1982
FREDERICK M. FOWKEX
1-01.67
MIXED MOSOLAYERS OF CETYL ALCOHOL A S D SODIUM CETYL SULFATE BY
FREDERICK n/I. FOWKES~
Shell Development Company, Emeryvzlle, Calzj Received filarch 11, 1963
A film balance study of mixed monolayers of various ratios of sodium cetyl sulfate and cetyl alcohol on a substrate of 5y0S a C l (in which the sulfate is insoluble) shows that when the monolayer contains over 50 (mole) yo of cetyl sulfate the sulfate ions are in a nearly ideal two-dimensional solution in the surface layer of mater molecules and the addition of cetyl alcohol makes no appreciable change in the cetyl sulfate pressure-area relations, except a t greatest compression. However, when the mixed monolayers are composed of 50Y0 or more of cetyl alcohol, the cetyl sulfate ions are removed from solution in the surface layer of water molecules and considerably smaller areas per cetyl sulfate ion are observed. This transition (once thought to result from formation of a 1: 1 complex) is likened t o the inversion of an emulsion from oil-in-water t o water-in-oil upon increasing the phase ratio of oil.
I n surface and interfacial monolayers, two or more coniponents often interact with another. Considerable investigation of the interaction of biologically important surface-active materials has led in the past to the conclusion that some substances interact by forming complexes. In particular, a number of studies of the interaction of water-soluble ionic surface-active substances with insoluble monolayers of long-chain alcohols or cholesterol have led investigators to postulate 1: 1 surface or interfacial complexes. However, the author has demonstrated for a number of these examples that there is no stoichiometric complex formed, as demonstrated by measurements of the colligative properties of the mon01ayers.~ Although there is no complex formed in these “model” biological monolayers, there is no doubt whatsoever that there is a sharp transition in the physical properties of these mixed monolayers when the molecular ratio of long-chain alcohol (or cholesterol) to ionic surface-active component is about 1: 1.4 Similar sharp transitions (as a function of mole ratio) of the physical properties of two-component adsorbed and insoluble monolayers have been observed in other systems. -4classic example is the penetration of surface films of stearic acid from the vapor phase by carbon tetrachloride or 2,3-dimethylbutane.j In these monolayers, an ideal two-dimensional solution of stearic acid in the condensed vapor is observed over a wide range of compositions providing that there are more molecules of condetised vapor than of stearic acid in the surface solution. HovieT-er, as the monolayer is compressed and the ratio gradually approaches 1: 1, there is a sharp reduction in the area per molecule (at a constant critical film pressure) as all or nearly all of the condensed vapor is squeezed out of the monolayer (see Fig. 2 of ref, 5 ) . A similar example is known for interfacial films adsorbed at the benzene-water interfaces; long-chain acids, alcohols, and esters gi1-e ideal solution isotherms at low pressures but suddenly lose the benzene solvent at critical film pressures of 10-20 dynes/cm. and a t benzene mole ratios of 0.3-0.5. Another example quite similar to the system discussed in this paper is the surface film adsorbed on solutions of sodium dodecyl sulfate.7 The surface film on these solutions is an ideal (1) Sprague Electric Company, North Adams, Mass. (2) D. G. Dervichian, in “Surface Phenomena in Biology a n d Chemistry,” b y J. F. Danielli, K. G. A. Pankhurst, and A. C. Riddiford, Pergamon Press, New York, N. P., 1958. (3) W.r/I. sawyer a n d F. 31. Fowkes, J . Phys. Chem., 62, 159 (1958). (4) F. M. Fowkes, ibid., 66, 355 (1961). ( 5 ) F. M. Fowkes, ihid., 66, 1863 (1962). (6) E. Hutohinson and D. Randall, J . Colloid Sei., 7 , 151 (1952). (7) F. 31. Fowkes, J . P h y s . Chena., 66, 385 (1962).
solution of dodecyl sulfate ions in the surface layer of water molecules. As film pressures increase, the ratio of dodecyl sulfate ions to water molecules in the surface solution approaches 1:1, a t which pressure there is a sharp decrease in the area per molecule to 26 A.2, the established partial molecular area of dehydrated dodecyl sulfate ions. It appears that the sharp transition in physical properties in the vicinity of a 1: 1 mole ratio in the system under study could result from a similar dehydration of the ionic species as the ratio of non-ionic to ionic component approximates unity. This possibility has been studied with film balance techniques, using mixed monolayers of cetyl alcohol and sodium cetyl sulfate spread on an aqueous substrate containing 5% of sodium chloride (to keep the sodium cetyl sulfate from dissolving into the substrate). Pressure-area isotherms have been obtained for a wide range of stoichiometric ratios. Theory and Notation A monolayer adsorbed or spread on the surface of an aqueous solution may be in one or two “states.” It may be dissolved into the surface layer of water molecules; Chis is the case of adsorbed aqueous detergents ivhich form ideal solutions with the water molecules of the surface layer, and in these films the measured area per detergent molecule (Al) includes the area of one or more water molecules. The ratio of water molecules to detergent inolecules in such monolayers (nz/n,) is a function of the film pressure ( T ) and of the partial moFor some detergent molelecular area of the water (4. cules, the partial molecular area (cl)is constant and consequently the area per molecule A1 is given by7 -41 = f f i $. (T22.(nz/n1) (1) where x is the number of colligatir-e particles per molecule of component 1 (degree of dissociation). The ratio nz/nlis easily calculated for ideal surface solutions from the relation of film pressure to the mole ratio of solvent in the monolayer ( ~ 2 ) ’ - kT T = In xzvz (2) 32
where c2 is the average partial molecular area of the water molecules over the pressure range. In the case of water, because of its isometric character and low compressibility, sz is 9.7 A.2 per molecule for all film pressures. The activity coefficient of the water molecules in the surface solution (pp?) has been shown to be essentially unity for a wide variety of two-component monolayers.
Oct., 1963
MIXEDh!!ONOL.4YERS
1983
O F C E T Y L ALCOHOL AND S O D I U X CETYL S U L F S T E
The second “state” for surface monolayers is where the polar groups are in contact with the surface layer of water molecules but are not actually dissolved into this layer. In this state, the surface concentration of surface-active molecules does not affect the chemical potential of the water molecules iii the surface layer nor does the area per molecule (Al) of the surface-active species include the surface area of water molecules in the film. A good example is the case of stearic acid spread on the surface of water in which the carboxyl groups are oriented by and in contact with the surface layer of water molecules but are not in solution in the surface layer except a t very low film pressures (gaseous film region). Changes in film pressure of stearic acid monolayers (outside of the gaseous film region) are not related in any way to the chemical potential of the water molecules nor do water molecules occupy any fraction of the surface layer of stearic acid. I n the system investigated in this paper, there are strong indica,tions that monolayers composed of only detergent molecules are in the surface solution state, that monolayers of only cetyl alcohol are formed on top of but not in the surface layer of water molecules, and that in the mixed monolayers a fairly sharp transition between these two “states” occurs in the vicinity of the 1 : 1 ratio of cetyl alcohol to sodium cetyl sulfate. Experimental Procedures The pressure -area isotherms were obtained with an automatic recording film balance, the construction and operation of which have been dericribed previously.*~9 The cetyl alcohol (1hexadecanol) was carefully purified by fractional distillation to give a product with a melting point of 48.5-49”. The sodium cetyl sulfate was prepared from the purified alcohol by R . T. Holm. The alcohol-free product was obtained by repeated recrystallization. RIonolayers of cetyl alcohol and of the mixtures were spread from dilute solution in freshly-distilled Phillips 99 mole yo n-hexane. Monolayers containing only sodium cetyl sulfate were spread from solution in n-hexane containing 20 vol. 70 of freshly distilled absolute ethanol. This addition of 0.04 ml. of ethanol to 2 1. of substrate appears innocuous to the film. The aqueous sodium chloride substrates were prepared from highly purified doubly-distilled water and reagent grade sodium chloride. The effect of salt concentration was tested with monolayers containing 50 mole % of sodium cetyl sulfate on substrates of 1, 5, and 10% sodium chloride. As there was negligible difference in these isotherms, all of the succeeding experiments were performed on the 5y0sodium chloride substrates. The barrier drive allowed complete compressions as fast as 30 sec. or as slow as several hours, but in these experiments nearly all isotherms were obtained within a 2-min. period. The temperature control system allowed reproducibility of a few hundredths of a degree, but for these monolayers, it was found that identical isotherws were obtained over a 2” temperature range. Consequently, these experiments were all conducted a t the temperature range of 24.5-26.5’.
Experimental Results Pressure-area isotherms were obtained for monolayers containing only sodium cetyl sulfate, for mixed monolayers with cetyl alcohol containing 67, 50, 40, 33, and 20% of sodium cetyl sulfate, and for monolayers containing only cetyl alcohol. Two to five isotherms were obtained with each composition. The reproducibility with respect to film pressure was within 0.2 dyne/ cm., as judged by the film pressures a t large areas per molecule or a t the first-order transitions. However, the reproducibility in area per molecule depended on the composition of the monolayer. For the cetyl alcohol monolayers or for the mixtures containing only 20 mole (8) W.&I. Sawyer and F. M. Fowkes, J . Phys. Chenz., 60, 1235 (1958). (9) M. J. Schick, J. Polymer Bcz., 25, 465 (1957).
40
I
li, ,
’
I
I
I
Area per hydrocarbon chain, 6.2. Fig. 1.-Pressure-area isotherms ( 2 5 ’ ) fcr mixed monolayers of cetyl alcohol and sodium cetyl sulfate on 5c/c aqueous sodium chloride substrate.
33%
0
20
25
Area per hydrocarbon chain,
30
b.1.
Fig. 2.-Details of pressure-area isotherms for the more compressed mixed monolayers of cetyl alcohol and sodium cet,yl sulfate on 5% aqueous sodium chloride substrate.
yo of sodium cetyl sulfate, reproducibility was within 0.03 A.2 per molecule. The reproducibility in monolayers containing only sodium cetyl sulfate or of mixed monolayers containing 67% sodium cetyl sulfate was also very good; standard deviations were 0.1 per molecule. However, for the mixed monolayers containing 33, 40, or 50 mole yosodium cetyl sulfate, the reproducibility was significantly poorer; standard deviations were 0.3-0.4 A.2 per molecule. The pressure-area isotherms are illustrated in Fig. 1; the area is expressed in per CI6hydrocarbon chain. Arrows indicate the first-order transitions observed in monolayers of cetyl alcohol or in mixed monolayers containing 20, 33, and 50 mole yo of sodium cetyl sulfate. These transitions occurred at, film pressures of 11.I, 17.3, 23.3, and 25.7 dynes/cm., respectix-ely(see rig. 2 ) . Collapse pressures are not shown in these figures. For cetyl alcohol was 36 * 5 dynes/cin. and for sodium cetyl sulfate, 29.5 i- 2 dynes/cm. However, with the mixed films T, was 42, 41, 40, 37, and 38 dynes/ cm. for films containing 20, 33, 40, 50, and 67 mole (34
1984
FREDERICK M. FOWKES
-t
/
/
O
/Q 4 0 67 I67 % SULFATE)
L
~
2 ’ 0 12(50 % SULFATE)
0
I
n
n
2: 0.12 ( 3 3 % SULFATE)
n
I
50% Sulfate 50% Alcohol
33% Sulfate 67% Alcohol
0% Sulfate 100% Alcohol
Fig. 4.-Diagram t o illustrate how increase in mole fraction of cetJyl alcohol removes cetyl sulfate from solution in aqueous surface layer ( 0 = water, 0= alcohol, 8 = sulfate).
of sodium cetyl sulfate; in the mixed films the standard deviation of was 1 dyne/cm.
Discussion The isotherms shown in Fig. 1 illustrate the condensing effect of added cetyl alcohol on the average area per hydrocarbon chain. However, it is of interest to consider how cetyl alcohol affects the area occupied by sodium cetyl sulfate. If we consider the mixed monolayer containing 67% of sodium cetyl sulfate and express the area in A.2 of surface per molecule of sodium cetyl sulfate, we obtain a t 5, 10, 15, and 20 dynes/cm. surface areas of 66, 55.5, 50, and 45 A.2 per molecule. Interestingly enough, these are almost identical with the areas observed in monolayers containing only sodium cetyl sulfate: 65, 56, 47.5, and 43 if.2, respectively. One might argue that the condensing effect of cetyl alcohol has just balanced the increase in number of hydrocarbon chains present for each sodium cetyl sulfate molecule. One might better say, however, that the added cetyl alcohol molecules are in the dehydrated state and, therefore, have no effect on the chemical potential of the water molecules in the surface layer of water. With increased ratios of cetyl alcohol, the area of film per cetyl sulfate molecule increases. In the mixed monolayer, it is reasonable to expect that the partial molecular area of the cetyl alcohol remains 19-20 A.z per molecule. By subtraction one can
Vol. 67
then obtain the area of the monolayer occupied by sodium cetyl sulfate and water molecules. At 10 dynes/cm. the area of monolayer per molecule of sodium cetyl sulfate, minus 20 A.2per cetyl alcohol molecule, is 56, 45.5, 37.2, 29.8, and 25 A.z per molecule for monolayers containing 100, 67, 50, 40, and 33 mole yo of sodium cetyl sulfate, respectively. This decrease, particularly in monolayers having 50 mole Yo or less sodium cetyl sulfate, shows the strong condensing effect of cetyl alcohol. A yet more informative approach in understanding the effect of added cetyl alcohol on the behavior of the monolayer is obtained by use of eq. 1; this gives a measure of how the increase in film pressure raises the chemical potential of water molecules in the monolayer and causes them to be transferred out of the monolayer into the substrate. The use of this equation for these monolayers is illustrated in Fig. 3. Here the ratio of water molecules to film molecules (nz/nl)is calculated from the film pressure for an ideal two-dimensional solution. Monolayers behaving as ideal two-dimensional solutions on dilute salt substrates will have z = l.0.7 Lower values of x indicate dehydration of the monolayer (ie.,transfer of some molecules from the surface solution to the dehydrated “state”). The monolayers containing only sodium cetyl sulfate are seen to behave as ideal surface solutions a t film pressures greater than 15 dynes/cm. This is also illustrated in Fig. 1 ; the ideal surface solution isotherm is indicated with dashed lines. It was shown previously that surface films of sodium dodecyl sulfate are ideal surface solutions on dilute aqueous substrates of sodium chloride7; for these x was 1.0 on substrates containing 0.1 N sodium chloride even a t film pressures as low as 4 dynes/cm. However, on substrates of 0.2 N sodium chloride (1.2 wt. %), some dehydration was observed a t pressures below 9 dynes/cm., but ideal surface solution behavior was observed (as in this case) at all higher film pressures. Thus we see that the deviations from ideality a t lower film pressures observed in Fig. 1 and 3 are in accord with previous studies with sodium dodecyl sulfate, and that one would expect ideal surface solution behavior to extend to much lower pressures on substrates of lower salt content. The plot in Fig. 3 of A1 vs. nz/nl for mixed monolayers containing 67 mole yo of sodium cetyl sulfate shows z = 0.67. This means that 67% of the surfaceactive molecules were in solution in the surface layer of mater molecules. This can only mean all of the cetyl sulfate ions in the monolayer have their sulfate groups in the surface layer of water molecules and that the cetyl alcohol molecules rest on top of the surface layer of water molecules but are not dissolved in it (see Fig. 4). The x value for the monolayers containing 50 mole yoof sodium cetyl sulfate is 0.32. This means that onethird of the sodium cetyl sulfate ions have been withdrawn from the surface solution “state.” Similarly, the z values for the nionolayers containing 33 and 40 mole yosodium cetyl sulfate indicate that two-thirds of the sodium cetyl sulfate molecules are withdrawn from the surface solution “state.” These results are interpreted diagrammatically in Fig. 4 to mean that in the mixed monolayers containing 50 mole % or less of sodium cetyl sulfate, the sulfate ions have been withdrawn from the surface layer of water molecules into
Oct., 1963
MIXEDMONOLAYERS OF CETYLALCOHOL AND SODIUM CETYLSULFATE
the layer of cetyl alcohol molecules. Some water molecules are carried into this layer along with the sulfate ions and these account for the observed x values; thus, in the mixed monolayer containing 33 mole yoof sodium cetyl sulfate, the sulfate ions are hydrated with about one-third as much water as if they still remained in the surface layer of water molecules. Water retained by the sulftite ions in the alcohol layer accounts for part of the area per molecule assigned to the cetyl sulfate ions and the amount of water retained in this layer is a function of film pressure, as demonstrated in Fig. 3. A reason for proposing that the sulfate ions have been retracted into the alcohol layer is that if they remained in the surface layer of water molecules, we would expect that in the mixed films of low sodium cetyl sulfate content, z values would go to zero at critical pressures corresponding to $2 values deterniined by two water molecules per cetyl alcohol (20 A.2/9.7 A.2). Such critical pressures would occur at 4.8, 9.4, and 12.3 dynes/cm. with monolayers containing 20, 33, and 40 mole % of sodium cetyl sulfate; however, the observed first-order transitions are at much higher pressures (Fig. 2). Since positive x values do mean that the film pressure in the mixed monolayers is a function of the chemical potential of water molecules, then water molecules must be “area-determining” and must be situated in the cetyl alcohol layer in monolayers rich in cetyl alcohol. This situation is illustrated in Fig. 4. Further evidence for the inclusion of water in the cetyl alcohol layer is given by the film pressures at the first-order transitions shown in Fig. 1 and 2. These transitions may be considered similar to a melting point or, more proplerly, a melting pressure such as one observes on compressing a liquid at constant temperature until a critical pressure is reached at which a first-order transition from a liquid to a solid phase occurs. In the case of the mixed monolayer, the first-order transition pressure is the film pressure at which “solid phase’’ monolayers of cetyl alcohol precipitate within the liquid mixed monolayer. It is seen that the addition of 20 mole % of sodium cetyl sulfate to cetyl alcohol raises the first order of transition pressure from 11.1 to 17.5 dynes/cm. This pressure rise reflects the entropy of dilution. ‘The mole fraction (xl) of cetyl alcohol in the mixed monolayer should be given by
1cT In x1 cpl =
-cl(rt
- rtO)
(3)
where rt is the first-order transition pressure in the mixed monolayer and ?rtO is the first-order transition pressure for the pure cetyl alcohol film. Past experience has shown us that p1 is normally unity in such monolayers. Application of this equation to the mixed monolayer containing 20 mole % of sodium cetyl sulfate gives an XI value of 0.75. This means there is 25 mole % of diluent in this monolayer, and since there is 19 mole of sodium cetyl sulfate, there must be 6 mole % of water in this monolayer. Similarly, in the case of the mixed monolayer containing 33 mole % of sodium cetyl sulfate, the r t is 23.3 and x1 is 0.56. This means that there is 44 mole Yo of diluent in the cetyl alcohol monolayer of which 28% is sodium cetyl sulfate and 16% must be water. This can be checked with the x value of 0.12 for this mixture. For ideal surface solutions at the pressure rt (23.3 dynes/cm.) nz/nlis 1.32, but the x value of 0.112 means that for each alkyl chain
1985
there must be (0.12 X 1.32 = 0.16) molecules of water. This amounts to 13.5 mole % of water as compared to the 16 mole % ’ of water calculated from eq. 3. As one might anticipate from the diagram of Fig. 4, the amount of water retracted into the alcohol layer in mixed monolayers having 50 mole % or more of cetyl alcohol is a function of the way in which the sulfate molecules are distributed within the monolayer and may also be a function of the way in which the hexane solution may have separated alcohol from sulfate molecules during evaporation. This may be an explanation for the significantly greater variation in reproducibility of the pressure-area isotherms with mixed monolayers containing 33, 40, and 50 mole % of sodium cetyl sulfate. For these three mixtures, the standard deviation of area per molecule was 0 . 3 - 0 . 4 A.2 per molecule as or less for compared with standard deviations of 0.1 the other monolayers. Conclusions The sharp transition in physical properties of mixed monolayers of sodium cetyl sulfate and cetyl alcohol which occurs at a mole ratio of approximately 1:l has been shown previously to be unexplainable on the basis of coniplex formation. The present study shows that this transition results from the fact that while cetyl sulfate ions tend to be dissolved in the surface layer of water molecules, cetyl alcohol molecules tend to be located above the surface layer of water molecules and are not dissolved in it. I n mixtures, the cetyl sulfate ions tend to remain in the surface layer of water molecules when the cetyl alcohol content is less than 50 mole %, but as the cetyl alcohol content is increased, the cetyl sulfate ions are withdrawn into thecetyl alcohol layer, carrying some water molecules with them, but far fewer thanwould be associated in solutionwith these ions were they to remain in the surface layer of water. This phenomenon explains the sharp transition in pressurearea isotherms with increasing cetyl alcohol content and the change in first-order transition pressures. This phenomenon does not involve the formation of any complexes but is more like the transition which occurs in oilin-water emulsions as the phase ratio of oil is increased until they invert into water-in-oil emulsions; it is a transition from one physical state to another without involving any stoichiometric complexes. These conclusions have considerable significance with regard to biological membrane studies. Such membranes are composed of mixtures of surface-active materials, some of which are sufficiently water-soluble to tend to give ideal solutions in the interfacial layer of water molecules. Other components are sufficiently insoluble in water that they tend to be oriented towards and adjacent to the interfacial layer of water molecules but are not dissolved in it. Thus, changes in the phase ratio of these components in membranes can influence very strongly their permeability. Membranes in which a large proportion of the molecules are an ideal solution in the adjacent monolayer of water molecules are normally very permeable, whereas if the phase ratio of insoluble material were greater, these molecules would be withdrawn from the adjacent monolayer of water molecules and provide a more tightly-packed and less penetrable membrane. The conclusions of this paper are also important in understanding the performance of detergent Eormula-
FREDERICK M. FOWKES
1986
tions, where surface-active substances of low water solubility are added to detergents to increase detergency, solubilizing capacity, and foam stability. The best-known example is the addition of about 15 mole % of dodecyl alcohol t o sodium dodecyl sulfate. Surface films on solutions of this composition are found to be highly condensed and very viscous and have been shown to contain 50 mole yoor more of dodecyl alcoh01.~ The effectiveness of the dodecyl alcohol in producing viscous films and in stabilizing foam depends on the adsorbed monolayers containing 50 mole yo or more of dodecyl alcohol. Negligible foam-stabilizing action results when the proportion of dodecyl alcohol or other foam-stabilizers in the adsorbed monolayers is less than 50 mole %. The reason for the effectivenessin stabilizing foam is probably the fact that the condensed monolayers have very steep pressure-area relations, and consequently the Gibbs elasticity lo is greatly enhanced. At room temperature some of these mixed monolayers are highly viscous and it was thought a t one time that the enhanced viscosity explained the greater foam stability. However, a t normal temperatures for use of household detergents (about 55-65'), there is no observable effect of these additives on surface viscosity,11 yet they are highly effective in promoting foam stability3; this is considered evidence in favor of the Gibbs elasticity mechanism. Acknowledgment.-The author wishes to express his thanks to Miss Helen L. Robbins for her care and precision in performance of the experimental work.
DISCUSSIOK V. K. La MER (Columbia University).--I
object to Dr. Fowkes' failure to recognize the pertinency of previous work of La Mer and collaborators in respect to a number of points he has just presented. Figure 2 of Fowkes' article on penetration of cetj-1 alcohol monolayers by cetyl sulfate follows closely the curves plotted by Robbins and La Mer [ J .CdEoid Sei., 15,137 (1960), Fig. 111where benzene was used as a penetrant in octadecanol monolayers. A detailed set of references will be presented where almost all of the points made by Fowkes on mixed monolayers have been given in somewhat different language by squeezing out as shown in Fig. 4 of Fowkes. See Archer and La Mer, J . Phys. Chem., 59, 200 (1955), and H. L. Rosano and 7'. K. La Mer, J . Phys. Chem., 60, 348 (1956).
F. &I. FOWKES.-PrOfeSSOr La Mer's classic work on the residual benzene in monolayers should not be overlooked. My excuse for omitting these references is that my papers were concerned with quantitative relations between the concentrations (or vapor pressures) of penetrants in both the monolayers and in adjacent phases. La Mer's findings give a good measure of how much benzene enters the monolayer, but I have not yet found in this work any information on the concentration of benzene in the adjacent substrate in equilibrium with the monolayer. However, if such information exists I would be very pleased to have the reference. (10) K. J. Mysels, M. C. Cox, and J. D. Skewis, J . Phys. Chem., 66, 1107 (1961).
(11) M. J. Schick, unpublished results.
Vol. 67
J. H. SCHULMAN (Columbia University).-The example given by Dr. Fowkes for a mixed insoluble monolayer of N a cetyl sulfate and cetyl alcohol on 5% NaCl solution to show that stable stoichiometric complexes do not exist in monolayers as measured by monolayer penetration techniques is not valid for the system given by him. In penetration experiments, the mixed film is in equilibrium with an adsorbed film of long chain sulfate. This can be shown by surface potential measurements of the mixed film alone on saline solutions and with long chain sulfate in the substrate. The penetration surface potential value agrees with the latter case [E. D. Goddard and J. H. Schulman, J . Colloid Xci., 8 , 309, 329 (1953)]. Compression of a cetyl alcohol monolayer on a Na cetyl sulfate solution in the presence of a dilute salt solution collapses a t a 1:1 complex when compressed a t a surface pressure just above the surface tension of the acetyl sulfate solution [J. H. Schulman and E. Stenhagen, Proc. Roy. SOC. (London), 126B,356 (1938)]. The fact that the surfaces of solutions of long chain sulfates are possibly bimolecular leaflets in structure as indicated by their surface potentials has been ignored. F. M. FowKEs.-The conclusion that no complexes in the colligative sense occur in these monolayers was demonstrated in a previous p ~ b l i c a t i o nusing ,~ data obtained on very dilute salt solutions. I agree that a change in area occurs near the 1:l ratio of sulfate to alcohol as shown here in Fig. 1 and 2, and believe that Fig. 4 explains how this can occur without formation of complexes. A. W. ADAMSON(University of Southern California).Your eq. 2 as well as the parent equation
kT In X I
+ nu1
=
kT In N1
(a)
(1 denoting solvent; ideal solutions assumed) appear to me to be based on a model rather than being general first- and second-law relationships. If they were the latter, i t should be possible to derive them from the usual form of the Gibbs equation
dn
=
rlkT d In N1
+ rl kT d In N z
(b)
Equation b leaves undetermined the manner of locating the dividing surface but then it appears approximate in this case to define it by the condition rlul rzoz = 1 (also XI = I'l/(I'l I$). If this be done, then eq. a can be written
+
dn
=
+
kT In N I - kT d In XI
and if d n be eliminated between this and (b), one obtains
Integration then yields a specific relationship between composition and adsorption and one that need not in general be expected to be valid. I would appreciate your comments on this general (and specific) matter. F. &I.FoTvKEs.-Equation 2 and its parent equation3-s7 are based on the model of a monomolecular film adsorbed from or spread upon a bulk phase, a phenomenon not appreciated in the time of Gibbs. Most of the many who have used this approach4 assume for ease of calculation that the surface tension is confined to the surface layer, but not all. This equation is far more convenient for surface films containing appreciable concentrations of solvent, where the above definition of X I becomes awkward. I prefer not t o use the surface excesses of Gibbs, but actual mole fractions. E. HUTCHINSON (Stanford University).-With regard to the question raised by Dr. Adamson, the Gibbs equation contains two unknowns and one variable, so that Dr. Fowkes is making use of a particular convention to interpret the Gibbs equation-as must be done in every situation in which this equation is used.
