*2.3. Time-Domain Relaxometry at 20 MHz and 60 MHz*

Bruker Minispec (Bruker, Billerica, MA, USA) mq20 and mq60 bench-top relaxometer operating at 20 MHz (magnetic field strength: 0.47 T) and 60 MHz (magnetic field strength: 1.41 T), respectively, are used to measure longitudinal relaxation times (T1). 1 mL and 300 µL of the prepared samples are used for the measurements at 20 and 60 MHz, respectively. Samples are placed into the NMR probe for about 15 min for thermal equilibration. T1 values are determined by both saturation (SR) and inversion recovery (IR) pulse sequences. The relaxation recovery curves are fitted using a multi-exponential model. Relaxivity, r1, is calculated from the slope of the regression line of the relaxation rate, R1 = 1/T1, versus HA concentration with a least-squares method, as showed in the following Equation (1):

$$\text{R1}\_{\text{HA}} = \text{R1}\_{\text{water}} + \text{r1}^\* [\text{HA}]\_\text{\textdegree} \tag{1}$$

where R1HA is the relaxation rate of the HA sample expressed in s−<sup>1</sup> , R1water is the relaxation rate of free water expressed in s−<sup>1</sup> , and [HA] is the polymer concentration expressed in %*w*/*v*.
