## 1 Introduction  
The rapid development of 5G communication technology has initiated a large-scale, worldwide effort to develop more sophisticated electronic systems requiring high-performance dielectric materials for printed circuit boards (PCBs). The main development directions of PCBs in the 5G era are a high layer count design, high frequency, and high levels of signal integrity, as well as high wiring density, which have incurred more stringent demands on the PCB substrate materials, i.e., copper clad laminates (CCL). In addition to lead-free compatibility and reliability requirements, a low dielectric constant (D\({}_{\text{k}}\)) and extremely low dielectric loss (D\({}_{\text{f}}\)) under high frequency are the most challenging material properties which have attracted great attention in both industry and academic institutions [1; 2; 3; 4; 5]. The D\({}_{\text{k}}\) and D\({}_{\text{f}}\) of traditional thermosetting CCL matrix materials, such as epoxy resin and cyanate ester (CE) resin, are intrinsically too high to meet the requirements of high-frequency applications [6; 7]. Therefore, new polymer systems with low D\({}_{\text{k}}\) and D\({}_{\text{f}}\) are being developed for high-frequency and high-speed applications. Among the available polymers, polyphenylene oxide (PPO) has great potential since it has a highly rigid skeleton structure with aromatic rings, without hydrolysable groups or polar side groups. These structural characteristics endow PPO with excellent hydrolytic stability, low moisture absorption, high thermal stability, and excellent electrical properties in a wide temperature range [8; 9; 10; 11]. For PCB applications, thermosetting PPO systems with excellent performance have been developed by capping the ends of PPO oligomers with reactive groups and curing with chemicals containing multiple functional groups, such as triallyl isocyanurate (TAIC), divinyl benzene, and 1,2-polybutadiene (PB), etc. [12; 13; 14; 15; 16; 17; 18], or copolymerizing with epoxy, cyanate ester, and benzoxazine, etc. [19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. Among the most significant developments, [PERSON] et al. [30] invented a methyl methacrylate capped bi-functional PPO oligomer (M-PPE-M) which was later commercialized by SABIC under the tradename of NORYLTM SA9000 and studied several cured systems with t-butyl styrene, divinyl benzene, TAIC, dibrominostyrene, etc., as crosslinking agents [31; 32; 33]. Outstanding dielectric, thermal and mechanical properties, as well as good water resistance, were achieved simultaneously in these systems. For example, for the TAIC cured systems at 1 GHz, the dielectric constant slightly changed between 2.5 and 2.57, whereas the dielectric loss was always as low as about 0.001 over a wide composition range (M-PPE-M/TAIC = 0% - 80%) [32]. Such dielectric properties were much better than that of traditional PCB substrate materials, such as epoxy-based (D\({}_{\text{k}}\approx\) 2.85, D\({}_{\text{f}}\approx\) 0.013 at 1 GHz) and cyanate ester-based systems (D\({}_{\text{k}}\approx\) 2.73, D\({}_{\text{f}}\approx\) 0.0051 \(\sim\) 0.0117 at 1 GHz) [32; 34]. In the past decade, several PPO-based substrate materials with similar formulations have been successfully commercialized and have started to play key roles in 5G devices [12; 13; 14; 15; 16] and a lot of research has been carried out regarding the combination of PPO oligomers with different crosslink agents, copolymers, or reinforcement components (DVB, PB, Epoxy, CE, etc.) [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. However, little work has been reported regarding the characterization of chemical structures and the relationships between crosslinked structures and the dielectric properties of thermosetting PPO-based ultralow dielectric loss systems. The dielectric properties of polymers are related to their polarizability.