5 research outputs found
Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations
The critical behavior of long straight rigid rods of length (-mers) on
square and triangular lattices at intermediate density has been studied. A
nematic phase, characterized by a big domain of parallel -mers, was found.
This ordered phase is separated from the isotropic state by a continuous
transition occurring at a intermediate density . Two analytical
techniques were combined with Monte Carlo simulations to predict the dependence
of on , being . The first involves
simple geometrical arguments, while the second is based on entropy
considerations. Our analysis allowed us also to determine the minimum value of
(), which allows the formation of a nematic phase on a
triangular lattice.Comment: 23 pages, 5 figures, to appear in The Journal of Chemical Physic
Entropy-driven phase transition in a system of long rods on a square lattice
The isotropic-nematic (I-N) phase transition in a system of long straight
rigid rods of length k on square lattices is studied by combining Monte Carlo
simulations and theoretical analysis. The process is analyzed by comparing the
configurational entropy of the system with the corresponding to a fully aligned
system, whose calculation reduces to the 1D case. The results obtained (1)
allow to estimate the minimum value of k which leads to the formation of a
nematic phase and provide an interesting interpretation of this critical value;
(2) provide numerical evidence on the existence of a second phase transition
(from a nematic to a non-nematic state) occurring at density close to 1 and (3)
allow to test the predictions of the main theoretical models developed to treat
the polymers adsorption problem.Comment: 14 pages, 6 figures. Accepted for publication in JSTA
Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition
Monte Carlo simulations and finite-size scaling analysis have been carried
out to study the critical behavior and universality for the isotropic-nematic
phase transition in a system of long straight rigid rods of length
(-mers) on two-dimensional lattices. The nematic phase, characterized by a
big domain of parallel -mers, is separated from the isotropic state by a
continuous transition occurring at a finite density. The determination of the
critical exponents, along with the behavior of Binder cumulants, indicate that
the transition belongs to the 2D Ising universality class for square lattices
and the three-state Potts universality class for triangular lattices.Comment: 7 pages, 8 figures, uses epl2.cls, to appear in Europhysics Letter
Nonmonotonic size dependence of the critical concentration in 2D percolation of straight rigid rods under equilibrium conditions
Numerical simulations and finite-size scaling analysis have been carried out
to study the percolation behavior of straight rigid rods of length
(-mers) on two-dimensional square lattices. The -mers, containing
identical units (each one occupying a lattice site), were adsorbed at
equilibrium on the lattice. The process was monitored by following the
probability that a lattice composed of sites
percolates at a concentration of sites occupied by particles of size
. A nonmonotonic size dependence was observed for the percolation threshold,
which decreases for small particles sizes, goes through a minimum, and finally
asymptotically converges towards a definite value for large segments. This
striking behavior has been interpreted as a consequence of the
isotropic-nematic phase transition occurring in the system for large values of
. Finally, the universality class of the model was found to be the same as
for the random percolation model.Comment: 21 pages, 4 figure