The primitive model and Debye-Hiickel DH theory

Consider a neutral mixture of charged hard spheres of diameter u, charge (where e is the charge of the electron), number density /j, = l, (where Ai, is the number of ions of species i enclosed in a volume V). The number of species is i. where is expressed in number of particles per cubic angstrom and is the stoichiometric coefficient. We will use Boltzmann s constant ks and write fi = 

We define the potential of mean force Wij(r) such that 

Our central problem will be to determine this potential of mean force. There are a number of requirements on it, however. 

If we assume Ci7( ) electrostatic potential must satisfy the Poisson 

Another limiting case is when the central ion is very large. Then v ((r) must be small, and we know that, for r - 00 then  

---