Structure and dynamics of hyaluronic acid semidilute solutions: A dielectric spectroscopy study

Dielectric spectroscopy is used to investigate fundamental length scales describing the structure of hyaluronic acid sodium salt (Na-HA) semidilute aqueous solutions. In salt-free regime, the length scale of the relaxation mode detected in MHz range scales with HA concentration as $c_{\text{HA}}^{-0.5}$ and corresponds to the de Gennes-Pfeuty-Dobrynin correlation length of polyelectrolytes in semidilute solution. The same scaling was observed for the case of long, genomic DNA. Conversely, the length scale of the mode detected in kilohertz range also varies with HA concentration as $c_{\text{HA}}^{-0.5}$ which differs from the case of DNA $\left(c_{\text{DNA}}^{-0.25}\right)$. The observed behavior suggests that the relaxation in the kilohertz range reveals the de Gennes-Dobrynin renormalized Debye screening length, and not the average size of the chain, as the pertinent length scale. Similarly, with increasing added salt the electrostatic contribution to the HA persistence length is observed to scale as the Debye length, contrary to scaling pertinent to the Odijk-Skolnick-Fixman electrostatic persistence length observed in the case of DNA. We argue that the observed features of the kilohertz range relaxation are due to much weaker electrostatic interactions that lead to the absence of Manning condensation as well as a rather high flexibility of HA as compared to DNA.

Figure 1

(a),(b) Double logarithmic plot of the frequency dependence of the (a) conductance and capacitance for 0.1 mg/mL HA solution and the matching reference 0.14 mM NaCl solution. (c),(d) Frequency dependence of the differential admittance components $G\left(\omega \right)=G^{\text{sample}}\left(\omega \right)-G^{\text{ref}}\left(\omega \right)$ and $C_p\left(\omega \right)=C_p^{\text{sample}}\left(\omega \right)-C_p^{\text{ref}}\left(\omega \right)$. The correction constants are denoted $G^{\text{corr}}$ and $C_p^{\text{corr}}$. The full line in panel (c) is the $G\left(\omega \right)$ spectrum calculated from the complex dielectric function fit (see text).

Figure 2

Double logarithmic plot of the frequency dependence of the imaginary $\left({\epsilon }^{″}\right)$ and real $\left({\epsilon }^{\prime }\right)$ part of the dielectric function for the 0.1 mg/mL HA pure water solution. The full lines are fits to the sum of the two Cole-Cole forms (see text); the dashed lines represent a single form.

Figure 3

Cole-Cole plot of the dielectric response for the 0.1 mg/mL HA pure water solution. The full line is a fit to the sum of the two Cole-Cole forms (see text). The LF mode contributes as the dominant arch, while the smaller HF mode is found near the origin of the axes.

Figure 4

Double logarithmic plot of the frequency dependence of the imaginary $\left({\epsilon }^{″}\right)$ and real $\left({\epsilon }^{\prime }\right)$ part of the dielectric function at $T=25°\text{C}$ of (a), (b) pure water HA solutions for representative a1-a3 (1, 0.1, 0.0125 mg/mL) HA concentrations and (c), (d) HA solutions of concentration $c_{\text{HA}}=0.03\text{mg}/\text{mL}$ for three representative b1-b3 (0, 0.12, 0.25 mM) added salt concentrations. The full lines are fits to the sum of the two Cole-Cole forms (see text); the dashed lines represent a single form.

Figure 5

Main panel: characteristic length of the HF mode $\left(L_{\text{HF}}\right)$ for pure water HA solutions as a function of HA concentration $\left(c_{\text{HA}}\right)$. The full line is a fit to the power law $L_{\text{HF}}\propto c_{\text{HA}}^{-0.48\pm 0.02}$. Inset: $L_{\text{HF}}$ for HA solutions with varying added salt $\left(I_{\text{s}}\right)$ for a representative HA concentration $c_{\text{HA}}=0.03\text{mg}/\text{mL}$.

Figure 6

Main panel: normalized dielectric strength of the HF mode $\Delta {\epsilon }_{\text{HF}}/\left(c_{\text{HA}}{L}_{\text{HF}}^2\right)$ as a function of HA concentration $c_{\text{HA}}$ for pure water HA solutions. Inset: $\Delta {\epsilon }_{\text{HF}}/\left(c_{\text{HA}}{L}_{\text{HF}}^2\right)$ for HA solutions with varying added salt $\left(I_{\text{s}}\right)$ for a representative HA concentration $c_{\text{HA}}=0.03\text{mg}/\text{mL}$. The dashed lines are guides for the eye.

Figure 7

(a) Characteristic length of the LF mode $\left(L_{\text{LF}}\right)$ for pure water HA solutions as a function of HA concentration $\left(c_{\text{HA}}\right)$. The full line is a fit to the power law $r_{\text{B}}=C{\left(B/b{c}_{\text{HA}}\right)}^{0.5\pm 0.02}$ with $C=4.3$ (see text). (b) $L_{\text{LF}}$ for HA solutions with varying added salt $\left(I_{\text{s}}\right)$ for a representative HA concentration: $c_{\text{HA}}=0.03\text{mg}/\text{mL}$. The full line is a fit to the expression $r_{\text{scr}}=C{\left\{B/\left[b\left(c_{\text{HA}}+2A{I}_{\text{s}}\right)\right]\right\}}^{0.5}$ with $C=4.3$ (see text). The dashed line corresponds to $L_{\text{p}}\propto I_{\text{s}}^{0.5}$. The dotted line denotes the value of $L_{\text{LF}}$ in salt-free limit for $c_{\text{HA}}=0.03\text{mg}/\text{mL}$.

Figure 8

(a) Normalized dielectric strength of the LF mode $\Delta {\epsilon }_{\text{LF}}/\left(c_{\text{HA}}{L}_{\text{LF}}^2\right)$ as a function of HA concentration $c_{\text{HA}}$ for pure water HA solutions. The full line is a fit to the power law $\Delta {\epsilon }_{\text{LF}}/\left(c_{\text{HA}}{L}_{\text{LF}}^2\right)\propto c_{\text{HA}}^{-0.37\pm 0.04}$. (b) $\Delta {\epsilon }_{\text{LF}}/\left(c_{\text{HA}}{L}_{\text{LF}}^2\right)$ for HA solutions with varying added salt $\left(I_{\text{s}}\right)$ for a representative HA concentration $c_{\text{HA}}=0.03\text{mg}/\text{mL}$.