Phase transitions soap films

A as a Function of pH and 7r. Since the area/molecule could not be ascertained from the 7r-A isotherm of a desorbing film, the A values were calculated by extrapolating kinetic data (Equation 2) to zero t (8). Abrupt phase transitions occurred with palmitic acid films, and the 7r of the phase transition varied directly with pH (Figure 4). The anomalous decrease in A that was found immediately before film expansion (Figure 4) suggested partial ionization and the formation of condensed acid soaps (6, 8, 28). Since fatty acid monolayers are partially ionized in the condensed state (8), the apparent pKa of the fatty acid could not be esti-... 

In this chapter we shall show how the observed phenomena may be explained by means of elementary catastrophe theory. In principle, the discussion will be confined to examination of non-chemical systems. However, some of the discussed problems, such as a stability of soap films, a phase transition in the liquid-vapour system, diffraction phenomena or even non-linear recurrent equations, are closely related to chemical problems. This topic will be dealt with in some detail in the last section. The discussion of catastrophes (static and dynamic) occurring in chemical systems is postponed to Chapters 5, 6 these will be preceded by Chapter 4, where the elements of chemical kinetics necessary for our purposes will be discussed. 

Many of the considered problems, such as the problem of stability of soap films, the liquid-vapour phase transition, the diffraction phenomena, descriptions of the heartbeat or the nerve impulse transmission, catastrophes described by non-linear recurrent equations have a close relation to chemical problems. 

Study of transitions between minimal surfaces of soap films discussed in Chapter 2 is an excellent exercise to understand the basics of phase transitions in much more complicated systems. Consider, for example, the four-pin arrangement between two parallel plates shown in Figure 3.1. 

Variation dL/ dx with x for the first order phase transition model and the equilibrium soap film configurations within the four-pin model, with the illustration of the corresponding energies with respect the configurations a and b. (a) Pair of pins are close to each other (b) pairs of pins are widely separated. Note that the lines in reality are two-dimensional, but their sizes do not change in the other dimension. 

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