Power generation from concentration gradient by reverse electrodialysis in ion-selective nanochannels

Abstract

In an aqueous solution, the surface of inorganic nanochannels acquires charges from ionization, ion adsorption, and ion dissolution. These surface charges draw counter-ions toward the surface and repel co-ions. In the presence of a concentration gradient, counter-ions are transported through nanochannels much more easily than co-ions, which results in a net charge migration of one type of ions. The Gibbs free energy of mixing, which forces ion diffusion, thus can be converted into electrical energy by using inorganic ion-selective nanochannels. Silica nanochannels with heights of 4, 26, and 80 nm were used in this study. We experimentally investigated the power generation from these nanochannels placed between two potassium chloride solutions with various combinations of concentrations. The power generation per unit channel volume increases when the concentration gradient increases, and also increases as channel height decreases. The highest power density measured was 7.7 W/m². Our data also indicate that the energy conversion efficiency and the ion selectivity increase with a decrease of concentrations and channel height. The best efficiency obtained was 31%. Power generation from concentration gradients in inorganic ion-selective nanochannels could be used in a variety of applications, including micro batteries and micro power generators.

Appendices

Appendix 1

1.1 Fabrication process for silica nanochannels

The whole process started with a silicon wafer. As the first step, nanochannels were patterned on the wafer by standard photolithography. Lam 4, an RIE (Reactive Ion Etching) instrument from Lam Inc., was used for the nanochannel etching. Two reactive gases were used during this step. SF₆ plasma was used to remove the native oxide layer on top of the silicon wafer and Cl₂ plasma was used to etch the silicon. By applying low power (50 W), we were able to achieve a slow etching rate as well as small surface roughness. After etching the nanochannels, microchannels for the flow passage were defined and etched. The microchannels are around 1-cm long and 500-μm wide. A standard DRIE recipe was run for 20 min to etch 60-μm deep microchannels. The top surface was then deposited as a 1-μm thick oxide layer using PECVD (plasma enhanced chemical vapor deposition) at 350°C. This layer serves as a protection layer for the following reservoir etching. Reservoirs were pattered from the back side and DRIE was again used to form straight etch-through reservoirs. The 1-μm thick oxide layer was removed by 5:1 HF solution after this step. Wafer was then sent into a furnace to grow thermal oxide at 1,000°C. 200 nm dry oxide and 300 nm wet oxide were grown uniformly on all wafer surfaces. The total 500-nm thick thermal oxide provides a good insulation layer for later electrical measurement. After that, this silicon wafer and a new Pyrex wafer were cleaned in hot piranha solution and blow-dried by nitrogen. Wafer-wafer anodic bonding was used to bond these two wafers together. The bonding process took around 30 min at 400°C and 600 V. The bonded wafer was then placed in a PECVD chamber with reservoir side up to grow a 3-μm thick PECVD oxide on all exposed surface. This additional oxide layer prevents electrical leakage from any sharp corner. To prevent solution contamination, a 1-μm thick PDMS was also coated on this surface using a stamp-stick technique.

Appendix 2

2.1 Validity of Eq. 2

In the present study, the electric potential generated in the nanochannel, V _channel, is not directly measured but calculated from measured V _app via Eq. 2. However, the error introduced by this indirect approach is less than 1% because Eq. 2 accurately predicts E _redox when the current from the nanochannels, I _channel, is much smaller than the exchange current of the Ag/AgCl electrodes, as shown below.

The real redox potential E _redox is given by:

$$ E_{\text{redox}} = E_{\text{eq}} + \eta , $$

(13)

where E _eq and η are the thermodynamic value of E _redox and the overpotential, respectively (Bard and Faulkner 2001). E _eq is simply given from the Nernst equation as:

$$ E_{\text{eq}} = \frac{RT}{zF}\ln {\frac{{\gamma_{{C_{\text{H}} }} c_{\text{H}} }}{{\gamma_{{C_{\text{L}} }} c_{\text{L}} }}}. $$

(14)

The overpotential η is the potential difference between the thermodynamically determined potential and the real potential. This overpotential is caused by the limited rate of electrochemical reactions on the electrodes. The overpotential is given from the Butler–Volmer equation as:

$$ I_{\text{channel}} = Ai_{0} \left[ {{\text{e}}^{{{\frac{\alpha F\eta }{RT}}}} - {\text{e}}^{{ - {\frac{(1 - \alpha )F\eta }{RT}}}} } \right], $$

(15)

where i ₀, A, and α are the exchange current density of the electrodes, the surface area of the electrode–solution interface, and the transfer coefficient, respectively.

In the present study, the cylindrical Ag/AgCl electrodes were dipped into the solutions. The diameter D of the electrodes and the dipping length L were about 0.8 and 2 mm, respectively. Therefore, the surface area of the electrode–solution interface is:

$$ A = {\frac{{\pi D^{2} }}{4}} + \pi DL \approx 0.06\;{\text{cm}}^{2} . $$

(16)

The exchange current density i ₀ of the Ag/AgCl electrodes is known to be higher than 10⁻³ A/cm² and the transfer coefficient is close to 0.5 (Deng et al. (2005)). As shown in Fig. 3, I _channel is much smaller than 10 nA in the present study. As a result, from Eq. 15, the overpotential η is smaller than 0.05 mV. Therefore, the overpotential is much smaller than E _eq (>5 mV) and the redox potential E _redox is approximately equal to the thermodynamic potential E _eq:

$$ E_{\text{redox}} \approx E_{\text{eq}} = \frac{RT}{zF}\ln {\frac{{\gamma_{{C_{\text{H}} }} c_{\text{H}} }}{{\gamma_{{C_{\text{L}} }} c_{\text{L}} }}}. $$

(17)

In Table 3, the redox potentials calculated from Eq. 17 also are compared with the experimental values presented in Janata (2009). The results indicate that Eq. 17 can predict the redox potential with a relative error of less than 1%.

Table 3 Redox potentials of Ag/AgCl electrodes

Appendix 3

3.1 Uncertainty analysis

To analyze the errors, an uncertainty analysis was conducted. The measurement error consists of the bias error and the precision error. The uncertainty U is given as follows (Beckwith et al. 1993):

$$ U = (B^{2} + P^{2} )^{1/2} , $$

(18)

where B and P are bias uncertainty and precision uncertainty, respectively. The precision uncertainty is determined by:

$$ P = t_{{ 9 5 {\text{\% ,v}}}} {\frac{S}{\sqrt N }}, $$

(19)

$$ v = N - 1,S = \sqrt {\frac{1}{N}\sum\limits_{i = 1}^{N} {(x_{i} - \bar{x})^{2} } } , $$

(20)

where $t_{{ 9 5 {\text{\% ,v}}}}$, S, v, N, $\bar{x}$ and x _i are t-distribution for a confidence level of 95%, standard deviation, degree of freedom, data number, sample mean, and measured value of a particular experiment.