Eur. Phys. J. E (2003) 11: 213-230
https://doi.org/10.1140/epje/i2003-10015-9

Original Paper

Irreversible adsorption from dilute polymer solutions

¹ Department of Chemical Engineering, Columbia University, 500 West 120th Street, NY 10027, New York, USA
² Department of Physics, Columbia University, 538 West 120th Street, NY 10027, New York, USA

^* e-mail: bo8@columbia.edu
^** e-mail: dv35@columbia.edu

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 $\tau_{\rm ads}$ are typically micro- to milli-seconds, for chemisorbing chains of N units we find experimentally accessible times $\tau_{\rm ads} = Q^{-1} N^{3/5}$, 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 $\omega(s) \sim s^{-7/5}$ of loop lengths s up to a maximum size $s^{\max} \approx (Q t)^{5/3}$ after time t. By times of order $\tau_{\rm ads}$ 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 $\Omega(s) \sim s^{-11/5}$ and density profile $c(z) \sim z^{-4/3}$ 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 $P(f) \sim f^{-4/5}$.