## 2 Results and Discussion
### Synthesis of Oil Soluble Hyperbranched Polymers

Table 1: Solvation properties of random structure copolymers prepared using a 2:8 ratio of alkyl reagent:DVB in base oil. Figure 2: Structures of the **(a)** random, **(b)** semi-block-like and **(c)** block-like HB copolymers. The red spheres represent multifunctional monomers, blue spheres the monofunctional monomers and green spheres the macromeric CTA fragments. These oligomer solutions were used in two methods to make HB polymers. To produce what were referred to as \"semi-block-like\" structures (Figure 2b), the CCTP oligomer solutions were polymerised with DVB in a ratio of 2:8, DVB:LMA oligomers (_v/v_), without any further purification, other than the removal of the residual PhCoBF catalyst. This ratio was chosen in an attempt to maximise the alkyl incorporation achieved. The term'semi-block-like' refers to the use of the monomer/dimer/trimer solution as a CTA. Thus, some of the polymer end groups will be terminated with the CTA's lauryl functionalised-olefin groups. However, as there will also be some LMA monomers present, some random polymerisation will be involved. Thus, the morphology of the HB polymer will also contain some random polymer characters. The 'block-like' structures (Figure 2c) were synthesised by reacting DVB with the same ratio (2:8) of a distilled solution of LMA CCTP oligomer products that reduced the monomer concentration from 60% to 19%. Consequently, the HB polymer had a higher probability of being terminated with the LMA CTA fragment, and reduced/no random character would be present. Subsequent application testing confirmed that both semi-block-like and block-like copolymers were soluble in the base oil at room temperature, indicating improved incorporation of LMA when using the oligomer CTAs. As a general procedure, all HB polymers were first synthesised until the gel point of the reaction was reached. Then, a repeat reaction was performed, which was quenched, and the polymer precipitated before the identified reaction gel time was reached. The results of all three reaction variants are summarised in Table 2, also an example of NMRs of the oligomer mediating agents and an example of an HB polymer have been included in the supporting information document, as Figure S1. The crude polymer yield, i.e., the yield of precipitated polymer with no further purification, is reported to give an indication of the efficiency of the reaction. This is because all the polymers synthesised exhibited a glass transition (T\({}_{\text{g}}\)) below room temperature. Thus, the precipitated product could not be fully recovered from the antisolvent without the risk of crosslinking reactions between the individual HB polymers. To bypass that, we focused on concentrating these materials with precipitation and applying heat to drive off the residual solvent, which is a standard method for methacrylate polymers. However, it was found that with HBs, this increased the likelihood of the HB-to-HB links occurring. The result of which was the formation of a gelled 3D network, thus, work-up was conducted at room temperature. The potential secondary actions of this nature have been observed with other architectural polymer types (i.e., polymers with three-dimensional structures) [56; 57]. From the data in Table 2, it is apparent that these reactions all produced a high yield of polymer compared to other literature-reported HB methods. Therefore, sufficient material could be generated for application testing [58; 59; 50; 52; 50; 51]. A key initial observation was that these LMA oligomers produced materials had very high D values but were, in fact, still solvent/base oil soluble. This allowed them to both undergo GPC analysis and be used in further material testing (see Figure S2). The D value of a random polymer was observed to