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Hypothetical Charge

An alternative method for calculating the asymptotic expressions for the double--layer interaction between two parallel plates at large separations is given below. This method, which was introduced by Brenner and Parsegian [6] to obtain an asymptotic expression for the interaction energy between two parallel cylinders, is based on the concept of hypothetical charge, as shown below. [Pg.276]

Consider two parallel plates at separation h in a general electrolyte solution. According to the method of Brenner and Parsegian [6], the asymptotic expression for the interaction energy V(Jt) per unit area is given by [Pg.276]

Here Gem ( = 1, 2) is the hypothetical charge per unit area of an infinitely thin plate that would produce the same asymptotic potential as produced by plate i and [Pg.276]

Consider the electric field produced by the above hypothetical infinitely thin plate having a surface charge density We take an x-axis perpendicular to the plate, which is placed at the origin x = 0. The electric field produced by this hypothetical plate at a distance h from its surface is thus given by [Pg.277]

The asymptotic expression for the unperturbed potential of plate i i= 1, 2) at a large distance h from the surface of plate i is given by [Pg.277]


Within the framework of the same dielectric continuum model for the solvent, the Gibbs free energy of solvation of an ion of radius and charge may be estimated by calculating the electrostatic work done when hypothetically charging a sphere at constant radius from q = 0 q = This yields the Bom equation [13]... [Pg.836]

Oxidation-reduction (redox) reactions involve the loss of electrons and increase in oxidation number (oxidation) by one substance or system, with an associated gain of electrons and decrease in oxidation number (reduction) by another substance or system. Thus for every oxidation reaction there must be a reduction reaction. The oxidation number of an atom represents the hypothetical charge an atom would have if the ion or molecule were to dissociate.46-47... [Pg.799]

Oxidation numbers are actual or hypothetical charges, assigned using a set of rules. They are used to describe redox reactions with covalent reactants or products. They are also used to identify redox reactions, and to identify oxidizing and reducing agents. In this section, you will see how oxidation numbers were developed from Lewis structures, and then learn the rules to assign oxidation numbers. [Pg.473]

Jj( 1) is the potential energy of interaction between the point charge of electron 1 and electron 2 considered to be smeared out into a hypothetical charge cloud of charge density (charge per unit volume) - e)Hartree-Fock method considers average interelectronic interactions, rather than instantaneous inter-... [Pg.37]

Let us assume internal equilibrium in Zf, which corresponds to the mutually open subsystems, Zfe=(Z/> Zf 2), with equalized chemical potentials, nf = nf = P.r = dE/dN, at the global chemical potential level. The internal stability refers to intra-5 (hypothetical) charge displacements, dA/y(A) = (A, — A), that preserve N. The corresponding quadratic energy change due to this polarizational displacement from the initial internal equilibrium state ... [Pg.113]

Fig. 2. Schematic plots outlining outer-shell free energy-reaction coordinate profiles for the redox couple O + e R on the basis of the hypothetical two-step charging process (Sect. 3.2) [40b]. The y axis is (a) the ionic free energy and (b) the electrochemical free energy (i.e. including free energy of reacting electron), such that the electrochemical driving force, AG° = F(E - E°), equals zero. The arrowed pathways OT S and OTS represent hypothetical charging processes by which the transition state, T, is formed from the reactant. Fig. 2. Schematic plots outlining outer-shell free energy-reaction coordinate profiles for the redox couple O + e R on the basis of the hypothetical two-step charging process (Sect. 3.2) [40b]. The y axis is (a) the ionic free energy and (b) the electrochemical free energy (i.e. including free energy of reacting electron), such that the electrochemical driving force, AG° = F(E - E°), equals zero. The arrowed pathways OT S and OTS represent hypothetical charging processes by which the transition state, T, is formed from the reactant.
Fig. 14. Diagram to show (A) the first excited state of a conjugated donor/acceptor aromatic, (B) inductive charge redistribution caused by isolated donor and acceptor atoms, and (C) a hypothetical charge delocahzation in a group 8 metal stilbazole complex. Fig. 14. Diagram to show (A) the first excited state of a conjugated donor/acceptor aromatic, (B) inductive charge redistribution caused by isolated donor and acceptor atoms, and (C) a hypothetical charge delocahzation in a group 8 metal stilbazole complex.
The oxidation number is a hypothetical charge assigned to atoms in molecules and ions using a set of specific rules. Since redox reactions involve transfers of electrons, identification of the atoms which change oxidation number will show the atoms, ions or molecules which are specifically involved in the redox process. [Pg.54]

Formal charge The hypothetical charge on an atom in a covalently bonded molecule or ion bonding electrons are counted as though they were shared equally between the two bonded atoms. [Pg.300]

Figure 13 shows the hypothetical charge distribution in a lamellar donor-acceptor system which accounts for the observed changes in spin signal. Whether an increase or decrease in the spin signal is observed,... [Pg.19]

For electron 2 (with charge -e), the charge density of the hypothetic charge cloud is P2 = -e s2p, and for electron 1, Qi = -e. Hence... [Pg.307]

The Hartree SCF method approximates the atomic wave function as a product of one-electron spatial orbitals [Eq. (11.2)] and finds the best possible forms for the orbitals by an iterative calculation in which each electron is assumed to move in the field jffo-duced by the nucleus and a hypothetical charge cloud due to the other electrons. [Pg.342]

Suppose the non-equilibrium solvent polarization around the D°A° pair can be produced as an equilibrium response to a DA state with hypothetical charges z + z and — z, which is labelled by D +A . By hypothetical charges , we mean the charges hypothetically put on the redox pair in order to produce a solvent polarization which is equivalent to the solvent fluctuation, or non-equilibrium polarization around the solute. In that sense, the hypothetical charges serve as an order parameter, or a reaction coordinate. It is convenient for an electron transfer process to define another reaction coordinate called solvent coordinate by... [Pg.34]

In both equations a state with the hypothetical charges (q = (1 — s) -b sq3+) is introduced to compute the solvation free energy (A/ig) and electrostatic potential on the solute site (Vg). [Pg.87]


See other pages where Hypothetical Charge is mentioned: [Pg.608]    [Pg.168]    [Pg.397]    [Pg.80]    [Pg.120]    [Pg.357]    [Pg.276]    [Pg.277]    [Pg.346]    [Pg.1259]    [Pg.426]    [Pg.36]    [Pg.289]    [Pg.65]    [Pg.43]    [Pg.289]    [Pg.838]    [Pg.1778]    [Pg.1724]    [Pg.91]    [Pg.34]    [Pg.87]    [Pg.396]    [Pg.132]    [Pg.140]    [Pg.150]    [Pg.277]    [Pg.300]    [Pg.838]    [Pg.238]   


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