Role of the ratio of biopolyelectrolyte persistence length to nanoparticle size in the structural tuning of electrostatic complexes

Aggregation of nanoparticles of given size $R$ induced by addition of a polymer strongly depends on its degree of rigidity. This is shown here on a large variety of silica nanoparticle self-assemblies obtained by electrostatic complexation with carefully selected oppositely charged bio-polyelectrolytes of different rigidity. The effective rigidity is quantified by the total persistence length $L_T$ representing the sum of the intrinsic ($L_p$) and electrostatic ($L_e$) polyelectrolyte persistence length, which depends on the screening, i.e., on ionic strength due to counter-ions and external salt concentrations. We experimentally show for the first time that the ratio L T /R is the main tuning parameter that controls the fractal dimension D f of the nanoparticles self-assemblies, which is determined using small-angle neutron scattering: (i) For $L_T /R<0.3$ (obtained with flexible poly-L-lysine in the presence of an excess of salt), chain flexibility promotes easy wrapping around nanoparticles in excess hence ramified structures with $D_f sim 2$. (ii) For $0.3<L_T /Rle1$ (semiflexible chitosan or hyaluronan complexes), chain stiffness promotes the formation of one-dimensional nanorods (in excess of nanoparticles), in good agreement with computer simulations. (iii) For $L_T /R>1$, $L_e$ is strongly increased due to the absence of salt and repulsions between nanoparticles cannot be compensated by the polyelectrolyte wrapping, which allow a spacing between nanoparticles and the formation of one dimensional pearl necklace complexes. (iv) Finally, electrostatic 2 screening, i.e. ionic strength, turned out to be a reliable way of controlling $D_f$ and the phase diagram behavior. It finely tunes the short-range interparticle potential, resulting in larger fractal dimensions at higher ionic strength.