## 1 Introduction
Irrespective of the cultivation method, a high cell-density culture with high PHA content and PHA productivity is a prerequisite for industrial-scale application. An additional requirement for gas fermentation is to avoid gas detonation when using O\({}_{2}\) combined with H\({}_{2}\). This can be achieved by keeping the O\({}_{2}\) concentration in the gas phase below the lower level of explosion. Higher cell mass concentration and lower gas concentration, however, inherently implies an increased risk of mass transfer limitation, causing premature shifting to the PHA production phase in the fully autotrophic cultivation system or incomplete biopolymer accumulation in the heterotrophic-autotrophic process. The latter process has been proven to be more promising for the direct conversion of CO\({}_{2}\) to PHA in terms of cell mass concentration and growth rate [7]. In addition, less of the still costly renewable H\({}_{2}\) is evidently needed; however, the total amount of CO\({}_{2}\) that can theoretically be converted into polymers is significantly reduced. For example, the potential emissions abatement and H\({}_{2}\) consumption is theoretically reduced by respectively 44% and 20% for autotrophic PHB production in glucose-grown biomass compared to a fully autotrophic process [5]. PHA can also be produced from CO\({}_{2}\) in an indirect manner through the use of acetic acid (i.e., autotrophic-heterotrophic-heterotrophic PHA production process). Acetogenic bacteria, an ancient group of strictly anaerobic microorganisms, are capable of reducing H\({}_{2}\) and CO\({}_{2}\) as sole energy and carbon sources and mainly produce acetate (Equation (4)) [11]. Acetic acid can be used subsequently by _C. necator_ for both biomass growth (Equation (5)) and PHA production (Equation (6)). \[2\;\mathrm{CO}_{2}+4\;\mathrm{H}_{2}\to\mathrm{C}_{2}\mathrm{H}_{4}\mathrm{O}_{2 }+2\;\mathrm{H}_{2}\mathrm{O} \tag{4}\]\[\text{C}_{2}\text{H}_{4}\text{O}_{2}+0.79\ \text{O}_{2}+0.22\ \text{NH}_{4} ^{+} \to 1.14\ \text{CH}_{1,74}\text{O}_{0.46}\text{N}_{0.19}+1.33\ \text{H}_{2}\text{O}+0.86\ \text{CO}_{2}+0.22\ \text{H}^{+} \tag{5}\] \[1.5\ \text{C}_{2}\text{H}_{4}\text{O}_{2}+0.75\ \text{O}_{2}\to 0.5\ \text{C}_{4}\text{H}_{6}\text{O}_{2}+1.5\ \text{H}_{2}\text{O}+\text{CO}_{2} \tag{6}\]  
Based on the mass balances, the indirect conversion of CO\({}_{2}\) to PHA through acetic acid is an interesting alternative for the direct production of PHA from CO\({}_{2}\) in terms of CO\({}_{2}\) fixation, H\({}_{2}\) consumption, substrate cost and safety. Compared to the autotrophic-autotrophic PHB production process, for example, this cultivation method could theoretically reduce equal amounts of CO\({}_{2}\) (2.84 ton CO\({}_{2}\)/ton PHB), while consuming 50% less H\({}_{2}\). On the contrary, commercial PHB (i.e., produced from glucose) emits at least 2.81 ton CO\({}_{2}\)/ton PHB according to the mass balances [5]. Most reports focused, however, on the use of acetic acid for PHA production by mixed cultures rather than a pure culture. Also, the utilisation of a mixture of short-chain carboxylates such as acetic, propionic, and butyric acid generated by the anaerobic conversion of organic wastes using undefined mixed cultures has been investigated frequently as a carbon source for PHA production by pure and mixed cultures [12]. Although the use of mixed microbial cultures or waste feedstock can improve the economics of PHA, mixed culture fermentation generates mixtures with variable carboxylate composition rather than a single product in high concentration [13]. Because the carboxylate composition determines the PHA monomers, which in turn strongly influence the polymer physical/mechanical properties [12; 14], such undefined and fluctuating carboxylate substrates are undesirable, in particular for high-end (such as medical) applications.