Atomistic molecular dynamics simulations of the structure of symmetric Polyelectrolyte block copolymer micelle in salt-free aqueous solution

The structure of a symmetric polystyrene-$b-$poly(acrylic acid) (PS-$b-$PAA) micelle in salt-free aqueous solution as a function of degree-of-neutralization (or ionization, $f$) of the PAA is studied via explicit-atom-ion MD simulations, for the first time for a polyelectrolyte block copolymer in a polar solvent. Micelle size increases with $f $in agreement with experimental observations in literature, due to extension of PAA at higher ionization. Pair RDF's with respect to water oxygens show that corona-water interaction becomes stronger with $f$ due to an increase in number density of carboxylate (COO$^{-}$) groups on the chain. Water-PAA coordination (carboxylate O's) increases with ionization. H-bonding between PAA and water increases with $f$ due to greater extent of corona-water affinity. With increase in $f$, atom and counter-ion $\rho $ profiles confirm extension of corona blocks and micelle existing in the ``osmotic regime,'' and a decrease in scattering peak intensity, in agreement with neutron scattering experiments and mean-field theory in literature. Inter-chain distance in PS core is found to decrease with ionization.