
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 liquidvapor
(liquidgas) 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 understand 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
Fowkes
Owens, Wendt geometric mean
Extended Fowkes
Wu harmonic mean
Lewis acid/base theory
Equationofstate
For wellknown, wellcharacterized 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
recomputationand 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 Equationofstate 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 Equationofstate
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 
Method 
Information 
Min.
no. of liquids 
Application 
Examples 
Zisman 
Critical
surface tension 
2 
Nonpolar
solids 
PE,
PTFE, waxes 
Fowkes 
Disperse
parts of surface free energy 
2,
nonpolar liquids 
Nonpolar
system 
PE,
PTFE, waxes 
OWRK 
Disperse
and polar? parts of surface
free energy 
2 
universal 
Polymers,
aluminum, coating, vanishes 
Extended
Fowkes 
Disperse,
polar and hydrogen parts of
surface free energy 
3 
Specific
questions of surface properties 
Plasma,
or corona treated polymers 
Wu
( Harmonik Mean ) 
Disperse
and polar? parts of surface
free energy 
2,
at least one polar liquid 
Low
energetic systems 
Organic
solutions, polymers, organic
pigments 
AcidBase
Theory 
Disperse,
acid and base parts of surface
free energy 
3 
Specific
questions of surface properties 
Biological
system 
Equation
of State Theory 
surface
free energy 
1 
universal 
Polymers,
aluminum, coating, vanishes 






