We perform dissipative particle dynamics (DPD) simulations to study phase separation of a binary mixture of immiscible surfactants adsorbed on a flat surface. Both patches and stripes have been reported for such systems in the experimental literature, and there is controversy regarding the preferred thermodynamic equilibrium phase. We previously showed that stripes form [1], rather than bulk phase separation, when the length mismatch between surfactants or the bulkiness of one of the tail groups is sufficient [2, 3]. Here we show that for critical and near critical mixtures, stripes are the preferred phase and patches are kinetically arrested patterns that form during phase separation, again when there is sufficient mismatch in surfactant length or bulkiness. We investigate generally under what conditions stripes or patches should form as a function of, e.g., degree of immiscibility, length difference, difference in tail-group bulkiness and surface coverage. Our simulations are in very good agreement with experiments on a wide variety of surfactant mixtures.

1. AM Jackson, JW Myerson, F Stellacci, “Spontaneous assembly of subnanometre-ordered domains in the ligand shell of monolayer-protected nanoparticles”, Nature Materials, 3, 330-336 (2004).

2. C Singh, PK Ghorai, MA Horsch, AM Jackson, RG Larson, F Stellacci and SC Glotzer, “Entropy-Mediated Patterning of Surfactant-Coated Nanoparticles and Surfaces”, Physical Review Letters 99, 226106 (2007).

3. RP Carney, GA DeVries, C Dubois, H Kim, JY Kim, C Singh, PK Ghorai, JB Tracy, RL Stiles, RW Murray, SC Glotzer and F Stellacci, "Size Limitations for the Formation of Ordered Striped Nanoparticles", Journal of American Chemical Society, (Communication), 130(3), 798-799 (2008).