Nonpolarizable potential

Mahoney MW, Jorgensen WL (2000) A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions, J Chem Phys, 112 8910-8922... 

Before discussing polarizable models, a useful starting point is to consider nonpolarizable models. A typical nonpolarizable potential for molecular systems is ... 

Lynch GC, Pettitt BM (1997) Grand canonical ensemble molecular dynamics simulations Reformulation of extended system dynamics approaches. J Chem Phys 107 8594-8610 Madura JD, Pettitt BM, Calef DF (1988) Water under high pressure. Mol Phys 64 325 Mahoney MW, Jorgensen WL (2000) A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions. J ChemPhys 112 8910-8922 March RP, Eyring H (1964) Application of significant stmcture theory to water. J Phys Chem 68 221-228 Martin MG, Chen B, Siepman JI (1998) A novel Monte Carlo algorithm for polarizable force fields. 

Obviously, QM/MM calculations are much more costly when explicit polarization of classical sites is accounted for, so that most QM/MM applications reported up to date have dealt with nonpolarizable potentials. 

The analytical calculation of the first derivatives of the energy with respect to the nuclear coordinates is straightforward, especially if nonpolarizable potentials are used. TTieir computation allows one to perform geometry optimization or to carry out molecular dynamics simulations for a large system described through QM-MM potentials. 

M. W. Mahoney and W. L. Jorgensen,/. Chem. Phys., 112, 8910 (2000). A Five-Site Model for Liquid Water and the Reproduction of the Density Anomaly by Rigid, Nonpolarizable Potential Functions. 

Nonpolarizable interfaces correspond to interfaces on which a reversible reaction takes place. An Ag wire in a solution containing Ag+ions is a classic example of a nonpolarizable interface. As the metal is immersed in solution, the following phenomena occur3 (1) solvent molecules at the metal surface are reoriented and polarized (2) the electron cloud of the metal surface is redistributed (retreats or spills over) (3) Ag+ ions cross the phase boundary (the net direction depends on the solution composition). At equilibrium, an electric potential drop occurs so that the following electrochemical equilibrium is established ... 

For an ideally polarizable electrode, q has a unique value for a given set of conditions.1 For a nonpolarizable electrode, q does not have a unique value. It depends on the choice of the set of chemical potentials as independent variables1 and does not coincide with the physical charge residing at the interface. This can be easily understood if one considers that q measures the electric charge that must be supplied to the electrode as its surface area is increased by a unit at a constant potential." Clearly, with a nonpolarizable interface, only part of the charge exchanged between the phases remains localized at the interface to form the electrical double layer. 

Equation (17) expresses the cell potential difference in a general way, irrespective of the nature of the electrodes. Therefore, it is in particular valid also for nonpolarizable electrodes. However, since

interfacial structure, only polarizable electrodes at their potential of zero charge will be discussed here. It was shown earlier that the structural details are not different for nonpolarizable electrodes, provided no specifically adsorbed species are present. 

The tip current depends on the rate of the interfacial IT reaction, which can be extracted from the tip current vs. distance curves. One should notice that the interface between the top and the bottom layers is nonpolarizable, and the potential drop is determined by the ratio of concentrations of the common ion (i.e., M ) in two phases. Probing kinetics of IT at a nonpolarized ITIES under steady-state conditions should minimize resistive potential drop and double-layer charging effects, which greatly complicate vol-tammetric studies of IT kinetics. 

The generation and propagation of action potentials and electrical impulses between the tissues in higher plants can be measured by reversible nonpolarizable electrodes [1]. Since both Ag/AgCl electrodes are identical, we decided to call them reference and working electrodes as shown in Fig. 4. The reference electrode (—) was usually inserted in the stem or in a root of a soybean plant, and the upper (working) electrode (-I-) inserted in the stem or a leaf of the plant. 

In electrochemistry, the electrode at which no transfer of electrons and ions occurs is called the polarizable electrode, and the electrode at which the transfer of electrons and/or ions takes place is called the nonpolarizable electrode as shown in Fig. 4-4. The term of polarization in electrochemistry, different from dipole polarization in physics, indicates the deviation in the electrode potential from a specific potential this specific potential is usually the potential at which no electric current flows across the electrode interface. To polarize" means to shift the electrode potential from a specific potential in the anodic (anodic polarization) or in the cathodic (cathodic polarization) direction. 

With nonpolarizable electrodes the polarization (the shift of the electrode potential) does not occur, because the charge transfer reaction involves a large electric current without producing an appreciable change in the electrode potential. Nonpolarizable electrodes cannot be polarized to a significant extent as a result. 

The nonpolarizable electrode may also be defined as the electrode at which an electron or ion transfer reaction is essentiaUy in equilibrium i. e. the electron or ion level in the electrode is pinned at the electron level of hydrated redox particles or at the hydrated ion level in aqueous electrolyte. In order for the electrode reaction to be in equilibrium at the interface of nonpolarizable electrode, an appreciable concentration of redox particles or potential determining ions must exist in the electrolyte. 

Next, we consider the interface M/S of a nonpolarizable electrode where electron or ion transfer is in equilibrium between a solid metal M and an aqueous solution S. Here, the interfadal potential is determined by the charge transfer equilibrium. As shown in Fig. 4-9, the electron transfer equilibrium equates the Fermi level, Enn) (= P (M)), of electrons in the metal with the Fermi level, erredox) (= P s)), of redox electrons in hydrated redox particles in the solution this gives rise to the inner and the outer potential differences, and respectively, as shown in Eqn. 4-10 ... 

The electrode potential defined in Sec. 4.3 applies to both nonpolarizable electrodes at which charge transfer reactions may take place and polarizable electrodes at which no charge transfer takes place. For nonpolarizable electrodes at which the charge transfer is in equilibrium, the interfacial potential is determined by the equilibrium of the charge transfer reaction. 

Imagine, however, at M2/S, a nonpolarizable20 interface (to be described further later) which is characterized by the fact that the potential across it does not change except under extreme duress (i.e., a large change in input potential). Then, for small changes 8 V at the external source, the potential difference across the nonpolarizable interface will not depart significantly from its fixed value, i.e.,... 

One can now resort to a simple artifice. Combine the interface understudy, M,/S, with an interface that resists changes in potential, i.e., a nonpolarizable interface M2/S (Fig. 6.32). By using this electrochemical system, or cell, all changes in the potential of the source find their way to only one interface, i.e., that under study. An excellent method of producing changes in potential at one interface only has thus been devised. 

Of course, this argument implies that the M, /S interface is completely polarizable. This is important. The point is that the power supply requires that the whole cell change its potential difference by an amount 8V. Only if one interface is completely nonpolarizable and the other one completely polarizable can the latter wholly accept the changes of potential put out by the source. If both interfaces are partially nonpolarizable, then the potential differences across both of them will change and the experimenter will be at a loss to know the magnitude of the individual changes at each interface. 

Are nonpolarizable and polarizable interfaces fictions, or can one find them in the laboratory The fact is that such interfaces can indeed be fabricated and have been used in double-layer studies. Of course, no interface is ideally nonpolarizable or ideally polarizable, i.e., nonpolarizable interfaces do change their potential to some extent and polarizable interfaces do resist such changes to some extent. The distinction is one of degree rather than kind. 

The essential feature of a nonpolarizable interface is that the potential difference across it remains effectively a constant as the potential applied to a cell that contains the nonpolarizable electrode changes. This property of nonpolarizable interfaces can be taken advantage of to develop a scale of relative potential differences across interfaces. 

Nonpolarizable Interfaces and Thermodynamic Equilibrium. It has just been shown that for an interface to be in thermodynamic equilibrium, the electrochemical potentials of all the species must he the same in both the phases constituting the interface. Since the difference in electrochemical potential of a species i between two phases is the work done to cany a mole of this species from one phase (e.g., the electrode) to the other (e.g., the solution), it must be the same as the work in the opposite direction. This implies a free flow of species across the interface. However, an interface that maintains an open border is none other than a nonpolarizable interface (see Section 63.3). 

Consider mercury as the liquid metal under study. One of the advantages of this metal is that the mercuiy/solution interface approaches closest to the ideal polarizable interface (see Section 6.3.3) over a range of 2 V. What this means is that this interface responds exactly to all the changes in the potential difference of an external source when it is coupled to a nonpolarizable interface, and there are no complications of charges leaking through the double layer (charge-transfer reactions). 

One electrochemical system that can be used to measure the surface tension of the mercuiy/solution interface is shown in Fig. 6.50. The essential parts are (1) a mercuiy/solution polarizable interface, (2) a nonpolarizable interface, (3) an external source of variable potential difference V, and (4) an arrangement to measure the surface tension of the mercuiy in contact with the solution.39... 

What are the capabilities of this system Since the system consists of a polarizable interface coupled to a nonpolarizable interface, changes in the potential of the external source are almost equal to the changes of potential only at the polarizable interface, i.e., the changes in zl< ) across the mercuiy/solution interface are almost equal to changes in potential difference Vacross the terminals of the source. Hence, the system can be used to produce predetermined zl< ) changes at the mercuiy/solution interface (Section 6.3.11). Further, measurement of the surface tension of the mercuiy/solution interface is possible, and since this has been stated /Section 6.4.5) to be related to the surface excess, it becomes possible to measure this quantity for a given species in the interphase. In short, the system permits what are called electrocapillary measurements, i.e., the measurement of the surface tension of the... 

The nonpolarizable interface has been defined above (Section 6.3.3) as one which, at constant solution composition, resists any change in potential due to a change in cell potential. This implies that (3s Ma< )/3V)jl = 0. However, the inner potential difference at such an interface can change with solution composition hence, Eq. (6.89) can be rewritten in the form of dM7ds< > = (RT/ZjF) d In a, which is the Nemst equation [see Eq. (7.51)] in differential form for a single interface. 

---