Comment on "effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods"

Orientational phase transition in monolayers of multipolar straight rigid rods: The case of 2-thiophene molecule adsorption on the Au(111) surface

Monte Carlo simulations and finite-size scaling theory have been carried out to study the critical behavior and universality for the isotropic-nematic (IN) phase transition in a system of straight rigid pentamers adsorbed on a triangular lattice with polarized nonhomogeneous intermolecular interactions. The model was inspired by the deposition of 2-thiophene molecules over the Au(111) surface, which was previously characterized by experimental techniques and density functional theory. A nematic phase, observed experimentally by the formation of a self-assembled monolayer of parallel molecules, is separated from the isotropic state by a continuous transition occurring at a finite density. The precise determination of the critical exponents indicates that the transition belongs to the three-state Potts universality class. The finite-size scaling analysis includes the study of mutability and diversity. These two quantities are derived from information theory and they have not previously been considered as part of the conventional treatment of critical phenomena for the determination of critical exponents. The results obtained here contribute to the understanding of formation processes of self-assembled monolayers, phase transitions, and critical phenomena from novel compression algorithms for studying mutual information in sequences of data.

Percolation thresholds of randomly rotating patchy particles on Archimedean lattices

We study the percolation of randomly rotating patchy particles on 11 Archimedean lattices in two dimensions. Each vertex of the lattice is occupied by a particle, and in each model the patch size and number are monodisperse. When there are more than one patches on the surface of a particle, they are symmetrically decorated. As the proportion χ of the particle surface covered by the patches increases, the clusters connected by the patches grow and the system percolates at the threshold χ_{c}. We combine Monte Carlo simulations and the critical polynomial method to give precise estimates of χ_{c} for disks with one to six patches and spheres with one to two patches on the 11 lattices. For one-patch particles, we find that the order of χ_{c} values for particles on different lattices is the same as that of threshold values p_{c} for site percolation on these lattices, which implies that χ_{c} for one-patch particles mainly depends on the geometry of lattices. For particles with more patches, symmetry becomes very important in determining χ_{c}. With the estimates of χ_{c} for disks with one to six patches, using analyses related to symmetry, we are able to give precise values of χ_{c} for disks with an arbitrary number of patches on all 11 lattices. The following rules are found for patchy disks on each of these lattices: (1) as the number of patches n increases, values of χ_{c} repeat in a periodic way, with the period n_{0} determined by the symmetry of the lattice; (2) when mod(n,n_{0})=0, the minimum threshold value χ_{min} appears, and the model is equivalent to site percolation with χ_{min}=p_{c}; and (3) disks with mod(n,n_{0})=m and n_{0}-m (m<n_{0}/2) share the same χ_{c} value. The results can be useful references for studying the connectivity of patchy particles on two-dimensional lattices at finite temperatures.

Self-assembled monolayer formation of pentamers-like molecules onto FCC(111) surfaces: the case of curcuminoids onto Au(111) surface

The adsorption of rigid straight electrically polarized pentamers over a FCC(111) surface is studied. The model was inspired by the deposition of 2-thiophene molecules over the Au(111) surface, which was previously characterized by experimental techniques and simulated under the frame of the density functional theory. We now obtain and report the charge distribution of the molecule which allows to propose a deposition model followed by Monte Carlo simulations over an ad-hoc lattice gas model. We show that for a certain value of the chemical potential there exists an isotropic-nematic phase transition which can explain the formation of a self-assembled monolayer like the one observed in the transmission electron microscopy images. An order parameter is defined to characterize the transition which presents a step-like behavior at a critical chemical potential value. The possible nature of the nematic transition in conjunction with an ergodicity breakdown is discussed as future work by means of statistical physics techniques.

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

The critical behavior of adsorbed monomers that reversibly polymerize into linear chains with restricted orientations relative to the substrate has been studied. In the model considered here, which is known as self-assembled rigid rods (SARRs) model, the surface is represented by a two-dimensional lattice and a continuous orientational transition occurs as a function of temperature and coverage. The phase diagrams were obtained for the square, triangular, and honeycomb lattices by means of Monte Carlo simulations and finite-size scaling analysis. The numerical results were compared with Bethe-Peierls analytical predictions about the orientational transition for the square and triangular lattices. The analysis of the phase diagrams, along with the behavior of the critical average rod lengths, showed that the critical properties of the model do not depend on the structure of the lattice at low temperatures (coverage), revealing a quasi-one-dimensional behavior in this regime. Finally, the universality class of the SARRs model, which has been subject of controversy, has been revisited.

Adsorption of self-assembled rigid rods on two-dimensional lattices

Monte Carlo (MC) simulations have been carried out to study the adsorption on square and triangular lattices of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with a discrete number of allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The process has been monitored by following the behavior of the adsorption isotherms (chemical potential μ as a function of the surface coverage θ) for different values of lateral interaction energy/temperature. The numerical data were compared with mean-field analytical predictions and exact functions for noninteracting and 1D systems. The obtained results revealed the existence of three adsorption regimes in temperature. (1) At high temperatures, above the critical one characterizing the IN transition at full coverage T(c)(θ = 1), the particles are distributed at random on the surface and the adlayer behaves as a noninteracting 2D system. (2) At very low temperatures, the asymmetric monomers adsorb, forming chains over almost the entire range of coverage, and the adsorption process behaves as a 1D problem. (3) In the intermediate regime, the system exhibits a mixed regime and the filling of the lattice proceeds according to two different processes. In the first stage, the monomers adsorb isotropically on the lattice until the IN transition occurs in the system and, from this point, particles adsorb, forming chains so that the adlayer behaves as a 1D fluid. The two adsorption processes are present in the adsorption isotherms, and a marked singularity can be observed that separates both regimes. Thus, the adsorption isotherms appear as sensitive quantities with respect to the IN phase transition, allowing us (i) to reproduce the phase diagram of the system for square lattices and (ii) to obtain an accurate determination of the phase diagram for triangular lattices.