Mechanisms of ZDDP—An Update

Three experimental techniques have become quite widely used to measure and map the topography of ZDDP, and indeed other additive tribofilms, over the last 20 years—atomic force microscopy (AFM), spacer layer interferometry (SLIM), and scanning white light interferometry (SWLI).

Atomic force microscopy (AFM) was first applied to study the tribofilms formed by ZDDP in 1997 [33] and in recent years it has become routinely employed to map the film thickness, topography, and friction of these films [34‐39]. In 2006 Topolovec et al. used AFM to show that the ZDDP tribofilms form only on rubbed tracks and not on the surrounding surface, as demonstrated in Fig. 4, which also illustrates clearly the pad-like structure of the film material [34]. These authors also pioneered the use of ethylenediamine-tetraacetic acid (EDTA) solution to remove ZDDP films from a selected part of the rubbed track to reveal the substrate beneath the film, both to measure wear and to provide a reference surface to determine accurately the ZDDP tribofilm thickness. In 2015 Kalin et al. used a combination of AFM and lateral force microscopy to map the topography, stiffness, and surface shear resistance of ZDDP tribofilms on both steel and DLC coatings [37]. They confirmed that the tribofilms had a pad-like structure and found that they formed only on the asperities and had lower friction and adhesion properties than the inter-pad regions. Rydel et al. employed AFM to study surfaces before and after ZDDP tribofilm removal to correlate microstructure with ZDDP film formation [38]. They found less tribofilm on carbides than on the martensitic matrix and suggested that this might originate from less adsorption of ZDDP on the carbides or preferential loss of film from the carbides due to weaker adhesion.

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An important development in 2015 was the use by Gosvami et al. of a liquid cell AFM to simultaneously generate and monitor ZDDP tribofilm formation in situ [40]. Rastering of the AFM tip back and forth in contact mode against a substrate immersed in ZDDP solution generated a tribofilm whose topography could be monitored continuously from the tip’s vertical displacement. The authors employed this to show the exponential dependence of film growth rate on contact pressure and explained this in terms of a mechanochemical reaction rate model. This important concept will be further discussed later in this review. Several researchers have subsequently applied this in situ AFM method to monitor ZDDP film formation on various substrates, e.g. [41‐48].

AFM normally employs a cantilever with a built-in, very small tip, typically of Si₃N₄ or Si. This gives very high spatial resolution but high contact pressure. To produce less severe conditions somewhat closer to macro-scale contacts, colloid probe AFM can be used, This uses a tiny sphere attached to the cantilever and was employed in 2005 by Topolovec et al. with a 10 μm diameter glass sphere to measure the friction of individual ZDDP tribofilm pads and also normal force curves during tip approach and withdrawal from a ZDDP tribofilm [49, 50]. The latter suggested that secondary ZDDP might have a thin outer crust of material harder than the film below it. More recently, Gosvami et al. have used AFM cantilever-mounted 50 μm diameter steel balls against a steel flat to study ZDDP tribofilm growth in situ [51]. They found similar tribofilm build up during rubbing in ZDDP solution to that seen using a small Si AFM tip.

Spacer Layer Interferometry (SLIM) was first employed in 2000 to measure and monitor ZDDP tribofilm thickness in rolling-sliding tests in a minitraction machine (MTM) [52]. In the MTM a ball is loaded and rubbed against the flat surface of a disc immersed in lubricant. To apply SLIM, the ball is periodically unloaded from the disc and loaded upward against an optical film-coated, transparent window. An interference image of the separation between window and the reflective steel ball surface is then captured. This separation originates from the presence on the ball surface of a transparent tribofilm, so calibration of interference colours can be used to obtain a map of the thickness of the ZDDP tribofilm [53, 54]. Since this is employed in situ, without cooling or removing the rubbed surface from the test rig, SLIM enables the development of the film to be monitored during a rubbing test as shown in Figs. 5 and 6. Figure 5 shows sets of typical SLIM interference images from the ball obtained during tests with a PCS Instruments MTM with different ZDDPs [34]. Figure 6 shows the effect of slide-to-roll ratio on mean tribofilm growth by a primary ZDDP obtained from SLIM images, in this case using a Wedeven Instruments WAM ball-on-flat-ring tribometer rather than an MTM [55].

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The durability of the film and its interaction with other additives can also be studied by replacing the ZDDP-containing lubricant with base oil or a formulated oil after the ZDDP tribofilm has formed and then continuing rubbing [56‐58]. As described later, SLIM has shown an evolution in the strength of ZDDP tribofilms during prolonged rubbing [59, 60]. It has also revealed that ZDDP films are often susceptible to partial or complete removal by additives that contain amine groups [56, 57, 61, 62]. Over the last decade the use of SLIM in an MTM (MTM-SLIM) has become a very widely used tool to study the kinetics of formation of ZDDP and other lubricant additive tribofilms [34, 39, 43, 59, 63‐67].

In the 2000s there was growing interest in applying interference microscopy, such as scanning white light interferometry (SWLI), to measure surface topography [68] and towards the end of this decade some researchers started to apply it to surfaces rubbed in ZDDP solutions, with the aim of measuring the wear beneath any tribofilm present. However, in 2009 Benedet et al. showed that this approach could suggest, misleadingly, a high level of wear that actually originated from internal reflections within the transparent tribofilm [36]. The authors also showed how this problem could be addressed by (i) removing part of the tribofilm with EDTA and (ii) coating the whole surface with a 25 nm thick reflective gold film. This enabled the ZDDP tribofilm thickness and topography as well as any wear beneath the film to be quantified.

Recently Dawcyzk et al. have compared the above three methods of measuring ZDDP tribofilm thickness and roughness and discussed their advantages and disadvantages [69]. Based on the many studies carried out using all the above methods, it is evident that ZDDP films grow over a period of typically one to four hours of rubbing to form solid tribofilms that, for simple ZDDP solutions on steel surfaces, stabilise at between 100 and 200 nm mean thickness. These films are generally very rough and consist of pads typically 1 to 5 μm in diameter separated by deep valleys, as can be seen in Fig. 4 and schematically in Fig. 3. In reciprocating contact, the pads can be circular, but in unidirectional sliding or rolling-sliding conditions they are often elongated in the sliding direction. In formulated engine oils, ZDDP tribofilms tend to be thinner, in the 20–60 nm range, are often smoother, and may consist of bands of different thicknesses oriented along the sliding direction.

It should be noted that the AFM and MTM/SLIM methods of monitoring the formation of ZDDP tribofilms described above are very different. The AFM has a single, very high pressure contact, sliding at very low speeds, while MTM/SLIM contacts are rolling/sliding, with much higher sliding speeds and generally lower pressure contact conditions; they are much more realistic of lubricated machine components. There appear to have been no systematic attempts to relate the two methods in terms of ZDDP tribofilm formation, except to note that both appear to form rough tribofilms films and give tribofilm formation rates that increase exponentially with temperature and shear stress. In in situ AFM experiments, films are generally formed by a tip rastering over an area between 1 and 100 μm square, and the morphology of the tribofilm appears to be scaled to this size, with primarily smaller pads than the 1–5 μm ones formed in the MTM. While some research has studied the durability of the tribofilms formed in the MTM, the extent to which film removal takes place during film growth in AFM contacts has not been established and may be considerable. The very great differences between the two methods makes it difficult to relate them but one possible way forward might be to carry out further work using colloid probe AFM as outlined above [51]. This forms a much larger contact, with lower pressure and less likelihood of indenting a tribofilm surface than the conventional AFM tip; it may provide a bridge to link the AFM and MTM methods. For comparison, SLIM could then be applied to monitor film formation on a macro-scale ball in pure sliding mode, as has been used previously both in the MTM [70] and in an in situ Raman study of tribofilm formation [71].

ZDDP tribofilms are too thin for their mechanical properties to be measured by macro-scale indentation methods, but since the early 1990s they have been studied by nanocontact techniques, such as AFM [33], interfacial force microscopy [72, 73], and surface forces apparatus [74]. In recent years there has been growing availability of commercial nanoindentation instruments and these have also been quite widely employed to map the elastic modulus and hardness of ZDDP tribofilms [75‐82]. A surprising variety of values of reduced elastic modulus, E/(1-v²), have been measured, ranging from about 40 GPa [77] [82] to between 80 and 150 GPa [47, 73, 75, 78, 80, 81]. One study has even determined a value of around 200 GPa on the top of ZDDP tribofilm pads, comparable to steel [73]. Some of this variation may represent differences in elastic moduli at different regions of the tribofilm [72] and varying conditions and times of rubbing, but some may originate from the depth of measurement into the film being studied and interactions with the substrate stiffness. Hardness measurements also span a quite wide range from 1.5 up to ca 6 GPa and from AFM measurements, Demmou et al. have suggested that both hardness and elastic modulus of the tribofilm increase linearly towards the film’s interface with the substrate [77].

One limitation of early work was that measurements were only made at room temperature, and it was not known whether the mechanical properties of ZDDP tribofilms might be quite different at elevated temperature, especially if the films had a glassy structure. More recent studies using commercial indenters with variable temperature capabilities have shown that the elastic modulus of ZDDP tribofilms is quite constant from room temperature up to 200 °C [77, 78, 80], though a few have shown that hardness may slightly decrease with increasing temperature [77].

All the above measurements were made at end of a rubbing test, after a ZDDP had fully formed. Recent work has used an AFM to form a tribofilm and study its properties in situ as it develops [48]. This indicates that, when initially formed some ZDDP tribofilms can flow slowly during sliding or under static squeeze, suggesting they are highly viscous, with viscosity ca 100 to 1000 GPa.s, comparable to a molten glass. This is consistent with the concept, discussed later in this review, that fast-forming ZDDP tribofilms are initially relatively weak with an amorphous structure, but become more crystalline and wear-resistant during prolonged rubbing.

It should be noted that accurate determination of the mechanical properties of sub-100 nm films on rubbed surfaces is problematic, even with modern instruments, and this may be the origin of some of the discrepancies in the literature. There are a variety of problems, including possible pile-up, limited depth resolution, extreme variations in thickness of film across the surfaces and decoupling the stiffness and hardness of the substrate from that of the film [83]. In general, it has been found that oscillatory methods, such as continuous stiffness measurement are more effective than individual loading/unloading cycles since they allow continuous measurement of stiffness along the loading curve [84, 85].

As indicated in Table 2, many analytical methods have been applied to study the composition of ZDDP tribofilms. Two key advances in the last fifteen or so years have been (i) the application of methods to study how tribofilm composition varies with depth, notably using focussed ion beam milling (FIB), and (ii) the development of ways to observe ZDDP tribofilm composition in situ, i.e. as the film is formed within a tribometer.

A limitation of most early ZDDP film analysis was that measurements were averages over the penetration depth of the technique. An exception was XANES that could provide information from two depth scales by measuring either emitted photons or electrons [86]. Another approach was to analyse a tribofilm while progressively etching away the surface, typically using an argon ion sputtering [87]. Both these approaches showed that the composition of ZDDP tribofilms often varies with depth, but both have limitations. XANES probes the average of two quite poorly defined depths, while argon etching may change the composition of the surface being probed [88]. Also, unless very small regions are etched and analysed, the roughness of ZDDP tribofilms complicates interpretation of depth information.

In 2007 Heuberger et al. used variable angle XPS to investigate the local variation of tribofilm structure through the first few nanometres of secondary C3/C6 ZDDP tribofilms and explore the degree of phosphate polymerisation as a function of depth, as discussed later in this review [89]. This approach avoids potential complications arising from sputtering and was extended in 2010 by Zhou et al., who employed synchrotron source-based XPS with variable energy photons to probe different depths of secondary C4/C6 ZDDP tribofilms [90].

A very significant advance in providing information as to how ZDDP tribofilms vary through their thickness has been to analyse lamellar samples milled and extracted from rubbed surfaces using a focussed ion beam (FIB). This was first employed to examine ZDDP tribofilms in 2004 [91], but in recent years has become quite extensively applied in tribology as the technique has become more widely available. In most applications of FIB, the surface of interest is first protected by a coating, typically of platinum, and then parallel vertical trenches are milled using a beam of high energy gallium ions to leave a thin wafer between them, as shown in Fig. 7A. The wafer is then extracted and thinned to provide a sample representing a cross section through the protective coating, the tribofilm, and the underlying substrate. This can then be analysed by techniques, such as transmission electron microscopy (TEM), X-ray diffraction (XRD), and energy dispersive X-ray spectroscopy (EDX) to determine how the structure or elemental composition of the film varies with depth. A typical TEM image of the cross section of a ZDDP tribofilm together with EDX analysis across the film is shown in Fig. 8 [92].

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Two limitations of using EDX analysis of a FIB wafer to obtain elemental distribution are (i) the wafer thickness and thus signal can vary across its width and (ii) the focussed electron beam excites a finite volume within the wafer with greater diameter than that of the beam itself and this limits the depth resolution to tens of nanometers [94].

One quite new method of obtaining higher resolution elemental distribution in ZDDP tribofilms is atom probe tomography (APT) [95, 96]. In this, a needle-shaped specimen is obtained using FIB, either from an extracted wafer or by annular milling of the rubbed surface [97]. This is then cooled to cryogenic temperatures and bombarded by a laser to emit ions that are collected by a mass spectrometer. Based on the sample tip geometry, a 3D map of the spatial origin of the detected ions can be constructed as illustrated in Fig. 9 [95]. To date APT has been applied only sparingly in tribology and has served to confirm compositional information obtained from other methods. The method is so new that its limitations are not yet fully determined. One is that very stringent solvent cleaning of the sample is required prior to analysis in vacuum, and this may remove some of the tribofilm [96]. It is also not known whether ion bombardment during sample preparation may result in changes to the tribofilm, an issue that is also relevant to other FIB-based analysis methods [93].

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In 2003 Piras et al. studied ZDDP tribofilm growth on an iron coating on a germanium crystal using attenuated total reflection infrared spectroscopy (ATR-FTIR) to probe the contact through the germanium. This enabled IR spectra of the film to be obtained in situ but was limited both by the fragility of the iron coating and because the ATR method measures an average spectrum over a large area. A more versatile approach has recently been developed by Okubo et al., who extended the MTM-SLIM approach to obtain Raman spectra from the rubbed track on a steel ball [71]. In MTM-SLIM the ball is periodically uploaded against a coated glass disc to capture an optical interference image, but Okubo also used a Raman spectrometer to obtain a spectrum from the ball track.

In general, X-ray and electron-based analytical methods cannot be applied to study tribofilms in situ due to adsorption of the exciting and emitted species by air or windows. One recent exception is the use of XANES to monitor tribofilm composition from a rubbed disc within a pin on disc tribometer [98, 99]. To prevent the relatively low energy x-rays required to obtain spectra from low atomic number elements of interest, such as P and S being absorbed by air, the tribometer was enclosed in a helium atmosphere during tribofilm analysis.

For all the above analyses, both ex situ and in situ, it is important to emphasise that mechanical and chemical analysis of ZDDP tribofilms is not straightforward. These films are thin, rough, inhomogeneous into their depth and possibly also across their area. They are also often fragile, at least in terms of conditions imposed by bombardment with ions, x-rays, or focussed laser beams, as used some analysis methods. Modern methods of mechanical and chemical surface analysis can address some of these problems, but it is important that the researcher be aware with their limitations as noted above.

For ZDDP to form tribofilms, its molecules or those of its decomposition products must first adsorb on the rubbing surfaces, and several researchers have studied the initial adsorption of ZDDP on a variety of surfaces. Early work used radiotracers based on ¹³C- and ⁶⁵Zn- labelled ZDDP [117‐123] and microcalorimetry [20], but recently quartz crystal microbalance (QCM) has been also applied [124‐126].

Dacre and Bovington used ⁶⁵Zn- and ¹³C- labelled isopropyl ZDDP and found that ZDDP adsorbed to form a monolayer (stated to be ca 0.9 nm²/molecule) on both iron powder and 1% Cr steel [120]. At low temperatures, the ratio of adsorbed ¹³C and ⁶⁵Zn atoms implied complete molecules on the surfaces, but above a critical temperature of about 60 °C, Zn was lost from the surface. The authors suggested that this corresponded to the splitting of ZDDP molecules into individual, adsorbed (RO)₂PSS⁻ ions. Early work using XANES provided some support for this loss of Zn [127]. Most other adsorption studies have also found monolayer adsorption of ZDDP on metals, with Langmuir-type dependence on solution concentration, although there are few discrepancies. For example one study found strong adsorption of a primary ZDDP on iron [122]. but another found no adsorption whatsoever of ZDDPs on very high purity iron powder [20].

Yamaguchi et al. used inelastic tunnelling spectroscopy to study the adsorption of both commercial and synthesised ZDDP on Al₂O₃ surface at cryogenic temperature and concluded that adsorption was via the S atoms, with the rest of the molecule oriented away from the surface [22, 128]. For an alkylaryl ZDDP, dissociation of the adsorbing molecules to form cresols was identified, but this was not seen with primary and secondary alkyl ZDDPs. Because of the use of dithiophosphates as mineral flotation agents, considerable research has also been carried out on their adsorption on metal sulphides and this confirms that the sulphur atoms in dithiophosphate ions bond initially to the metal ions in the sulphides [129, 130]

Overall, it appears that ZDDP adsorbs readily on surfaces and that monolayer adsorption is effectively complete at low concentrations (< 500 ppm P), so that tribofilm formation rate becomes independent of concentration above this value [125]. Recent QCM work has shown that ZDDP also adsorbs on ceramics, but at a lower coverages than on metal oxides at comparable concentrations, and it has been suggested that the extent of adsorption depends on a ceramic’s ionicity [125].

One outstanding question is what happens after initial, physical adsorption to form a monolayer? No recent studies appear to have progressed beyond the important observation by Dacre and Bovington of a chemical reaction at elevated temperature that releases Zn and possibly forms a ferrous dithiophosphate. This type of cation exchange has been observed in solution [131‐133] and might well occur on surfaces and, since FeDDP is known to be much less chemically stable than ZDDP [131]. It may be an important precursor in the subsequent reaction described below to form a ferrous sulphide. As considered later in this review, molecular modelling may help resolve this question in future.

Several early studies identified a sulphur-rich layer at the tribofilm/substrate interface [74, 134], but others found sulphur to be distributed throughout the tribolayer [87, 91]. Quite recently Soltanahmadi et al. used FIB/EDX to analyse ZDDP-derived tribofilms on rubbed tracks from a micropitting rig. They identified a sulphur-rich layer of thickness 5 to 10 nm between the steel substrate and the phosphate film [135]. Since this layer was not associated with a zinc-rich layer they ascribed it to iron sulphide. A sulphur-rich layer between the substrate and the main tribofilm formed from a secondary ZDDP has also been very recently detected using atom probe analysis [96].

In 2016, Shimizu et al. employed AFM to measure the morphology of the film formed by a primary C8 ZDDP on an MTM ball during the first minute of rubbing in pure sliding conditions [39, 70]. After 30 s rubbing, they observed large lumps of a sulphur-rich material, typically 10 μm diameter and up to 700 nm high. After a few minutes rubbing these lumps broke up into smaller fragments and then became mixed with, and overlain by, a P-rich tribolayer. These sulphur-rich particles were only formed on the stationary ball that was continually in contact and not on the disc, nor were they formed in rolling-sliding conditions where both surfaces move through the contact. The authors suggested that their formation was favoured under severe conditions when a phosphate film that might prevent their growth was unable to form rapidly on the surface. This ability of ZDDP to form a sulphide film most easily when a phosphate film could not develop was also noted by Kontou et al., who studied the tribofilm formed by ZDDP in lubricants that also contained carbon black particles and dispersant in rolling-sliding conditions [136]. As discussed later in this review, soot and carbon black can rapidly abrade ZDDP tribofilms, and using FIB and EDX, Kontou found that with some dispersants this resulted in the formation of surfaces having no phosphate tribofilm but instead a quite thick iron sulphide layer, as shown in Fig. 11.

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Recently Dorgham et al. have used XAS to monitor tribofilm formation on the disc of a pin-on-disc apparatus by a secondary ZDDP using a synchrotron X-ray beam. Their results indicated the initial formation of a zinc or iron sulphate, but then, as rubbing continued, mainly sulphide was produced. The authors suggested that the sulphate might have been formed only until the initial iron oxide layer on the steel was consumed [98, 137].

From the above it is evident that iron sulphide can form very rapidly on ferrous surfaces rubbed in ZDDP. It appears that sulphide generation is more prevalent in pure sliding conditions and before the development of a phosphate film, or when such a film cannot develop. As discussed later in this review, this may illustrate the extreme pressure role of ZDDP – to form a metal sulphide in extreme conditions, such as the sliding cam-follower interface and thereby prevent scuffing even when a phosphate-based antiwear film cannot be maintained.

An outstanding question concerning tribofilm formation by ZDDPs is whether, prior to phosphate film formation, alkyl groups in the dialkyldithiophosphate are transferred from O to S to form the structural isomer di(thioalkyl)phosphate via the reaction; and whether this reaction plays a key role in driving tribofilm formation.

Thiophosphates and dithiophosphates are known to be strong alkylating agent and to be able to self-alkylate as shown in Eq. 3 [138]. In 1981, Coy and Jones studied the thermal decomposition of primary and secondary C4 ZDDPs at 180 °C and used ¹H and ³¹P NMR to identify a range of intermediates that contained RS groups bonded to P [139, 140]. It is quite appealing to consider that similar transfer might occur in tribofilm formation at lower temperatures, since a thioalkyl RS- group bonded to P might be expected to be more easily displaced than an alkoxy group RO-, leading to easier phosphate polymerisation. In 1998 Fuller et al. applied XANES (XAS) to study the formation of tribofilms on surfaces from mixed primary/secondary ZDDP solutions preheated at 200 °C for several hours and observed peaks that they tentatively ascribed to the di(thioalkyl) phosphate species shown in Eq. 3 [141]. No reference samples were, however, available to confirm this.

At present there is no direct experimental evidence that the reaction shown in Eq. 3 helps drive ZDDP tribofilm formation in low temperature rubbing contacts (ca 20–120 °C). However, there is some indirect evidence that this type of rearrangement is not essential for tribofilm formation, since, as indicated later in this review, sulphur-free zinc dialkylphosphates (ZDPs) form thick polyphosphate and phosphate tribofilms on rubbing surfaces at a similar rate, to a similar thickness and with a similar dependence of alkyl structure to their zinc dialkyldithiophosphate analogues [142, 143].

We do know, however, that most of the sulphur in ZDDP is lost during tribofilm formation, so it is probable that the type of exchange shown in Eq. 3 must occur at some stage to facilitate the loss of alkyl sulphides. The outstanding question is whether this precedes and enables the formation of the phosphate film or occurs only during and after film formation. Modelling work by Mosey and Woo has suggested that it occurs relatively slowly and at higher temperature than other potential phosphate tribofilm-forming reactions [144]. In situ Raman analysis may help resolve this question in future research.

It has been known since the 1950s that the bulk of a ZDDP tribofilm consists of zinc phosphate-based material [100, 101], and since the 1980s much research has been devoted to determining the precise composition of this film and thereby its mechanism of formation. Metal phosphates have been widely studied outside of tribology because of their use as phosphate glasses [145] and they are well known to form a range of molecular structures based on P-O-P bonds [146]. The various possible phosphate structures are shown in Fig. 12 below, taken from [1]

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In a ZDDP tribofilm, the negatively charged oxygen atoms will generally be balanced by positively charged Zn or Fe cations. The polyphosphate shown in Fig. 12c has four P atoms, but much longer chains are possible. In metaphosphates, ring structures are formed so that there is only one anionic charge on each phosphorus group, while in ultraphosphates some phosphorus groups have no anionic charge since three of their O atoms form bridges to other phosphorus atoms. In the extreme case, the ultraphosphate has no PO⁻ moieties at all and thus no overall charge; so forming an allotrope of P₂O₅. The extent of polymerisation is often described by the ratio of the number of bridging oxygen atoms (BO) that link two P atoms to the number of oxygens that are connected to just one P and are thus non-bridging (NBO). This ratio varies between zero (orthophosphate) and 1.5 (extreme ultraphosphate), and in tribofilms it has been quantified using XANES [147], XPS [89], infrared [148], and Raman [149] surface analysis.

It was gradually realised during the 1990s that the phosphate material in ZDDP tribofilms was a mixture of short chain phosphates and longer chain polyphosphates, with generally a higher polyphosphate content close to the outer surface of the film and short chain phosphate closer to the metal substrate [147]. Very little, if any, sulphur was present except close to the steel surface. Since polyphosphate is found in the upper layers of the tribofilm it is presumed to be formed initially during rubbing and its formation to be mechanochemically driven by the high shear stresses present at asperity contacts.

There is growing evidence that the initial structure and properties of ZDDP tribofilms depend on how rapidly they are formed. Some initial ZDDP tribofilms can be quite soft and may even flow at elevated temperatures, as described in Sect. 3.2. This might explain the elongated island shape seen in some conditions [48]. Several studies using SLIM have shown that when ZDDPs form tribofilms very quickly, part of the film can be lost during rubbing. This can be seen in Fig. 6 at high SRR, and was also noted by Fujita et al. [56] and, very recently, by Ueda et al. [150]. Ueda et al. used XPS to analyse the surfaces of tribofilms formed very rapidly by short chain, secondary ZDDPs and found that these had a significant ultraphosphate component, as also noted in previous work using similar ZDDPs [89, 90]. However, when the tribofilm was partially lost, the remaining film was predominately short chain polyphosphate. It thus appears that fast-forming ZDDP tribofilms are initially long chain poly- and ultra-phosphates with few Zn cations and are thereby quite soft and easily worn. However, as described in the next section, during extended rubbing (or in slow growth rate conditions) they progressively depolymerise, taking up more Zn and eventually Fe cations, to become harder and more wear resistant.

One of the least well understood aspects of the formation of polyphosphate tribofilms concerns the molecular mechanisms by which dialkyldithiophosphate ions or their structural isomer di(thioalkyl)phosphate ions (Eq. 3) link together to form P-O-P bridges and thence ultra- or polyphosphate. The general process is presumed to involve attack by an oxygen from one phosphate ion on the P atom of another, but we still have very limited information about how this occurs.

Most of our insights come from quite early research studying the volatile products evolved during thermal degradation of ZDDPs using gas chromatography. This detected alkenes and alkylsulphides and proposed three main decomposition mechanisms to form the phosphate ion as summarised in Fig. 13. Two involve loss of alkene, either equation (a) by direct cleavage of O-C bonds to form carbocations [16, 151] or equation (b) by extraction of a H atom from the second carbon atom of the alkyl group [14]. In the third, equation (c), there is transfer of an alkyl group from O to S as shown in Eq. 3 in the previous section [122]. Equations (a) to (c) in Fig. 13 all generate phosphate ions that may then displace OR or SR groups from a neighbouring ZDDP molecule to form a P-O-P bridge.

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Unfortunately, all the above reactions are based on high temperature thermal decomposition studies and there is, as yet, no direct experimental evidence that they occur in tribofilm formation at much lower temperatures. However, one molecular modelling study has proposed that a primary ZDDP may react via equation (b) in Fig. 13 while secondary ones, that should form more stable carbocations, may undergo equation (a) [144].

Quite recently it has been determined that, while the main initial process of tribofilm formation is polymerisation to polyphosphate and even meta- and ultraphosphate, this is followed by a much slower depolymerisation of most of the film to form short chain polyphosphates and eventually pyro- and orthophosphate, driven by Zn cation take-up and then, if available, Fe(III) ions. This process results in a structural change that causes the tribofilm to become more durable during rubbing.

In 2005, Fujita et al. used MTM-SLIM to show that once thick tribofilms had formed from both primary C8 and a secondary C3/C6 ZDDP solutions, these films remained largely unchanged even when the ZDDP solution was replaced by base oil and rubbing was resumed [56]. This suggested that the films were able to withstand the rolling-sliding rubbing condition used, and that the limiting film thicknesses did not represent a balance between continuous film formation and removal. The films were partially removed when the ZDDP solution was replaced by an aminic solution but this was ascribed to chemical attack of the amine on the films, possibly involving sequestration of the Zn ions [56].

Recently, however, Parsaeian et al. found using MTM-SLIM that if ZDDP solution was replaced by base oil before a thick tribofilm had fully developed, then the tribofilm film that had formed was partially removed during subsequent rubbing, as illustrated in Fig. 14 [59]. This implied that the tribofilm formed initially was relatively soft, but that it became harder and more wear-resistant during prolonged rubbing. The authors measured the ratio of BO to NBO in the tribofilm using XPS and found that the observed increase in strength of the film during rubbing was associated with a decrease in this ratio, suggesting that it resulted from shortening of the polyphosphate chains.

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This finding was further explored by Ueda et al. in 2019, who used FIB/TEM to determine the structure of tribofilms formed by primary C8 and secondary C6 ZDDPs at various stages of their formation in MTM tests [60]. They confirmed Parsaeian’s work and also found that the initially formed tribofilm was largely polyphosphate and had an amorphous structure. However, during rubbing this gradually converted to a shorter chain, nanocrystalline and thus much more wear-resistant film. This conversion began close to the steel substrate but progressed through almost the whole film during prolonged rubbing. Based on EDX measurements on FIB samples the authors proposed that the conversion was driven largely by diffusion of iron into the film. This is supported by a study by Berkani et al. who used zinc metaphosphate particles dispersed in base oil to lubricate a rubbing ball on disc contact. They found when the ball and disc were steel, the particles were depolymerised to orthophosphate during rubbing. No such conversion took place in a sapphire/sapphire contact. However if FeOOH (goethite) particles were included in the base oil, depolymerisation of the metaphosphate occurred even in a sapphire/sapphire rubbing system [152].

All the above suggests that a ZDDP tribofilm after prolonged rubbing consists of a ferrous sulphide sublayer covered by pads of nanocrystalline ferric/zinc phosphate with the top of the pads, that represents material most recently formed, being a thin layer of polyphosphate.

One question still outstanding is when and how such a ZDDP tribofilm is eventually lost from the rubbing surfaces to allow wear; is it removed mechanically via abrasive/adhesive wear or fatigue, or chemically via corrosive wear, or some combination of the two? Jahanmir found that while a primary C4/C5 ZDDP reduced wear in low load, sliding contacts, it could increase wear rate compared to the base oil at very high loads [153]. He related this to an absence of phosphorus and loss of sulphur from the rubbed track and suggested that sulphide particles were delaminating from the rubbed surface. Mourhatch and Aswath examined ZDDP tribofilm surfaces after scuffing using FIB and identified regions where patches of film had been torn off [154]. Both the above studies were based on pure sliding contacts, which are of limited relevance to the rolling-sliding conditions present in components such as gears and rolling bearings. MTM-SLIM studies have shown that once a film has formed in rolling-sliding conditions it persists with thickness almost unchanged for long periods of rubbing, so long as film-removing species, such as dispersants and soot are not introduced [56]. Some caveats should be noted however. One is that no systematic, very long duration test studies appear to have been made to determine whether the ZDDP tribofilms eventually fail. A second is that most ZDDP research has used very smooth test specimens, so contact stress conditions are relatively mild at the asperity level.

It has been shown that the phosphorus compounds formed when ZDDP acts as an antioxidant are unable to generate tribofilms, so that when all the ZDDP initially present is used up a tribofilm can no longer form [9]. In this case it was found that the tribofilm thickness fell to zero and high wear ensued, promoted by the presence of corrosive sulphur species from the reacted ZDDP. However, the mechanism by which the ZDDP tribofilm was removed was not identified.

From the above it is evident that considerable further work is needed to determine the conditions at which, and mechanisms by which, ZDDP tribofilms are lost from rubbing surfaces. Clearly such information is needed to complete our understanding of the antiwear action of ZDDP and it is also required to develop reliable models of the tribofilm formation of ZDDP, as discussed later in this review.

It has been known for many years that ZDDP can contribute to a decrease in engine efficiency [170], and in the late 1990s friction measurements in mixed rolling/sliding conditions showed that as ZDDP formed a tribofilm this led to a progressive increase in friction at intermediate entrainment speed conditions [171, 172]. This is illustrated in Fig. 16a, which shows a series of Stribeck (friction coefficient versus entrainment speed) curves taken during a two hour MTM test using a ZDDP-containing lubricant in mixed lubrication conditions [69]. It is evident that as rubbing progresses and a tribofilm forms, a higher and higher entrainment speed is needed to enter mixed and, ultimately, full EHD film lubrication. In a crankcase engine this implies that as a tribofilm develops more and more of the piston/liner and cam-follower cycle will operate in high friction boundary and mixed lubrication. This is now realised to be due to the roughness of ZDDP tribofilms. As was shown in Fig. 3, ZDDP tribofilms have a pad-like structure, with regions of thick film separated by deep valleys where almost no tribofilm is present. This means that as the pad height grows, the surface roughness increases. Dawcyzk et al. measured Stribeck friction curves at different stages in MTM tests and used AFM to measure ZDDP tribofilm roughness at each stage, from which they determined the lambda ratio, the ratio of EHD film thickness to composite surface roughness [69]. Figure 16b shows that all the measured Stribeck curves collapse on to a single line when plotted against the prevailing lambda ratio, indicating that the increase in friction as the test progresses originates entirely from the impact of ZDDP tribofilm roughness on EHD film formation. Figure 16 shows results for a primary ZDDP but similar friction behaviour and dependence of lambda ratio was also observed for a secondary ZDDP.

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Dawycz et al. found that although for a given ZDDP the friction curves collapsed onto single curves when plotted against lambda ratio, the boundary friction coefficient (ca 0.14 in Fig. 16b) varied from ZDDP to ZDDP. Several other studies have also shown that ZDDP boundary friction depends on alkyl structure, with linear alkyl groups giving lower friction that branched or cyclic ones [142, 173, 174], analogous to organic friction modifiers.

Micropitting is a form of damage found in gears and rolling bearings when these operate in mixed boundary/EHD conditions. The high stresses that occur as asperities rub against one another lead to the formation of numerous, asperity-scale, shallow-angle fatigue cracks. As these cracks develop, they undermine the material above them, which is then easily removed to form tiny pits and eventually rapid wear known as micropitting wear. Two key, related drivers of micropitting are the roughness of the surfaces and the lambda ratio, and it has been shown that ZDDP can promote micropitting because it forms protective tribofilms so rapidly that these prevent smoothing of surfaces due to running-in. In consequence asperity peaks are not removed and severe asperity stresses continue during normal operation, leading to micropitting [175‐177]. This is illustrated in Fig. 17 where a test in secondary C6 ZDDP solution gives much more micropitting wear, measured as loss of diameter of a cylindrical specimen, than in the corresponding base oil, or, indeed, where surfaces were initially rubbed in base oil to enable running-in, followed by replacement of the base oil by ZDDP solution.

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A third issue concerning the use of ZDDP in engine oils is that it can lose much of its antiwear ability when high levels of engine soot are present. This has grown in importance due to longer oil drain intervals, exhaust gas recirculation, and the widespread use of direct injection gasoline engines, all of which increase soot content in the lubricant. Throughout the 1970s to 2000s many possible mechanisms for this effect were suggested [178], but since the 2010s it has become widely accepted that much, if not all of it originates from a corrosive-abrasive mechanism [65, 179‐181]. Soot is not generally hard enough to abrade hardened steels, but it is hard enough to abrade a ZDDP tribofilm. This means that when a high concentration of soot particles is present in an oil, any ZDDP tribofilm that forms is immediately worn off. In consequence, a blend of ZDDP and soot can give much higher wear rate than the corresponding blend in which ZDDP (or soot) is absent, as illustrated in Fig. 18 [182]. Recently it has been shown that this wear process is much faster with some steel alloys than others [183], and that it can be alleviated, at least to some extent, by appropriate choice of dispersants and steel hardness [136, 184]. It has also been shown that similar corrosive-abrasive wear due to combined soot/ZDDP occurs in fully formulated heavy duty diesel engine oils during use [185].

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The influence of overbased detergents on ZDDP friction, wear, and tribofilm formation is complex since these detergents are colloidal, based on nano-scale particles of Ca or Mg carbonate or hydroxide base. In the absence of ZDDP the latter accumulate on the rubbed tracks in both rolling [191] and rolling-sliding [192] conditions to form solid tribofilms that can reach more than 100 nm thickness. In rolling-sliding conditions they may form such films considerably faster than ZDDP. This means that as well as chemically interacting with ZDDP, overbased detergents can complement or compete with ZDDP’s tribofilm formation at a purely physical level. Thus XANES and XPS analysis has indicated that the Ca from Ca sulphonate and salicylate is present in ZDDP tribofilms both as calcium phosphate and as CaCO₃ and that when detergent is present, ZDDPs form shorter polyphosphate chains [190, 193‐196]. In terms of chemical effect, Huq et al. showed that overbased detergents increased the thermal decomposition temperature of ZDDP [197], while Yu et al. found that they reduced the rate of thermal ZDDP film formation [198]. Most studies have found that overbased detergents degrade the antiwear performance of ZDDPs, and in the past most research has focussed on Ca-based detergents with limited study of Mg-based ones. The growing importance of the latter may change this and recent work has suggested that Mg detergents may damage ZDDP tribofilms more than Ca-based ones [199]. In terms of friction, early work suggested that a Ca-sulphonate detergent increased the boundary friction of ZDDP tribofilms [200] but it has subsequently been found that the friction of sulphonate detergents depends very strongly on the linearity of their alkyl chains [201], so this deleterious response may not occur with linear alkyl chain detergents.

There has been considerable research on the interaction of succinimide polyamine dispersants with ZDDPs [187], mostly using IR and ³¹P NMR analysis to detect changes in P-S bonds and the P electronic environment. The structure of these is illustrated in Fig. 19 from [124]. They are the most commonly used engine oil dispersants and act to sterically stabilise colloidal soot particles.

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Early work showed that succinimide molecules interact in solution with ZDDP molecules [202] and it soon became evident that Zn ions combine with NH and NH₂ groups of the dispersant to form coordination complexes [188, 203‐205]. Kapur et al. showed that this association was stronger with mono-succinimides, that have free NH₂ groups, than bis-succinimides, and that primary ZDDPs interacted more strongly than a secondary one [182]. This complexation, it has been suggested, may explain why dispersants reduce the rate of ZDDP tribofilm formation [206]. However more recently, MTM-SLIM has been widely used to monitor the impact of dispersant on ZDDP tribofilms [56, 62, 124, 178], and, while this has confirmed that dispersants do significantly reduce the rate of tribofilm formation, it has shown that dispersants also actively and very rapidly remove pre-formed ZDDP tribofilms during rubbing. As can be seen in Fig. 20, only part of the tribofilm is removed and, based on recent understanding of the evolution of ZDDP tribofilms during rubbing [60], it is likely that the dispersant removes Zn-based polyphosphate film by complexing out Zn ions, but leaves any underlying Fe phosphate film intact. Recently Tabibi has explored the influence of a range of succinimide structures and found quite large differences in their effect on ZDDP, confirming the difference between mono- and bis-succinimides [124].

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From the above would appear difficult to disentangle the two main mechanisms by which dispersants might suppress ZDDP tribofilm growth; does the dispersant tie up the ZDDP molecules in solution or at surfaces, rendering them less reactive and thereby reducing tribofilm growth rate? Or does the dispersant simply extract Zn from the tribofilm as the latter forms, weakening it, or even preventing its growth altogether? Or, indeed, both?

Although there has been much study of the interactions between dispersants and ZDDPs, there has been surprisingly little published on the actual impact of dispersants on wear rate. Zhang et al. showed that the addition of dispersant could increase wear rate by a factor of between 2 and 8 depending on dispersant type and concentration [62]. Of course, in the context of engine oils, the intrinsic influence of dispersants on wear may well be minor compared to their influence on the wear promoted by soot particles, since it has been found that some dispersant types are much more effective at suppressing soot wear than others [136].

In 2007 Topolovec et al. explored the effect of a range of friction modifier additives on ZDDP friction and tribofilm formation in pure sliding and rolling-sliding contact conditions [61]. They studied both the impact of FMs on secondary ZDDP tribofilm growth rate and the impact of FMs on pre-formed ZDDP tribofilms. For surfactant-type organic friction modifiers (OFMs), response was very varied; OFMs having basic functional groups, such as amine and amide were effective in reducing boundary friction while others were much less so. However, the amine and amide both supressed ZDDP film formation and in the case of amine, rapidly removed the tribofilm. This is reminiscent of the impact of succinimide dispersant on ZDDPs and suggests that basic nitrogen functionalities, while adsorbing strongly on a ZDDP tribofilm, may also weaken it. Matsui et al. studied the impact of organic friction modifiers as well as functionalised polymers and a succinimide dispersant on primary C8 ZDDP tribofilm formation and friction [207]. As shown in Fig. 21, electron probe microanalysis was used to measure the elemental composition of the rubbed surfaces and showed that different OFMs had a quite selective effect on the composition of the tribofilm with some, notably those with acid and alcohol groups, reducing sulphur content, while those with aminic groups reducing phosphorus and zinc. Matsui et al. also used ³¹P NMR to assess the interaction of the OFMs with ZDDP in solution and found that additives with acid groups increased the neutral to basic ZDDP ratio in solution while those with amino groups had the opposite effect. It is thus possible that some of the effect of other additives on ZDDP might originate from their influence on the chemical nature of the ZDDP in solution.

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Several other recent studies have compared the effect of different amine structures on tribofilm build up and removal [57, 208, 209], but findings have been contradictory, with some research showing reductions in film formation while others not. All studies have, however shown that amine surfactants are very effective at reducing boundary friction of ZDDP tribofilms. As well as amines, some other OFMs and also polymeric friction modifiers have been shown to reduce boundary friction in combination with ZDDP, without overly inhibiting tribofilm formation [210, 211].

Since the 1990s, driven by engine fuel economy requirements, there has been a great deal of research concerning the frictional properties of combinations of ZDDP with the friction modifier additive molybdenum dialkyldithiocarbamate (MoDTC) [212]. MoDTC reduces friction by forming nanocrystals of low shear strength MoS₂ on rubbed surfaces and tends to be relatively indifferent to the solid surface on which it forms, including ZDDP tribofilms [212]. FIB/TEM analysis of surfaces rubbed in solutions containing both ZDDP and MoDTC has shown the presence of MoS₂ nanocrystals both within and close to the surface of ZDDP tribofilms [213, 214] and MoDTC has been found to reduce friction both when blended with ZDDP and when a pre-formed ZDDP tribofilm is rubbed in MoDTC solution [61]. While MoDTC is able to form MoS₂ and reduce friction in the absence of ZDDP, it has been suggested that the presence of ZDDP helps protect the MoS₂ from wear, limits the formation of MoO₃, sulphurises MoDTC, and extends the useful life of MoDTC by acting as an alternative peroxide decomposer [132, 133, 213, 215, 216]. One Raman-based study has found MoS₂ formation by MoDTC only when ZDDP was present [71]. All of the above describes the effect of ZDDP on MoDTC; in terms of the opposite, MoDTC appears to produce a slight reduction in the thickness of tribofilm formed by ZDDPs, leading to partial loss of ZDDP antiwear performance [215, 216].

While ZDDP appears to improve the friction-reducing performance of MoDTC, or at least its longevity, its effect on other sulphur-free Mo-based additives is much more striking. In principle, without any sulphur content the latter cannot form MoS₂, but it has been found that when ZDDP is present, they are able to form MoS₂ and produce a consequent reduction in boundary friction [217, 218]. It appears that the sulphur atoms present in ZDDP are sufficiently labile that they can contribute to MoS₂ formation.

As well as other lubricant additives, ZDDP also encounters and must retain effectiveness in the presence of two important contaminants, engine soot and water. The levels of both these have been increasing in recent years, the latter due to growth in biofuel use and the introduction of hybrid engines that often operate intermittently and at relatively low temperatures. The impact of soot on ZDDP was outlined in the previous section. Systematic study of the influence of water on ZDDP tribofilm formation is relatively recent. In 2011 Nedelcu et al. compared the behaviour of a primary C4 ZDDP with and without low levels of added water (0.5 to 2%) in a rolling four-ball tester and found that the water reduced tribofilm thickness and also the length of polyphosphate chains in the film [219]. This was extended by Cen et al. who used a sliding pin-on-disc tribometer and showed that increase of water level, either from an increase in relative humidity (RH) or by adding water to the lubricant directly, reduced tribofilm thickness and also increased wear rate [220]. Several other researchers have come to similar conclusions [221‐223]. Parsaeian et al. used MTM-SLIM to show that increase of RH did not significantly affect the rate of ZDDP film growth but rather the thickness at which the ZDDP tribofilm stabilised [221]. Costa et al. compared the response of blends of anhydrous and hydrated ethanol (the latter contains 5% water) in both a solution of ZDDP in base oil and a commercial engine oil containing secondary ZDDP. They found that both ethanols removed pre-formed tribofilm, but the hydrated ethanol did so much faster and more completely [224]. Various mechanisms have been suggested for the deleterious effect of water on ZDDP film formation and wear, including water molecules blocking the surface, direct corrosive-abrasive wear of steel by water, and Fe ions produced by corrosion depolymerising the tribofilm.

Overall, from the above it appears ZDDP is remarkably tolerant of the presence of other additives at the concentrations generally used in engine oil, perhaps just as well considering the melange of species present in crankcase engine oils. The main exception appears to be some additives containing primary aminic groups, though even here ZDDP appears to function effectively so long as the molar ratio of amine to ZDDP remains low [208].

A recent study compared the film-forming behaviour of antiwear additives on four different ferrous alloys and concluded that a mixed primary/secondary ZDDP’s response (though not that of ashless antiwear additives) was very similar regardless of the alloying elements present [225]. This is, perhaps, not surprising if we believe that the initially formed polyphosphate tribofilm is based largely on zinc cations, with iron cations coming along later, as discussed in Sect. 5 of this review. Ito et al. also showed that a secondary C6 ZDDP formed tribofilms readily on oxidised steel surfaces consisting predominantly of Fe₃O₄ [92], and most ferrous alloys will have some iron oxide at the surface. A few previous studies have looked at the behaviour of ZDDP on non-ferrous metals. These have been mainly been confined to measuring adsorption [96, 97] and thermal film formation [187], probably because the hardness of different metals varies greatly, and makes comparison of their tribological interactions with ZDDP problematic. This was addressed recently by Ueda et al. who used ion implantation to produce thin films rich in a range of non-ferrous metals on steel surfaces; so thin as not to affect the overall stiffness or hardness and thus contact pressure [67]. They found that secondary C6 ZDDP formed tribofilms faster on Ni-rich surfaces than Fe-rich ones but formed films only slowly on Cr- and Mo-rich surfaces. The rate of film formation on Cr and Mo surfaces increased with ZDDP concentration, suggesting that the differences originated from different levels of ZDDP adsorption on the various metallic or metal oxide surfaces. Other researchers have also noted that ZDDP adsorbs less easily on Cr-rich surfaces [100]. Using fully formulated engine oils Zhu et al. compared the films formed on cast iron and Cr-plated cylinder liners rubbed against CrN -coated rings [226] in a fully formulated engine oil and found S/P/Zn-containing films on the cast iron cylinders but none on the plateaux of the Cr-plated liners.

The ability of ZDDP to form tribofilms on engineering ceramics, such as Si₃N₄ and WC has also been investigated. Most studies employed a ceramic tribo-element rubbing against a ferrous one, which, while of practical relevance, makes it difficult to isolate the behaviour of ZDDP on the ceramic itself because of the possibility of transfer of metal ions or tribofilm from one surface to the other. However, Sheasby et al. studied the behaviour of a secondary ZDDP in Si₃N₄/ Si₃N₄ and ZrO₂/ZrO₂ contacts and noted the presence of a pad-like film on Si₃N₄, comparable to the formed on steel [227]. In a recent study, Ueda et al. used an MTM to study Si₃N₄, SiC and WC ball and disc tribopairs [125]. They found that a secondary ZDDP formed a thick ZDDP tribofilm on the Si₃N₄ and WC surfaces in both mixed and full EHD film conditions, but that negligible film was generated on SiC. The films formed on Si₃N₄ and WC were, however, quite weak compared to those formed on steel, being easily removed by rubbing in base oil. They concluded that, while ZDDP could, in principle, form tribofilms via mechanochemical action on all surfaces, in the absence of ferrous ions this film remained amorphous and thus relatively soft. The lack of a film on SiC was ascribed to very limited adsorption of ZDDP on this essentially metal-free material.

In the context of engine lubrication, two surfaces of strong interest in recent years have been hypereutectic Al/Si alloy, used to cast lightweight engine blocks, and diamond-like carbon (DLC) coatings that are becoming ubiquitous on many machine components including those in crankcase engines.

Hypereutectic Al/Si alloys contain typically 16–18% Si (more Si than the eutectic level of 12.6%), with the pro-eutectic silicon dispersed in Al/Si eutectic in the form of large Si particles up to tens of micron across. These Si particles are very hard compared to the matrix and so provide surfaces that are wear-resistant enough to be used directly as tribologically active aluminium cylinder surfaces, without the need for separate steel liners. In 2005 Nicholls et al. used AFM and spatially resolved XAS to study the tribofilm-forming properties of a mixed primary/secondary (C8/C4) ZDDP on hypereutectic Al/Si alloy rubbing against a steel counterface [228]. They found polyphosphate present initially on both Si particles and the surrounding matrix, but that the eutectic matrix was rapidly worn away to leave protruding Si particles. ZDDP tribofilm was present as pads on the Si particles, just as on steel, with a similar polyphosphate composition. These findings have been broadly confirmed by several other studies [229‐231]. One question that arises is whether a ZDDP tribofilm can form on Al or eutectic matrix, both of which are relatively soft. The above studies certainly identified tribofilm on the matrix, but it is possible that this was transferred from the Si particles or the ferrous counterface. This was resolved by Gosvami et al. who used an AFM to rub an Al₂O₃ colloid probe against an Al flat and observed tribofilm formation from a mixed primary/secondary ZDDP on both surfaces. They suggested that extensive plastic deformation and consequent strain hardening of the soft Al enabled local stresses to become high enough to promote mechanochemical reaction of the ZDDP [44].

Research on the behaviour of ZDDP on DLC surfaces is complicated by the fact that there are several different structures of DLC coatings in use. Distinction must be drawn between those containing largely graphitic, sp² C–C bonding (e.g. a-C) as compared to those based mainly on diamond-like sp³ bonding (ta-C), and also between DLCs that are largely hydrogenated (e.g. a-C:H) and those that are not (e.g. a-C). In addition, some DLCs contain significant proportions of atoms other than carbon, for example Si, W, and WC. As with ceramics, it is also important to distinguish between studies where DLC is rubbed against steel, where Fe ions or ZDDP tribofilm might transfer from steel to the DLC counterface, and studies of DLC against DLC.

In 2008 the behaviour of DLC/DLC lubricated by ZDDP solution was studied in both sliding [232] and rolling-sliding [192] contact. In both studies, patchy tribofilms were observed though, unlike the films formed on steel, these were easily rinsed off by cyclohexane [232]. A systematic study of the behaviour of lubricant additives on a wide range of types of DLC surface was carried out in 2011 by Vengudusamy et al. [66]. Like previous studies, he found that ZDDP formed a patchy film on most types of DLC surface but a pad-like structure similar to that formed on steel was only observed on DLCs containing a significant proportion of W, and was present only on the W inclusions [233, 234]. Different types of DLC gave very different wear behaviour in both DLC/DLC and DLC/steel contacts as shown in Fig. 22 [66].

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Vengudusamy also assessed the durability of the ZDDP tribofilms by rubbing pre-formed films in base oil and found partial film removal in all cases [235]. Interestingly he found that, unlike in ZDDP tribofilms on steel, most of the sulphur in the films on DLC was close to the upper surface, with almost none at the DLC/tribofilm interface, where instead phosphate was present.

Kalin et al. studied the mechanical properties of ZDDP tribofilms formed on DLC surfaces rubbed against steel [79, 236]. They found that these films had a dual structure with some regions that were hard and stiff, while others were extremely soft.

Okubo et al. studied the influence of ZDDP alkyl structure on friction and tribofilm formation on two types of DLC surface in both DLC/DLC and DLC/steel contacts [237, 238]. As with steel, they found that secondary ZDDPs formed tribofilms much faster than primary ZDDPs on DLC and the effect of alkyl structure on boundary friction was also similar, with linear chains giving lower friction than branched ones. They found a difference in behaviour of a highly basic and a more neutral ZDDP on one of the DLCs. Ueda et al. also studied a DLC/DLC tribopair [125] and found no measurable ZDDP film formation in either mixed or full film rolling/sliding conditions, nor any adsorption of ZDDP on a carbon coating using QCM.

From the above, it appears that ZDDP can form a tribofilm on a range of material surfaces so long as (i) the ZDDP adsorbs on the surface and (ii) the contact pressure and thus shear stress is large enough to induce a mechanochemical reaction. However, if no metallic ions are present, as is the case of most DLCs, the film remains relatively soft and easily worn since it is based only on the initially formed amorphous zinc polyphosphate and cannot progress to a more crystalline phosphate. Interpretation is confused by the fact that many studies rubbed a DLC coated surface against a steel one and then studied the tribofilm formed on the DLC, and it is not possible to discount the possibility that tribofilm formation was controlled by metal or metal oxide transferred to DLC from the steel. The role of the S in ZDDP during its tribofilm formation on non-metallic surfaces does not appear to have been much, if at all, explored.

The first model of ZDDP tribofilm formation appears to have been by So and Lin in 1994 [107]. They assumed that ZDDP film formation was a balance between film formation and removal and that the rate of formation was controlled by a combination of Arrhenius kinetics and diffusion, while film removal was due to asperity indentation and consequent scaping away of film material. This early work was constrained by lack of experimental data on the kinetics of ZDDP tribofilm growth, but the development of the SLIM method described in Sect. 3.1 has made such data quite readily accessible and, in recent years, has supported the development of a series of models [239‐248]. All these incorporate; (i) a solid contact model to determine the pressure (and thus the shear stress and temperature) across a contact and (ii) expressions for film formation and film removal rate. Tribofilm thickness then evolves across the contact during rubbing over a series of time steps from the difference between film growth and film removal rates.

Most models have employed a numerical contact mechanics model with elastic-perfectly plastic deformation, although recently Lyu et al. used an analytical rough surface model [248]. Most studies have assumed boundary lubrication, with all the applied load supported by contacting asperities, but a few have included fluid film pressure [243, 247]. Initial work in 2012 that preceded general appreciation of the importance of mechanochemistry was based solely on flash temperature-controlled, Arrhenius film formation [239], but all subsequent work has included a stress-activated film growth model. Generally this has used the Eyring equation (Eq. 1), but one group [240, 243, 245] have employed a model by Bulgarevich based on an inverted Boltzmann assumption, where the surface atoms are activated by rubbing to much higher energy than those in the subsurface [249].

As described earlier in this review, experimental work shows that ZDDP tribofilm is generally initially rapid and then levels out to an asymptotic value, but that an overshoot is seen where some of the film is suddenly lost, if the film growth rate is initially very large. To develop models that show a similar response, various approaches have been adopted. One is to use a film growth rate equation where the rate diminishes steadily to zero as a critical film thickness is approached [239, 240]. Another is simply to impose a critical film thickness at which film growth abruptly stops [247]. Alternatively, the rate of film removal can been required to increase with film thickness [248]. Many models [239, 240, 242, 243, 248] also assume that the hardness decreases linearly away from its interface with the substrate, as suggested by one experimental work [77]. To achieve the temporary overshoot in film thickness seen in some experiments, one study has employed a time lag in the film growth response [242].

Most researchers have assumed that tribofilm removal rate follows an Archard wear equation, though two models have been based on a removal rate equation developed experimentally [240, 243], A few models have also allowed wear of the metallic substrate to occur [240, 248].

Overall, the various models have been found to predict the rate of average ZDDP tribofilm growth quite well, as might be expected since they have all been based largely on equations and rate constants derived experimentally. Most also show the expected growth of a pad-like structure on pre-existing surface asperities due to stress activation. However, few, if any, of the models so far developed seem reliable enough to teach us much about ZDDP tribofilm formation beyond information that is already provided from experiment. One study has shown a possible impact of different forms of surface roughness on tribofilm formation, but this still needs to be experimentally confirmed [245].

The main stumbling-block in developing useful models of ZDDP film formation appears to lie in our as-yet limited understanding of both the tribofilm removal process and the evolving nature of the tribofilm mechanical properties during rubbing. Until these have been fully resolved and related to the contact conditions and initial ZDDP structure, macro-scale models may remain of little practical value.

Progress in modelling the tribofilm-forming behaviour of ZDDP at the atomic and molecular level has been controlled to a very large extent by progress in developing quantum mechanics approximations to describe the electronic processes involved, together with the growth in performance of computer systems required for such modelling. Two recent reviews provide general backgrounds to the application of computational molecular modelling to tribochemistry [250, 251]. Martini et al. identified two main approaches, one based on density functional theory (DFT) that considers the electronic structure of whole systems consisting of atoms and molecules, and the other reactive force fields that focuses on bonds between individual pairs of atoms. They concluded that there was still a lack of useful force fields for ZDDP. This is unfortunate since modelling using reactive force fields is much faster in terms of computing time than DFT, and so can be included in molecular dynamics simulations (MD), where the motion of a large ensemble of molecules of interest is simulated over time based on intermolecular interactions and Newtonian mechanics. Reactive force fields can then determine whether bonds break or form in response to these interactions [252]. With DFT, individual molecules and pairs can be simulated using molecular dynamics, but it is generally impractical to consider larger ensembles.

ZDDP was first modelled in the mid-1990s using ab initio quantum chemistry to test possible structures and simulate the adsorption of ZDDP molecules on surfaces [253, 254]. This confirmed the structures of both neutral and basic forms determined by crystallography and spectroscopy, and that the two P-S bonds in the dithiophosphate are equivalent. Jiang et al. compared the bonding energy of different alkyl ZDDPs on iron oxide and correlated this with their wear performance [255].

In the early 2000s, Mosey and Woo applied quantum chemistry (QC) and DFT to model ZDDP reactivity, including the number of S atoms coordinated with Zn, the monomer/dimer equilibrium and P-O and O-C cleavage processes [144, 256, 257]. Initially they proposed homolytic C-O bond cleavage to form free radicals [256], but subsequently modified this to heterolytic cleavage to form ions [144]. They evaluated the energetics of the various reaction mechanisms developed from thermal decomposition studies which were summarised in Fig. 13 earlier in this review and concluded that the most likely reaction based solely on energetics was unimolecular Ei elimination for primary ZDDPs and that alkyl transfer from O to S was unlikely at low temperatures.

In 2005 Mosey et al. applied ab initio molecular dynamics (AIMD) to model the structural response to pressure of a triphosphate molecule together with one or two zinc phosphate molecules in a cell [258]. Their simulation found that the number of O atoms coordinated with a Zn atom grew from between 2 and 4 at low pressure to 6 at a pressure of 17 GPa and that this resulted in a large increase in bulk modulus and hardness. The authors suggested that the implied pressure-induced cross-linking was practically important and could explain why ZDDP was relatively ineffective on soft metals, such as aluminium. Various researchers questioned whether such very high pressures were possible in metal–metal contacts and a series of experimental studies followed using IR, Raman, and XPS to observe zinc phosphate at very high pressure [259‐261]. Some evidence of irreversible structural distortions of the phosphate structure at high pressure was found but none of an increase in coordination number, or indeed of polyphosphate chain length. As well as identifying cross-linking via the zinc atoms as described above, Mosey and Woo also used ab initio DFT to model the interactions between metathiophosphate molecules, which they proposed were formed by high temperature decomposition of ZDDP [262]. They found that these all dimerised readily but that one structure, RSP(= O)₂, could link together to form polyphosphate. They suggested that this pointed towards a pathway for the formation of polyphosphates from ZDDP.

Onodera et al. modelled the behaviour under shear of a zinc metaphosphate film and how this interacted with small particles of iron oxide [263‐265]. The objective was to test the conjecture that ZDDP tribofilms reduce wear by digesting abrasive iron oxide. Initially they used classical molecular dynamics simulation but later augmented this with quantum chemical MD to model the chemical interactions between phosphate and metal oxide more realistically. They concluded that iron and some other metal oxides could be digested by phosphate under a combination of high pressure and shear.

In an ingenious paper in 2009, Onodera et al. combined MD with finite element analysis to study diffusion of iron atoms from an Fe₂O₃ substrate into a ZDDP tribofilm and the effect of this on the mechanical properties of the film [266]. They found that when the tribofilm was subject to shear force, iron atoms diffused rapidly to form a graded composition in the tribofilm, in agreement with experimental work on ZDDP tribofilms described in Sect. 5.4 [60]. The researchers then derived a relationship between iron concentration and elastic properties using quantum chemistry-based MD simulations and employed this to determine the elastic modulus and hardness profile through the tribofilm. As might be expected, iron atom diffusion resulted in a harder and stiffer interfacial region.

In 2021, Salinas Ruiz et al. carried out a combined experimental and QC modelling study of the behaviour of ZDDP in contacts between various different types of DLC/DLC [267]. Their modelling work found that for hard ta-C DLC, the very high pressure and shear stress present at asperities resulted in sulphur from the ZDDP penetrating and weakening the DLC. This did not occur for less hard DLCs. For all DLCs, the ZDDP molecules were found to break down into atoms and small fragments within the sliding contact.

As outlined in Sect. 5.1 earlier, the first stage in ZDDP tribofilm formation must be surface adsorption, and early experiments have revealed intriguing processes, such as loss of zinc atoms into the solution. Recently DFT has been applied to investigate this initial stage. In 2022 Peeters et al. explored the adsorption of ZDDP molecules on Al/Mg alloy surfaces [268]. They confirmed that ZDDP’s sulphur atoms bond to the Al substrate but found that, while ZDDP adsorbed on pure Al and Mg surfaces, it only dissociated under pressure to release dithiophosphate units on a Mg₁₇Al₁₂ alloy surface.

Very recently, Benini et al. have applied DFT to model the role of adsorption and consequent effect of shear stress on ZDDP reaction on iron, partially oxidised iron, and iron oxide surfaces, with a focus on the role of the sulphur atoms [269]. They found that for non-adsorbed molecules, molecular dissociation was endothermic but that it became exothermic and thus favoured when ZDDP molecules were adsorbed on iron surfaces. When ZDDP molecules were adsorbed on an iron substrate, applied shear stress promoted the detachment of organophosphorus groups from the central Zn–S units, as a presumed first stage of ZDDP tribofilm formation. Interestingly, they found that surface oxidation of the iron substrate significantly reduced adsorption of ZDDP molecules on the substrate. This finding is debateable since experimental work has shown that ZDDP tribofilms form readily on an iron oxide surface, albeit with very little sulphur content [92]. However the study is important in being the first to model the initial stages of ZDDP tribofilm formation on ferrous surfaces in a systematic fashion.

Overall, in the author’s view, atomic and molecular modelling of ZDDP reactions to date are tantalising and serve to confirm, as least in part, deductions from experimental work. However, they do not appear to be reliable enough to predict beyond what is already surmised. In particular, they are not yet able, or at least have not been applied, to explore reaction pathways beyond one or two steps. In the ideal world we would enjoy a full simulation of the sequence of reactions by which ZDDP molecules adsorb, react initially to form a sulphide film, and then progress to form thereon a polyphosphate tribofilm. Perhaps one day this will be possible …