No Arabic abstract
Adsorption of polymers to surfaces is crucial for understanding many fundamental processes in nature. Recent experimental studies indicate that the adsorption dynamics is dominated by non-equilibrium effects. We investigate the adsorption of a single polymer of length $N$ to a planar solid surface in the absence of hydrodynamic interactions. We find that for weak adsorption energies the adsorption time scales $ sim N^{(1+2 u)/(1+ u)}$, where $ u$ is the Flory exponent for the polymer. We argue that in this regime the single chain adsorption is closely related to a field-driven polymer translocation through narrow pores. Surprisingly, for high adsorption energies the adsorption time becomes longer, as it scales $sim N^{(1+ u)}$, which is explained by strong stretching of the unadsorbed part of the polymer close to the adsorbing surface. These two dynamic regimes are separated by an energy scale that is characterised by non-equilibrium contributions during the adsorption process.
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 $(1+ u)^{-1}$ where $ uapprox 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.
Employing Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene between graphite walls we show that the mass exchange between layers close to the walls is a slow process already in the melt state. For the glass transition of confined polymers this process competes with the slowing down due to packing effects and intramolecular rotation barriers.
We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple equations for the adsorption-desorption transition line. We show that the adsorption threshold is the same for systems with quenched and annealed disorder. The results are discussed with respect to their implications for the physics of molecular recognition.
We examine the phase transition of polymer adsorption as well as the underlying kinetics of polymer binding from dilute solutions on a structureless solid surface. The emphasis is put on the properties of regular multiblock copolymers, characterized by block size M and total length N as well as on random copolymers with quenched composition p of sticky and neutral segments. The macromolecules are modeled as coarse-grained bead-spring chains subject to a short-ranged surface adhesive potential. Phase diagrams, showing the variation of the critical threshold for single chain adsorption in terms of M and p are derived from scaling considerations in agreement with results from computer experiment. Using both scaling analysis and numerical data from solving a system of coupled Master equations, we demonstrate that the phase behavior at criticality, and the adsorption kinetics may be adequately predicted and understood, in agreement with the results of extensive Monte Carlo simulations. Derived analytic expressions for the mean fraction of adsorbed segments as well as for Probability Distribution Functions of the various structural building blocks (i.e., trains, loops, tails) at time t during the chain attachment process are in good agreement with our numeric experiments and provide insight into the mechanism of polymer adsorption.
Single-molecule fluorescence imaging of adsorption onto initially-bare surfaces shows that polymer chains need not localize immediately after arrival. In a system optimized to present limited adsorption sites (quartz surface to which polyethylene glycol (PEG) is exposed in aqueous solution at pH = 8.2) we find that some chains diffuse back into bulk solution and re-adsorb at some distance away, sometimes multiple times before either they localize at a stable position or else diffuse away into bulk solution. This mechanism of surface diffusion is considerably more rapid than the classical model in which adsorbed polymers crawl on surfaces while the entire molecule remains adsorbed. The trajectories with jumps follow a truncated Levy distribution of step size with limiting slope -2.5, consistent with a well-defined, rapid surface diffusion coefficient over the times we observe.