An All-vanadium Continuous-flow Photoelectrochemical Cell for Extending State-of-charge in Solar Energy Storage

Greater levels of solar energy storage provide an effective solution to the inherent nature of intermittency, and can substantially improve reliability, availability, and quality of the renewable energy source. Here we demonstrated an all-vanadium (all-V) continuous-flow photoelectrochemical storage cell (PESC) to achieve efficient and high-capacity storage of solar energy, through improving both photocurrent and photocharging depth. It was discovered that forced convective flow of electrolytes greatly enhanced the photocurrent by 5 times comparing to that with stagnant electrolytes. Electrochemical impedance spectroscopy (EIS) study revealed a great reduction of charge transfer resistance with forced convective flow of electrolytes as a result of better mass transport at U-turns of the tortuous serpentine flow channel of the cell. Taking advantage of the improved photocurrent and diminished charge transfer resistance, the all-V continuous-flow PESC was capable of producing ~20% gain in state of charge (SOC) under AM1.5 illumination for ca. 1.7 hours without any external bias. This gain of SOC was surprisingly three times more than that with stagnant electrolytes during a 25-hour period of photocharge.


b. Electrochemical reactions and transport characteristics
Photons with energy higher than the TiO2 bandgap could generate electron-hole pairs. The photogenerated holes (h + ) oxidize VO 2+ according to the following reaction: h + + VO 2+ + H2O → VO2 + + 2H + The kinetics of the above light-driven reaction can be described by where 1 j is the current density, F is the Faraday's constant, 1 k is the standard rate constant for the photoelectrode, and 4 V C  and h C are the concentrations of VO 2+ and hole, respectively. In this study, first-order reaction kinetics are assumed; therefore, both a and b are taken as unity.

c. Governing equations and source terms
Steady-state simulation was performed on the 3D domain in Fig. S1. The governing equations incorporating the aforementioned electrochemical reaction and the source terms accounting for the species generation/consumption are:

Continuity:
where  is the density,  is the porosity,  is the electrolyte viscosity, p is pressure, and K is the permeability.
Electrons (only in the photoelectrode): I , z , and recomb k are electron diffusion coefficient, electron concentration, electron injection efficiency, wavelength-dependent absorption coefficient, incident photon flux, distance to the semiconductor/electrolyte surface (see Fig. S1), and the charge recombination rate constant, respectively. A N is the Avogadro's number. The 1 st and 2 nd terms on the RHS stand for the electron generation rate and consumption rate (due to charge recombination), respectively.
Holes (only in the photoelectrode): where 1 a is the specific active surface area of the photoelectrode (m 2 /m 3 ). The 1 st , 2 nd , and 3 rd terms on the RHS of the above equation represent the electron generation rate, consumption rate due to charge recombination, and consumption due to photoelectrochemical reaction with VO 2+ , Vanadium VO 2+ : only in the photoelectrode. The effective diffusion coefficients of vanadium species in the porous electrodes are calculated using the following equation, i.e., 5 . 1 Vanadium VO 2 + :

d. Boundary conditions
The simulation was performed under the steady-state condition with a constant current flowing into the photoelectrode (at 0 z  in Fig. S1). Non-flux wall boundary conditions are applied to all other surfaces. Vanadium redox concentrations at the inlet boundary are constant and velocity varies during the simulation. The simulation was conducted by the SIMPLER algorithm in a commercial CFD software Fluent 6.3.26. User defined functions (UDFs) were written to account for diffusivity and source terms for different species in the photoelectrode and flow channels. Some of the parameters employed in the simulation are listed in Table S1.

a. Electrochemical reactions
The electrochemical redox reaction occurring in the cathode half-cell is as follows: The transfer current 2 j for the above reaction is described as 7 : a is the specific active surface area of the carbon paper (m 2 /m 3 ), E is the electrode potential, 3 2 V V E  is equilibrium potential of V 3+ /V 2+ which is and 2 k is the standard rate constants for the cathode reaction. It should be noted that species migration is ignored here 8 , because its contribution to species transport is not significant in the redox flow battery according to reference 4 .

b. Governing equations and source terms
Simulation was conducted on the 3D domain in Fig. S2. The governing equations for flow, vanadium redox species, and electrode potential are listed in Table S2.

c. Boundary conditions
Steady-state simulation was performed under galvanostatic operation and a constant current density is applied to the carbon paper/current collector interface, i.e., 0 z  (Fig. S2) where E is the electrode potential. Non-flux wall boundary conditions are applied to all other surfaces. Vanadium redox concentrations at the inlet boundary remain constant and velocity varies during the simulation. The simulation was conducted at different current and the resultant electrode potential E at the carbon paper/current collector interface was plotted against the applied current in Fig. 6 of the main text.