## 1 Introduction  
Direct formic acid fuel cells (DFAFCs) are a promising type of direct liquid fuel cell due to their favorable oxidation kinetics which enable low temperature operation (50-80 \({}^{\circ}\)C), a high theoretical open-circuit voltage (1.45 V), and a relatively low fuel crossover through the Nafion membrane [1, 2]. Platinum (Pt) and palladium (Pd) have been widely studied as anode catalysts for DFAFCs because of their interactions with formic acid, in which Pd tends to break the O-H bonds across the entire potential window, and Pt discriminates between the cleavage of O-H bonds at a high overpotential and the cleavage of C-O and/or C-H at a low overpotential [1; 3; 4; 5]. The difference between the reaction pathways for formic acid oxidation on the Pt and Pd catalysts was pointed out by [PERSON] et al. [6]; it was also experimentally confirmed that no CO build-up occurred and a higher current density was achieved for formic acid oxidation on Pd [5]. In fact, DFAFCs exhibiting high power densities were reported when Pd- or Pd-based catalysts were used as the anode catalysts [7]. It has been reported that supported catalysts with a high surface area, good electrical conductivity, good electrochemical stability, and suitable porosity exhibit a good stability and higher activity than unsupported catalysts [8; 9; 10; 11; 12]. Catalyst support materials have been roughly classified as carbon-based supports and non-carbon-based supports [9]. Non-carbon-based supports, such as titania [13; 14; 15], indium oxide, alumina, silica [13], ceria [15], zirconia, tungsten oxide, and conducting polymers [9], can improve reaction kinetics due to metal-support interactions; however, their electrical conductivity is lower than that of carbon. The electrical conductivity increases when non-carbon materials are embedded with carbon nanofibers (CNFs) as the catalyst support, as pointed out by [PERSON] et al. [14] and [PERSON] et al. [15]. In their studies, the PtRu catalyst on non-carbon supports, such as ceria particles [15] and titania particles [14], gave lower performances for methanol oxidation compared to the carbon-based supports. By embedding the non-carbon material into the CNFs, metal-support interactions were obtained as a result of the high electrical conductivity of the CNFs. In our previous studies, we also demonstrated that Pd supported by TiO\({}_{2}\), SiO\({}_{2}\), and carbon black (CB) (Vulcan) embedded into the CNFs showed higher formic acid oxidation reaction (FAOR) activities than unembedded CNFs [13]. The high FAOR activity of the TiO\({}_{2}\)- and SiO\({}_{2}\)-embedded CNFs results from the metal-support interactions with a high electrical conductivity similar to the case in [PERSON]'s study [14] and [PERSON]'s study [15]. On the other hand, in the case of Vulcan XC-72, which has a high electrical conductivity but no or fewer metal-support interactions, it is considered that the metal-support effect becomes significant or the CB properties (such as the surface area or pore volume) change through the heat treatment of CB, as the CB-embedded CNF is prepared over several heat treatment steps, namely, stabilization, carbonization, and steam activation. There are several reports related to the effect of the heat treatment of CB on its properties and electrochemical reaction. An enhancement of the surface area caused by heat treatment has been reported by [PERSON] et al. for Vulcan XC-72 and Ketjen black. They revealed that a significant enhancement of the surface area through heat treatment (carbonization) concomitantly occurred with an improvement in the catalytic activity by increasing the specific electrochemical surface area (ECSA) [11]. [PERSON] et al. also proposed that heat treatment of CB affects oxygen reduction reaction (ORR) activity of the Pt surfaces [16]. Heat treatment of the carbon-based supports improved the electrocatalytic activity and stability of the ORR catalysts [17; 18; 19].