Monolayer phase transitions: first-order

The difference between the static or equilibrium and dynamic surface tension is often observed in the compression/expansion hysteresis present in most monolayer Yl/A isotherms (Fig. 8). In such cases, the compression isotherm is not coincident with the expansion one. For an insoluble monolayer, hysteresis may result from very rapid compression, collapse of the film to a surfactant bulk phase during compression, or compression of the film through a first or second order monolayer phase transition. In addition, any combination of these effects may be responsible for the observed hysteresis. Perhaps understandably, there has been no firm quantitative model for time-dependent relaxation effects in monolayers. However, if the basic monolayer properties such as ESP, stability limit, and composition are known, a qualitative description of the dynamic surface tension, or hysteresis, may be obtained. 

Ag(lOO) 140-250 100-140 100-120 0-100 Step decoration and formation of expanded Ag 100)-c(2 X 2) Pbajj structure at terraces Formation of a condensed 2D hep Pbaja phase from an expanded 2D Pbajs phase via first-order phase transition starting at steps Formation and limited growth of 2D Pbads clusters on top ofthe first Pbads monolayer Completion and compression ofthe 2D hep Pbads phase at terraces... 

Stigter and Dill [98] studied phospholipid monolayers at the n-heptane-water interface and were able to treat the second and third virial coefficients (see Eq. XV-1) in terms of electrostatic, including dipole, interactions. At higher film pressures, Pethica and co-workers [99] observed quasi-first-order phase transitions, that is, a much flatter plateau region than shown in Fig. XV-6. 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

Monolayer Films at the A/W Interface. Previous studies of phospholipid monolayers at gas-liquid interfaces have shown that it is possible to follow the first order thermodynamic phase transition of these monolayer films using the infrared reflectance techniques described in this manuscript (see e.g. ref. 6 and references cited therein). For long chain hydrocarbon molecules, it has been demonstrated that the frequencies of the antisymmetric and symmetric CH2 stretching vibrations are conformation-sensitive, and may be empirically correlated with the order (i.e. the trans-gauche character) of the hydrocarbon chains (9-11). 

Modern methods of vibrational analysis have shown themselves to be unexpectedly powerful tools to study two-dimensional monomolecular films at gas/liquid interfaces. In particular, current work with external reflection-absorbance infrared spectroscopy has been able to derive detailed conformational and orientational information concerning the nature of the monolayer film. The LE-LC first order phase transition as seen by IR involves a conformational gauche-trans isomerization of the hydrocarbon chains a second transition in the acyl chains is seen at low molecular areas that may be related to a solid-solid type hydrocarbon phase change. Orientations and tilt angles of the hydrocarbon chains are able to be calculated from the polarized external reflectance spectra. These calculations find that the lipid acyl chains are relatively unoriented (or possibly randomly oriented) at low-to-intermediate surface pressures, while the orientation at high surface pressures is similar to that of the solid (gel phase) bulk lipid. 

Henon, S. Meunier, J. Microscope at the Brewster angle direct observation of first-order, phase transitions in monolayers. Rev. Sci. Instrum. 1991, 62, 936. 

Overbeck, G. A. Honig, D. Mobius, D. Visualization of first and second order phase transitions m eicosanol monolayers using Brewster angle microscopy. Langmuir 1993, 9, 555. 

To illustrate the interpretation of such sub-steps, the monolayer isotherms for the adsorption of Xe on FeCl2 (Larher, 1992) are shown in Figure 4.2. At temperatures below 99.57 K, there is a single vertical step, which corresponds to the transformation of 2-D gas to the solid phase. Very little further compression of the monolayer is possible before its completion at Point B. A smaller sub-step becomes apparent at temperatures above 99.57 K. As a result of the careful studies of Thorny and Duval and Larher, the consensus interpretation is that this small sub-step represents a first-order transition between the 2-D liquid and solid phases. It is evident that, in the case of the Xe/FeCl2 system, 99.57 K is the two-dimensional triple point. 

In many physically important cases of localized adsorption, each adatom of the compact monolayer covers effectively n > 1 adsorption sites [3.87-3.89, 3.98, 3.122, 3.191, 3.214, 3.261]. Such a multisite or 1/n adsorption can be caused by a crystallographic Me-S misfit, i.e., the adatom diameter exceeds the distance between two neighboring adsorption sites, and/or by a partial charge of adatoms (A < 1 in eq. (3.2)), i.e., a partly ionic character of the Meads-S bond. The theoretical treatment of a /n adsorption differs from the description of the 1/1 adsorption by a simple Ising model. It implies the so-called hard-core lattice gas models with different approximations [3.214, 3.262-3.266]. Generally, these theoretical approaches can only be applied far away from the critical conditions for a first order phase transition. In addition, Monte Carlo simulations are a reliable tool for obtaining valuable information on both the shape of isotherms and the critical conditions of a 1/n adsorption [3.214, 3.265-3.267]. 

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