Hydrogen-bond dynamics of water in a quasi-two-dimensional hydrophobic nanopore slit

We perform molecular dynamics simulations to investigate hydrogen-bond dynamics of the TIP5P (transferable intermolecular potential with five points) model of water confined in a quasi-two-dimensional hydrophobic nanopore slit. We find that even if the average number and the lifetime of hydrogen bonds are affected by nanoconfinement, the characteristics of hydrogen-bond dynamics in hydrophobic confined water are the same as in bulk water—such as an Arrhenius temperature dependence of average hydrogen-bond lifetime and a nonexponential behavior of lifetime distributions at short time scales. The different physical properties of water in hydrophobic confinement compared to bulk water—such as $\sim 40\text{K}$ temperature shift—may be primarily due to the reduction of the lifetime of hydrogen bonds in confined environments. We also find that the hydrogen-bond autocorrelation function exhibits a power-law tail following a stretched exponential behavior. The relaxation time of hydrogen bonds in confined water is smaller than in bulk water. Further, we find that the temperature dependence of the relaxation time follows a power-law behavior, and the exponents for bulk and confined water are similar to each other.

Figure 1

(Color online) The average number of hydrogen bonds per water molecule, $⟨n_{\text{HB}}⟩$, as a function of temperature. For both confined and bulk water, $⟨n_{\text{HB}}⟩$ decreases as temperature increases. Due to the geometric constraints and the hydrophobic property, $⟨n_{\text{HB}}⟩$ is smaller in confined water than in bulk water.

Figure 2

(Color online) Shown in a semilogarithmic plot are the distributions $P\left(t\right)$ of hydrogen-bond lifetimes $t$ at different temperatures. The plots, except $T=300\text{K}$ for confined water, are shifted up for clarity. $P\left(t\right)$ indicates that there is a region which shows a nonexponential behavior, followed by an exponential tail for all temperatures investigated. Note that $P\left(t\right)$ for $T=260\text{K}$ for confined water and $T=300\text{K}$ for bulk water overlap, corresponding to the 40 K shift proposed in Refs. [18, 19, 32] for hydrophobic confinement. The line segment has slope ${\tau }_C^{-1}$ (see Fig. 3), since $P\left(t\right)\sim \text{exp}\left(-t/{\tau }_C\right)$ in long time scales.

Figure 3

(Color online) Shown in an Arrhenius plot is the characteristic time ${\tau }_C$ of the exponential tail in $P\left(t\right)$ $\left[\sim \text{exp}\left(-t/{\tau }_C\right)\right]$ as a function of temperature for confined water. It shows that the temperature dependence of ${\tau }_C$ can be fitted by an Arrhenius form (line).

Figure 4

(Color online) The average HB lifetime ${\tau }_{\text{HB}}$ as a function of $1/T$ in an Arrhenius plot. Two blue lines indicate the fits, ${\tau }_{\text{HB}}={\tau }_0\text{exp}\left(E_A/k_{B}T\right)$. For confined water, ${\tau }_{\text{HB}}$ can be fitted by an Arrhenius behavior, which is preserved as in bulk water, even if ${\tau }_{\text{HB}}$ and the number of hydrogen bonds in confined water are smaller than in bulk water. The magnitude of activation energy calculated for confined water $\left(E_A^C=4.92\pm 0.07\text{kJ}/\text{mol}\right)$ is around half of that in bulk water $\left(E_A^B=9.80\pm 0.53\text{kJ}/\text{mol}\right)$. $E_A^B$ is consistent with previous experimental and simulation results for the activation energy associated with fast hydrogen-bond dynamics. The triangle symbols are for bulk water at temperatures shifted lower by $\Delta T=40\text{K}$.

Figure 5

(Color online) Shown in a log-log plot are the HB autocorrelation functions $c\left(t\right)$ for (a) bulk and (b) confined water. In a short-time regime, $c\left(t\right)$ shows a stretched exponential behavior. In an asymptotic limit, $c\left(t\right)$ exhibits a power-law behavior $\left[c\left(t\right)\propto t^{-\beta }\right]$. The exponent $\beta$ of the tail depends on the dimensionality $d$ of the system $\left(\beta =d/2\right)$. For bulk $\left(d=3\right)$, the value of $\beta$ is around 1.38, which is close to 1.5 at the asymptotically long time. For water confined in a quasi- two-dimensional nanopore slit $\left(d=2\right)$, the value of $\beta$ is around 1.02.

Figure 6

(Color online) The HB relaxation time ${\tau }_R$ as a function of temperature. Note that ${\tau }_R$ in confined water is smaller than in bulk water. As temperature decreases, ${\tau }_R$ rapidly increases for both confined and bulk water. The temperature response of ${\tau }_R$ in confined water is less pronounced than in bulk water.

Figure 7

(Color online) Shown in a log-log plot is the HB relaxation time ${\tau }_R$ as a function of $\left(T-T_C\right)/T_C$. ${\tau }_R$ follows a power-law behavior, ${\tau }_R\sim {\left(T-T_C\right)}^{-\gamma }$. $T_C$ for confined water $\left(\simeq 215\text{K}\right)$ is different from for bulk water $\left(\simeq 235\text{K}\right)$, but the exponents for bulk $\left(\gamma \simeq 2.18\right)$ and confined water $\left(\gamma \simeq 2.29\right)$ are similar.