a strong household tape has a modulus greater than 0.3 MPa, it does not work (it has no stickiness) – this really is strength through (a special type of) weakness.
It is unfortunate that the words stress and strain start with the same three letters and in common language mean the same thing, but we are stuck with the terms and you just have to get used to remembering which is which.
Figure 2.5 When we apply a Stress, Force/Area (F/A) in Pa we get an elongation, ΔL of the original length L. Their ratio is ε, which is the Strain, which is unitless. The ability to resist stresses is the Modulus, Stress/Strain, also in Pa.
We often have to discuss work of adhesion and surface energy, each of which is measured as Joules per square metre, J m−². It happens that work is the same as energy, which is why the two measures have the same units and why “work of adhesion” is sometimes called “energy of adhesion”.
The strength of an adhesive joint is often measured in force per unit length, i.e. N m−1. If you sit down and do the sums (or if you go to my app page https://www.stevenabbott.co.uk/practical-adhesion/basics.php) you will find that a peel strength of 1 N m−1 is the same as a work of adhesion of 1 J m−² (Figure 2.6).
Figure 2.6 Classically, adhesion is measured as the force, N, per width, m in N m−1, or as work, J, to create 1 m² of separated adhesive, in J m−². The two measures are exactly the same!
It is tricky to know whether to add a space between a number and a unit. Some prefer 1N m−1, others prefer 1 N m−1. For clarity and readability I have standardized on using the space.
2.4 ADHESION TERMS
The word for the stuff doing the sticking is “glue” or “adhesive”. What about the word for the thing being stuck? “Adherend” is the technical term, which can lead to phrases such as “… the adhesive attaches to the adherend…” This isn't particularly elegant, but there is no obviously better term to use.
We often have to discuss adhesion in terms of peel (pulling vertically) and shear (pulling horizontally). There is a different sort of vertical pull, the butt pull. Figure 2.7 gives you a visual indication of what these terms mean.
Figure 2.7 Whether a joint is tested in peel (vertical forces), shear (horizontal forces), or butt (whole sample vertical pull) makes a great difference to the effective strength.
2.5 SURFACE TENSION AND ENERGY
If you go into your kitchen, take a random assortment of smooth, flat surfaces and place drops of either water, water with a dash of dishwashing liquid, or oil onto the surfaces you will see that the drops form different shapes, depending on both the liquid and the surface.
The liquids have different surface tensions, that is, different forces pulling the liquid together at the surface. Why are there forces pulling the liquid together at the surface? Molecules in the liquid are attracted to each other (if they weren't the liquid would instantly vaporize). At the surface of a drop this self-attraction becomes visible because the way to maximize their self-attraction (or minimize the number of missing attractions at the surface) is to form the smallest-possible surface which is a sphere. Drops containing dishwashing liquid have much weaker attractions at the surface because the surface is covered by a monolayer of the surfactant/detergent with long hydrocarbon tails that interact rather weakly; similarly, the oil has a low surface tension because it is made up mostly of long tails.
The surfaces have different surface energies. This arises for the same reasons – the molecules at the surface want to be with each other to a greater or lesser extent.
If the molecules at the solid surface have a large surface energy (for example a metal surface) compared to the drop then the drop will prefer to spread out on the surface, gaining maximum surface-liquid interaction, rather than curl up on itself in air. On a surface with a low surface energy, such as a Teflon frying pan, the same drop will spread out far less. Oil has a low surface tension and will spread out more on any of your kitchen surfaces than a drop of water, though the difference will depend on the surface itself. The water with the detergent also has a low surface tension so it too will spread out easily on many surfaces – one of the reasons we add detergents.
If you were to look carefully at each drop you would find that it makes a specific angle, called the contact angle, which is diagnostic of the relative surface tensions and surface energies (Figure 2.8).
Figure 2.8 A drop of liquid forms a shape that depends on a combination of the surface tension and surface energy. The result is that the liquid meets the surface at a contact angle, θ.
If you have a Teflon frying pan, then this is “hydrophobic” (water hating) so a water drop does not spread. Even oil is unimpressed by Teflon's surface energy and oil drops hardly spread. With some tricks it is possible to make a “superhydrophobic” surface where a water drop is so unimpressed by the surface that it will roll along at the slightest tilt. These superhydrophobic surfaces have attracted a lot of excitement as self-cleaning surfaces but, although they are marvellous as lab demos, they are generally unsuited to the real world.
It is a common myth that surface energy is important for adhesion. As we will learn in Chapter 3, it is irrelevant for any sort of strong adhesive bond and is used only for those cases where easy breaking of the bond is a requirement – such as when a gecko needs to walk, or you need some temporary adhesion for wrapping a sandwich in a thin plastic film.
2.6 VISCOSITY
We are familiar with the fact that some adhesives are thin and runny while others are thick and resistant to flow. A thick adhesive can be said to be “viscous” and the measure of the ease of flow is “viscosity”. If we define water as having a viscosity of 1 (the units are cP, which means centipoise) then some typical numbers for familiar materials are found in Table 2.1.
Table 2.1 Typical viscosity measurements of familiar materials.
| Liquid | Viscosity, cP |
| Water | 1 |
| Olive oil | 100 |
| Glycerine | 1000 |
| Honey | 5000 |
| Ketchup | 50 000 |
| Lard | 100 000 |
| Peanut butter |
|
