# A Determination of the Phase Diagram of Relaxed Langmuir Monolayers of Behenic Acid

 Title: A Determination of the Phase Diagram of Relaxed Langmuir Monolayers of Behenic Acid Author: Bommarito, G. M.; Foster, W. J.; Pershan, Peter S.; Schlossman, M. L. Note: Order does not necessarily reflect citation order of authors. Citation: Bommarito, G. M., W. J. Foster, Peter S. Pershan, and M. L. Schlossman. 1996. A determination of the phase diagram of relaxed Langmuir monolayers of Behenic acid. Journal of Chemical Physics 105(12): 5265-5285. Full Text & Related Files: Bommarito_Determination.pdf (2.113Mb; PDF) Abstract: Grazing incidence x‐ray scattering (GIXS) and Brewster angle microscopy (BAM) are used to determine the $$\pi–T$$ phase diagram of Behenic acid monolayers supported on the surface of water (pH=2.0) over the temperature range of 3$$^\circ$$C to 20.6$$^\circ$$C. The phase diagram is constructed from measurements taken during isothermal compressions in which the surface pressure relaxed to a stable value at each surface density, and during temperature scans at fixed average surface density. The phase diagram is different than those previously reported for Behenic acid primarily because of the surface pressure relaxation. For temperatures less than 12$$^\circ$$C the phase diagram exhibits similar phases and topology as the published diagrams, although the location of the phases in the $$\pi–T$$ plane is different. Temperature scans combined with the isotherms, and the Clausius–Clapeyron relation are used to determine three coexistence lines that meet in a triple point. Changes in entropy across the phase boundaries are determined. Near room temperature (20.6$$^\circ$$C) only one phase is measured over the range of surface pressure from 0 dynes/cm to the collapse pressure in contrast to reported measurements on monolayers out of equilibrium (i.e., when the surface pressure is not allowed to relax) that exhibit several phases near room temperature at pressures higher than the collapse pressure. Discrepancies are observed between the average area per molecule ($$A_T$$) and the area per molecule determined from measurements of the unit cell ($$A_X$$) in the close packed regions of the phase diagram. It is conjectured that the $$\pi–A_X$$ plane is a better representation of the ordered equilibrium monolayer phases than the $$\pi–A_T$$ plane. Isotherms plotted in the $$\pi–A_X$$ plane are used to determine the compressibility of the ordered phases and the nature of the phase transitions. Published Version: doi:10.1063/1.472367 Other Sources: http://alumni.caltech.edu/~bill/foster_jcp.pdf Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10357479 Downloads of this work: