Charge distribution around spheres

There are monopolar fluctuations of the net charge on the colloid and its surrounding solution there are dipolar fluctuations, the first moment of the ionic-charge distribution around the colloid as well as polarization of the colloid itself. Monopolar and dipolar fluctuations couple to create a hybrid interaction, d-m, again in the limit of the n = 0 sampling frequency at which the ions are able to fluctuate. The salt solution screens even the dipolar fluctuation the same way that the low-frequency-fluctuation term is screened in planar interactions. For dielectric spheres of radius a, ss whose incremental contribution to dielectric response is a =... 

R is the radius of the polyion sphere, Z is the charge number of the polyion, C, is the concentration of added salt (mol/1), and k is the reciprocal length of ionic atmosphere. If we calculate the free charge distribution around the polyion sphere, we have Figure 3, and the effective charge of the polyion sphere [ ] is [4]... 

Fig. 3. Charge distribution around a spherical polyion in simple salt solutions. (Reproduced from Reference [4]). Curves 2 and 3 denote the net charge distribution inside and outside the sphere. Lines 4 denote the centres of those distributed positive and negative charges. Z = 1070, R = 3.94 x X 10 8 cm and NaCl cone. = 1.31 x 10" N were assumed.

Some difficulties in comparing the experimental kinetic data with the outer-sphere reorganization energy calculated from the Marcus formula (28) result from several assumptions made in this theory. The reactant was assumed to have a spherical shape with a symmetric charge distribution. No field penetration into the metal was considered. Also, the spatial dispersion of the dielectric permittivity of the medium was not taken into account. In fact, the positions and orientations of dipoles around a given ion are correlated with each other therefore the reorientation of one dipole, under the influence of the external field, changes to some extent the reorientation of other dipoles within the distance defined by the correlation length. 

It seems reasonable to suppose that the more symmetrical structures (a) are consistent with the efficient packing of the ions, regarded as incompressible spheres having spherical charge distributions. If the ions are to pack as closely as possible the determining factor will be the number of the larger ions that can pack around one of the smaller ions (usually the cation A). The c.n. of the larger ion follows from the fact that in A X the c.n. s of A and X must be in the ratio n m. 

A dissolved chromophore is surrounded by a solvation sphere. The solvent molecules are oriented around the chromophore so that their ED moments align with the dipole moment of the chromophore. The charge distribution, as well as the polarity of both the chromophore and the solvent molecules, hence plays a major role in the solvation of the chromophore. Since the charge density is related to the MOs of the chromophore, the solvation influences the energy of the electrons in the MOs. The solvation sphere may be compared with the coordination sphere of a metal ion (in the case of a metal ion, sometimes the coordination sphere is a solvation sphere). The solvation sphere generates a solvation field around the chromophore, which perturbs the electronic levels of the chromophore. 

Consider a spherical colloidal particle with a n ativety charged surface. This potyelectrotyte will tend to attract the positive ions from the dispersion medium around itself. As a result, the macromolecule will soon be surroimded by an ton atmosphere, a region in which there will be a statistical preference for ions of the opposite sign. Helmholtz likened this situation to the charge distribution in a parallel plate condenser. The condenser consists of two concentric spheres of opposite signs, and the two plates of the condenser constitute the so called rigid double layer (see Figure 3.7). 

Monte Carlo calculations on simplified model systems representing the DNA, counterions, and water solvent have been carried out by several research groups. Le Bret and Zimm o reported two such calculations. The first used an impenetrable cylinder embedded with a linear array of charges to represent DNA backbone and the other used a double-helical charge array on an impenetrable cylinder. The mobile ions were treated as hard spheres, and the ionic interaction between the ion and the model DNA were modulated by the solvent, which was treated as a dielectric continuum with a dielectric constant of 80. Ion distributions around the cylinders were calculated and compared, but there were no significant differences between the two models, possibly because... 

Let us estimate the value of electronic polarization. As an example, take a simplified model of an atom. Assume that the electron charge Ze is uniformly distributed around the nucleus in a sphere of radius R, i.e., with constant electron density p=Q/((4/3)jt/ )=Z e /((4/3) tR ). In the absence of an external electric field, the nucleus is in the center of a spherically symmetric electronic cloud, the centers of positive and negative charges coincide the atom does not possess a dipole moment. We can impose an origin with negative charge center. 

In view of this equation the effect of the ionic atmosphere on the potential of the central ion is equivalent to the effect of a charge of the same magnitude (that is — zke) distributed over the surface of a sphere with a radius of a + LD around the central ion. In very dilute solutions, LD a in more concentrated solutions, the Debye length LD is comparable to or even smaller than a. The radius of the ionic atmosphere calculated from the centre of the central ion is then LD + a. 

Ions of opposite charge are distributed in a spherical fashion around the central ion. This sphere around the central ion is called the ionic atmosphere (Fig. 2.15). This arrangement is dynamic that is, there is a continuous interchange between ions contained in the ionic atmosphere and ions in the solution. 

Nuclear Atom. From the results of the experiments, Rutherford concluded that the mass in the positive charge of an atom, instead of being distributed throughout the volume of a sphere of the order of 10-3 centimeter in radius, was concentrated in a very small volume of the order of 10-12 centimeter in radius, He thus developed the idea of a nuclear atom. I he atom was pictured as a small solar system with the very heavy and highly charged nuclens occupying the position of the sun, and with electrons moving around it, as planets in their respective orbits. 

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