Hierarchical structure growth across different length scales in the two-phase coexistence region of myristic acid Langmuir monolayers: correlation of static and dynamic heterogeneities.

We investigated the hierarchical structure growth of myristic acid monolayers at the air-water interface across different length scales in the two-phase coexistence region of the first order liquid expanded (LE)-liquid condensed (LC) phase transition. A combined study of surface pressure-area (π-) isotherm measurements with Brewster angle microscopy (BAM) observations was done at different temperatures. At the nanometer scale, the analysis of the π- isotherm by application of a thermodynamic cluster equation allowed us to obtain the π dependence of cluster size (cluster distribution) in the LE-LC coexistence region. The cluster distributions showed a peak at the midpoint pressure of the transition. At higher temperature the larger nanocluster size was obtained at the transition midpoint. At the micrometer scale, BAM showed that LC domains have characteristic textures depending on the temperature. At low temperature domain density was lower and the average size of circular domains was larger. A large number of circular domains revealed a virtual boojum texture from the initial to the late stage of the transition. At the final stage some circular domains coalesced to form larger circular stripe domains and others coalesced to each other without the formation of stripe domains, finally resulting in a uniform texture over the entire water surface. At high temperature the domain texture was predominantly uniform, and a small number of domains only included straight line defects from the intermediate to the late stage of the transition. All domains coalesced to each other without the development of any texture including the stripe, different from the case at low temperature. The phase boundary line tension is highly likely to play a key role for understanding the hierarchical growth and coarsening (coalescence) process in the LE-LC transition between the different length scales from the nanometer to the micrometer scale consistently together.