Irreversible adsorption from dilute polymer solutions.
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).
O'Shaughnessy
B
B
Department of Chemical Engineering, Columbia University, 500 West 120th Street, NY 10027, New York, USA. bo8@columbia.edu.
Vavylonis
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D
Department of Chemical Engineering, Columbia University, 500 West 120th Street, NY 10027, New York, USA.|Department of Physics, Columbia University, 538 West 120th Street, NY 10027, New York, USA.
D000327:Adsorption; D001703:Biophysics / Q000379:methods; D007700:Kinetics; D008962:Models, Theoretical; D011108:Polymers; D012996:Solutions; D013053:Spectrophotometry; D013816:Thermodynamics; D013997:Time Factors
D011108:Polymers; D012996:Solutions