Theoretical interpretation of rheology measurements on two-dimensional films containing rigid rod molecules

The work in this thesis was motivated by experiments done in the Fuller lab that study the rheological properties of two dimensional thin films containing rigid rod molecules and undergoing a flow. The films also sit atop bulk water. 1n the first experiment, a biaxial extensional flow causes the molecules to orient along the flow lines and the degree of ordering of the system is measured as a function of time. In the second experiment a uniaxial shear flow is effected. The experiment measures linear visoelastic properties under this flow.; The work presented here first proposes a qualitative rod model for the interactions of the rigid rod molecules in the film. Next we calculate the theoretical quantities that correspond to the experimental observables, including an equation for the two dimensional modulus. In doing this, we derive several equations, including the equation for the time evolution of the distribution function, known as the Smoluchowski equation. We also derive equations for the velocities and stress tensors in the film and the underlying water.; We found that the rod model is a reasonable one to use for this system. In addition, any potential attempting to explain the data must contain attractive forces as one containing only repulsive forces grossly underestimates the values of the moduli. Further, the strength of the attractive interaction needed to fit the data is quite large.; We also extracted some characteristic relaxation times from the data and found that there are several possible theoretical explanations for the type of physical relaxation that each time scale corresponds to. This is because the experimental data is noisy and the theory is qualitative.