Spreading pressures, equilibrium

If equilibrium spreading pressure is to be included, it must be subtracted from the right hand side of Eq. 3, i.e. 

Determination of the equilibrium spreading pressure generally requires measurement and integration of the adsorption isotherm for the adhesive vapors on the adherend from zero coverage to saturation, in accord with the Gibbs adsorption equation [20] ... 

The question may then be raised as to whether insoluble monolayers may really be treated in terms of equilibrium thermodynamics. In general, this problem has been approached by considering (i) the equilibrium spreading pressure of the monolayer in the presence of the bulk crystalline surfactant, and (ii) the stability of the monolayer film as spread from solution. These quantities are obtained experimentally and are necessary in any consideration of film thermodynamic properties. In both cases, time is clearly a practical variable. 

The surface shear viscosity of a monolayer is a valuable tool in that it reflects the intermolecular associations within the film at a given thermodynamic state as defined by the surface pressure and average molecular area. These data may be Used in conjunction with II/A isotherms and thermodynamic analyses of equilibrium spreading to determine the phase of a monolayer at a given surface pressure. This has been demonstrated in the shear viscosities of long-chain fatty acids, esters, amides, and amines (Jarvis, 1965). In addition,... 

Enantiomeric recognition was clearly displayed in films spread from solution and films in equilibrium with their crystals, and was sharply dependent on the acidity of the subphase. Protonation of the amide group appeared to be necessary for spreading to stable monolayers. For example, the crystals of the racemate deposited on a 10n H2S04 solution at 25°C spread quickly to yield a film with an ESP of 7.7 dyn cm"1, while the single enantiomers spread only to a surface pressure of 3.9 dyn cm-1 (Table 1). Similar effects are observed at 15 and 35°C. The effect of stereochemistry on equilibrium spreading is even more pronounced at lower subphase acidities. On 6n sulfuric acid, the racemate spread to an equilibrium surface pressure of 4.9 dyn cm-1, while the enantiomeric systems spread to less than 1 dyn cm-1. 

Table 1 Equilibrium spreading pressures (ESPs) of racemic and optically pure N-(a-methylbenzyl)stearamides at various temperatures and subphase acidities.0 1 ... 

These results for spread film and equilibrium spreading suggest that films of racemic N-(a-methylbenzy 1) stearamide may be resolved by seeding the racemic film with crystals of either pure enantiomer. Indeed, when a monolayer of racemic jV- (a-methylbenzyl) stearamide is compressed to 45 A2/molecule (27 dyn cm-1), deposition of a crystal of either R( +)- or S( — )-enantiomer results in a decay of surface pressure from the initial 28 dyn cm-1 film pressure to 3.0 dyn cm-1, the ESP of the enantiomeric systems on a pure 10n sulfuric acid subphase (Table 1). When the experiment is repeated with racemic crystals, the system reaches an equilibrium surface pressure of 11 dyn cm-1, nearly the ESP of the racemic crystal on the clean acidic interface. In either case, equilibrium pressure is reached within a two hour time period. 

The Yl/A isotherms of the racemic and enantiomeric forms of DPPC are identical within experimental error under every condition of temperature, humidity, and rate of compression that we have tested. For example, the temperature dependence of the compression/expansion curves for DPPC monolayers spread on pure water are identical for both the racemic mixture and the d- and L-isomers (Fig. 13). Furthermore, the equilibrium spreading pressures of this surfactant are independent of stereochemistry in the same broad temperature range, indicating that both enantiomeric and racemic films of DPPC are at the same energetic state when in equilibrium with their bulk crystals. 

The instability of these chiral monolayers may be a reflection of the relative stabilities of their bulk crystalline forms. When deposited on a clean water surface at 25°C, neither the racemic nor enantiomeric crystals of the tryptophan, tyrosine, or alanine methyl ester surfactants generate a detectable surface pressure, indicating that the most energetically favorable situation for the interfacial/crystal system is one in which the internal energy of the bulk crystal is lower than that of the film at the air-water interface. Only the racemic form of JV-stearoylserine methyl ester has a detectable equilibrium spreading pressure (2.6 0.3dyncm 1). Conversely, neither of its enantiomeric forms will spread spontaneously from the crystal at this temperature. 

Table 5 Equilibrium spreading pressures of SSME and surface free energies, enthalpies, and entropies of spreading for the resulting film". 

Taken together, the equilibrium spreading pressures of films spread from the bulk surfactant, the dynamic properties of the films spread from solution, the shape of the Ylj A isotherms, the monolayer stability limits, and the dependence of all these properties on temperature indicate that the primary mechanism for enantiomeric discrimination in monolayers of SSME is the onset of a highly condensed phase during compression of the films. This condensed phase transition occurs at lower surface pressures for the R( —)- or S( + )-films than for their racemic mixture. 

Fig. 23 Equilibrium spreading pressures of (R,S)-( +)- and(R)-( +)-stearoyltyrosine on an aqueous subphase of pH 6.86 (potassium phosphate/disodium phosphate buffer) as a function of temperature. Film type II is the film at temperatures above the transition and film type I is the film at temperatures below the transition. Reprinted with permission from Arnett et al, 1990. Copyright 1990 American Chemical Society.

C temperature range. However, when spread from their bulk crystalline phases, the equilibrium spreading pressures of these films are clearly dependent on stereochemistry (Fig. 23) across the same temperature range. The conclusion that can be reached from these preliminary data is... 

In order to test the mechanism of recognition, equilibrium spreading pressures of both racemic and enantiomeric forms of SSME were obtained in pre-spread films of palmitic acid/SSME mixtures. The films were spread from solution and then compressed to their lift-off areas. A crystal of the racemic SSME was placed on surface film mixtures of the fatty acid with racemic SSME, and the enantiomeric crystals were placed on surface film mixtures of the fatty acid and enantiomeric SSME. The results of the equilibrations are given in Fig. 27. 

Fig. 27 Equilibrium spreading pressure versus film composition for crystals of palmitic acid and racemic and enantiomeric stearoylserine methyl ester deposited on palmitic acid/SSME monolayers (a) enantiomeric crystals on enantiomeric SSME/palmitic acid films (b) racemic crystals on racemic SSME/palmitic acid films (c) palmitic acid crystals on either racemic or enantiomeric SSME/palmitic acid films.

Table 12 shows the equilibrium spreading pressures of each diacid. It is immediately apparent that for three of the diastereomeric pairs there are statistically significant differences. These distinctions relate stereochemical preferences in the spontaneous spreading of (+)- versus meso-monolayers in equilibrium with their respective crystalline phases. However, there appears to be no discernible trend in either the ( )- or meso-ESPs as a function of carbonyl position despite clear trends seen in their monolayer properties in the absence of any bulk crystalline phase. 

Table 14 Equilibrium spreading pressures IF and surface excess free energies, entropies, and enthalpies of spreading for first and second eluting C-15 6,6 -A amide diacids. 

The detached amounts of cadmium octadecanoate LB films at the water surface with various temperatures are shown in Figure 18. The detached amount increased linearly with increasing the subphase temperature. The detachment of LB films is concerned with equilibrium spreading pressure (ESP), which represents the equilibrium between bulk lipid crystals and a lipid monolayer on the water surface [45]. ESPs... 

Figure 10. Development of equilibrium spreading pressure of film spread from pure crystals. Film pressure is measured on a Langmuir balance with barriers stationary. From Thompson (101).

Equilibrium spreading pressures, like static surface tension measurements, provide a means to determine surface energies under equilibrium conditions. On lOA H2SO4, racemic crystals (Fig. 10) spread within 5 min to an equilibrium pressure of 8.6 dynes/cm, whereas about 8 hr was required by either (i )-(+)- or (5)-(-)- crystals to spread to a final pressure of 5.5 dynes/cm. 

Given such evidences of nonthermodynamic behavior of compressed monolayers, it was important to test film stability at various points along the ir-A isotherms for the normal rate of slow compression. The racemic film maintained a steady film pressure over at least 10 min after the barrier drive was stopped, showing little or no tendency to relax from the compressed state to one of lower energy. The enantiomer film in contrast showed a tendency to relax steadily from a compressed metastable state to a more stable and better packed condition approaching the equilibrium spreading pressure. 

A racemic film was compressed nearly to its collapse point. It was then seeded by sprinkling crystals of pure enantiomeric amide on the surface. A rapid decrease in surface pressure was observed approaching the equilibrium spreading pressure of the enantiomer. A control experiment in which racemic crystals were sprinkled on the compressed racemic film produced a pressure drop that slowly approached, but did not reach, the ESP of the racemic film. The observed behavior was consistent with what would be expected if the enantiomer seed crystals had removed molecules of the same enantiomer from the racemic film, leaving a monolayer composed mainly of molecules of the opposite configuration. 

Figure 30 presents the n-A isotherms for the PBA brushes spread on water. Compression of the PBA brushes was fully reversible as expected for equilibrium spreading. The isotherms can be divided onto three characteristic regions. In region I the pressure onset occurred at a surface area of about 35 A /BA-mo-nomer. Linear extrapolation of the isotherm to zero pressure gave the area Aq = 28 1 A, consistent to a monomer area of 27 A measured for linear PBA [172]. The pressure in the plateau region III tt = 21 mN/m was similar to that of linear PBA (22 mN/m). The values indicate that practically all BA monomer units are in contact with the water surface, whereby the butyl tails are oriented towards air perpendicular to the surface. In between the expanded and the... 

It is important to remember the significance of irv. It refers specifically to the equilibrium between two surface states. There is a danger of confusing ttv with the equilibrium spreading pressure ire, introduced in Chapter 6. The latter is the pressure of the equilibrium film that exists in the presence of excess bulk material on the surface. It is the equilibrium spreading pressure that is involved in the modification of Young s equation (Equation (6.49)), for which a bulk phase is present on the substrate. For tetradecanol at 15°C, the equilibrium spreading pressure is about 4.5 10 2 N m so ire and irv are very different from one another. 

Because of the near linearity of these portions of the isotherm, it is easy to extrapolate both regions to their value at ir = 0. The intercepts for the solid and liquid-condensed regions, as and o c, respectively, differ only slightly. Values of a°c for alcohols are about 0.22 nm2, and for carboxylic acids about 0.25 nm2, more or less independent of the length of the hydrocarbon chain. The intercept as° has a value of about 0.20 nm2, independent of both the length of the chain and the nature of the head. The film pressures in the condensed states (LC or S) are of the same magnitude as the equilibrium spreading pressure for amphipathic molecules. 

Additional compression eventually leads to the collapse of the film. The pressure nc at which this occurs is somewhere in the vicinity of the equilibrium spreading pressure. Figure 7.7 represents schematically how this film collapse may occur. The mode of film buckling shown in Figure 7.7 is not the only possibility head-to-head as well as tail-to-tail configurations can be imagined. The second structure strongly resembles that of cell membranes, which we discuss in the next chapter. 

The equilibrium thermodynamic functions describing the retention process are essentially related to the net retention volume. For example, the intermolecular adsorption of Gibbs free energy, —AGa, for one mole of solute vapor from a reference gaseous state with the partial pressure, Po, to a reference adsorbed state with the equilibrium spread pressure (or two-dimensional pressure), no, is given as [115]... 

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