*2.1. E*ff*ect of Pore Distribution*

The primary motivation of using carbon nanomaterials for direct electrocatalysis, at the early stage, is ascribed to the high enzyme loading because of its large specific surface area. Although we agree that enzyme loading is essential to the performance of direct bioelectrocatalysis, several recent studies have proposed that the microstructure and the surface physiochemistry of carbon nanomaterials also play important roles in DET-type bioelectrocatalysis. For example, carbon cryogels with a controlled average pore radii of 5–40 nm have been utilized for FDH immobilization [32]. It has been found that, although the estimated Brunauer–Emmett–Teller (BET) specific surface area of a carbon cryogel with an average pore radius of 40 nm is the smallest, the DET-type bioelectrocatalytic current of fructose oxidation in a carbon cryogel with an average pore radius of 40 nm is the highest (~5 mA cm−<sup>2</sup> ), compared to those of carbon cryogels with radii of 5, 11, 16, and 26 nm, which have higher BET specific surface areas. Similar results have been obtained for MgO-templated carbon nanomaterial electrodes using different redox enzymes, including FDH [33], BOD [34], and H2ase [35]. Rather than a high specific surface area, carbon nanomaterials with suitable pore size distributions are apparently more essential for the DET-type bioelectrocatalysis of redox enzymes.

A theoretical model of a randomly oriented spherical enzyme adsorbed in a planar or three-dimensional electrode was proposed [36,37] (Figure 2). In that model, spherical pores with a radius close to that of the enzyme improves the interfacial electron transfer kinetics thanks to increased probability of orientations with a short distance during the interfacial electron transfer (Figure 2). This effect is referred to as the curvature effect of porous structures [12,13]. These porous structures can be found at the surface of mesoporous carbon materials or can be formed through primary carbon nanoparticle aggregation. For example, in a comparative study, three types of carbon materials—Ketjen Black EC300J (KB), Vulcan XC-72R (Vulcan), and high-purity exfoliated graphite J-SP (JSP)—were utilized as scaffolds for the DET-type bioelectrocatalysis of BOD [38]. The results show that the micropores at the JSP surface are highly effective for the DET-reaction of BOD, whereas gaps between several primary particles in the KB and Vulcan aggregates play important roles as scaffolds for *Mv*BOD.

**Figure 2.** Schematic model of an adsorbed enzyme on (**A**) planar and (**B**) porous electrodes. Reprinted from [37]. Copyright (2016), with permission from American Chemical Society.

μ <sup>−</sup> μ <sup>−</sup> − − − Notably, the optimization of carbon nanomaterials for DET-type bioelectrocatalysis requires balancing the ratio of macro-, meso-, and micropores for the construction of a hierarchical three-dimensional structure effective for the mass transport of an electrolyte solution and substrates as well as the penetration of enzymes into the nanostructures, and enhancing the interfacial electron transfer kinetics of macromolecular redox enzymes. The dispersion parameter of H2ase in MgO-templated carbon with a pore size of 35 nm is notably smaller than that in MgO-templated carbons with a pore size of 150 nm [35], which can be explained by the curvature effect [36,37], as mentioned above. However, the H2-oxidation bioelectrocatalytic current produced by H2ase in MgO-templated carbons with a pore size of 150 nm (~450 µA cm−<sup>2</sup> ) is higher than that in MgO-templated carbons with a pore size of 35 nm (~50 µA cm−<sup>2</sup> ) owing to greater enzyme penetration in carbon with larger pores [35]. Furthermore, a hierarchical dual MgO-templated carbon, with a mixture of 33% macropores (150 nm) and 67% mesopores (40 nm), was prepared for the DET-type bioelectrocatalysis of BOD [39]. The results show that the oxygen reduction current in dual MgO-templated carbon reached to around 10 mA cm−<sup>2</sup> , which is much higher than that in a MgO-templated carbon electrode with only meso- or macro-porous structures (~5.6 mA cm−<sup>2</sup> or ~5.1 mA cm−<sup>2</sup> ). These results clearly show the importance of the pore distribution in carbon nanomaterials in DET-type bioelectrocatalysis.
