Theory and experiment of chain length effects on the adsorption of polyelectrolytes onto spherical particles: the long and the short of it

We study here the role of polyelectrolyte chain length, that is number of repeat units (mers), in the competitive adsorption of a simple model polyanion, poly(acrylic acid), onto 85 nm spherical silica particles capped with a model polycation, poly(allylamine hydrochloride). Performing fluorescence spectroscopy experiments, we measured chain-length dependence of dilute aqueous polyelectrolyte adsorption, at full surface coverage, onto an oppositely charged polyelectrolyte overtop spherical silica nanoparticles (10−3 g L−1). Preferential adsorption was determined by comparing the characteristic fluorescence intensities of the two fluorophore-labeled and narrowly disperse polyacrylic acid samples (NMA–PAA450k and Dan–PAA2k) of 450k- and 2k-molecular weight (6250- and 28-mers), respectively. To compare and validate experimental results, a lattice model was developed for computing the probabilities of the different arrangements of two polymer chain lengths of polyacrylic acid on the surface of the silica nanosphere. We then determined which numbers of long and short adsorbed chains corresponded to the most configurations in our model. Both spectroscopic experiment results and the combinatorial model demonstrated that there is an entropic preference for complete adsorption of the longer 450k polyacrylic acid chain vs. 2k. This study provides insights on entropy driven chain-length dependence of polyelectrolyte adsorption onto spherical nanoparticle surfaces for directing and optimizing their layer-by-layer self-assembly in organic films.