Surface Energy

A wonderful 2023 paper from the Toyota Central R&D Laboratories, Masakazu Murase and Daisuke Nakamura, Hansen Solubility Parameters for Directly Dealing with Surface and Interfacial Phenomena, for the first time provides a robust tool for predicting contact angles from liquids on polymer surfaces with known HSPs or the reverse, finding the surface HSPs from a known contact angle. Here their idea is implemented in reverse. You get predicted surface tensions and surface energies from known HSPs but also you can change the surface energy with a slider to see how the contact angle changes for an unknown surface. Unknown? Yes,you might not know the surface energy of your polymer and for a known polymer the surface HSP might be different from the bulk HSP:

Surface Energy

σS mN/m
σL mN/m
σLS mN/m

The core science

We know that for a polymer with a surface energy σS, a liquid surface tension σL and an interfacial tension σLS the contact angle θ is given via Young's equation:

σSLSLcos θ

The problem is that although we might know σL, it's hard to know what σLS might be. And although it has been known for many years that there should be a strong link between HSP and these surface effects, no generally useful relationships have been available. Attempts to measure HSP via correlations with contact angles were frequently found to be unsatisfactory - which is not surprising because both σS and σLS need to be known, and σLS was not taken properly into account in these attempts.

The paper carries out a lot of hard work to reach the conclusion that you can get a good estimate of σL (if you happen not to know it) and of σLS just from the HSP of the solvent and the polymer substrate. A single equation does the work for σ12 where 1 is the liquid and 2 is either air (so the HSP values are zero) or the polymer:

σ12 = 0.0947(δD1-δD2)²+0.0315(δP1-δP2)²+0.0238(δH1-δH2

The app calculates σL and σLS and takes your σS value to calculate a contact angle. If you have a contact angle and want to know σS, just slide the σS slider till you achieve your known contact angle.

The authors point out that their fitting parameters are in the ratio 4:1.3:1, close to the classic 4:1:1 ratio for HSP Distance, encouraging the idea that the fit represent a fundamental relationship, not some arbitrary QSAR.

The Toyota measured Bulk values for their specific 5 polymers are at the start of the polymer options. See below for the Surface values. The bulk values might differ from the standard values in the table - such variations are normal, presumably reflecting differences between the "same" polymers made in different ways.

Not the right answer!

Although the correlation works very well, you can readily find deviations. This is a feature, not a bug. Very often, the surface interactions are governed by the bulk HSP values. But sometimes the surface (e.g. with polar groups avoiding the surface) can be different from the bulk. A contact angle different from what you expect is evidence for this sort of effect. You can compare the Surface values in the table with the Bulk ones. Equally, for polymers such as nylon, moisture absorption at the surface can give a different surface HSP. The fact that this approach highlights these issues makes the paper especially useful

Measured surface energies

Using the Surface HSP values, Toyota found the following surface energies in mN/m:

The help of Dr Nakamura in refining this page is gratefully acknowledge.

The official site of Hansen Solubility Parameters and HSPiP software.