3,602 research outputs found
Polymers in disordered environments
A brief review of our recent studies aiming at a better understanding of the
scaling behaviour of polymers in disordered environments is given. The main
emphasis is on a simple generic model where the polymers are represented by
(interacting) self-avoiding walks and the disordered environment by critical
percolation clusters. The scaling behaviour of the number of conformations and
their average spatial extent as a function of the number of monomers and the
associated critical exponents and are examined with two
complementary approaches: numerical chain-growth computer simulations using the
PERM algorithm and complete enumerations of all possible polymer conformations
employing a recently developed very efficient exact counting method.Comment: 11 pages, 5 figure
Knot localization in adsorbing polymer rings
We study by Monte Carlo simulations a model of knotted polymer ring adsorbing
onto an impenetrable, attractive wall. The polymer is described by a
self-avoiding polygon (SAP) on the cubic lattice. We find that the adsorption
transition temperature, the crossover exponent and the metric exponent
, are the same as in the model where the topology of the ring is
unrestricted. By measuring the average length of the knotted portion of the
ring we are able to show that adsorbed knots are localized. This knot
localization transition is triggered by the adsorption transition but is
accompanied by a less sharp variation of the exponent related to the degree of
localization. Indeed, for a whole interval below the adsorption transition, one
can not exclude a contiuous variation with temperature of this exponent. Deep
into the adsorbed phase we are able to verify that knot localization is strong
and well described in terms of the flat knot model.Comment: 27 pages, 10 figures. Submitter to Phys. Rev.
Stretching of a chain polymer adsorbed at a surface
In this paper we present simulations of a surface-adsorbed polymer subject to
an elongation force. The polymer is modelled by a self-avoiding walk on a
regular lattice. It is confined to a half-space by an adsorbing surface with
attractions for every vertex of the walk visiting the surface, and the last
vertex is pulled perpendicular to the surface by a force. Using the recently
proposed flatPERM algorithm, we calculate the phase diagram for a vast range of
temperatures and forces. The strength of this algorithm is that it computes the
complete density of states from one single simulation. We simulate systems of
sizes up to 256 steps.Comment: 13 pages, 7 figure
Adsorption of Multi-block and Random Copolymer on a Solid Surface: Critical Behavior and Phase Diagram
The adsorption of a single multi-block -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 of sticking monomers , and on the total length 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
Layering transitions for adsorbing polymers in poor solvents
An infinite hierarchy of layering transitions exists for model polymers in
solution under poor solvent or low temperatures and near an attractive surface.
A flat histogram stochastic growth algorithm known as FlatPERM has been used on
a self- and surface interacting self-avoiding walk model for lengths up to 256.
The associated phases exist as stable equilibria for large though not infinite
length polymers and break the conjectured Surface Attached Globule phase into a
series of phases where a polymer exists in specified layer close to a surface.
We provide a scaling theory for these phases and the first-order transitions
between them.Comment: 4 pages, 4 figure
Temperature effects in the mechanical desorption of an infinitely long lattice chain: Re-entrant phase diagrams
We consider the mechanical desorption of an infinitely long lattice polymer chain tethered at one end to an adsorbing surface. The external force is applied to the free end of the chain and is normal to the surface. There is a critical value of the desorption force ftr at which the chain desorbs in a first-order phase transition. We present the phase diagram for mechanical desorption with exact analytical solutions for the detachment curve: the dependence of ftr on the adsorption energy (at fixed temperature T) and on T (at fixed ). For most lattice models ftr(T) displays a maximum. This implies that at some given force the chain is adsorbed in a certain temperature window and desorbed outside it: the stretched state is re-entered at low temperature. We also discuss the energy and heat capacity as a function of T; these quantities display a jump at the transition(s). We analyze short-range and long-range excluded-volume effects on the detachment curve ftr(T). For short-range effects (local stiffness), the maximum value of ftr decreases with stiffness, and the force interval where re-entrance occurs become narrower for stiffer chains. For long-range excluded-volume effects we propose a scaling ftr~T1-(Tc-T)/ around the critical temperature Tc, where =0.588 is the Flory exponent and 0.5 the crossover exponent, and we estimated the amplitude. We compare our results for a model where immediate step reversals are forbidden with recent self-avoiding walk simulations. We conclude that re-entrance is the general situation for lattice models. Only for a zigzag lattice model (where both forward and back steps are forbidden) is the coexistence curve ftr(T) monotonic, so that there is no re-entranc
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