Lecture 20 Lattice gas with interactions

1. 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