Bioinspired leaves-on-branchlet hybrid carbon nanostructure for supercapacitors

Designing electrodes in a highly ordered structure simultaneously with appropriate orientation, outstanding mechanical robustness, and high electrical conductivity to achieve excellent electrochemical performance remains a daunting challenge. Inspired by the phenomenon in nature that leaves significantly increase exposed tree surface area to absorb carbon dioxide (like ions) from the environments (like electrolyte) for photosynthesis, we report a design of micro-conduits in a bioinspired leaves-on-branchlet structure consisting of carbon nanotube arrays serving as branchlets and graphene petals as leaves for such electrodes. The hierarchical all-carbon micro-conduit electrodes with hollow channels exhibit high areal capacitance of 2.35 F cm−2 (~500 F g−1 based on active material mass), high rate capability and outstanding cyclic stability (capacitance retention of ~95% over 10,000 cycles). Furthermore, Nernst–Planck–Poisson calculations elucidate the underlying mechanism of charge transfer and storage governed by sharp graphene petal edges, and thus provides insights into their outstanding electrochemical performance.

The results reveal a relationship between the edge density of GPs and capacitance of CNT/GP micro-conduit electrodes, and indicate that an optimal GP growth time should exist for superior electrochemical performance because of a balance between surface area and ion transfer kinetics. Figure 10│ (a) Nyquist plot recorded from 0.1 Hz to 1 MHz for a CNT microconduit electrode (the inset shows the equivalent circuit). (b) Nyquist plot recorded from 0.1 Hz to 1 MHz for a CNT/GP micro-conduit electrode. The bulk electrolyte resistance R e of CNT and CNT/GP micro-conduit electrodes is measured to be 1.85 and 2.8 Ω, respectively. Moreover, negligible semicircles in the high frequency region from impedance spectra of both electrodes indicate a low charge transfer resistance R ct of CNT and CNT/GP micro-conduit electrodes.

Supplementary Figure 21│
Comparative Ragone plot (based on active material mass) of contemporary energy devices and the present symmetric CNT/GP micro-conduit device. The energy and power densities of the preset device were calculated using both cyclic voltammetry (CV, in red circle) and constant-current charge/discharge (CD, in black rectangle) methods. The results calculated from the two methods agree well with each other. Energy density of the present symmetric device reaches up to 16.4 Wh kg -1 (calculated based on the CV results), and the device also deliver a power density up to 27 kW kg -1 (calculated based on the CD results), which are significantly higher than those of contemporary carbon-based supercapacitors 1, 2, 3, 4, 5 , indicating outstanding overall performance of the symmetric all-carbon supercapacitor in this work.

Supplementary Figure 22│ Schematic of the ion transport and accumulation behavior, and the directions of diffusion and electrostatic driving forces for both counter-ions (SO 4 2-) and co-ions (H + ).
During supercapacitor operation, the electrostatic force generally opposes the diffusion force. Equilibrium is achieved once the two driving forces reach a balance.  Figure 26│ Schematic representation of the molecular dynamics simulation systems for a confined NaCl electrolyte. Grey spheres represent graphene carbon atoms, and two face-to-face graphene sheets construct a channel. Yellow spheres represent Na + ions, dark green spheres represent Clions, and red and white spheres represent oxygen and hydrogen atoms of water, respectively.  Decorating GPs on CNT micro-conduits: For GP growth, CNT micro-conduits on CC substrates, elevated 15 mm above a 55-mm-diameter Mo puck by ceramic spacers, were inserted into the same MPCVD system. This plasma is sufficient to heat the samples from room temperature up to approx. 1100 °C, as measured by a dual-wavelength pyrometer (Williamson PRO 92). The GP growth process is catalyst-free. The mass loading of active materials (e.g., CNT, GPs) was evaluated by measuring the weight difference of a substrate before and after the MPCVD process using a microbalance with an accuracy of 1 μg. Mass measurements were carried out at least three times with different samples, and the averaged value was used as the active mass of CNT/GPs. The specific capacitance based on total mass of CNT/GP/CC is calculated to be 73.6 F g -1 at 1 mA cm -2 .

Electrodeposition of pseudocapacitive materials on CNT/GP micro-conduit nanotemplates:
Electrodeposition of Ni-Co hydroxide (or PANI) on micro-conduits was conducted in a threeelectrode system consisting of a CNT/GP micro-conduit as the working electrode, a Pt mesh as the counter electrode, and a saturated calomel electrode (SCE) (or Ag/AgCl) as the reference electrode. The detailed procedures have been previously described in detail elsewhere 22,23 .
Briefly, Ni-Co hydroxide was electrodeposited on electrochemically treated CNT/GP micro- Electrochemical tests: Cyclic voltammogram at different scan rates and constant current galvanostatic charge/discharge measurement techniques were adopted to characterize both single electrodes and supercapacitor devices for evaluation of electrochemical performance.
Electrochemical impedance spectroscopy (EIS) measurements were carried out with an AC perturbation amplitude of 5 mV in the frequency ranging from 1 MHz to 0.1 Hz. The methods to calculate specific capacitances, energy and power densities are provided below.

Calculation details:
The specific capacitance of the electrodes/devices is calculated from charge/discharge curve based on: where C M can represent specific capacitance (F g -1 ), areal capacitance (F cm -2 ) or volumetric capacitance (F cm -3 ). I (A) is the applied current, Δt (s) is the discharge time, ΔV (V) is the discharge potential range, and M can be mass, geometric area or volume of the electrodes/devices in g, cm 2 or cm 3 , respectively.
Specific capacitances derived from CV tests are calculated from: where s is scan rate in V/s; V h and V l are high and low potential limits of the CV tests in V; I is the instantaneous current in CV curves; and V is the applied voltage in V.
The average energy density E (Wh kg -1 ) and power density P (W kg -1 ) derived from galvanostatic charge/discharge tests are calculated from: Where V (V) is the applied voltage, C (F) is the capacitance of the symmetric devices, M is the total active material mass of both electrodes in symmetric devices, and ∆t (s) is the discharge time.
The coulombic efficiency (η) is the ratio of the number of unit charges supplied during charging compared to the number extracted during discharging, reflecting the electrode charge storage efficiency. The coulombic efficiency measured in this study is calculated from: η= Q discharge /Q charge = It discharge /It charge = t discharge /t charge (5)

Nernst-Planck-Poisson modeling details:
Nernst-Planck-Poisson (NPP) calculations of the Gouy-Chapman model were employed to elucidate the underlying mechanisms of charge transfer and storage, as well as ion diffusion, governed by the Poisson equation and the Nernst-Plank equation respectively, where ε 0 is the permitivity of vacuum, ε r is the relative permittivity of the medium,  is the elestrostatic potential, D i is the diffusivity of chemical species i, C i is the density of the species, z i is the valency of the species, e is the elementary charge, k B is Boltzmann's constant, and T is temperature. All other boundaries were specified as zero flux. Areal capacitance from the non-uniform charge distribution is calculated as where s  and A are the surface charge density and occupied area corresponding to the point of interest x, respectively. V is the applied voltage.
Since the electrolyte domain size is much larger than that of electrode, the eletrolyte boundary in our half model was considered as the middle of bulk electrolyte solution. Therefore, the boundary conditions for Eq. 7 were specified as the eletrolyte boundary ionic concentration of 1 M SO 4 2and 2 M H + . All other boundaries were specified as zero flux. The required material properties were specified as the relative permittivity of electrolyte: 3, CNT: 15 and GPs: 81. The diffusion coefficients were set as H + : 6.5x10 5 cm 2 s -1 and SO 4 2-: 2x10 5 cm 2 s -1 , according to Ref. [24]. To establish grid independence, the system mesh was set as 333816 tetrahedral elements with a smallest element size of 0.2 nm based on solution convergence trials.

Molecular Dynamics simulation details:
Molecular dynamics (MD) simulations were performed to calculate the size effect of the ion diffusion coefficients in the confined graphene nanochannels. Fig. S26 shows a schematic representation of the simulation model of confined eletrolyte NaCl. The simulations were performed in a cubic box at room temperature. The pressure for bulk systems is 300 ±150 atmospheres, similar to in the literature. 25 The results show that the behavior of ions diffusion is almost unchanged once the size of confined nanochannels exceed 5 nm. According to Ref. [ . Thus, such a over 5 nm size-indepence bahavior is fairly spectulated for the H 2 SO 4 electrolyte.
Based on statistically calculation of experimental results indicates the gap between two graphene petals are about 10-40 nm. In this regard, the size effect of confined nanochannels is reasonably ignored.