Thermodynamic phase transition, monolayer

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). 

A thermodynamic treatment, similar to that used for microemulsions, as well as an approximate statistical mechanical one, are developed to explain the phase transition in monolayers of insoluble surfactants [3.8], A similar thermodynamic approach is applied to multilamellar liquid crystals, and it is shown that, for a given set of interactions and bending moduli, only narrow ranges of the thicknesses of the water and oil layers are allowed [3.9]. 

A general thermodynamic theory and a statistical thermodynamic approach are presented, which describe the phase transitions in insoluble monolayers, particularly the inclined transition from a liquid-expanded to a liquid-condensed phase. 

In conclusion, the LE/LC transition becomes inclined when, because of the lower repulsion than in a separated condensed bulk phase, the condensed phase prefers to be distributed as islands in the expanded one. This can occur only if the repulsive interaction is of long range and the attractive one is of short range. Whereas thermodynamics provides some insight into the phase transitions in monolayers, it cannot provide detailed predictions. 

A thermodynamic treatment is first suggested on the basis of which one can explain the inclined phase transition that occurs in monolayers of insoluble surfactants. By minimizing the Helmholtz free energy of the monolayer, the equilibrium radius and the equilibrium area fraction of the LC islands are obtained as functions of the average molecular surface area A. The mixing entropy provides a negligible effect on... 

Micellar aggregates are considered in chapter 3 and a critical concentration is defined on the basis of a change in the shape of the size distribution of aggregates. This is followed by the examination, via a second order perturbation theory, of the phase behavior of a sterically stabilized non-aqueous colloidal dispersion containing free polymer molecules. This chapter is also concerned with the thermodynamic stability of microemulsions, which is treated via a new thermodynamic formalism. In addition, a molecular thermodynamics approach is suggested, which can predict the structural and compositional characteristics of microemulsions. Thermodynamic approaches similar to that used for microemulsions are applied to the phase transition in monolayers of insoluble surfactants and to lamellar liquid crystals. 

Over a long period of time experimental results on amphiphilic monolayers were limited to surface pressure-area ( r-A) isotherms only. As described in sections 3.3 and 4, from tc[A) Isotherms, measured under various conditions, it is possible to obtain 2D-compressibilities, dilation moduli, thermal expansivities, and several thermodynamic characteristics, like the Gibbs and Helmholtz energy, the energy cmd entropy per unit area. In addition, from breaks in the r(A) curves phase transitions can in principle be localized. All this information has a phenomenological nature. For Instance, notions as common as liquid-expanded or liquid-condensed cannot be given a molecular Interpretation. To penetrate further into understanding monolayers at the molecular level a variety of additional experimental techniques is now available. We will discuss these in this section. 

Phase Transitions in Lipid Assemblies. The rich polymorphism of amphiphilic systems, of which the multilamellar and the Hn phases are only two structures, was made evident from the seminal work of Luzzati and co-workers. Since that early work, an immense variety of water-induced phase transitions have been observed and rationalized in terms of an apparently systematic connection between water content and polar group molecular area. Therefore, the recent observation of a double transition—Hn to lamellar back to Hn—from continual hydration of dioleoylphosphatidyl-ethanolamine (40) was a surprise. Furthermore, an estimate of the cost of uncurling the monolayer in the formation of bilayers based on the previously described bending modulus far exceeds the osmotic work that actually produced the transition. Although this transition sequence can successfully be accounted for by simple thermodynamical principles, it, in fact, contains many geometry-dependent free energy contributions that we simply do not yet understand (41). 

Ben-Shaul, A. and Gelbart, W.M., Statistical thermodynamics of amphiphile self-assembly Structure and phase transition in micellar solution, in Micelles, Microemulsions, and Monolayers, W.M. Gelbart, A. Ben-Shaul, and D. Roux (eds.). Springer, New York, 1994, p. 1. 

In general, a phase transition, I II, in a monolayer may thermodynamically be treated analogously to that in a 3D system (cf. Section 3.7.1). Thus, the Clapeyron equation (Equation 3.40) relating the variation of n with T reads... 

The spectroscopic and thermodynamic data presented above suggest a correlation between molecular order, interfacial packing and the gel to liquid crystalline phase transition temperature. Aqueous phospholipid vesicles above their transition temperature readily form tightly packed, well-ordered monolayers at a water/CCU interface (e.g. DLPC). Vesicles below their transition temperature possess greater stability, forming monolayers which are considerably expanded and which show greater disorder (i.e. DPPC and DSPC). 

Using Eqs. (75) [or Eq. (76)] and (74), we can easily obtain the adsorption isotherm assumed for the adsorption energy distribution. In the framework of the mean field approximation expressions for any thermodynamic quantity (e.g. internal energy, heat capacity) can be readily derived [234]. Adsorption on randomly heterogeneous surfaces has been studied in terms of the above-described approach. It has been demonstrated that this mean-field-type theory was valid only at very high temperatures. Below the critical two-dimensional temperature, the predictions of theory seriously underestimate the heterogeneity effects on phase transitions in adsorbed monolayers [12,234],... 

As will be detailed in the following, there are two important questions about these phase diagrams the existence and location of critical or triple points, and the thermodynamic order of the phase transitions, especially for the liquid-solid equilibrium. Following the pioneering work of Thorny and Duval [37], many investigations of phase transitions occiuring in physisorbed monolayers on solid siufaces have been made, and some broad reviews can be foimd in articles and books [9,10,12,15,65,67,96-99]. 

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