# Using the peel test to measure the work of adhesion in a confined elastic film

The authors present theoretical and experimental work in an effort to characterize the strength of adhesion forces between a thin elastomeric film bonded to a rigid surface and a flexible plate. The peel test is used to measure the adhesive forces: a spacer of known height is slipped between the flexible plate and the rigid surface, such that a crack forms between the adhesive and the flexible plate. The height of the spacer (<math> \Delta </math>) and the length of the crack (*a*) are used with other parameters to quantify the strength of the adhesive force, as a stronger adhesive should correspond to a shorter crack. The authors examine the limits of perfect adhesion and of perfect slippage in this analysis.

## General Information

**Keywords**: surface force, peel test, adhesion

**Authors**: Animangsu Ghatak, L. Mahadevan, and Manoj K. Chaudhury.

**Date**: June 19, 2004.

Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138

*Langmuir* **21**, 1277-81. [1]

## Summary

The authors first develop a theoretical framework for analyzing the adhesion strength of a thin elastomer film in terms of the length of the crack that is formed by a spacer in the peel test. Arguments are made based on boundary conditions in terms of incompressibility as well as continuity and smoothness of the displacement vector field of the coverslip, or flexible glass plate. The result of the theoretical analysis is:

<math> \frac{\Delta D^{1/2} k^2}{\gamma^{1/2}} = ({\frac{W}{12 \gamma}})^{1/2} f_1 (ak) </math>

where <math>\gamma</math> is the surface energy of the films, *W* is the work of adhesion, *D* is the bending stiffness, <math>f_1</math> is a complicated function that comes out of the theory with imposed boundary conditions, and *k* is a characteristic length scale of the deformable plate. Experimental work was performed to determine values of the parameters in this equation so that the work of adhesion *W* could be found experimentally and compared with the theory. Similarly, the theoretical work produced the equation

<math> \frac{\Delta D^{1/2} k^2}{\gamma^{1/2}} = C ({\frac{W}{108 \gamma}})^{1/2} f_2 (ak) </math>

where the constant *C*, which depends on the maximum tensile stress, could be determined from experimental results as well.

The experimental results agree well with the theoretical predictions, as one can see from the graphs of the scaled displacement under various scenarios. However, the data were not precise enough to confirm the theoretical predictions for the limiting cases of perfect bonding or perfect slippage. They do, however, suggest that the critical failure stress is "orders of magnitude smaller than that estimated from the van der Waals disjoining pressure [...] at the open surfaces of the crack."

## Connection to soft matter

This article presents a new way of measuring adhesion strength by including effects related to the thickness of the adhesive film or the flexibility of the plate in contact with the film. Previous attempts to compare experimental adhesive strength results with theory did not adequately take these effects into account. The authors additionally propose dimensionless quantities that can be associated with an adhesive material and geometry more generally. Adhesion is an important concept in soft matter as it is a surface force, a topic which physicists have been studying for hundreds of years.