The Dynamic Response Function chi(T)(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 (1-D). In addition, we also include the cases of hydration water oil 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 a-relaxation process at long time. We can then construct the Dynamic Response Function chi(T)(Q,t) = -dF(H)(Q,t)/dT. chi(T)(Q,t) as a function of t at constant Q shows a single peak at the characteristic alpha-relaxation time <tau >, 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 chi(T)(Q,t) decreases after passing the crossover temperature T-L. We make all argument to relate the occurrence of the extremum of the peak height in chi(T) to the existence of the dynamic crossover temperature in each of these cases.