Doniach Lattice Gas on Bipartite Lattices in the Mean-Field Approximation

The Doniach lattice gas (DLG) consists of a statistical model that can be mapped into a spin-1 Ising model with highly degenerate single-site states and the inclusion─using the nomenclature of the analogous magnetic model─of dipole-quadrupole interactions, besides the usual dipole-dipole, Zeeman-effect and crystal-field interactions. Its formulation was motivated aiming at the study of phase transitions in supramolecular structures of zwitterionic phospholipids, in particular, allowing an alternative description of density fluctuations in the system, already included in a certain class of lattice models (Nagle, J. F. <i>J. Chem. Phys.</i> <b>1973</b>, <i>58</i>, 252; Nagle, J. F. <i>J. Chem. Phys.</i> <b>1975</b>, <i>63</i>, 1255), but not considered in previous proposals of Ising-type models (Doniach, S. <i>J. Chem. Phys.</i> <b>1978</b>, <i>68</i>, 4912). In this work, we investigate the DLG model, considering the division of the system into two interpenetrating sublattices, under the framework of the mean-field approximation. This analysis of the model on bipartite lattices allowed the investigation of staggered phases, which were overlooked in the first analysis of the model in the mean-field approach (Guidi, H. S.; Henriques, V. B. <i>Phys. Rev. E</i> <b>2014</b>, <i>90</i>, 052705), precisely because it was only assumed the presence of uniform phases, i.e., without splitting the system into two distinct sublattices. However, such staggered phases were observed for this model in the pair approximation on bipartite lattices (de Oliveira, F. O.; Tamashiro, M. N. <i>Phys. Rev. E</i> <b>2019</b>, <i>99</i>, 012147; de Oliveira, F. O.; Tamashiro, M. N. <i>Langmuir</i> <b>2019</b>, <i>35</i>, 3848). Throughout the work, in addition to the staggered phase, we also observed intermediate topologies of representative phase diagrams (μ̅/<i>z</i>, <i>t</i>/<i>z</i>), which explain the development of the main topologies as we change the parameters (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>l</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>, <i>k̅</i>) associated with the effective Hamiltonian interactions. Finally, we perform a parameter fitting between theoretical results and isothermal compression experimental data for the phospholipid 1,2-dimyristoyl-<i>sn</i>-glycero-3-phosphocholine (DMPC), allowing also a comparison between the fittings obtained using the mean-field and the pair approximations.