title: Charge-regulation phase transition on surface lattices of titratable sites adjacent to electrolyte solutions: An analog of the Ising antiferromagnet in a magnetic field.
abstract: We report a charge-patterning phase transition on two-dimensional square lattices of titratable sites, here regarded as protonation sites, placed in a low-dielectric medium just below the planar interface between this medium and a salt solution. We calculate the work-of-charging matrix of the lattice with use of a linear Debye-Hückel model, as input to a grand-canonical partition function for the distribution of occupancy patterns. For a large range of parameter values, this model exhibits an approximate inverse cubic power-law decrease of the voltage produced by an individual charge, as a function of its in-lattice separation from neighboring titratable sites. Thus, the charge coupling voltage biases the local probabilities of proton binding as a function of the occupancy of sites for many neighbors beyond the nearest ones. We find that even in the presence of these longer-range interactions, the site couplings give rise to a phase transition in which the site occupancies exhibit an alternating, checkerboard pattern that is an analog of antiferromagnetic ordering. The overall strength W of this canonical charge coupling voltage, per unit charge, is a function of the Debye length, the charge depth, the Bjerrum length, and the dielectric coefficients of the medium and the solvent. The alternating occupancy transition occurs above a curve of thermodynamic critical points in the (pH-pK,W) plane, the curve representing a charge-regulation analog of variation of the Néel temperature of an Ising antiferromagnet as a function of an applied, uniform magnetic field. The analog of a uniform magnetic field in the antiferromagnet problem is a combination of pH-pK and W, and 1/W is the analog of the temperature in the antiferromagnet problem. We use Monte Carlo simulations to study the occupancy patterns of the titratable sites, including interactions out to the 37th nearest-neighbor category (a distance of √74 lattice constants), first validating simulations through comparison with exact and approximate results for the nearest-neighbor case. We then use the simulations to map the charge-patterning phase boundary in the (pH-pK,W) plane. The physical parameters that determine W provide a framework for identifying and designing real surfaces that could exhibit charge-patterning phase transitions.
authors.affiliation: School of Physics and Astronomy, Rochester Institute of Technology, Rochester, New York 14623-5603, USA.
authors.forename: Joel D
authors.initials: JD
authors.lastname: Shore
authors.affiliation: School of Physics and Astronomy, Rochester Institute of Technology, Rochester, New York 14623-5603, USA.
authors.forename: George M
authors.initials: GM
authors.lastname: Thurston
mesh_terms: D017097:Electric Impedance; D004573:Electrolytes / Q000737:chemistry*; D060526:Magnetic Fields; D060328:Magnetic Phenomena; D008958:Models, Molecular; D008968:Molecular Conformation; D044367:Phase Transition; D011522:Protons; D012996:Solutions; D055672:Static Electricity; D013499:Surface Properties
chemical_list: D004573:Electrolytes; D011522:Protons; D012996:Solutions