Surface pressure versus area isotherms

Figure 1. Surface pressure versus area isotherm for a long-chain fatty acid material.

The material in this chapter is organized broadly in two segments. The topics on monolayers (e.g., basic definitions, experimental techniques for measurement of surface tension and sur-face-pressure-versus-area isotherms, phase equilibria and morphology of the monolayers, formulation of equation of state, interfacial viscosity, and some standard applications of mono-layers) are presented first in Sections 7.2-7.6. This is followed by the theories and experimental aspects of adsorption (adsorption from solution and Gibbs equation for the relation between... 

Fig. 3.17 Surface pressure versus area per molecule isotherm for a long-chain organic compound. The surface pressure and area are in arbitrary units [a.u]. (From ref. [38])...

Figure 10.2 Surface pressure versus area per molecule isotherm of arachidic acid on a subphase of ZnS04 at pH = 5.6 and T = 25 C. The drawings on the right are a...

To form a Langmuir monolayer, the molecule of interest is dissolved in a volatile organic solvent (frequently chloroform or hexane) that will not react with or dissolve in the subphase (1,2,4). A quantity of this solution is placed on the surface of the subphase, and as the solvent evaporates, the siuTactant molecules spread and alter the surface pressure of the water surface. A barrier designed to measure this surface pressure (D), relative to that of the pin-e subphase, is the principle behind the Langmuir balance. Alternatively, the siuTace pressure is measured as the difference between the surface tension (y) of the monolayer and that of the pure subphase iyo), n = yo — K- A common method for measining surface tension involves using a Wilhelmy plate, usually a piece of platimun or paper that is wetted by the subphase, suspended from a balance. As the monolayer is compressed by using the moveable barrier to reduce the sinface area, the surface pressure increases. A plot of the siuTace pressin-e versus surface area is called a pressure versus area isotherm (or Il-A isotherm). Isotherms are normally plotted in terms of area/molecule, and the imits of surface pressure are mN/m. 

The experimentally estimated k2 value (= 0s tr[Os(II)]// ru) (36X107 s-1) for the A- Ru(II)/A-Os(II) pair is much larger than that (8.5 X 107 s-1) for the A- Ru(II)/A-Os(II) pair. This result is consistent with the chirality effect on the surface pressure versus molecular area (tt-A) isotherms, in which the A-ruthen-ium(II) complex forms a more compact monolayer than the racemic mixture of the ruthenium(II) complex in other words, the racemic mixture induces some steric repulsion between A- and A-ruthenium(II) complexes. 

Figure 4.33. Typical surface pressure versus molecular area (n-A) isotherms...

Chart 4.1 shows stearic acid, a molecule in which 16 CH2 groups form a long hydrophobic chain. The other end of the molecule terminates in a hydrophilic carboxylic acid group. When dissolved in a suitable solvent and spread on the surface of water, molecules may be compressed with the aid of a barrier. Figure 4.1 shows a plot of the surface pressure (differential surface tension) versus area occupied per molecule for stearic acid. The monolayer undergoes a number of phase transformations during compression the well-defined sequence can be viewed as the two-dimensional analogue of the classical transitions observed with pressure-volume isotherms. 

While the barrier confines the amphiphiles to a smaller area, the force exerted by the monolayer is continuously measured and a surface pressure (I7)-area (A) isotherm can be drawn at a constant temperature. This curve plots the surface pressure (force per unit length) versus the mean molecular area occupied by the amphiphiles at the air/water interface. Usually, a U-A isotherm shows four interesting regions [21]. An initial horizontal region where the mean molecular area is large and the interaction between molecules is small so the surface pressure is approximately constant. The first linear region deviates from the... 

A nanoparticulate Ti02-stearate (Ti02-St) monolayer was obtained directly using Ti02 hydrosol as the subphase. The surface pressure versus surface area isotherm showed that the monolayer could be compressed to a mean molecular area of 0.25 nm The monolayer was transferred onto hydrophobic and hydrophilic /i-type, p-type Si substrates at a dipping speed of 18 cm/min under a surface pressure of 25 mN/m. The transfer ratio was 1.0 0.1. The transmission electron microscopic (TEM) images of TiOi-stearate monolayers showed relatively densely... 

A second example involves reflectance infrared spectroscopic structural analysis of polydimethylsiloxane at the air-water interface. Surface pressure versus surface area or surface concentration isotherms of polydimethylsiloxane on water have been studied since 1947 at least (223). Upon compression, the isotherm begins at zero surface pressure at surface concentrations significantly below 0.75 mg/m. Around f 1 0.75 mg/m, the surface pressure tt jumps substantially to about 9 mN/m, where it exhibits a plateau until about T2 1.6 mg/m, where a small Tt jump occurs followed by a smaller rise (Fig. 31). Structural features associated with the various transitions have often been debated. Particular controversy is associated with the ix plateau aroimd 9 mN/m between Fi and T2 (224,225). In conjimction with other techniques, such as epifluorescence microscopy, external reflectance infrared spectroscopy was used to study microstructural features (coexistence of two phases) of polydimethylsiloxane CH3—[Si(CH3)2—Oln—SKCHala, spread at the air-water interface in the vicinity of the n plateau at 9 mN/m (226). A broad band containing several components is foimd in the 1000-1100 cm ... 

Traditional amphiphiles contain a hydrophilic head group and the hydrophobic hydrocarbon chain(s). The molecules are spread at molecular areas greater (-2-10 times) than that to which they will be compressed. The record of surface pressure (II) versus molecular area (A) at constant temperature as the barrier is moved forward to compress the monolayer is known as an isotherm, which is analogous to P-V isotherms for bulk substances. H-A isotherm data provide information on the molecular packing, the monolayer stability as de-... 

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... 

Fig. 4 Idealized surface pressure n versus area A isotherm detailing the inferred molecular orientation and aggregation states during a compression cycle. Reprinted with permission from Arnett et al, 1989. Copyright 1989 American Chemical Society.

Figure 17 shows the 11/A isotherms of racemic and enantiomeric films of the methyl esters of 7V-stearoyl-serine, -alanine, -tryptophan, and -tyrosine on clean water at 25°C. Although there appears to be little difference between the racemic and enantiomeric forms of the alanine surfactants, the N-stearoyl-tyrosine, -serine, and -tryptophan surfactants show clear enantiomeric discrimination in their WjA curves. This chiral molecular recognition is first evidenced in the lift-off areas of the curves for the racemic versus enantiomeric forms of the films (Table 2). As discussed previously, the lift-off area is the average molecular area at which a surface pressure above 0.1 dyn cm -1 is first registered. The packing order differences in these films, and hence their stereochemical differentiation, are apparently maintained throughout the compression/expansion cycles. 

It is found that, even a monolayer of lipid (on water), when compressed can undergo various states. In the following text, the various states of monomolecular films will be described as measured from the surface pressure, n, versus area, A, isotherms, in the case of simple amphiphile molecules. On the other hand, the Il-A isotherms of biopolymers will be described separately since these have a different nature. 

Surface pressure/area isotherms of mixtures of the cationic lipid (20, n = 12) with distearoylphosphatidylcholine (DSPC) are shown in Fig. 30. For all mixtures only one collapse point is observed. The collapse pressure increases continuously with increasing amount of DSPC, indicating miscibility of the two components. Plotting A versus molar ratio (Fie. 3D results in considerable deviation from linearity, which also suggests miscibility of the two compounds in monolayers. This is also confirmed by the fact that the polymerization rate, as measured by the increase of optical density at 540 nm, is reduced by a factor of 100 when the DSPC molar ratio is increased from 0 to 0.52,... 

Example 13.4. The result of a typical X-ray measurement is shown in Fig. 13.10 for a galactocerebroside [605], The plot on the left side shows the normalized reflected X-ray beam intensity versus the incident angle a for two different film pressures. The pressure-area isotherm is shown in the inset, together with the points of measurement a and b. On the right side are the extracted electron density profiles normal to the film surface taken at the same film pressures. At 0 A we find the monolayer surface (top of the alkyl chains), a depth of -40 A corresponds to pure water. In between is the film. The measurement is so sensitive that we even find two different electron densities within the monolayer. This is illustrated by the dashed boxes denoted by film 1 and film 2 (shown for curve b only) which represents the simplified electron density distribution in the so-called two-box model. A box is defined as a part in the film of a certain thickness where the electron density is constant. In the two-box model the film is divided into two layers. Film 1 represents the hydrocarbon tails, film 2 corresponds to the mean electron density of the head groups. 

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