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We have made a series of Quasi-Elastic Neutron Scattering (QENS) studies of supercooled water confined in 3-D and 1-D geometries, specifically, interstitial water in aged cement paste (3-D) and water confined in MCM-41-S and Double Wall Nano Tube DWNT (1-D). In addition, we also include the cases of hydration water on protein surface and other biopolymer surfaces (pseudo 2-D). By analyzing the QENS spectra using Relaxing Cage Model (RCM), we are able to extract accurately the self-intermediate scattering function of hydrogen atoms F H (Q,t), at low-Q as a function of temperature T, showing an α-relaxation process at long time. We can then construct the Dynamic Response Function χ T (Q,t) = -dF H (Q,t)/dT. χ T (Q,t) as a function of t at constant Q shows a single peak at the characteristic  α -relaxation time 〈 τ 〉, the amplitude of which grows as we approach the dynamic crossover temperature T L  observed before in each of these geometries. However, the peak height of χ T (Q,t) decreases after passing the crossover temperature T L . We make an argument to relate the occurrence of the extremum of the peak height in χ T  to the existence of the dynamic crossover temperature in each of these cases.

The Dynamic Response Function χ T (Q,t) of Confined Supercooled Water and its Relation to the Dynamic Crossover Phenomenon