## 1 Introduction  
Industrial lubricants have had to evolve to match the increasingly stringent demands of evolving transportation technologies. For example, requirements have extended from acting as simple wear reduction and heat transfer media in cast-iron machinery. Now they are also expected to function as antioxidants and provide protective film coatings in modern combustion engines [1, 2]. Two common components of current industrial lubricants are viscosity and friction modifiers, which increase operational efficiency and reduce wear, respectively [3]. Friction modifiers (FM) reduce energy losses generated by internal friction and maintain boundary films to prevent wear [4]. In practice, whilst the base oil gives some boundary friction reduction, it is not regarded as a true FM [5]. Rather, additional additives, including polymers, are used to reduce friction [6]. However, there are concerns related to polymeric additive shear stability in this context [7]. Traditionally, these additives are amphiphilic molecules, i.e., they contain both a straight-chain hydrocarbon \"tail\" group and a polar \"head\" group, such as amines, amides, carboxylic acids and phosphoric/phosphonic acids. The latter is proposed to interact with the metal surfaces within the engine to anchor the materials [8, 9, 10]. Alternatives to polymeric additives are inorganic additives, such as molybdenum disulphide (MoS\({}_{2}\)), which has a crystal structure. These deposit on the metal surface, and allow sliding and shearing to occur [3, 11]. More recently, the use of MoS\({}_{2}\) nanoparticles has been found to give ultralow friction coefficients [12]. Viscosity modifiers (VMs) are often high molecular weight, linear polymers added to improve the viscosity index of the oil. This allows the oil to operate efficiently over a wider temperature range. These multi-grade oils enable easier cold cranking and starting, which delivers improved fuel efficiency. Commonly used VMs are linear olefin copolymers, such as ethylene-propylene, hydrogenated styrene-diene and poly(alkyl)methacrylate copolymers [3]. However, these suffer from strong, attractive and intermolecular/chain interactions, which limit the minimum viscosity that can be achieved at low temperatures. These interactions have been shown to be reduced if nonlinear, 3-dimensional (3D) polymer structures are used [13]. Of these, hyperbranched (HB) and dendrimeric polymers have been shown to exhibit the greatest difference from linear materials, in terms of viscosity build when they are added to liquid media [14]. The high level of branching is hypothesised to impart what is referred to as a \"globular\" molecular structure that limits interchain contact. Dendrimers are extremely branched, well-defined (monodisperse), 3D macromolecules, typically synthesised via highly controlled, multistage, sequential and iterative reactions [15; 16; 17]. Their \"porous\" structures emanate from a central core and have been shown to be ideally suited for encapsulating small molecules. Consequently, they have been shown to transport molecules for fragrance distribution, drug delivery, diagnostics, catalysis and light-emission applications [18; 19; 20; 21]. Their material properties, which include altered polymer melt-flow characteristics, have also garnered interest [22; 23]. However, research into their potential end-use applications has been hampered by the labour, time and cost-intensive routes required for their production [16; 24; 25]. By contrast, HB polymers can be more rapidly (hours rather than weeks), cheaply (single, not multistep) and flexibly (larger range of applicable reagent monomers) synthesised than dendrimers [26; 27; 28; 29; 30]. Producing structures similar to dendrimers but less well-defined, with the potential to deliver the same performance at a much-reduced cost [26]. This has led to an interest in them running from petrochemical applications, such as in this study, through to glycopomers for use in biomedical applications [9; 31; 32].