1. Lattice gas with interactions
Lecture 20
Lattice gas with interactions
The model
Partition function
Bragg-Williams (mean field) approximation and absorption transition

2. Lattice model adsorption with interactions
N atoms on the surface, each has c (coordination) neighboring sites. Using symbol N11 - number of nearest neighbors links with occupied sites and symbol N10 for number of nearest neighbors links with one occupied site. Simple counting for occupied sites gives
cN = 2N11 + N01
And for unoccupied sites
c(M-N) = 2N00 + N01
From which the interaction energy
Where w is the interaction energy between occupied sites

3. Bragg-Williams approximation
We can estimate average number of N11by assuming regular solutions. With this each site has on average
11 type of links. Multiplying by number of occupied sites and dividing by two to avoid double counting
And the partition functions is

4. Helmholz free energy and chemical potential
The thermodynamic function F
An the chemical potential
For the ideal lattice gas the last term is missing

5. The isotherm equation Similarly to ideal lattice gas where
Consider as a function of

6. The isotherm equation Taking derivative with respect to coverage
We can calculate when the derivative is zero
For a given pressure there are two
different coverages - adsorption
transition