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Register a new userRole of the ratio of biopolyelectrolyte persistence length to nanoparticle size in the structural tuning of electrostatic complexes
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Li Shi
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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.
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The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a singular logarithmic dependence on $h$. We derive a general form for this energy in terms of the singular capacitance of two spheres in near contact $c(h)$, together with nonsingular geometric features of the cluster. Using this form, we determine the energies of various clusters, finding that more compact clusters are more stable. These energies are proposed to be significant for metal-semiconductor binary nanoparticle lattices found experimentally. We sketch how these effects should dictate the relative abundances of metal nanoparticle clusters in nonpolar solvents.
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The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a strong logarithmic dependence on $h$. We give a general law for the strength of this logarithmic correction in terms of a) the energy at contact ignoring the charge quantization effects and b) an adjacency matrix specifying which spheres of the cluster are in contact and which is charged. We verify the theory by comparing the predicted energies for a tetrahedral cluster with an explicit numerical calculation.
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