Surface pressure-area curves

The clearest results were obtained with the normal, saturated fatty acids and alcohols. These formed stable films, which would stand considerable compression laterally, and (at room temperature on distilled water) gave a very clearly marked critical area at which the surface pressure first appeared, this point being of course Pockels s critical point of the first diminution of surface tension. As the area was reduced from large initial areas no surface pressure could be detected until the area had reached about 22 sq. A. per molecule and at 20 5 sq. A. the pressure increased very rapidly indeed with further increase of pressure. The curve I of Fig. 15 shows the relation between surface pressure and area per molecule, which is obtained with accurate apparatus for the fatty acids on water curve III is that obtained with the alcohols.3... 

The thermographic activity on the pressure vessel was carried out considering a part of it because of the axial symmetry. Three different partially overlapping area were inspected since it was optically impossible to scan the curved surface of the pressure vessel by a single sweep. The selected areas are shown in fig.7 and the correspondent positions of the thermographic scan unit are also illustrated. The tests were performed with a load frequency of 2, 5 and 10 Hz. 

Fig. IV-21. Surface pressure versus area for monolayers of immiscible components a monolayer of pure cadmium arachidate (curve 1) and monolayers of mixed merocyanine dye, MC2, and cadmium arachidate of molar ratio r = 1 10 (curve 2) 1 5 (curve 3), 1 2 (curve 4), and pure MC2 (curve 5). The subphase is 2.5 x 0 M CdC, pH = 5.5 at 20°C. Curve 3a (O) was calculated from curves 1 and 5 using Eq. IV-44. (From Ref. [116].)...

The force exerted on a submerged planar surface of area A is given by F = p A where p is the pressure at the geometrical centroid of the surface. The center of pressure, the point of application of the net force, is always lower than the centroid. For details see, for example. Shames, where may also be found discussion of forces on curved surfaces, buoyancy, and stability of floating bodies. 

FIG. 23 Surface pressure vs. area/molecule isotherms at 300 K from molecular dynamics simulations of Karaborni et al. (Refs. 362-365). All are for hydrocarbon chains with carboxylate-like head groups, (a) (filled squares) A 20-carbon chain, (b) (filled circles) A 16-carbon chain with a square simulation box the curve is shifted 5 A to the right, (c) (open squares) A 16-carbon chain with a nonsquare box with dimensions in the ratio xly = (3/4) to fit a hexagonal lattice the curve is shifted 5 A to the right. (Reproduced with permission from Ref. 365. Copyright 1993 American Chemical Society.)... 

Salts of fatty acids are classic objects of LB technique. Being placed at the air/water interface, these molecules arrange themselves in such a way that its hydrophilic part (COOH) penetrates water due to its electrostatic interactions with water molecnles, which can be considered electric dipoles. The hydrophobic part (aliphatic chain) orients itself to air, because it cannot penetrate water for entropy reasons. Therefore, if a few molecnles of snch type were placed at the water surface, they would form a two-dimensional system at the air/water interface. A compression isotherm of the stearic acid monolayer is presented in Figure 1. This curve shows the dependence of surface pressure upon area per molecnle, obtained at constant temperature. Usually, this dependence is called a rr-A isotherm. 

At the curved surface of the sphere, a force is acting that is directed toward the center of the sphere and tends to reduce its surface area. Hence, the gas pressure in the nucleus will be higher than the pressure Pq in the surrounding medium. An infinitely small displacement dr of tfie surface in the direction of the sphere s center is attended by a surface-area decrease dS = Snrdr) and a volume decrease dV (= dr). The work of compression of the nucleus is given by (Pnuci It... 

The results of this study demonstrated that the rate of oxygen transfer across a clean air-water interface was diffusion-controlled on the time scale of SECM measurements. The rate of this transfer process was, however, significantly reduced with increasing compression of a 1-octadecanol monolayer. Figure 28 illustrates this point, showing approach curves for O2 reduction recorded with the monolayer at different surface pressures. The transfer rate was found to depend on the accessible free area of the interface, as described by the following equation ... 

We studied the surface pressure area isotherms of PS II core complex at different concentrations of NaCl in the subphase (Fig. 2). Addition of NaCl solution greatly enhanced the stability of monolayer of PS II core complex particles at the air-water interface. The n-A curves at subphases of 100 mM and 200 mM NaCl clearly demonstrated that PS II core complexes can be compressed to a relatively high surface pressure (40mN/m), before the monolayer collapses under our experimental conditions. Moreover, the average particle size calculated from tt-A curves using the total amount of protein complex is about 320 nm. This observation agrees well with the particle size directly observed using atomic force microscopy [8], and indicates that nearly all the protein complexes stay at the water surface and form a well-structured monolayer. 

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. 

Mixtures of N-(a-methylbenzyl) stearamides with both stearoyltyrosine and stearoyltryptophan methyl esters show no discrimination in their pressure-area relationships at 35°C, regardless of the surface pressure to which the films are compressed (Fig. 34). The Yl/A curves for homo- and hetero-chiral pairs are exactly coincident. 

Furthermore, we employ the same assumptions to describe a different set of hysteresis experiments a monolayer with surface pressure it at equilibrium is subjected to expansion at a constant speed of v cm /sec. The theoretical curves of surface pressure are plotted against area for various q-values in Figure 4. The curves show that the reduction of surface pressure decreases when the expansion rate is decreased for a given mono-layer, i.e. as q becomes more negative. In Figure 5, curves are plotted for q = -2 with the two different modes initial compression and initial expansion. Because the theoretical curves of the second and subsequent cycles in both modes almost coincide, we can expect that the surface pressure vs. area curves will be independent of how the hysteresis experiment starts after about two initial cycles. 

Figure 6 shows the effects of compression rate on the ji-A curve for the PhDA2-8 thin film at air/water interface. Accompanied with the increase in the compression rate, the hump becomes more significant and the maximum surface pressure of the hump shifts toward the larger surface area. It is to be noted that the region with zero surface pressure appears only with appropriate compression rates of 3 - 7.5 (A2/molecule)/min as in (d), (e), and (f). 

Figure 17. (A) Time trace of surface pressure with periodic change of the surface area for the DOPC thin film at an air/water interface. (B) Dynamic it-A curve. After two or three cycles, the curve begins to trace a single closed loop.

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 ... 

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... 

The monolayer behavior of A-stearoyltyrosine (Fig. 16) was more complex. Under conditions (0.0liV HCl, 22 C) where the racemic material formed a condensed film having a limiting molecular area of 39 2 A, the force-area curve of L-(+)-A-stearoyltyrosine exhibited a liquid-expanded film at large areas (ca. 100-45 per molecule) followed by a transition beginning at 16.5 dynes/cm surface pressure to a condensed phase having a smaller limiting molecular area of 34 2 A . However, both these latter samples exhibited only the liquid-expanded phase on distilled water alone. 

The force-area curves for racemic and (5)-(+)-2-tetracosanyl acetate recorded with a barrier speed of 5 cm/min are shown in Figures 17 and 18, respectively. Again, both enantiomers showed identical monolayer behavior. The film balance behavior of the racemic acetate was indistinguishable from that of the pure enantiomers at temperatures above about 27°C however, below this temperature the force-area curves differed markedly even at low surface pressures, which indicates that racemic compound formation occurs at relatively large areas per molecule. 

In Figure 2 the ir-A and AV-A plots for SODS on O.OIM NaCl sub-solutions having different pH values are shown. In all cases, phase transitions from liquid-expanded to liquid-condensed state are evident ( ). Acidification of the subsolution Increases the transition pressure but the transition is less pronounced at the lowest pH studied. This is also accompanied by an expansion of the condensed part of the curve. Small negative surface potentials are observed over most areas. The highest potential is obtained for film spread on the pH 2.2 subsolution. For small areas, the surface potential attains a positive value. This may be related to reorientation of the dipole moments of the molecules which occur once a threshold surface concentration is exceeded (O. Mlnglns and Pethlca (7) studied the monolayer properties of SODS on various sodium chloride solutions (0.1, 0.01 and O.OOIM) at 9.5 C, and they showed that the monolayer is only stable on the more concentrated salt solutions (0.1 and O.OIM). In this work, no noticeable... 

At high surfactant concentrations the surface pressure - area curves tend towards the surface pressures of the pure surfactant i(AII -r 0). Thus the integrals in equation 15 appear to be zero for > 1.4 nm2 molecule" and the adsorptions are then equal to the adsorptions for the monolayer-free system. In contrast, the Pethica equation at this area still imposes a significant correction factor on the adsorption the slope (3II/3 Inmg) for Am = 1.4 nm molecule" equals that for the monolayer-free system but (2m-2m)/... 

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