Hydrodynamics and electrokinetics of spherical liposomes with coatings of terminally anchored poly(ethylene glycol): Numerically exact electrokinetics with self-consistent mean-field polymer

Abstract

A detailed theoretical model is presented to interpret electrokinetic experiments performed on colloids with uncharged polymer layers. The methodology removes many of the degrees of freedom that otherwise have to be accounted for by adopting multiple empirical fitting parameters. Furthermore, the level of detail provides a firm basis for future studies examining liposome surface chemistry and charge, surface-charge mobility, and the dynamics of adsorbed polymer on fluidlike membranes. The model predictions are compared with experimental measurements of the electrophoretic mobility of stealth liposomes with molecular weights of terminally anchored poly(ethylene glycol) (PEG) in the range 0.35-10 kg mol(-1) [J.A. Cohen and V.A. Khorosheva, Colloids Surf. A 195, 113 (2001)]. The experimental data are interpreted by drawing upon self-consistent mean-field calculations of the polymer segment density distributions and numerically exact solutions of the governing transport equations [R.J. Hill, D.A. Saville, and W.B. Russel, J. Colloid Interface Sci. 258, 56 (2003)]. The approach leads to excellent agreement between theory and experiment with one adjustable parameter--the hydrodynamic size (Stokes radius) a(s) approximately equal to 0.175 A of the statistical PEG segments with (Kuhn) length l=7.1 A . The remarkably small Stokes radius is demonstrated to be consistent with other applications of the well-known Debye-Brinkman model and, consequently, this work reveals important limitations of the mean-field hydrodynamic model. Despite such limitations, the "full" electrokinetic model is robust in its predictive capacity. The molecular weights of the terminally anchored PEG span the range where the coatings undergo a transition from mushroomlike to brushlike conformations, and the hydrodynamic size and electrophoretic mobility of the liposomes are demonstrated to be sensitive to the PEG chain length and the effects of double-layer polarization.