Adsorption of Multi-block and Random Copolymer on a Solid Surface: Critical Behavior and Phase Diagram

The adsorption of a single multi-block $AB$-copolymer on a solid planar substrate is investigated by means of computer simulations and scaling analysis. It is shown that the problem can be mapped onto an effective homopolymer adsorption problem. In particular we discuss how the critical adsorption energy and the fraction of adsorbed monomers depend on the block length $M$ of sticking monomers $A$, and on the total length $N$ of the polymer chains. Also the adsorption of the random copolymers is considered and found to be well described within the framework of the annealed approximation. For a better test of our theoretical prediction, two different Monte Carlo (MC) simulation methods were employed: a) off-lattice dynamic bead-spring model, based on the standard Metropolis algorithm (MA), and b) coarse-grained lattice model using the Pruned-enriched Rosenbluth method (PERM) which enables tests for very long chains. The findings of both methods are fully consistent and in good agreement with theoretical predictions.Comment: 27 pages, 12 figure

Forced-induced desorption of a polymer chain adsorbed on an attractive surface - Theory and Computer Experiment

We consider the properties of a self-avoiding polymer chain, adsorbed on a solid attractive substrate which is attached with one end to a pulling force. The conformational properties of such chain and its phase behavior are treated within a Grand Canonical Ensemble (GCE) approach. We derive theoretical expressions for the mean size of loops, trains, and tails of an adsorbed chain under pulling as well as values for the universal exponents which describe their probability distribution functions. A central result of the theoretical analysis is the derivation of an expression for the crossover exponent $\phi$, characterizing polymer adsorption at criticality, $\phi = \alpha -1$, which relates the precise value of $\phi$ to the exponent $\alpha$, describing polymer loop statistics. We demonstrate that $1-\gamma_{11} < \alpha < 1 + \nu$, depending on the possibility of a single loop to interact with neighboring loops in the adsorbed polymer. The universal surface loop exponent $\gamma_{11} \approx -0.39$ and the Flory exponent $\nu \approx 0.59$. We present the adsorption-desorption phase diagram of a polymer chain under pulling and demonstrate that the relevant phase transformation becomes first order whereas in the absence of external force it is known to be a continuous one. The nature of this transformation turns to be dichotomic, i.e., coexistence of different phase states is not possible. These novel theoretical predictions are verified by means of extensive Monte Carlo simulations.Comment: 24 pages, 14 figure

Hopping diffusion of two coupled particles in random trap model

We show that the hopping dynamics of two strongly connected particles can be mapped exactly to single particle dynamics. In this way we are able to calculate the exact asymptotic diffusion coefficient of two connected particles on a linear chain in the random trap model. In particular we calculate the diffusion coefficient for exponentially distributed site energies and show that there exists a critical temperature below which a subdiffusive behavior appears. It turns out that this critical temperature is twice higher than the critical temperature in the single particle case [S. Havlin, B. L. Trus, and G. H. Weiss, J. Phys. A: Math. Gen. 19, L817 (1986)]