Two-dimensional (2D) molecular self-assembly allows for the formation of well-defined supramolecular layers with tailored geometrical, compositional, and chemical properties. To date, random intermixing and entropic effects in these systems have largely been associated with crystalline disorder and glassy phases. Here we describe a 2D crystalline self-assembled molecular system that exhibits random incorporation of substitutional molecules. The lattice is formed from a mixture of trimesic acid (TMA) and terthienobenzenetricarboxylic acid (TTBTA), C3-symmetric hydrogen-bonding units of very different sizes (0.79 and 1.16 nm, respectively), at the solution-highly oriented pyrolitic graphite (HOPG) interface. Remarkably, the TTBTA substitutes into the TMA lattice at a fixed stoichiometry near 12%. The resulting lattice constant is consistent with Vegard's law prediction for an alloy with a composition TMA0.88TTBTA0.12, and the substrate orientation of the lattice is defined by an epitaxial relation with the HOPG substrate. The Gibbs free energy for the TMA/TTBTA lattice was elucidated by considering the entropy of intermixing, via Monte Carlo simulations of multiplicity of the substitutional lattices, and the enthalpy of intermixing, via density functional theory calculations. The latter show that both the bond enthalpy of the H-bonded lattice and the adsorption enthalpy of the molecule/substrate interactions play important roles. This work provides insight into the manifestation of entropy in a molecular crystal constrained by both epitaxy and intermolecular interactions and demonstrates that a randomly intermixed yet crystalline 2D solid can be formed through hydrogen bonding of molecular building blocks of very different size.
Keywords: entropy; hydrogen bonding; scanning tunneling microscopy; self-assembly; solid solution.