The steady-state permeation current (J_ss) of hydrogen transient curves gives information about the subsurface concentration of hydrogen atoms at the charging surface (C₀):

When only reversible trapping is important and the permeation transient can be represented by Fick’s first law of diffusion, then:

where D_eff is the effective diffusivity of atomic hydrogen. This characteristic parameter can be calculated based on three different methods.

1. The elapse time (t_lag) method considers the following equation when the normalized flux of atomic hydrogen (J(t)/J_ss) is equal to 0.63:

2. The breakthrough time (t_b) method is based on the following equation:

3. With the slope method, D_eff can be calculated from the slope of a plot of log(|J_ss–J(t)|) vs. 1/t.

In order to remove the hydrogen already present in the iron samples, metallic sheets are pretreated at 80 ºC overnight before the experiments are performed.

The charging cell is filled with 0.1 mol/L HCl and 0.2 g/L As₂O₃ as hydrogen precursor, while 0.1 mol/L NaOH is used in the detection cell. Hydrogen permeation studies involve the following procedure:

1. Initially, amperometric detection is performed in the detection cell by applying +0.30 V. The charging cell is not activated.

2. Decay of the current must be observed in the detection cell. The decay time depends on the sample that is being tested.

3. Once the current acquired in the detection cell is close to 0 μA, a cathodic polarization is carried out in the charging cell. According to ASTM G148 [1], charging transient is performed considering currents of -1 mA/cm². Potentiometric detection at -1.8 mA is applied in the experiments shown in this Application Note.

Detection of hydrogen flux through the WE requires different times depending on the properties of the sheet (e.g., composition, structure, porosity, etc.).

4. In order to carry out a decay transient, the electrochemical generation of hydrogen in the charging cell is stopped while the detection cell continues the amperometric measurement.

Steps 3 and 4 can be repeated to produce consecutive charging and decay transients, respectively.

Two iron sheets of 2 mm thickness are evaluated using the procedure explained in the previous section. Figure 2 shows the charging and decay transients obtained with these samples.

Different electrochemical profiles are obtained depending on the properties of each sample. For example, iron sheet 1 (Figure 2, in orange) exhibits the highest hydrogen diffusivity due to the higher current recorded. On the other hand, sample 2 (Figure 2, in blue) not only shows a lower current, but also a delay in the hydrogen transport due to its lower permeability.

Experimental results are analyzed using the H₂ permeation module implemented in DropView 8400M. To facilitate the understanding of this tool, only the permeation through sample sheet 2 is explained.

1. Select the electrochemical curve and click on «H₂ Permeation» in the Data Analysis drop-down menu (Figure 3). Then, select the «Analysis» option.

2. In the empty fields, type the thickness and the exposed area of the sample used in the experiment (Figure 4). Click the «Calculate» button to obtain the characteristic parameters associated with the evaluated sample.

3. Two points must be selected: the first one before the charging transient starts, and the second one when the system achieves a steady state (Figure 5).

4. Different parameters such as the effective diffusivity of atomic hydrogen (D_eff), the subsurface concentration of atomic hydrogen at the charging side (C₀), and the time to achieve a value of normalized flux of atomic hydrogen (J(t)/J_ss) = 0.63 (t_lag) are then automatically calculated (Figure 6).

5. In Figure 7, two additional curves are plotted in the graphical representation apart from the raw curve (in blue): «CalcFlux» (red line) corresponds to the applied algorithm and «NormFlux» (black line) is associated with the normalized hydrogen flux (secondary axis).

The obtained results are always available just by selecting the «CalcFlux» curve (Figure 7, in red) and the «View results» option included in the H₂ permeation module (Figure 3).

Following the described steps, D_eff, C₀, and t_lag for the two iron samples are obtained (Table 1).

This Application Note illustrates the use of the Metrohm DropSens μStat-i Multi16 instrument to perform hydrogen permeation experiments according to ASTM G148. This instrument allows users to work with two channels in floating mode and offers the required sensitivity for these studies.

μStat-i Multi16 allows users to perform multi-hydrogen permeation experiments with up to eight H cells in only one instrument.

The H cell used in this study consists of two compartments: the charging cell to generate hydrogen and the detection (or oxidation) cell to detect the hydrogen permeated through the working electrode.

DropView 8400M software includes dedicated tools for the analysis of these experiments. The H₂ permeation module allows easy and quick fitting of the hydrogen transients and the automatic calculation of experimental parameters such as the effective diffusivity and the concentration of hydrogen.