Structural Transitions of One and Two Polymer Mushrooms

A polymer mushroom here refers to a group of homopolymer chains end-grafted at the same point on a flat and impenetrable substrate. Using lattice self-consistent field (LSCF) calculations with the Kronecker δ-function interactions (instead of the commonly used nearest-neighbor interactions), we have studied the structures of one and two polymer mushrooms in an explicit solvent as a function of the polymer volume fraction in the system, solvent quality characterized by the Flory-Huggins χ parameter, and distance between the two mushrooms. We have constructed phase diagrams showing the coil-globule transition of one mushroom and how it is coupled with the fused-unfused transition of two mushrooms. Since LSCF results are exact only in the limit of number of grafted chains n→∞, we also use fast lattice Monte Carlo (FLMC) simulations with the same Hamiltonian as in LSCF theory to examine how this limit is approached with increasing n. Direct comparisons between LSCF and FLMC results without any parameter-fitting quantify the fluctuation/correlation effects neglected in LSCF theory.