## 4 Experimental Methods
The degassed LMA monomer (100.0 mL, 86.8 g, 341.2 mmol), toluene (5.0 mL, 4.335 g, 47.2 mmol), PhCoBF (78.0 mg, 0.120 mmol) and AlBN (866 mg, 5.274 mmol) were introduced into a Schlenk flask equipped with a magnetic stirrer bar and containing an inert argon atmosphere. The reaction vessel was then immersed in a preheated oil bath, which was thermostatically controlled to remain at 80 \({}^{\circ}\)C. After 24 hrs, the vessel was removed from the oil bath and quenched to prevent further reaction, and an oligomer concentration of 40% was obtained. Preparation of Purified Lauryl Methacrylate Oligomers. A crude oligomeric solution of LMA was synthesised by the procedure outlined above: the crude product was then vacuum distilled to increase the oligomer concentration in the solution to 81%. The remaining 19% was lauryl methacrylate monomer. _Hyperbranched Functional Polymer Synthesis_ via _Copolymerisation of DVB and LMA Dimer:_ Degassed DVB-80 (12.5 mL, 11.4 g, 87.8 mmol) and cyclohexanone (10 mL, 9.48 g, 96.6 mmol) were transferred to a Schlenk flask containing LMA oligomer (50 mL), PhCoBF (39.0 mg, 0.0601 mmol), a magnetic stirrer bar and containing an inert argon atmosphere. Again, no initiator in the reagent formulation was included as the reactions were allowed to self-initiate. The resulting solution was then heated rapidly to 150 \({}^{\circ}\)C by immersion in a preheated oil bath and held at that temperature for 35 min, after which it was immediately quenched to prevent gelation. Once cooled, the solution was added dropwise to cold (0 \({}^{\circ}\)C) methanol. The resulting precipitation that was formed via introducing the mixture to the low temperature solvent was collected via filtration at this reduced temperature. It was then warmed to room temperature to provide a brown/white, viscous liquid, which was then dried to constant mass. Yield = 63%. GPC: M\({}_{\text{n}}\) = 37000, D = 102.7. The brown colouration was attributed to a small amount of retained cobalt catalyst. However, the precipitation solvent was highly coloured indicating that the majority of the PhCoBF has been removed via this separation process. _Polymer Characterisation - Gel permeation chromatography (GPC):_ This was performed using a refractive index (RI) detector with HPLC THF as the eluent. Analysis was performed at 40 \({}^{\circ}\)C with a flow rate of 1 mL min\({}^{-1}\) through two PolarGel-M columns with a calibration range of 580\(-\)377 400 Da calibrated with 10 poly(styrene) narrow molecular weight distribution standards. All GPC equipment and standards were supplied by Polymer Laboratories (Varian). GPC data were analysed using the Cirrus GPC and Astra offline software packages. _Nuclear Magnetic Resonance (NMR):_\({}^{1}\)H NMR spectra were obtained in CDCl\({}_{3}\) on a Bruker AV3400 (400 MHz) spectrometer. Chemical shifts were referenced against residual solvent signal (\({}^{1}\)H = 7.26 ppm, \({}^{13}\)C = 77.16 ppm) and processed using the MestReNova software. In this study NMR was primarily used for oligomer analysis as the resonances in the spectra of the HB materials were too broad to allow for additional structural information to be identified. _Application Testing:_ All tribological application testing was undertaken under the guidance of bp/Castrol at their facility in Pangbourne, UK. PAO4 was used as the control base oil medium in all tests. The tribological features of the polymers produced were tested under both hydrodynamic and boundary conditions to test both the viscosity of the solutions and film formation at surfaces. _Base Oil Solubility Testing:_ The solubility of different polymers produced in the above test methods was analysed through adding a small amount (20-100 mg) of the produced polymer into PAO4. The tests started at room temperature, and then with stirring, the temperature of the PAO4 was increased in 10 \({}^{\circ}\)C intervals.