An adsorption-desorption process on a line: kinetics of the approach to closest packing

We study an adsorption-desorption process of rods on a line. The desorption rate is infinitely small, so that each desorption event is instantly followed by the insertion of one or two new rods. Due to the latter possibility, the system evolves continuously to a close-packed state. The asymptotic kinetics of the densification process is analysed with the aid of gap distribution functions. If it is assumed that the system relaxes completely to equilibrium after each density increment, we show that 1- rho (t) approximately 1/ln(t), while an improved description yields 1- rho (t) approximately 1/ln(2t(ln2t)2). The range of validity of the asymptotic expressions is established by comparison with the results of a numerical simulation of the process.