Area per molecule

If the surface tension of a liquid is lowered by the addition of a solute, then, by the Gibbs equation, the solute must be adsorbed at the interface. This adsorption may amount to enough to correspond to a monomolecular layer of solute on the surface. For example, the limiting value of in Fig. Ill-12 gives an area per molecule of 52.0 A, which is about that expected for a close-packed... 

The material of interest is dissolved in a volatile solvent, spread on the surface and allowed to evaporate. As the sweep moves across, compressing the surface, the pressure is measured providing t versus the area per molecule, a. Care must be taken to ensure complete evaporation [1] and the film structure may depend on the nature of the spreading solvent [78]. When the trough area is used to calculate a, one must account for the area due to the meniscus [79]. Barnes and Sharp [80] have introduced a remotely operated barrier drive mechanism for cleaning the water surface while maintaining a closed environment. 

A film at low densities and pressures obeys the equations of state described in Section III-7. The available area per molecule is laige compared to the cross-sectional area. The film pressure can be described as the difference in osmotic pressure acting over a depth, r, between the interface containing the film and the pure solvent interface [188-190]. 

Barnes and Hunter [290] have measured the evaporation resistance across octadecanol monolayers as a function of temperature to test the appropriateness of several models. The experimental results agreed with three theories the energy barrier theory, the density fluctuation theory, and the accessible area theory. A plot of the resistance times the square root of the temperature against the area per molecule should collapse the data for all temperatures and pressures as shown in Fig. IV-25. A similar temperature study on octadecylurea monolayers showed agreement with only the accessible area model [291]. 

Fig. IV-25. The evaporation resistance multiplied by the square root of temperature versus area per molecule for monolayers of octadecanol on water illustrating agreement with the accessible area model. (From Ref. 290.)...

The most common situation studied is that of a film reacting with some species in solution in the substrate, such as in the case of the hydrolysis of ester monolayers and of the oxidation of an unsaturated long-chain acid by aqueous permanganate. As a result of the reaction, the film species may be altered to the extent that its area per molecule is different or may be fragmented so that the products are soluble. One may thus follow the change in area at constant film pressure or the change in film pressure at constant area (much as with homogeneous gas reactions) in either case concomitant measurements may be made of the surface potential. 

For adsorption on Spheron 6 from benzene-cyclohexane solutions, the plot of N N2/noAN2 versus N2 (cyclohexane being component 2) has a slope of 2.3 and an intercept of 0.4. (a) Calculate K. (b) Taking the area per molecule to be 40 A, calculate the specific surface area of the spheron 6. (c) Plot the isotherm of composition change. Note Assume that is in millimoles per gram. 

A drop of a dilute solution (1%) of an amphiphile in a solvent is typically placed on tlie water surface. The solvent evaporates, leaving behind a monolayer of molecules, which can be described as a two-dimensional gas, due to tlie large separation between tlie molecules (figure C2.4.3). The movable barrier pushes tlie molecules at tlie surface closer together, while pressure and area per molecule are recorded. The pressure-area isotlienn yields infonnation about tlie stability of monolayers at tlie water surface, a possible reorientation of tlie molecules in tlie two-dimensional system, phase transitions and changes in tlie confonnation. Wliile being pushed togetlier, tlie layer at... 

Figure C2.4.3. Pressure-area isotlienn for a fatty acid. The molecules are in a gaseous, liquid or solid state, depending on tire area per molecule available. If tire pressure is furtlier increased, a mechanical instability occurs and tire film breaks down.

The monolayer resulting when amphiphilic molecules are introduced to the water—air interface was traditionally called a two-dimensional gas owing to what were the expected large distances between the molecules. However, it has become quite clear that amphiphiles self-organize at the air—water interface even at relatively low surface pressures (7—10). For example, x-ray diffraction data from a monolayer of heneicosanoic acid spread on a 0.5-mM CaCl2 solution at zero pressure (11) showed that once the barrier starts moving and compresses the molecules, the surface pressure, 7T, increases and the area per molecule, M, decreases. The surface pressure, ie, the force per unit length of the barrier (in N/m) is the difference between CJq, the surface tension of pure water, and O, that of the water covered with a monolayer. Where the total number of molecules and the total area that the monolayer occupies is known, the area per molecules can be calculated and a 7T-M isotherm constmcted. This isotherm (Fig. 2), which describes surface pressure as a function of the area per molecule (3,4), is rich in information on stabiUty of the monolayer at the water—air interface, the reorientation of molecules in the two-dimensional system, phase transitions, and conformational transformations. 

The plateaus ia the isotherm, where pressure does not change and area per molecule decreases, iadicates an increasing orientational order. 

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... 

Bilayers have received even more attention. In the early studies, water has been replaced by a continuous medium as in the monolayer simulations [64-67]. Today s bilayers are usually fully hydrated , i.e., water is included exphcitly. Simulations have been done at constant volume [68-73] and at constant pressure or fixed surface tension [74-79]. In the latter case, the size of the simulation box automatically adjusts itself so as to optimize the area per molecule of the amphiphiles in the bilayer [33]. If the pressure tensor is chosen isotropic, bilayers with zero surface tension are obtained. Constant... 

Static Involving Use of Adsorption Isotherms BRUNAUER, EMMETT, AND TELLER (B.E.T.). In this method tire surface area is not measured directly, but the number of molecules of the adsorbed substance required to give a monolayer (N) is determined. If the mean area per molecule (a) of the adsorbed substance is known by other means, the area of the solid may... 

Alkyl chain Ether units Area per molecule (A2) T(°Q Ref. 

C,4—C20 AOS surfactants were laboratory-prepared by Tuvell et al. [2]. Table 3 shows the CMC values of these single-carbon-cut AOS surfactants and of reference compounds, their areas per molecule at the water-air interface inferred from plots of surface tension vs. In (concentration), and the surface tension at the CMC, all at 23°C. The area of the molecule is proportional to the equilibrium adsorptivity, which in turn is taken as a comparative measure of the surface activity of the molecule. Tuvell et al. [2] argue that the greater the... 

Initially, the compression does not result in surface pressure variations. Molecnles at the air/water interface are rather far from each other and do not interact. This state is referred to as a two-dimensional gas. Farther compression results in an increase in snrface pressure. Molecules begin to interact. This state of the monolayer is referred as two-dimensional liquid. For some compounds it is also possible to distingnish liqnid-expanded and liquid-condensed phases. Continnation of the compression resnlts in the appearance of a two-dimensional solid-state phase, characterized by a sharp increase in snrface pressure, even with small decreases in area per molecule. Dense packing of molecnles in the mono-layer is reached. Further compression results in the collapse of the monolayer. Two-dimensional structure does not exist anymore, and the mnltilayers form themselves in a non-con trollable way. 

TABLE 6 Surface Density and Area per Molecule of Cytochrome P450scc wild type and Recombinant in LB Film Deposited onto Solid Substrate... 

FIG. 29 Oxygen-transfer rate constants derived from Fig. 28 as a function of the reciprocal of the interfacial area per molecule. (Reprinted from Ref 19. Copyright 1998 American Chemical Society.)... 

Harkins et al., 1940), where ne is the ESP, and Ae is the average area per molecule at the ESP as obtained from the 11/ 4 isotherm of the spread film. The temperature dependence of the ESP may then be used to calculate the excess surface entropies from (5) and enthalpies of spreading from (6). 

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