Pore-size dependence and characteristics of water diffusion in slitlike micropores

The temperature dependence of the dynamics of water inside microporous activated carbon fibers (ACF) is investigated by means of incoherent elastic and quasielastic neutron-scattering techniques. The aim is to evaluate the effect of increasing pore size on the water dynamics in these primarily hydrophobic slit-shaped channels. Using two different micropore sizes ($\sim 12$ and 18 Å, denoted, respectively, ACF-10 and ACF-20), a clear suppression of the mobility of the water molecules is observed as the pore gap or temperature decreases. This suppression is accompanied by a systematic dependence of the average translational diffusion coefficient $D_r$ and relaxation time $\langle {\tau }_0\rangle$ of the restricted water on pore size and temperature. The observed $D_r$ values are tested against a proposed scaling law, in which the translational diffusion coefficient $D_r$ of water within a porous matrix was found to depend solely on two single parameters, a temperature-independent translational diffusion coefficient $D_c$ associated with the water bound to the pore walls and the ratio $\theta$ of this strictly confined water to the total water inside the pore, yielding unique characteristic parameters for water transport in these carbon channels across the investigated temperature range.

Figure 1

Observed quasielastic neutron-scattering intensity $I(Q,E)$ on the BASIS instrument, as a function of energy transfer $E$ for water in ACF-20 (average slit size $d\simeq 18$ Å) at selected momentum transfer $Q$ and temperature $T=250$ K. Although the actual energy window investigated is symmetric in energy ($\pm 120\mu \mathrm{eV}$), only the neutron energy gain side is shown for display purposes. The relative error bars are smaller than the symbols.

Figure 2

Temperature and pore size dependence of the energy-integrated elastic intensity $I\left(T\right)={\int }_{-{\mathrm{\Gamma }}_r}^{{\mathrm{\Gamma }}_r}dE{S}_T(Q,E)$ of water confined in carbon fibers, at a selected momentum transfer $Q$ of 1.3 Å, where ${\mathrm{\Gamma }}_r$ is the instrument energy resolution width ($\mathrm{HWHM}=1.75\mu \mathrm{eV}$). The onset of observable diffusive dynamics on BASIS is marked by the departure from a monotonically varying slope in $I\left(T\right)$ at low temperatures to a more rapidly changing slope at the higher temperatures. The solid lines are model fits to data, corresponding to an activation energy of $E_A=16$ and 21 kJ/mol for ACF-10 and ACF-20, respectively. The error bars are smaller than the symbols.

Figure 3

Intrinsic intermediate scattering function $I_{\mathrm{in}}(Q,t)$ of water confined in activated carbon fibers, as obtained from Fourier transforming the observed $S(Q,E)$ data, and removing resolution contributions at a selected $Q$ of $0.9$ Å, as explained in the text. The top panel compares the results derived for water in ACF-10 (open circles) and ACF-20 (closed circles) at temperature $T=$ 280 K. The bottom panel makes a similar comparison of the data collected at 230 K. The solid black lines are model fit using the stretched exponential model, described in the text. The errorbars associated with $I_{\mathrm{in}}(Q,t)$ are less than 1% within the time range shown.

Figure 4

Temperature and momentum transfer dependence of the observed $A_0$ (offset elastic incoherent structure factor) for ACF-10 (open circles) and ACF-20 (solid squares).

Figure 5

Best fit stretching exponent parameter $\beta$ as a function of $Q$ at $T=250$ K for ACF-10 (open circles) and ACF-20 (solid squares), determined within 0.5% precision. The solid and dashed lines represent the $Q$-averaged $\langle \beta \rangle$ values for ACF-10 (0.68) and ACF-20 (0.71), respectively. In the present work, $\beta$ for each $Q$ and $T$ were used instead of $\langle \beta \rangle$, as is often the case.

Figure 6

Inverse of the average relaxation time as a function of $Q^2$ and temperature. The solid squares are the characteristic values obtained for ACF-20 and the open circles those for ACF-10. The colored lines are the best representative fits using the jump diffusion model discussed in the text. The associated error bars are between 2 and 9%.

Figure 7

Mean relaxation time $\langle {\tau }_0\rangle$ of water confined in ACF-10 (open circles) and ACF-20 (solid circles) plotted as a function of $1000/T$. Data for bulk water [1, 50], observed at comparable temperatures, are also shown. Dashed lines are fits to an Arrhenius temperature dependence.

Figure 8

Net translational diffusion coefficient as a function of $1000/T$ for ACF-10 (open circles) and ACF-20 (solid squares), as compared to that of bulk water (solid diamonds). Dashed lines are fits to an Arrhenius behavior $\sim D_0{e}^{-E_a/RT}$.

Figure 9

Translational diffusion coefficient ($D_r$) of water restricted within the pores of activated carbons at the three temperatures investigated plotted against the corresponding values for bulk water ($D_{\mathrm{bulk}}$). The lowest $D_{\mathrm{bulk}}$ value (230 K) is based on an extrapolation of the Arrhenius behavior of $D_{\mathrm{bulk}}$ shown in Fig. 8. The dashed lines represent the scaling behavior $D_r\left(T\right)=\theta D_c+(1-\theta )D_{\mathrm{bulk}}\left(T\right)$ proposed in Ref. [21], where $D_c$ is a temperature-independent diffusion coefficient associated with the strictly confined water (i.e., most influenced by the pore walls) and $\theta$ is the ratio between this water and the total water inside the pores. The gray shaded area is not physically accessible since $D_r\left(T\right)$ cannot exceed the bulk value. The characteristic $\theta$ and $D_c$ parameters for water diffusing in ACF-10 and ACF-20 are summarized in Table 5.