Irreversible multilayer adsorption of semirigid $k$-mers on one-dimensional lattices of size $L$ is studied by numerical simulations complemented by exhaustive enumeration of configurations for small lattices. The deposition process is modeled by using a random sequential adsorption algorithm, generalized to the case of multilayer adsorption. The paper concentrates on measuring the jamming coverage for different values of $k$-mer size and number of layers $n$. The bilayer problem ($n\le 2$) is exhaustively analyzed, and the resulting tendencies are validated by the exact enumeration techniques. Then, the study is extended to an increasing number of layers, which is one of the noteworthy parts of this work. The obtained results allow the following: (i) to characterize the structure of the adsorbed phase for the multilayer problem. As $n$ increases, the $(1+1)$-dimensional adsorbed phase tends to be a “partial wall” consisting of “towers” (or columns) of width $k$, separated by valleys of empty sites. The length of these valleys diminishes with increasing $k$; (ii) to establish that this is an in-registry adsorption process, where each incoming $k$-mer is likely to be adsorbed exactly onto an already adsorbed one. With respect to percolation, our calculations show that the percolation probability vanishes as $L$ increases, being zero in the limit $L\to \infty$. Finally, the value of the jamming critical exponent ${\nu }_j$ is reported here for multilayer adsorption: ${\nu }_j$ remains close to 2 regardless of the considered values of $k$ and $n$. This finding is discussed in terms of the lattice dimensionality.

• Received 15 April 2020
• Accepted 9 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.012106