Single polymers at surfaces: adsorption and detachment
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Abstract
This thesis is concerned with the adsorption and detachment of polymers
at planar, rigid surfaces. We have carried out a systematic investigation of
adsorption of polymers using analytical techniques as well as Monte Carlo
simulations with a coarse grained off-lattice bead spring model. The investigation was carried out in three stages.
In the first stage the adsorption of a single multiblock AB copolymer on a
solid surface was investigated by means of simulations and scaling analysis.
It was shown that the problem could be mapped onto an effective homopolymer problem. Our main result was the phase diagram of regular multiblock
copolymers which shows an increase in the critical adsorption potential of
the substrate with decreasing size of blocks. We also considered the adsorption of random copolymers which was
found to be well described within the
annealed disorder approximation.
In the next phase, we studied the adsorption kinetics of a single polymer on a
flat, structureless surface in the regime of strong physisorption. The idea of
a ’stem-flower’ polymer conformation and the mechanism of ’zipping’ during
the adsorption process were used to derive a Fokker-Planck equation with
reflecting boundary conditions for the time dependent probability distribution function (PDF) of the number of adsorbed monomers. The numerical
solution of the time-dependent PDF obtained from a discrete set of coupled
differential equations were shown to be in perfect agreement with Monte
Carlo simulation results.
Finally we studied force induced desorption of a polymer chain adsorbed on
an attractive surface. We approached the problem within the framework of
two different statistical ensembles; (i) by keeping the pulling force fixed while
measuring the position of the polymer chain end, and (ii) by
measuring the
force necessary to keep the chain end at fixed distance above the adsorbing
plane. In the first case we treated the problem within the framework of the
Grand Canonical Ensemble approach and derived analytic expressions for
the various conformational building blocks, characterizing the structure of
an adsorbed linear polymer chain, subject to pulling force of fixed strength.
The main result was the phase diagram of a polymer chain under pulling. We
demonstrated a novel first order phase transformation which is dichotomic
i.e. phase coexistence is not possible. In the second case, we carried out our
study in the “fixed height” statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain end is
kept fixed at height h over the solid plane at different adsorption strength ε.
The phase diagram in the h − ε plane was calculated both analytically and
by Monte Carlo simulations. We demonstrated that in the
vicinity of the
polymer desorption transition a number of properties like fluctuations and
probability distribution of various quantities behave differently, if h rather
than the force, f, is used as an independent control parameter.