Charge neutrality equation

For an explicit example, consider the transformation of (30) for H+ diffusing in p-type material. With ne = n = 0, the charge neutrality equation is... 

The charge neutrality equation, however, remains the same or as Eq. (18), because the trapped holes make the acceptor centers only neutral (A ) in the present case. Otherwise, it would have to be modified to include the acceptors with different effective charges due to hole trapping. 

The value of is the difference in partial molal volume between the transition state and the initial state, but it can be approximated by the molar volume. Increasing pressure decreases the value of AV and if A V is negative the reaction rate is accelerated. This equation is not strictly obeyed above lOkbar. If the transition state of a reaction involves bond formation, concentration of charge, or ionization, a negative volume of activation often results. Cleavage of a bond, dispersal of charge, neutralization of the transition state and diffusion control lead to a positive volume of activation. Reactions for which rate enhancement is expected at high pressure include ... 

Electroneutrality At all times the crystal must remain electrically neutral. Equations (7.9) and (7.10) define the formation of charged species, so that the appropriate electroneutrality equation is... 

Abstract We investigate the phase structure of color superconducting quark matter at intermediate densities for two- and three flavor systems. We thereby focus our attention on the influence of charge neutrality conditions as well as /3-equilibrium on the different phases. These constraints are relevant in the context of quark matter at the interior of compact stars. We analyze the implications of color superconductivity on compact star configurations using different hadronic and quark equations of state. 

Figure 2. The graphical representation of the solution to the charge neutrality conditions (thick dash-dotted line) and the solution to the gap equation for three different values of the diquark coupling constant (thick solid and dashed lines). The intersection points represent the solutions to both. The thin solid line divides two qualitatively different regions, A < S/i and A > S/i. The results are plotted for fi = 400 MeV and three values of diquark coupling constant Go = r/Gs with i] = 0.5, i] = 0.75, and i] = 1.0.

Figure 6. Solutions of the gap equations and the charge neutrality condition (solid black line) in the /// vs //, plane. Two branches are shown states with diquark condensation on the upper right (A > 0) and normal quark matter states (A = 0) on the lower left. The plateau in between corresponds to a mixed phase. The lines for the /3-equilibium condition are also shown (solid and dashed straight lines) for different values of the (anti-)neutrino chemical potential. Matter under stellar conditions should fulfill both conditions and therefore for //,( = 0 a 2SC-normal quark matter mixed phase is preferable.

Tanford examined the application of Debye-Huckel theory and found the theory not to be valid because the high charge density generatedby the closely spaced head groups leads to substantial charge neutralization by counter ions Alternatively, he equated the work of... 

Because we are generally able to define the chemistry of an aqueous solution containing n chemical elements by analytical procedures, n equations such as 8.48 and 8.49 exist, relating the bulk concentration of a given element mj to all species actually present in solution. Associated with mass balance equations of this type may be a charge balance equation expressing the overall neutrality of the solution ... 

The hydrocarbons are good candidates for highlighting the merits of our master equation (12.8), its salient features and some intricacies plaguing the interpretation of trends observed for the breaking of chemical bonds. The use of Eq. (12.8) requires the appropriate RE energies (Table 12.3) as well as the charge neutralization energies, CNE [Eq. (12.7)]. 

The sum equation around F3 is redundant since it is determined by the condition of charge neutrality. 

We shall now develop an exact expression for Dl which includes the coupling of Vcu and Of through the charge neutrality condition given by eqn (1.188). Starting with the first equation in eqn (1.196) and following a similar procedure to that used in developing eqn (1.193), we can get ... 

The activating effect of Mg2+ upon the cleavage of the phosphoryl group from the ATP could reflect the enhancement of an SN2 reaction at phosphorus by electron withdrawal and charge neutralization via coordination to the metal (equation 1). Support for an SN2 mechanism comes from a consideration57 of the inhibition by vanadate. Coordination of the transferable phosphoryl group would inhibit the SN1 mechanism. 

The definition of electric charge density in Eq. (76) agrees with our opinion that 0 in Maxwell s equations represents charge neutrality (see Section HI) the simplest case is 5+ + S = 0. Also note that X/ defined by Eq. (74) is independent of pe thus allowing for the existence of a displacement current in the absence of electric charge, as also discussed in Section HI. 

Abstract In a thermodynamic framework which exploits the entropy inequality to obtain constitutive equations, it is common practice to assume charge neutrality and enforce this restriction using Lagrange multipliers. In this paper we show that the Lagrange multiplier used to enforce charge neutrality does not correspond to any known physical parameter, raising the question of whether charge neutrality can really be enforced. 

Proton balance and electrical neutrality. For bulk solutions in their natural condition the overall charge of all the soluble chemical species is zero, therefore, this constraint can be imposed if it is not possible to use an MBE. The example in the section on carbonate equilibria (Section 5.2.6.4) provides an example of the use of an electrical neutrality equation (ENE) to calculate pEL... 

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