Electrochemical potential, ions equilibrium across

The only potential that varies significantly is the phase boundary potential at the membrane/sample interface EPB-. This potential arises from an unequal equilibrium distribution of ions between the aqueous sample and organic membrane phases. The phase transfer equilibrium reaction at the interface is very rapid relative to the diffusion of ions across the aqueous sample and organic membrane phases. A separation of charge occurs at the interface where the ions partition between the two phases, which results in a buildup of potential at the sample/mem-brane interface that can be described thermodynamically in terms of the electrochemical potential. At interfacial equilibrium, the electrochemical potentials in the two phases are equal. The phase boundary potential is a result of an equilibrium distribution of ions between phases. The phase boundary potentials can be described by the following equation ... 

For the simplified case of only a single permeant ion, the equilibrium or Nernst potential defines the condition at which there is no net change in ion concentration. Under this condition of equilibrium, the electrochemical potential julj for moving the ion y across the membrane will be zero, and... 

Equality (1.20) is of primary importance because of the following reason. It is customary in most ionic transport theories to use the local electroneutrality (LEN) approximation, that is, to set formally e = 0 in (1.9c). This reduces the order of the system (1.9), (l.lld) and makes overdetermined the boundary value problems (b.v.p.s) which were well posed for (1.9). In particular, in terms of LEN approximation, the continuity of Ci and ip is not preserved at the interfaces of discontinuity of N, such as those at the ion-exchange membrane/solution contact or at the contact of two ion-exchange membranes or ion-exchangers, etc. Physically this amounts to replacing the thin internal (boundary) layers, associated with N discontinuities, by jumps. On the other hand, according to (1-20) at local equilibrium the electrochemical potential of a species remains continuous across the interface. (Discontinuity of Cj, ip follows from continuity of p2 and preservation of the LEN condition (1.13) on both sides of the interface.)... 

Although the equilibrium principle was available (equality of electrochemical potential of each ion that reversibly equilibrates across an immiscible liquid/liquid interface), the elementary theory and consequences were not explored until recently (6). To develop an interfacial potential difference (pd) at a liquid interface, two ions M, X that partition are required. However,... 

Membrane potential and pH gradient are always determined separately. Since a membrane potential is a delocalized parameter for a given membrane, it follows that the membrane potential generated by the translocation of protons across the membrane will be felt by all ions distributed across the membrane. If an electrical uniport pathway exists for one of these ions, then it will tend to come to an equilibrium when its electrochemical potential gradient is zero ... 

The diffusion of charged ions is more complicated because of the law of electroneutrality, which states that the sum of the positive charges on each side of the membrane must equal the sum of the negative charges. In addition to the concentration gradient, the electrical potential difference determines the Bnal equilibrium of a substance across the membrane. Therefore at equilibrium, the concentration of an ionic species may be unequal across the membrane and this gradient will balance the electrical difference across the membrane. The driving force for transport in this situation is defined as the electrochemical potential. The Nemst equation describes the equilibrium situation for ions... 

The Cu" ions are separated from the Zn ions by a membrane which is permeable for the corresponding counter ions, such as SO4 ions, but not for the metal ions. Accordingly, an electrical connection across the membrane is achieved by the transport of the SO " ions. An equilibrium throughout the whole cell does not exist because exchange of the metal ions between the two partial systems has been made impossible. On the other hand, equilibrium still exists in the two half-cells, i.e. between the Cu electrode and the Cu in the left compartment and between the Zn electrode and the Zn in the right one. However, the electrochemical potentials of the electrons in the two electrodes are different. The electrochemical potentials of the electrons for the reactions (3.31a) and (3.31b) can be derived by applying Eq. (3.29). Tlieir difference is then given by... 

The first and last terms are interfacial potential differences arising from an equilibrium balance of selective charge exchange across an interface. This condition is known as Donnan equilibrium (24, 51). The magnitude of the resulting potential difference can be evaluated from electrochemical potentials. Suppose we have Na" and as interfacially active ions. Then at the a/m interface,... 

If the membrane is semipermeable to a certain ion, because of the electroneutrality as well as the equality fjLjo = /iji) of the electrochemical potential for the permeable ionic species across the membrane at equilibrium state, the electrical potential difference between the two phases could be maintained at equilibrium ... 

When a metal, M, is immersed in a solution containing its ions, M, several reactions may occur. The metal atoms may lose electrons (oxidation reaction) to become metaUic ions, or the metal ions in solution may gain electrons (reduction reaction) to become soHd metal atoms. The equihbrium conditions across the metal-solution interface controls which reaction, if any, will take place. When the metal is immersed in the electrolyte, electrons wiU be transferred across the interface until the electrochemical potentials or chemical potentials (Gibbs ffee-energies) on both sides of the interface are balanced, that is, Absolution electrode Until thermodynamic equihbrium is reached. The charge transfer rate at the electrode-electrolyte interface depends on the electric field across the interface and on the chemical potential gradient. At equihbrium, the net current is zero and the rates of the oxidation and reduction reactions become equal. The potential when the electrode is at equilibrium is known as the reversible half-ceU potential or equihbrium potential, Ceq. The net equivalent current that flows across the interface per unit surface area when there is no external current source is known as the exchange current density, f. 

The membrane is permeable for the ionic species K and the solvent, i.e. water molecules. When an uncharged membrane is placed between two solutions containing two different activities and of species K, then a phase transfer of charge carriers occurs. The direction of this transfer depends on the gradient of the electrochemical potential. This results in a charging of the phase boundary and creation of an electric field. The initially favoured ion transfer will be slowed down and in the end a further net transfer will be stopped because of electrostatic repulsion forces, and the forth and back transfer of ions will cancel. In electrochemical equilibrium both reactions have the same rate, and the potential difference is constant. Assuming that (i) no temperature or pressure gradient exists across the membrane, (ii) the solvent in both solutions is the same, e.g. water and (iii) no diffusion potential within the membrane occurs, then the electrochemical potentials in the two phases are equal in case of electrochemical equilibrium ... 

Membranes may have various physical and chemical structures and hence are able to restrict transport processes by having different permeabilities for different substrates. Determining properties of equilibrium across and within a membrane may help in understanding the transport phenomena through membranes. Besides thermal equilibrium, the principle of electroneutrality is also satisfied. Because of the absence of mechanical equilibrium, a pressure difference known as osmotic pressure exists between subsystems separated by the membrane. In the case of substrates in ion form, both nonpermeating and permeating ions create an electrical potential difference known as membrane potential across the membrane. For the separated parts of A and B, electrochemical equilibrium for permeating species k is... 

It is important for the system analysis that redox sites are confined to the polymer matrix, i.e., electrochemical potentials of ox and red in the electrolyte, fired and filx are not defined/ Therefore the equilibrium potential across the polymer/electrolyte interface is defined by the ion-(in particular X ) partitioning equilibria, Eqn. 5. The electrode potential ( measured with the reference electrode in the electrolyte) of the electrode coated with the electroactive polymer film can thus be formulated as... 

In the last decade increasing attention has been paid to the electeochemical studies on the kinetics and equilibrium of ion transfer at the oil/water interfaces that are polarized in the sense that the interface is of the ideal-polarized nature for all ions (here Bi, Ai, B2, and A2) except transferring ion or ions (here B3) (for reviews see [31-38].) In such cases the nontransferable ions serve as the supporting electrolytes for the transport process of the transferable ions across the interface. It has been shown that the oil/water interface works as an ion-selective electrode surface for both vol-tammetric (and amperometric) and potentiometric measurements of ions, both based on the same electrochemical principle of ion transfer across the interface [43,44]. There it is essential that the oil/water interface is of the ideal-polarized nature for all ions (such as counter ion and supporting electrolyte ion so-called potential window) except the monitored ion or ions (voltammetry). 

When selective voltage probes are used which can exchange orfly electrons or only ions, the net current vanishes (provided a high-impedance voltmeter is used). However, this is a dynamic equilibrium where the mobile species are transported across the probe/sample interface with a net zero flux. The probes, then, are used to transfer information, namely, the electrochemical potential of ions or electrons. 

The movement of solute across a semipermeable membrane depends upon the chemical concentration gradient and the electrical gradient. Movement occurs down the concentration gradient until a significant opposing electrical potential has developed. This prevents further movement of ions and the Gibbs-Donnan equilibrium is reached. This is electrochemical equilibrium and the potential difference across the cell is the equilibrium potential. It can be calculated using the Nemst equation. 

Potentiometric transducers measure the potential under conditions of constant current. This device can be used to determine the analytical quantity of interest, generally the concentration of a certain analyte. The potential that develops in the electrochemical cell is the result of the free-energy change that would occur if the chemical phenomena were to proceed until the equilibrium condition is satisfied. For electrochemical cells containing an anode and a cathode, the potential difference between the cathode electrode potential and the anode electrode potential is the potential of the electrochemical cell. If the reaction is conducted under standard-state conditions, then this equation allows the calculation of the standard cell potential. When the reaction conditions are not standard state, however, one must use the Nernst equation to determine the cell potential. Physical phenomena that do not involve explicit redox reactions, but whose initial conditions have a non-zero free energy, also will generate a potential. An example of this would be ion-concentration gradients across a semi-permeable membrane this can also be a potentiometric phenomenon and is the basis of measurements that use ion-selective electrodes (ISEs). 

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