Theoretical Approaches to Neutral and Charged Polymer Brushes
  Neutral or charged polymers that are densely end-grafted to surfaces form brush-like structures and are highly stretched under good-solvent conditions. We discuss and compare relevant results from scaling models, self-consistent-field methods and MD simulation techniques and concentrate on the conceptual simple case of planar substrates. For neutral polymers the main quantity of interest is the brush height and the polymer density profile, which can be well predicted from self-consistent calculations and simulations. Charged polymers (polyelectrolytes) are of practical importance since they are soluble in water. Counterion degrees of freedom determine the brush behavior in a decisive way and lead to a strong and non-linear swelling of the brush. 
Ali Naji, Christian Seidel, Roland R. Netz