B Apparent Diffusion Coefficients of Surfactants

As mentioned above, the value of t, has been shown to be related to the coverage of the air-aqueous solution interface by the surfactant and to its apparent diffusion coefficient, Dap (equation 5.7). To calculate the values of Dap at short times, equation 5.8 (Bendure, 1971), based upon the short-time approximation equation of Ward and Tordai (equation 5.6), and using dynamic short-time surface tension data, may be used  

At constant surfactant concentration, C, in the solution, a plot of (y0 — yt) versus f1/2 should be linear, if adsorption is diffusion-controlled (generally true, for simple-structured surfactants) and permits evaluation of Dap from the slope of the plot. 

Apparent diffusion coefficients may also be calculated from longer-time dynamic surface tension data by use of equation 5.9 (Joos, 1992)  

Interaction between two surfactants, producing an increase in the molecular weight of the complex, decreases the value of Dap considerably (Gao, 1994 Rosen, 1995). When interaction between the two surfactants is weak, the surface tension at short times (f 1 s) is close to that of the component with the lower surface tension value at longer times, it is closer to that of the component that has the lower equilibrium tension. When interaction is strong, the surface tension at short times is greater than that of either component (Gao, 1994). 

A fair correlation has been found (Smith, 2000) between diffusion coefficients and wetting times for cotton twill tape (using a modified Draves wetting test (Chapter 6, Section IIC). 

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