Deformation of contacting interface between polymer hydrogel and silica sphere studied by resonance shear measurement

The deformation of the interfaces between a soft material and hard material in contact plays an important role in the friction and lubrication between them. We recently reported that the elastic property of the contact interface dominated the friction of the interface between a flat polymer hydrogel [double network (DN) gel of 2-acrylamide-2-methylpropanesulfonic acid and N,N-dimethylacrylamide] and a silica sphere [Ren et al., Soft Matter 11, 6192-6200 (2015)]. In this study, in order to quantitatively describe the dependence of the elastic response on the geometrical parameters of the deformed interfaces, we employed the resonance shear measurement (RSM) and investigated the deformation of the interfaces between a flat DN gel and silica spheres by varying the curvature radius (R = 18.3, 13.8, 9.2, 6.9 mm). Resonance curves were analyzed using a mechanical model consisting of the elastic (k ₂) and viscous (b ₂) parameters of the contact interface. The obtained elastic parameter (k ₂) increases at higher loads and for smaller silica spheres, while the viscous parameter (b ₂) was negligibly low for all the conditions. The relations between the elastic parameter (k ₂), geometric parameters of the deformed contact interface, and the applied normal load were investigated. The elastic parameter (k ₂) was found to be proportional to the arc length (arc) (radius of contact area, r), i.e., k ₂ ∝ arc or k ₂ ∝ r. We introduced the term "elastic modulus of the contact interface, E _contact" as a proportionality constant to describe the elastic parameter of the deformed interfaces (k ₂): k ₂ (N/m) = arc (m) × E _contact (Pa). Thus, the friction (f) between the DN gel and the silica sphere can be described by the following equation: f = f _elastic = arc (m) × E _contact (N/m²) × Δx (m) (Δx: shear deformation of the contact interface between the DN gel and silica sphere). The E _contact value determined from the slope k ₂ vs arc was 493 ± 18 kPa. The RSM measurement and the analysis presented here can be a unique method for characterizing the specific properties of the deformed interfaces between soft and hard materials.