## 1 Introduction  
The 2030 framework for climate and energy policies contains a binding target to cut emissions in EU territory by at least 40% with respect to 1990 levels by 2030 [1]. This target enables the EU to take cost-effective steps towards its long-term objective of cutting emissions by 80-95% by 2050, and contributes to the Paris Agreement. As theoretical limits of efficiency are being reached and process-related emissions are unavoidable in some sectors, the utilisation of CO2 for the production of fuels, chemicals and materials, also referred to as Carbon Capture and Utilization (CCU), has emerged as a promising CO2 mitigation tool. In addition, CCU has the potential to address resource efficiency and growth while defining a new landscape and business opportunities for European industry [2]. In particular, CO2-based polymers look promising, as this approach benefits the environment in several ways. Firstly, the use of CO2 for the manufacturing of plastics can substitute petroleum as raw material and does not compete with food production in contrast with corn-based plastics. Secondly, in a circular economy approach, CO\({}_{2}\) is the only abundant source of carbon in the long term and the ultimate sustainable resource for the plastic industry. Polyhydroxyalkanoateates (PHA) are biological polyesters synthesised by a variety of organisms as an intracellular storage material from renewable resources. The homopolymer of 3-hydroxybutyrate (3 HB), also known as poly(3-hydroxybutyrate) (PHB), is the most common type of PHA and displays several interesting properties comparable to polypropylene [3]. Through the inclusion of other monomers in the polymer, the synthesis of copolymers with improved mechanical properties such as poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) in cells is possible, potentially increasing the value of the final product [4]. The most frequently applied cultivation method for PHA production consists of cell growth under favourable growth conditions, followed by PHA synthesis under imbalanced growth conditions. The model organism for this cultivation process is _Cupriavidus necator_, a metabolically versatile organism capable of shifting between heterotrophic growth (utilising organic compounds as a carbon and energy source) and autotrophic growth (utilising CO\({}_{2}\) as carbon source, H\({}_{2}\) as energy source and O\({}_{2}\) as electron acceptor). While most work was carried out using organic substrates as carbon source, attempts to produce PHB from CO\({}_{2}\) have also been undertaken. Two cultivation methods exist to directly utilise CO\({}_{2}\) for PHB production by _C. necator_. The first cultivation method (i.e., autotrophic-autotrophic PHB production process) uses a gas mixture of CO\({}_{2}\), H\({}_{2}\) and O\({}_{2}\) for both cell mass growth (Equation (1)) and PHB accumulation (Equation (2)), while the second method (i.e., heterotrophic-autotrophic PHB production process) consists of heterotrophic growth on an organic substrate such as glucose (Equation (3)), followed by autotrophic PHB production [5; 6]. \[21.36\;\mathrm{H}_{2}+6.21\;\mathrm{O}_{2}+4.09\;\mathrm{CO}_{2}+0.76\;\mathrm{ NH}_{3}\to\mathrm{C}_{4.09}\mathrm{H}_{7.13}\mathrm{O}_{1.89}\mathrm{N}_{0.76}+18.7\; \mathrm{H}_{2}\mathrm{O} \tag{1}\]  
\[33\;\mathrm{H}_{2}+12\;\mathrm{O}_{2}+4\;\mathrm{CO}_{2}\to\mathrm{C}_{4} \mathrm{H}_{6}\mathrm{O}_{2}+30\;\mathrm{H}_{2}\mathrm{O} \tag{2}\]  
\[\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}+1.97\;\mathrm{O}_{2}+0.72\;\mathrm{ NH}_{4}{}^{+}\to 3.79\;\mathrm{CH}_{1.74}\mathrm{O}_{0.46}\mathrm{N}_{0.19}+2.21\; \mathrm{CO}_{2}+0.72\;\mathrm{H}^{+}+3.78\;\mathrm{H}_{2}\mathrm{O} \tag{3}\]  
Experimental work on PHB production from CO\({}_{2}\) has been performed with a view to optimising the production of PHB using either pure synthetic CO\({}_{2}\)[7; 8; 9] or industrial off-gases [5]. In addition, a few studies have investigated mixotrophic PHA copolymer production in which CO\({}_{2}\) was supplied in combination with an organic co-substrate [10].