# 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  
PMMA was used as a model polymer to study the effect of flame retardants on dielectric losses of polar polymers such as methacrylate end-capped PPO. 1H NMR reveals that the PMMA used in this study was atactic with syndio-triads of 51%, a significant fraction [26]. Since both the flame retardants and PMMA are polar, the solubility of DOPO-HM and DOPO-Me in PMMA is expected to be high. Indeed, all DOPO-Me and DOPO-HM dissolve in PMMA when their contents are equal to or less than 20%, as evidenced by the absence of peak of the flame retardants in X-ray diffraction of the flame retardant blends. In terms of the dielectric loss of the flame retardant PMMA (PMMA/FR), except at two resonant frequencies of PMMA at 8.6 GHz and 13.7 GHz, their Df values generally increase with the flame retardant content at high loadings as shown in Figure 4 and Table 4. However, it is surprising to note that both DOPO-Me and DOPO-HM cause an initial Df drop of PMMA upon the addition of a very small amount of the flame retardants, albeit with DOPO-HM having a much smaller effect. The early Df reductions are rather unexpected because the presence of amorphous flame retardants should have led to an increase in the Df values at low loadings as it does at high loadings. The opposite results suggest that the flame retardants at low loadings may have decreased net polarity of PMMA, resulting in a drop in the dielectric loss. Since the dielectric loss of pure PMMA at high frequencies primarily arises from its ester group with other accompanied methylene group [27; 28], the presence of the flame retardants might have changed the spatial arrangement of the polar ester groups which are dependent on specific conformations. Figure 4: Df and T\({}_{1}\) relaxation time constant of carbonyl carbon of PMMA/FR (Df values are taken at 20 GHz): (**a**) PMMA-DOPO-Me; (**b**) PMMA-DOPO-HM. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \multicolumn{3}{c}{**Df at 20 GHz**} \\ \hline  & \multicolumn{2}{c}{DOPO-Me} & \multicolumn{2}{c}{DOPO-HM} \\ \cline{2-4}  & crystal & amorphous & crystal & amorphous \\ \hline from FR & 0.000733 & & 0.000533 & \\ from PS/FR & & 0.0129 & & 0.0185 \\ from PMMA/FR & & 0.0135 & & 0.0168 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Df values of DOPO-Me and DOPO-HM at 20 GHz. To test the above hypothesis, experiments were first carried out on PMMA with different cooling rates. It was reasoned that conformations of PMMA chains can be better preserved at a fast cooling rate than at a slow cooling rate so a different degree of certain spatial arrangement of the polar ester groups can be produced. Since PMMA main chains have been documented to exist dominantly in a trans-trans (tt) conformation in melts [29; 30] and since extra extended chains, which has a tt conformation, are generated by high pressure used in fabricating test samples, there should be an above-normal concentration of tt conformations in PMMA at room temperature after rapid cooling. The tt conformation leads to a longer distance between intra-chain ester groups than trans-gauche (tg) or gauche-gauche (gg) conformations, as shown in Figure 5; as a result, the dipole-dipole interactions of intra-chain ester groups are weak and the Df values should increase. Indeed, the PMMA sample obtained at a fast cooling rate (PMMA-170-quick) features Df values higher than that attained at a slow cooling rate (PMMA-170-slow), as noted in Table 4, fully in agreement with the above assumption. Moreover, when PMMA was rapidly cooled from 190 \({}^{\circ}\)C, PMMA-190 gained a higher Df value than PMMA-170. Apparently, the high pressure used in making PMMA samples produced more tt conformations at 190 \({}^{\circ}\)C than at 170 \({}^{\circ}\)C because of the higher mobility of PMMA chains at a higher temperature. Thus, there were even more tt conformations in PMMA-190 than in PMMA-170, which is strongly supported by an increased \(T_{g}\) of the former, as shown in Table 4[31].