Random Sequential Adsorption on Imprecise Lattice

Abstract

We report a surprising result, established by numerical simulations and analytical arguments for a one-dimensional lattice model of random sequential adsorption, that even an arbitrarily small imprecision in the lattice-site localization changes the convergence to jamming from fast, exponential, to slow, power-law, with, for some parameter values, a discontinuous jump in the jamming coverage value. This finding has implications for irreversible deposition on patterned substrates with pre-made landing sites for particle attachment. We also consider a general problem of the particle (depositing object) size not an exact multiple of the lattice spacing, and the lattice sites themselves imprecise, broadened into allowed-deposition intervals. Regions of exponential vs. power-law convergence to jamming are identified, and certain conclusions regarding the jamming coverage are argued for analytically and confirmed numerically.

References in corpus (5)

• Random Sequential Adsorption: From Continuum to Lattice and Pre-Patterned Substrates
• Locally Frozen Defects in Random Sequential Adsorption with Diffusional Relaxation
• Collective Effects in Random Sequential Adsorption of Diffusing Hard Squares
• Morphology of Fine-Particle Monolayers Deposited on Nanopatterned Substrates
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Cited by in corpus (4)

• Nonstandard Convergence to Jamming in Random Sequential Adsorption: The Case of Patterned One-Dimensional Substrates
• "Paris car parking problem" for partially ordered discorectangles on a line
• Random Sequential Adsorption on mobile patches
• Monte Carlo simulation of selective adsorption in a binary hard-disk mixture on patterned adhesive surfaces