Structural and phase transitions of one and two polymer mushrooms in poor solvent

Using the recently proposed fast lattice Monte Carlo (FLMC) simulations and the corresponding lattice self-consistent field (LSCF) calculations based on the same model system, where multiple occupancy of lattice sites is allowed [Q. Wang, Soft Matter 5, 4564 (2009); Q. Wang, Soft Matter 5, 6206 (2010)], we studied the coil-globule transition (CGT) of one-mushroom systems and the fused-separated transition (FST) of two-mushroom systems, where a polymer mushroom is formed by a group of n homopolymer chains each of N segments end-grafted at the same point onto a flat substrate and immersed in a poor solvent. With our soft potential that allows complete particle overlapping, LSCF theory neglecting the system fluctuations/correlations becomes exact in the limit of n → ∞, and FLMC results approach LSCF predictions with increasing n. Using LSCF calculations, we systematically constructed the phase diagrams of one- and two-mushroom systems. A second-order symmetric-asymmetric transition (SAT) was found in the globule state of one-mushroom systems, where the rotational symmetry around the substrate normal passing through the grafting point is broken in each individual configuration but preserved by the degeneracy of different orientations of these asymmetric configurations. Three different states were also found in two-mushroom systems: separated coils, separated globules, and fused globule. We further studied the coupling between FST in two-mushroom systems and CGT and SAT of each mushroom. Finally, direct comparisons between our simulation and theoretical results, without any parameter-fitting, unambiguously and quantitatively revealed the fluctuation/correlation effects on these phase transitions.