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In order to determine the surface tension component at the solid / liquid interf

ID: 1884584 • Letter: I

Question

In order to determine the surface tension component at the solid / liquid interface (YsuU from contact angle measurements, we must assume some additional relation between (YsL and(Ysv ). In Fowke's method of surface tension components, this is done by separating the two terms, and postulating that the interfacial tension is the geometric mean of the surface tension of the pure phases, and primarily arises from the dispersive forces in the pure materials (so we don't have an equation relating (YsL)and (Ysv) to each other, but rather to their pure components) a) Based on Fowke's work (referenced in the text), how do you find (Yds? b) How does Fowke's method lead you to (Ys)?

Explanation / Answer

The Fowke's method assumes that the surface free energy (SFE) of a solid is a sum of independent components, associated with specific interactions:

Ys = Ysv = Ysd + Ysp + Ysh + Ysi + Ysab + Ys0                                               (1)

where    Ys = Ysv is the SFE of the solid,

Ysd is the dispersion component

Ysp is the polar component

Ysh is the hydrogen bond component

Ysi is the induction component

Ysab is the acid-base component

Ys0 refers to all remaining interactions

According to Fowke’s, the dispersion component of SFE is connected with the London interactions, arising from the electron dipole fluctuations. These interactions commonly occur in matter and result from the attraction between adjacent atoms and molecules. Fowke’s considered the systems in which only the dispersion interactions appear, and determined the SFE corresponding to the solid-liquid interface as follows:

Ysl = Ys + Yl - 2(YsdYld )0.5                                                                        (2)

where    Ysl is the SFE of the solid-liquid interface

Yl is the SFE of the measuring liquid

Yld is the dispersion component for SFE of the measuring liquid

The Young equation is given by:

Ys = Ysl + Yl cosq                                                                                  (3)

where q is the contact angle between the solid and the measuring liquid

Combining equations (2) and (3), the Young Fowke’s equation is obtained as:

Ysl = Ysl + Yl cosq + Yl – 2(YsdYld )0.5

Ysd = [Yl (1 + cosq)]2/(4Yld)                                                                      (4)

(a) Therefore, Ysd can be found by using the measured values of contact angle and known values of surface tension components of the measuring liquid in equation (4).

(b) For a non polar solid Ys = Ysd. For other solids, the following equations are valid:

Ys = Ysd + Ysp                                                                                        (5)

Yl = Yld + Ylp                                                                                          (6)

Owen and Wendt expanded Fowke’s idea by adding polar components to equation (2) giving,

Ysl = Ys + Yl - 2(YsdYld )0.5 - 2(YspYlp )0.5                                                     (7)

As there are two unknowns Ysd and Ysp, two liquids with known dispersive and polar components are required to solve it. The liquid with dominant dispersive component should be used as one measuring liquid and the one with dominant polar component as the other one. For a dispersion liquid with Yl = Yld, equation (4) reduces to:

Ysd = 0.25Yl (1 + cosq)2                                                                         (8)

The contact angle (q) for the dispersion liquid is measured, and then Ysd is calculated using equation (8). Similarly, the contact angle (qp) for the polar liquid is measured, and then Ysp is calculated using the following equation:

Ysp = [0.5Yl (1 + cosqp) – (YsdYld )0.5]2/ Ylp                                                  (9)

Finally, Ys can be obtained by using equation (5).

It should be noted that, this method is based on the independence and additivity of the dispersion and polar interactions.

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