F S (Q z , t) for water in silica pores of diameters 20 and 40 Å.
ISFs for Q = Q x (top) and Q = Q z (bottom) for water in a 30 Å diameter pore. Shown is F S (Q, t), obtained from Eq. (5), and the result of the product approximation, Eq. (6).
Translational (top) and rotational (bottom) ISFs for water in 20 and 40 Å diameter pores for two values of Q = Q z .
The connected portion of the ISF for Q along the pore axis for water in 20, 30, and 40 Å diameter pores, plotted vs. log t. The top panel is for Q = 2.51 Å−1 and the bottom panel for Q = 1.26 Å−1.
A comparison of F S (Q x , t) and F S (Q z , t) for water in the 30 Å diameter pore at four values of Q.
Translational (top) and rotational (bottom) components of the water ISF in a 30 Å diameter pore at four values of Q. Comparison between and is shown in the top panel and between and is in the bottom panel.
Comparison of the MD results (dashed line) with the FDC model (full line) results for the translational ISF for Q in the radial (top) and axial (bottom) directions of water in a 40 Å diameter pore.
The top panel illustrates the division of the water density profile (centered on water O) vs radial distance ρ from the pore center into three regions: outer ρ > d/2 (d = the nominal pore diameter), surface: d/2−6 Å ≤ ρ < d/2, and core: 0 ≤ ρ < d/2−6 Å. The bottom panel shows the probability distribution of , where is the surface normal pointing into the water phase and a unit vector along the water OH bond, in the three regions illustrated in the top panel.
Translational ISFs, , for water in 20 Å (top) and 40 Å (bottom) silica pore at Q = 1.26 Å−1 and for Q along x and z. Depicted are pore-averaged results and the results for water molecules in the three concentric regions.
Rotational ISFs in the three concentric regions for water in a 40 Å diameter pore. The top panel illustrates the results for Q = 1.26 Å−1 and the bottom panel for Q = 2.51 Å−1. In both panels, the results for and in each region are compared.
Orientational correlations (top panel) and (bottom panel) of water in the three concentric regions of a 40 Å diameter pore. In both panels, the results for and are compared.
Exact and approximate rotational ISFs (top panel) and (bottom panel) at Q = 1.26 Å−1 for water in a 40 Å diameter pore are compared. In each panel are shown the results for the outer and for the surface regions. The results for the surface region are shifted downward by 0.1 for clarity. The results of the direct (“direct = anisotropic sum”) calculation (Eq. (8)) are compared to those for the Rayleigh expansion for the isotropic system (Eq. (9), “isotropic sum”) and for the Rayleigh expansion containing only diagonal terms (Eq. (14) with n = 0, “diagonal sum”) for the anisotropic system.
System size parameters and fit parameters to free-diffusion-in-a-cylinder model.
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