Dynamics of confined water reconstructed from inelastic x-ray scattering measurements of bulk response functions

Nanoconfined water and surface-structured water impacts a broad range of fields. For water confined between hydrophilic surfaces, measurements and simulations have shown conflicting results ranging from “liquidlike” to “solidlike” behavior, from bulklike water viscosity to viscosity orders of magnitude higher. Here, we investigate how a homogeneous fluid behaves under nanoconfinement using its bulk response function: The Green's function of water extracted from a library of $S(q,\omega )$ inelastic x-ray scattering data is used to make femtosecond movies of nanoconfined water. Between two confining surfaces, the structure undergoes drastic changes as a function of surface separation. For surface separations of $\approx$9 Å, although the surface-associated hydration layers are highly deformed, they are separated by a layer of bulklike water. For separations of $\approx$6 Å, the two surface-associated hydration layers are forced to reconstruct into a single layer that modulates between localized “frozen’ and delocalized “melted” structures due to interference of density fields. These results potentially reconcile recent conflicting experiments. Importantly, we find a different delocalized wetting regime for nanoconfined water between surfaces with high spatial frequency charge densities, where water is organized into delocalized hydration layers instead of localized hydration shells, and are strongly resistant to `freezing' down to molecular distances ($<$6 Å).

Figure 1

(a) The geometry of the inelastic x-ray scattering experiment: (0) Synchrotron x-rays are conditioned by a monochromator, which reduces their bandwidth to $\delta E\approx 1$ meV. These x rays (initial energy $E_i$ and momentum $k_i$) are scattered from a sample (1) to an energy discriminating analyzer (2). The analyzer focuses the scattered x rays with final energy $E_f$ and momentum $k_f$ to be counted at a scintillation detector (3). The dynamic structure factor $S(q,\omega )$ is measured as a function of momentum transfer $q=k_f-k_i$ and the energy transfer $\omega =E_f-E_i$. In an IXS experiment, $k_i$ and $E_f$ are fixed, so $q$ and $\omega$ are determined by varying the position of the analyzer and incident energy from the monochromator $E_i$, respectively. The measured intensity $I(q,\omega )$ is the convolution of the physical quantity $S(q,\omega )$ with the instrumental resolution profile $R\left(\omega \right)$. (b) We implement a model hydrophilic surface as follows. A square lattice of dipoles (lattice constant $a=7$ Å) is embedded in a confining surface. (In the diagram, the square lattices of dipoles extend into the page.) Each confining surface is treated as an excluded volume of semi-infinite half-space. The geometrically flat interface which borders this excluded volume represents the idealized model solid-water interface. Each subsurface dipole is composed of charges $\pm q$ separated by $d=2$ Å (yellow spheres represent positive charges; green spheres represent negative charges), centered at $z_0=2$ Å below each solid-water interface. Changing the depth of the dipoles away from the geometric surface does not qualitatively change the results described here.

Figure 2

The dependence of the variance of the induced density on the distance from the surface. The variance was chosen to highlight the decay of surface-induced structure. The raw data (solid black line) and two exponential fit (dashed blue line) show that near the surface, the decay of the density is sharp (${\lambda }_{\text{ad}}\approx 0.5$ Å). This is due to the density fluctuations representing water adhered to the interaction site. For larger distances, the variance decreases with a decay length of $\lambda \approx 3.5$ Å, indicating that the influence of the surface on local density ordering of water is only strong in the first few molecular layers and is nearly zero for $z>10$ Å.

Figure 3

(a) Density $\Delta \rho \left(z\right)$ for liquid water confined by hydrophilic surfaces. For subnanometer confinement ($D=6$ Å, $D=9.2$ Å), density oscillations about the bulk density (dotted line) can be observed. For larger gaps ($D=15.2$ Å, $D=40$ Å), the density oscillations are localized near each surface, with nearly constant bulk densities in the center of the gap. The vertical scale is linear and measured in identical units for all four plots. (b) Confinement is implemented as two single sheets from Fig. 1b separated by a distance $D$. Shear is induced by moving the top interface relative to the bottom interface at $V$. We assume that the response function of the bulk fluid is not altered by the shear.

Figure 4

The time-dependent density profile for confined water in the $XZ$ plane containing the surface dipoles on each sheet. The top sheet is shearing with velocity $V$ in the $X$ direction, $Z$ is the direction of confinement, and these densities are integrated from a 2-Å slab in the $Y$ direction centered on the dipoles. For $D=9.2$ Å, the in registry hydration structure of the confining surfaces (a) is characterized by bulklike water sandwiched between well-defined surface-structured hydration layers. As the top surface is sheared at $V=200$ m/s (b), (c), the hydration layers are distorted and exhibit cycles of deformation and recovery as the dipole sites on the top and bottom surfaces move into and out of registry. For the $D=6$ Å case, the two hydration structures are forced to reconstruct into one. When the surfaces are in registry (d), the confined water has a highly localized structure. As the top surface is sheared, the hydration structure deforms to bridge the two surfaces (e). When the surfaces are out of registry, the water in the center of the channel appears to be “shear melted,” with densities close to that of bulk water (f). The hydration returns to the well-defined structure (d) as the interaction sites come into registry again.

Figure 5

The (a) in-registry and (b) out-of-registry hydration structure in the $D=6$ Å confining gap between square lattice ($a=3.5$ Å) hydrophilic surfaces. The top surface is sheared at $v_x=200$ m/s to compare to the $a=7$ Å case. The increase in interaction site density eliminates the dynamical formation of dense, localized hydration structures as seen for lower site density cases. (c) The order can be quantified by comparing the density structure factor $S_{\text{center}}(k={\mathbf{k}}_1)$ in the center of the gap to the structure factor of adhered hydration structure at the stationary surface $S_{\text{adhesion}}(k={\mathbf{k}}_1)$, where ${\mathbf{k}}_1$ is the reciprocal lattice vector in the direction of shear ($|{\mathbf{k}}_1|=2\pi /a$). For large surface lattice spacing ($a=14\AA$, $a=7\AA$), the order ratio $\Theta =S_{\mathrm{center}}\left({\mathbf{k}}_1\right)/S_{\mathrm{adhesion}}(k={\mathbf{k}}_1)$ shows periodic oscillation between $\Theta =0$, indicating complete delocalization of water density in the $XY$ plane, and $\Theta =0.8$, indicating that the hydration structure in the gap is nearly as ordered as it is at the stationary interface. As the interaction site density is increased ($a=3.5$ Å), $\Theta \approx 0$ at all times. (d) The maximum order ratio ${\Theta }_{\text{max}}$ during shear for different values of $D$ and $a$ is represented in a dynamical phase diagram for confined water. For subnanometer gaps and high interaction site density (region I), the hydration structure induced is in a constant delocalized state of frustrated liquidlike water. The freeze-melt transition regime (region II) occurs for lower interaction site densities and small gaps ($D\approx 10$ Å). For large gaps ($D\ge 10$ Å, region III), the surfaces have little effect in the middle of the gap ($\langle \delta {\rho }^2\rangle \approx 0$), resulting in bulklike water between single-surface hydration structures. This crossover occurs for gap distances $D$ that permit more than three layers of water molecules (two adhered layers and one shared first hydration layer).