Highly charged sphere

Self-assembly of highly charged colloidal spheres can, under the correct conditions, lead to 3D crystalline structures. The highly charged spheres used are either polystyrene beads or silica spheres, which are laid down to give the ordered structures by evaporation from a solvent, by sedimentation or by electrostatic repulsion (Figure 5.34). The structures created with these materials do not show full photonic band gap, due to their comparitively low relative permittivity, although the voids can be in-filled with other materials to modify the relative permittivity. 

The anions MeF6 and X approach each other closely to form the heptacoordinated complex MeF6X(n+1)", or separate from one another, according to the polarization potential of the outer-sphere cation (alkali metal cation -M+). This process is unique in that the mode frequencies of the complexes remain practically unchanged despite varying conditions. This particular stability of the complexes is due to the high charge density of Ta5+ and Nbs+. 

FIGURE 2.14 When a small, highly charged cation is close to a large anion, the electron cloud of the anion is distorted in the process we call polarization. The green sphere represents the shape of anion in the absence of a cation. The gray shadow shows how the shape of the sphere is distorted by the positive charge of the cation. 

The radius rs is sometimes called the Wigner-Seitz radius and can be interpreted to a first approximation as the average distance between two electrons in the particular system. Regions of high density are characterized by small values of rs and vice versa. From standard electrostatics it is known that the potential of a uniformly charged sphere with radius rs is proportional to l/rs, or, equivalently, to p( r,)17 3. Hence, we arrive at the following approximate expression for Ex (Cx is a numerical constant),... 

The Huggins coefficient kn is of order unity for neutral chains and for polyelectrolyte chains at high salt concentrations. In low salt concentrations, the value of kn is expected to be an order of magnitude larger, due to the strong Coulomb repulsion between two polyelectrolyte chains, as seen in the case of colloidal solutions of charged spheres. While it is in principle possible to calculate the leading virial coefficients in Eq. (332) for different salt concentrations, the essential feature of the concentration dependence of t can be approximated by... 

This divergent behaviour at the origin can be avoided by considering instead of a point-like nucleus a uniform charged sphere of radius i [ 10,11,12], Then the density is forced to drop to zero at the center of the nucleus, which makes it normalizable, and the energy is finite. However, this quantity as well as p near the nucleus are highly overstimated, and for example the relativistic correction to the energy... 

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. 

Using optical microscopy and cryo-TEM, we have recently discovered block liposomes, which are liposomes consisting of connected, but distinctly shaped, nanoscale liposome blocks spheres or pears connected to tubes or rods [58, 96, 97]. The key to this discovery is the curvature stabilizing ability of our new, highly charged DL MVLBisG2 (see Sect. 4) [24],... 

The feeblest type of chemical interaction occurs between neutral atoms, not in their valence state, and is typified by inert-gas crystals. In this case the atoms occur close-packed with a very small accumulation of charge on the interstitial sites. These charges are generated by mutual polarization of vibrating atomic charge spheres. Under high pressure an increased amount of valence density is squeezed into interstitial sites until a metal structure is formed. 

Aerosol particles may occur by themselves or may be formed into chains of spheres or cubes. These are called agglomerates or floes. Agglomerates are usually formed from highly charged small particles such as are found in dense smokes or metal fumes. 

Figure 6.8 shows as a function of the ratio dia of the polyelectrolyte layer thickness d to the core radius a for two values of Q (5 and 50) at = 10 . Note that as dIa tends to zero, the polyelectrolyte-coated particle becomes a hard sphere with no polyelectrolyte layer, while as dia tends to inhnity, the particle becomes a spherical polyelectrolyte with no particle core. Approximate results calculated with Eq. (6.155) for Q = 5 (low charge case) and Eq. (6.168) for Q = 50 (high charge case) are also shown in Fig. 6.8. Agreement between exact and approximate results is good. For the low charge case, the surface potential is essentially independent of d and is determined only by the charge amount Q. In the example given in Fig. 6.8, for the high charge case, the particle behaves like a hard particle with no polyelectrolyte layer for dia 10 and the particle behaves like a spherical polyelectrolyte for dia 1.

---