Critical behavior of a two-dimensional complex fluid: Macroscopic and mesoscopic views

Liquid disordered (L_{d}) to liquid ordered (L_{o}) phase transition in myristic acid [MyA, CH_{3}(CH_{2})_{12}COOH] Langmuir monolayers was studied macroscopically as well as mesoscopically to locate the critical point. Macroscopically, isotherms of the monolayer were obtained across the 20^{∘}C-38^{∘}C temperature (T) range and the critical point was estimated, primarily from the vanishing of the order parameter, at ≈38^{∘}C. Mesoscopically, domain morphology in the L_{d}-L_{o} coexistence regime was imaged using the technique of Brewster angle microscopy (BAM) as a function of T and the corresponding power spectral density function (PSDF) obtained. Monolayer morphology passed from stable circular domains and a sharp peak in PSDF to stable dendritic domains and a divergence of the correlation length as the critical point was approached from below. The critical point was found to be consistent at ≈38^{∘}C from both isotherm and BAM results. In the critical regime the scaling behavior of the transition followed the two-dimensional Ising model. Additionally, we obtained a precritical regime, over a temperature range of ≈8^{∘}C below T_{c}, characterized by fluctuations in the order parameter at the macroscopic scale and at the mesoscopic scale characterized by unstable domains of fingering or dendritic morphology as well as proliferation of a large number of small sized domains, multiple peaks in the power spectra, and a corresponding fluctuation in the peak q values with T. Further, while comparing temperature studies on an ensemble of MyA monolayers with those on a single monolayer, the system was found to be not strictly ergodic in that the ensemble development did not strictly match with the time development in the system. In particular, the critical temperature was found to be lowered in the latter. These results clearly show that the critical behavior in fatty acid monolayer phase transitions have features of both complex and nonequilibrium systems.