# Transient Nanoscale Tribofilm Growth: Analytical Prediction and Measurement
## 4 Discussion
The surface monolayer adsorption and the shear-promoted thermal activation can therefore be modelled as a symbiotic loop in which molecules adsorb over a given period of time, with a scanning pass activating some proportion of these. Therefore, a new surface coverage is determined, and adsorption is allowed over the next time period before another scanning pass occurs. Another factor that should be considered concerns the removal of the adhered molecules which are unsuccessful in the bonding reaction. If the expended shear energy is sufficient, these molecules may be removed from the surface and return to their dissolved state in the bulk oil. As the desorption rate is energy dependent, it would be logical to relate the desorption rate to the generated thermal and mechanical energies, while only using the former for desorption occurring outside the contact domain. As a result, a process may be conceived as illustrated in Figure 6. A similar process was described by [PERSON] et al. [56] for the tribochemical film formation of ZDDP using MTM. Applying the multi-molecular layer model yields the results shown in Figure 7, where the average depth of the adsorbed film is added to the activated tribofilm height predicted by the Arrhenius equation. An estimated layer height of 2.4 nm has been applied here as this has been reported as the mean molecular length of free ZDDP molecules determined by [PERSON] et al. [57] using dynamic light scattering. Figure 8 shows the predicted fraction of the surface covered with bonded molecules 1, 2, 3, 4 and 5 layers deep within the test period. It can be seen that the mono-layer coverage reduces after 60 min as it becomes increasingly covered with further molecular layers. Figure 6: Cyclic process illustrating adsorption and activation of additives by a cyclic tribological event. \[\Delta E_{mech}=\tau\Delta V \tag{2}\]0 Growth of tribofilm height with time as measured and modelled using the BET adsorption model paired with the Arrhenius shear-promoted thermal activation model. Figure 9 shows that the total predicted surface coverage stabilises at 85% of the surface after 180 min, although there remains slight fluctuation due to changes in shear stress and activation rate. Referring back to Figure 7, it is shown that the multi-molecular layer adsorption model not only provides a reduced initial growth rate in comparison with the use of the Arrhenius model alone (Figure 5), but also provides an explanation for the reducing film growth at the end of the test period. With additional testing for further understanding of the adsorption and desorption rates for each of the multi-molecular layers, it is expected that even better conformance of predictions to the measured data may be achieved. In micro-scale contacts, some change would have to be made to the cyclic process shown in Figure 6 as the adsorbed multi-molecular layers, predicted through BET, may be sheared-off under the contact conditions, particularly in asperity-pair ploughing. The unusual case of the AFM scanning probe removes this issue in the current investigation as  
\[\Delta E_{mech}=\tau\Delta V \tag{2}\]1 The predicted fraction of the surface coverage of multi-molecular layers within the test period. \[\Delta E_{mech}=\tau\Delta V \tag{2}\]2 Total predicted fraction of substrate surface coverage in the test period. the fixed end of the cantilever holding the tip is a reactive loading system, which adjusts the tip height in order to maintain a constant load over varying topography. This is of course, not the case in micro-scale contacts. Figures 7 and 8 show that the rate of growth of the tribofilm predicted through the new combined BET and Arrhenius model begins to fall as the adsorbed film tends to an average depth of 3 molecules.