Question

Many techniques exist to measure the surface energy between a liquid and a liquid or a liquid and a gas (see e.g. the wiki page).

Methods to measure the surface energy between a solid and a fluid are rare, but still there is a method developed by Zisman (see e.g. here) that allows you to at least estimate it by extrapolation for solid/gas or solid/liquid, depending on the environment that you use in your experiment

What I wonder: is there a method to measure the surface energy between two non-elastic solids?

One option I could think of is that you could melt one of the solids and then use the technique of Zisman, but this will limit your knowledge to high temperature surface energy, whereas the ones at low temperature are the thing you are typically interested in.

Answer 1

I have done some searching and found out that there is a technique that has been around for roughly 10 years already and it is surprisingly simple (if you have the right, expensive, equipment). It can be found in this JCIS paper (which is also freely available here).

The technique works as follows: an atomic force microscope (AFM) with a well-defined spherical tip made out of solid 1 is brought into contact with solid 2. Then the tip is pulled of the surface again and the work of adhesion is measured. Based on the pull-off force and theoretical contact mechanics models (for details see the paper) you can calculate the surface energy ? between the two solids from the following equation:
?=F2?cR
where F is the pull-off force, R is the tip radius and c is a constant between 1.5 and 2 depending on the details of the contact model. The paper explains how to choose which model is appropriate for the type of measurement you do.

Some conditions (assumptions) for the theoretical models apply:

deformations of materials are purely elastic, described by classical continuum elasticity theory
materials are elastically isotropic
both Young