The Squeeze-Out of Lubricant

dry state (a) lubricated state (b) trapped

lubricant

Figure 2.4.: Deformation of a ball on a flat in the dry state (a) and in the lubricated state (b).

the U.S. Food and Drug Administration (FDA) officially allowed a special lubricant class for direct food contact: Perfluorinated Polyethers (PFPE), like e.g the PFPE high performance lubricant, whose chemical formula is shown in figure 2.3. Resulting from the ether bridges, their molecular structure renders PFPEs flexible, yet PFPEs are chemically inert, because of the perfluorinated alkyl segments. Perfluorinated alkyl segments are highly stable because of the very strong carbon-fluorine bond on the one hand, and the high electron density at the fluorine atoms on the other. The high electron density at the fluorine atoms in connection with the rather short carbon-fluorine bonds protects the carbon atoms from nucleophilic attacks. In addition to the chemical inertness, PFPE molecules are advantageous for lubrication because PFPEs are longer chain polymers.

The technical data sheet of the Krytox^® family lubricants states that the number of repeating unitsn starts from ten for low viscosity lubricants and ranges up to 60. The longer the chain of a lubricant molecule the more difficult the molecules are to squeeze-out, as will be discussed in the next section. Molecules difficult to squeeze out are high-performance boundary lubricants.

Chapter 2. Contact 2.4. The Squeeze-Out of Lubricant

Figure 2.4 exemplary shows the trapping of lubricant by the altered deformation of a ball on a flat with lubricant present. There will be no trapping of lubricant in the limiting case of zero pressure increase rate, because over time all the molecules have the possibility to leave the high pressure area. In contrast to that in the limiting case of infinite pressure increase rate, all lubricant that may be trapped, will be trapped. Balls in a bearing often move with velocities that are in the intermediate regime concerning the entrapment of lubricant. In this case the entrapment is limited to the junction areas, not only because of the speed, but also, because the exaggerated depiction in figure 2.4 and in figure 7 in reference [3] refer to a highly elastic ball, while a ceramics ball with an elastic modulus of 320 GPa most certainly is not very elastic.

In addition to the question, whether there is enough time for the molecules to leave the high pressure area before the liquid enters a quasi-solid state, the length of the molecule backbone is of importance for the squeeze-out. From the review on squeeze-out by Persson and Mugele [3] as well as the underlying article by Sivebaek, Samoilov and Persson [22]

it becomes clear from MD simulations of united atom representations of hydrocarbons under squeeze-out conditions, that there is a linear dependence of the pressure necessary for the initiation of a layering transition on the chain length. A layering transition is the transition of n monolayers to n−1 monolayers. Simulations by Persson and Ballone, published in the year 2000 [23, 24], show the influence of density fluctuations on the induction of a layering transition. As with crystallization the layering transition needs a nucleus to start [25]. Density fluctuations stem from thermal molecule motion (Brownian motion) or surface roughness. Persson and coworkers investigated the layering transitions for hydrocarbons from propane on. Extrapolating the linear correlation to one carbon atom, the resulting pressure to squeeze out even the last layer of methane molecules is about 2750 bar. An even smaller pressure will be required for water molecules that are between two approaching hydrophobic surface asperities.

The influence of surface roughness on the layering transition has already been mentioned.

Not only the density fluctuations induced by an asperity protruding into the bulk liquid facilitates squeeze-out, also the molecular state of the lubricant is of relevance. Once the molecular state changes to solid-like because of the high pressure, the mobility of the molecules is drastically decreased. Another publication by Persson and coworkers [26]

states the fact that “surface roughness hinders the formation of solid-like lubricant struc-ture and liquid-like (disordered) layers are observed. This in turn leads to a reduction in squeeze-out pressure”.

Another hidden factor in squeeze-out was highlighted in the same publication: the surface commensurability. Figure 28 shows a representation of the two different possibilities for friction partner surfaces: Either the surfaces are commensurate, which means the structure is very similar, and thus the molecules may be clamped by the surface, or the

commensurate, while locked Δh

commensurate, while sliding

incommensurate incommensurate, but pinned lubricant layer

surface

Figure 2.5.: Schematic representation of the commensurability and lubricant pinning.

The surfaces are represented by the smaller circles filled grey, while the larger circles represent the lubricant. The height difference Δh has to be overcome when the sliding of a commensurate system takes place. The height difference in the incommensurate but pinned system will be even higher, while it will be less in the incommensurate system.

surfaces are incommensurate, which means that the surface structuring of the one surface does not fit to the other surface structure. In case of surface asperities, the lubricant molecules also may be pinned by the asperities [26]. For the initiation of sliding, the pinning results in the requirement of either a large deformation of the surface or a large height difference. The energy necessary for the deformation or the increase in surface separation increases the friction.

Consequently the surface roughness influences the frictional characteristics of a surface by three main factors: Firstly the surface roughness induces density variations that is necessary for the initiation of the squeeze-out of lubricant molecules, secondly the surface roughness prevents the formation of a quasi-solid lubricant structure thereby facilitating squeeze-out and as a third factor the pinning of the remaining lubricant molecules increases the friction that is created during the sliding process.

Chapter 3. Plasma Surface Coating