# Effects of Organophosphorus Flame Retardants on the Dissipation Factor of Flame-Retardant Polymers
## 3 Results and Discussion
### Effect of OH on Df of PMMA/FR
\begin{table}
\begin{tabular}{c c c c} \hline
**Sample** & **T1** & **Df at 20 GHz** & \(T_{g}\) (\({}^{\circ}\)**C**) \\ \hline PMMA-170-slow & 24.6 & 0.003254 & 110.7 \\ PMMA-170-quick & 27.0 & 0.004110 & 113.4 \\ PMMA-190-quick & 29.8 & 0.004287 & 116.1 \\ \hline PMMA-170-DOPO-Me-quick & & & \\ \hline
0\% & 27.0 & 0.004110 & 113.4 \\
0.25\% & 25.1 & 0.003670 & 112.3 \\
0.5\% & 24.5 & 0.003502 & 111.9 \\
1\% & 22.1 & 0.003644 & 109.8 \\
5\% & 28.1 & 0.004008 & 101.8 \\
10\% & 28.4 & 0.004688 & 93.7 \\
20\% & / & 0.005223 & 76.1 \\ \hline PMMA-170-DOPO-HM-quick & & & \\ \hline
0\% & 27.0 & 0.004110 & 113.4 \\
0.1\% & / & 0.004097 & 115.0 \\
0.25\% & 29.6 & 0.003840 & 114.0 \\
0.5\% & 30.2 & 0.004321 & 111.9 \\
1\% & 29.8 & 0.004140 & 110.8 \\
5\% & / & 0.004761 & 103.7 \\
10\%Furthermore, solid-state NMR experiments were performed to extract the T\({}_{1}\) relaxation time constant of carbonyl carbon of PMMA to distinguish dipole-dipole interactions in PMMA samples made at different processing temperatures. It was expected that dipole-dipole interactions, foreseeably originating from tg or gg conformations that lead to the curl-up of PMMA chains, would reduce the T\({}_{1}\) value. In fact, PMMA-170-slow has a lower T\({}_{1}\) value of 24.6 s than PMMA-170-quick, which itself has a lower T\({}_{1}\) value of 27.0 s compared to that of PMMA-190-quick, 29.8 s, as listed in Table 4. Therefore, the T\({}_{1}\) data clearly differentiate the dipole-dipole interactions in these PMMA samples and imply a relationship between the dielectric loss and tt conformations of PMMA, which is forged through dipole-dipole interactions. Now, for PMMA/FR, particularly PMMA-170-DOPO-Me-quick, flame retardants work in another way, but with a similar effect, to change the distribution of tt conformations of PMMA. As inferred in Table 4, DOPO-Me acts as a plasticizer to effectively lower the glass transition temperature of PMMA. The plasticizer enables PMMA main chains to gain enough mobility [32] to overcome their torsional barrier and acquire tg or gg conformation, achieving a comparable effect as in slow cooling. As a result of forming the tg or gg conformations, which can facilitate dipole-dipole interactions of intra-chain ester groups, both the T\({}_{1}\) and Df values reduce initially, as demonstrated in Figure 4 and Table 4.  
However, intramolecular dipole-dipole coupling of ester groups can be easily destroyed by excess DOPO-Me by solvation. After 1%, the T\({}_{1}\) values of PMMA-170-DOPO-Me-quick rise again and eventually reach a number around 28 s. On the other hand, the Df values of PMMA-170-DOPO-Me-quick continuously keep increasing, mainly due to a large Df value of amorphous DOPO-Me. In short, the initial decrease in the dielectric loss of PMMA/DOPO-Me at low loadings of the flame retardant is owed to an abnormally high concentration of tt conformation of PMMA chains, while its increase at high loadings can be largely attributed to the amorphous form of DOPO-Me. On the other hand, DOPO-HM displays a much more complicated effect than DOPO-Me. At low loadings, DOPO-HM actually works as an anti-plasticizer to restrict the mobility of PMMA chains, as evidenced by the increased \(T_{g}\) values of PMMA-170-DOPO-HM-quick (to see Table 4). Obviously, the anti-plasticization originates from hydrogen bonds between PMMA ester groups and hydroxyl groups of DOPO-HM [33; 34]. Thus, more PMMA chains stay in extended conformation when they are rapidly cooled from a high temperature, which is consistent with an increased T\({}_{1}\) value of PMMA-170-DOPO-HM-quick at 0.25% DOPO-HM. However, the values of the dielectric loss slightly decrease instead of increasing, due to hydrogen bonds that slow down dipole alignment of both ester groups and hydroxyl groups in an applied electric field [35]. So, the reasons for the changes in T\({}_{1}\) and Df values of PMMA-170-DOPO-HM-quick are entirely different from those in PMMA-170-DOPO-Me-quick at low loadings. Figure 5: Newman projections of backbone t, g\({}^{+}\) and g\({}^{-}\) states of PMMA.