Co-adsorption of \textit{n} Monomer Species on Terraces and Nanotubes

We consider the partition function, $Z$, of the system of $n$ monomer species adsorbed on a terrace or a nanotube of arbitrary periodic lattice geometry, $L $atomic sites in length, and $M$' sites in the width of the terrace or in the normal cross-section of the nanotube. $Z$ is related to the eigenvalues of a real and non-negative matrix (\textbf{T} matrix) of rank ($n$+1)$^{M}$, where $M$ is an integer multiple of $M$'. In the infinite-$L$ limit, we also prove that $Z$ is the largest eigenvalue of the \textbf{T}-matrix, raised to the power 1/$M$. Because the rank of this matrix increases exponentially with $M$, we develop a technique for its recursive construction applicable to any lattice geometry, which is easily programmed and efficiently adaptable for supercomputing and multiparallel processing. As examples, we consider the co-adsorption on square, equilateral triangular, and honeycomb surfaces. This general formulation can now be applied to model a whole new set of experiments involving the coadsorption of two or more monomer species, on terrace or nanotube surfaces with various periodic lattice structures.