Contact angle

2.8 The acid-base method according to OSS & GOOD

OSS and GOOD also differentiate between a polar and a disperse fraction of the surface energy. However, in contrast to the previously described authors, they describe the polar fraction with the help of the acid-base model according to Lewis. According to this model, the polar fraction of the surface energy of the solid and the surrounding drop liquid is split into an electron acceptor fraction corresponding to a Lewis acid (=”electron receiving” fraction \sigma^+ and an electron donor corresponding to a Lewis base (=“electron donor” fraction) \sigma^- .

Owing to the attraction of opposite charges there are interactions between the particular counter poles of the polar components of the solid and the liquid. The Equation for the surface tension of FOWKES and OWENS, WENDT, RABEL, KAELBLE (Equation 37) is adapted accordingly:

\gamma_{sl} = \sigma_s + \sigma_l -2 ( \sqrt{\sigma_s^D \cdot \sigma_l^D} + \sqrt{\sigma_s^+ \cdot \sigma_l^-} + \sqrt{\sigma_s^- \cdot \sigma_l^+}) (Equation 54)

In order to calculate the 3 fractions of the surface energy of a solid from contact angle data Equation 54 is combined with YOUNG's Equation:  

\sigma_s = \gamma_{sl} + \sigma_l \cdot \cos\theta (Equation 55)

to ontain

(1 + \cos\theta)\sigma_l = 2 (\sqrt{\sigma_s^D \cdot \sigma_l^D} + \sqrt{\sigma_s^+ \cdot \sigma_l^-} + \sqrt{\sigma_s^- \cdot \sigma_l^+}) (Equation 56)

In order to solve this equation, i.e. to determine the disperse fraction \sigma^D_s , the acid fraction \sigma^+_s and the base fraction \sigma^-_s of the solid, contact angle data from at least 3 test liquids are required; at least 2 of these must have a known acid and base fraction > 0.

Moreover, at least one of the liquids must have equal basic and polar parts. Usually water is chosen for this purpose because it serves as neutral point in the LEWIS scale.