Spreading pressure

The spreading pressure, n, is normally defined as the negative value of the surface tension. One may utilize the x theory to obtain n in terms of 

Using the fact that RTd In P=d one may substitute into the Gibbs- Duhem 

At this point there are two integrations (see the article A [21], which is the same as here except that it is expressed in terms of x) that can be performed. If the reference is the hquid state as is required for excess surface work then 

It is usually conceded that 7r0=O (or 7t=0 when n d=0 as Eq. (154) would then imply). This implies that % =EJfA.  

The relationship to the disjoining pressure and excess surface work may be also derived. 

When positive adsorption takes place at the solution surface, it lowers the surface tension of the pure solvent, y0, and the surface tension of the solution, y, can be determined experimentally. If the solution is dilute, then yean also be calculated from the Gibbs adsorption equation (Equation 224). The spreading pressure (or surface pressure), n, is defined as the decrease in the surface tension with the presence of an adsorbed monolayer 

The Helmholtz surface free-energy change due to the formation of a monolayer is the difference between the Helmholtz free energy of the pure solvent surface and that of the solution surface (ymonola) er = FS- Ps0). The Helmholtz free energy at the surface was defined 

If the Gibbs convention is also adopted so that the Gibbs dividing plane is located such that the surface excess of the water sub-phase is zero ( w = 0), we may then write 

Equation (427) shows that when no monolayer is present over the water surface ( = 0), there is only pure water and we may write, = yAs- Then, the Helmholtz surface free energy due to the presence of a monolayer may be given as 

When Equation (428) is combined with Equation (424) we have 

In the thermodynamic discussion of bulk phases the fundamental differential equation which summarizes the first and second law of thermodynamics may be written 

Integration of this equation, holding the intensive variables 7, P, and p constant yields 

If we consider the adsorbed phase as a solution of n, moles of sorbale and moles of nonvolatile adsorbent, Eq. (3.15) becomes 

It is evident that represents the change in internal energy per unit of adsorbent due to the spreading of the adsorbate over the surface or through the micropore volume of the adsorbent. For adsorption on a two-dimensional surface, the surface area is directly proportional to while for adsorption in a three-dimensional microporous adsorbent the micropore volume T is proportional to n . We may therefore write 

Defined in this way v corresponds to the difference in surface tension between a clean surface and a surface covered with adsorbate. 

---

Equations of state are also used for pure components. Given such an equation written in terms of the two-dimensional spreading pressure 7C, the corresponding isotherm is easily determined, as described later for mixtures [see Eq. (16-42)]. The two-dimensional equivalent of an ideal gas is an ideal surface gas, which is described by... 

Equation (16-36) with y = 1 provides the basis for the ideal adsorbed-solution theoiy [Myers and Prausnitz, AIChE J., 11, 121 (1965)]. The spreading pressure for a pure component is determined by integrating Eq. (16-35) for a pure component to obtain... 

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] ... 

Rowley H.H. and Innes W.B. Relationship between the spreading pressure, adsorption and wetting. 1942. 

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. 

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

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. 

---