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Random sequential adsorption on Euclidean, fractal, and random lattices.

P M Pasinetti1, L S Ramirez1, P M Centres1

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This study models irreversible object adsorption on various lattices using random sequential adsorption. Results show jamming transition exponents and coverage probabilities scale with system size M as M^(1/2), revealing universal behaviors across different lattice types.

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Area of Science:

  • Statistical Physics
  • Materials Science
  • Complex Systems

Background:

  • Adsorption phenomena are crucial in diverse scientific fields.
  • Understanding jamming transitions in disordered systems is a key challenge.
  • Lattice dimensionality and topology significantly influence adsorption dynamics.

Purpose of the Study:

  • To investigate irreversible adsorption on Euclidean, fractal, and random lattices.
  • To model the adsorption process using the random sequential adsorption algorithm.
  • To analyze coverage probability and jamming transition exponents.

Main Methods:

  • Simulation of random sequential adsorption on 1D, 2D, and 3D Euclidean lattices.
  • Adsorption modeling on Sierpinski carpets (fractal lattices) with dimension 1 < d < 2.
  • Analysis of adsorption on Erdős-Rényi random graphs.
  • Measurement of coverage probability W_{L(M)}(θ) and jamming exponent ν_{j}.

Main Results:

  • Adsorption behavior on Euclidean, fractal, and random lattices exhibits universal scaling.
  • Quantities derived from jamming probability scale asymptotically as M^(1/2).
  • For Euclidean and fractal lattices, ν_{j} = 2/d, linking jamming to lattice dimension.

Conclusions:

  • The study reveals universal scaling laws for irreversible adsorption across diverse lattice structures.
  • The jamming transition exponent is directly related to the fractal dimension of the substrate.
  • Findings provide insights into the fundamental mechanisms governing packing and jamming in disordered systems.