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Evaluation Methods and Influencing Factors CHAPTER 2 63
Table 2.10 Surface Energy of Measuring Liquids
2
p
2
2
P
d
Measuring Liquids γ (mJ/m ) γ (mJ/m ) γ (mJ/m ) γ =γ d L Polarity
L
L
L
L
Water 51 21.8 72.8 2.36 Polarity
N-hexadecane 0 27.6 27.6 0 Nonpolarity
γ 5 γ 1 γ P (2.20)
d
L L L
d d 1=2 p p 1=2
γ ð1 1 cosθÞ 5 2ðγ γ Þ 1 2ðγ γ Þ (2.21)
L
L
s
s
L
In the equation, the free energy γ of the solid surface can be divided into dis-
s
p
D
persion part γ and polarity part γ s .
s
γ Free energy of the liquid surface can also be divided into dispersion part
L
p
d
γ and polarity part γ .
L L
From the Eq. (2.21) it can be seen that if the surface free energy γ , dispersion
L
p
d
part γ , and polarity part γ of liquid are known and contact angle θ of the
L
L
liquid on solid surface is measured, it still results in two unknown values, γ d
p s
and γ s , in the equation. Two equations are needed to obtain these unknown
values. Thus two kinds of measuring liquids are adopted, and the equations
are established as follows:
d d 1=2 P P 1=2
γ ð1 1 cosθ 1 Þ 5 2ðγ γ Þ 1 2ðγ γ Þ (2.22)
L1
s
L1
L1
s
d d 1=2 P P 1=2
γ ð1 1 cosθ 2 Þ 5 2ðγ γ Þ 1 2ðγ γ Þ (2.23)
L2
s
L2
L2
s
The data in Table 2.10 is used in Eqs. (2.19) (2.23)
d d
P P
Water: γ ð1 1 cosθ water Þ 5 2ðγ γ 1=2 1 2ðγ γ 1=2 (2.24)
water s water Þ s water Þ
Inn-hexadecane:γ inn2hexadecane ð1 1 cosθ inn2hexadecane Þ
(2.25)
d d
5 2ðγ γ 1=2 1 2ðγ γ 1=2
P P
s inn2hexadecane Þ s inn2hexadecane Þ
Following are acquired by using the polarity part and dispersion part of water
and n-hexadecane into Eqs. (2.24) and (2.25):
p ffiffiffiffiffiffi q ffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffi q ffiffiffiffiffi
P
72:8ð1 1 cosθ water Þ 5 2 51 γ 1 2 21:8 γ d (2.26)
S S
p ffiffiffi q ffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffi q ffiffiffiffiffi
P
27:6ð1 1 cosθ inn2hexadecane Þ 5 2 0 γ 1 2 27:6 γ d (2.27)
S S
The following are acquired by working out the Eqs. (2.26) and (2.27):
q ffiffiffiffiffi 126:8 1 191:23cosθ water 2 64:43cosθ inn2hexadecane
P
γ 5 (2.28)
S
37:52
