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

Abstract

A nonhorizontal slope in the isotherm has been observed in the two-phase coexisting region of the firstorder 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 (ε 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 − ε 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.

Exploring Pathways to Equilibrate Langmuir Polymer Films

“…Various ideas have been put forward to explain this observation of a nonzero slope in the Π−A isotherm. 14,16−24 Perturbations by impurities, 14,16−21 coupling between density and chain tilt, 22 or a difference in the ranges of attractive and repulsive interactions between molecules have been suggested. 23 Furthermore, the formation of (domains of) 2D aggregates coexisting with a high fluidity matrix were hypothesized to cause a finite rigidity that was kinetically controlled by the rate of domain growth.…”

“…In Π– A isotherms, the coexistence of phases can be identified through the presence of a plateau, where the surface pressure remains constant upon changing the area. ,, However, for many Langmuir monolayers of small amphiphilic molecules or polymers, the surface pressure in this coexistence region was found to change; i.e., the plateau was not horizontal, which is inconsistent with two coexisting phases in thermodynamic equilibrium. Various ideas have been put forward to explain this observation of a nonzero slope in the Π– A isotherm. ,− Perturbations by impurities, ,− coupling between density and chain tilt, or a difference in the ranges of attractive and repulsive interactions between molecules have been suggested . Furthermore, the formation of (domains of) 2D aggregates coexisting with a high fluidity matrix were hypothesized to cause a finite rigidity that was kinetically controlled by the rate of domain growth …”

Statistical mechanical determination of nanocluster size distributions in the phase coexistence region of a first order phase transition from the isotherms of DMPC monolayers at the air–water interface

“…7,8 Of the isotherms that exhibit transitions, the isotherm behavior in the liquid expanded (LE) -liquid condensed (LC) phase transition region has been much addressed due to the appearance of a non-horizontal plateau in the coexistence region. 9,10,11 Although it was suggested that this transition is not first-order, FM and BAM clearly showed the twophase coexistence (or a heterogeneous pattern composed of the LE and LC domains) through the transition region and the changes in the relative amounts of the phases followed the lever rule. 7 The first-order character of this broad transition is thus no doubt.…”

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

“…14,27 Of the isotherms that exhibit phase transitions, the isotherm behavior in the liquid expanded (LE)-liquid condensed (LC) transition has been much paid attention. 28,29 It is usually found that the pressure does not remain constant but there is an upward slope of the p-A curve during the transition. Since in an exact thermodynamic treatment a first-order phase transition is defined as a transition for which there is a discontinuity in thermodynamic function, the non-horizontal behavior in this transition region observed by most researchers is different from that expected from a conventional first order transition.…”