(175a) Structure, Thermodynamics, and Solubility in Polyomino Fluids

The directed self-assembly of small molecules or objects in two dimensions is an ongoing challenge in nanotechnology and surface science [1,2]. As the number and complexity of components increases, the microstructure of the resulting phase, and location of any phase transitions, is difficult to predict. In simple systems such as rods, nematic transitions are readily observed [3,4]. When a variety of sizes [5], or sizes and shapes [6] are present, there can be rich behavior for both interacting and non-interacting objects.

In order to better understand the self-assembly of small molecules and nanoparticles adsorbed at interfaces, we have performed Monte Carlo simulations of hard polyominoes, connected shapes which occupy a certain number of lattice sites. Calculations are performed in the grand canonical ensemble, and are analogous to real systems in which molecules or nanoparticles reversibly adsorb to a surface or interface from a bulk reservoir. The model studied is athermal; objects in these simulations avoid overlap but otherwise do not interact. As a result, all of the behavior observed is entropically driven.

We have extensively studied the family of tetrominoes (polyominoes that occupy four lattice sites, of which there are seven) as both pure and mixed fluids, and identified a wealth of fascinating behavior, including non-ideal mixing, pronounced "microscale phase separation", and short-range geometric ordering[7]. In subsequent analyses, we demonstrate how the observed phenomena may be explained using classical thermodynamic concepts such as virial coefficients, volume of mixing, and Henry's Law. No sharp phase transitions have been observed, but this appears to be due to the small size of tetrominoes.

We then examined larger polyominoes, which have more structure than tetrominoes and, as a result, even more interesting phase behavior. For pure fluids, we recover the isotropic-nematic transition for rod-like species of sufficient length-to-width ratio. Polyominoes of sufficient size are demonstrated to exhibit a first-order phase transition similar to that of hard disks. We also examine more exotic shapes, and identify self-ordering that resembles crystallization, dimerization in mixtures, and immiscibility. These phenomena are again rationalized using classical thermodynamic concepts, from which we identify heuristics that qualitatively predict trends in self-assembly.

[1] Cicoira and Rosei, Surf. Sci., 600, 1 (2006)

[2] Bowden et al., Science, 276, 233 (1997)

[3] Bates and Frenkel, J. Chem. Phys., 112, 10034 (2000)

[4] Ghosh and Dhar, Euro. Phys. Lett., 78, 20003 (2007)

[5] Panagiotopoulos, J. Chem. Phys., 123, 104504 (2005)

[6] Davis et al., Ind. Eng. Chem. Res., 45, 5421 (2006)

[7] Barnes, Siderius, and Gelb, Langmuir, DOI:10.1021/la900196b (2009)