occurs, each process gives rise to a term in the dissipation function consisting of the product of an appropriate force and its conjugate flow. In the case of active transport of the cation, as found, for example, in certain epithelial tissues, the cation flux is coupled to a metabolic reaction. If we represent the flow or velocity of the reaction per unit area of membrane by Jr, the appropriate force driving the reaction is... 

The cation fluxes can be expressed as usual using Eqn. (4.49). If we consider the simplest case by neglecting all flux couplings other than those through site conservation and electroneutrality, Eqn. (8.8) yields (see Eqn. (4.99))... 

The flux of cations is coupled with the flux of anions. The total current density is given by Faraday s law ... 

The model geometry is described in two dimensions. In x-direction the flux of ions and electrons accounts for charge transport perpendicular to the cell layers. The influence of ohmic drops within the current collectors is assumed to be zero, thus only three domains are taken into account. These are the anode (graphite), a porous separator and the cathode (LiFeP04). The solid diffusion within the electrode s active material particles is calculated in an additional pseudo-dimension in spherical coordinates. So at every point x within an electrode domain a second dimension r is used to describe this flux directed to or away from the particle s centre. The dimensions are coupled at the particle s surface. A binary electrolyte (one salt in one solvent) is assumed, whereas only the cation flux is described, since the anions do not contribute to the electrochemical reaction of the cell. The subscript + indicates the aforementioned cationic species (LE). 

In practice, one can say that the transport coefficients of the individual ions are generally rather different from one another. In oxide spinels, the diffusion of oxygen is negligible compared to the cationic diffusion. Therefore, we can eliminate a number of the mechanisms shown in Fig, 6-3. Furthermore, if ideal contact is maintained at the phase boundaries so that the gas phase cannot enter, then the only remaining probable reaction mechanism is the counterdiffusion of cations. In this mechanism, the two cation fluxes in the reaction product are coupled through the condition of electroneutrality. 

According to Jost, the reactants AX and BY are separated from one another by the product phases AY and BX. A layer of BX grows to cover the reactant AX, and a layer of AY grows to cover the reactant BY. This situation results from the fact that only the cations are mobile. In order that the reaction can proceed, it is necessary that there be a slight solubility of A" ions in BX and of B" " ions in AY, since these ions must diffuse through the product phases. In order that this problem may be treated quantitatively, it is, in principle, necessary that the partial pressures of X2 and Y2 in the surrounding gas phase, as well as P and T, be fixed. The activity, gradients of the cations in the product phases are then uniquely determined, and if the transport coefficients are known, the increase in thickness can be easily calculated, since the cation fluxes at the phase boundary BX/AY must be coupled. 

Nelson N and Eytan E (1979) Approach to the membrane sector of the chloroplast coupling device. In Mukohata Y and Packer L, eds. Cation flux across biomembranes, pp 409-415. New York Academic Press. 

Neurotransmitter transport can be electrogenic if it results in the net translocation of electrical charge (e.g. if more cations than anions are transferred into the cell interior). Moreover, some transporters may direction-ally conduct ions in a manner akin to ligand-gated ion channels this ion flux is not coupled to substrate transport and requires a separate permeation pathway associated with the transporter molecule. In the case of the monoamine transporters (DAT, NET, SERT) the sodium current triggered by amphetamine, a monoamine and psychostimulant (see Fig. 4) is considered responsible for a high internal sodium concentration... 

We have pointed out before that during creep, demixing of solid solutions is to be expected. Creep in compounds, however, occurs in such a way that the rate is determined by the slowest constituent since complete lattice molecules have to be displaced and the various constituent fluxes are therefore coupled. If extra fast diffusion paths operate for one (or several) of the components in the compound crystal, the coupling is cancelled. Therefore, if creep takes place in an oxide semiconductor surrounded by oxygen gas, it is not necessarily the slow oxygen diffusion that determines the creep rate. Rather, the much faster cations may determine it if oxygen can be supplied to or taken away from the external surfaces via dislocation pipes. 

The equation must be written separately for each species in solution (the anion and cation of the electrolyte, the oxidized and reduced forms of the electroactive couple, and any ion accompanying the initial state of the electroactive substance). Note that the charge of each species (z) controls the direction of the migrational flux, and for a neutral molecule (z = 0), the term on the right disappears as expected. Simultaneous solution of the five equations and evaluation over the appropriate boundary conditions gives the current for conditions when migration of either (or both) members of the electroactive couple can occur. 

The performance of calixarenes as cation carriers through H20-organic solvent H20 liquid membranes has also been studied.137 In basic metal hydroxide solutions, the monodeprotonated phenolate anions complex and transport the cations, while [18]crown-6 does not, under the same conditions. Low water solubility, neutral complex formation and potential coupling of cation transport to reverse proton flux have been cited as desirable transport features inherent in these molecules.137... 

The demonstration by Crane (1960, 1965) that Na+ ions were essential for the translocation of monosaccharides by segments of the intestine brought in a new era of understanding of the central role of ion coupled transport, particularly in higher organisms. While Na+ is clearly the predominant cation involved in cation driven solute accumulation in mammalian systems, current work has provided examples of H+ driven solute transport in intestine and kidney (Jessen et al., 1989 Ganapathy and Leibach, 1986). Conversely, in yeast and bacteria, H+ driven mechanisms are in the majority (Seaston et al., 1973 Hirata et al., 1973), but examples of Na+-cou-pled fluxes exist, e.g., proline transport (Dibrov, 1991). 

Since micro-gravimetry with the EQCM lacks specificity only the difference of cation and anion fluxes can be obtained by microgravimetry and therefore an independent measurement of specific ions is needed. Scanning electrochemical microscopy (SECM) coupled with a quartz crystal microbalance with independent potential control of the tip and substrate has been recently done by Cliffel and Bard [28]. In this experiment generation at the substrate (EQCM crystaj) working electrode and collection at the tip of an ultramicroelectrode (UNE) that was approached perpendicular to the EQCM crystal was employed with measurement of A/. Hillier and Ward [8] had previously used a scanning microelectrode to map the mass sensitivity across the surface of the QCM crystal. Reflection of longitudinal waves at the UME tip limits these experiments due to oscillations. 

As examples of coupled counter-transport (see Figure 13.2d) and coupled cotransport (see Figure 13.2e) the transport of titanium(lV) from low acidity (pH = 1) and high acidity ([H+] = 7 M) feed solutions, respectively using the HUM system [1,2] may be presented. The di-(2-ethyUiexyl) phosphoric acid (DEHPA) carrier reacts with Ti(IV) ion to form complexes on the feed side (see Equations 13.25 and 13.26) and reversible reactions take place on the strip side (see Equations 13.27 and 13.28). Energy for the titanium uphill transport is gained from the coupled transport of protons in the direction opposite to titanium transport from the strip to the feed solutions. In the second case (high-feed acidity), Cl anion cotransported with Ti(IV) cation in the same direction. In both cases fluxes of titanium, protons, and chlorine anion are stoichiometrically coupled. 

Energy for the titanium uphill transport is gained from the coupled transport of protons in the opposite to titanium transport from the strip to the feed solutions. In the second case (high feed acidity) Cl anion cotransported with Ti(IV) cation in the same direction. In both cases, fluxes of titanium, protons, and chlorine anion are stoichiometrically coupled. As a rule, coupled transport used combining with the facihtated transport. 

Membrane Diffusion in Dilute Solution Environments. The measurement of ionic diffusion coefficients provides useful information about the nature of transport processes in polymer membranes. Using a radioactive tracer, diffusion of an ionic species can be measured while the membrane is in equilibrium with the external solution. This enables the determination of a selfdiffusion coefficient for a polymer phase of uniform composition with no gradients in ion or water sorption. In addition, selfdiffusion coefficients are more straightforward in their interpretation compared to those of electrolyte flux experiments, where cation and anion transport rates are coupled. 

Ca " is a critical cation necessary for cardiac function in terms of automaticity/ pacemaker activity, conduction of electrical signals, and excitation-contraction coupling of myocytes. Drugs and chemicals that influence Ca flux in cardiac tissue also have a profound effect on the electrical and mechanical function of the heart. The slow Ca " current is mediated, in part, via the voltage-gated L-type Ca channels, one that can be influenced by Ca channel antagonists such as verapamil, D600, and diltiazem. Cardiac toxicity associated with the blockade of this channel can result in the disruption of rhythm and rate, as well as contraction and relaxation, of the heart. 

---