We present the results of coarse grained molecular dynamics simulation using a charge free model that is able to capture different regions of the morphological phase diagram of charged diblock copolymers. Specifically, we were able to reproduce many phases of the poly(acrylic acid)-(1,4)-polybutidiene (PAA-PBA) diblock copolymer, Ca2+ and water systems as a function of pH and calcium concentration with short-range LJ type potentials. The morphologies observed range from bilayers to cylinders to spherical micelles. Such polyanionic/cationic amphiphiles in water typically present multiple challenges for molecular simulations, particularly due to the many charge interactions that are long ranged and computationally costly. Further, it is precisely these interactions that are thought to modulate large amphiphile assemblies of interest such as lipid rafts. However, our model is able to reproduce different morphologies due to pH and with or without the addition of Ca2+ as well as the lateral phase segregation and the domain registration observed in neutral and charged diblock copolymer mixtures. The results suggest that the overall effect of charges is a local structural rearrangement that renormalizes the steric repulsion between the headgroups. This simple model, which is devoid of charges, is able to reproduce the complex phase diagram and can be used to investigate collective phenomena in these charged systems such as domain formation and registration or colocalization of lipid rafts across bilayer leaflets.