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

PASINETTI, P. M.; RAMIREZ-PASTOR, A. J.; VOGEL, E. E.; SARAVIA, G.

Physical Review E

APS

Año: 2021 vol. 104

2470-0045

Polymers are frequently deposited on different surfaces, which has attracted the attention of scientists fromdifferent viewpoints. In the present approach polymers are represented by rigid rods of length k (k-mers), andthe substrate takes the form of an L × L square lattice whose lattice constant matches exactly the interspacingbetween consecutive elements of the k-mer chain. We briefly review the classical description of the nematictransition presented by this system for k 7 observing that the high-coverage (θ) transition deserves a morecareful analysis from the entropy point of view. We present a possible viewpoint for this analysis that justifiesthe 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 phaseas a function of the coverage, and then to explore the different phases (and orientational transitions) thatappear 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 incomparison with recent analytical results [D. Dhar and R. Rajesh, Phys. Rev. E 103, 042130 (2021)]. Thecomparative study allows us to establish the applicability range of the theoretical predictions. Finally, thestructure of the high-coverage phase is characterized in terms of the statistics of k × l domains (domains of lparallel k-mers adsorbed on the surface). A distribution of finite values of l (l L) is found with a predominanceof k × 1 (single k-mers) and k × k domains. The distribution is the same in each lattice direction, confirmingthat 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.