66
where
γ
is the contact angle
,
γ
l
is liquid surface tension and
γ
s
is the solid surface tension, or free
energy. The addition of d and p in the superscripts refer to the dispersive and polar components of each.
This equation is of type y = mx + b.
When is graphed against the slope of the line is
p
s
and the y-intercept is
d
s
. The total free surface energy is then the sum of its two component forces.
The method labeled Simple Fowkes in Theta SFE software calculates just the dispersive component of
the surface free energy, based on one or more measurements with non-polar liquids:
In the method labeled OWRK / Extended Fowkes, the surface free energy (including dispersive and polar
components) of a solid is calculated based on contact angle measurements of two or more drops which
should include both polar and non-polar liquids. The values are obtained for N drops by finding values for
d
s
and
p
s
such that the following square error function is minimized:
That is a generalized version of the Extended Fowkes method, in which two drops are used to create a
pair of equations from which
d
s
´
and
p
s
are solved.
Harmonic Mean (Wu):
This method utilizes a similar approach but uses a harmonic mean equation to
sum the dispersive and polar contributions. Contact angles against two liquids with known values of
d
and
p are measured. The values for each experiment are put into the following equation;
(1 + cos
)
l = 4(
ld
sd /
ld +
sd +
lp
sp /
lp +
sp )
where
refers to surface tension (surface free energy), the subscripts l and s refer to liquid and solid,
and the superscripts d and p refer to dispersive and polar components. You then have two equations
with two unknowns and can solve for
sd and
sp.
Acid-Base (van Oss):
Contact angles against at least three liquids with known values of
d,
+ and
-
are measured. The values for each experiment are put into the following equation:
d
l
p
l
d
l
l
2
)
cos
1
(
4
cos)
1
(
2
d
d
s
l
2
1
2
)
cos
1
(
d
s
d
li
p
li
p
s
d
li
li
N
i
Summary of Contents for Theta
Page 1: ...Theta User manual OneAttension Optical Tensiometer Revision 1 0...
Page 3: ...6 3 Theory of surface free energy 65 7 TECHNICAL SPECIFICATIONS 70 8 CONTACT INFORMATION 71...
Page 41: ...38 Figure 4 15 Device controls and recipe sheet parameters for multiliquid dispenser...
Page 54: ...51 Figure 4 30 Analysis tab of the PD 200 experiment Figure 4 31 Calculated results...
