Charge neutrality constraint

Charge conservation can be imposed in two ways. A charge neutrality constraint can be applied to the entire system, thus allowing charge to move from one atomic site to another until the electronegativities are equal on all the atoms of the system. 

With (85,87) the boundary conditions (7 0 and charge neutrality constraint (75) become... 

Differentiating ip z) with respect to z, and using the charge neutrality constraint of Equation (8), yields at z = 0... 

When the concentration of trapped holes is no longer negligible compared to that of the free holes, it is possible to rewrite Eq. (40), due to the mass conservation constraint, Eq. (34), and the charge neutrality constraint, Eq. (18), as ... 

Considering the charge neutralization constraint between the surface and the diffuse-layer charge densities (ctq + = 0) and supposing that J/j = iJ/q at x = 0, we have... 

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. 

We have discussed the homogeneous 2-flavor quark matter when charge neutrality conditions are satisfied locally, and found that the local charge neutrality conditions impose very strong constraints on determining the ground state of the system. 

In Ref. [24] it has been investigated whether with the above three- flavor quark matter EoS of the NCQM strange quark matter can appear in the interior of compact stars. The constraints of fl equilibrium and charge neutrality have been applied (see below) in order to constrain the partial densities of electrons and up-, down-, strange quarks, see Fig. 3. It can be seen that strange... 

The key argument is rooted in a simple observation concerning any dissociation KL K + L. The individual subunits K and L are in general not electroneutral while they are part of the original host molecule, whereas the corresponding radicals certainly satisfy electroneutrality. A charge neutralization accompanies the transformations K K and L L. This constraint solves our problem. A few examples (Table 12.1) help us understand why this argument is important. 

The general constraints for the design of any dyes for ADPM SHG in poled polymer systems rapidly narrow the choice of chromophores. The dyes should be overall charge neutral (to facilitate poling) and highly soluble in polymer matrices. The first excited electronic state should be well separated from higher energy states for two reasons (1) since the vibronic envelope associated with an... 

Subject to Constraints Frozen Atoms Total Charge Neutral... 

In contrast to pure metals and elemental crystals for which point defects are rather straightforward to describe (because only one type of atom is involved and charge neutrality is not an issue), the situation in ceramics is more complex. One overriding constraint operative during the formation of ceramic defects is the preservation of electroneutrality at all times. Consequently, the defects occur in neutral bunches and fall in one of three categories ... 

In cases where a continuous and coherent layer of oxide film is present, further reaction can proceed only by diffusion of some of the reactants across the film. There are several possible mechanisms for this transport of material. In many solids, the passage of neutral atoms is less likely than the transport of charged particles, ions and electrons. In such cases, called ambipolar diffusion, the concentration gradient is not the only constraint on the system. In addition, and at all times, overall charge neutrality needs to be maintained. 

The number of components equals the total number of independent chemical compounds of a system minus the number of unequivocal, i.e. true chemical reactions that can occur among these compounds. The number of independent compounds mean the total number minus the number of all constraints such as mass equihbria or charge neutrality. An unequivocal chemical reaction means a reaction that carmot simply by formulated as an extension of other reactions within the system (Moore, 1972). 

The appearance of charge neutrality on an intermediate length scale provides an important constraint on the network connectivity leading to these different network... 

In Eq. (9-62) MjL is the mass of atom //. The mass mq does not correspond to any physical mass and is simply set to a value small enough such that the charges follow the atomic coordinates adiabatically. The Lagrangian also includes an Nmoiec number of constraints to ensure that each molecule remains electrostatically neutral. 

Although these examples demonstrate the feasibility of using calculated values as estimates, several constraints and assumptions must be kept in mind. First, the diffusant molecules are assumed to be in the dilute range where Henry s law applies. Thus, the diffusant molecules are presumed to be in the unassociated form. Furthermore, it is assumed that other materials, such as surfactants, are not present. Self-association or interaction with other molecules will tend to lower the diffusion coefficient. There may be differences in the diffusion coefficient for molecules in the neutral or charged state, which these equations do not account for. Finally, these equations only relate diffusion to the bulk viscosity. Therefore, they do not apply to polymer solutions where microenvironmental viscosity plays a role in diffusion. 

Beta equilibrium, neutrino trapping, charge and color neutrality. The stellar matter in equilibrium has to obey the constraints of /3-equilibrium (d — u + e + ve,u + e — d + ve), expressed as... 

In order to stably levitate an object, the net force on it must be zero, and the forces on the body, if it is perturbed, must act to return it to its original position. The object must be at a local potential minimum that is, the second derivatives with respect to all spatial coordinates of the potential must be positive. This may seem, at first sight, to be trivial to arrange. However, any system whose potential is a solution to Laplace s equation is automatically unstable A statement in words of Laplace s equation is that the sum of the second partial derivatives of the potential is zero, and so not all can be simultaneously positive. This has long been known for electrostatic potentials, having been stated by Earnshaw(n) Millikan s scheme for suspending charged particles is thus only neutrally stable, since the fields within a Millikan capacitor provide no lateral constraint. 

I wish to respond to Professor Ubbelohde s question regarding what thinness, per se, of biological membranes could be important. For ion movements across membranes as mediated catalytically by carriers or channels, the thinness permits local deviations from the electroneutrality constraint that, for example, enables neutral molecules to carry cations across the membrane as charged species, leaving their counterions behind in the aqueous solutions. This is not possible when the thickness of the system becomes large. 

Enrico Fermi on his voyage to the new world postulated that a third particle was needed to balance the emission of the electron in 3 decay. However, the existing conservation laws also had to be satisfied, so there were a number of constraints on the properties of this new particle. Focusing on the decay of a neutron as a specific example, the reaction is already balanced with respect to electric charge, so any additional particle must be neutral. The electrons were observed with energies up to the maximum allowed by the decay Q value so the mass of the particle must be smaller that the instrumental uncertainties. Initially, this instrumental... 

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... 

Direct attachment of biomolecules to the surface can introduce a steric constraint to reactivity of the molecule which is not encountered when considering molecules free in a solution. This effect can be minimized if, for example, a spacer is introduced between the biomolecule and the linking group. The spacer can be of nearly any desired length and possess a variety of chemical characteristics, that is, it can be rigid or flexible, hydrophilic or hydrophobic, charged or neutral.1,9... 

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