Diffusion-Controlled Growth of Oxygen Bubble Evolved from Nanorod-Array TiO₂ Photoelectrode

1. Introduction

Hydrogen production by photoelectrochemical water splitting is a promising source for carbon-free energy [1–3]. In order to increase the energy conversion efficiency, a lot of research on transfer process enhancement of photo-electron has been carried out with great progress by photoelectrode surface modification with special micro-nano structure [4–7]. But for this kind of heterogeneous photocatalytic or photochemical conversion system, many issues concerning interface of such micro-nano structure semiconductor and liquid still remain unsolved, such as the nature of the active sites, mechanism for heterogeneous photocatalytic reaction of water splitting, and effects of interfacial interaction during reaction product transfer.

Although much progress has been made on the bubble growth, effects of the solid surface structure are still to be understood. Wei et al. investigated the bubble behavior on micro-pin-fined surface and considered a large capillary force leading to easy bubble detachment [14]. Yang et al. studied the bubble-solid interaction indicating the importance of electrolyte concentration and DLVO surface forces [15]. The interaction between the micro-nano structure surface with electrolyte and gas-liquid interface should be investigated more deeply.

In this paper, to investigate nanostructure effects on bubble behavior evolved from nanoscale structure photoelectrode, a study on nanorod-array structure surface characteristics and single oxygen bubble growth dynamics is carried out.

2. Experimental

TiO₂ film modified by nanorod-array was used as the anode in the investigation, and its SEM shows in Figure 1 with rod height of about 870 nm and rod diameter of nearly 120 nm. The optical contact angle meter model SL200 was applied to study the wettability of its surface.

The experiments on bubble evolution were conducted in an electrolytic cell, as shown in Figure 2. Na₂SO₄ in deionized water with different concentrations of 0.495, 0.354, 0.261, 0.206, and 0.170 mol/L was used as the electrolyte. Pt was used as a cathode. The bubble evolution process was observed by the microscope camera system. The image intense CCD whose resolution is 1376*1040 and objective lens is 5x /0.15 was applied. All the experiments were conducted under the conditions of ambient temperature 25°C and ambient pressure 1 atm.

3. Results and Discussion

3.1. Wettability of Nanorod-Array TiO₂ Film

In order to investigate the interaction, especially wettability between nanorod-array film and water, we carry out the experiment on contact angle firstly. Figure 3 shows measurement results of about 80^° ± 1^°, indicating a general hydrophilic ability.

3.2. Oxygen Bubble Behavior Evolved from Nanorod-Array TiO₂ Film

Figure 4 shows the general characteristics of bubble growth. Compared to bubble growth during boiling and common electrolysis, bubble evolved from nanorod-array surface stays longer and smaller, which is determined by the forces acting on them. In our experiment, the proper effects include gravity, gas-liquid interfacial surface tension, marangoni force, electric force (with the possibility of gas-liquid interface being charged), and interfacial interaction with elastic materials. Among those, the most possible and important effects to prevent the bubble departure and keep bubble staying are marangoni force due to nonhomogeneous gas adsorption at the interface and the capillary force caused by contact behavior with nanorod-array surface structure.

Besides the dynamics aspect, we are much concerned about the mechanism driving the bubble growth. We investigate the relationship of R_B(t) ~ t^x, as show in Figure 5. It indicates the R_B(t)² is linear to the time, which is to say x = 0.5 for equation R_B(t) ~ t^x.

3.3. Oxygen Bubble Growth Model from Nanorod-Array TiO₂ Film

The bubble growth is driven by the concentration difference between the electrolyte bulk and the bubble interface, which is an analogy to the bubble growth during boiling. But the acquisition of the concentration data, key to electrolysis, is much difficult than that of the temperature data for boiling. So the modelling of bubble growth driven by the concentration difference is less developed than that driven by the temperature difference.

From the above analysis, we obtained R_B(t) ~ t^0.5 relationship, which is first growth mechanism showed in Figure 6. According to Vogt’s theory [12, 13], effects on bubble growth in one circle, meaning the process of bubble departure and movement excluded, include two parts, which are the diffusion due to the concentration gradient of dissolved gases in the aqueous electrolyte and the microconvection caused by the bubble interface movement.

For the diffusion effect, we can describe it by the following mass transfer around the bubble, assuming a steady state:

$$ (2)

And the boundary conditions are as follows:

$$ (3)

And then, we can solve the equation, obtaining concentration distribution as follows:

$$ (4)

So diffusion flow of the gas transferred across the bubble interface can be described as

$$ (5)

where $$ is the diffusion coefficient of oxygen gas.

For the microconvection effect caused by the bubble interface movement, we refer to the surface renewal theory by Danckwerts [16] described as follows:

$$ (6)

where S is ratio of the increasing surface area to the total surface area,

$$ (7)

So the total mass-transfer flow into a bubble is

$$ (8)

On the other hand, from the aspect of mass conservation, the net mass-transfer flow is equal to the gas molecules variation in the bubble, which is

$$ (9)

And then, we obtain

$$ (10)

Letting R_B = Bt^0.5 according to our experimental results and substituting it to (10), we conclude that

$$ (11)

where A = V_mol(c₀ − c_i).

So the bubble radius is

$$ (12)

Equation (12), as the bubble growth model, can describe the diffusion-controlled bubble growth process including diffusion and microconvection effects.

4. Conclusions

In this paper, we carried out research on nanorod-array structure surface characteristics and single oxygen bubble growth dynamics. By experimental studies of wettability on the photoelcectrode nanorod-array surface and oxygen bubble growth from anode, we analyzed the interaction affecting the gas-solid-liquid contact behaviors and product transportation mechanism, which is controlled by diffusion due to the concentration gradient of dissolved gases in the aqueous electrolyte and the microconvection caused by the bubble interface movement and we emphasize the importance of marangoni force due to nonhomogeneous gas adsorption at the interface and the capillary force caused by contact behavior with nanorod-array surface structure on bubble growth period. In the end, based on the bubble growth characteristics of R_B(t) ~  t^0.5 in the experiment, a model describing the product transport mechanism was presented.

Conflict of Interests

The authors declare no conflict of interests.