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

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), Article 042110. 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: 2470-0053
• 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
• Contract Date: Apr 1, 2019