Consider a surfactant molecule containing a hydrophobic group of 12 saturated carbon atoms synthesized with a head group that is subject to decomposition at low pH. At high pH the molecule has an area per head group of 0.7 nm (70 ) but at low pH the area drops to 0.45 nm (45 ). Present a quantitative argument for the type of aggregates formed by this surfactant as a function of pH. Speculate how the viscosity of a solution of that surfactant would change with the change in pH.