MD Overview
Model 100P
Model 100SL
Model 100SB
Model 100E
Model 200
Model 300
Model 400
Auto Dispensing Unit
Motorized Stage
Tilting Stage
Temperature Chamber
Measurement Methods
Surface Free Energy
Contact us
About us
Surface Free Energy
Surface energy is the popular term given to the interfacial tension of a solid. To explain this, first think of a liquid. The tension across a liquid-vapor (liquid-gas) interface is called surface tension and is written gLV. This is actually well defined. It would seem that you could define a similar term for a solid and write it gSV. In fact you can define it but you cannot measure it.? The physical reason for this is that a solid will not deform the way a liquid will; more specifically, a solid will support a shear stress.

Young’s equation expresses the equilibrium situation:
gSV - gLS = gLV cos q

where q is the contact angle. The left hand side is what we can calculate from the things we can measure on the right hand side. We can only calculate the difference between the two quantities on the left hand side. In essence, gSV hides behind gLS, which is the interfacial tension between the liquid and solid. We have one equation and two unknowns.

There is no exact answer to this dilemma. There are models which provide approximate answers by giving us another equation with which to separate gSV and gLS. It is very important to under-stand that these are, indeed, very approximate. The models are based on independent knowledge of how liquids and solids adhere to one another. There are seven models, which are widely used, and a number of others which have their own small followings. These seven models are often called by different names, so it becomes tedious to keep track of all of them. For the record, these models and their synonyms are

     Zisman critical wetting tension
     Owens, Wendt geometric mean
     Extended Fowkes
     Wu harmonic mean
     Lewis acid/base theory

For well-known, well-characterized surfaces, there can be a 25% difference in the answers provided by each model. Each model does better with one type of surface or another, but there is no recognized “correct” answer.

Why do people bother with surface energy? Primarily they would like to characterize surfaces without having to explicitly describe the test fluid. The right hand side of Young’s equation is the product of the test liquid surface tension and the contact angle, so surface energy is more “fundamental,” even if it cannot be accurately measured with today’s understanding.? Secondly, the surface energy description mimics the surface tension description for liquids, so similar terminology is used for both. Thirdly, the inaccuracies in today’s models are acceptable to some.

Calculation procedures of surface energy on MD software:

     Measure contact angles with test fluids for which you know the surface tension.

     Click on the icon SE in the toolbar, choose a method to supply the missing equation. See what others in your industry have chosen.

     Enter the surface tension for the test liquids and the measured contact angles for each in the Surface Energy Computation. This is purposefully left as a manual transfer because you may wish to average many readings before entering the data. After you choose the model, you click re-computationand the equations are solved.

In one sense, this is very easy, taking only three steps. However, in another sense, it is subtle because you are restricting the available answers when you choose the model. The real issue is choosing a model.

Wetting Behavior Analyzer
SFE Data Center
The models vary significantly in complexity. The biggest difference is how many different test liquids are required for a single determination. If a method requires two liquids, contact angles must be measured with both liquids on the sample. Obviously, one measures at different, but close, positions on the sample with each liquid.
The Equation-of-state method is the only model that provides an answer with only one test liquid. The Zisman method requires at least two fluids, although using more improves the results. The geometric and harmonic mean methods require two test fluids and the acid/base model requires three. Furthermore, the geometric, harmonic, and acid/base models require additional knowledge about the test fluids (these parameters are provided for common test fluids in the MD software). All of these methods are discussed in basic physical chemistry references, a list of which is provided in the Application Note file. A real understanding of them requires substantial study.

A good place to start is the Equation-of-state method with water as the test liquid. This is the simplest and gives a good idea of what the surface energy is. The Fowkes method is best at low contact angles and worst at high. Because the method has an adjustable parameter, F, which is normally set equal to 1, the model can be tweaked to provide better answers at high contact angles. By “better,” we mean more like the other methods. To do this, we must have a “known” surface energy and contact angle. We use Teflon as the reference material and call this the extended Fowkes method.

Finally, most workers use surface energy numbers on a relative basis in the final analysis. For example, if they wish to increase the wettability of a polymer by plasma treatment, they would be happy by a change of 25 to 35 but they would be just as happy with a change of 30 to 40.

Calculation of Surface Free Energy



Min. no. of liquids




Critical surface tension


Non-polar solids

PE, PTFE, waxes


Disperse parts of surface free energy

2, non-polar liquids

Non-polar system

PE, PTFE, waxes


Disperse and polar? parts of surface free energy



Polymers, aluminum, coating, vanishes

Extended Fowkes

Disperse, polar and hydrogen parts of surface free energy


Specific questions of surface properties

Plasma, or corona treated polymers

( Harmonik Mean )

Disperse and polar? parts of surface free energy

2, at least one polar liquid

Low energetic systems

Organic solutions, polymers, organic pigments

Acid-Base Theory

Disperse, acid and base parts of surface free energy


Specific questions of surface properties

Biological system

Equation of State Theory

surface free energy



Polymers, aluminum, coating, vanishes

2009 Sindatek Instruments Co., Ltd.   All Rights Reserved.