The objective of this study was to measure the coefficients of friction of CMHA-S films with and without methylcellulose against sclera for the purpose of offering insight into designs to improve retention of hydrogel films in the eye. The static coefficients of friction of the CMHA-S films significantly increased with sliding velocity. This rate dependence is likely due to the viscoelastic adhesion properties of the lubricant and/or the viscoelastic mechanical properties of the CMHA-S films and sclera. Static friction is defined by a critical shear that is required to initiate sliding between the two surfaces. This point is affected by the amount of overlap of surface asperities, and the stiffness of these asperities to resist shearing. Thus, at the onset of shearing, the overlapping asperities undergo a time-dependent relaxation suggesting that the critical shear, and also the static coefficient of friction, is dependent on rate. The inability of the lubricant to displace quickly at high rates would increase the rate dependence further. The differences in the viscoelastic properties of CMHA-S with and without methylcellulose likely explain why the materials were not equally affected by rate. Material characterizations of both materials in our lab have shown that CMHA-S with methylcellulose has a slower rate of stress relaxation than CMHA-S. Therefore, the stress and resistance to shearing of CMHA-S with methylcellulose is more time dependent, and will be more strongly affected by sliding rate.
A limitation of the static coefficient of friction measurements for the two quicker sliding velocities is the large rheometer inertial effects seen within the first 0.1 second of the test. Subtracting out the inertial effects from the raw torque measurements worked well for 0.3- and 1.0-mm/s sliding velocities, but overestimated
μstatic and
μstatic,Neq for Teflon-on-Teflon by 0.007 to 0.017 at 10- and 30-mm/s sliding velocities. The coefficients of friction of the CMHA-S films were an order of magnitude higher than the Teflon; therefore, the inertial effects will be smaller. This suggests that the CMHA-S static coefficients of friction measured in this study are less affected by the error. In fact, trends and ranges of static coefficients of friction reported in the literature for cornea and hydrogel contact lens biointerfaces
9,10,14 are similar to those reported for CMHA-S in this study. Thus, we believe the measured static coefficients of friction of CMHA-S films are realistic approximations, despite the errors seen during validation.
Kinetic coefficients of friction were mostly constant across velocities; however, some discrepancy to this finding was observed in the two different calculations for kinetic coefficient of friction in CMHA-S with methylcellulose. Throughout the test, normal load readings were challenging to maintain within the enforced load limits, especially at higher rates. At the two higher velocities, the axial load feedback control was slower than the sampling rate. This caused the axial load to overcorrect or extend above the enforced load limits. Therefore,
μkinetic, which was inversely related to instantaneous load,
N, saw erroneously low values during rotation. An example of this is seen in
Figure 8A, where
μkinetic of CMHA-S with methylcellulose drastically decreases at sliding velocities of 10 and 30 mm/s. These erroneous values caused average
μkinetic calculations to be skewed from the majority of the data. Consequentially,
μkinetic tended to be lower than
μkinetic,Neq, which was calculated instead with an equalized load,
Neq, recorded after 12 seconds of relaxation. Based on these observations and the results of the validation studies, it is concluded that
μkinetic,Neq calculations are more accurate. Further, the differences between
μkinetic,Neq and
μkinetic in this study mirror the differences that are seen by Schmidt and Sah.
13 They also concluded
μkinetic,Neq more accurately measured the frictional response when fluid pressurization effects are present in a boundary lubrication method.
CMHA-S films with methylcellulose had 60% to 80% higher coefficients of friction than CMHA-S films without methylcellulose. This increase was not statistically significant, but CMHA-S with methylcellulose films also experienced notable wear during testing at higher loads and velocities. The increased friction and wear of the CMHA-S films with methylcellulose may be due to its low stiffness compared with the stiffness of the unmodified CMHA-S film material. Gong et al.
26 developed a surface repulsion model to investigate mechanisms of frictional properties of various hydrogels. According to their model, it was found that a lower elastic moduli of the hydrogels resulted in higher predictions of friction. We have experimentally measured the elastic modulus of CMHA-S with methylcellulose and found it to be 94% lower than the elastic modulus of CMHA-S. This lower modulus decreases the ability of the surface asperities of the CMHA-S with methylcellulose to support the applied loads, thus bringing more asperities into contact.
27 Increased asperity contact would describe the increased friction observed in the films with methylcellulose. Furthermore, the asperities of the CMHA-S with methylcellulose would be less resistant to shear stress due to the lower modulus, and increase the wear rate as observed in this study.
The presence of wear supports that CMHA-S film friction was measured with a boundary lubrication regime versus a hydrodynamic regime. Boundary lubrication, by definition, is a monolayer of thin film lubrication that coats and adheres to the asperities in order to reduce penetration of the opposing surface asperities. This results in reduced shear strength at the interface. Boundary lubricants are effective in reducing asperity penetration, but they are slow to recover from displacement. Specifically, at quick sliding velocities, the regeneration of the lubrication monolayer is not rapid enough to replenish the fluid film over the asperities,
28 therefore increasing susceptibility to wear. This may have exacerbated the wear seen at higher sliding velocities.
The increase in friction from the addition of methylcellulose to CMHA-S suggests that this may be a viable method to improve retention of hydrogel films at the ocular surface and in the inferior fornices. However, the observed wear of CMHA-S with methylcellulose must be carefully considered in design. CMHA-S with methylcellulose substantially wore down at 0.5 N at 30 mm/s. This is representative of the physiological pressure and sliding velocity seen on the eye during blinking and normal eye movement, and suggests that the formulation with methylcellulose may wear rapidly following placement into the eye. However, if the film is designed such that the methylcellulose is placed only in contact with the inner eyelid, the relative motion between the eyelid and CMHA-S with methylcellulose would be reduced, and the rate of degradation of CMHA-S with methylcellulose may be slower in vivo than what was seen in the experimental tests. Literature suggests that wear may also be reduced up to 60% by increasing the crosslinking density of hydrogel polymer.
29 The tribological and wear effects due to changing crosslinking density of CMHA-S with methylcellulose could be evaluated in future work.
The boundary lubricant also plays a role in the friction and wear rate of CMHA-S films. Tear film is a highly-ordered and surface-tethered fluid, containing mucins and lubricin glycoproteins that effectively reduce shear stresses secondary to eyelid blinking.
9,10,14,30,31 Hyaluronic acid–based drops, which are a standard of care treatment for dry eye in parts of the world,
32 help solve some of deficiencies in normal boundary lubrication that can occur at the ocular surface.
33,34 Because hyaluronic acid–based drops are effective for increasing lubrication for the treatment of dry eye, we assumed the use of hyaluronic acid–based lubricating eye drops was a sufficient representation of the tear film in the eye. The lubricant exhibited non-Newtonian behavior during viscosity testing, similar to human tears, but had slightly higher viscosity magnitudes. Film degradation during testing suggests the load bearing was carried by the surface asperities and not the lubrication fluid. This is indicative of a boundary lubrication regime.
35 In this regime, the coefficient of friction measurements of the films would not be dependent on flow properties of the lubrication. Therefore, we believe the slight measured differences in viscosity magnitude between the lubricant and human tears will not change the tribological behavior of CMHA-S measured in this study.
The sliding velocities at which the coefficients of friction were experimentally measured are representative of those reported for blinking, but much slower than saccadic eye movements, which can reach velocities up to 140 mm/s. Therefore, the question arises how the coefficients of friction for CMHA-S will change up to velocities of 140 mm/s, and how to best approximate these values. Extrapolation of
μstatic values up to sliding velocities of 140 mm/s would push friction coefficients unrealistically close to a value of one, and is therefore not appropriate. Tribological phenomenon between lubricated surfaces is traditionally described by the Stribeck curve, in which the coefficient of friction is categorized into lubrication regimes depending on the sliding parameters such as load, sliding speed, and lubricant viscosity. However, hydrogel materials and ocular lubrication are reported to have tribological behavior that is qualitatively different than the Stribeck curve. Specifically, the parameters at which hydrogel materials transition from a boundary lubrication regime to a mixed lubrication regime are not well defined.
31,36 Therefore, it is unclear how the kinetic coefficient of friction for the CMHA-S films will change for sliding speeds up to 140 mm/s, and answers will only be obtained through further experimentation.
One final consideration is how the CMHA-S films will uphold in injured or diseased eyes, in which these films are intended for use. In these eyes, it is hypothesized that the harsh, inflammation-ridden environment with elevated catalases and enzymes will increase the degradation rate of the CMHA-S polymer. It is unknown whether this altered environment will uniformly degrade CMHA-S formulations with and without methylcellulose. Future work will need to evaluate the likely changes in degradation rate, and friction and wear properties of each CMHA-S formulation while in the presence of proinflammatory conditions.