# Monolayer Spreading on a Chemically Heterogeneous Substrate Source: [Monolayer Spreading on a Chemically Heterogeneous Substrate]() Collection index: [llms.txt]() Data updated: 2025-10-24T20:30:18.930Z Authors: N. Pesheva, G. Oshanin (2) \_\_INSTITUTION\_2\_\_ Institute of Mechanics -BAS, Sofia, Bulgaria; (2) LPTL, University of Paris 6, Paris, France) Published: 2002-04-25T11:40:34.000Z ## Abstract We study the spreading kinetics of a monolayer of hard-core particles on a semi-infinite, chemically heterogeneous solid substrate, one side of which is coupled to a particle reservoir. The substrate is modeled as a square lattice containing two types of sites -- ordinary ones and special, chemically active sites placed at random positions with mean concentration $\\alpha$. These special sites temporarily immobilize particles of the monolayer which then serve as impenetrable obstacles for the other particles. In terms of a mean-field-type theory, we show that the mean displacement $X\_0(t)$ of the monolayer edge grows with time $t$ as $X\_0(t) = \\sqrt{2 D\_{\\alpha} t \\ln(4 D\_{\\alpha} t/\\pi a^2)}$, ($a$ being the lattice spacing). This time dependence is confirmed by numerical simulations; $D\_{\\alpha}$ is obtained numerically for a wide range of values of the parameter $\\alpha$ and trapping times of the chemically active sites. We also study numerically the behavior of a stationary particle current in finite samples. The question of the influence of attractive particle-particle interactions on the spreading kinetics is also addressed. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()