Langmuir 1986,2, 349-354
349
does not in other cases. A main difference between two structure which, in turn, is impossible with long alcohols. kinds of interfaces is stressed: the hydrophobic tails of The presence of a surface interaction energy depending surfactants either at least partly escape or do not escape on the chain length revealed by the data reported in this contact with water molecules. The observed behaviors are paper gives weight to the treatment of the interphase by better described in terms of hydrophobic interactions than means of activity coefficient^.^^ Given this analogy bein terms of van der Waals forces which would have also tween a surface layer composed of an aliphatic compound had a noticeable influence at free surfaces. and water, the isotherm plateau could be understood as The interactions that influence the solution behavior arising from something like a surface d e m i ~ i n g . ~ ~ should thus be also taken into account for describing those The notion of interfacial activity coefficient or surface working in microscopic phases. The lower dimensionality interaction energy can also explain why congruence with of the latter and the interfacial electrical field should respect to the polar head was not found. As shown by quantitatively change the effects of a given interaction with Conway and et al.159the displacement of a dipolar molecule respect to the bulk phase in some and perhaps all cases. from infinity into the surface layer involves an electrostatic energy and leads to the addition of a term e ~ p ( p ~ O ~ / ~ The / ~ ) hydrophobic interaction which is thought responsible for surfactant adsorption works also in surface layers and in the isotherm expression; p is the perpendicular comprobably in any region of microphases containing some ponent of the dipole moment of a molecule adsorbed, 0 the amount of water. If the variation with the chain length coverage, and E the bulk dielectric constant. The dipole of a related property was found to be smaller than the moments of butanol, butyric acid, and butyramide are variation of the activity coefficient in the aqueous phase, respectively equal to 1.66,1.65, and 3.48 pD at 25 OC@ , ' and the presence of water in the interfacial regions rich in thus congruence of butanol with butyric acid but not with surfactant might be suspected. butyramide could be predicted. It would be useful to examine in further papers how 5. Conclusion other interactions changing the solubility of aliphatic The differences in the Traube coefficient according to species influence the adsorption behavior. One would have the conditions used may be interpreted in a simple way to appreciate to what extent the latter is controlled as well by taking into account the presence of activity coefficients by interactions actually localized in interfacial regions. in the surface layer. The properties would depend on the Such information could help to better understand how area of the adsorbed molecules in contact with water; this these interactions work in polyphased systems with surarea does depend on the chain length in some cases but factants. (58)Privat, M;Bennes, R. J. Colloid Interface Sci. 1982, 90,454. (59)Conway, B. E.;Barradas, R. S. Electrochim. Acta 1961,5, 319. (60) Smith, J. W. Electric Dipole Moments; Butterworths: London, 1955.
Registry No. Hg, 7439-97-6;butanol, 71-36-3; pentanol, 7141-0; hexanol, 111-27-3;octanol, 111-87-5;propanoic acid, 79-09-4; butyric acid, 107-92-6;pentanoic acid, 109-52-4;hexanoic acid, 142-62-1.
Static and Dynamic Properties of Pentadecanoic Acid Monolayers at the Air-Water Interface Yen-Lane Chen,? Masahito Sano,* Masami Kawaguchi,t Hyuk Yu,*i and George Zografi*t School of Pharmacy and Department of Chemistry University of Wisconsin-Madison, Madison, Wisconsin 53706 Received December 4, 1985. I n Final Form: January 31, 1986 The static and dynamic properties of pentadecanoic acid at the air-water interface have been examined by using the surface light scattering technique combined with the Wilhelmy plate method. Surface pressure ( A ) vs. area per molecule ( A ) plots for films studied by stepwise compression or by one-shot spreading, over the range of 500-20 A2, exhibited a distinct plateau between the liquid-expanded (LE) to liquidcondensed (LC) phase transition at 31.2 A2. Surface scattering measurements of capillary waves at well-defined wavenumbers for the same monolayer allowed estimation off,, the frequency shift at maximum intensity, and Af,,, the instrument-width-correctedspectral full width at half-height. In contrast to previously reported surface scattering data with less pure pentadecanoic acid, a sharp first-order discontinuity was observed at the LE/LC phase transition. From 500 A2 to the phase transition, A and the corresponding dynamic counterpart increased monotonically, showing little change from pure water at A > 50 A2. However, Afs,c,a measure of the temporal damping of the capillary waves, exhibited a significant increase from 100 to 50 A2, followed by a continued decrease to the LE/LC transition. Static and dynamic elastic moduli were compared and their correspondence and disparity were found at different regions of surface concentration.
Introduction Monolayers of amphiphilic molecules at the air-water and oil-water interface have been of great interest to scientists in diverse fields. They have long been used to 'School of Pharmacy. 1Department of Chemistry.
investigate the structure and properties of biological membranes,' and more recently there has been increasing interest in their use to study the two-dimensional properties of polymers.2 Of some importance are the viscoe(1) Shah, D. 0. Prog. Surf. Sci. 1972, 3. (2) Takahashi, A.; Kawaguchi, M. Adu. Polym. Sci. 1982, 46, 1.
0743-7463f 86f 2402-0349$01.50f 0 0 1986 American Chemical Society
350 Langmuir, Vol. 2, No. 3, 1986
Chen et al.
lastic properties of the monolayer and their relationship to processes such as membrane permeability, polymer adsorption, and emulsion stability. In particular, dynamic parameters, e.g., dilational and shear viscosity, have been typically deduced from studies of monolayer flow3 and by the spatial damping of mechanically induced surface waves.@ The results from these studies are often difficult to interpret because the system is usually perturbed significantly from the equilibrium state. The surface light scattering technique on the other hand probes the surface capillary waves spontaneously induced by thermal fluctuations of the underlying liquids, thus eliminating this shortcoming by imposing no physical contact with the liquid other than the incident photons. The theory of capillary waves' and light scattering techniques has been reviewed recently. Consequently, for the sake of brevity, only a few salient equations will be presented in discussing the essential features of capillary waves. For a pure liquid in contact with air, capillary waves are governed by the Lamb-Levich dispersion equationgJO (iw +
+ g k + ( u l z 3 ) / p = 4u2k4[1+ O / ( V ~ ~ ) ] ' (1) /~
where the complex angular frequency, w , is given by w =
idk
+ ir
(2)
with wk being the angular frequency of a wave with wavenumber k (=2a/X) and r being the temporal damping constant of the wave, u the kinematic viscosity ( q / p ) , p the liquid density, g the gravitational constant, and u the surface tension. A first-order approximation to the solution of eq l9 is expressed as w
= [gk
+ (uk3)/pI1/' + i2uk2
(3)
By comparison of eq 2 and 3,
and
r
= 2uk2
(5)
in this approximation. Further, in the range of experimentally accessible k, 100-1OOOcm-l, the gravitational part (gk) of eq 4 is negligible, hence the angular frequency wk is simply related to surface tension and density of the liquid as
The light scatteringtheory of surface capillary waves was first developed by Bouchiat, Langevin, and Meunier,l'!l2 whereas the first experimental feasibility was shown by (3)Joly, M. In Recent Progress in Surface Science; Danielli, J. F., Pankhurst, K. G. A., Riddiford, A. C., Eds.; Academic Press: New York, 1964;VOl. 1, p 1. (4)Mann, J. A.;Hansen, R. S. J. Colloid Sci. 1963, 18,757. (5)Lucassen, J. J. Trans. Faraday SOC.1968,64,2230. (6)Lucassen, J.; van den Tempel, M. J. Colloid Interface Sci. 1972, 41,491. (7)Stone, J. A.; Rice, W. J. J . Colloid Interface Sci. 1977,61,160. (8)Langevin, D.J. Colloid Interface Sci. 1981,BO, 412. (9)Lamb, H. Hydrodynamics, 6th ed.; Dover: New York, 1932;p 627. (10)Levich, V. G.Physicochemical Hydrodynamics; Prentice-Hall: Englewood Cliff, NJ, 1962;p 603. (11)Bouchiat, M. A.; Meunier, J. J.Phys. (Les Ulis, Fr.) 1971,32,561. Bouchiat, M. A. C. R. Acad. Sci., Ser. B. 1971,272, (12)Langevin, D.; 1422.
Katyl and Ingard.13 This was followed by a clear demonstration of McQueen and LundstrOml4and Langevin15 that Q and Y could be deduced from the dynamic surface light scattering. The Doppler-shifted power spectrum of scattered light from capillary waves at a specific scattering angle having a particular scattering wave vector arises exclusively from the surface wave with the same wavenumber k . Hence the power spectrum is shown to be a Lorentzian,
where the frequency shift, f,, corresponds to such that Wk2
= (2?rf,)2= ( u k 3 ) / p
wk
of eq 4' (7)
and the spectral fullwidth at half-height, 4,,corresponds to the temporal damping constant r of eq 5. A and B are constants that depend on the efficiency of the photodetector and the shot noise, respectively. The observed width 4,must,however, be corrected for the instrumental width arising principally from the Gaussian intensity profile of the incident laser beam. After the appropriate correction (see below) then it can be equated to via 2r(Af8,J2) =
r
= 2uk2
(8)
where Af,,, is the corrected spectral full width at halfheight. The applicability of eq 7 and 8 is now well establi~hed11~J~ and we have recently shown with the use of three test liquids, water, anisole, and ethanol, that our instrument calibration performs well with these identitiese20 Notwithstanding the first-order approximation imbedded in eq 7 and 8, as contrasted to solving for the f d dispersion equation, eq 1,their validity is now well accepted and the spatial damping constant obtained through eq 8 has recently been used to test various theories of capillary waves on the air-water interface by Byrne and Earnshaw.ls When the liquid surface is covered with monolayers of amphiphilic molecules, the power spectrum is no longer a simple Lorentzian as in eq 6, but rather it is a complex expression having a profile close to, but not exactly, a Lorentzian. The most general expression for the power spectrum due to capillary waves from a film-covered surface is given by Langevins as
where the relevant dispersion is given by D ( S ) = S2[(1+ S)2+ Y - (1 + 2S)'/'] + (aY + OS) X (S2(1+ 2sp + ( Y + yS)[(l + 2S)'/2 - 11)+ $33 (10) where Y Eup/4v2k,s = iw0,T~ = p/27k2, CY = e/u, /3 ~ k / 2 7 , and y & / 2 q , e and K are the dynamic elasticity and viscosity, and N is the transverse viscosity of the monolayer. (13)Katyl, R.H.; Ingard, U. Phys. Reu. Lett. 1967,64,19;1968,65, 270. (14)McQueen, D.;LundstrBm, I. J. Chem. SOC.,Faraday Trans. 1 1973,69, 694. (15)Langevin, D.J. Chem. Soc., Faraday Trans. 1 1974,70,95. (16)Hard, S.;Hamnerius, Y.; Nilsson, 0.J. Appl. Phys. 1976,47,2433. (17)Byme, D.;Earnshaw, J. C. J . Phys. D 1979,12,1133. (18)Byrne, D.;Earnshaw, J. C. J . Phys. D 1980,13,1145. (19)Edwards, R.V.;Sirohi, R. S.; Mann, J. A.; Shih, L. E.; Landing, L.Appl. Opt. 1982,21,3555. (20)Sano, M.; Kawaguchi, M.; Chen, Y.-L.;Skarlupka, R. J.; Chang, T.;Zografi, G.;Yu, H. Reu. Sci. Instrum., in press.
Langmuir, Vol. 2, No. 3, 1986 351
Properties of Pentadecanoic Acid Monolayers
I t should be noted that both t and K consist of dilational and shear components. To date, a number of experiments with lipid and polymer monolayers have been reported in the literature, using The results, so far, suffer from some this uncertainty because of experimental imprecision and because of discrepancies in the viscoelastic parameters estimated in different studies. HArd and NeumanZ3have reported data for two fatty acids and one phospholipid which exhibit considerable improvement in precision, but some question still remains as to the interpretation of their results and the level of purity of their samples. For example, they were unable to observe through static or dynamic measurements the first-order liquid-expanded to liquid-condensed (LE/LC) phase transition recently demonstrated by the careful work of Pallas et al.24325 The purpose of this study is to (1)determine the surface pressure-area curves for a model compound, pentadecanoic acid, by the Wilhelmy plate method, using an extensively purified sample, (2) test the capability of a newly developed light scattering apparatus,m (3) measure the dynamic properties of this monolayer relative to earlier studies, and (4) compare the static and dynamic properties of this system.
Experimental Section Materials. Pentadecanoic acid (Nuchek Prep, Elysian, MN) had a stated purity of 99% and was further purified by slowly recrystallizing it 5 times in double distilled spectrophotometric grade n-hexane (Aldrich Chemicals, Milwaukee, WI). The equilibrium Spreading pressure at 25 OC was in excellent agreement with that reported previously.26*nThe purity of distilled hexane was checked by placing it on the clean water surface and allowing it to evaporate. It was considered free of surface-active impurities if no change in surface tension was detected upon compression of the surface. The aqueous subphase was 0.01 N HCl solution prepared from concentrated HC1 (Hi-pure Chemicals Inc., Nazareth, PA) and deionized water. The house-distilled water was further deionized and purified with a Millipore Milli-Q filtering system with one carbon and two ion-exchange stages. Methods. All monolayer experiments were performed in a Teflon trough (28.5 X 11.1 X 1.0 cm) inside a Plexiglas box (68 x 30 X 24 cm). The temperature was controlled at 25 “C (*0.1 “C) by circulating thermostated water through a glass coil placed in the bottom of the trough. Several beakers with wetted filter papers were placed inside the box to maintain high relative humidity. Monolayers were formed by spreading a hexane solution of pentadecanoic acid on the aqueous subphase delivered from an Alga or a Hamilton micrometer syringe. At least 15-20 min were allowed for hexane to evaporate. The surface pressure was measured by a platinum plate connected to a Cahn 2000 electrobalance. The surface concentration was varied either by stepwise compression with a Teflon barrier or by spreading an appropriate amount of solution on a clean surface to give the desired surface concentration (one-shot spreading). The surface pressure and light scattering measurements were undertaken as soon as thermal and vapor equilibrium were reached. A complete light scattering measurement at one surface concentration usually required 20 min. A light scattering experimental setup and a demonstration of accuracy and precision with three pure solvents have been reported previously.20 The power spectrum, acquired on a spectrum an(21) Hard, S.; Lofgren, H. J. Colloid Interface Sci. 1977, 60, 529. (22) Langevin, D.; Griesmar, C. J.Phys. D 1980, 13, 1189. (23) Hard, S.; Neuman, R. D. J. Colloid Interface Sci. 1981,83, 315. (24) Pallas, N. R. Ph.D. Thesis, Clarkson University, Potadam, NY, 1983. (25) Pallas, N. R.; Pethica, B. A. Langmuir 1985,1, 509. (26) Middleton, S. R.; Iwahashi, M.; Pallas, N. R.; Pethica, B. A. Roc. R. SOC.London, Ser. A 1984,396, 143. (27) Iwahashi, M.; Maehara, N.; Yoshihide, K.; Seimiya, T.; Middleton, S.;Pallas, N. R.; Pethica, B. A.; J.Chem. Soc., Faraday Trans. 1 , 1985, 81, 973.
1 -
I
”
’
PENTADECANOIC ACID
--
I
I
VI
I Figure 1. Power spectra for pentadecanoic acid monolayers at different areas per molecule are shown at k = 323.5 cm-’ spread on 0.01 N HCl at 25 OC. In the inset, It dependence of power spectra is shown at A = 30.3 A2/molecule. alyzer (Nicolet 444A), is fitted to a Lorentzian function to obtain the frequency shift cf,, at the peak and the full width at half-height
(Af,). Results and Discussion Figure 1 shows typical power spectra obtained for the pentadecanoic acid monolayer at one surface concentration and three surface wavenumbers (260.6,323.5,368.1 cm-l) as well as the progression of power spectra as A , the monolayer area per molecule, is decreased from to 23.5 A2. The frequency shift and width at half-height obtained from the best fit of the Lorentzian function have an error within 1%and lo%, respectively. To account for the Gaussian instrument function, the width was further corrected by the procedure of HArd et a1.16 as Afs,, = Afs - ( A f ? / A f s )
(11)
where Afi is the Gaussian instrumental width, which was separately determined for each k by the method of intensity profiling.16 The surface pressure vs. surface area per molecule isotherm (T-A),obtained by both compression and “one-shot spreading” from 45 to 20 A2, is shown in Figure 2A. A distinct plateau is observed in the region of the LE/LC phase transition. At A 1 23.5 A2,surface pressure remains constant over the entire time course of the measurement. Below 23.5 A2, a slow loss in surface pressure with time was noted. This is presumably due to desorption and not leakage since it occurred with both the compression and “one-shot spreading” technique. The data points below 23.5 A2 were taken after 2-3 h when equilibrium was not reached but the time dependence was substantially attenuated. The results of the two methods show no difference at lower surface concentrations, not however, at the end of the LE/LC transition region: the surface pressure obtained by the compression method is slightly higher than that by the “one-shot”method. Such behavior was also noted by Pallas et al.24325 Turning to the dependence of the spectral shift fs on A, we have devised a simple experimental function analogous to the surface pressure. Since r,as deduced from the static
Chen et al.
352 Langmuir, Vol. 2, No. 3, 1986
I
I
I
I
I
I
4
L 7
? I
20
O.'t 10
25
Q
? I
s.. 9
001-
35 ' A/i2/molecu le 30
IO0
40
?,
.
45
Figure 3. Values of T d ( p ) estimated from eq 13 in text for three values of p, 1.00 ( b ) ,1.10 (o),and 1.20 ( 9 ) g/cm3, vs. area per molecule, A , compared with the static surface pressure, T (e),for pentadecanoic acid monolayers spread on 0.01 N HC1 at 25 "C.
L-
I
I 31.2 I d
06 bo
I
I
A
0
,
As for the behavior of the corrected spectral width Af,,, relative to A, the results are presented as follows. As dictated by eq 8, Af,,,/k2 is plotted against A in Figure 2C. The temporal damping constant, r (proportional to Af,,,), shows a break at the same A, 31.2 A2, as in a and rd'. Again, we claim the same point as in ad', that this sort of correspondence between the static and dynamic quantities has not hitherto been reported. It should be pointed out that in Figure 2C the damping coefficient decreases as surface concentration increases until the onset of the phase transition. We now come to the empirical basis for proposing a&), vs. as defined in eq 13. In Figure 3, three plots of A are compared directly to the a-A isotherm. Despite the scatter in a&), it is remarkable that Td(1.10) and a agree so well in their absolute values. Here we are, indeed, comparing the absolute values of a d at p equal to 1.10 and those of a and not just their dependence on A. The agreement starts to worsen at A equal to around 40 A2, which is to be expected since the effective density, p, should become smaller as we dilute the surface concentration. Two other ?rd(p) data sets are shown to indicate how sensitively a d depends on the adjustable parameter p . The pivotal point here is to provide an affirmative test of the hypothesis that the pentadecanoic acid covered water surface could be treated operationally as another liquid surface having a slightly higher density than water. Whether such a scheme might be applicable to all monolayer- or film-covered surfaces at moderately high surface concentrations remains to be examined. In any event, we have provided by this demonstration a sensible rationale for defining the "dynamic surface pressure", as in eq 13, a useful experimental quantity readily obtainable by the light scattering method. We emphasize here, however, that eq 13 is defined with the approximation of eq 7, which is valid only to a first order even for a simple liquid not covered with a monolayer. Hence, eq 13 should be viewed as a primitive step to draw a parallel with the static a from the light scattering spectral shift results. The agreement shown in Figure 3 between a and a d should be regarded at best as an interesting comparison but without attributing any profound physical significance. The "uniform density", p , is an adjustable parameter whose meaning is obscure. To explore the capabilities of the light scattering technique further, experiments were carried out at lower surface concentrations where a, as reported by pal la^,^^ is
Langmuir, Vol. 2, No. 3, 1986 353
Properties of Pentadecanoic Acid Monolayers I
386.1 323.5 6 260.6
0
6
Q
-
E
,u4
c
U
W
'L
i
0
2 I
i C
)
8 31.2 I
1
I
40
60
80
0O0Q
100
A (82/motecute) Figure 5. Elasticities vs. area per molecule for pentadecanoic acid monolayers spread on 0.01 N HCl at 25 O C : static elasticity, (a),and dynamic elasticity, t, at 386.1 (0-) and 323.5 cm-' (-0).
c)
E 4
0. I
A/f2/moiecute
Figure 4. Values of lrd' (A) and 4&,/k2 (Bjv8. area per molecule, A , for pentadecanoic acid monolayers spread on 0.01 N HCl at 25 "C, for values of A out to 500 A2 per molecule.
constant at around 0.16 dyn/cm. In Figure 4A, B, where f, and Afa,,are plotted against A out to 500 A2, it can be seen that these parameters remain essentially unchanged from a value close to that of water until about 100-125A2. Whereas no change in a occurs from about 125 to 50 A2, both f, and Af4,. undergo some change. Note, in particular, the significant increase in Af,,, to a maximum at about 50 A2. We will shortly return to this maximum in the temporal damping constant, which is directly proportional to 4%,. Simultaneously we observe that ad exhibits a plateau in the same region of A while a remains small and constant at around 0.16 dyn/cm. It seems certain that the two dynamic variables, a d and r, reflect some changes in the monolayer state while the static variable, a,is rather insensitive to such in the range 50 A2 IA I200 A2. Furthermore, we note that the damping constant is anomalously scattered in the same range of A. We have, however, noted no specific time dependence in the power spectra of scattered light. Similar observations, believed to be due to heterogeneities caused by "island" formation, were reported by HBrd and NeumanSz3 We now return to the observed maximum in Af,,,, which amounts to a maximum in the temporal damping coefficient, I', of capillary waves (eq 8). As early as 1951, Dorrestein28 reported that a maximum in the spatial damping coefficient, a,should occur. More than 20 years ago, a quantitative theory was d e v e l ~ p e to d ~predict ~~~ a maximum in a,at some finite surface elasticity, E. Experimental verification of the prediction f o l l o ~ e d . ~The ~?~~ situation has been well reviewed by Hansen and Ahmad.33 Paralleling the spatial damping coefficient, the temporal damping coefficient has also been shown to go through a (28) Dorrestein, R. Proc. K.Ned. Akad. Wet.,Ser. B Phys. Sci. 1951, 54, 260. (29) Hansen, R. S.; Mann, J. A. J. Appl. Phys. 1964,35, 152. (30) van den Tempel, M.; van den Riet, R. P. J.Chem. Phys. 1965,42, 2769. (31) Lucaseen, J.; Hansen, R. S. J. Colloid Interface Sci. 1966,22,32. (32) Lucassen, J.; Hansen, R. S. J.ColZoid Interface Sci. 1967,23,379. (33) Hansen, R. S.; Ahmad, J. Prog. Surf. Membr. Sci. 1971, 4, 1.
maximum at an intermediate value of e/ a; Langevid has given a clear review of its development. This can be shown by numerically solving for eq 9 with eq 10. A maximum in I? occurs when the capillary wave is optimally coupled to the longitudinal wave, at the same finite value of tlu. From what we see in Figure 4,such a point occurs when A 50 A2. We should now ask, what is the molecular organization of the pentadecanoic acid monolayer at 50 A2? On the basis of the phase diagram of pentadecanoic acid,% we surmise that this may be where biphasic coexistence of the LE and gaseous monolayer states is terminated and the uniphasic LE state is just attained. If one could confirm this unambiguously, then it suggests an intriguing corollary that r, deduced from the light scattering technique, may be a far more sensitive probe for detecting various phase changes in a monolayer than static a. In any event, one must search for significance of the phase behavior when r maximizes, in contrast to just observing that such behavior should take place at a finite t / u by virtue of wave mode coupling.8 To pursue further the light scattering results, surface viscoelastic parameters were estimated from the light scattering data according to eq 9. As in earlier studies,18,21,23 the transverse surface viscosity ( p ) was assumed to be negligible, while dilational elasticity (e) and surface viscosity ( K ) were obtained by matching the experimental f a - 4a,c pair to the theoretical f ,- 4,,, pair calculated from eq 9. It should be kept in mind that numbers generated by curve fitting to eq 9 have a substantial uncertainty in view of the assumptions made and the errors associated with the measurements of f , and, especially, Af,,,. The values of static elasticity, E,, were obtained from the a-A isotherm by using the following equation:34 t, = -A(da/dA) (14) Figure 5,comparing static (ea) and dynamic (E) elasticities as a function of A, reveals interesting similarities and differences. In the region of A less than 45 A2,t and e, exhibit very similar values, which might be expected for an insoluble monolayer.35 However, at higher areas the dynamic elasticity clearly reflects behavior not observable with static measurements. Surface viscosities K calculated from eq 9 appear to fall in the range of lo4 to lo4 surface (34) Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Gas Interfaces; Interscience: New York, 1966. (35) Lucassen-Reynders, E. H. In Anionic Surfactants; LucassenReynders, E. H., Ed.; Marcel Dekker: New York, 1981; p 173.
Langmuir 1986,2,354-361
354
poise and are very small relative to the dynamic ekticities. Since the dynamic modulus e* is defined36as e* = e + iWK (15) for a monolayer, for example, with a a of 2.5 dyn/cm and f , equal to 9596 Hz, the estimated surface dynamic viscosity is 7.5 X lo4 surface poise. This corresponds to a contribution of viscosity to dynamic modulus of about 0.45 dyn/cm (wK),as opposed to 28.5 dyn/cm from the dynamic elasticity.
Conclusions 1. A surface light scattering method for studying spread monolayers, developed in our laboratory,% has been used to give precise measurements with pentadecanoic acid. The demonstration of the first-srder LE/LC phase transition, with measurements of frequency shifts and damping coefficients, reinforces the importance of extensive purification of the sample in the study of monolayers and confirms that the equipment, as designed, should be useful in assessing the behavior of other monolayer systems.36 2. A dynamic analogue of the static surface preeaure has been proposed and used for testing affirmatively the hypothesis that the monolayer-covered water surface can be (36) Kawaguchi, M.; Sano, M.; Chen, Y.-L.; Zografi, G.; Yu, H. submitted for publication in Macromolecules.
approximated as another homogeneous liquid surface having an effective density higher than the subphase liquid. 3. By carrying out studies from 500 A2per molecule to just beyond the plateau region it was possible to observe dynamic properties not previously reported by using light scattering studies. Of particular interest are the changes in fr uency shift and damping coefficient from about 125 to 50 2, believed to be the end of the region of coexistence between the "gaseous" and liquid-expanded phases.24 4. In general, from an application of the dispersion equation, it has been shown that surface elasticity plays a much greater role than surface viscosity in determining the dynamic properties of this monolayer system.
1
Acknowledgment. This study was supported in part by the University Exploratory Research Program of Procter and Gamble Co. and by the Research Committee of the University of Wisconsin-Madison. We are most grateful to Dr.John C. Eamshaw of Belfast and Dr. Ronald D. Neuman of Auburn University for fruitful discussions. We also thank our colleague, Bryan B. Sauer, for his constructive critique of the data analysis and interpretation. .One of the referees for this paper is also acknowledged for a number of critical comments which were used to revise the original manuscript. Registry No. Pentadecanoic acid, 1002-84-2.
Electrostatic Model To Describe Mixed Ionic/Nonionic Micellar Nonidealities James F. Rathman and John F. Scamehorn* School of Chemical Engineering and Materials Science and Imtitute for Applied Surfactant Research, University of Oklahoma, Norman, Oklahoma 73019 Received October 23, 1985. In Final Form: February 5, 1985 Critical micelle concentrations were measured as a function of compmitionfor three binary ionic/nonionic surfactant mixtures. These systems exhibit large negative deviations from ideality. Two models based on electrostatic considerations alone were developed to describe mixed micellar nonidealities. One model considers the micelle pseudophase to consist of surfactant components only, while the other also includes bound counterions. Both models give a priori predictions of mixture behavior and give excellent agreement with experimental data. These results indicate that the factors giving rise to the thermodynamicnonidealities are primarily electrostatic in nature.
Introduction The understanding of physical mechanisms involved in the formation of micelles composed of mixtures of surfadants and the modeling of this process are areas of great theoretical and practical interest. One model commonly used to describe micelle formation is the pseudophase separation modell which considers the micelles as a thermodynamic phase in equilibrium with the monomer. By treatment of the monomer and micelle as pseudophases, the cmc of a mixture of similarly structured ionic surfactants'* or nonionic s~rfactantalJ-'~ can be predicted reasonably well by assuming that ideal solution theory is obeyed in the micellar phase. However, the cmc of ionic/nonionic surfactant mixtures can be much less than that predicted by ideal solution This *Towhom correspondence should be addressed.
indicates that mixed-micelle formation between these dissimilar surfactants is enhanced, relative to that between (1) Shinoda, K. In Colloidal Surfactants; Shinoda, K., Tamamushi, B., Nakagawa, T., Isemura, T., Eds.; Academic Press: New York, 1963; Chapter 1. (2) Scamehom, J. F.; Schechter, R. S.; Wade, W. H. J.Colloid Interface Sci. 1982,85, 479. (3) Shinoda, K. J. Phys. CheM. 1954,58,641. (4) Mysels, K. J.; Otter,R. J. J. Colloid Sci. 1961, 16, 474. (6) Barry. B. W.; Morrison,. J. c.;. Russell, G. F. J. J. Colloid Interface Scii iwo, 33,554. (61 Shedlovekv. _ .L.:. Jakob. C. W.:. Eostein. . . M. B. J.Phvs. Chem. 1963. 67, '2075. (7) Nishikido, N.;Moroi, Y.; Matuura, R. Bull. Chem. SOC. Jpn. 1975, 48,1387. (8) Lange, H.; Beck, K. H. Kolloid 2.2.Polym. 1973,251, 424. (9) F u n d , N.; Hada, 5.J. Phya. Chem. 1979,83, 2471. (10) Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983,87, 1984. (11) Nishikido, N. J. Colloid Interface Sci. 1977, 60, 242. (12) Moroi, Y.; Akiaada, H.; Saito, M.; Matuura, R. J.Colloid Interface Sci. 1977, 61, 233.
0743-7463/S6/2402-0354$01.50/00 1986 American Chemical Society
