Irreversible adsorption from dilute polymer solutions.

ABSTRACT

We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two broad cases are considered, distinguished by the magnitude of the local monomer-surface sticking rate Q chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single-chain adsorption. While single-chain physisorption times tau ads are typically micro- to milli-seconds, for chemisorbing chains of N units we find experimentally accessible times tau ads=Q(-1)N(3/5), ranging from seconds to hours. We establish 3 chemisorption universality classes, determined by a critical contact exponent zipping, accelerated zipping and homogeneous collapse. For dilute solutions, the mechanism is accelerated zipping zipping propagates outwards from the first attachment, accelerated by occasional formation of large loops which nucleate further zipping. This leads to a transient distribution omega(s) approximately s(-7/5) of loop lengths s up to a maximum size smax approximately (Qt)(5/3) after time t. By times of order tau ads the entire chain is adsorbed. The outcome of the single-chain adsorption episode is a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb onto, late-arriving chains form a diffuse outer layer. In a simple picture we find for both chemisorption and physisorption a final loop distribution Omega(s) approximately s(-11/5) and density profile c(z) approximately z(-4/3) whose forms are the same as for equilibrium layers. In contrast to equilibrium layers, however, the statistical properties of a given chain depend on its adsorption time; the outer layer contains many classes of chain, each characterized by a different fraction of adsorbed monomers f. Consistent with strong physisorption experiments, we find the f values follow a distribution P(f) approximately f(-4/5).