title: Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases.
abstract: The short-range attraction and long-range repulsion between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces, or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion. At the ground state of the model (T = 0) the lattice is empty for small values of the chemical potential μ, and fully occupied for large μ. For intermediate values of μ periodically distributed clusters, bubbles, or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For T > 0 we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.
authors.affiliation: Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland.
authors.forename: J
authors.initials: J
authors.lastname: Pȩkalski
authors.affiliation: Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warszawa, Poland.
authors.forename: A
authors.initials: A
authors.lastname: Ciach
authors.affiliation: Instituto de Química Física Rocasolano, CSIC, Serrano 119, E-28006 Madrid, Spain.
authors.forename: N G
authors.initials: NG
authors.lastname: Almarza
mesh_terms: D019277:Entropy; D046911:Macromolecular Substances / Q000737:chemistry; D015394:Molecular Structure; D053758:Nanoparticles / Q000737:chemistry; D011789:Quantum Theory
chemical_list: D046911:Macromolecular Substances