Proton Diffusion in Ice Bilayers

A diamond-anvil-cell (DAG) is a small high pressure cell most suitable for the spectroscopic measurement of molecular or atomic diffusion. The DAG is used for various kinds of spectroscopic investigations on liquids and solids at pressures up to several tens of GPa [19-22]. The optically transparent nature of diamond over a wide wavelength span allows in situ optical measurements in combination with conventional equipment such as visible light or infrared spectrometers. The protonic diffusion in ice is measured by a traditional diffusion-couple method, in the present case, with an H2O/D2O ice bilayer. The mutual diffusion of hydrogen (H) and deuteron (D) in the ice bUayer is monitored by measuring the infrared vibrational spectra. The experimental details are described in the following sections. 

Protonic diffusion in ice has been investigated by a spectroscopic method. This method is based on the isotope effect on molecular vibrations. The mass difference between hydrogen and deuteron results in a frequency difference by a factor of V2 for the stretch mode. The peak positions are well separated in the spectra and hence their heights are converted to the H(D) concentrations with good accuracy. The diffusion process is monitored by measuring the reflection spectra of an H2O/ D2O ice bilayer, for which the equation of diffusion is described in analytical form. The H/D mutual diffusion coefficient measured at 400 K shows a monotonic decrease by two orders of magnitude as the pressure increases from 8 to 63 GPa. 

Figure 24.5 shows an optical setup for high-pressure diffusion measurement with a DAC. An H2O/D2O ice bilayer is already prepared in the sample chamber. The dimension of each ice layer is typically 120 pm in diameter and 20 pm in thickness. The detailed procedure for preparing the ice bilayer has been described in the literature [24]. The surface concentration of proton, Ch, at x = 1 can be... 

The protonic diffusion process in the ice bilayer is clearly monitored by the vibrational spectroscopic measurement. The reflection spectra measured after annealing at 400 K and 10.2 GPa are sho vn in Fig. 24.7. Panels A and B present the spectral changes vith time measured for the back surfaces of D2O and H2O ice layers, respectively. The OH stretch peak is located around 3200 cm , whereas the OD stretch peak is located around 2500 cm, lower by a factor of approximately I/V2, as expected from a square root of the mass ratio [5]. The... 

Molecular diffusion is suppressed in the high pressure phase of ice VII. No signal for molecular diffusion is detected. Reflection spectra measured for the back surfaces of an H2 0 /H2 0 ice bilayer are shown in Fig. 24.9. The aimealing temperature and pressure are 400 K and 10.2 GPa, respectively, the same as those for the protonic diffusion measurement. The abscissa axis is expanded to emphasize the peak positions of the and OH stretch vibrations. Separation by... 

For the bilayer configuration of H2O/D2O ice, the equation of diffusion can be described with an analytical form under appropriate boundary conditions. The protons (deuterons) initially contained in the H2O (D2O) ice layer diffuse into the D2O (H2O) ice layer by H/D exchange reaction. The initial distribution of proton, which is described with a step-function as shown in Fig. 24.4, deforms gradually with time and eventually reaches a homogeneously distributed state. Starting with Fick s second law, we can derive a one-dimensional diffusion equation for the concentration of H at time t and location x under the following boundary and initial conditions [23]. 

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