# Surface free energy

The work which has to be expended in order to increase the size of the surface of a phase is referred to as the surface free energy. As energy per unit area, the surface free energy has the unit mJ/m2, wherein the equivalent unit mN/m is frequently used. The symbol used in formula is σ (lower case sigma).

The term surface free energy is normally used for solid surfaces. When a liquid phase is concerned, reference is usually (and in this glossary) made to surface tension (SFT).

## Background

Contact angle and surface free energy

As it is difficult to differentiate the work required to increase the size of the surface from the deformation work by measurement, the surface free energy is normally measured indirectly with the help of the contact angle, usually with several liquids.

According to Young’s equation, there is a relationship between the surface free energy σs of the solid, the contact angle θ, the surface tension of the liquid σl  and the interfacial tension σsl between liquid and solid:

Schematic diagram of contact angle

A number of methods exists with which the surface free energy can be calculated with the help of contact angle data. With most models, a second equation which has the following general form is set up to calculate the interfacial tension:

The models differ in the way in which these interactions are interpreted and which interaction components of the individual phases are made responsible for producing the surface tension or surface free energy σ.

Models for calculating the surface free energy

Model according to author(s)Interaction components of the SFT
FowkesDisperse part and non-disperse part
Owens-Wendt-Rabel & KaelbleDisperse and polar part
WuDisperse and polar part
SchultzDisperse and polar part, measurement in bulk liquid phase
Oss, Good (acid-base)Lewis acid part and Lewis base part
Extended FowkesDisperse and polar part and hydrogen bond part
ZismanNo division into components; determination of critical surface tension
Neumann Equation of StateNo division into components

## Significance

The surface free energy of a solid has a decisive effect on its wettability. Its knowledge also enables the contact angle, the work of adhesion and the interfacial tension with liquids with known properties to be roughly predicted. This information is relevant for processes such as coating, painting, cleaning, printing, hydrophobic or hydrophilic coating, bonding, dispersion etc.

## Measuring methods

• Drop shape analysis: (DSA): The contact angle is measured using the image of a sessile drop at the points of intersection (three-phase contact points) between the drop contour and the surface (baseline in the image). Instruments: DSA100, DSA30, DSA25, MSA, MobileDrop
• Wilhelmy plate method: The force acting in vertical direction when moving a plate-shaped solid vertically in a liquid is measured. This force depends on the contact angle as well as on the surface tension and the wetted length. Instrument: K100
• Powder contact angle measurement using the Washburn method: A powder-filled tube which is attached to a scale is dipped into the liquid. Due to the capillary force, the measured weight increases with time. The rate of weight increase depends, among other things, on the contact angle. Instrument: K100
• Top-view distance method: The curvature of the drop surface associated with the contact angle is measured using the distance between light spots which are reflected on the top of a drop surface. Instrument: TVA100