Adsorption-Desorption Kinetics of Line Segments in One Dimension

Abstract

I. INTRODUCTIONThe irreversible adsorption of large molecules has beenreported for systems of colloids, proteins, latex spheres,polymers, etc. [1{12]. The simplest model of irreversibleadsorption is random sequential adsorption (RSA). Thelarge molecules impact sequentially on the surface. If theimpact surface is empty, the molecules adsorb on the sur-face and do not detach from the surface. If the impactsurface is occupied by molecules, the molecules cannotadsorb on the surface. Therefore, we expect the forma-tion of a monolayer. In the RSA model the coveragefraction of the surface approaches a limiting value, theso-called jamming limit after a long time. In the latticemodel of RSA, the coverage fraction (t) follows an ex-ponential behavior as (t) = (1) Aexp( Bt), where(1) is a jamming limit, and Aand B are constantsdepending on the dimensionality of the surface and theshape of the molecules. In the continuous model of RSAor the parking-lot problem, the coverage fraction followsa power-law behavior as (t) = (1) At , where Ais aconstant and the exponent depends on the dimension-ality and the shape of the object. RSA is an oversimpli- ed model of the adsorption of large molecules. Indeed,there are many e ects such as transport of the molecules,di usion of adsorbed molecules, and the desorption fromthe surface to the bulk solution [12{18].There are many studies on the e ects of desorption onRSA for physical, chemical, and biological systems [1{3].A simple example of RSA with desorption is a parking lotproblem. Identical cars adsorb (or park) on a line (curb)at a rate K