Kinetics and Jamming Coverage in a Random Sequential Adsorption of Polymer Chains

Using a highly efficient Monte Carlo algorithm, we are able to study the growth of coverage in a random sequential adsorption of self-avoiding walk chains for up to ∼${10}^{12}$ time steps on a square lattice. For the first time, the true jamming coverage ${\theta }_J$ is found to decay with the chain length $N$ with a power law ${\theta }_J\propto N^{-0.1\mathrm{}}$. The growth of the coverage to its jamming limit can be described by a power law $\theta \mathrm{}\left(t\right)\mathrm{}\approx {\theta }_J-\frac{c}{t^y}$ with an effective exponent $y$ which depends on the chain length, i.e., $y\simeq 0.50$ for $N=4\mathrm{}$ to $y\simeq 0.07$ for $N=30\mathrm{}$ with $y\to 0$ in the asymptotic $\mathrm{limit} N\to \infty$.