Comment on “Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods” (original) (raw)
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Physical Review E, 2012
We comment on the nature of the ordering transition of a model of equilibrium polydisperse rigid rods, on the square lattice, which is reported by López et al. to exhibit random percolation criticality in the canonical ensemble, in sharp contrast to (i) our results of Ising criticality for the same model in the grand canonical ensemble [Phys. Rev. E 82, 061117 (2010)] and (ii) the absence of exponent(s) renormalization for constrained systems with logarithmic specific heat anomalies predicted on very general grounds by Fisher [M.E. Fisher, Phys. Rev. 176, 257 (1968)].
Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods
Physical Review E, 2010
Extensive Monte Carlo simulations were carried out to investigate the nature of the ordering transition of a model of adsorbed self-assembled rigid rods on the bonds of a square lattice [Tavares et. al., Phys. Rev E 79, 021505 (2009)]. The polydisperse rods undergo a continuous ordering transition that is found to be in the two-dimensional Ising universality class, as in models where the rods are monodisperse. This finding is in sharp contrast with the recent claim that equilibrium polydispersity changes the nature of the phase transition in this class of models [López et. al., Phys. Rev E 80, 040105(R)(2009)].
Physical Review E, 2009
Monte Carlo simulations have been carried out for a system of monomers on square lattices that, by decreasing temperature or increasing density, polymerize reversibly into chains with two allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The results show that the self-assembly process affects the nature of the transition. Thus, the calculation of the critical exponents and the behavior of Binder cumulants indicate that the universality class of the IN transition changes from two-dimensional Ising-type for monodisperse rods without self-assembly to q = 1 Potts-type for self-assembled rods. PACS numbers: 05.50.+q, 64.70.mf, 61.20.Ja, 64.75.Yz, 75.40.Mg Self-assembly is a challenging field of research, driven principally by the desire to design new materials. Moreover, self-assembly is used permanently in biological systems to construct supramolecular structures such as virus capsids, filaments, and many others large molecular complexes. So, understanding the rules of self-assembly has important applications to both materials science and biology [1].
The Journal of chemical …, 2010
Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with Mean Field (MF) and Real Space Renormalization Group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.
The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices
We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length k on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for k = 7. On the square lattice, our best estimates of the critical exponents differ from those of the Ising model, but we cannot rule out a crossover to Ising universality class at larger length scales. On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class. We study the correlations in the high-density non-nematic phase, and find evidence of a very large correlation length 2000.
Critical behavior of self-assembled rigid rods on triangular and honeycomb lattices
The Journal of chemical …, 2010
Using Monte Carlo simulations and finite-size scaling analysis, the critical behavior of selfassembled rigid rods on triangular and honeycomb lattices at intermediate density has been studied. The system is composed of monomers with two attractive (sticky) poles that, by decreasing temperature or increasing density, polymerize reversibly into chains with three allowed directions and, at the same time, undergo a continuous isotropic-nematic IN transition. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the IN transition belongs to the q = 1 Potts universality class.
Polydispersity and Ordered Phases in Solutions of Rodlike Macromolecules
Physical Review Letters, 1996
We apply density functional theory to study the influence of polydispersity on the stability of columnar, smectic and solid ordering in the solutions of rodlike macromolecules. For sufficiently large length polydispersity (standard deviation σ > 0.25) a direct first-order nematic-columnar transition is found, while for smaller σ there is a continuous nematic-smectic and first-order smectic-columnar transition.
The criticality of self-assembled rigid rods on triangular lattices
2010
The criticality of self-assembled rigid rods on triangular lattices is investigated using Monte Carlo simulation. We find a continuous transition between an ordered phase, where the rods are oriented along one of the three (equivalent) lattice directions, and a disordered one. We conclude that equilibrium polydispersity of the rod lengths does not affect the critical behavior, as we found that the criticality is the same as that of monodisperse rods on the same lattice, in contrast with the results of recently published work on similar models.
Communication: The criticality of self-assembled rigid rods on triangular lattices
Chemical Physics, 2011
The criticality of self-assembled rigid rods on triangular lattices is investigated using Monte Carlo simulation. We find a continuous transition between an ordered phase, where the rods are oriented along one of the three (equivalent) lattice directions, and a disordered one. We conclude that equilibrium polydispersity of the rod lengths does not affect the critical behavior, as we found that the criticality is the same as that of monodisperse rods on the same lattice, in contrast with the results of recently published work on similar models.
Universal sequence of ordered structures obtained from mesoscopic description of self-assembly
Physical Review E, 2008
Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived by a systematic coarse-graining procedure. For particles interacting with spherically symmetric potentials of arbitrary form, the grand-thermodynamic potential consists of two terms. The first term is associated with microscopic length-scale fluctuations, and has the form of the standard density functional. The second term is associated with mesoscopic length-scale fluctuations, and has the form known from the statistical field theory. For the correlation function between density fluctuations in mesoscopic regions, a pair of equations similar to the Ornstein-Zernicke equation with a new closure is obtained. In the special case of weak ordering on the mesoscopic length scale, the theory takes a form similar to either the Landau-Ginzburg-Wilson ͑LGW͒ or the Landau-Brazovskii ͑LB͒ field theory, depending on the form of the interaction potential. Microscopic expressions for the phenomenological parameters that appear in the Landau-type theories are obtained. Within the framework of this theory, we obtain a universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered, for increasing density well below the close-packing density. The sequence of phases agrees with experimental observations and with simulations of many self-assembling systems. In addition to the above phases, more complex phases may appear depending on the interaction potentials. For a particular form of the short-range attraction long-range repulsion potential, we find the bicontinuous gyroid phase ͑Ia3d symmetry͒ that may be related to a network-forming cluster of colloids in a mixture of colloids and nonadsorbing polymers.