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The conformational transition of a single bottle-brush polyelectrolyte with charged and neutral side chains is studied through MD simulations. Counterions are included explicitly and no additional salt is added. The structure of the polyelectrolyte and the counterion condensation are found to depend greatly on the Bjerrum length. As the Bjerrum length increases, the neutral side chains in a poor solvent can condense into clusters with variable size. Moreover, the polyelectrolyte forms globular structures at large or very small Bjerrum lengths. This transition is quite different from that in the case of a good solvent, in which there are not observable clusters and a globular structure is only formed at large Bjerrum lengths.

The conformational characteristics of polyelectrolytes end-grafted on two apposing walls are studied. The monovalent and multivalent counterions are explicitly treated. It is found that the polyelectrolyte brushes undergo a collapse transition in the presence of multivalent counterions at large wall separations. Moreover, the brush thickness is linearly proportional to the grafting density and independent of the counterion valence. The effects of normal compression on the density profiles of monomers and counterions, the pressure, the net charge density and the degree of interpenetration are also studied. The density profiles of counterions exhibit an asymmetrical distribution in systems with a mixture of monovalent and trivalent counterions.