Phase diagrams compressed monolayers

Figure 3.19. Schematic sketch of a generic phase diagram for a langmulr monolayer. Generally the pressure (and the compression) increase from right to left. The LE + G coexistence phase has a critical point this may or may not be the case for the LE + LG coexistence. The dashed line represents a possible second order LE-LC transition. In region 1 several condensed phases may occur, exhibiting different order in one or more quantities.

BAM has been widely used for studying the formation and morphological features of condensed domains in the LE-LC coexistence region and to observe and analyze the phase diagrams of Langmuir monolayers ). Upon rapid compression of a monolayer across a phase transition, non-equilibrium structures like dense-... 

Suresh et al. have argued that the formation of dendritic structures during compression of tetradecanoic acid monolayers at the LE-LC transition is related to the vanishing of the line tension between the phases with the approach to a critical point. They believe that for tetradecanoic acid lies at about 31°C, which, if we apply the rule of thumb that there is a 10 K change in the phase diagram per CHj, would place an LE-LC critical point for PDA at 40°C. If the LC and LE phases do not have the same symmetry, e.g., if the LC phase is an ordered solid, then the coexistence region cannot... 

F re 36. Compressed-monolayer and low-temperature phase diagram of N2 on graphite (solid lines) based on heat capacity measurements. Filled circles represent positions of heat capacity peaks. Hatched regions denote two-phase coexistence, and dashed lines as well as boundaries separating UIO -I- TI, UID, and TI phases are speculative. The following abbreviations have been used Commensurate -73 solid (C), incommensurate Vs solid (I), uniaxial (U), triangular (T), orientationally disordered (D), orientationally ordered (O). (Adapted from Fig. 2 of Ref. 394.)... 

Figure 46. Phase diagram of N2 on graphite based on adiabatic heat capacity data coverage is reported in units of the complete n/S monolayer. Orientationally ordered commensurate phase (CO), orientationally disordered commensurate phase (CD), orientationally ordered uniaxially compressed incommensurate phase (UIO), orientationally disordered uni-axially compressed incommensurate phase (UID), triangular compressed incommensurate phase (TI), fluid phase (F), speculative reentrant fluid phase (RF). The measurement path for the highest coverage in Fig. 45 is sketched by the dashed line. (Adapted from Fig. 10 of Ref. 156.)...

The freezing transition from the reentrant fluid to the commensurate solid monolayer seems to be of first order at low temperatures and changes to a continuous transition at a tricritical point near 85 K. This interpretation of the heat capacity and compressibility data [112], however, needs further experimental confirmation, and the corresponding tricritical point shown in the phase diagram Fig. 51 as an open triangle is only tentative. There are also conflicting theoretical predictions concerning the order of the RF - CD transition [77, 78, 151, 260], and the present resolution of the calorimetric data [112] does not allow us to draw a firm conclusion in this respect. 

Beyond a compression to about 1.4 monolayers, evidence for a second-layer fluid on top of the incommensurate monolayer solid is found in the calorimetric study [112] (see the phase diagram. Fig. 49). A second-layer... 

Figure 10. Pressure-area (IT — A) isotherm for a hypothetical amphiphile organized as a monomolecular layer at the water-air interface showing a phase transition from a fluid-expanded to a solid-condensed state upon compression. The insets show cross-sectional diagrams of the Langmuir trough with the compressed monolayer in different phase states.

The four possible stereomers of a chiral surfactant with two asymmetric centers within the polar head group have been synthesized and their absolute configuration determined by X-ray diffraction. One of the diastereomers exhibits a chiral discrimination when spread on water interface the monolayer racemic film undergoes a phase transition from a liquid-expanded towards a liquid-condensed phase upon compression, while the pure enantiomers only have a liquid-expanded phase, as revealed by the measured pressure-area isotherms. The transition pressure-composition diagram indicates that heterochiral interactions are favored. Our results are compared to predictions of Andelman and de Gennes based upon a statistical model. 

Various states can be seen in the monolayer in analogy to pV-diagrams of three-dimensional systems at low pressures a gas analogous phase (a) can be formed which obeys a two-dimensional gas law. Compression leads to an expanded or liquid... 

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