Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

Abstract

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.

Dynamical density functional theory for colloidal particles with arbitrary shape

“…Rod-like particles [11,12] like spherocylinders, spheroids, and ellipsoids are the most simple anisotropic colloidal particles. They are convex and apolar and of big importance since they may evolve the industrially important nematic phase and serve as excellent model systems for most liquid crystals [13][14][15]. A further member of convex and apolar particles are the platelets [16][17][18][19][20].…”

Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations

“…6); and (d) a logarithmic decrease with θ of the critical curve when θ → 0, in agreement with other analytical approach. 9 In an earlier study, 22 in which the critical behavior of SARRs on the square lattice was addressed, it was shown that in the full coverage case (θ = 1.0), the Hamiltonian of the SARRs model maps exactly onto the Ising model one (q = 2 Potts model) with coupling constant w I sing = w SARRs /4. In contrast, the 2D SARRs model on the triangular lattice cannot be mapped on q = 3 Potts model, as can be easily seen from Eq.…”

“…Figure 3 shows the critical line reported in Ref. 22 and only one point (the lowest coverage obtained) of the critical line reported in Ref. 16.…”

“…21 Among the studies of the second group, the temperaturecoverage phase diagram of SARRs on square lattices was calculated in Ref. 22. By using MC simulations, mean-field theory, and a renormalization group (RSRG) approach, the critical line which separates regions of isotropic and nematic stability was obtained and characterized.…”

“…[11][12][13][14] From the seminal work by Tavares et al, 9 a series of papers exploring the self-assembled rigid rods (SARRs) model have been published. [15][16][17][18][19][20][21][22][23] These studies can be separated in two groups: (i) those dealing with the nature and universality of the phase transition occurring in the system [15][16][17][18][19][20][21] and (ii) those dealing with the temperature-coverage phase diagram of the system. 22,23 With respect to the first point, the universality class of the model has been a subject of controversy.…”