Emergence of a linear slope region of the isotherm in the first-order liquid-expanded-liquid-condensed phase transition in Langmuir monolayers.

A nonhorizontal slope in the isotherm has been observed in the two-phase coexisting region of the first-order liquid-expanded (LE)-liquid-condensed (LC) phase transition in Langmuir monolayers for many decades. We show that the simple analysis of a phenomenological Landau free energy involving the coupling-energy contributions of molecular lateral density (ρ) with spontaneous collective chain tilt (θ) and two-dimensional strain (ɛ_{s}) inside the LC domain enables one to understand the origin of a nonhorizontal straight-line slope in the LE-LC phase coexistence region of the isotherm. The presence of ρ-ɛ_{s} coupling must be essential for the appearance of the straight-line shape of a nonhorizontal plateau in the isotherm. Moreover, it is found from the comparison of the two-dimensional contour plots of the free energy that an LE phase may persist significantly even at the later stage of the straight-line regime beyond a transition midpoint surface pressure in the presence of this coupling. The persistence of the LE phase may lead to the delay of transition progress as manifested more clearly by the appearance of a compressibility plateau in the coexistence region that indicates the existence of persistent equilibrium density fluctuations in the monolayer.