Adsorption Kinetics of a Single Polymer on a Solid Plane

Details Adsorption Kinetics of a Single Polymer on a Solid Plane Adsorption Kinetics of a Single Polymer on a Solid Plane

2008-03-18

arxiv.org/abs/0803.2688v3

Phys. Rev. E 77, 061603 (2008)

Physics

Condensed Matter

Soft Condensed Matter

14 pages, 8 figures; typos were corrected

Scientific paper

10.1103/PhysRevE.77.061603

We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying notion of a ``stem-flower'' polymer conformation, and the related mechanism of ``zipping'' during the adsorption process are shown to lead to a Fokker-Planck equation with reflecting boundary conditions for the time-dependent probability distribution function (PDF) of the number of adsorbed monomers. The theoretical treatment predicts that the mean fraction of adsorbed segments grows with time as a power law with a power of $(1+\nu)^{-1}$ where $\nu\approx 3/5$ is the Flory exponent. The instantaneous distribution of train lengths is predicted to follow an exponential relationship. The corresponding PDFs for loops and tails are also derived. The complete solution for the time-dependent PDF of the number of adsorbed monomers is obtained numerically from the set of discrete coupled differential equations and shown to be in perfect agreement with the Monte Carlo simulation results. In addition to homopolymer adsorption, we study also regular multiblock copolymers and random copolymers, and demonstrate that their adsorption kinetics may be considered within the same theoretical model.

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