Crystallization patterns of monomers with a nearest-neighbor interaction on a multilayered semi-infinite square lattice.
The absorption of an external monomer gas in a square lattice of L layers, infinite in one direction and finite (M sites) in the other, is studied with a finite nearest-neighbor repulsion energy V11<0. In a physical system, the monomer chemical potential μ1 is determined by the external gas pressure. For a temperature below (-V11/5kB)log10e the curves of entropy S versus lattice coverage θ1 exhibit two cusps for L=1 and 2, and three cusps for L=3, at S=0. Crystallization pattern analysis at the cusps leads, in terms of M and L, to exact expressions of θ1 and the number θ2 of nearest neighbors per site which are linear in 1/M. Setting M=∞ yields, for L=1 and 2, one cusp at (θ1=1/2, θ2=0), and for L=3, two cusps at (θ1=1/2, θ2=0) and at (θ1=5/6, θ2=5/3). The change in μ1 required to unlock the structural ordering is shown to be proportional to V11. Other features of the system below the critical temperature reported above are also discussed.