Osmotic Properties of Poly(Ethylene Glycols): Quantitative Features of Brush and Bulk Scaling Laws

Abstract

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 fits the intermembrane distance versus applied osmotic stress data of Kenworthy et al. for poly(ethylene glycol)-grafted multilamellar liposomes. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equivalent monomer density, the polymer osmotic pressure is independent of polymer molecular weight (the des Cloizeaux semidilute regime of bulk polymer solutions). The condition that attached polymers behave as semidilute bulk solutions offers a rigorous criterion for brush scaling-law behavior. There is a deep connection between the behaviors of semidilute 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 to the Kenworthy et al. data yield effective monomer lengths of 3.3-3.6 A, which agree with structural predictions. The fitted distances between grafting sites are larger than expected from the nominal mole fraction of poly(ethylene glycol)-lipids; the chains apparently saturate the surface. Osmotic stress measurements can be used to estimate the actual densities of membrane-grafted polymers.

From dispersed nanodiscs to thin films of layered organic material via reversible swelling

“…At the largest osmotic pressures, this additional amount corresponds to 1-2 water molecules per surfactant, and strongly increases only if the osmotic pressure reaches sufficiently low values. This is a general behaviour already described for polymer chains alone [25].…”

Translocation of short and long polymers through an interacting pore

“…The interest of the simulations here are to gain some qualitative insight. However, if one where to take mm = 35 meV 39 , σ = 0.35 nm 40 and m = 44 amu as the PEG monomer binding energy, length and mass respectively. We would have a temperature of about 20…”

Quantification of Surface Ligands on NaYF4 Nanoparticles by Three Independent Analytical Techniques

“…These relationships are unlikely to apply to chains as short as PEG750, but there is some evidence that they can apply at high surface coverage to PEG2000 and PEG5000. 35 We estimate the distance between polymer chains on the NP surface by assuming that the area occupied by each ligand is a circle with a diameter equal to the distance between adjacent chains. On the basis of this approximation, the distances among PEG750, PEG2000, and PEG5000 ligands are 1.1, 1.4, and 2.5 nm, respectively.…”