Periodic films

The proof of the importance of iron sulfide in the interaction between the corrosion inhibitor and the metal surface was brought in 1970 when it was shown (3U) that corrosion inhibition was considerably enhanced and prolonged when the corrosion inhibitor was adsorbed on a presulfided specimen rather than on the nonsulfided surface. These measurements were made electrochemically and gave support to the practical well-known fact that periodic "filming" could inhibit the corrosion for relatively long periods of tdme. 

Fig. 3.9. A reduced boundary value problem for a periodic film/substrate configuration which includes a single period of extent p, showing the total force / which acts on the planes of reflective symmetry of the configuration this force is the resultant of the normal stress distribution

Analysis of buckling behavior for spatially periodic film deflections... 

Figure 5-46. Film rupture/slip dissolution mechanism periodical film ruptures and dissolution transients (Lacombe and Parkins, 1977).

In addition, this model is unable to predict the specificity of the SCe systems, since in many systems, periodic film breakdown by plastic strain or creep does not lead to any crack initiation or propagation. 

In thin fiat liquid films (oil and aqueous thin films, thin films of aqueous electrolyte and surfactant solutions, and both free films and films on solid substrates), the disjoining pressure acts alone and determines their thickness. However, if the film surface is curved or uneven, both the disjoining and the capillary pressures act together. In the case of partial wetting, their simultaneous action is expected to yield nonfiat equilibrium shapes. For instance, due to the S-shaped disjoining pressure isotherm, microdrops, microdepressions, and equilibrium periodic films could exist on fiat solid substrates. We shall establish a criteria for both existence and stability of such nonfiat equilibrium liquid shapes. On the other hand, we... 

FIGURE 2.8 Equilibrium periodic film, denotes maximum thickness, and h denotes minimum thickness x is the length of the half-period of the film. 

Hence, the profile of the equilibrium periodic film is described by the following... 

The origin is placed at the position of the maximum height (Figure 2.8) and Equation 2.31 is written for a half period of the periodic film from x = 0, which corresponds to the position of the maximum, to x = x, which corresponds to the position of the minimnm height (Eignre 2.8). Notice that h, ft+, and x are to be determined. 

The excess free energy of a half period, x (Figure 2.8), of the periodic film is given by the same relation (2.20) where we, however, omit the additive constant determined by the reference state. The latter, as we see in the following text, is unimportant. From Equation 2.31, we can express... 

FIGURE 2.9 Isotherm of disjoining pressure used for calculations of the excess free energy of periodic films. 

As the volume of the half period per unit length of the periodic film is V = jhdx = V(hJ,... 

Conditions 2.35 completely determine the equilibrium shape of the periodic film. 

The procedure suggested in Equation 2.35 (minimization of the excess Iree energy) is consistent with Euler s Equation (Equation 2.23), which minimizes the same excess free energy. Computer calculations shown in the following text indicate that there is a unique h+ value satisfying conditions (2.35). These conditions prove the thermodynamic stability of periodic films. 

FIGURE 2.10 The excess free energy of periodic films, (/ +), calculated according to Equation 2.34, using the isotherm of disjoining pressure presented in Figure 2.9. (1) =... 

Let us compare the excess free energy of the corresponding P-film, p, of the same length as a half period of the periodic film. 

This would mean that close to the maximum value of the disjoining pressure isotherm, periodic films are more stable than P-films, that is, the periodic films are a transitional state before rupture of P-films. 

It was previously mentioned that periodic films exist only in the case of partial wetting, that is, if S > S+. Periodic films are to be experimentally discovered. 

The case pip, > 1, when P, < 0, can be treated similarly. It is possible to show that in this case, the maximum thickness of periodic films can be outside the range of the disjoining pressure action, that is, periodic films in this case are actually a periodic array of drops. 

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