In solid crystals such as NaCl, electrical charges are localized on those sites that form the lattice. These lattice sites are occupied not by neutral atoms, but by negatively charged chlorine or positively charged sodium ions and the crystal is held together by the columbic forces that exist between all electrically oppositely charged species. The energy of interaction between two particles of charge q1 and q2 at a distance r from one another is given by
U12 = q1-q2/ 4πεrε0r
Where εr is the relative permittivity of the medium and ε0 the permittivity of free space. The energy is positive when q1 and q2 have opposite signs. The corresponding force between the two particles is a vector quantity, directed along the inter-particle axis, r, if the two charges have the same sign, the force F is repulsive.
These coulombic forces are very powerful and ions are drawn close together before short-range repulsive forces come into play and an equilibrium interionic distance is established. The result that very large amounts of energy are needed to break down the lattice, leading, for example, to the familiar observation of high melting points in ionic crystals. The actual calculation of the energy required completely to break up the crystal lattice can be carried out provided some analytical form for the ionic repulsion can be written down. Commonly, this repulsion is deemed to take the form R12 = B/rn, where B depends on the relative extension of valence and core-electron clouds.
The ability of an electrolyte solution to sustain the passage of electrical current depends on the mobility of its constituent charged ions in the electric field between electrodes immersed in the solution. Ions of charge ze0, accelerated by the electric field strength, E, are subject to a frictional force, F, that increases with velocity, v, and is given, for simple spherical ions of radius r1, by the Strokes formula, F = 6πnriv, where n is the viscosity of the medium. The result is that after a short induction period, the velocity attains a limited value, vmax, corresponding to the exact balance between the electrical and frictional forces.
Ze0|E| = 6πnr1vmax
And the terminal velocity is given byIt follows that for given values of n and |E|, each type of ion will have a transport velocity dependant on the charge and the radius of the solvated ion and a direction of migration dependant on the sign of the charge.
Vmax = ze0|E|/ 6πnr1
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