Polar-nonpolarizable

Let us suppose that the uniform electric field F (having been applied to the assembly of polar nonpolarizable symmetric top molecules at a time t = —oo so that equilibrium conditions prevail by the time t = 0) is switched off at t 0. In addition, it is supposed that the field is weak (i.e., pF linear response condition). For t > 0, the evolution of W satisfies Eq. (265). Just as a = 1, Eq. (4) is independent of the angles ip and / so that for the problem in question one may ignore the dependence of W on cp and /. Thus, we seek a solution of Eq. (265) by using the method of separation of variables in the form of the series... 

II. Polar-Nonpolarizable Fluids Theory in the Context of the Hoye-Stell Formulation. 187... 

III. Polar-Nonpolarizable Fluids Alternative Formulations, Quantitative Results,... 

II. POLAR-NONPOLARIZABLE FLUIDS THEORY IN THE CONTEXT OF THE H0YE-STELL FORMULATION... 

III. POLAR-NONPOLARIZABLE FLUIDS ALTERNATIVE FORMULATIONS, QUANTITATIVE RESULTS, AND COMPUTER SIMULATIONS... 

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 ... 

Most liquid phase molecular simulations with explicit atomic polarizabilities are performed with MD rather than MC techniques. This is due to the fact that, despite its general computational simplicity, MC with explicit polarization [173, 174] requires that Eq. (9-21) be solved every MC step, when even one molecule in the system is moved, and the number of configurations in an average Monte Carlo computation is orders of magnitude greater than in a MD simulation. For nonpolarizable, pairwise-additive models, MC methods can be efficient because only the... 

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. 

To determine an overpotential, however, it is necessary to alter the above two-electrode system by introducing an extra auxiliary electrode, which is termed the auxiliary or counter-electrode. Thus a three-electrode arrangement is set up as shown in Fig. 736. In such a setup, the counter electrode is connected to the test electrode via a polarizing circuit (e.g., a power source) through which a controllable current is made to pass and produce alterations in the potential of the test electrode. Between the nonpolarizable reference electrode and test electrode is connected an instrument that is capable of measuring the potential difference between these electrodes. 

The conventional viewpoint, which assumes that the ionic atmosphere is spherically symmetric, does not take account of the inevitable effects of ionic polarization. From an analysis of the general solution (19), however, it is evident that the ionic atmosphere must be spherically symmetric for nonpolarizable ions, and the DH model is therefore adequate. (Moreover, in very dilute solution polarization effects are negligibly small, and it does not matter whether we choose a polarizable or unpolarizable sphere for our model.) But once we have made the realistic step of conferring a real size on an ion, the ion becomes to some extent polarizable, and the ionic cloud is expected to be nonspherical in any solution of appreciable concentration. Accordingly, we base our treatment on this central hypothesis, that the time-average picture of the ionic solution is best represented with a polarizable ion surrounded by a nonspherical atmosphere. In order to obtain a value for the potential from the general solution of the LPBE we must first consider the boundary conditions at the surface of the central ion. 

Because the flow of electric current always involves the transport of matter in solution and chemical transformations at the solution-electrode interface, local behavior can only be approached. It can be approximated, however, by a reference electrode whose potential is controlled by a well-defined electron-transfer process in which the essential solid phases are present in an adequate amount and the solution constituents are present at sufficiently high concentrations. The electron transfer is a dynamic process, occurring even when no net current flows and the larger the anodic and cathodic components of this exchange current, the more nearly reversible and nonpolarizable the reference electrode will be. A large exchange current increases the slope of the current-potential curve so that the potential of the electrode is more nearly independent of the current. The current-potential curves (polarization curves) are frequently used to characterize the reversibility of reference electrodes. 

Equation 2.40 shows that the solvent power (as measured by 6) of an SF is governed by two factors (25). First, it is regulated by the liquid value 8Viq (see Table 2.1), reflecting the polarity and other chemical properties of molecules of the parent liquid. Highly polar substances like ammonia would thus yield high 8s. By contrast, small relatively nonpolarizable species like helium have negligible solvent effects under any circumstances. 

The behavior of the platinized platinum electrodes is entirely different from that of the Ag/Ag halide electrodes, both under flow conditions and at rest. Whereas the nonflow potential for the nonpolarizable electrodes remained constant with time, the rest potential for two platinized platinum electrodes increased with time. Also, the flow of liquid produced a more pronounced effect on the platinum electrodes than on the Ag/Ag halide electrodes. The erratic behavior of the platinum electrodes appears to be due to polarization effects which are difficult to eliminate. In Figure 3 the effect of flow on both Ag/AgCl and platinized electrodes can be assessed. The effect of flow on the platinum electrodes was known to Helmholtz (19) and still appears to remain unexplained. 

Isopotential lines are parallel to the electrode surfaces for what is known as the primary current distribution (no interfacial electrode polarization, or zero polarization resistance). Said another way, the solution adjacent to an electrode surface is an equipotential surface (1). This primary current distribution applies to the case of extremely fast electrochemical reactions (e.g., nonpolar-izable electrode reactions). This current distribution situation is only of interest to the corrosion engineer in cases where high current densities might be flowing (i.e., in relatively nonpolarizable cells). 

An -> ideal nonpolarizable electrode is one whose potential does not change as current flows in the cell. Much more useful in electrochemistry are the electrodes that change their potential in a wide potential window (in the absence of a - depolarizer) without the passage of significant current. They are called -> ideally polarized electrodes. Current-potential curves, particularly those obtained under steady-state conditions (see -> Tafel plot) are often called polarization curves. In the -> corrosion measurements the ratio of AE/AI in the polarization curve is called the polarization resistance. If during the -> electrode processes the overpotential is related to the -> diffusional transport of the depolarizer we talk about the concentration polarization. If the electrode process requires an -> activation energy, the appropriate overpotential and activation polarization appear. 

The polarizable point dipole model has also been used in Monte Carlo simulations with single particle moves.When using the iterative method, a whole new set of dipoles must be computed after each molecule is moved. These updates can be made more efficient by storing the distances between all the particles, since most of them are unchanged, but this requires a lot of memory. The many-body nature of polarization makes it more amenable to molecular dynamics techniques, in which all particles move at once, compared to Monte Carlo methods where typically only one particle moves at a time. For nonpolarizable, pairwise-additive models, MC methods can be efficient because only the interactions involving the moved particle need to be recalculated [while the other (N - 1) x (]V - 1) interactions are unchanged]. For polarizable models, all N x N interactions are, in principle, altered when one particle moves. Consequently, exact polarizable MC calculations can be... 

It is now well understood that the static dielectric constant of liquid water is highly correlated with the mean dipole moment in the liquid, and that a dipole moment near 2.6 D is necessary to reproduce water s dielectric constant of s = 78 T5,i85,i96 holds for both polarizable and nonpolarizable models. Polarizable models, however, do a better job of modeling the frequency-dependent dielectric constant than do nonpolarizable models. Certain features of the dielectric spectrum are inaccessible to nonpolarizable models, including a peak that depends on translation-induced polarization response, and an optical dielectric constant that differs from unity. The dipole moment of 2.6 D should be considered as an optimal value for typical (i.e.. 

Dynamic properties, such as the self-diffusion constant, are likewise strongly correlated with the dipole moment. This coupling between the translational motion and the dipole moment is indicated in the dielectric spectrum. Models that are overpolarized tend to undergo dynamics that are significantly slower than the real physical system. The inclusion of polarization can substantially affect the dynamics of a model, although the direction of the effect can vary. When a nonpolarizable model is reparameterized to include polarizability, the new model often exhibits faster dynamics, as with polarizable versions of TIP4P, ° Reimers-Watts-Klein and reduced... 

Transferability from the solid state to the liquid state is equally problematic. A truly transferable potential in this region of the phase diagram must reproduce not only the freezing point, but also the temperature of maximum density and the relative stability of the various phases of ice. This goal remains out of reach at present, and few existing models demonstrate acceptable transferability from solid to liquid phases.One feature of water that has been demonstrated by both an EE model study and an ab initio study °° is that the dipole moments of the liquid and the solid are different, so polarization is likely to be important for an accurate reproduction of both phases. In addition, while many nonpolarizable water models exhibit a computed temperature of maximum density for the liquid, the temperature is not near the experimental value of 277 Eor example, TIP4P and... 

According to Onsager, a reaction field is the electric field arising from an interaction between an ideal nonpolarizable point dipole and a homogeneous polarizable dielectric continuum in which the dipole is immersed [80]. The reaction field is the electric field felt by the solute molecule due to the orientation and/or electronic polarization of the solvent molecules by the solute dipole. 

It may be appropriate to ask here why the potential at a reversible electrode should change at all with current density. This does not occur because "no system is really ideally polarizable", and one is observing a small polarization. Indeed the relationship shown in Eq. 17D holds strictly only when the interphase is ideally nonpolariz-able. Each value of the potential given by Eq. 17D represents the reversible potential for the concentration of the species at the surface, C(s). These concentrations deviate, however, from the corresponding bulk concentrations C° as a result of mass-transport limitations, according to Eq. 13D. 

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