This thesis explores the glass transition of amorphous ices in connection to the hypothesis that water may exist in two distinct liquid states: a high-density liquid (HDL) and a low-density liquid (LDL). These states are predicted by the liquid-liquid critical point hypothesis but are challenging to study directly due to rapid crystallization in the supercooled region known as "No man’s land." Instead, we investigated this complex behavior indirectly by examining the glass transitions in high-density (HDA) and low-density (LDA) amorphous states of water, which serve as experimental proxies for HDL and LDL.

Using a new sample design, allowing access to freestanding amorphous ice layers in vacuum, we conducted Fourier Transform infrared spectroscopy (FTIR) and X-ray scattering experiments to characterize the HDA-LDA transition. We report the first FTIR spectra of HDA, obtained from pressure-induced amorphization and observed shifts in the OD-stretch frequency that reveal a first-order-like character in the transition. Additionally, small-angle X-ray scattering (SAXS) provided insights into nanostructural transformations, while X-ray photon correlation spectroscopy (XPCS) at the PETRA III beamline P10 examined the dynamic properties of HDA at both ambient and elevated pressures. Our XPCS results revealed an oscillatory signal, suggesting the formation of static LDA "seeds" within a diffusive HDL matrix and highlighting a complex transition pathway from glassy HDA to an ultraviscous HDL, and eventually to LDA or LDL. For high-pressure studies, we developed a specialized setup combining a diamond anvil cell (DAC) with cryogenic XPCS capabilities, enabling the first high-pressure, cryogenic XPCS measurements on amorphous ice. This setup allowed us to observe a diffusion coefficient of 40 Ų/s at 124 K and 0.08 GPa, aligning with a glass transition temperature (T_g) estimate near 124 K. These high-pressure capabilities demonstrate promising potential for future experiments to expand the pressure range and provide deeper insights into the behavior of both HDA and LDA. In summary, our findings outline a transition pathway from HDA to HDL to LDA(L), suggesting that the dynamic behavior can reveal evidence for two distinct liquid states in water, providing indirect support for the liquid-liquid critical point hypothesis.