Biomedical Engineering Reference
In-Depth Information
γ
−
γ
cos
θ
=
SV
SL
(6.2)
γ
LV
Rearranging
γ
=+
γ
γ
cos
θ
(6.3)
SV
SL
LV
where
is the equilibrium contact angle. Equation (6.3) is called Young's equation
although Young did not prove this equation and suggests that by knowing
θ
γ
SV
,
γ
LV
,
and
θ
,
γ
SL
can be calculated. Substituting into (6.1)
WW
=
=
γ
+
γ
cos
θγ
+
−
γ
A
SL
SL
LV
LV
SL
Hence,
(
)
W
=
γ
1cos
+
θ
(6.4)
A
LV
To determine
W
A
, the contact angle of various liquids whose
γ
LV
are known
(see Table 6.2) are measured on a given surface. Then 1/
γ
LV
is plotted against (1
+
cos
) and from the slope
W
A
is determined. The plot used to determine
W
A
by this
technique is called Zeisman plot. Typically, higher surface tension corresponds to
a lower contact angle.
θ
EXAMPLE 6.1
Yan and Lin [6] reported a modification strategy to improve the polyurethane films with
dimethyol propionic acid PUDPA. They measured the contact angles (in degrees) of two
different dry PUDPA films with different test liquids (see the table). Using these values,
calculate the adhesive work of the two membranes.
Ethylene
Glycol Glycerol Formamide
PUDPA1 98 73.3 93.3 83.1
PUDPA2 82.7 65.3 82.7 77.7
Solution: Obtain the
γ
LV
from Table 6.2 and compute the following.
Polymer
Water
PUDPA1
PUDPA2
γ
LV
1/gLV
Degree
Radians
Cos(
θ
)
1+Cos(
θ
)
Degree
Radians Cos(
θ
)
1+Cos(
θ
)
Water
72.8 0.0137
98
1.710
0.139
0.861
82.7
1.443
0.127
−
Ethylene glycol
48.3 0.0207
73.3
1.279
0.287
1.287
65.3
1.140
0.418
1.418
Glycerol
63.4 0.0158
93.3
1.628
−
0.058
0.942
82.7
1.443
0.127
1.127
Formamide
58.2 0.0172
83.1
1.450
0.120
1.120
77.7
1.356
0.213
1.213
Then plot these using the Young equation and determine the slope to obtain the
adhesive function.
As shown in the graph,
W
A
for PUDPA1 is 69.885 dyne/cm and for PUDPA2 it is
62.504 dyne/cm.
