Molecular structure and thermodynamic behavior of micelles formed by polyelectrolyte-neutral block copolymer chains, in particular polystyrene-b-poly(acrylic acid) (PS-b-PAA), in salt-free aqueous solution was studied via detailed explicit atomistic molecular dynamics simulations as a function of the copolymer composition (X-ps ) and the fractional charge (f) of ionizable PAA blocks. Micelle formation occurs via self-aggregation of PS-b-PAA copolymer chains with formation of PS core and PAA corona. The size of the PS core shows power-law dependence with respect to number of PS units per chain with an exponent 0.56 in agreement with scaling relations and experimental observations. The overall size of the micelle increases linearly with X-ps . Increase in X-ps results in a linear increase in micelle size and change in shape from spherical to prolate. The number of hydrogen bonds, pair correlation functions and various interatomic pair-wise energetic contributions to solvation enthalpy indicate favorable copolymer-water interaction. Micelle solvation is significantly influenced by hydrogen bonding interactions of carboxylic hydrogen atoms with water oxygens. Atom density profiles, solvation enthalpy and correlation functions of copolymer-Na+ ion pairs confirm the existence of micelle in osmotic regime, in agreement with mean-field theory.