Metastable states and activated dynamics in thin-film adhesion to patterned surfaces

We consider adhesion due to London–van der Waals attraction between a thin film and a patterned surface with nanometer asperities. Depending on the surface topography and the stiffness of the film, three regimes of adhesion are identified: complete contact adhesion, partial contact adhesion, and glassy adhesion. For complete contact adhesion, the film conforms to the undulations of the surface, whereas for partial contact and glassy adhesion, the adhesive interface breaks down into microscopic areas of contact. When a film in the glassy regime is peeled off the surface, metastable states develop at which the crack front becomes arrested, analogously to the frustrated motion of the three-phase contact line across a heterogeneous surface. For this glassy regime, we use transition state theory to model the thermally activated progression of the crack front. This theoretical treatment suggests that the rate of the adhesive failure increases exponentially with the applied force.

Figure 1

(a) Rendering of a film adhering to a grid of protrusions with aspect ratio $\lambda /b=5$. (b) A film adhering to a corrugated surface with aspect ratio $\lambda /b=5$. (c) Model for surface-film interactions using a grid of spheres. (d) Model for surface-film interactions using a raster of cylinders.

Figure 2

(a) Peel-off using a couple $M$ applied to the edge of the film. (b) Geometry of the model used for estimating the film-surface interaction potential.

Figure 3

The normalized potential as a function of the nondimensionalized adhered length for different values of ${\lambda }^2/R\delta$: ${10}^0$ (solid blue line), ${10}^1$ (dashed green line), ${10}^2$ (dotted red line), and ${10}^3$ (dash-dotted cyan line).

Figure 4

Phase diagram of thin-film adhesion to a surface with a grid of protrusions.

Figure 5

Peel-off geometry for a force $F$ applied to the edge of an adhered film. The suspended part of the film traces an arc $\mathcal{P}\mathcal{Q}\mathcal{D}$ in one instance. When a crack propagates a distance $-d\xi$, the film assumes a new shape ${\mathcal{P}}^{\prime }{\mathcal{Q}}^{\prime }{\mathcal{D}}^{\prime }$.

Figure 6

Normalized total energy as a function of nondimensional adhesion length for ${\lambda }^2/R\delta =10$ and different values of the nondimensional, generalized force $Q\lambda /V_0$: 0 (solid blue line), 1 (dashed green line), $1.68$ (dotted red line).

Figure 7

Energy landscape of a glassy adhesive system with ${\lambda }^2/R\delta =10$ and $Q\lambda /V_0=1.20$. Local extrema are indicated by points.

Figure 8

Backward energy barrier as a function of applied force for different values of ${\lambda }^2/R\delta$: 3 (solid blue line), 10 (dashed green line), 30 (dotted red line), and 100 (dash-dotted cyan line). Adhesive failure occurs when $Q\lambda /V_0>1$. Instantaneous failure occurs when $\Delta {\Phi }_{-}$ reaches zero.

Figure 9

Regimes of different types of adhesion for the gecko spatula adhesion system.

Figure 10

(a) Backward energy barrier as a function of force for spatula adhesion on a glass surface with $\lambda =10$ nm and $b=4$ nm. (b) Force-rate relation for spatula adhesion.

Figure 11

The relative error in the interaction potential due to the approximation of surface protrusions by spheres.

Figure 12

The normalized potential for a film adhering to a corrugated surface as a function of the nondimensionalized adhered length for different values of ${\lambda }^2/R\delta$: ${10}^0$ (solid blue line), ${10}^1$ (dashed green line), ${10}^2$ (dotted red line), and ${10}^3$ (dash-dotted cyan line).