347 research outputs found
Individual Entanglements in a Simulated Polymer Melt
We examine entanglements using monomer contacts between pairs of chains in a
Brownian-dynamics simulation of a polymer melt. A map of contact positions with
respect to the contacting monomer numbers (i,j) shows clustering in small
regions of (i,j) which persists in time, as expected for entanglements. Using
the ``space''-time correlation function of the aforementioned contacts, we show
that a pair of entangled chains exhibits a qualitatively different behavior
than a pair of distant chains when brought together. Quantitatively, about 50%
of the contacts between entangled chains are persistent contacts not present in
independently moving chains. In addition, we account for several observed
scaling properties of the contact correlation function.Comment: latex, 12 pages, 7 figures, postscript file available at
http://arnold.uchicago.edu/~ebn
Renormalization of the one-loop theory of fluctuations in polymer blends and diblock copolymer melts
Attempts to use coarse-grained molecular theories to calculate corrections to
the random-phase approximation (RPA) for correlations in polymer mixtures have
been plagued by an unwanted sensitivity to the value of an arbitrary cutoff
length, {\it i.e.}, by an ultraviolet (UV) divergence. We analyze the UV
divergence of the inverse structure factor predicted by a
`one-loop' approximation similar to that used in several previous studies. We
consider both miscible homopolymer blends and disordered diblock copolymer
melts. We show, in both cases, that all UV divergent contributions can be
absorbed into a renormalization of the values of the phenomenological
parameters of a generalized self-consistent field theory (SCFT). This
observation allows the construction of a UV convergent theory of corrections to
SCFT phenomenology. The UV-divergent one-loop contribution to are
shown to be the sum of: (i) a -independent contribution that arises from a
renormalization of the effective parameter, (ii) a -dependent
contribution that arises from a renormalization of monomer statistical segment
lengths, (iii) a contribution proportional to that arises from a
square-gradient contribution to the one-loop fluctuation free energy, and (iv)
a -dependent contribution that is inversely proportional to the degree of
polymerization, which arises from local perturbations in fluid structure near
chain ends and near junctions between blocks in block copolymers.Comment: 35 pages, 2 figure
Unusual metallic phase in a chain of strongly interacting particles
We consider a one-dimensional lattice model with the nearest-neighbor
interaction and the next-nearest neighbor interaction with filling
factor 1/2 at zero temperature. The particles are assumed to be spinless
fermions or hard-core bosons. Using very simple assumptions we are able to
predict the basic structure of the insulator-metal phase diagram for this
model. Computations of the flux sensitivity support the main features of the
proposed diagram and show that the system maintains metallic properties at
arbitrarily large values of and along the line ,
where is the hopping amplitude, and . We think that close
to this line the system is a ``weak'' metal in a sense that the flux
sensitivity decreases with the size of the system not exponentially but as
with .Comment: To appear in J. Phys. C; 9 revtex preprint pages + 4 ps figures,
uuencode
Renormalized one-loop theory of correlations in polymer blends
The renormalized one-loop theory is a coarse-grained theory of corrections to
the self-consistent field theory (SCFT) of polymer liquids, and to the random
phase approximation (RPA) theory of composition fluctuations. We present
predictions of corrections to the RPA for the structure function and to
the random walk model of single-chain statics in binary homopolymer blends. We
consider an apparent interaction parameter that is defined by
applying the RPA to the small limit of . The predicted deviation of
from its long chain limit is proportional to , where
is chain length. This deviation is positive (i.e., destabilizing) for weakly
non-ideal mixtures, with \chi_{a} N \alt 1, but negative (stabilizing) near
the critical point. The positive correction to for low values of
is a result of the fact that monomers in mixtures of shorter
chains are slightly less strongly shielded from intermolecular contacts. The
depression in near the critical point is a result of long-wavelength
composition fluctuations. The one-loop theory predicts a shift in the critical
temperature of , which is much greater than the predicted
width of the Ginzburg region. Chain dimensions deviate
slightly from those of a random walk even in a one-component melt, and contract
slightly with increasing . Predictions for and single-chain
properties are compared to published lattice Monte Carlo simulations.Comment: submitted to J. Chem. Phy
Geometrical Properties of Two-Dimensional Interacting Self-Avoiding Walks at the Theta-Point
We perform a Monte Carlo simulation of two-dimensional N-step interacting
self-avoiding walks at the theta point, with lengths up to N=3200. We compute
the critical exponents, verifying the Coulomb-gas predictions, the theta-point
temperature T_theta = 1.4986(11), and several invariant size ratios. Then, we
focus on the geometrical features of the walks, computing the instantaneous
shape ratios, the average asphericity, and the end-to-end distribution
function. For the latter quantity, we verify in detail the theoretical
predictions for its small- and large-distance behavior.Comment: 23 pages, 4 figure
Adsorption transition of a self-avoiding polymer chain onto a rigid rod
The subject of this work is the adsorption transition of a long flexible
self-avoiding polymer chain onto a rigid thin rod. The rod is represented by a
cylinder of radius R with a short-ranged attractive surface potential for the
chain monomers. General scaling results are obtained by using renormalization
group arguments in conjunction with available results for quantum field
theories with curved boundaries [McAvity and Osborn 1993 Nucl. Phys. B 394,
728]. Relevant critical exponents are identified and estimated using geometric
arguments.Comment: 19 pages, 4 figures. To appear in: J. Phys.: Condens. Matter, special
issue dedicated to Lothar Schaefer on the occasion of his 60th birthda
Consistent coarse-graining strategy for polymer solutions in the thermal crossover from Good to Theta solvent
We extend our previously developed coarse-graining strategy for linear
polymers with a tunable number n of effective atoms (blobs) per chain [D'Adamo
et al., J. Chem. Phys. 137, 4901 (2012)] to polymer systems in thermal
crossover between the good-solvent and the Theta regimes. We consider the
thermal crossover in the region in which tricritical effects can be neglected,
i.e. not too close to the Theta point, for a wide range of chain volume
fractions Phi=c/c* (c* is the overlap concentration), up to Phi=30. Scaling
crossover functions for global properties of the solution are obtained by
Monte-Carlo simulations of the Domb-Joyce model. They provide the input data to
develop a minimal coarse-grained model with four blobs per chain. As in the
good-solvent case, the coarse-grained model potentials are derived at zero
density, thus avoiding the inconsistencies related to the use of
state-dependent potentials. We find that the coarse-grained model reproduces
the properties of the underlying system up to some reduced density which
increases when lowering the temperature towards the Theta state. Close to the
lower-temperature crossover boundary, the tetramer model is accurate at least
up to Phi<10, while near the good-solvent regime reasonably accurate results
are obtained up to Phi<2. The density region in which the coarse-grained model
is predictive can be enlarged by developing coarse-grained models with more
blobs per chain. We extend the strategy used in the good-solvent case to the
crossover regime. This requires a proper treatment of the length rescalings as
before, but also a proper temperature redefinition as the number of blobs is
increased. The case n=10 is investigated. Comparison with full-monomer results
shows that the density region in which accurate predictions can be obtained is
significantly wider than that corresponding to the n=4 case.Comment: 21 pages, 14 figure
Static Scaling Behavior of High-Molecular-Weight Polymers in Dilute Solution: A Reexamination
Previous theories of dilute polymer solutions have failed to distinguish
clearly between two very different ways of taking the long-chain limit: (I) at fixed temperature , and (II) ,
with fixed. I argue that the modern
two-parameter theory (continuum Edwards model) applies to case II --- not case
I --- and in fact gives exactly the crossover scaling functions for
modulo two nonuniversal scale factors. A Wilson-type renormalization group
clarifies the connection between crossover scaling functions and continuum
field theories. [Also contains a general discussion of the connection between
the Wilson and field-theoretic renormalization groups. Comments solicited.]Comment: 10 pages including 1 figure, 181159 bytes Postscript
(NYU-TH-93/05/01
Interacting Crumpled Manifolds: Exact Results to all Orders of Perturbation Theory
In this letter, we report progress on the field theory of polymerized
tethered membranes. For the toy-model of a manifold repelled by a single point,
we are able to sum the perturbation expansion in the strength g of the
interaction exactly in the limit of internal dimension D -> 2. This exact
solution is the starting point for an expansion in 2-D, which aims at
connecting to the well studied case of polymers (D=1). We here give results to
order (2-D)^4, where again all orders in g are resummed. This is a first step
towards a more complete solution of the self-avoiding manifold problem, which
might also prove valuable for polymers.Comment: 8 page
Evidence for ideal insulating/conducting state in a 1D integrable system
Using numerical diagonalization techniques we analyze the finite
temperature/frequency conductance of a one dimensional model of interacting
spinless fermions. Depending on the interaction, the observed finite
temperature charge stiffness and low frequency conductance indicate a
fundamental difference between integrable and non-integrable cases. The
integrable systems behave as ideal conductors in the metallic regime and as
ideal insulators in the insulating one. The non-integrable systems are, as
expected, generic conductors in the metallic regime and activated ones in the
insulating regime.Comment: revtex file, followed by 5 uuencoded postscript figure
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