# Effects of Organophosphorus Flame Retardants on the Dissipation Factor of Flame-Retardant Polymers
## 3 Results and Discussion
### Effect of OH on Df of PS/FR  
Polystyrene is a non-polar amorphous polymer and was chosen as a model polymer for hydrocarbon polymers like styrene-butadiene-styrene copolymer and polybutadiene, which have been commonly used in PPO-based formulations. Considering that processing temperatures might affect the mixing of the flame retardant and polymer, two temperatures were used, i.e., flame-retardant polystyrene was processed at 150 \({}^{\circ}\)C and 190 \({}^{\circ}\)C, respectively, and obtained by cooling under pressure from the processing temperature. Since polystyrene has a resonant frequency around 8.6 GHz, the Df values of polystyrene/flame retardant (PS/FR) are not useful at this point. However, apart from this resonant frequency, the effects of flame retardants on the dielectric loss of flame-retardant polystyrene are clear in the range of frequencies from 7 to 20 GHz. For PS-150-DOPO-Me, its Df values increase linearly with the amount of the flame retardant until they reach an inflection point around 5% of DOPO-Me, after which the Df values still remain a good linear relationship with DOPO-Me but the lines become less steep, as seen in Figure 3. The bending point at 5% DOPO-Me is apparently caused by a change in the neighboring environment of the flame retardant in PS. This explanation is readily supported by DSC results. Figure 2: Df and Dk of flame retardants. DSC thermograms indicate that DOPO-Me exists as an amorphous form in PS-150-DOPO-Me, because there is no melting peak observed for DOPO-Me. At low concentrations, each DOPO-Me molecule is surrounded by non-polar polystyrene chains. However, at high loadings, molecules of DOPO-Me start to aggregate. In line with this aggregation, the \(T_{g}\) curve of PS-150-DOPO-Me also bends at 5% due to less plasticization per DOPO-Me molecule. The aggregation creates local potential gradients and increases the activation energy to rotate a polarized DOPO-Me molecule. Subsequently, the ability of P=O dipole realignment is reduced in an applied electric field and the rate of Df increases slows down at high loadings of DOPO-Me. However, the overall Df values continue to rise due to a high dielectric loss of amorphous DOPO-Me. On the other hand, PS-150-DOPO-HM produces a somewhat different pattern. Although the Df values of PS-150-DOPO-HM increase linearly with the flame retardant content, the linear relationship is only found at very low loadings of DOPO-HM (0-0.5%), far narrower than the broad range (0-5%) found in PS-150-DOPO-Me, implying that DOPO-HM is easier to aggregate. After 1%, the Df values of PS-150-DOPO-HM reach a plateau, resulting from a balance of the opposite actions of an increasing loading of the flame retardant and a decreasing concentration of amorphous DOPO-HM. Indeed, DSC thermograms of PS-150-DOPO-HM show increasing crystallinity of DOPO-HM from 19% in 2.5%-DOPO-HM to 90% in 30%-DOPO-HM. Compared with PS-150-DOPO-Me, PS-150-DOPO-HM has notably lower Df values at high loadings of the flame retardant. Even when cooled from a higher processing temperature which enables complete melting of DOPO-HM, PS-190-DOPO-HM still produces lower Df values at 20 GHz than PS-190-DOPO-Me, which has almost identical Df values as PS-150-DOPO-Me. Obviously, poorer plasticization of amorphous DOPO-HM, as evidenced by less reduced \(T_{g}\) values shown in Figure 3, could not enhance mobility of PS chains as great as amorphous DOPO-Me does. In other words, DOPO-HM is more associated at high loadings and hence the Df increases slow down. From the above results, it can be seen that organophosphorus flame retardants with a hydroxyl group can actually be advantageous in non-polar polymers in keeping a low dielectric loss of the latter. In addition, to quantify the Df values of amorphous DOPO-Me and DOPO-HM, linear regression of the Df values of the flame-retardant polystyrene as a function of the flame retardant content was used. The concentration of DOPO-HM was limited to a range from 2.5% to 10% due to a mass exodus beyond 10%.