Structure Dynamics of the Proton in Liquid Water Probed with Terahertz Time-Domain Spectroscopy

We study the hydration of protons in liquid water using terahertz time-domain spectroscopy and polarization-resolved femtosecond midinfrared pump-probe spectroscopy. We observe that the addition of protons leads to a very strong decrease of the dielectric response of liquid water that corresponds to $19\pm 2$ water molecules per dissolved proton. This depolarization results from water molecules ($\sim 4$) that are irrotationally bound to the proton and from the motion of water (corresponding to the response of $\sim 15$ water molecules) involved in the transfer of the proton charge.

Figure 1

(a) Terahertz pulses as transmitted through an empty cuvette and through cuvettes filled with a $1\mathrm{mol}/\mathrm{kg}$ solution of NaCl and HCl, respectively. (b) Extracted dielectric function of 1 m HCl and 1 m NaCl. The thick lines that go through the data points are a fit to Eq. (1) with $S_1$ for the salt fixed to its literature value [17]. The thin lines represent the dielectric response after it has been corrected for the conductivity contribution. (c) Differential dielectric response $\Delta \widehat{ϵ}$ for 1 m HCl-NaCl, with the fit according to Eq. (2). Error bars indicate the 95% confidence interval.

Figure 2

The decay of the anisotropy $R$ is independent of the proton:cation ratio, corroborating the assumption that ${\tau }_D$ remains the same for protons and cations.

Figure 3

The depolarization induced by protons for different proton concentrations. Each data point corresponds to a differential measurement for an acid-salt combination and is slightly horizontally offset for clarity. The line is a linear fit to all data points. The slope is a direct measure for the number of water molecules that is affected by the presence of the proton. Above concentrations of $1.5\mathrm{mol}/\mathrm{kg}$, the relation becomes nonlinear, indicating overlapping hydration layers [26, 27].