Tribological Classification of Contact Lenses: From Coefficient of Friction to Sliding Work

A crucial aspect of the eye’s blinking cycle is the low frictional losses that the eyelid experiences as it glides back and forth across the cornea. The two soft epithelia are supported by tear films—a complex lubricant system consisting of a stratified, lipid-covered protein mixture, whose structure is broken and reformed during the opening and closing phase of a blink [1, 2]. The lid-wiper region of the palpebral conjunctiva travels at speeds that can reach 12 cm/s, suggesting a primarily hydrodynamic lubrication regime. Thus, during the majority of a blink cycle, the sliding resistance is governed by the viscous shear of the lubricant [3]. At the reversal points, where the speed invariably approaches zero, the glycocalyx and associated mucus layer ensure low interfacial shear stresses, which can minimize strain-induced wear of the epithelium [4, 5].

The presence of a soft contact lens (SCL) between the cornea and the eyelid disrupts the natural function of the tear-film, leading to changes in the tear-exchange rate, and in the stability and activity of lipids and proteins in the lubricant as they interact with the lens surface [6‐8]. In addition, the contact-lens surface naturally lacks a glycocalyx, which may lead to increased strain on the eyelid epithelium during the reversal points of the blink cycle. SCL wearers may experience complications due to these effects, with changes in comfort being the most common reason for interrupted wear [9]. There is evidence that comfort of SCLs is correlated with the frictional properties of the lens material [10, 11]. In this context, the coefficient of friction of fresh human corneas (measured within 12 h post-mortem) against a mucin-coated glass disk in a physiologically relevant, tear-like fluid (TLF) has been measured and was reported to lie between 0.006 and 0.015 [12]. As shown by Roba et al. [13] under similar conditions (with a lubricant that contained only serum and lysozyme, with no added lipids), the CoF of a number of commercially available SCL falls within, or even below, this range. This would suggest that some SCL would be completely exempt from issues related to comfort. However, it is well known that SCL accumulate proteins and lipids, both at the surface and in the bulk, depending on the SCL material, which leads to changes in surface properties of the pristine lens—a topic recently reviewed by Luensmann and Jones [14]. Indeed, a recent report revealed that some SCL that underwent an in vitro aging process, consisting of constant immersion and withdrawal from TLF for 18 h, had an increase in CoF [15]. This indicates that the frictional losses during blinking may build up over a day’s wear, increasing the energy expended by the eyelid to overcome the dynamic friction. The correlation between comfort and CoF, and the possibility of predicting the performance of SCLs from in vitro experiments, has led to numerous studies dealing with the characterization of the frictional properties of SCLs [16‐21].

Characterizing the tribological behavior of soft materials, such as a hydrated SCL or rubbers, by a CoF, can be useful to a first approximation. However, the linear dependence between frictional and normal forces that is assumed when calculating a CoF is frequently not observed in hard-soft and soft–soft contacts [22‐24]. The mechanical origin of the linearity between frictional and normal forces has been suggested to arise from the asperity–asperity contacts that define the real area of contact between two hard surfaces. With increasing normal load, an increasing number of asperities comprises the contact area, resulting in a linear dependence between normal force and real contact area [25, 26]. In contrast, Hertzian contact mechanics predicts that the contact area varies with \(F_{N}^{\tiny{{{\raise0.7ex\hbox{$2$}\kern1pt \!\mathord{\left/ {\vphantom {2 3}}\right.\kern1pt} \!\lower0.7ex\hbox{$3$}}}}}\) [27]. For soft materials, asperities are likely to completely deform, and the real contact area can approach the apparent value, resulting in a deviation from linearity between friction and normal forces [28]. SCL typically have elastic moduli of or below 1 MPa [29], and as a consequence, the CoF may not adequately describe the tribological characteristics over different normal loads.

In this publication, an alternative strategy is proposed to characterize the friction behavior of SCL materials by a single figure of merit, namely average work. Average work is defined as the average value of a nonlinear function fitted to the friction versus normal force data, multiplied by a relevant sliding distance. The friction force is described as a function of the contact area, as derived from the elastic foundation model (EFM) as presented by Rennie et al. [19] and the interfacial shear stress. The transition from CoF to work not only circumvents the necessity for a linear relationship between the lateral and normal forces, but also represents the energy consumed when two interfaces slide over each other. To illustrate the work concept from an eyelid-SCL perspective, three commercial SCL materials, which have previously been reported to have different CoF under similar conditions, were tested. From low to high CoF, the three lens materials were senofilcon A (silicone hydrogel), etafilcon A (hydrogel), and lotrafilcon B (silicone hydrogel) [13]. The lenses were characterized by means of microtribometry, using a modified version of the experimental set-up described by Roba et al. [13], which allowed for accurate determination of the contact area. The sliding work expended on the SCL was compared to that on a rabbit cornea, which acted as a model for the in-eye situation in the absence of a SCL. A classification of the frictional properties of SCL in terms of average work, or energy consumed over a certain sliding distance, allows the cumulative study of influences that external parameters (wear time, aging conditions, cleaning procedures) exert on the tribological behavior of SCL.

A methodology has been presented to characterize frictional drag on soft materials in terms of work. The main advantage of using work as opposed to CoF is that it allows a single figure of merit to be assigned to a tribological system without requiring a linear relationship between friction and normal forces—an uncertain assumption for materials such as soft polymers or tissue. Another approach to distinguish between the frictional properties of the lenses in this paper could be to rely solely on interfacial shear stress. However, such an approach would lack the time-dependent perspective, an important part of the work concept, which allows for cumulative measurements of expended frictional energy to be carried out. By characterizing a tribo-contact in terms of work, changes in drag that may occur over time due, for example, to wear, can be accommodated in a single figure of merit. As such, the work concept may have interesting clinical applications regarding SCL comfort where the subjective sensation of the SCL may not necessarily be correlated with the instantaneous drag between the lens and the eyelid, but to the cumulative work dissipated over the course of a day.

In the calculation of average work, it was assumed that the only contributor to the lateral force was interfacial shear stress under the experimental conditions employed. For viscoelastic materials, such as hydrogels, bulk dissipation effects can, however, also affect the friction force. A number of models have been proposed to describe friction on rubber and gel materials. Gong et al. [35] have explained the frictional response of gels at different sliding velocities from an adhesion-repulsion perspective, based on polymer scaling laws. The adhesion-repulsion model resulted in a modified Stribeck curve, with an increase in friction with speed, followed by a decrease during the elasto-hydrodynamic transition, and an increase again due to viscous shear at higher velocities [36]. At low speeds, the frictional response was described by the adhesive interactions of the gel interfaces, resulting in interfacial shear stress. Rennie et al. applied a modified elastic foundation model based on a Winkler description of the surface that included a damping term to account for viscoelasticity. They applied the model to the study of SCL and considered the contribution of interfacial shear stress, viscoelastic dissipation and viscous shear to the friction force [19]. They found that that at low speeds (<0.1 mm/s) and low pressures, the only significant contributor was interfacial shear stress. Scaraggi and Persson [37] recently developed a mean field theory for viscoelastic lubrication of rubber and also reported on a Stribeck curve with a local maximum when transitioning from the boundary to the elasto-hydrodynamic regime in the presence of a low viscosity lubricant. The explanation was an increase in the surface rolling friction, representative of viscous dissipation in the bulk. At low velocities, the interfacial shear stress was the main contributor to the frictional force. In addition, Dunn et al. [3] modeled the tribological characteristics of the eyelid as it slides over a contact lens, and using a viscosity based on natural tears reported that below 0.2 mm/s the shear stress was constant and the sliding system was in the boundary lubrication regime. The coherence between the experimental and theoretical studies (outlined above and with respect to the contributors to the frictional force) makes it plausible that at low velocities, and low viscosity of the lubricant, the greater part of the friction force will be due to shear stress acting in the conformal contact between the glass disk and SCL or cornea.

The applicability of Eq. 7 is based on the assumption that the interfacial shear stress is load independent over the range of applied loads. In this case, a linear relationship between frictional force and contact area should be found. In order to further test whether this assumption holds for the lenses tested in this publication, line fits to the data shown in Fig. 6 were plotted on linear–linear plots together with 95 % confidence intervals and residuals (see Supporting Information S3). For lens A, this relationship holds well, as represented by small and equally distributed residuals across the fitted line. Lens B show scatter in the acquired data, where some lenses deviate in their measured friction force with regard to the mean. This is likely due to a variation in the tested lenses, possibly resulting in different levels of adsorption of proteins and lipids from the TLF and a higher friction force. As a result, the residuals are biased toward negative values. For Lens C, after 0 and 50 cycles, the situation is similar; however, after 100 cycles a systematic deviation from linearity is found in the data. This is discussed further below. Removing a series which appear to deviate from the mean response of the lenses would remedy the fitting errors to a large extent but such an action would be difficult to justify. For example, in the classification of SCL by average work, variations between lenses would be interesting to assess. Nevertheless, the data are essentially described by Eq. 7.

Application of the EFM to the corneal contact area versus normal force curves allowed for extraction of an effective elastic modulus of the cornea (approximately 10.6 kPa). However, we were unable to unambiguously confirm the applicability of the EFM to the cornea, as the literature values for thickness, radius of curvature and elastic modulus show a large spread. For example, the elastic modulus of the cornea appears highly dependent on the measurement technique. Data extracted from two-dimensional strip extensiometry gave an elastic modulus of the rabbit cornea of 1.98 MPa [38], whereas indentation studies on a rabbit cornea with atomic force microscopy reported only a few kPa, depending on which corneal layer was probed [39]. In addition, Shaw et al. [40] used AFM to study the frictional properties of corneal epithelium cells and applied the EFM to extract the mechanical properties of the cells and found an effective elastic modulus of 16.5 kPa. The square-root dependence of normal load on area in the EFM has been proposed to be valid when the ratio of the thickness of the material to the radius of the counter-surface is less then 0.1 [33]. The thickness of the cornea was found to be around 700 µm, compared to below 100 µm for the SCL. The higher thickness may thus lead to the contact area being closer to a Hertzian value, as the influence of the support becomes less important. However, the contact area was still found to vary as F _n ^1/2, which is in accordance with the EFM. In addition, it should be noted that the method of obtaining the contact area versus normal force on the cornea is less precise and more prone to experimental error, compared to the SCL case where the contact area was defined by Newton’s rings and the normal force measured in situ. This is mainly due to the difficulty in assigning a border defined by a fluorescence-intensity gradient and to measure a small deflection of the cantilever by image analysis. Future efforts will be targeted to attain a more precise measure of the contact area of corneal tissue. However, to support the results, we also performed indentation analysis on the cornea using a glass disk as counter-surface, fitted the data with the EFM, and found a similarly low elastic modulus of approximately 20 kPa (see supporting information Figure S2). Therefore, during a typical friction experiment, the first tens of micrometers of the epithelium are probed and the glass disk slid over an extremely compliant surface.

In the measurements taken in this study, the average work on the cornea was found to be approximately twice that measured on lens A. This would indicate that the eyelid does less work while sliding over the lens than over the corneal epithelium. However, comparing the interfacial shear stresses, it is clear that the value on the cornea is at least one order of magnitude lower than that on lens A. In boundary lubrication, the frictional force is intimately linked to the real contact area [25]. Therefore, part of the reason for the similarity in work between the cornea and the SCL, is the extremely low elastic modulus of the cornea, which results in a contact area that is approximately an order of magnitude higher than that on the lenses. However, this is strictly a result of the contact geometry used, where a hard flat disk is pressed against a soft sphere. The contact geometry in vivo is likely to be closer to that of two soft, flat surfaces pressed against each other; consider the matching curvatures of the eyelid and the cornea, and the reported flattened epithelium that characterizes the lid wiper [41, 42]. Thus, in the eye, the effective contact area will be very similar on the cornea and on a SCL. Therefore, the frictional force is only dependent on the shear stress. If a simple assumption is made that the lid wiper is approximately 0.2 mm wide and 10 mm long, from the shear stress, the work performed by the eyelid over a 2 mm sliding distance across the surface of the cornea, and lenses A, B and C is approximately 50/500/1000/12,000 nJ, respectively. This highlights the importance of quantifying the contact area in addition to collecting friction and normal force data, in order to avoid over-simplified conclusions. However, among the SCL the contact area was found to vary little; therefore, the difference in terms of average work between the SCL can be representative of differences in comfort experienced in vivo.

The thought experiment above may provide some insight into how to decrease adverse strain on the eyelid epithelium during sliding over a SCL. The tested lenses were chosen on the basis of differences in bulk material as well as surface properties. Lens C had the highest number for average work and the highest interfacial shear stress. Lens C is a silicone hydrogel with a 25 nm plasma-generated surface layer [43], which can be assumed to result in a stiff interface that lacks sufficient mechanisms to relax applied strain. Lens B is a conventional hydrogel with low elastic modulus and a net negative charge. The combination of softness and high water content may result in an interface that is easily sheared. Lens A has a polymeric wetting agent that is believed to form dense dangling chains at the interface that can provide a lubricious plane of low shear strength, analogous to the behavior of a polymer brush and the glycocalyx. The boundary-lubricating effects of polymer brushes in good solvents are well documented in the literature [44]. Lens A is the lens with the lowest average work and interfacial shear stress. However, compared to the cornea, the interfacial shear stresses on all the lenses were significantly higher. It is hypothesized that the combination of the very soft interface and the presence of the glycocalyx, which associates with the mucin in the lubricant, is the reason for the extremely low shear stresses (0.01 kPa) measured on the cornea. This could potentially serve as a model for the design of future SCL materials.

In the current study, a rabbit cornea acted as a model for the human counterpart. The rabbit and human cornea are of comparable dimensions [45]; however, they have been reported to differ in collagen organization in the stroma and elastic modulus [39, 46, 47]. In particular, the rabbit cornea is slightly softer than the human one. Therefore, the contact area on a human cornea is likely to be smaller under the same experimental conditions. Further, Royle et al. [48] reported on differences in glycan structure in the glycocalyx between rabbits and humans, which could potentially influence the friction properties in the boundary lubrication regime. However, the frictional forces measured on a human cornea, as reported by Wilson et al. [12], under the exact same conditions as applied in this work, was reported to be approximately 0.06 mN (at 4 mN normal load), in accordance with the results obtained herein on the rabbit cornea, see Fig. 5. As a result, it is believed that the results in terms of sliding work acquired on rabbit and human cornea are comparable. However, due to the potentially smaller contact area on the human cornea, as mentioned above, the involved shear stresses may be higher.

The contact geometry and the nature of the counter-surface have a significant impact on the experimentally determined friction force. Apart from the contact geometry being different in vivo, the compliance of the interacting bodies is also different. Both the cornea and the eyelid have surfaces of very low elastic modulus—in the range of a few kPa—and are coated with a hydrogel-like mucus layer [5]. The frictional behavior of model hydrogel–hydrogel contacts has recently been studied by Dunn et al. [49] and was compared to the same situation where one of the sliding partners was rigid. They found a decrease in friction with speed when one of the surfaces was hard, but almost no dependence of friction on speed in the hydrogel–hydrogel “gemini” contact. Urueña et al. [50] expanded on this study and investigated the influence of sliding velocity and crosslink density of the hydrogels in a “gemini” contact on the friction force. The friction force was found to correlate with the crosslink density, which was explained by a reduced ability of the gel to relax applied shear strain with an increasing number of cross-links. At speeds up to 10 mm/s, the friction force was constant. Above this speed, the friction force increased, which was explained by an increase in the effective viscosity at the interface consisting of both the polymer chains and the fluid. The counter-surface in our study was coated with a monolayer of mucin, which mimics the glycocalyx of the cornea and the eyelid, albeit with a modulus that is defined by the glass. To further mimic the in vivo situation, a soft counter-surface would be desirable. As found by Dunn et al. in a migrating contact between a hard and soft material, the friction force at a velocity of 0.1 mm/s (used in this work) was higher than at increased velocities (0.2–1.5 mm/s). The friction force measured with the counter-surface in our study could thus generate an overestimation of the drag between eyelid and the contact lenses in vivo. Future studies will be devoted to developing a counter-surface where the interface and the modulus more closely resemble that of the cornea-eyelid system.

It is interesting to note the deviation from linearity between friction force and contact area on lens C after 100 cycles. This could indicate that the area of contact is non-conformal, possibly due to an increase in the surface roughness of the lens due to testing. Lens C is also the stiffest of the three lenses, see Table 2, which would make the influence of surface roughness more pronounced. Inspection of the friction versus normal force curves (Fig. 6) also shows that after 100 cycles a linear relationship between the two forces is approached. This makes surface roughness a likely cause of deviation from a linear relationship between friction and area. In addition, wear can be expected to be more severe on lens C as a consequence of the higher frictional forces involved during sliding.

In the calculation of average work, as discussed above, the only contributor to the friction was assumed to be interfacial shear stress. This limits the applicability of the work concept as described herein to situations where other contributions to the friction force are negligible. For example, to acquire the total energy expended by the eyelid during one blink cycle, it would be necessary to account for the different lubrication regimes that dominate at different speeds. In particular, on viscoelastic materials, in the transition from boundary-to-hydrodynamic lubrication, a speed interval may persist where bulk dissipation dominates the friction force. To account for these effects, the model would have to be extended. However, as far as a classification of SCL materials is concerned, the most relevant clinical parameter can be argued to be represented by the reported value for average work based on the observed correlation between CoF (acquired using similar conditions as in the present study) and comfort [10].

For soft, elastic materials, characterizing the sliding performance in terms of work instead of CoF circumvents the necessity to assume a linear relationship between frictional and normal forces. A single value of merit for work can be attained by calculating the average function of work over a range of normal forces, which can be used as a comparative measure to evaluate the sliding performance of different SCL materials. Especially, the potential to calculate cumulative work over time could provide a valuable tool to comprehensible rank the performance of different SCL materials over extended periods of wear.

The nonlinearity in the friction-to-normal force relationship often encountered on soft elastic materials complicates an assessment of sliding performance on the basis of a CoF. To circumvent this, a methodology has been presented that extracts the average sliding work from a nonlinear function between the lateral and normal force data. The work concept was demonstrated on three contact lens materials and a cornea. Discussing contact lens performance in terms of work opens up the possibility to calculate cumulative energy dissipation, which becomes especially useful as a comparative number if the frictional properties of the lens surface change over time, for example due to the onset of wear processes. Average work represents a single figure of merit on contact lens material performance, which can additionally incorporate eventual changes in lubricity occurring during wear.