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.

中文翻译：

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沉积在一维晶格上的半刚性k-mers的不可逆多层吸附。

半刚性的不可逆多层吸附 $ķ$单体在尺寸的一维晶格上 $\mathrm{大号}$通过数值模拟研究，辅以详尽列举小格构型。通过使用随机顺序吸附算法对沉积过程进行建模，推广到多层吸附的情况。本文着重于测量不同值的干扰覆盖率。$ķ$-mer大小和层数 $ñ$。双层问题（$ñ\le 2$）进行了详尽的分析，并通过精确的枚举技术验证了生成的趋势。然后，将研究扩展到越来越多的层，这是这项工作中值得注意的部分之一。获得的结果允许以下：（i）表征多层问题的吸附相的结构。如$ñ$ 增加， $（\mathrm{1个}+\mathrm{1个}）$维吸附相往往是由“塔”（或塔）的宽度组成的“局部壁” $ķ$，由空旷的山谷隔开。这些谷的长度随着增加而减少$ķ$; （ii）确定这是注册内吸附过程，其中每次传入$ķ$-mer可能会完全吸附在已经吸附的分子上。关于渗滤，我们的计算表明渗滤概率随​​着$\mathrm{大号}$ 增加，极限为零 $\mathrm{大号}\to \infty$。最后，干扰临界指数的值${\nu }_{Ĵ}$ 在这里报道了多层吸附： ${\nu }_{Ĵ}$ 无论考虑的值是多少，都保持接近2 $ķ$ 和 $ñ$。根据晶格尺寸讨论了这一发现。