Nematic and gas-liquid transitions for sticky rods on square and cubic lattices

Interplay of orientational order and roughness in simulated thin film growth of anisotropically interacting particles

Roughness and orientational order in thin films of anisotropic particles are investigated using kinetic Monte Carlo simulations on a cubic lattice. Anisotropic next-neighbor interactions between the lattice particles were chosen to mimic the effects of shape anisotropy in the interactions of disk- or rodlike molecules with van der Waals attractions. Increasing anisotropy leads first to a preferred orientation in the film (which is close to the corresponding equilibrium transition) while the qualitative mode of roughness evolution (known from isotropic systems) does not change. At strong anisotropies, an effective step-edge (Ehrlich-Schwoebel) barrier appears and a nonequilibrium roughening effect is found, accompanied by reordering in the film which can be interpreted as the nucleation and growth of domains of lying-down disks or rods. The information on order and roughness is combined into a diagram of dynamic growth modes.

Entropy-driven phases at high coverage adsorption of straight rigid rods on two-dimensional square lattices

Polymers are frequently deposited on different surfaces, which has attracted the attention of scientists from different viewpoints. In the present approach polymers are represented by rigid rods of length k (k-mers), and the substrate takes the form of an L×L square lattice whose lattice constant matches exactly the interspacing between consecutive elements of the k-mer chain. We briefly review the classical description of the nematic transition presented by this system for k≥7 observing that the high-coverage (θ) transition deserves a more careful analysis from the entropy point of view. We present a possible viewpoint for this analysis that justifies the phase transitions. Moreover, we perform Monte Carlo (MC) simulations in the grand canonical ensemble, supplemented by thermodynamic integration, to first calculate the configurational entropy of the adsorbed phase as a function of the coverage, and then to explore the different phases (and orientational transitions) that appear on the surface with increasing the density of adsorbed k-mers. In the limit of θ→1 (full coverage) the configurational entropy is obtained for values of k ranging between 2 and 10. MC data are discussed in comparison with recent analytical results [D. Dhar and R. Rajesh, Phys. Rev. E 103, 042130 (2021)2470-004510.1103/PhysRevE.103.042130]. The comparative study allows us to establish the applicability range of the theoretical predictions. Finally, the structure of the high-coverage phase is characterized in terms of the statistics of k×l domains (domains of l parallel k-mers adsorbed on the surface). A distribution of finite values of l (l≪L) is found with a predominance of k×1 (single k-mers) and k×k domains. The distribution is the same in each lattice direction, confirming that at high density the adsorbed phase goes to a state with mixed orientations and no orientational preference. An order parameter measuring the number of k×k domains in the adsorbed layer is introduced.

Alternative characterization of the nematic transition in deposition of rods on two-dimensional lattices

We revisit the problem of excluded volume deposition of rigid rods of length k unit cells over square lattices. Two new features are introduced: (a) two new short-distance complementary order parameters, called Π and Σ, are defined, calculated, and discussed to deal with the phases present as coverage increases; (b) the interpretation is now done beginning at the high-coverage ordered phase which allows us to interpret the low-coverage nematic phase as an ergodicity breakdown present only when k≥7. In addition the data analysis invokes both mutability (dynamical information theory method) and Shannon entropy (static distribution analysis) to further characterize the phases of the system. Moreover, mutability and Shannon entropy are compared, and we report the advantages and disadvantages they present for their use in this problem.