Pressure films

Such a monolayer may be considered to exert a film pressure ir, such that... 

The deviation of Gibbs monolayers from the ideal two-dimensional gas law may be treated by plotting xA// 7 versus x, as shown in Fig. III-15c. Here, for a series of straight-chain alcohols, one finds deviations from ideality increasing with increasing film pressure at low x values, however, the limiting value of unity for irAfRT is approached. 

Data for equilibrium film pressures on mercury are from Ref. 11. 

Spreading velocities v are on the order of 15-30 cm/sec on water [39], and v for a homologous series tends to vary linearly with the equilibrium film pressure, it", although in the case of alcohols a minimum seemed to be required for v to be appreciable. Also, as illustrated in Fig. IV-3, substrate water is entrained to some depth (0.5 mm in the case of oleic acid), a compensating counterflow being present at greater depths [40]. Related to this is the observation that v tends to vary inversely with substrate viscosity [41-43]. An analysis of the stress-strain situation led to the equation... 

If the spreading is into a limited surface area, as in a laboratory experiment, the film front rather quickly reaches the boundaries of the trough. The film pressure at this stage is low, and the now essentially uniform film more slowly increases in v to the final equilibrium value. The rate of this second-stage process is mainly determined by the rate of release of material from the source, for example a crystal, and the surface concentration F [46]. Franses and co-workers [47] found that the rate of dissolution of hexadecanol particles sprinkled at the water surface controlled the increase in surface pressure here the slight solubility of hexadecanol in the bulk plays a role. 

The film pressure is defined as the difference between the surface tension of the pure fluid and that of the film-covered surface. While any method of surface tension measurement can be used, most of the methods of capillarity are, for one reason or another, ill-suited for work with film-covered surfaces with the principal exceptions of the Wilhelmy slide method (Section II-6) and the pendant drop experiment (Section II-7). Both approaches work very well with fluid films and are capable of measuring low values of pressure with similar precision of 0.01 dyn/cm. In addition, the film balance, considerably updated since Langmuir s design (see Section III-7) is a popular approach to measurement of V. 

This method suffers from two disadvantages. Since it measures 7 or changes in 7 rather than t directly, temperature drifts or adventitious impurities can alter 7 and be mistakenly attributed to changes in film pressure. Second, while ensuring that zero contact angle is seldom a problem in the case of pure liquids, it may be with film-covered surfaces as film material may adsorb on the slide. This problem can be a serious one roughening the plate may help, and some of the literature on techniques is summarized by Gaines [69]. On the other hand, the equipment for the Wilhelmy slide method is simple and inexpensive and can be just as accurate as the film balance described below. 

Film pressure is often measured directly by means of a film balance. The principle of the method involves the direct measurement of the horizontal force on a float separating the film from clean solvent surface. The film balance has been considerably refined since the crude model used by Langmuir and in many... 

While the canal viscometer provides absolute viscosities and the effect of the substrate drag can be analyzed theoretically, the shear rate is not constant and the measurement cannot be made at a single film pressure as a gradient is required. Another basic method, more advantageous in these respects, is one that goes back to Plateau... 

Figure IV-10 illustrates how F may vary with film pressure in a very complicated way although the v-a plots are relatively unstructured. The results correlated more with variations in film elasticity than with its viscosity and were explained qualitatively in terms of successive film structures with varying degrees of hydrogen bonding to the water substrate and varying degrees of structural regularity. Note the sensitivity of k to frequency a detailed study of the dispersion of k should give information about the characteristic relaxation times of various film structures.

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]. 

The alternative approach is to treat the film as a nonideal two-dimensional gas. One may use an appropriate equation of state, such as Eq. Ill-104. Alternatively, the formalism has been developed for calculating film activity coefficients as a function of film pressure [192]. 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

Fig. IV-20. Film pressure-area plots for cerebronic acid (a long-chain a-hydroxy carboxylic acid) and cholesterol (see insert) and for an equimolar mixture. At low pressures the r-a plot is close to that of the average (dashed line), an unanticipated kink then appears, and finally, the horizontal portion probably represents ejection of the cholesterol. (From Ref. 239.)...

Fig. IV-22. Excess free energy of mixing of condensed films of octadecanol-docosyl sulfate at 25°C, at various film pressures. Top curve t = 5 dyn/cm bottom curve ir = 50 dyn/cm intermediate curves at 5-dyn/cm intervals. The curves are uncorrected for the mixing term at low film pressure. (From Ref. 246.)...

Some fairly typical results, obtained by LaMer and co-workers [275] are shown in Fig. IV-24. At the higher film pressures, the reduction in evaporation rate may be 60-90%—a very substantial effect. Similar results have been reported for the various fatty acids and their esters [276,277]. Films of biological materials may offer little resistance, as is the case for cholesterol [278] and dimyristoylphosphatidylcholine (except if present as a bilayer) [279]. 

The study of reactions in monomoiecuiar films is rather interesting. Not only can many of the usual types of chemical reactions be studied but also there is the special feature of being able to control the orientation of molecules in space by varying the film pressure. Furthermore, a number of processes that occur in films are of special interest because of their resemblance to biological systems. An early review is that of Davies [298] see also Gaines [1]. 

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. 

Case 1. A chemical reaction occurs at constant film pressure. To the extent that area is an additive property, one has... 

Because mole numbers are additive, it follows that the product A. A V will be an additive quantity provided that a for each species remains constant during the course of the reaction. This last condition implies, essentially, that the effective dipole moments and hence the orientation of each species remain constant, which is most likely to be the case at constant film pressure. Then... 

Fig. IV-27. Rate of lactonization of 7-hy-droxystearic acid as a function of film pressure.

A surfactant for evaporation control has an equilibrium film pressure of 15 dyn/cm. Assume a water surface and 25°C and calculate the distance traveled by the spreading film in 8 sec. 

The film pressure of a myristic acid film at 20°C is 10 dyn/cm at an area of 23 A per molecule the limiting area at high pressures can be taken as 20 A per molecule. Calculate what the film pressure should be, using Eq. IV-36 with / = 1, and what the activity coefficient of water in the interfacial solution is in terms of that model. 

Many solids show marked swelling as a result of the uptake of a gas or a liquid. In certain cases involving the adsorption of a vapor by a porous solid, a linear relationship exists between the percentage of linear expansion of Ae solid and the film pressure of the adsorbed material [134, 135]. 

The film pressure can be subjected to further thermodynamic manipulation, as discussed in Section XVII-13. Thus... 

It is important to keep in mind that the phases are mutually in equilibrium. In particular, the designation is a reminder that the solid surface must be in equilibrium with the saturated vapor pressure and that there must therefore be an adsorbed film of film pressure (see Section X-3B). Thus... 

Values for x , the film pressure of the adsorbed film of the vapor (of the liquid whose contact angle is measured), are scarce. Vapor phase adsorption data, required by Eq. X-13, cannot be obtained in this case by the usual volumetric method (see Chapter... 

Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

Fowkes and Harkins reported that the contact angle of water on paraffin is 111° at 25°C. For a O.lAf solution of butylamine of surface tension 56.3 mJ/m, the contact angle was 92°. Calculate the film pressure of the butylamine absorbed at the paraffin-water interface. State any assumptions that are made. 

As discussed in Chapter III, the progression in adsoiptivities along a homologous series can be understood in terms of a constant increment of work of adsorption with each additional CH2 group. This is seen in self-assembling monolayers discussed in Section XI-IB. The film pressure r may be calculated from the adsorption isotherm by means of Eq. XI-7 as modified for adsorption from dilute solution ... 

The Washburn equation has most recently been confirmed for water and cyclohexane in glass capillaries ranging from 0.3 to 400 fim in radii [46]. The contact angle formed by a moving meniscus may differ, however, from the static one [46, 47]. Good and Lin [48] found a difference in penetration rate between an outgassed capillary and one with a vapor adsorbed film, and they propose that the driving force be modified by a film pressure term. 

If an ionic surfactant is present, the potentials should vary as shown in Fig. XIV-5c, or similarly to the case with nonsurfactant electrolytes. In addition, however, surfactant adsorption decreases the interfacial tension and thus contributes to the stability of the emulsion. As discussed in connection with charged monolayers (see Section XV-6), the mutual repulsion of the charged polar groups tends to make such films expanded and hence of relatively low rr value. Added electrolyte reduces such repulsion by increasing the counterion concentration the film becomes more condensed and its film pressure increases. It thus is possible to explain qualitatively the role of added electrolyte in reducing the interfacial tension and thereby stabilizing emulsions. 

The behavior of insoluble monolayers at the hydrocarbon-water interface has been studied to some extent. In general, a values for straight-chain acids and alcohols are greater at a given film pressure than if spread at the water-air interface. This is perhaps to be expected since the nonpolar phase should tend to reduce the cohesion between the hydrocarbon tails. See Ref. 91 for early reviews. Takenaka [92] has reported polarized resonance Raman spectra for an azo dye monolayer at the CCl4-water interface some conclusions as to orientation were possible. A mean-held theory based on Lennard-Jones potentials has been used to model an amphiphile at an oil-water interface one conclusion was that the depth of the interfacial region can be relatively large [93]. 

Stigter and Dill [98] studied phospholipid monolayers at the n-heptane-water interface and were able to treat the second and third virial coefficients (see Eq. XV-1) in terms of electrostatic, including dipole, interactions. At higher film pressures, Pethica and co-workers [99] observed quasi-first-order phase transitions, that is, a much flatter plateau region than shown in Fig. XV-6. 

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