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.
Highlights
The kinetics of a monolayer growth by surface adsorption, deposition of particles onto solid substrates, has been studied extensively over the last many decades [1,2,3,4,5,6]
The development of a theoretical understanding of the kinetics of adsorption poses many fundamental challenges owing to its non-equilibrium nature which means that the well-developed formalism of equilibrium statistical physics cannot be applied
The simplest case of random sequential adsorption (RSA) process was that considered by Alfred Renyi in 1958 [16,17,18], which is known as the ‘car parking’ problem, in which one-dimensional ‘cars’ of a uniform length σ are ‘parked’ sequentially at random available positions in a car park of length L ≫ σ
Summary
The kinetics of a monolayer growth by surface adsorption, deposition of particles onto solid substrates, has been studied extensively over the last many decades [1,2,3,4,5,6]. Viot et al [24] considered a generalised ballistic deposition model in which identical particles land and roll, either joining an existing cluster, or adsorbing to the substrate and become a new nuclei. Whilst their theoretical analysis is similar to what we present below; since our model differs from theirs, our results are different.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
