Gaseous monolayer

This simple model is sufficient to reproduce properties such as crystal structure, vibrational frequencies, dispersion curves, and elastic constants [40-43], These calculations were applied also to other organized media such as monolayer gaseous films on graphite [44,45], liquid crystals, and Langmuir Blodgett films. 

Figure 3.7. Possible orientations of amphiphilic molecules in an interface. The lower phase is aqueous, (a) Monolayer gaseous (b), (c), (d) and (e), from liquid expanded via liquid condensed to a solid state (0 eollapse.

Because of the charged nature of many Langmuir films, fairly marked effects of changing the pH of the substrate phase are often observed. An obvious case is that of the fatty-acid monolayers these will be ionized on alkaline substrates, and as a result of the repulsion between the charged polar groups, the film reverts to a gaseous or liquid expanded state at a much lower temperature than does the acid form [121]. Also, the surface potential drops since, as illustrated in Fig. XV-13, the presence of nearby counterions introduces a dipole opposite in orientation to that previously present. A similar situation is found with long-chain amines on acid substrates [122]. 

The most common two-dimensional phases in monolayers are the gaseous, liquid-expanded, liquid-condensed, and solid phases. A schematic II-A isotherm is shown in Figure 3 for a fatty acid for the phase sequence gas (G) — G -l- liquid-expanded (LE) — LE — ... 

The measured NMR signal amplitude is directly proportional to the mass of adsorbate present, and the NMR signal versus pressure (measured at a fixed temperature) is then equivalent to the adsorption isotherm (mass of adsorbate versus pressure) [24-25]. As in conventional BET measurements, this assumes that the proportion of fluid in the adsorbed phase is significantly higher than the gaseous phase. It is therefore possible to correlate each relaxation time measurement with the calculated number of molecular layers of adsorbate, N (where N = 1 is monolayer coverage), also known as fractional surface coverage. 

The film balance may be regarded as a two-dimensional piston, and the most commonly studied property is the surface pressure (n) versus area (A) isotherm. The analogy to a PV isotherm is so appropriate that in the gaseous monolayer regime the two-dimensional analogue of the ideal gas law pertains 114 = nRT. It is therefore reasonable to relate discontinuities in n/A isotherms as the monolayer film is compressed in two dimensions to... 

These assumptions have been expanded upon (Shah and Capps, 1968 Lucassen-Reynders, 1973 Rakshit and Zografi, 1980), especially in regard to the application of the ideal mixing relationship in gaseous films (Pagano and Gershfeld, 1972). It has been pointed out that water may contribute to the energetics of film compression if the molecular structures of the surfactants are sufficiently different (Lucassen-Reynders, 1973). It must be noted that this treatment assumes that the compression process is reversible and the monolayer is truly stable thermodynamically. It must therefore be applied with considerable reservation in view of the hysteresis that is often found for II j A isotherms. 

All of the experiments in pure and mixed SSME systems, as well as in the Af-stearoyltyrosine systems, have one common feature, which seems characteristic of chiral molecular recognition in enantiomeric systems and their mixtures enantiomeric discrimination as reflected by monolayer dynamic and equilibrium properties has only been detected when either the racemic or enantiomeric systems have reverted to a tightly packed, presumably quasi-crystalline surface state. Thus far it has not been possible to detect clear enantiomeric discrimination in any fluid or gaseous monolayer state. 

We now turn to a more complex instance of the Davydov-split spectral lines corresponding to the bending vibrations of C02 molecules in a monolayer adsorbed on the NaCl(100) surface. A molecule C02 in gaseous phase exhibits two degenerate bending vibrations in the plane perpendicular to the long molecular axis. 

Figure 4. Principle of monolayer characterization via surface pressure (n)-area (A) isotherms (a) gaseous phase, (b) liquid expanded phase, (c) condensed phase (head packing), (d) condensed phase...

One may consider a series of physical states ranging from the crystalline, where molecular aggregation and orientation are large, to the dilute gaseous state, where there are no significant orientational limits. States of intermediate order are represented by micelles, liquid crystals, monolayers, ion pairs, and dipole-dipole complexes. In the crystalline state, the differences between pure enantiomers, racemic modifications, and diastereomeric complexes are clearly defined both structurally and energetically (32,33). At the other extreme, stereospecific interactions between diastereomerically related solvents and solutes, ion pairs, and other partially oriented systems are much less clearly resolved. 

One end of each surface-active molecule in a monolayer is anchored firmly to the Uquid surface by the attraction of the polar head group for the aqueous subphase, while the hydrophobic portion is displaced easily from it. If the molecules are separated widely as in a gaseous monolayer, the simple two-dimensional gas law is approached, namely, irA = kT, where k is the Boltzmann constant. The hydro-phobic chains are free to assume almost any orientation above the surface and may sweep out circles with radii as long as their tails by rotating around their point of attachment at the head group. However, intermolecular translational movements are restricted to the two-dimensional interfacial plane because the hydrophilic head groups cannot leave the aqueous surface. 

The primary evidence for the conversion of gaseous monolayers at the air-water interface to other intermediate states lies in the abrupt changes found on the n-A isotherms of many film-forming compounds. So many of these isotherms have been reproduced in fine detail in a number of laboratories under a variety of conditions that they cannot possibly be rejected wholesale as artifacts. The sharp transitions from curves to plateaus, where the molecular area varies readily at constant surface pressure, may be related... 

In the physisorption process a gas molecule interacts with several atoms at the surface of the solid. Once a monolayer of adsorbate molecules is formed the gaseous molecule interacts with a surface of the liquid or solid adsorbate. Therefore, the binding energy of the second layer of adsorbate molecules is similar to the latent heat of sublimation or vaporization of the adsorbate. 

From these descriptions, it is seen that the films may, under given experimental conditions, show three first-order transition states, such as (i) transition from the gaseous film to the liquid-expanded (Lex), (ii) transition from the liquid-expanded (Lex) to the liquid-condensed (Lco), and (iii) from Lex or Lco to the solid state if the temperature is below the transition temperature. The temperature above which no expanded state is observed has been found to be related to the melting point of the lipid monolayer. 

The reaction of solids occurs in the monolayer of molecules adsorbed on the surface of the solid B, as sketched in Figure 9-3. Therefore, this process can be regarded as a surface reaction with rate r", just hke the catalytic reactions of Chapter 7 except that now the molecules of the solid react with the gaseous molecules to form a gaseous product and remove solid molecules. The rate of the reaction should therefore be... 

Pacific Northwest National Laboratory (PNNL) is researching the use of self-assembled monolayers on mesoporous supports (SAMMS) technology for the removal of metals and radionuclides from liquid and gaseous hazardous wastes. SAMMS combines two technologies—mesoporous ceramic material and functionalized monolayers. The ceramic material has pores that increase its surface area. This ceramic material is coated with functionalized monolayers that form stable, covalent bonds with the contaminants. 

Numerical data are available from our earlier penetration work for a number of monolayer/surfactant systems. The simplest of these systems was selected for this initial analysis the penetration of cholesterol monolayers by hexadecyl-trimethyl-ammonium bromide (CTAB) J). Cholesterol monolayers at 298 K exhibit a single, highly incompressible, condensed phase with the transition to a gaseous phase occurring at a negligibly low surface pressure. CTAB does not appear to undergo surface hydrolysis (10) and the gaseous-to-expanded phase transition occurs at a low concentration (0.043 mmol kg ) and a low surface pressure (1.0 mN m l). 

The measurement of the equilibrium between the gaseous and the chemisorbed state is frequently difficult because of the very low equilibrium pressures required to saturate the surface. Often, in the case of strong interactions the monolayer is completed at very low pressures, even less than 1 torr, as shown in Fig. 19.1. 

Fig. 6. Surface-pressure/surface-area isotherm of an AA monolayer floating on an aqueous 5.0 x 10-4 M Pb(N03)2 solution at room temperature. Regions of gaseous (G), liquid (L), and solid (S) are indicated by arrows...

As evident from the above discussion, if measurements can be made at sufficiently low pressures, all monolayers will display gaseous behavior, represented by region G in Figure 7.6. The gaseous region is characterized by an asymptotic limit as n - 0. In the limit of very low film pressures, a two-dimensional equivalent to the ideal gas law applies ... 

It is not difficult to propose and develop a model for the gaseous state of insoluble monolayers. The arguments parallel those developed in kinetic molecular theory for three-dimensional gases and lead to equally appealing results. The problem, however, is that many assumptions of the model are far less plausible for monolayers than for bulk gases. To see this, a brief review of the derivation seems necessary. 

---