*3.4. Considerations about Di*ff*usion Data*

Taking into consideration the limits of precision in the determination of the absolute value of diffusion coefficients by DOSY due to the available strength of the gradient of the 700 MHz instrument (6G), these results are an interesting example of the utility of this technique for the study of polymer fragmentation. In particular, the diffusion measure of the HA standards proved to discriminate properly the different MWs, considering that a good comparison can be performed for species possessing the same molecular characteristics. In fact, this is a recommendation formulated [29] for a good comparison of the molecular weights, where the use of similar structures eliminates systematic errors related to the use of standards with different chemical features.

In the diffusion measurements of DAC® in D2O, the unique front shown in Figure 3 has a D = 1.23 × 10−<sup>9</sup> m<sup>2</sup> s −1 . The values of the diffusive fronts in Figure 6b, are as follows: front (a) D = 1.30 × 10−<sup>10</sup> m<sup>2</sup> s <sup>−</sup><sup>1</sup> and front (b) (fragment distribution) from 3.0 to 2.54 × 10−<sup>9</sup> m<sup>2</sup> s −1 .

In the case of HA certified standard fragments the diffusion coefficients were: 13 kDa D = 2.22 × 10−<sup>10</sup> m<sup>2</sup> s −1 ; 50 kDa D = 1.11 × 10−<sup>10</sup> m<sup>2</sup> s −1 ; 208 kDa D = 5.18 × 10−<sup>11</sup> m<sup>2</sup> s −1 .

Moreover, a detailed study of the possible interferences between these types of polymers was carried out. In fact, the possibility of entangling should be further investigated. These experiments consist of the DOSY measure of the mix of two standard fragments with different MWs. This was made by observing DOSY in the diffusion coefficient of the same standards using either a mix of the 13 kDa and the 208 kDa samples and the mix of the 50 kDa and 208 kDa. These experiments are reported in Figures S2 and S3.

In the first case (13 kDa and 208 kDa) the diffusion coefficients of the diffusive fronts were D = 2.29 × 10−<sup>10</sup> m<sup>2</sup> s −1 for the 13 kDa fragments and 1.20 × 10−<sup>10</sup> m<sup>2</sup> s −1 for the 50 kDa instead of the same fragments alone which were 2.22 × 10−<sup>10</sup> m<sup>2</sup> s <sup>−</sup><sup>1</sup> and 1.11 × 10−<sup>10</sup> m<sup>2</sup> s −1 respectively.

The other experiment was performed on a mix of the 13 kDa and the 208 kDa fragments. Results were for the 13 kDa front D = 4.07 × 10−<sup>10</sup> m<sup>2</sup> s <sup>−</sup><sup>1</sup> and for the 208 kDa one D = 4.09 × 10−<sup>11</sup> m<sup>2</sup> s −1 . Additionally, in this case, a difference is clearly visible between the diffusion D of the fragment alone reported above and the same in the mixture.

In fact, in the case of fragments alone for 13 kDa D = 2.22 × 10−<sup>10</sup> m<sup>2</sup> s <sup>−</sup><sup>1</sup> and for 208 kDa D = 5.18 × 10−<sup>11</sup> m<sup>2</sup> s −1 . The differences are not very large but are indicative that the presence of other macromolecules in the solution can affect the absolute value of the diffusion coefficient. This can be also due either to entangling between macromolecules or to an effect of the change in solution viscosity.

The diffusion of water in these systems (plot of Figure 3) was monitored. The D value of the trace of the deuterium hydrogen oxide (HDO) resonance was 1.86 × 10−<sup>9</sup> m<sup>2</sup> s −1 .

On the other hand, in Figure 6b the diffusion front of a resonance at 4.76 ppm due to HDO shows a value of 3.79 × 10−<sup>9</sup> m<sup>2</sup> s −1 . This is the value experimentally determined in the presence of HA-PLA macromolecules and the fragments upon fragmentation. Moreover, the D value of the resonance of HDO molecule in the mix of fragments reported above shows a variable value of D of HDO, in fact in the mix of 13 kDa and 208 kDa D was measured in 4.45 × 10−<sup>9</sup> m<sup>2</sup> s −1 . On the basis of the literature diffusion of net water as a trace of the protonated water molecule, in practice HDO (1% of H2O in D2O) a value D = 1.12 × 10−<sup>9</sup> m<sup>2</sup> s −1 is reported also with NMR [37–39] and with other physical techniques [40,41]. The variability of the diffusion of the HDO molecule is evidently strongly affected by the size and the dispersity of the macromolecules in the solution. It is also important to consider that HA contains a large number of hydroxyl groups able to alter the property of protons of HDO by the prototropic exchange.

In addition, the preliminary experiments included also the use of a High MW hyaluronic acid purchased as reported in Materials and Methods. The MW was with a value about MW ≥ 500 kDa.

The results are not suitable for publication due to the bad quality of the very noisy spectra but it is interesting that the diffusive profiles on the left of the DOSY spectra indicate the presence of three broad peaks with D = 1.69 × 10−<sup>11</sup> m<sup>2</sup> s −1 , 2.51 × 10−<sup>11</sup> m<sup>2</sup> s <sup>−</sup><sup>1</sup> and 4.68 × 10−<sup>11</sup> m<sup>2</sup> s −1 . In the same experiment, the lactic acid molecule (100 Da) gave a value of 4.3 × 10−<sup>9</sup> m<sup>2</sup> s −1 .
