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Loncarević I, Budinski-Petković Lj, Vrhovac SB, et al. Adsorption, desorption, and diffusion of k-mers on a one-dimensional lattice. Phys Rev E Stat Nonlin Soft Matter Phys. 2009;80(2):021115doi: 10.1103/PhysRevE.80.021115.
Loncarević, I., Budinski-Petković, L. j., Vrhovac, S. B., & Belić, A. (2009). Adsorption, desorption, and diffusion of k-mers on a one-dimensional lattice. Physical review. E, Statistical, nonlinear, and soft matter physics, 80(2), 021115. https://doi.org/10.1103/PhysRevE.80.021115
Loncarević, I, et al. "Adsorption, desorption, and diffusion of k-mers on a one-dimensional lattice." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 80,2 (2009): 021115. doi: https://doi.org/10.1103/PhysRevE.80.021115
Loncarević I, Budinski-Petković Lj, Vrhovac SB, Belić A. Adsorption, desorption, and diffusion of k-mers on a one-dimensional lattice. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2):021115. doi: 10.1103/PhysRevE.80.021115. Epub 2009 Aug 20. PMID: 19792085.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2):021115. doi: 10.1103/PhysRevE.80.021115. Epub 2009 Aug 20.

Adsorption, desorption, and diffusion of k-mers on a one-dimensional lattice.

Physical review. E, Statistical, nonlinear, and soft matter physics

I Loncarević, Lj Budinski-Petković, S B Vrhovac, A Belić

Affiliations

  1. Faculty of Engineering, Trg D. Obradovi?a 6, Novi Sad 21000, Serbia.

PMID: 19792085 DOI: 10.1103/PhysRevE.80.021115

Abstract

Kinetics of the deposition process of k -mers in the presence of desorption or/and diffusional relaxation of particles is studied by Monte Carlo method on a one-dimensional lattice. For reversible deposition of k-mers, we find that after the initial "jamming," a stretched exponential growth of the coverage theta(t) toward the steady-state value theta(eq) occurs, i.e., theta(eq)-theta(t) is proportional to exp[-(t/tau)(beta)]. The characteristic time scale tau is found to decrease with desorption probability P(des) according to a power law, tau is proportional to P(des)(-gamma), with the same exponent gamma=1.22+/-0.04 for all k-mers. For irreversible deposition with diffusional relaxation, the growth of the coverage theta(t) above the jamming limit to the closest packing limit (CPL) theta(CPL) is described by the pattern theta(CPL)-theta(t) is proportional to E(beta)[-(t/tau)(beta)], where E(beta) denotes the Mittag-Leffler function of order beta(0,1) . Similarly to the reversible case, we found that the dependence of the relaxation time tau on the diffusion probability P(dif) is consistent again with a simple power-law, i.e., tau is proportional to P(dif)(-delta). When adsorption, desorption, and diffusion occur simultaneously, coverage always reaches an equilibrium value theta(eq), which depends only on the desorption/adsorption probability ratio. The presence of diffusion only hastens the approach to the equilibrium state, so that the stretched exponential function gives a very accurate description of the deposition kinetics of these processes in the whole range above the jamming limit.

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