31 research outputs found
Phase diagram of a bidispersed hard rod lattice gas in two dimensions
We obtain, using extensive Monte Carlo simulations, virial expansion and a
high-density perturbation expansion about the fully packed monodispersed phase,
the phase diagram of a system of bidispersed hard rods on a square lattice. We
show numerically that when the length of the longer rods is , two continuous
transitions may exist as the density of the longer rods in increased, keeping
the density of shorter rods fixed: first from a low-density isotropic phase to
a nematic phase, and second from the nematic to a high-density isotropic phase.
The difference between the critical densities of the two transitions decreases
to zero at a critical density of the shorter rods such that the fully packed
phase is disordered for any composition. When both the rod lengths are larger
than , we observe the existence of two transitions along the fully packed
line as the composition is varied. Low-density virial expansion, truncated at
second virial coefficient, reproduces features of the first transition. By
developing a high-density perturbation expansion, we show that when one of the
rods is long enough, there will be at least two isotropic-nematic transitions
along the fully packed line as the composition is varied.Comment: 7 pages, 4 figure
Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice
We study the Bethe approximation for a system of long rigid rods of fixed
length k, with only excluded volume interaction. For large enough k, this
system undergoes an isotropic-nematic phase transition as a function of density
of the rods. The Bethe lattice, which is conventionally used to derive the
self-consistent equations in the Bethe approximation, is not suitable for
studying the hard-rods system, as it does not allow a dense packing of rods. We
define a new lattice, called the random locally tree-like layered lattice,
which allows a dense packing of rods, and for which the approximation is exact.
We find that for a 4-coordinated lattice, k-mers with k>=4 undergo a continuous
phase transition. For even coordination number q>=6, the transition exists only
for k >= k_{min}(q), and is first order.Comment: 10 pages, 10 figure
Entropy of polydisperse chains: solution on the Bethe lattice
We consider the entropy of polydisperse chains placed on a lattice. In
particular, we study a model for equilibrium polymerization, where the
polydispersivity is determined by two activities, for internal and endpoint
monomers of a chain. We solve the problem exactly on a Bethe lattice with
arbitrary coordination number, obtaining an expression for the entropy as a
function of the density of monomers and mean molecular weight of the chains. We
compare this entropy with the one for the monodisperse case, and find that the
excess of entropy due to polydispersivity is identical to the one obtained for
the one-dimensional case. Finally, we obtain an exponential distribution of
molecular weights.Comment: 5 pages, 2 figures. Reference place
Semi-flexible trimers on the square lattice in the full lattice limit
Trimers are chains formed by two lattice edges, and therefore three monomers.
We consider trimers placed on the square lattice, the edges belonging to the
same trimer are either colinear, forming a straight rod with unitary
statistical weight, or perpendicular, a statistical weight being
associated to these angular trimers. The thermodynamic properties of this model
are studied in the full lattice limit, where all lattice sites are occupied by
monomers belonging to trimers. In particular, we use transfer matrix techniques
to estimate the entropy of the system as a function of . The entropy
is a maximum at and our results are compared to earlier
studies in the literature for straight trimers (), angular trimers
() and for mixtures of equiprobable straight and angular
trimers ().Comment: 6 pages, 4 figure
Entropy of chains placed on the square lattice
We obtain the entropy of flexible linear chains composed of M monomers placed
on the square lattice using a transfer matrix approach. An excluded volume
interaction is included by considering the chains to be self-and mutually
avoiding, and a fraction rho of the sites are occupied by monomers. We solve
the problem exactly on stripes of increasing width m and then extrapolate our
results to the two-dimensional limit to infinity using finite-size scaling. The
extrapolated results for several finite values of M and in the polymer limit M
to infinity for the cases where all lattice sites are occupied (rho=1) and for
the partially filled case rho<1 are compared with earlier results. These
results are exact for dimers (M=2) and full occupation (\rho=1) and derived
from series expansions, mean-field like approximations, and transfer matrix
calculations for some other cases. For small values of M, as well as for the
polymer limit M to infinity, rather precise estimates of the entropy are
obtained.Comment: 6 pages, 7 figure
Potential of mean force and the charge reversal of rodlike polyions
A simple model is presented to calculate the potential of mean force between
a polyion and a multivalent counterion inside a polyelectrolite solution. We
find that under certain conditions the electrostatic interactions can lead to a
strong attraction between the polyions and the multivalent counterions,
favoring formation of overcharged polyion-counterion complexes. It is found
that small concentrations of salt enhance the overcharging, while an excessive
amount of salt hinders the charge reversal. The kinetic limitations to
overcharging are also examined.Comment: To be published in the special issue of Molecular Physics in honor of
Prof. Ben Wido
Polymers with attractive interactions on the Husimi tree
We obtain the solution of models of self-avoiding walks with attractive
interactions on Husimi lattices built with squares. Two attractive interactions
are considered: between monomers on first-neighbor sites and not consecutive
along a walk and between bonds located on opposite edges of elementary squares.
For coordination numbers q>4, two phases, one polymerized the other
non-polymerized, are present in the phase diagram. For small values of the
attractive interaction the transition between those phases is continuous, but
for higher values a first-order transition is found. Both regimes are separated
by a tricritical point. For q=4 a richer phase diagram is found, with an
additional (dense) polymerized phase, which is stable for for sufficiently
strong interactions between bonds. The phase diagram of the model in the
three-dimensional parameter space displays surfaces of continuous and
discontinuous phase transitions and lines of tricritical points, critical
endpoints and triple points.Comment: 7 pages, 6 figure