Problem 2

These problems are appropriate for students in an undergraduate/graduate thermodynamics or physical chemistry course. The Level 1 questions are well-defined tasks, whereas the Level 2 questions are designed to be more open-ended.

Level 1

(a) Using the default simulation parameters, calculate the coexisting (vapor and liquid) densities and the surface tension of the fluid at a temperature of 0.80. This will serve as your baseline for comparison. Then, perform a series of simulations, all with a total of 20 surfactants in the simulation. In these simulations, vary the surfactant parameters by keeping the tail diameter fixed (1.0) and vary the head epsilon (1.0, 2.0, 3.0, 4.0, and 5.0). Then, perform another set of simulations with the head epsilon fixed (1.0) and vary the tail diameter (1.1, 1.2, 1.3, 1.4, 1.5, and 1.6). As you perform these simulations, examine the density tab, and identify any changes in the surfactant density profile, with respect to the surfactant parameters. Plot the surface tension as a function of the surfactant parameters. Also, plot the coexisting densities as a function of the surfactant parameters. Were there any noticable trends in the surfactant density profiles, as a function of the parameters? Do you observe any unusual behavior, as compared to your previous simulations of the pure fluid? In each case, are the surfactants evenly distributed or do they tend to prefer certain locations in the simulation cell?

(b) During the simulations in part (a), examine the surfactant orientation profiles. Plot the maximum and minimum values of the surfactant orientations as a function of the surfactant parameters. In each case, does the head or the tail prefer the liquid phase?

(c) During the simulations in part (a), examine the chemical potential profiles at equilibrium. How does the value of the chemical potential compare among the vapor phase, liquid phase, and at the interface?

(d) How is the vapor pressure affected when the surfactants are added? Plot the vapor pressure of the fluid as a function of the surfactant parameters.

(e) Repeat part (a) with a total of 40 surfactant molecules. Are the surface tension values of the coexisting densities significantly affected?

Level 2

(a) Why are the surfactants randomly oriented in the bulk liquid and gas phases (orientation ~ 0.0), while there is a preferrential orientation at the interface? Furthermore, can you explain the shifts in the surfactant orientation as a function of the surfactant parameters?

(b) In the simulations above, you varied the surfactant parameters and measured the effect on the interfacial tension and the behavior of the surfactants. Are your simulated results at least qualitatively consistent with experimental data in the literature? Find some experimental data in the literature that can be compared with your results. Experimentally, how can the epsilon of the head group or the diameter of the tail group be modified for a real surfactant molecule?