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*In Situ* Electrochemical Porosimetry of Vertically-Aligned Carbon Nanotube Carpets through Impedance Spectroscopy

*In Situ*Electrochemical Porosimetry of Vertically-Aligned Carbon Nanotube Carpets through Impedance Spectroscopy

*in situ*, thereby preserving the carpet and accurately calculating the electrochemically active geometry.

To link impedance data with geometry, we utilize a transmission line model developed by De Levie [5] and further expanded by Song et al. [6] where pores are modeled as having an ion transport resistance that depends on geometric factors. We begin by modeling the voids between VA-CNTs as inverse cylinders, with the nanowire spacing as the diameter and forest height as the length of the nanotube. By assuming the diameter of the nanowire spacings in the VA-CNT array have a log normal distribution we can characterize the relationship between distribution shape and CNT density, giving us full geometric understanding of the system.

Experimental VA-CNT carpet samples were grown on 1x1 cm^{2 }substrates to heights of ~1mm. Carpets were mechanically densified using bi-axial compression. Volume fractions (Vf) of carpets are defined as the growth substrate area, divided by the final planar area, following compression. We examined the porosimetry of carpets with volume fractions of 1% (as grown) to 20% (Figure 1a-d). VA-CNT carpets were bonded to a non-corrosive current collector using a gold-gold thermocompression, outlined in [7]. In order to ensure proper boundary conditions, the electrode was fully sealed with electromasking tape, with only a window cut to expose the CNT carpet.

Cylic voltammetry tests were performed to determine the appropriate voltage window for studying purely capacitive effects, which was 0-0.5 V vs Ag/AgCl as shown in Figure 1e. Impedance spectroscopy from 1 kHz to 100 mHz was conducted on the cell. Figure 1f shows there is a characteristic 45° angle at high frequencies (characteristic of transmission line model), and a < 90° slope at low frequencies (characteristic of materials with a distribution of pore sizes [6]).

Applying the transmission line model to impedance data and assuming a lognormal distribution for the pores show that the 1% Vf has a mean penetration depth of 0.87 and sigma 1.91. The 5% Vf has a mean of 0.62 and sigma 0.68. The decreasing sigma with increasing volume fraction indicates that densification leads to reduced variation in nanowire spacing. The fitting results were extended to determine the electrode ionic resistance, total pore volume and average interspacing, based on measurements of the mass, length, and outer diameter of the CNTs.

These experimental studies allow us to determine the role of geometry on electrode properties. Through impedance spectroscopy and simple geometric modeling for porous materials we can determine the distribution of CNT spacing, which can be used to predict packing and performance of VA-CNT carpets.

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