Osmotic properties of polyethyleneglycols: quantitative features of   brush and bulk scaling laws
  From glycosylated cell surfaces to sterically stabilized liposomes, polymers attached to membranes attract biological and therapeutic interest. Can the scaling laws of polymer "brushes" describe the physical properties of these coats? We delineate conditions where the Alexander - de Gennes theory of polymer brushes successfully describes the intermembrane distance vs. applied osmotic stress data of Kenworthy et al. for PEG-grafted multilamellar liposomes [Biophys. J. (1995) 68:1921]. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equivalent density, the polymer osmotic pressure is independent of polymer molecular weight (the des Cloizeaux semi-dilute regime of bulk polymer solutions). The condition that attached polymers behave as semi-dilute bulk solutions offers a rigorous criterion for brush scaling-law behavior. There is a deep connection between the behaviors of polymer solutions in bulk and polymers grafted to a surface at a density such that neighbors pack to form a uniform brush. In this regime, two-parameter unconstrained fits of the Alexander - de Gennes brush scaling laws yield effective monomer lengths of 3.3 to 3.5 AA, which agree with structural predictions. The fitted distances between grafting sites are larger than expected from the nominal content of PEG-lipids; the chains apparently saturate the surface. Osmotic stress measurements can be used to estimate the actual densities of membrane-grafted polymers. 
Per Lyngs Hansen, Joel A. Cohen, Rudi Podgornik, and V. Adrian   Parsegian