Phase diagrams monolayers

Fig. IV-17. A schematic phase diagram illustrating the condensed mesophases found in monolayers of fatty acids and lipids.

Fig. XII-8. A schematic friction phase diagram showing the trends found in the friction forces of surfactant monolayers. (From Ref. 53.)...

It was estabhshed ia 1945 that monolayers of saturated fatty acids have quite compHcated phase diagrams (13). However, the observation of the different phases has become possible only much more recendy owiag to improvements ia experimental optical techniques such as duorescence, polarized duorescence, and Brewster angle microscopies, and x-ray methods usiag synchrotron radiation, etc. Thus, it has become well accepted that Hpid monolayer stmctures are not merely soHd, Hquid expanded, Hquid condensed, etc, but that a faidy large number of phases and mesophases exist, as a variety of phase transitions between them (14,15). 

In this section we review several studies of phase transitions in adsorbed layers. Phase transitions in adsorbed (2D) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo, Gibbs ensemble Monte Carlo (GEMC), and finite size scaling techniques. Phase diagrams of fluids with internal quantum states are analyzed. Adsorbed layers of H2 molecules at a full monolayer coverage in the /3 X /3 structure have a higher transition temperature to the disordered phase compared to the system with the heavier D2 molecules this effect is... 

FIG. 8 Phase diagrams for monolayer films on surfaces with boundary potential equal to 0.25 (a), 0.50 (b), and 0.75 (c). (Reprinted with permission from Langmuir 9 2562-2568, October 1993. 1993, American Chemical Society.)... 

Another interesting class of phase transitions is that of internal transitions within amphiphilic monolayers or bilayers. In particular, monolayers of amphiphiles at the air/water interface (Langmuir monolayers) have been intensively studied in the past as experimentally fairly accessible model systems [16,17]. A schematic phase diagram for long chain fatty acids, alcohols, or lipids is shown in Fig. 4. On increasing the area per molecule, one observes two distinct coexistence regions between fluid phases a transition from a highly diluted, gas -like phase into a more condensed liquid expanded phase, and a second transition into an even denser... 

FIG. 4 Phase diagram of Langmuir monolayers at low and intermediate surface coverage (schematic). Not shown are the various phases on the condensed side at high surface coverage. 

FIG. 8 Phase diagram of a Langmuir monolayer in a model of grafted stiff Lennard-Jones chains. LE denotes a disordered expanded phase, LC-U a condensed phase with untilted chains, LC-NN and LC-NNN condensed phases with collective tilt towards nearest neighbors and next-nearest neighbors, respectively, and LC-mod a phase which has a superstructure and an intermediate direction of tilt. (From Stadler and Schmid [151].)... 

Fig. 6. Phase diagram for the binary mixture of terminally polar mesogens showii the reentrant nematic (N), monolayer (Ai), partially bilayer (Ad) and two-dimensional (C) phases (Lobko et al. [47])...

The surface phase diagram of vanadium oxides on Rh(l 11) has been investigated in a series of papers of our group [4, 18, 19, 90, 101-103]. It is characterized by pronounced polymorphism and many different oxide structures have been detected as a function of coverage and growth temperature. The vanadium oxide structures for coverages up to the completion of the first monolayer formed on Rh(l 11) under the different preparation conditions may be subdivided into highly oxidized phases... 

When a reversible transition from one monolayer phase to another can be observed in the 11/A isotherm (usually evidenced by a sharp discontinuity or plateau in the phase diagram), a two-dimensional version of the Gibbs phase rule (Gibbs, 1948) may be applied. The transition pressure for a phase change in one or both of the film components can be monitored as a function of film composition, with an ideally miscible system following the relation (12). A completely immiscible system will not follow this ideal law, but will... 

Behm et al. have measured LEED diffraction intensities for H monolayers on Pd(100) surfaces as function of temperature at different coverages (Fig. 13b). Taking the temperature Ti,2 where the intensity has dropped to 50% of its low-temperature value as estimated for Td ), they constructed the phase diagram shown by crosses in Fig. 13a. (Alternatively using the inflection points of the I vs T curves (Fig. 13b) yields similar results.)... 

From LEED measurements of H monolayers adsorbed on Fe(110) Imbihl et al. proposed a phase diagram as shown in Fig. IS. In addition to lattice gas and lattice fluid phases, two commensurate ordered phases were identifled, denoted as (2 x 1) and (3 x 1) in the figure (cf. Fig. 16). The shaded regions are interpreted as incommensurate phases or as phases composed of antiphase domains their signature is that the LEED spot does not occur at the Bragg position but rather the peak is splitted and satellites appear (Fig. 17). 

Reverse micelles are well known to be spherical water in oil droplets stabilized by a monolayer of surfactant. The phase diagram of the surfactant sodium bis(2-ethylhexyl) sulfosuccinate, called Na(AOT), with water and isooctane shows a very large domain of water in oil droplets and often forms reverse micelles (3,23). The water pool diameter is related to the water content, w = [H20]/[ AOT], of the droplet by (23) D(nm) = 0.3w. From the existing domain of water in oil droplets in the phase diagram, the droplet diameters vary from 0.5 nm to 18 nm. Reverse micelles are dynamic (24-27) and attractive interactions between droplets take place. 

Fig. 1. Phase diagram of mixed PVPC6 + L monolayers. Variation of PVPC6 collapse pressure with segment fraction of lipid xL.

The analogy between three- and two-dimensional phase diagrams can be carried much further. Monomolecular amphiphilic films show ordered phases similar to three-dimensional systems [579], The phases of an amphiphilic monolayer can be detected most conveniently in pressure-area (7r-versus-OA) isotherms. These may look different for different substances. The behavior of simple amphiphilic molecules, like long-chain alcohols, amines, or acids, was extensively investigated (reviews Refs. [580,581]). In monolayers so-called mesophases can occur. In a mesophase the tail groups are ordered over relatively large areas, while the order in the hydrophilic head groups is only over a much smaller distances. 

At low temperatures, the simulation of adsorption requires more careful modelling because of the larger contribution of potential energy to the total energy. Furthermore, it has been shown that a permanent quadrupole moment in the adsorbate molecule (of, say, N2 or C02) may have a major influence on the structure of the adsorbed monolayer at low temperature (Steele, 1996). For example, it seems that the remarkable difference between the 2-D phase diagrams for N2 and 02 on graphite is in large measure due to the quadrupolar nature of N2. 

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