Structures of One and Two Polymer Mushrooms

A polymer mushroom here is referred to as a group of chains end- grafted at the same point on a flat and impenetrable substrate. Using lattice self-consistent field (LSCF) calculations with the Kronecker $\delta$-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 $\chi$ parameter, and distance between the two mushrooms. Since LSCF results are exact only in the limit of number of chains $n \to \infty$, we also use fast lattice Monte Carlo (FLMC) simulations\footnote{Q. Wang, \textbf{Soft Matter, 5}, 4564 (2009).} 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.