55 research outputs found

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### Knots, links, anyons and statistical mechanics of entangled polymer rings

The field theory approach to the statistical mechanics of a system of N polymer rings linked together is extended to the case of links whose paths in space are characterized by a fixed number 2s of maxima and minima. Such kind of links are called 2s-plats and appear for instance in the DNA of living organisms or in the wordlines of quasiparticles associated with vortices nucleated in a quasi-two-dimensional superfluid. The path integral theory describing the statistical mechanics of polymers subjected to topological constraints is mapped here into a field theory of quasiparticles (anyons). In the particular case of s=2, it is shown that this field theory admits vortex solutions with special self-dual points in which the interactions between the vortices vanish identically. The topological states of the link are distinguished using two topological invariants, namely the Gauss linking number and the so-called bridge number which is related to s. The Gauss linking number is a topological invariant that is relatively weak in distinguishing the different topological configurations of a general link. The addition of topological constraints based on the bridge number allows to get a glimpse into the non-abelian world of quasiparticles, which is relevant for important applications like topological quantum computing and high-TC superconductivity. At the end an useful connection with the cosh-Gordon equation is shown in the case s=2. © 201

### Tension enhancement in branched macromolecules upon adhesion on a solid substrate

The effect of self-generated tension in the backbone of a bottle-brush (BB)
macromolecule, adsorbed on an attractive surface, is studied by means of
Molecular Dynamics simulations of a coarse-grained bead-spring model in the
good solvent regime. The BB-molecule is modeled as a backbone chain of $L$
beads, connected by breakable bonds and with side chains, tethered pairwise to
each monomer of the backbone. Our investigation is focused on several key
questions that determine the bond scission mechanism and the ensuing
degradation kinetics: how are frequency of bond scission and self-induced
tension distributed along the BB-backbone at different grafting density
$\sigma_g$ of the side chains? How does tension $f$ depend on the length of the
side chains $N$, and on the strength of surface adhesion $\epsilon_s$? We
examine the monomer density distribution profiles across the BB-backbone at
different $\epsilon_s$ and relate it to adsorption-induced morphological
changes of the macromolecule whereby side chains partially desorb while the
remaining chains spread better on the surface. Our simulation data are found to
be in qualitative agreement with experimental results and recent theoretical
predictions. Yet we demonstrate that the interval of parameter values where
these predictions hold is limited in $N$. Thus, at high values of $\epsilon_s$,
too long side chains mutually block each other and freeze effectively the
bottle-brush molecule.Comment: 6 pages, 8 figure

### Star Polymers Confined in a Nanoslit: A Simulation Test of Scaling and Self-Consistent Field Theories

The free energy cost of confining a star polymer where $f$ flexible polymer
chains containing $N$ monomeric units are tethered to a central unit in a slit
with two parallel repulsive walls a distance $D$ apart is considered, for good
solvent conditions. Also the parallel and perpendicular components of the
gyration radius of the star polymer, and the monomer density profile across the
slit are obtained. Theoretical descriptions via Flory theory and scaling
treatments are outlined, and compared to numerical self-consistent field
calculations (applying the Scheutjens-Fleer lattice theory) and to Molecular
Dynamics results for a bead-spring model. It is shown that Flory theory and
self-consistent field (SCF) theory yield the correct scaling of the parallel
linear dimension of the star with $N$, $f$ and $D$, but cannot be used for
estimating the free energy cost reliably. We demonstrate that the same problem
occurs already for the confinement of chains in cylindrical tubes. We also
briefly discuss the problem of a free or grafted star polymer interacting with
a single wall, and show that the dependence of confining force on the
functionality of the star is different for a star confined in a nanoslit and a
star interacting with a single wall, which is due to the absence of a symmetry
plane in the latter case.Comment: 15 pages, 9 figures, LaTeX, to appear in Soft Matte

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### Spatial segregation of mixed-sized counterions in dendritic polyelectrolytes

Langevin dynamics simulations are utilized to study the structure of a dendritic polyelectrolyte embedded in two component mixtures comprised of conventional (small) and bulky counterions. We vary two parameters that trigger conformational properties of the dendrimer: the reduced Bjerrum length, λ∗B, which controls the strength of electrostatic interactions and the number fraction of the bulky counterions, fb, which impacts on their steric repulsion. We find that the interplay between the electrostatic and the counterion excluded volume interactions affects the swelling behavior of the molecule. As compared to its neutral counterpart, for weak electrostatic couplings the charged dendrimer exists in swollen conformations whose size remains unaffected by fb. For intermediate couplings, the absorption of counterions into the pervaded volume of the dendrimer starts to influence its conformation. Here, the swelling factor exhibits a maximum which can be shifted by increasing fb. For strong electrostatic couplings the dendrimer deswells correspondingly to fb. In this regime a spatial separation of the counterions into core–shell microstructures is observed. The core of the dendrimer cage is preferentially occupied by the conventional ions, whereas its periphery contains the bulky counterions

### Unexpected crossover dynamics of single polymer in a corrugated tube

We present molecular dynamics study of a generic (coarse-grained) model for
single-polymer diffusion confined in a corrugated cylinder. For a narrow tube,
i.e., diameter of the cylinder $\delta < 2.3$, the axial diffusion coefficient
$D_{||}$ scales as $D_{||} \propto N^{-3/2}$, with chain length $N$, up to $N
\approx 100$ then crosses over to Rouse scaling for the larger $N$ values. The
$N^{-3/2}$ scaling is due to the large fluctuation of the polymer chain along
its fully stretched equilibrium conformation. The stronger scaling, namely
$N^{-3/2}$, is not observed for an atomistically smooth tube and/or for a
cylinder with larger diameter.Comment: 10 pages, 3 figures, LaTeX, version accepted by J. Chem. Phy

### Detachment of semiflexible polymer chains from a substrate - a Molecular Dynamics investigation

Using Molecular Dynamics simulations, we study the force-induced detachment
of a coarse-grained model polymer chain from an adhesive substrate. One of the
chain ends is thereby pulled at constant speed off the attractive substrate and
the resulting saw-tooth profile of the measured mean force vs height
$D$ of the end-segment over the plane is analyzed for a broad variety of
parameters. It is shown that the observed characteristic oscillations in the $<
f >$-$D$ profile depend on the bending and not on the torsional stiffness of
the detached chains. Allowing for the presence of hydrodynamic interactions
(HI) in a setup with explicit solvent and DPD-thermostat, rather than the case
of Langevin thermostat, one finds that HI have little effect on the -$D$
profile. Also the change of substrate affinity with respect to the solvent from
solvophilic to solvophobic is found to play negligible role in the desorption
process. In contrast, a changing ratio $\epsilon_s^A / \epsilon_s^B$ of the
binding energies of $A$- and $B$-segments in the detachment of an
$AB$-copolymer from adhesive surface strongly changes the $$-$D$ profile
whereby the $B$-spikes vanish when $\epsilon_s^A / \epsilon_s^B < 0.15$.
Eventually, performing an atomistic simulation of a (bio)-polymer {\it
polyglycine}, we demonstrate that the simulation results, derived from our
coarse-grained model, comply favorably with those from the all-atom simulation.Comment: Latex, 12 pages, 8 figures, to appear in JC

### Controlling the Interactions between Soft Colloids via Surface Adsorption

By employing monomer-resolved computer simulations and analytical
considerations based on polymer scaling theory, we analyze the conformations
and interactions of multiarm star polymers strongly adsorbed on a smooth,
two-dimensional plane. We find a stronger stretching of the arms as well as a
stronger repulsive, effective interaction than in the three dimensional case.
In particular, the star size scales with the number of arms $f$ as $\sim
f^{1/4}$ and the effective interaction as $\sim f^{2}$, as opposed to $\sim
f^{1/5}$ and $\sim f^{3/2}$, respectively, in three dimensions. Our results
demonstrate the dramatic effect that geometric confinement can have on the
effective interactions and the subsequent correlations of soft colloids in
general, for which the conformation can be altered as a result of geometrical
constraints imposed on them.Comment: 17 pages, LaTeX, 5 figures, to appear in Macromolecule

### Polymer chain scission at constant tension - an example of force-induced collective behaviour

The breakage of a polymer chain of segments, coupled by anharmonic bonds with
applied constant external tensile force is studied by means of Molecular
Dynamics simulation. We show that the mean life time of the chain becomes
progressively independent of the number of bonds as the pulling force grows.
The latter affects also the rupture rates of individual bonds along the polymer
backbone manifesting the essential role of inertial effects in the
fragmentation process. The role of local defects, temperature and friction in
the scission kinetics is also examined.Comment: 6 pages, 7 page

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