The dynamic response function _χT(Q,t) of confined supercooled water and its relation to the dynamic crossover phenomenon

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 (l-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 _χT(Q,t) = -dF_H(Q,t)/dT. _χT(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 _χT(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 _χT to the existence of the dynamic crossover temperature in each of these cases.