Page 86 - Handbook of Adhesives and Sealants

54 Chapter Two

A rather simple method of estimating the surface energy of solids
5
was developed by Zisman. Zisman proposed that a critical surface
tension, , can be estimated by measuring the contact angle of a se-
C
ries of liquids with known surface tensions on the surface of interest.
These contact angles are plotted as a function of the LV of the test
liquid. The critical surface tension is defined as the intercept of the
horizontal line cos 1 with the extrapolated straight line plot of
cos against LV as shown in Fig. 2.3. This intersection is the point
where the contact angle is 0 degrees. A hypothetical test liquid hav-
ing this LV would just spread over the substrate.
The critical surface tension value for most inorganic solids is in the
hundreds or thousands of dynes/cm, and for polymers and organic
liquids, is at least an order of magnitude lower than that of inorganic
solids. Values of critical surface tensions for common solids and sur-
face tensions of common liquids are shown in Table 2.2. Critical sur-
face tension is an important concept that leads to a better understand-
ing of wetting. This will be discussed in coming sections.

2.2.3 Work of adhesion and cohesion
If a bulk material is subjected to a sufficient tensile force, the material
will break thereby creating two new surfaces. If the material is com-
pletely brittle, the work done on the sample is dissipated only in cre-
ating the new surface. Under those assumptions, if the failure is truly
cohesive where both sides of the broken material are of the same com-
position, then
W 2
C

where W is defined as the work of cohesion.
C
Now similarly consider separating an adhesive (material 1) from a
substrate (material 2). The energy expended should be the sum of the
two surface energies and . However, because the two materials
1 2
were in contact, there were intermolecular forces present before the
materials were split apart. This interfacial energy can be represented
as . W , the work of adhesion, may be defined by the surface en-
12 A
ergies of the adhesive and the adherend:

W 12
A
1
2
6
This is the classical Dupre equation, which was developed in 1869.
This equation could also be represented as:
W LV SV SL
A