Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods

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)].

Figure 1

(Color online) Fourth order Binder cumulant as a function of $\mu$ for different system sizes, at $T^{\ast }=0.25$ and $T^{\ast }=0.30$.

Figure 2

(Color online) Derivative of the density, $\rho$, as a function of the chemical potential, $\mu$, for different system sizes, at $T^{\ast }=0.25$ and $T^{\ast }=0.30$. A singularity is clearly signaled at both temperatures.

Figure 3

(Color online) System size dependence of the maximum of $k_{B}T{\left(\partial \rho /\partial \mu \right)}_T$, at $T^{\ast }=0.25$ and $T^{\ast }=0.30$. Simulation results are represented by points. Lines are fits to the scaling laws discussed in the text.

Figure 4

(Color online) System size dependence of the pseudocritical chemical potentials. See the text and the legend for details. Lines are least-squares fits to the MC results.

Figure 5

(Color online) Critical line of the SARR model. The diamonds and square are from Refs. [12, 14], respectively.

Figure 6

(Color online) Fourth order Binder cumulant as a function of $\mu$ for different system sizes, at $T^{\ast }=0.15$ and $T^{\ast }=0.40$.

Figure 7

(Color online) Critical lines from MC simulation (points), theory of self-assembly (dashed), and mean-field theory (dashed-dotted). Crossover line is the full line. Left panel: $\mu ,T$ diagram. Right panel: $\rho ,T$ diagram. See text for details.

Figure 8

(Color online) Internal energy per particle on the critical line. Points: MC simulation, dashed: theory of self-assembly, dashed-dotted: mean-field theory. See text for details.

Figure 9

(Color online) Fourth order Binder cumulants for different system sizes as a function of the scaling densities in the $q=1$ and $q=2$ universality classes, at $T^{\ast }=0.30$.