## 4 2001-2007: The Memory Function-Based Modeling of IXS Spectra of Noble Gases
### Microscopic vs. Structural Relaxations
This comparison seems particularly meaningful due to the disparate nature of microscopic structure and, in particular, to the presence of a large-scale connectivity in water. Figure 12: The Q-dependence of reduced relaxation time \(\Psi=\tau_{\alpha}/\tau_{c}\) as obtained from Ne data at the thermodynamic conditions indicated in the plot. Data are adapted with permission from [6] copyrighted by American Physical Society. The horizontal line marks the unit value characteristic of the collisional regime. A meaningful reference to compare viscoelastic effects in different materials is provided by the generalized longitudinal viscosity, whose link the viscoelastic spectral parameters is given by the formula:  
\[\eta_{l}=\frac{\rho(\omega_{\infty}^{2}-\omega_{0}^{2})\tau}{Q^{2}} \tag{15}\]  
Figure 7 displays the \(Q\)-dependence of \(\eta_{l}\) extracted (through Equation (15)) from the viscoelastic modeling of neon spectra in [6] at the thermodynamic conditions considered in Figure 4. Results on neon are compared with those obtained in liquid water from an _IXS_[13] and a joint _INS_ and _INS_ result on heavy water [78]. Some clear features readily emerge from the comparison:  
1. Viscosity curves of Ne are only weakly dependent on thermodynamic conditions, although the macroscopic viscosity in the spanned thermodynamic interval undergoes important variations. Combined thermodynamic [72] and bulk viscosity data [28] of neon lead to estimate a more than 300% variation of \(\eta_{l}\) within the probed thermodynamic range, clearly non reproduced by mesoscopic measurements. Conversely, viscosity data of water in the same plot have a \(T\) dependence as sharp as the one of macroscopic viscosity [96]. This discrepancy is likely due to the large weight of structural processes in water, especially at the low _Qs_ covered by data of [13]. Structural relaxations, owing to their collective nature can only be observed over long distances, or, equivalently, at high _Qs_ and are expected dominating in associate liquids. 2. High \(T\) values of \(\eta_{l}\) approach from above low-\(Q\) neon data. This seems consistent with the inferred link between structural relaxation and local readjustment of the hydrogen bond (HB) network in water [12; 13]. At the highest _Ts_ the average number of HBs per molecule is sensibly lower which weakens the strength of structural relaxations [13; 19]. 3. The strong \(Q\)-dependence of \(\eta_{l}\) in water suggests that at \(Q\) higher than the values covered by Ref. [13], viscosity curves of water and neon tend to get closer to each other also considering that the latter have an essentially flat \(Q\)-dependence at high _Qs_. This impression is confirmed by \(\eta_{l}\) data derived from extremely high resolution _INS_ measurements of on deuterated water (line + open squares symbols) at \(T=288\) K, which covered a \(Q\)-range larger than those of other water data reported in the same plot. Overall, data in Figure 13 lead to the conclusion that the merely collisional component of relaxation in water becomes more relevant either at high \(T\), _i.e._, upon approaching supercritical condition, or at high _Qs_, where structural relaxation become less prevalent. Figure 13: Longitudinal viscosity data derived using Equation (15) either from _IXS_ measurements [13], on normal water (line + squares symbols), or from joint _IXS_ and _INS_ measurements [78] on heavy water (line + open squares). Data are redrawn with permission from [13] and [78] copyrighted by the American Physical Society. The temperatures are indicated in the plot. Neon data correspond to the same thermodynamic conditions and symbols as in Figure 4 and are redrawn with permission from [6] copyrighted by American Physical Society.