Towards uniform distributions of reactants via the aligned electrode design for vanadium redox flow batteries

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Towards uniform distributions of reactants via the aligned electrode design for vanadium redox flow batteries J. Suna,1, H.R. Jianga,1, B.W. Zhangb, C.Y.H. Chaoc, T.S. Zhaoa,

⁎

a

Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Special Administrative Region, China b State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China c Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong Special Administrative Region, China

HIGHLIGHTS

with aligned electrospun carbon fibers are developed. • Electrodes in-plane distribution of reactants is achieved with aligned electrodes. • Uniform ordered electrodes exhibit an energy efficiency of 79.1% at 150 mA cm . • The • The aligned electrodes enable a limiting current density of 900 mA cm . −2

−2

ARTICLE INFO

ABSTRACT

Keywords: Aligned fiber Uniform distribution Concentration polarization Electrospinning Vanadium redox flow battery

Enhancing the hydraulic permeability of electrodes along both the through-plane and in-plane directions is essential in flow-field structured vanadium redox flow batteries, as it can promote uniform distributions of reactants, lower the concentration overpotential, and therefore improve battery performances. In this work, uniaxially-aligned carbon fiber electrodes with the fiber diameter ranging from 7 to 12 µm (average ~10 µm) are fabricated by electrospinning method. Attributed to the enhanced permeability of the aligned structure, the battery assembled with the prepared electrodes exhibits an energy efficiency of 84.4% at a current density of 100 mA cm−2, which is 13.2% higher than that with conventional electrospun fiber electrodes. The permeability in the in-plane direction is further tailored by adjusting the orientation of aligned fibers against the flow channels. Results show that when the orientation of aligned fibers is perpendicular to the direction of flow channels, the battery delivers the largest discharge capacity and the highest limiting current density (~900 mA cm−2). Such an enhancement in the battery performance can be ascribed to the more uniform inplane distribution of reactants and current by maximizing the permeability along the direction vertical to the flow channels, as evidenced by a three-dimensional model.

1. Introduction Renewable sources such as wind and solar are alternatives to address the issues including fossil fuel shortage and environmental pollution [1,2]. However, the contradiction between the continuous demand for electricity and the intermittent nature of renewables necessitates the development of electrical energy storage systems [3]. Benefitted from the decoupled energy and power, the redox flow batteries (RFBs) represent a promising approach for large-scale energy storage, as the energy is decided by the volume and concentration of

electrolyte while the power is determined by the size of the power stack [4,5]. Other advantages of RFBs include long cycle life, low operation cost, and adjustable design [6,7]. Among the existing flow battery systems [8–10], vanadium redox flow batteries (VRFBs) gain the most attention due to the employment of the same element in both anolyte and catholyte, which can eliminate the cross-contamination issue of electroactive species existed in many other RFBs [11]. However, the broad market penetration of VRFB is still hindered by its high capital cost, the reduction of which requires the development of VRFBs that can be operated at high current densities with high energy efficiency

Corresponding author. E-mail address: [email protected] (T.S. Zhao). 1 These authors contributed equally to this work. ⁎

https://doi.org/10.1016/j.apenergy.2019.114198 Received 10 June 2019; Received in revised form 21 October 2019; Accepted 18 November 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: J. Sun, et al., Applied Energy, https://doi.org/10.1016/j.apenergy.2019.114198

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Nomenclature

ε βF θ σ ϕ η ω α

List of symbols u p f k df kck N D c z F R T i k0 a E km SOC

velocity vector [m s−1] pressure [Pa] volume force vector [N m−3] permeability [m2] fiber diameter [µm] dimensionless Carman-Kozeny constant [-] species molar flux [mol m−2 s−1] diffusive of ions [m2 s−1] molar concentration [mol m−3] charge number [-] Faraday constant [C mol−1] universal gas constant [J mol−1 K−1] temperature [K] current density [mA cm−2] reaction rate constant [m s−1] active area [m−1] equilibrium potential [V] mass transport coefficient [m s−1] state of charge [-]

Superscripts eff s 0

effective properties surface standard condition or initial state

Subscripts i l s c a neg V2+ V3+ H+ HSO4−

Greek symbols ρ µ

porosity of the electrode [-] Forchheimer drag coefficient [m−1] angle of fiber to the x-axis [°] electric conductivity [S m−1] potential [V] overpotential [V] flow rate [mL min−1] charge transfer coefficient [-]

density of electrolyte [kg m−3] viscosity [Pa s]

[12,13]. The electrode is a crucial component to determine the battery performance, which is evaluated in terms of the coulombic efficiency, voltage efficiency, and energy efficiency, as it is the main contributor to the cell voltage losses, including the activation loss, ohmic loss, and concentration loss [14,15]. Typically, the commercial carbon materials such as carbon felts and carbon papers have been employed as electrodes in VRFBs, due primarily to their high electrical conductivity and good chemical stability [16,17]. However, such electrodes always suffer from relatively low electrochemical activity, leading to a high activation loss. Therefore, lots of work has been done to tailor the surface properties of carbon electrode through heteroatom doping [18], catalyst deposition [19,20], and surface etching [21,22]. Apart from the efforts done to modify the electrodes to improve the reaction kinetics, attention should also be paid to reduce the ohmic loss. Previously, the flow-through architectures were constructed in RFB cells. In such architectures, to maintain a relatively low pressure drop, thick electrodes with a small compression ratio should be applied, which, however, results in a large ohmic loss and thereby causes poor battery performances [23]. A remarkable reduction in ohmic loss can be achieved by replacing the flow-through architecture with the flow-by architecture [24–26]. However, mass transport is sacrificed in the flowby structure according to the principles of convective mass transfer [27,28]. In addition, due to the co-existence of under-channel and under-rib regions in the flow-by architecture, the distribution of reactants, which is achieved by the convection and diffusion of electrolyte from the flow channels to the porous electrode, is non-uniform. The non-uniform distribution of reactants would not only enhance concentration polarization but also lead to local overcharge and gas evolutions. Therefore, seeking effective strategies to promote the uniform distribution of reactants is imperative for the flow-by structured VRFBs. Achieving the uniform distribution of electrolyte requires to design the geometrical structures of porous electrodes [29]. Unfortunately, the commercial carbon materials which are used as the typical electrodes for VRFBs, have fixed intrinsic geometrically structural properties such

i-th chemical species liquid phase solid phase cathode anode negative side V2+ ion V3+ ion H+ ion HSO4− ion

as the fiber diameter, fiber arrangement, porosity, and pore size. Up to now, only a trace of work has experimentally studied the effect of the abovementioned structural properties on the hydraulic permeability of the electrodes. Mayrhuber et al. demonstrated that introducing perforations to the carbon paper using CO2 laser can enhance the accessibility of electrolyte and thereby improve the battery performances [30]. However, applying such a method to generate holes was at the sacrifice of active surface area. More importantly, the intrinsic pore structures among the fibers remained the same after laser treatment, leaving limited space for further enhancement. Another more promising method to bottom-to-up design the electrode structure is electrospinning technology. However, due to the stack of densely woven fiber with the diameter in the range of several hundreds of nanometers to around 1 µm, the conventional electrospun carbon material suffers from low hydraulic permeability and thus reduced electrode utilization [31]. To address this issue, researchers have proposed several strategies to tune the structures of the electrospun carbon material. For example, a mixture of polyacrylonitrile (PAN) and polyvinylpyrrolidone (PVP) binary fiber web was prepared using a horizontally-opposed blending electrospinning method, and the pores were expanded while the fiber diameter was kept unchanged by later dissolving the PVP fibers [32]. Additionally, by forming fiber bundles, the pore sizes and fiber diameter were augmented simultaneously, promoting the transport of electrolyte to the surface of fibers [33]. Even progress has been made; previous methods only focused on the through-plane hydraulic permeability of the electrode; the in-plane hydraulic permeability so far has not been tailored. Enhancing the in-plane hydraulic permeability can strengthen the mass transport from the under-channel to the underrib regions, which is effective to achieve the uniform in-plane distribution of reactants, and thus reduce the concentration polarization and benefit the battery performance. Therefore, seeking effective methods to tailor the hydraulic permeability of the electrode in the inplane direction is in urgent demand. In this study, to simultaneously enhance the mass transport of electrolyte in the through-plane and in-plane directions, we designed 2

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and fabricated aligned electrospun carbon fiber (ECF) mat with a fiber diameter of around 10 µm for the first time [34,35], which can be applied as free-standing electrodes in VRFBs. Firstly, the as-synthesized aligned electrodes and conventional electrospun carbon electrodes were compared in the battery tests. Secondly, by varying the orientations of aligned fiber against the serpentine flow fields, the impact of in-plane permeability on the reactant transport and distribution was studied. To get insights into the current density and reactant distributions in the aligned electrodes, a three-dimensional computational model was conducted. The experimental and computational results show that by arranging the aligned fibers with the orientation perpendicular to the flow channels, the reactants can be uniformly distributed in the porous electrodes, thus lowering the concentration polarization and improving the battery performances. 2. Experimental

direction were examined which were denoted as parallel direction, diagonal direction, and vertical direction. The electrodes were cut into squares (2 cm × 2 cm) with an uncompressed thickness of 700 µm and were employed as electrodes on both positive and negative sides with a compression ratio of 30%. Nafion 212 (3.5 cm × 3.5 cm, Dupont) was used as the membrane. The catholyte containing 1 M V(IV) + 3 M H2SO4 and anolyte containing 1 M V(III) + 3 M H2SO4 were supplied to the cell by a peristaltic pump (BT600-2J, Longerpump) with a flow rate of 20 mL min−1. The rate and cycling performance of the cell was evaluated using a potentiostat/galvanostat (Arbin Instrument). The batteries were tested at constant current densities ranging from 60 mA cm−2 to 250 mA cm−2 with cut-off voltages were 1.65 V and 0.9 V for charge and discharge, respectively. The polarization curve was conducted from the full charge state. Then, the battery underwent a quick discharge process at increasing current densities until the voltage reaches zero.

2.1. Electrode materials

3. Computational model

The electrode with aligned fibers was fabricated using the electrospinning method. Polyacrylonitrile (PAN, MW 150,000, Sigma-Aldrich) polymer solution was prepared by dissolving 4.5 g PAN in 25.5 g N, Ndimethylformamide (DMF, ≥99%, Sigma-Aldrich) at 70 °C for 12 h with vigorous stirring to form the 15 wt% solution. Then the resulting solution was loaded to a syringe with a flow rate of 1 mL h−1 for electrospinning. The distance between the needle and the aluminumfoil-covered collector is 16 cm with a high voltage of 16 kV applied between the tip of the needle and the collector. The conventional electrospun fibers were prepared in the environment of around 40% relative humidity and the rotating rate of the collector of 100 rpm. The aligned electrospun fibers were fabricated with the same polymer solution under the relative humidity to be around 55% and the rotating rate to be 200 rpm. After electrospinning, the as-prepared electrospun fibers were preoxidized at 250 °C for 2 h in the air to stabilize the polymer fiber by intermolecular crosslinking, so that the PAN fiber can survive high-temperature pyrolysis without decomposing [36]. Then, the as-stabilized polymer mat was carbonized at 1100 °C for 1 h in the nitrogen atmosphere to get the conventional ECF and aligned ECF.

3.1. Governing equations In order to gain insights into the current and species distribution inside the electrodes under different arrangement orientations of aligned ECFs with the serpentine flow field, a computational model was conducted. The computational domain was constructed based on the experimental set-up, which composes a flow field and a porous electrode with the projected area to be 2 cm × 2 cm. The flow field consisted of a serpentine flow channel with 1 mm wide by 1.5 mm deep channels and 1 mm wide ribs as shown in Fig. 1(a) and (b). The current three-dimensional model focused on the negative halfcell of vanadium redox flow battery during the charging process with the electrochemical reaction written as:

V 2+

e

ch arg e

(1)

V 3+

Conservation of mass was applied in both the channel and porous media: (2)

·u = s

where ρ is the density of the electrolyte, u the velocity and s the source term in the electrode which is related to the electrochemical reactions. The momentum conservation of electrolyte flowing through the flow channel and the porous electrode was computed by employing the Navier-Stokes equation and Brinkman equation respectively:

2.2. Material characterizations The arrangement of conventional and aligned ECFs with respect to the flow fields was recorded by a high-resolution camera. The morphology of the as-prepared ECFs and the commercial carbon paper was characterized by a scanning electron microscope (SEM, JEOL 6390). The X-ray photoelectron spectroscopy (XPS) was performed by a Physical Electronics PHI 5600 multi-technique system using an Al monochromatic X-ray with a power of 350 W.

(u · ) u = (u · )

u

=

p+ p+

(3)

·[µ ( u + ( u )T )] + f ·

µ

( u + ( u )T )

µ + k

F

|u | u + f (4)

where ε is the porosity of the porous electrode, p is the pressure, µ is the dynamic viscosity of the fluid and k is the permeability of the porous electrode which is calculated by the Carman-Kozeny equation.βF is the Forchheimer drag coefficient which is neglected in the simulation. And

2.3. Single-cell performance All the battery performances were evaluated in a homemade flowby battery set up with the serpentine flow field [37]. Three different arrangements of the fiber direction with respect to the flow field

f is the body force acting on the flow, which is zero here as gravity is

Fig. 1. (a) Schematic of the 3D computational domain. (b) Cross-sectional views of the flow channel and electrode. (c) The permeability of flow to aligned fibers with an angle of θ to the x-axis. 3

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where the index i represents the species i ∈{ V2+, V3+, H+, HSO4−}, and Ni is the flux of the species. Si is the species molar source term, which is related to the electrochemical reactions. ci and zi are molar concentration and charge number of species i, respectively. R is the ideal gas constant, T is temperature, and F is Faraday’s constant. The effective diffusivity Dieff is corrected according to the Bruggeman correction Dieff = 3/2Di [41]. ϕl is the potential in the liquid phase. The dissociation of HSO4− is neglected in this simulation. Charge conservation is solved in the porous electrode as

not taken into consideration. For the aligned electrospun carbon fiber electrodes, the fiber geometry was approximated as a set of cylinders with the diameter df equal to 10 μm, the value of which is averaged from the SEM measurements. The porosity of the material ε was determined experimentally using mercury intrusion porosimetry, which is around 0.9. Thus, the permeability can be calculated using Carman-Kozeny relationship, which relates to the fiber diameter, material porosity, and the fiber morphology:

df2

k=

3

(5)

)2

16kck (1

· is =

where kck is the dimensionless Carman-Kozeny constant, the value of which is associated with the arrangement of fibers with the flow direction shown in Fig. 1(c). According to Ref. [38], the Carman-Kozeny constant for flow parallel to the cylinder is expressed as:

kck,// =

2 (1

)[2 ln 1

1

where is is the current density in the solid phase, il is the current density in the liquid phase and the expressions of these two parameters are:

is =

3

3 + 4(1

)

)2]

(1

(6)

1

1 (1 1 + (1

)2 )2

k m (c V 3 +

+ k sin2

k// cos sin

cVs 3 +) =

k cos sin

sin k//sin2

km = 1.6 × 10

k cos

+ k cos2

RT

cV 2+

exp

aF RT

(15)

RT F

ln

c 3+ V c 2+ V

. E0 is the ne-

k m (c V 2 +

cVs 2 +) =

ineg aF

(16)

z i ci Dieff F RT

l

+ u ci

4

u

0.4

(17)

3.2. Numerical details

(9)

The inlet of the channel was supplied with a constant flow rate of electrolyte (20 mL min−1). The concentration of the species at the inlet depended on the state of charge (SOC) of the electrolyte. 0 cV0total + SOC ·cV0total , c V2 + = SOC ·cV0total , and c V3 + = (1 SOC )·cV0total , c H + = cacid 0 0 0 cHSO4 = cacid + 2cVtotal , where cVtotal is the initial total vanadium con0 centration which is set to 1 M, and cacid is the initial sulfuric acid concentration and is assumed to 3 M. The outlet boundary is assumed to be zero pressure as the reference. Zero electric potential was applied at the contact of the current collector and the porous electrode, and the potential was set to Eeq at the interface between the electrode and membrane. A uniform current was applied at the electrode boundary. All the other boundaries were assumed to be impermeable to the mass, electron and ion transfer. The parameters for the battery structure, electrode, electrolyte, and operating conditions were listed in Table1. The above equations were solved based on a finite-element method with a mesh that consists of 289,569 domain elements, 43,798 boundary elements, and 3339 edge elements. The relative tolerance was set to 1 × 10−6. The steady state of the battery during discharge at a current density of 100 mA cm−2 was simulated for the three different

Then the permeability tensor can thereby be calculated as 6.24e 10 for the vertical direction arrange4.13e 11 4.13e 11 4.13e 11 ment and for parallel direction 6.24e 10 4.13e 11 3.33e 10 2.91e 10 arrangement, and 2.91e 10 3.33e 10 for the diagonal 4.13e 11 direction arrangement with θ equal to 45°. The transport of dilute species in the porous electrode was modeled by the Nernst-Plank equation [40] which describes the flux of species from diffusive, migrative, and convective contributions: (10)

The conservation of each species can be expressed as

· Ni = Si

cVs 2 +

where km is the mass transfer coefficient described as [42]

k

Dieff ci

cF

gative equilibrium potential at the standard condition. And the concentration of vanadium ions on the surface of the electrode can be determined by solving the equation that describes the balance of mass transport flux and the electrochemical reaction rate.

k zz

Ni =

cV3+

exp

where the equilibrium potential Eeq = E 0 +

k xx k xy k yx k yy

k// cos sin

cVs 3 +

where k0 is the reaction constant of the negative half-reaction, a is the specific surface area, αa and αc are anodic and cathodic charge transfer coefficient, respectively, and η = ϕs − ϕl − Eeq is the overpotential,

k// cos sin k cos sin k//sin2 + k cos2

where θ is the angle of fiber to the x-axis. Since the arrangement of aligned electrode only varies on the XY plane, the flow along the z-axis is always perpendicular to the fiber; the permeability tensor can be written as

=

)3/2

ineg = aFk 0 c V 2c+ cV 3a+

(8)

k// cos2

(14)

where = (1 s is the effective electric conductivity of the solid electrode from the Bruggermann correction. s is the electronic conductivity of the electrode. The source term Si is dependent on the electrochemical reaction rate ineg. For the negative electrode, SV 2 + = ineg / F , SV 3 + = ineg /F . Meanwhile, the source term is obtained by the Butler-Volmer equation [40]:

(7)

+ k sin2 k cos sin

z i Ni eff s

Thus the Carman-Kozeny constant for liquid flowing parallel to the cylinders and perpendicular to the cylinders can be calculated as 0.73 and 11.03, respectively. In our simulations, the permeability tensor [39] of different arrangements of fiber to the flow field in the XY plane can be written as:

k xx k xy k//cos2 = ky x k yy k// cos sin

(13)

s

i

2 3 (1 ) 1

eff s

il = F

While for flow perpendicular to the cylinder, the Carman-Kozeny constant is expressed as

kck, =

(12)

· il = ineg

(11) 4

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compared with the graphite felt. The commercial carbon materials have fixed geometrical structures and the structural properties are usually treated as isotropic. However, when these materials are applied as electrodes in the flow-field-structured VRFBs, the co-existence of the under-channel and under-rib regions in the serpentine flow field results in uneven distributions of reactants in the isotropic porous electrode. Therefore, to enhance the permeability along both the through-plane and in-plane directions, the novel aligned electrospun electrode with anisotropic properties were fabricated with modified electrospinning conditions.

Table 1 Modeling parameters related to operating conditions, electrolyte and electrode properties, electrochemistry, and cell structures. Symbol

Description

Operating conditions T Operating temperature (K) i Current density (mA cm−2) ω Inlet volumetric flow rate (mL min−1) Pout Outlet pressure (Pa) Initial species concentrations CII0 Initial V(II) concentration (mol m−3) CIII0 Initial V(III) concentration (mol m−3) Initial H+ concentration in negative side (mol C-,H0 m−3) Initial HSO4− concentration in negative side (mol C-,HSO40 m−3) Default values for constants related to the transport of charges and DVII V(II) diffusion coefficient in electrolyte (m2 s−1) DVIII V(III)diffusion coefficient in electrolyte (m2 s−1) Proton diffusion coefficient (m2 s−1) DH DHSO4 HSO4 diffusion coefficient (m2 s−1) ρ Electrolyte density (kg m−3) μ Electrolyte viscosity (Pa·s) Default values of the constants related to the structure h Carbon electrode thickness (µm) h_channel Channel depth (mm) w_channel Channel width (mm) Le Electrode width (cm) df Carbon electrode fiber (µm) ε Carbon electrode porosity a Specific surface area (m−1) Electrode conductivity (S m−1) σs Default values of constants related to electrochemistry k0 The standard reaction rate constant of the negative side αa Anodic charge transfer coefficient for the negative side αc Cathodic charge transfer coefficient for the negative side E0 Standard potential (negative) (V)

Value 298.15 100 20 0 500 500 2500

4.2. Electrospun carbon fiber characterization

4. Results and discussion

It is known that the diameter of the electrospun PAN fibers increases as the concentration of polymer solution increases [34]. Therefore, to obtain the large fiber, PAN with a high concentration of 15 wt% was used as the precursor solution for electrospinning. In the conventional electrospinning process, the ECF is generally fabricated at relatively low humidity (~40%) and a low rotating rate of the collector (100 rpm) [35], as illustrated in Fig. 2(a), which leads to a dense surface after carbonization (Fig. 2(b)). The SEM images of the conventional ECF under different magnifications are displayed in Fig. 2(c)–(e). It is seen that the mat is composed of randomly-arranged fine fibers with a diameter between 1 and 2 μm, forming small pores with the size around 10 μm. Herein, even with one of the highest concentrations of PAN solution reported in the open literature [34,47,48], the ECF mat fabricated by the conventional method still results in a dense structure, which is unfavorable for the transport of electrolyte flow and may lead to a large concentration overpotential for VRFBs. On the contrary, it is interesting to find that by increasing the relative humidity to ~55% and the rotating rate of the collector to ~200 rpm while keeping other conditions unchanged (Fig. 2(f)), the uniaxially aligned fibers can be obtained, which shows great potential to address the mass transport issues in conventional ECF. The digital photo of the uniaxially-aligned electrospun fiber mat is shown in Fig. 2(g). It is seen that the fibers are orientated along the vertical direction, and the aligned ECF is much looser than the conventional one. Fig. 2(h)–(j) displays the SEM images of aligned ECF at different magnifications. The electrospun fibers show a strong uniaxially-aligned tendency, which is mainly determined by the large fibers with a diameter ranging from ~7 µm to ~12 µm (average ~ 10 µm) (Fig. S1). In addition, the aligned ECF mat exhibits good flexibility and mechanical properties during repeated bending (Fig. S2), ensuring it to withstand the compression during battery assembly. The chemical compositions from X-ray photoelectron spectroscopy (XPS) analysis of conventional ECF and aligned ECF show similar element content of carbon, oxygen, and nitrogen (Table S1), which demonstrates that the two samples should have the same surface properties.

4.1. Structure of vanadium redox flow batteries

4.3. Battery performance of aligned electrodes

In VRFBs, electrolytes containing the electroactive materials are continuously pumped from the external tanks into the cell during the operation. For the serpentine flow-field-structured VRFBs (Fig. 1(a)), the electrolyte flows in the channels and convects and diffuses into the porous electrode where the redox reactions take place. Conventional electrode materials include carbon or graphite felt/paper due to the high electronic conductivity, excellent chemical resistance, and good mechanical strength of these materials. The graphite felt can be classified according to the raw materials as PAN-, rayon- and pitch-based. Among these, the most widely used graphite felt is the needle-punched PAN-based graphite felt, which is light in weight and can stand hightemperature oxidization. In addition, the graphite felt is always as thick as several centimeters and exhibits a binder-free fibrous morphology. For the carbon or graphite electrode, the carbon remnants of the binder are visible in the structure and are usually thinner (280 μm, SGL, 39AA)

Then we compared the battery performances of the cells assembled with conventional ECF and novel aligned ECF, as shown in Fig. 3. Here, the orientation of the aligned ECF electrodes tested followed the parallel direction arrangement (Fig. 4(a)). Fig. 3(a)–(c) show the chargedischarge profiles at the current densities of 60, 80, and 100 mA cm−2, respectively. It is found that the battery with aligned ECF electrodes outperforms that with the conventional ECF electrodes, as evidenced by the lower charge plateau and higher discharge plateau at all investigated current densities. In addition, the discharge and charge curves are obviously prolonged, especially at the final stages where the mass transport dominates, indicating the enhanced transport properties of the aligned ECF. The coulombic efficiency (CE), voltage efficiency (VE) of the batteries with these two electrodes are compared in Fig. 3(d) and the corresponding energy efficiency (EE) are summarized in Fig. 3(e). Notably, the battery assembled with aligned ECF electrodes

5000 mass 2.40E−10 2.40E−10 9.31E−09 1.33E−09 1.45E+03 4.93E−03

[43] [43] [40] [40] [44]

500 1.5 1 2 10 0.9 2.00E+06 [41] 500 [41] 7.00E−08 [45] 0.5 0.5 −0.225 [46]

arrangements of the aligned electrode. Similar to the simulations conducted on the negative side, the corresponding positive side simulations are also carried out. Therefore, we can get the charge-discharge curves of the full cell under different states of charge (SOC). Fig. S4 indicates that the potential profile of the simulated results agrees well with the experimental data with only an average of 0.8% relative difference observed. The discrepancy may be resulted from neglecting the side reactions, especially at the final stages of charge and discharge.

5

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Fig. 2. (a) Schematic of electrospinning set up and the conditions to fabricate conventional ECF. (b) Digital photo of the conventional electrospun mat. (c)–(e) SEM images of conventional ECFs under different magnifications. (f) Schematic of electrospinning set up and the conditions to fabricate aligned ECF. (g) Digital photo of the aligned electrospun mat. (h)–(j) SEM images of the aligned ECFs under different magnifications.

achieves an EE of 84.4% at 100 mA cm−2, which is 13.2% higher than that with conventional ECF electrodes. More prominently, a 79.1% EE can be delivered at a current density of 150 mA cm−2 for the battery with aligned ECF electrodes, but the battery with conventional ECF electrodes fails to be operated at such a high current density due to the enlarged cell polarization. To clarify the origin of the enhanced

performance, polarization curves were further tested (Fig. 3(f)). It is seen that the two polarization curves almost coincide at the current densities lower than 100 mA cm−2, so the activation polarizations varied little for the batteries assembled with these two kinds of electrodes. As the current density increases, the concentration polarization, which is decided by the transport of reactants in the porous electrodes,

Fig. 3. (a)-(c) Charge-discharge profiles of the batteries with conventional ECF and aligned ECF electrodes at the current densities of 60, 80, and 100 mA cm−2. (d) CE and VE comparison of the two kinds of electrodes. (e) EE comparison of the two kinds of electrodes. (f) Polarization curves of batteries with conventional ECF and the aligned ECF electrodes. 6

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Fig. 4. Schematic diagrams of the vertical direction, diagonal direction, and parallel direction configurations. (a)–(c): 3D view of the serpentine channels with different orientations of aligned fiber electrodes. (d)–(f): Top views of three configurations: red line denotes the main flow direction in the channels, and the black line represents the fiber orientation.

gradually dominates the voltage loss. It is found that the battery with conventional ECF reaches the concentration dominant region at only 200 mA cm−2 and undergoes a rapid decay in voltage, resulting in a low limiting current density of 400 mA cm−2. On the contrary, until reaching a high current density of 600 mA cm−2, the concentration polarization dominates the voltage loss for the battery with aligned ECF electrodes, ensuring a limiting current density of 700 mA cm−2, which is 75% higher than that with the conventional one. Therefore, the enhanced performance of the aligned ECF can mainly be ascribed to its excellent transport properties.

channels. Therefore, achieving a high permeability along the direction perpendicular to the flow channel can reduce the flow resistance and thus promote a more uniform distribution of electrolyte. As the permeability along one direction is closely related to the corresponding length for mass transport, the in-plane permeability is tailored by adjusting the orientation of the aligned fibers against the flow channels. In this work, the interplay between the fiber orientation and the flow field was examined in three different arrangements, as shown in Fig. 4. Fig. 4(a) and (d) show the parallel-direction arrangement, under which case the direction of the fibers is parallel to the orientation of electrolyte flow in the vertical channels. Fig. 4(b) and (e) represent the diagonal-direction arrangement with the orientation of aligned fibers along the diagonal line of the serpentine flow field, forming a 45° slanting angle. Fig. 4(c) and (f) depict the vertical direction arrangement with the slanting angle to be 90°. Optical images of the as-prepared electrodes against flow fields are provided in Fig. S3. To directly characterize the in-plane permeability under different configurations, the fluorescence microscopy and particle tracking methods proposed by

4.4. Influence of the in-plane permeability on the battery performance With the aligned structure, the influence of the in-plane hydraulic permeability of the electrodes on battery performance was further explored. It is known that in the flow-by structure, electrolyte transports inside the porous electrode from the under-channel region to the underrib region driven by the pressure drop between the neighboring

Fig. 5. Charge-discharge profiles of three different arrangements of aligned electrodes to flow field at current densities ranging from 60 to 250 mA cm−2. 7

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Wang and Aziz et al. [49] can be applied to visualize the flow of electrolyte in the in-plane direction and get the velocity field in our future work. To evaluate the battery performances of the cells employing different arrangements of the aligned carbon fiber electrodes against the serpentine flow field, single-cell tests were conducted. As shown in Fig. 5, the cells were charged and discharged at current densities ranging from 60 to 250 mA cm−2. Since the electrodes employed in the cells only differed in the orientation of fiber direction with respect to the flow field, the variance in battery performances of these three configurations can only be ascribed to the varied mass transport process. It is found that the cell with vertical direction arrangement outperforms the other two configurations, evidenced with the smallest charge-discharge overpotential and the largest discharge capacity at all current densities. Specifically, at low current densities (60–100 mA cm−2), the charge-discharge curves for the three configurations almost coincide at initial stages since the cells are kinetically controlled when sufficient reactant is supplied to the electrode. However, at the final stages of charge and discharge process when the active species are gradually depleted, the curves begin to diverge, and the battery performances are dominantly affected by the mass transport process of the electrolyte inside the electrodes. More significantly, at higher current densities (150–250 mA cm−2), distinctions are amplified with the charge-discharge curves diverging at an earlier time, and the difference of the charge-discharge overpotentials become larger. The improvement trend of battery performance is witnessed when switching the fiber-to-electrode configurations gradually from the parallel direction to the vertical direction at all current densities. The above analysis demonstrates that the battery achieves the highest performance among

the three configurations when the aligned electrodes are vertically arranged to the flow channels. Aiming to quantify the battery performances, the coulombic efficiency (CE), voltage efficiency (VE), and energy efficiency (EE) of each electrode configuration were analyzed in Fig. 6. The CE of each cell is all above 97%, indicating a good airtightness of the battery set up. As shown in Fig. 6(a)-(b), the battery with vertical direction arrangement of aligned electrodes exhibits the highest VE and EE among these three configurations which can deliver an 81.2% VE and 80.7% EE at a current density of 150 mA cm−2, respectively. The polarization curves were employed to compare the contribution of different types of voltage losses in the three cells. The overlapping of the three polarization curves at the initial stages reveals similar activation overpotential and internal resistance of the electrodes because the physicochemical properties of these electrodes are identical. However, these three curves begin to diverge at higher current densities when concentration polarization begins to dominate the voltage loss, resulting in a significant variance on the limiting current densities. As shown in Fig. 6(c), the vertical-direction configuration can reach a limiting current density of ~900 mA cm−2, which is much higher than that of the parallel direction arrangement (~700 mA cm−2). The enhancement in the limiting current densities mainly results from the reduced concentration polarization, which indicates improved mass transport process inside the vertical direction arranged electrode. In addition, the discharge capacities of the three batteries with different electrode arrangements are analyzed in Fig. 6(d). The battery with a vertical direction electrode configuration gains the largest discharge capacity of 9.1 Ah L−1 at a current density of 80 mA cm−2. More importantly, an additional 56% depth of discharge is achieved by changing the fiber arrangement from

Fig. 6. (a) CE and VE of the batteries with three different aligned electrode arrangements. (b) EE of the batteries with three different aligned electrode arrangements. (c) Polarization curves and (d) Discharge capacity of the three different electrodes configurations. 8

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the parallel direction to vertical direction at the current density of 200 mA cm−2. Therefore, it can be concluded from the above battery performance that when the aligned electrospun electrode is vertically arranged against the flow direction in the serpentine flow field, the mass transport properties of electrolyte inside the electrodes are enhanced, resulting in increased energy efficiency and discharge capacity, as well as the prolonged limiting current density. Subsequently, the cycling performances of vertical-direction cells were evaluated by charging and discharging the battery for 200 cycles at a current density of 100 mA cm−2. As shown in Fig. 7(a), the CE, VE, and EE remain stable during repeated charge and discharge processes. The discharge capacity is gradually declined over the cycles with a decay rate of 0.25% per cycle, which is mainly due to the imbalance of the active materials on the two sides resulting from the crossover of active species through the membrane. The cycling performances of the aligned electrospun electrodes confirm that the as-prepared electrodes are potentially stable over long battery cycles.

Uc

To explain the results observed in the above experiments, the numerical simulations with the computational model were conducted which provide insights into the current distribution and active species distribution in the electrode. In our simulations, all the conditions were kept the same except the permeability tensor for the three arrangements. When the aligned fibers were placed against the flow field with different orientations, the corresponding hydraulic permeability tensor varied, thereby affecting the electrolyte distribution and current distribution. The calculated velocity field, current density distribution, and the reactant distribution were plotted in Fig. 8. The calculated velocity fields show that on the same cut plane along the z-axis, the vertical-direction arrangement brings about the largest velocity magnitude (Fig. 8(a)–(c)) among the three configurations. Therefore, the electrode can be accessed with a large flow rate of electrolyte when it is placed with the vertical-direction arrangement. In addition, it is found that the velocity is higher in the under-rib regions than that of under channel regions for all the three configurations which is due to the existence of bypass flow. Additionally, the calculated velocity field agrees well with the fiber direction arrangement. By incorporating electrochemical reactions into the model, the current density distribution and the species distribution can be calculated. The current density is a function of the reactant concentration and overpotential according to the Butler-Volmer equation. It is found that the current density reaches its maximum near the inlet where the concentration of the reactants is the highest for all the three configurations. As shown in Fig. 8(d), the current density is highly heterogeneous for the parallel-direction arrangement with maxima appeared under the ribs and minima under the channels. Compared with the parallel-direction arrangement, the diagonal-direction arrangement shows significantly improved uniformity of the current density distribution with local maxima evidenced near the inlet and along the diagonal directions. When the aligned electrode is vertically placed with the flow field, the current density gains the most homogeneous distribution in the in-plane direction, as shown in Fig. 8(f). The reactant shows similar in-plane distribution profiles (Fig. 8(g)–(i)) with the current density distributions (Fig. 8(d)–(f)). A decrease in V2+ concentration from the inlet to the outlet in all three configurations is observed because V2+ ions are gradually depleted during the discharge process. To quantitatively describe the uniformity of the in-plane distribution of current and react distribution, we define the uniformity factor for current density and reactant [23]:

1 ci,¯loc

1 dA

(ci, loc

ci,¯loc )2dA

=1

1 cV¯2 +

1 dA

(c V 2 +

c V¯2 + )2dA

(19)

where Ui, loc (Ui, loc ∈[0,1])is the uniformity factor of current density, Uc 2 +(Uc 2 +∈[0,1])is the uniformity factor of V2+ concentration. When V V both the two uniformity factors approach 1, the current density and the reactants reach homogenous distributions. It is found in Fig. S6 that both Ui, loc and Uc 2 + are the largest for the vertical-direction arrangeV ment. To be specific, on a fixed cut plane, for example, at z = 0.1 mm, Ui, loc for the parallel direction, diagonal direction and vertical direction arrangements are 0.437, 0.823, and 0.877 respectively and Uc 2 + for the V three configurations are 0.899, 0.962, and 0.973 respectively, which indicates that the more uniform distribution of reactants and current are achieved in the vertical-direction configuration. From the above analysis of the computational results, the verticaldirection arrangement of the electrode against the flow field facilitates the uniform distribution of current and reactants, which provides explanations for the higher limiting current density and increased discharge capacities examined in the battery with vertical direction arranged electrodes.

4.5. Computational analysis

Ui, loc = 1

V2+

4.6. Future electrode optimization and real application Our work presented a novel electrode structure which is composed of aligned fibers of around 10 µm in diameter and was produced with the electrospinning method. Extending from the abovementioned results, we want to discuss the future electrode optimization and real applications of this aligned electrode structure. Based on the improved mass transport properties of the aligned electrode structure, future electrode optimization can be focused on surface modifications of the material to improve the kinetics and boost the battery performances. And for the real applications, this aligned structure can be adopted by the fiber production industry when fabricating carbon materials for the electrode in flow battery systems. In addition, the lab-scale production of the electrospun carbon fibers shows potentials in large-scale fabrication which can be realized with industrial-scale electrospinning equipment [50]. 5. Conclusions In this work, the uniaxially-aligned fibers were fabricated to enhance the through-plane and in-plane hydraulic permeability of

Fig. 7. Cycling performance of the vertical-direction assembly of the aligned electrodes. (a) Efficiency and (b) specific capacity over 200 cycles.

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Fig. 8. (a)–(c) Velocity magnitude and vector on the cut plane z = 0.1 mm for the three arrangements. (d)–(f) Current density distribution on the cut plane z = 0.1 mm for the three arrangements. (g)-(i) The distribution of concentration of species V2+ on the cut plane z = 0.1 mm.

electrospun materials for the typical serpentine flow-by cell architecture. Firstly, benefitting from the novel aligned electrode structure with large fibers, the battery assembled with aligned ECFs achieved an energy efficiency of 84.4% while the battery with conventional ECF only delivered 71.2% EE at the current density of 100 mA cm−2. Secondly, the arrangement orientation of aligned fibers against the flow field was optimized under three different configurations. The experimental results showed that the battery with vertical-direction arrangement achieved a limiting current density of 900 mA cm−2 which was 28.6% higher than that tested with the parallel-direction arrangement. Notably, the battery with vertical-direction arrangement achieved an additional 56% discharge depth compared with the parallel-direction configuration at the current density of 200 mA cm−2. The enhanced limiting current density and discharge capacity demonstrated that the vertical direction arrangement can effectively lower concentration polarization. Such improvement in battery performances was further explained by the computational simulations which showed that more homogenous in-plane distributions of reactant and current were achieved in the vertical direction arrangement. In summary, the electrodes with aligned carbon fibers are promising for flow battery

systems which enable an improved mass transport of the electrolyte, and this structured design using the electrospinning method also provides inspirations for future electrode design. Furthermore, the aligned electrode fabricated with current lab-scale electrospinning equipment can be mass-produced with industrial-scale electrospinning production line in the future, providing a new approach to manufacturing costeffective carbon fibers with designed structures. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgments The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. T23-601/17-R) and HKUST Fund of Nanhai (Grant No. FSNH-18FYTRI01). 10

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Appendix A. Supplementary material

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