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Effects of competition between random sequential nucleation of point-sized seeds and island growth by adsorption of finite-sized grains

Khanam, Aklima; Wattis, Jonathan A.D.; Hassan, M. Kamrul

Authors

Aklima Khanam

M. Kamrul Hassan



Abstract

We study random sequential adsorption of particles from a pool onto a one-dimensional substrate following ballistic deposition rules with separate nucleation and growth processes occurring simultaneously. Nucleation describes the formation of point-sized seeds, and after a seed is sown, it acts as an attractor and grows in size by the addition of grains of a fixed size. At each time step either an already-nucleated seed can increase in size, or a new seed may be nucleated. We incorporate a parameter m to describe the relative rates of growth to nucleation. We solve the model analytically to obtain a gap size distribution function and a general expression for the jamming coverage as a function of m . We show that the jamming coverage θ(m) reaches its maximum value of θ(m)=1 in the limit m→∞ following a power-law θ(∞)−θ(m)∼Km−1/2 for some constant K . We also perform an extensive Monte Carlo simulation and find good agreement between analytic and numerical results.

Citation

Khanam, A., Wattis, J. A., & Hassan, M. K. (2019). Effects of competition between random sequential nucleation of point-sized seeds and island growth by adsorption of finite-sized grains. Physical Review E, 99(4), https://doi.org/10.1103/PhysRevE.99.042110

Journal Article Type Article
Acceptance Date Mar 24, 2019
Online Publication Date Apr 5, 2019
Publication Date Apr 5, 2019
Deposit Date Apr 1, 2019
Publicly Available Date Apr 1, 2019
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 1550-2376
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 99
Issue 4
Article Number 042110
DOI https://doi.org/10.1103/PhysRevE.99.042110
Public URL https://nottingham-repository.worktribe.com/output/1723929
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.042110

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