## 2 Results and Discussion  
### Synthesis of Oil Soluble Hyperbranched Polymers  
Hyperbranched divinylbenzene (hbDVB) homopolymers are of interest as friction modifiers due to their ability to exhibit oil solubility, so that they can be delivered as part of a liquid lubricant formulation. They also exhibit the potential to cross-link _in situ_ on hot engine surfaces to produce protective films [55]. For this study, the \"oil\" of interest was poly(alpha-olefin) base oil 04 (PAO4), a hydrocarbon base oil used in the final lubricant formulations. However, an initial inspection of hbDVB solubility showed that it was essentially insoluble in PA04, this was attributed to the aromatic nature of DVB. Hence, the DVB monomer (Figure 1a) was initially directly copolymerised with a range of mono-olefin acrylate/methacrylate monomers (structures shown in Figure 1b-e). These contained long pendant alkyl chains to improve the base oil solubility of the subsequent HB copolymers. It was found that by using a ratio of either 1:9 or 2:8 (_v/v_) DVB:mono-olefin monomer when conducted in the presence of either bis[(difluoro  
Figure 1: Structures of monomers and oligomer reagents used in synthesising functional HB polymers. Monomers = (**a**) DVB, (**b**) lauryl methacrylate, (**c**) lauryl acrylate, (**d**) stearyl methacrylate and (**e**) stearyl acrylate. Oligomers = (**f**) dimer created from lauryl/stearyl methacrylate, where n is 11 (lauryl) or 17 (stearyl). (PhCoBF) (acrylate) or 2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) (methacrylate), oil soluble copolymers were produced with identifiable gel points. These direct copolymers were proposed to be statistical copolymers, with a purely random mix of DVB and a monofunctional monomer. A representation of this copolymer structure is shown in Figure 2a. The copolymers synthesised from DVB and lauryl methacrylate/acrylate (Figure 1b,c) were chosen for further study. This was because they demonstrated the greatest level of base oil solubility (fully dissolving in PAO4 at 50 \({}^{\circ}\)C, Table 1) and exhibited the most straight-forward processing conditions, as shown in Figure 1c-e, in copolymers due to their physical form. A key reason behind the processing advantages with LMA and LA was their low melting points of -7 \({}^{\circ}\)C and 4 \({}^{\circ}\)C, respectively, which reduced mixing issues with the DVB. By comparison, the melting points of SMA (18-20 \({}^{\circ}\)C, Figure 1d) and SA (32-34 \({}^{\circ}\)C, Figure 1e) lead to very lengthy mixing times to achieve homogeneous mixtures. However, the direct CCTP mediated polymerisation with DVB at both the 1:9 and 2:8 ratios was found to be inefficient. Thus, only relatively low levels of LMA could be incorporated into this random structure, which limited the achievable solubility of the final copolymer. Thus, to improve both the efficiency of copolymerisation and produce polymers with higher alkyl content, an alternative copolymerisation strategy was adopted. The new method centres on producing low molecular weight oligomers of LMA from the pure alkyl monomer by employing a high concentration of the CCTP catalyst, PhCoBF. In this way, a solution of monomer/dimer/trimer, with an oligomer yield of -40% was achieved and confirmed by NMR/GPC analysis. LA was not used in this strategy because of the relative inefficiency of CCTP with acrylate monomers. These CCTP methacrylate-based dimer/trimer species can act as CTAs via a \(\beta\)-scission mechanism, so simultaneously control the polymerisation to produce hbDVB and introduce the required hydrocarbyl character [53]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Commoner** & **Solvation Temp (\({}^{\circ}\)C)** & **Appearance in Solution** \\ \hline SA & 70 & Colloidal Suspension \\ \hline SMA & 70 & Clear Solution \\ \hline LA \({}^{\text{a}}\) & 50 & Clear Solution \\ \hline LMA & 50 & Clear Solution \\ \hline \hline \end{tabular} \({}^{\text{a}}\) Species was unable to be isolated from the reaction mixture.  
\end{table}