Liquid Solid
2.1.3 Determination of Surface Free Energy
2.1.3 Determination of Surface Free Energy
Good–Girifalco Method
Good and Girifalco in the 1950s proposed the following equation to describe the surface energy of interfacial phase systems: [6-8]
2 ( )1/ 2
ab a b a b
γ =γ +γ − Φ γ γ (2.6)
The subscripts a and b refer to the two phases, which may be liquid or solid. is a onstant between interfaces of a system and is defined as:
Φ
rface between phases A and B, per cm
Fa
∆
2, =γab −γa− and γb ∆Fnc = free energy of cohesion for phase N 2= γn. Equation (2.6) can be rewritten as the well known Good and Girifalco equation
2 ( )1/ 2
uations 2.5 and 2.9 yield:
(1 cos ) 2 ( )1/ 2
lculated from contact angle data w
rifalco suggested that Φ was equal to unity.
Fowkes’ Method
Fowkes [9,10] proposed that “the surface tensions are a measure of the attractive forces between surface layers and liquid phase, and that such forces and
their contribution to the free energy are additive.” He designated, in the case of the surface tension of water, the surface tension c ld be considered thou e sum of
ontributions from dispersion forces (γd) and dipole interactions, mainly hydrogen c
where superscript h refers to hydrogen bonding, and d to dispersion. In addition, at the interface between a liquid and solid, as Fowkes pointed out, the interfacial molecules are attracted by the bulk liquid from one side and from the other side by the intermolecular forces between the two phases. Fowkes defined the dispersion force
rface tension of the solid in terms of the interaction with the dispersion forces
Strictly speaking, eq. (2.14) provides a method to estimate the value of of the liquid. As a result, the Young–Good–Girifalco equation can be modified as:
2( d d )1/ 2
SL S LV S LV
γ =γ +γ − γ γ (2.13)
Combine eqs. (2.5) and (2.13) results in:
(1 cos ) 2( d d )1/ 2
but not total γS, from a single contact angle measurement, where only dispersion forces operate in the liquid, such as a hydrocarbon liquid. The γSd of any solid can be determined using a “dispersion force only” liquid.
Owens, Wendt, and Kaelble’s Method (Two-Liquid Geometric Method)
Owens and Wendt [11] and Kaelble [12] extended Fowkes’ equation to a more general form:
1/ 2 1/ 2
polar (nondispersion) component, including all the interactions established between the solid and liquid, such as dipole–
onding, etc.
Combine eqs. (2.5) and (2.15) yield:
(1 cos ) 2( d d )1/ 2 2( p p
γ + θ = γ γ + γ γ 1/ 2
t d refers to a dispersion (nonpolar) component, and p refers to a
dipole, dipole-induced dipole and hydrogen b
Since γS is the sum of surface tension components contributed from dispersion and polar parts:
S
d p
S S
γ =γ +γ (2.17)
d
Equations (2.15) and (2.16) provide a method to estimate surface tension of solids.
Using two liquids with known γL and γLp for contact angle measurements, one
This method uses the contact angles
harmo n. ult
olymer melt method, and the equation of state method.
of two testing liquids and the nic-mean equatio The res agree remarkable well with the liquid homolog method, p
Based on “harmonic” mean and force addition, Wu proposed the following
Equation (2.19) can be written as follows with the aid of eq. (2.5):
(2.19)
Equations (2.19) and (2.20) provide a method to estimate surface tension of solids. Using two liquids with known
+ = +
Lifshitz–van der Waals Acid-Base Theory (Three-Liquid Acid-Base Method)
Van Oss et al. has proposed a methodology that represents both Fowk
lar,” the later cannot be represented by a single parameter such as
γ γ
+ +
Wu [13] claimed that this method applied accurately between polymers and between a polymer and an ordinary liquid.
es–Owens–Wendt–Kaelble and Wu. This methodology introduces a new meaning of the concepts, “apolar” and “po
γ p.
As shown in eq. (2.22), surface tension γ could be divided into an apolar ng component or (more generally) acidbase component and a hydrogen bondi
interaction. One may follow Fowkes’ approach [15,16] and separate surface energy into several components as:
d dip ind h ...
γ γ= +γ +γ +γ + (2.22)
d AB
γ γ +γ (2.23)
where the superscripts, d, dip, ind, and h refer to (London) dispersion, (Keesom) dipole– dipole, (Debye) induction, and hydrogen bonding forces, respectively. And the superscript AB refers to t
=
he acid-base interaction.
By regrouping com surface ener
ponents in eq. 2–22, van Oss and Good expressed the gy as:
LW AB
γ γ= +γ (2.24)
LW d dip ind
γ =γ +γ +γ (2.25)
where LW stands for Lifshitz–van der Waals. Because a hydrogen bond is a proton
rogen, a hydrogen bonding is an example of Lewis acid (electron acceptor) and
hydrogen bonding as
-sharing interaction between an electronegative molecule or group and an electropositive hyd
Lewis base (electron donor). Van Oss et al., [17-23] therefore, treated Lewis acid-base interactions. In addition, van Oss et al. [17- 19]
created two parameters to describe the strength of Lewis acid and base interactions:
γ+ = Lewis acid parameter of the surface free energy
Based on these definitions, a material is classified as a bipolar substance if both γ+ and its γ− are greater than 0 (γAB ≠ 0). In other words, it has both nonvanishing γ+ and γ−. A monopolar material is one having either an acid or a base characters, which means either γ+= 0 and γ− > 0 or γ+ > 0 and γ−= 0. An
apolar material is neither an acid nor a base (both its γ+ and its γ− are 0). For both monopolar and apolar materials, their γAB= 0. Therefore, according to the Fowkes notation, the criterion for a substance to be apolar, is, γAB= 0. This is not true in the van Oss and Good’s met dology.
How do we calculate these surface energy parameters? van Oss, Good, and their coworkers, have developed a “three-liquid procedure” (Equation rmine
S
In short, to determine the components of cos ) 2(θ γ γLW LW γ γ+ − γ γ− + )
+ = + + (2.27)
γS of a polymer solid, it was recommended [24,25] to select three or more liquids f om the reference liquids table, with two of them being polar, the othe . Moreover, the polar pairs—water and ethylene glycol, and water and form ide— were recommended to give good results, while aploar liquids are either diiodomethane or a-bromonaphthalene. Because the LW, Lewi ewis base parameters of
r parameters of γS by solving these three equations simultaneously.
Critical Surface Tension – Zisman plot
The concept of critical surface tension was first proposed by Fox and Zisman [26-28]. An empirical rectilinear relation was found between cosθ and γLV for a series of testing liquid on a given solid. When homogeneous liquids are used as the
testing liquids, a straight line is often obtained. When nonhomologous liquids are used, however, the data are often scattered within a rectilinear band or give a curved line.
The intercept of the line at cosθ = 1 is the critical surface tension γc. When a band is obtained, the intercept of lower line of the band is defined as the critical surface tension. The cosθ versus γLV plot is known as the Zisman plot. The example is given in Figure 2-6.
Figure 2-6. Zisman plot for poly(tetrafluoroethylene) (PTFE) using various testing liquids.