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 biopolyelectrolytes of different rigidity. The effective rigidity is quantified by the total persistence length $L_{\mathrm{T}}$ representing the sum of the intrinsic $\left(L_{\mathrm{p}}\right)$ and electrostatic $\left(L_{\mathrm{e}}\right)$ polyelectrolyte persistence length, which depends on the screening, i.e., on ionic strength due to counterions and external salt concentrations. We experimentally show that the ratio $L_{\mathrm{T}}/R$ is the main tuning parameter that controls the fractal dimension $D_{\mathrm{f}}$ of the nanoparticles’ self-assemblies, which is determined using small-angle neutron scattering: (i) For $L_{\mathrm{T}}/R<0.3$ (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 $D_{\mathrm{f}}\sim 2$. (ii) For $0.3<L_{\mathrm{T}}/R\le 1$ (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 $L_{\mathrm{T}}/R>1,L_{\mathrm{e}}$ is strongly increased due to the absence of salt and repulsions between nanoparticles cannot be compensated for by the polyelectrolyte wrapping, which allows a spacing between nanoparticles and the formation of one-dimensional pearl necklace complexes. (iv) Finally, electrostatic screening, i.e., ionic strength, turned out to be a reliable way of controlling $D_{\mathrm{f}}$ and the phase diagram behavior. It finely tunes the short-range interparticle potential, resulting in larger fractal dimensions at higher ionic strength.

Figure 1

Sequence of phase behaviors in the PEL-SiNP concentration plane at $T=20{}^{\circ }\mathrm{C}$ and high ionic strength. For chitosan, hyaluronan, and PLL systems, mixtures are prepared in ${\mathrm{H}}_2\mathrm{O}$ in the presence of 0.2 $M \mathrm{C}{\mathrm{H}}_3\mathrm{COONa}$, 0.1 $M$ NaCl, and 0.2 $M$ KBr, respectively. The continuous gray, red, and blue lines indicate the stoichiometric thresholds corresponding to a charge ratio $[+]/\left[\text{–}\right]=1$ for chitosan, HA, and PLL complexes, respectively.

Figure 2

SANS profiles collected in domain I (excess of PELs) at high ionic strength (presence of an excess of salt) and 20 °C, of the three systems examined. For clarity, the HA and the PLL spectra have been shifted by two and three log units along the $y$ axis, respectively. While the 0.5 g/l PLL–1 g/l SiNP sample is biphasic in ${\mathrm{H}}_2\mathrm{O}$ (close to the separation line between domains I and II), it is monophasic and representative of domain I in ${\mathrm{D}}_2\mathrm{O}$, showing the slight isotopic effect on the position of the phase transition line.

Figure 3

SANS profiles collected in domain II (coacervates) at high ionic strength (presence of an excess of salt) and 20 °C, of the three systems examined. For clarity, spectra have been shifted by one or two log units along the $y$ axis with respect to each other. The arrows indicate the position $q^{*}$ of a characteristic correlation peak (see text, Sec. 3b).

Figure 4

(a) SANS profiles collected at high ionic strength, $I$, and 20 °C, of the three PEL complexes: 0.01 g/l chitosan-10 g/l SiNP, 0.01 g/l HA–2 g/l SiNP, and 0.01 g/l PLL–10 g/l SiNP (monophasic and representative of domain III in ${\mathrm{D}}_2\mathrm{O}$) solutions are prepared in the presence of 0.2 $M \mathrm{C}{\mathrm{H}}_3\mathrm{COONa}$, 0.1 $M$ NaCl, and 0.2 $M$ KBr, respectively. For clarity, hyaluronan and chitosan complexes spectra have been shifted by two and three log units along the $y$ axis with respect to that of PLL complexes, respectively. All curves exhibit the first oscillation associated with the form factor of the SiNPs cross section occurring around $6.5\times {10}^{-2}\AA {}^{-1}$ (9.2 nm $\mathrm{SiN}{\mathrm{P}}^{-}$) or $3.5\times {10}^{-2}\AA {}^{-1}$ (17 nm $\mathrm{SiN}{\mathrm{P}}^{+}$) for chitosan and PLL or hyaluronan complexes, respectively (see dashed lines and Appendix). The inset represents the variation of $D_{\mathrm{f}}$ with the characteristic ratio $L_{\mathrm{T}}/R$ (in the presence of 0.1 or 0.2 $M$ external salt, $L_{\mathrm{T}}=L_{\mathrm{p}}$). (b) Same as (a), but for other PEL and NP concentrations (domain III, excess of NPs). For clarity, the hyaluronan data have been shifted by one log unit along the $y$ axis with respect to those of PLL.

Figure 5

Sequence of phase behaviors in the HA-SiNP concentration plane at high (presence of external salt) and low (salt-free systems) ionic strength, $I$. The red dashed lines represent boundaries between characteristic domains at high $I$, whereas gray dashed lines represent boundaries at low $I$. The shaded area corresponds to the coacervate region expansion when $I$ is increased (diagram obtained in ${\mathrm{H}}_2\mathrm{O}$).

Figure 6

SANS patterns collected in domain II (coacervates) at low ionic strength (salt-free mixtures) and 20 °C, of the two systems examined. For clarity, the PLL data have been shifted by one log unit along the $y$ axis with respect to those of HA.

Figure 7

SANS patterns collected in domain III (excess of NPs) at low ionic strength (salt-free mixtures) and 20 °C, of the two systems examined. For clarity, the spectra have been shifted by one log unit along the $y$ axis with respect to each other. While the $C_{\mathrm{hyaluronan}}=0.1\mathrm{g}/\mathrm{l}\text{–}{C}_{\mathrm{SiNP}}=2\mathrm{g}/\mathrm{l}$ sample is biphasic in ${\mathrm{H}}_2\mathrm{O}$ (close to the separation line between domains II and III), it is monophasic and representative of domain III in ${\mathrm{D}}_2\mathrm{O}$, showing the slight isotopic effect on the position of the phase transition line.

Figure 8

SANS profiles collected at high (0.1 $M$ NaCl) and low ionic strength (salt-free mixtures) for HA complexes in domains II and III. Concentrations are ${\mathrm{C}}_{\mathrm{HA}}=1.5\mathrm{g}/\mathrm{l}$ and ${\mathrm{C}}_{\mathrm{SiNP}}=10\mathrm{g}/\mathrm{l}$ for coacervates (filled symbols), whereas concentrations are equal to ${\mathrm{C}}_{\mathrm{SiNP}}=2\mathrm{g}/\mathrm{l}$ and ${\mathrm{C}}_{\mathrm{HA}}=0.01\mathrm{g}/\mathrm{l}$ (at high $I$) or 0.05 g/l (at low $I$) for mixtures in domain III (open symbols). For clarity, the spectra have been shifted by one or two log units along the $y$ axis with respect to each other. $q^{*}$ indicates the position of the characteristic correlation peak.

Figure 9

Influence of the ratio $L_{\mathrm{T}}/R$ on the fractal exponent $D_{\mathrm{f}}$ of the self-assemblies in domain III. The $L_{\mathrm{T}}/R$ range is obtained by varying the nature of the PEL as well as the ionic strength $I$, which depends on the external salt, PEL, and NP concentration. Low $I$ data are on the right-hand side of the vertical dotted line. Error bars depend on both the quality of the fit of the data and of the number of samples [different runs and concentrations; see Figs. 4, 4, 7, and 8].

Figure 10

SiNP form factor, $P\left(q\right)$, obtained using SAXS experiments performed at 5 g/l and 20 °C. The continuous blue line corresponds to the best fit of the data using the form factor expression derived for hard spheres of radius $R=9.2\mathrm{nm}$ with $\sigma =0.12$.

Figure 11

SAXS profiles collected at various positively charged SiNP concentrations. The dashed lines indicate the oscillations associated with the form factor of the SiNPs.