Thermal fluctuations in supercrystal stripe phases of Langmuir monolayers

We predict the magnitude of fluctuations of two-dimensional, supercrystal stripe phases of Langmuir monolayers, composed of polar molecules, in the low temperature regime. Our model includes both the microscopic line tension and the interdomain, long-range dipolar interactions. We calculate (in the long wavelength approximation) the elastic energy of the stripes and show that the stripes exhibit long-range orientational order. We predict that the stabilization of the stripe width by the dipolar interactions tends to decrease the thermal roughness of the domain walls compared with systems with only short-range interactions. In the case of crystalline stripes our results suggest a possible finite-temperature first-order roughening transition.