There were two possible reasons why the COF decreased with time before the system reached a steady state. Firstly, because the friction pair was temporarily separated when cleaning and adding the surfactant solutions before each experiment, the relative position of the friction pair was changed when contacted again. Therefore, the friction pair would run-in again for a short time. Secondly, at the beginning of the transition phase, the adsorption state of the surfactants in the contact zone had not yet reached a steady state. After a period of friction, the number of molecules adsorbed in the contact zone reached a dynamic equilibrium. The arrangement characteristics, such as the molecular conformation and orientation also reached a balance, and the COF could then reach a stable value. To explore the reason why the time required for the transition phase of SDS and AOT was different, the influencing factors of the above two aspects were respectively verified.
The four-ball friction test apparatus and its supporting microscope were used to conduct friction experiments and observe wear scars, the results for SDS and AOT are respectively shown in Fig. 5 and Fig. 6. The experiment consisted of two stages, stage 1 contained the rising edge of the COF and was stopped after the COF reached its peak value, and stage 2 contained the falling edge of the COF and was stopped when the COF tended to be stable. The purpose of doing this was to compare the wear scars at different moments of the transition phase, to verify whether the transition phase was caused by running-in.
Figure 5(a) shows the COF over time with 5 mM SDS as lubricant. The applied normal load was 5 N, and the angular velocity of the upper ball was 300 rpm. Before starting, the friction pair had been run-in with DW under a normal load of 5 N, and the wear scar of one of the lower ball is shown in Fig. 5(b). Then the SDS solution was added as lubricant to start friction, which was stage 1 in Fig. 5(a). During this period, the COF first increased, and then began to decrease. So the friction was stopped, and the solution was poured out and blow-dried to observe the wear scar of the lower balls, as shown in Fig. 5(c). After that, new SDS solution was added to start the friction again, which was stage 2 in Fig. 5(a). In this stage, the COF increased slightly again, and gradually decreased in the following 30 s until the COF tended to be stable. So the friction was stopped again to enable observation of the wear scar, as shown in Fig. 5(d). Although the COF curve in Fig. 5(a) appears similar to the running-in curve under boundary lubrication [15], changes of COF in Fig. 5(a) is actually different from a pure running-in, because in comparing the size and internal morphology of wear scars in Figs. 5(b)–(d), it could be seen that the size in 5(c) along the friction direction was approximately 0.2% larger than that of 5(b), and the internal grooves were slightly shallower, while the size and grooves of 5(d) showed no obvious changes compared with 5(c). This demonstrates that when the COF of stage 1 increased significantly, a slight running-in occurred in the contact zone, while the change of wear scar in stage 2 was not obvious, and the continuous decline of COF was not only related to running-in.
Similar experiments were also performed with 5 mM AOT solution (Fig. 6), and a similar phenomenon was observed. During each stage, the COF first increased for several seconds, and then decreased. The size and internal grooves of the wear scars changed slightly, similar to Fig. 5. The main difference with Fig. 5 was the duration of the falling edge of COF; thus, the main difference in the duration of the transition phase between AOT and SDS should have been related to molecular behavior, rather than running-in.
Since the transition phase was not completely caused by running-in, the changes in the adsorption state of lubricant molecules could have also been related to the changes in COF. Therefore, the adsorption rates of different concentrations of SDS and AOT solutions were compared, as shown in Fig. 7. Typical curves of the adsorbed number of molecules per unit area are depicted in Fig. 7(a), where the adsorption amount gradually increased and tended to stabilize, and AOT reached saturation faster than SDS. The change in the adsorbed molecular number as a function of time was fitted using the first-order adsorption kinetic equation [41]:
$${log}\left({q}_{e}-{q}_{t}\right)=log{q}_{e}-\frac{{k}_{ads}}{2.303}t$$
2
where \({q}_{e}\) and \({q}_{t}\) denote the maximum value and the value at time \(t\) of the adsorbed molecular number, respectively, and \({k}_{ads}\) represents the rate constant, where a larger \({k}_{ads}\) indicates a higher adsorption rate. The change in\({log}\left({q}_{e}-{q}_{t}\right)\) as a function of time is depicted in Fig. 7(b), and it can be fitted using Eq. (2). Thus, the value of \({k}_{ads}\) for different solutions can be calculated, as presented in Table 1. The values of \({k}_{ads}\) for AOT were larger than those for SDS at all concentrations, indicating that the adsorption of AOT was faster than SDS.
Table 1
Adsorption rate \({k}_{ads}\) of different solutions.
Solution | 5 mM SDS | 5 mM AOT | 10 mM SDS | 10 mM AOT |
Kads (s-1) | 0.0274 | 0.0507 | 0.0343 | 0.0440 |
In comparing the final adsorption amount in Fig. 7(a), the final adsorption amount of SDS was greater than that of AOT. This is because SDS with a linear structure can be more densely packed than AOT with a branched structure [6, 42] on solid surface. Moreover, the difference in the molecular structure and adsorption amount of SDS and AOT led to different lubrication effects, as shown in Figs. 2–4. Under steady-state lubrication, the COF of SDS as lubricant was lower than that of AOT in boundary and mixed lubrication regions. There were two possible reasons, firstly, the boundary film of SDS was denser (Fig. 7(a)); secondly, in boundary lubrication regions, some parts of contact zones were very limited in space, with only one or a few molecular diameters. SDS molecules were able to enter these contact zones due to their smaller steric hindrance, while AOT molecules were difficult to enter with their larger steric hindrance (Fig. 8). Thus, the adsorption amount as well as the surficial-coverage of SDS in the contact zone were gradually increased in the transition phase, and eventually achieved a value greater than that of AOT under steady-state lubrication. The diffusion time of confined molecules could be considerably longer than that of bulk molecules [43], so the duration of transition phase was longer for SDS.
In summary, in the friction tests, the relative position of the friction pair changed slightly before and after adding the surfactant solutions as lubricant; in the step-up-normal-load tests, the area of the contact zone increased after each loading. Thus, the contact zone would experience a slight running-in at the beginning of each transition phase, leading to the generation of fresh surfaces that required rapid adsorption of surfactant molecules. A larger adsorption rate of AOT enabled a faster replenishment into the contact zones, so its COF decreased rapidly; SDS had a lower adsorption rate, but also a larger adsorption amount in confined zones due to its smaller steric hindrance, showing a COF curve that decreased more slowly and continuously to a lower stable value. Therefore, the duration of transition phase of SDS was much longer than that of AOT.