4,103 research outputs found
Identification of a polymer growth process with an equilibrium multi-critical collapse phase transition: the meeting point of swollen, collapsed and crystalline polymers
We have investigated a polymer growth process on the triangular lattice where
the configurations produced are self-avoiding trails. We show that the scaling
behaviour of this process is similar to the analogous process on the square
lattice. However, while the square lattice process maps to the collapse
transition of the canonical interacting self-avoiding trail model (ISAT) on
that lattice, the process on the triangular lattice model does not map to the
canonical equilibrium model. On the other hand, we show that the collapse
transition of the canonical ISAT model on the triangular lattice behaves in a
way reminiscent of the -point of the interacting self-avoiding walk
model (ISAW), which is the standard model of polymer collapse. This implies an
unusual lattice dependency of the ISAT collapse transition in two dimensions.
By studying an extended ISAT model, we demonstrate that the growth process
maps to a multi-critical point in a larger parameter space. In this extended
parameter space the collapse phase transition may be either -point-like
(second-order) or first-order, and these two are separated by a multi-critical
point. It is this multi-critical point to which the growth process maps.
Furthermore, we provide evidence that in addition to the high-temperature
gas-like swollen polymer phase (coil) and the low-temperature liquid drop-like
collapse phase (globule) there is also a maximally dense crystal-like phase
(crystal) at low temperatures dependent on the parameter values. The
multi-critical point is the meeting point of these three phases. Our
hypothesised phase diagram resolves the mystery of the seemingly differing
behaviours of the ISAW and ISAT models in two dimensions as well as the
behaviour of the trail growth process
Unbiased sampling of globular lattice proteins in three dimensions
We present a Monte Carlo method that allows efficient and unbiased sampling
of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit
each lattice site exactly once. They are often used as simple models of
globular proteins, upon adding suitable local interactions. Our algorithm can
easily be equipped with such interactions, but we study here mainly the
flexible homopolymer case where each conformation is generated with uniform
probability. We argue that the algorithm is ergodic and has dynamical exponent
z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers.
Results are presented for the effective interaction between end points, and the
interaction with the boundaries of the system
On the orientational ordering of long rods on a lattice
We argue that a system of straight rigid rods of length k on square lattice
with only hard-core interactions shows two phase transitions as a function of
density, rho, for k >= 7. The system undergoes a phase transition from the
low-density disordered phase to a nematic phase as rho is increased from 0, at
rho = rho_c1, and then again undergoes a reentrant phase transition from the
nematic phase to a disordered phase at rho = rho_c2 < 1.Comment: epl.cl
Non-Equilibrium in Adsorbed Polymer Layers
High molecular weight polymer solutions have a powerful tendency to deposit
adsorbed layers when exposed to even mildly attractive surfaces. The
equilibrium properties of these dense interfacial layers have been extensively
studied theoretically. A large body of experimental evidence, however,
indicates that non-equilibrium effects are dominant whenever monomer-surface
sticking energies are somewhat larger than kT, a common case. Polymer
relaxation kinetics within the layer are then severely retarded, leading to
non-equilibrium layers whose structure and dynamics depend on adsorption
kinetics and layer ageing. Here we review experimental and theoretical work
exploring these non-equilibrium effects, with emphasis on recent developments.
The discussion addresses the structure and dynamics in non-equilibrium polymer
layers adsorbed from dilute polymer solutions and from polymer melts and more
concentrated solutions. Two distinct classes of behaviour arise, depending on
whether physisorption or chemisorption is involved. A given adsorbed chain
belonging to the layer has a certain fraction of its monomers bound to the
surface, f, and the remainder belonging to loops making bulk excursions. A
natural classification scheme for layers adsorbed from solution is the
distribution of single chain f values, P(f), which may hold the key to
quantifying the degree of irreversibility in adsorbed polymer layers. Here we
calculate P(f) for equilibrium layers; we find its form is very different to
the theoretical P(f) for non-equilibrium layers which are predicted to have
infinitely many statistical classes of chain. Experimental measurements of P(f)
are compared to these theoretical predictions.Comment: 29 pages, Submitted to J. Phys.: Condens. Matte
Dynamics of Spreading of Small Droplets of Chainlike Molecules on Surfaces
Dynamics of spreading of small droplets on surfaces has been studied by the
molecular dynamics method. Simulations have been performed for mixtures of
solvent and dimer, and solvent and tetramer droplets. For solvent particles and
dimers, layering occurs leading to stepped droplet shapes. For tetramers such
shapes occur for relatively deep and strong surface potentials only. For wider
and more shallow potentials, more rapid spreading and rounded droplet shapes
occur. These results are in accordance with experimental data on small non -
volatile polymer droplets. PACS numbers: 68.10Gw, 05.70.Ln, 61.20.Ja, 68.45GdComment: to appear in Europhys. Letters (1994), Latex, 12 page
Elastic Energy and Phase Structure in a Continuous Spin Ising Chain with Applications to the Protein Folding Problem
We present a numerical Monte Carlo analysis of a continuos spin Ising chain
that can describe the statistical proterties of folded proteins. We find that
depending on the value of the Metropolis temperature, the model displays the
three known nontrivial phases of polymers: At low temperatures the model is in
a collapsed phase, at medium temperatures it is in a random walk phase, and at
high temperatures it enters the self-avoiding random walk phase. By
investigating the temperature dependence of the specific energy we confirm that
the transition between the collapsed phase and the random walk phase is a phase
transition, while the random walk phase and self-avoiding random walk phase are
separated from each other by a cross-over transition. We also compare the
predictions of the model to a phenomenological elastic energy formula, proposed
by Huang and Lei to describe folded proteins.Comment: 12 pages, 23 figures, RevTeX 4.
Pattern formation driven by nematic ordering of assembling biopolymers
The biopolymers actin and microtubules are often in an ongoing
assembling/disassembling state far from thermal equilibrium. Above a critical
density this leads to spatially periodic patterns, as shown by a scaling
argument and in terms of a phenomenological continuum model, that meets also
Onsager's statistical theory of the nematic--to--isotropic transition in the
absence of reaction kinetics.
This pattern forming process depends much on nonlinear effects and a common
linear stability analysis of the isotropic distribution of the filaments is
often misleading. The wave number of the pattern decreases with the
assembling/disassembling rate and there is an uncommon discontinuous transition
between the nematic and the periodic state.Comment: 4 pages, 3 figure
Phases and Transitions in Phantom Nematic Elastomer Membranes
Motivated by recently discovered unusual properties of bulk nematic
elastomers, we study a phase diagram of liquid-crystalline polymerized phantom
membranes, focusing on in-plane nematic order. We predict that such membranes
should enerically exhibit five phases, distinguished by their conformational
and in-plane orientational properties, namely isotropic-crumpled,
nematic-crumpled, isotropic-flat, nematic-flat and nematic-tubule phases. In
the nematic-tubule phase, the membrane is extended along the direction of {\em
spontaneous} nematic order and is crumpled in the other. The associated
spontaneous symmetries breaking guarantees that the nematic-tubule is
characterized by a conformational-orientational soft (Goldstone) mode and the
concomitant vanishing of the in-plane shear modulus. We show that long-range
orientational order of the nematic-tubule is maintained even in the presence of
harmonic thermal luctuations. However, it is likely that tubule's elastic
properties are ualitatively modified by these fluctuations, that can be studied
using a nonlinear elastic theory for the nematic tubule phase that we derive at
the end of this paper.Comment: 12 pages, 4 eps figures. To appear in PR
Splitting of Andreev levels in a Josephson junction by spin-orbit coupling
We consider the effect of spin-orbit coupling on the energy levels of a
single-channel Josephson junction below the superconducting gap. We investigate
quantitatively the level splitting arising from the combined effect of
spin-orbit coupling and the time-reversal symmetry breaking by the phase
difference between the superconductors. Using the scattering matrix approach we
establish a simple connection between the quantum mechanical time delay matrix
and the effective Hamiltonian for the level splitting. As an application we
calculate the distribution of level splittings for an ensemble of chaotic
Josephson junctions. The distribution falls off as a power law for large
splittings, unlike the exponentially decaying splitting distribution given by
the Wigner surmise -- which applies for normal chaotic quantum dots with
spin-orbit coupling in the case that the time-reversal symmetry breaking is due
to a magnetic field.Comment: 6 pages, 3 figure
Microscopic Model for Granular Stratification and Segregation
We study segregation and stratification of mixtures of grains differing in
size, shape and material properties poured in two-dimensional silos using a
microscopic lattice model for surface flows of grains. The model incorporates
the dissipation of energy in collisions between rolling and static grains and
an energy barrier describing the geometrical asperities of the grains. We study
the phase diagram of the different morphologies predicted by the model as a
function of the two parameters. We find regions of segregation and
stratification, in agreement with experimental finding, as well as a region of
total mixing.Comment: 4 pages, 7 figures, http://polymer.bu.edu/~hmakse/Home.htm
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