Direct estimation of the adhesion of solid polymers

“Contact” of Nanoscale Stiff Films

“…We assume the coated substrate will act as a homogeneous half-space when indented in the normal direction; that is, the bulk effective elastic modulus of the coated substrate is constant. The assumption has been shown to be reasonable for thin films coated onto a substrate with a low elastic modulus ( E < 10 MPa) and when the ratio of contact radius to film thickness is large ( a / h > 20). , Thus, we can directly apply eq to a thin film bonded system, where the subscript “(f)” indicates “with thin film”, and R sys = R sys(f) , since the influence of the thin film coating on R sys is negligible. .25ex2ex P sys ( f ) = P sys false( normalf false) normale − P sys false( normalf false) normala = 4 E sys(f) * a 3 3 R sys − 8 π a 3 W sys ( f ) E sys(f) * E sys(f) * = true( 1 E sub(f) * + 1 E tip * true) − 1 R sys = true( 1 R sub + 1 …”

“…They are in good agreement with each other and with the documented gold modulus of 98 GPa despite the substantial changes in substrate elasticity and coating thickness between the samples, validating our analytical solution and the associated method. Although we have not examined other film thicknesses, we expect the technique to be fairly accurate up to 200 nm (where a / h > 10 3 ) based on literature information. , …”

“…The assumption has been shown to be reasonable for thin films coated onto a substrate with a low elastic modulus (E < 10 MPa) and when the ratio of contact radius to film thickness is large (a/h > 20). 49,50 Thus, we can directly apply eq 1 to a thin film bonded system, where the subscript "(f)" indicates "with thin film", and R sys = R sys(f) , since the influence of the thin film coating on R sys is negligible.…”

“…It has been shown from finite element calculations that when the contact radius a is orders of magnitude larger than the film thickness h, which is the case in this study, the error associated with the calculation of the work of adhesion W sys(f) using E sys(f) * is insignificant. 49,50 The effective elastic moduli of gold thin film E f * determined for different samples are shown in Figure 6b. They are in good agreement with each other and with the documented gold modulus of 98 GPa despite the substantial changes in substrate elasticity and coating thickness between the samples, validating our analytical solution and the associated method.…”

First yield in the Maugis‐adhesive contact of elastic spheres

“…Table 1 shows exemplary values for the parameter for contacts between equal materials. 1 While the contacts of both metals presented are described by values for that are situated well inside the range where yield occurs instantly at no 1 Elastic and mechanical properties were taken from [24] and [25], surface energies (i.e., half the work of adhesion for contacts between equal materials) from [26] and [27].…”