## 1 Introduction  
Rigid polyurethane (PUR) foams are highly desirable materials, particularly for thermal insulation applications, due to their beneficial characteristics [1]. The formation of PUR foams involves several competing chemical reactions. During urethane formation, the polymer backbone forms. Hydroxyl groups (\(-\)OH) from polyol react with \(-\)NCOgroups from isocyanate to form urethane linkages [2]. When water is used as a chemical blowing agent, it reacts with isocyanate groups to produce unstable carbamic acid, which immediately decomposes to form a urea linkage and release carbon dioxide, acting as a blowing agent and forming the cellular structure. Then, the amine formed during the water-isocyanate reaction can further react with another isocyanate group to form a urea linkage and subsequently with another isocyanate group to form a biuret linkage, which contributes to additional cross-linking and rigidity in the PUR foams [3]. Such materials have a low density, thermal conductivity, and water absorption, as well as sufficient dimensional stability and a relatively high mechanical performance. Currently, the demand for such products in various sectors, including building, automotive, food packaging, furniture, medical, and aviation, has increased [4]. PUR products have become irreplaceable in the modern industry. Its global production exceeds 21.3 million tons annually, making it the sixth-largest category of synthetic materials worldwide [5]. The estimated value of the PUR products market in 2021 was USD 77.9 billion. According to predictions, this value is expected to increase to USD 105.3 billion by 2026 [6]. The popularity of PUR products can be attributed to the increasing cost of energy and growing awareness of the importance of energy conservation. Along with the energy-related aspects, environmental awareness associated with petroleum-based polyurethane PUR foams is of great interest to the scientific and industrial communities. Significant effort has been invested in converting petroleum-based PUR foams into more environmentally friendly alternatives. For instance, polyol is dependent on petroleum-based feedstocks, and its synthesis using biomass such as oils is in high demand. The commonly incorporated vegetable oils for bio polyol synthesis are soybean [7; 8], castor [9; 10], palm [11; 12], rapeseed [13; 14], sunflower [15; 16], and even waste cooking oils [17]. In addition, [PERSON] et al. [18] proposed a straightforward and efficient method for obtaining furfural from fructose. Furfural often serves as an intermediate or starting point in multi-step processes and can be utilized in the synthesis of furan-based diols, as indicated by [PERSON] et al. [19]. The synthesis of polyurethane from furan-based diols is similar to the synthesis from conventional polyols, except that the furan-based ones have two primary hydroxyl groups and a furan ring, which enhance the rigidity, stiffness, and thermal stability of the resulting product [20]. Furthermore, studies by [PERSON] et al. [21] and [PERSON] et al. [22] have shown that furan-based compounds can increase surface water contact angles and reduce the flammability of the resulting products, demonstrating great potential for future use as a main compound in the synthesis of polyurethane. However, few studies indicated that replacing petroleum-based polyols with bio-polyols can lead to the degradation of several properties. [PERSON] et al. [23] determined that adding a rapeseed oil-based polyol slows the reaction time, reduces compressive strength and apparent density, and deteriorates the closed-cell structure. Moreover, the thermal insulating properties also showed an adverse effect with an increase in the amount of rapeseed oil-based polyol. In addition, [PERSON] et al. [24] determined that the thermal conductivity of PUR foams made from biopolyols ages faster than that of conventional ones. It was also noted by [PERSON] et al. [25] that water absorption and dimensional instability were increased for PUR foam made from a palm oil-based polyol.