## 1 Introduction  
Anaerobic digestion (AD) is a multifunctional and flexible technology, offering solutions for the treatment and management of a multitude of organic wastes, while allowing the production of renewable energy carriers [1; 2; 3; 4]. The generated methane, after upgrading to biomethane, can replace natural gas or be used for the production of electricity, combined heat and power, or chemicals [1; 5; 6]. In AD systems, the conversion of organic matter to methane relies on the coordinated activity of several microbial groups [7; 8]. After hydrolysis and acidogenesis, the majority of AD substrates is converted, inter alia, to volatile fatty acids, (VFA, e.g., butyrate) and alcohols (e.g., ethanol) [7; 8]. The degradation of these compounds is generally syntrophic, yielding acetate and H2/formate which are the direct substrates for methanogens. Syntrophic reactions are dependent on the activity of hydrogenotrophic methanogens or other H2/formate-consumers, in order to turn these reactions thermodynamically feasible [9; 10; 11]. AD microbiomes are highly complex and maintaining a balance among the activities of different trophic groups is difficult when transient conditions are applied [12]. The influence of conductive materials on AD processes, and particularly on methane production, has gained attention during recent years [13; 14; 15; 16]. These materials are reported to facilitate direct interspecies electron transfer (DIET) in anaerobic microbial communities, a mechanism that can prevail over indirect hydrogen and formate interspecies transfer [17; 18; 19; 20]. Conductive materials are redox mediators, useful for catalysis due to their stability, reacting with many organic and inorganic compounds, and offering large surface areas [21; 22]. For example, granular activated carbon (GAC) was reported to enrich for methanogens and accelerate the onset of methanogenesis during a reactor startup [21; 23; 24]. Other compounds, such as carbon cloth, graphite, and biochar were reported to affect the microbial community's composition, to enhance syntrophic ethanol metabolism, and methane production in upflow anaerobic sludge blanket (UASB) reactors [25]. Also, multi-walled carbon nanotubes (MWCNT) accelerated the methane production from butyrate in microbial enrichments [26]. MWCNT were also reported to accelerate methane production in pure cultures of hydrogenotrophic methanogens [27], showing a direct effect of MWCNT on the activity of methanogens independently of the occurrence of other mechanisms such as DIET. Additionally, conductive materials may also enhance microbial activity by providing a support for biofilm growth, rather than by their conductive characteristics [28; 29]. On the other hand, carbon nanotubes (CNT) have also been reported as toxic, reducing the microbial growth. For example, [PERSON] et al. [30] demonstrated that single-walled CNT can have a strong antimicrobial activity toward _Escherichia coli_, and MWCNT also decreased the microbial viability and activity in UASB reactors [31]. Reduced methanogenesis or complete inhibition by other conductive nanomaterials, such as ferrihydrite and carbon black, is also described [14; 32]. Although there are several studies on the effect of conductive materials in anaerobic digestion, there are still no reports on their application in full scale bioreactors, nor studies on economic or environmental impact. In lab scale experiments, complex wastes such as real/synthetic wastewater, sludge, food wastes, swine manure or leachate have been tested, but most studies were performed with simple substrates, such as glucose, ethanol, or acetate [13; 14; 15; 16]. While investigation on this topic still requires research and development, it is also important to deeply understand the effect of these materials on the activity of complex microbial communities which generate methane.