Oct., 19162
PENETRATION OF
HYDROCARBONS IN MONOLAYERS
Gibbs writes not about surface elasticity but about film elasticity on the page quoted (ref. 2). Furthermore, the films with which Gibbs was concerned were not the Langmuir monolayor films to which Dr. Goodrich refers in connection with his first equation. They were soap films composed of two surfaces plus a thin layer having bulk properties in between. Thus Gibbs’s film elasticity is not a simple surface property but one dependent upon the amount of bulk phase present. Since IGibbs’s film elasticity is a well defined operational
1863
quantity which can be directly measured [J. Phys. Chern., 65, 1107 (1961)] and thermodynamically calculated for special cases (Oibbs, ref. 2, p. 303), it does not seem advisable to apply the same name or a very similar one t o a diderent concept which Gibbs did not formulate explicitly. As an alternative, I would like to suggest “areal elasticity” since i t seems to be the exact two-dimensional analog of what is called volume elasticity for three-dimensional systems. “Areal viscosity” then would be the corresponding viscosity coefficient just as there is a volume viscosity.
IDEAL TWO-DIMENSIONAL SOLUTlONS. 111. PENETRATION OF HYDROCARBONS IN MONOLAYERS BY FREDERICK M, FOWKES* Xhell Developmefit Cornpang, Emeryville, Calif. Received March 8, 1068
Insoluble monolayers of stearic acid on aqueous substrates are subject to penetration by hydrocarbons or other solvents from the vapor phase. Similarly interfacial monolayers of stearic acid a t the oil-water interface are subject to penetration by oil molecules. In both cases, it is shown that the stearic acid and penetrating solvent form ideal two-dimensional solutions. Monolayers of long chain quaternary ammonium salts a t the oil-water interface are penetrated by both oil and water simultaneously; this gives rise to the 3kT in the gas equation approximation of the equation of state.
Introduction As surface active molecules (species 1) adsorb or spread as monolayers a t liquid surfaces, molecules of the substrate (species 2) originally present in the surface are forced into the adjacent liquid phase. Howevor, in many cases an appreciable mole fraction xz of substrate molecules remains in the surface layer. These remaining substrate molecules and thLe surface-active molecules form a twodimensional solution in which the film pressure T and partial molecular area of substrate molecules CTZ determine 22 naz =
-1cT In z24z
(1)
where q l 2 is the activity coefficient of the substrate molecules in the surface solution. Such monolayers with +Z equal to unity are termed “ideal twodimensional solutions” and have been found to occur in a great many instances; in fact, ideality of such solutions appears to be the rule with few exceptions. Of course a great many insoluble monolayers and some adsorbed monolayers are essentially free of substrate molecules ( 4 ~approaches infinity), but when monolayers do include substrate molecules, 42 is generally very close to unity. Many investigators have found this to be the case for small molecules, and the author has shown this to be the rule for detergents and so-called (‘gaseous” Other two-component monolayers formed by penetration of detergent molecules (species 2 ) into an insoluble monolayer of species 1 display the same ideality and obey eq. 1 where i r is the increase in film pressure as a function of ~ 2 . ~ - 6
*
Spragae Electrio Go., North Adama, Mass. (1) E.Q., A. Schuahowitzky, Acto Physzeoehim. URSS. 19, 176, 508 (1944). (2) F . I I L Fowkes, J . Phys. Chem., 66, 385 (19132). (3) W. .M. Sawyer and F. M. Fowkes, ibid., 62, 169 (1958). (4) F. Xd. Fowkes, zbid., 66, 355 (1961). (5) F. M. Fowkes, ”Prooeedings of the Third International Congress of Surface Activity,” Cologne, Vol. 11, 1060, p. 161.
This paper is concerned with the penetration of hydrocarbon molecules (species 2) into insoluble or adsorbed monolayers of species 1 a t surfaces or interfaces; in these systems of eq. 1 is generally unity or else no penetration occurs. The Surface Phase.-The surface layer (or layers) of molecules in liquids may well be considered to be a phase separate from the bulk liquids. I n this phase the intermolecular distance is considerably greater than in the liquid phase, the surface tension affects the chemical potential of this phase only (except for the pressure effect on the liquid phase in some systems), the composition and chemical potential of species of the surface phase of solutions is quite different from the liquid phase, solutes are far more soluble in the surface phase, and the activity coefficients in surface solutions are far closer to unity than in bulk solutions. Equilibria between the surface phase and liquid phase are established when molecules can be readily exchanged between phases. In the case of insoluble surface films such as stearic acid on water no equilibrium is established with dissolved stearic acid in any of the usual film balance studies. However, in “gaseous” monolayers of stearic acid the surface phase is composed mainly of water and this is in dynamic equilibrium with the water substrate, In the case of detergent monolayers adsorbed on aqueous solutions, both the detergent and water molecules of the surface phase are in equilibrium with the liquid phase. I n this paper we consider insoluble surface monolayers of stearic acid (not in equilibrium with any other phase) penetrated by hydrocarbon molecules in equilibrium with hydrocarbon vapor. At interfaces between dissimilar liquids such as hydrocarbons and water the interfacial region includes two interfacial phases (the adjacent layers of both liquids); these two phases have different tensions, intermolecular distances, and compositions than the liquid phases.6 Some surface active
+
(6) F. hl. Fowkes, J . Phys. Chern., 66, 382 (1962).
FBEDERICK M.FOWICES
6864
molecules occupy only one interfacial phase, but others can occupy both a t once as will be shown. Theory.-The same equations will be used as in previous articles of this s e r i e ~ . ~The , ~ subscript 1 refers to the species forming the monolayer to be penetrated and subscript 2 to the penetrating species. If a second species penetrates the monolayer subscript 3 is used. Penetration is the equilibration of a species (2) between two phases; at equilibrium its partial molar free energy (G2) is equal in the two phases. However, when one of the phases has a different pressure, tension, or gravitational constraint the chemical potential p2 is different in the two phases. For equilibria between a liquid or vapor phase with the surface phase (at constant pressure and temperature) dG2(surface) = dpz(surface) - N m d r dGz(substrate) = dpz(substrate) dGz(vapor) = dpz(vapor) dG2(surface) = dGz(substrate) = dG2(vapor) dy2(surface) = RT d In xe& dy2(substrate) = RT d In czf2 dpz(vapor) = RT d In p2* where x2 and 42 are the mole fraction and activity coefficient in the surface phase, c2 and f2 are the mole fraction and activity coefficient in the substrate, and pz" is the fugacity of species 2 in the vapor space. After equilibration of species 2 between substrate and surface phases
1cT d In x2$2
- uzdy
- 1cT d In czf2
=0
(2)
and between vapor and surface phases
IcT d In x&
- aady - kT d In ps"
=
0
(3) For vapor-surface equilibria in which the vapor acts as an ideal gas, and the changes in surface tension are expressed as film pressure .rr, eq. 3 becomes
kT d 1n x&
- kT
d In (p2/'pzo) = -mda
(4)
where pz/p20 is the relative vapor pressure (pzo is the vapor pressure of pure liquid species 2). In integrated form eq. 4 is
kT In 2242 - kT In (pzlp2O) = -u2 (T - nzo) ( 5 ) where 7r20 is the equilibrium spreading pressure of species 2 on the substrate, and 8%is the average partial molecular area of species 2 as defined by 82
=
$io w i n T
-
7rzo
To compute .c2 for a mixed monolayer from measured values of A I (the area of monolayer per molccule of species l), it is necessary to liriow uz and ul. The two-thirds power of the molecular volume has been found adequate for predicting 6 2 of small symmetrical molecules such as water and propylene carbonate.2 For less symmetrical molecules m may have to be evaluated from .rr vs. p2 data at constant x2. Under these conditions we see that eq. 4 leads to
Vol. 86: d In pz Xl
I n computing xz it is also necessary to know m and whether or not species 1 is dimerized in the mixed monolayer. These points can be established by use of the relat'ion2 A1 = CTl
+
(E)
d m
(7)
where z is thc dissociation coefficient for molecules of species 1 in the mixed monolayer. If x in unity no association or disassociation occurs; if dimers were formed z would equal 0.5. The value of nz/nlz is calculated from
Thus for each value of n a corresponding value of
nz/nlx is calculated and an A1 vs. n2/nlxplot derived from the normal AI vs. .rr relation. The slope gives z, and the intercept q . Penetration of Surface Monolayers by Solvent Vapors.-The data of Dean and c o - ~ o r k e r s ~ - ~ ~ on the effect of hydrocarbon and carbon tetrachloride vapors on the film pressure of stearic acid monolayers may be treated as an ideal two-dimensional solution in which the vapor is in equilibrium with solvent in the monolayer, although a different interpretation was offered originally. In Fig. 1 and 2 are shown the effects of carbon tetrachloride and dimethylbutane on the film pressure of extremely dilute monolayers of stearic acid.' These molecules are nearly spherical in shape so that u2 is calculated as the two-thirds power of the molecular volumes (28 and 34 respectively). The value of u1 is expected to be the maximum molecular area for stearic acid in its most expanded form, 45 A check of this value is given in Fig. 1 where the data are plotted according to eq. 7 and the intercepts are 40 and 45 A.2, respectively. These mixed monolayers are very simpleoones. The stearic acid molecules occupy 45-46 As2 a t pressures less t!han the "critical demixing prcssure" (see Fig. 2), so that the area available to solvent ul. With this area and the molecules is A1 known values of u2, x2 values are calculable for each ralue of A1. Then from eq. 5 a n-AI relation is calculable for any fixed value of pz. The data of Dean and Li are for p , = p20, and are shown in Fig. 2 to fit the calculated pressure-area curves very well. Data obtained later with n-hexane also fit the ideal solution equation for monolayer^.^ Penetration of Oil Molecules into Oil-Soluble Monolayers Adsorbed at the Oil-Water Interus consider the monolayer adsorbed face.-Let between water and a dilute solution of stearic acid (1) in a highly refined naphthenic oil (2).
-
(7) R. B. Dean and Fa-Si Li, J . Am. Chsm. Soc., 72, 3979 (1950). (8) R . B. Dean and K. E. Hayes, zbid., 78, 5583 (1951). (9) K. E. Hayes and R. B. Dean, ibzd., 7 8 , 5584 (1951). (IO) R. B. Dean and K. E. Hayes, ihzd., 74, 5982 (1952). (11) K.E. Hayes and R . B. Dean, J . Phys. Chem., 67, 80 ( 1 9 S l .
PENETRATION OF BYDROCARBOSS IA- M o x o ~ a s ~ n s
Oct., 1962
1865
AT SUIiFACE
1
0
2
3
nl/nls.
Fig. 1.-Surface solution plot of stearic acid penetrated hy CCll (triangles) or dimethylbutane (circles) at 25“. Lines calculated for ideal solutions, points are from data of Dean and ILi.
20
6 vi
C 0
2. 1 0 -
I
ACID OKLY
ooLL--J---J 50
I00
150
A , . A‘/IRIOLbCLLE
Fig. 2.--Yressure-area isotherms for stearic acid penetrated by CClr or dimethylbutane vapor at 25’. Lines are calculated for ideal surface solutions, points are from Dean and Li.
Water is not soluble in the stea,ric acid monolayer, nor vice versa, so this is essentially a binary system with oil niolecules and stearic acid molecules mixed together in the monolayer as an ideal solution. The pressure-area isotherm may be derived from eq. 2 and abbreviated to -kT In z242 (9) TIT=
$2
using appropriate values of $2 and u1 (25 A.2 for each), and 42 = 1, as is illustrated in Fig. 3. The experimental points are from interfacial tension measurements by Dr. W. 34. Sawyer (of these Laboratories) with areas per molecule (A1) calculated with Gibbs’s adsorption equation modified as suggested by LangmuirI2 for adsorption of fatty acids from solutions in which they are predominantly -kl’
/ d In c l \
One point, from the york of Zisman14 also is shown. The value of ~2 (25 A.2) has not been obtained independenlly, but is an estimated value. Figure 4 (12) I. Langmuir, J . Franklin Inst., 218, 143 (1934). (13) D.S. Sarkadi and J. H. deBoer, Rec. t m v . chzm., 76, 628 (1957). (14) W. A. Zisman, J . Chem. Phys., 9, 534 (1941).
0
I P2’”
.
2
3
Fig. 4.-Ideal two-dimensional solution plot of stearic acid adsorbed at oil-water interface at 25‘. Effect of various values of 3z,
illustrates the effect of using various values of u2. All values (20,25, or 30 fit the data equally well and give identical a-A1 relations. The difference is only in the predicted value of ul, the partial molecular area of stearic acid. An independent measure such as the orientation potential is needed to decide which is correct. This example shows the frequently observed effect of the expansion of a monolayer at the oilwater interface as compared with its pressurearea relation on the surface of water (Fig. 3). Though the effect usually is explained as resulting from “releasing the forces of cohesion” in the monolayer it is obvious that the expansion is only the area of the oil molecules in an ideal binary solution with the adsorbed molecules and that the exact pressure-area relations of the interfacial film are calculable from known values of g1 and $2. Not all surface-active agents form ideal twodimensional solutions in oil. At least one case of complete insolubility has come to our attention, octadecanol in white oil at 260.16 Here there was no swelling of the monolayer in oil. It is to be expected that at high film pressures a critical pressure may be reached where the activity coefficient $2 suddenly becomes very large and the Sawyer ‘I. and F. M. Fowkes, J . Phys. Chem., 60, 1235 (15) W. > (1956).
lS66
FREDERICK M, FOWKES
Vol. 66
film changes from a solvated to non-solvated film. contrast to stearic acid). The long hydrocarbon This has been shown before4 and appears again for chains formed an ideal solution with the oil at thc dimethylbutane in stearic acid at 23 dynes/cm. and same time as the quaternary ammonium and the for carbon tetrachloride in stearic acid a t 17 dynes/ chloride ions formed an ideal solution with the cm. (Fig. 2). Some polymeric monolayers swell at the water. If we call the water component 3 and the oil-water interface as oil molecules penetrate them, oil component 2, the film pressure of this system but the equations for ideal solutions do not fit such should be polymers. A later publication will give the proper equations to use in these cases. = = - kT In (1 - zxl) - IcT In (1 - xl) (10) Water-Soluble Monolayers at the Oil-Water Q3 c2 Interface.-J. T . Davies has measured the pressure-area relations for long chain quaternary If we follow the derivation of the “gas” equations2 ammonium salts a t the oil-water interface, and and make the usual linear approximation of In xl) = -xl, and the usual assumption that applied the “gas” equations to the data.16 While (1 previous investigators had found that ionic films A1 - (m - m) or A1 - (a - a) can be approxiare more expanded than non-ionic, so that the mated by A1 - Ao,eq. 10 becomes “gas” equations required 2kT, Davies found that a ( A 1 - Ao) = ( z 1)lCT (11) in his system (when the aqueous phase had a low ionic strength) the trgas”equation required a value where x is the number of ions per long chain quaterof 3kT. nary ammonium chloride molecule. It is obvious This is now easily explained as due to the quater- why on very dilute salt solutions where x was nearly nary ammonium chloride having a double function 2.0 that 3kT was needed in the ‘(gas” equation, in this film. That is, these molecules occupy both but when saturated salt substrates were used (and adjacent interfacial monolayers, being oil-soluble the long chain amine salt was “salted-out” so that 2nd yet having ionic groups soluble in water (in x was less than unity) the “gas” equations required only 1-2kT. (16) J. T. Davies, Proc. Roy. SOC.(London), 8208, 224 (1951).
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+
