1620
J . Phys. Chem. 1986, 90. 1620-1625
relationship between the spectral response and its microenvironment. In more complicated systems such as mixed micelles or polymeric solutions, the singular value analysis may be useful to determine the linearly independent components and thus offers an insight into the heterogeneity of the system.
Protocol 313R07139 to R.W.W. The authors are indebted to R. M. Fitch and H. A. Hakemi at SCJ for their critical comments and also express thanks to Sheila Loughran at USUHS and J. R. Allaway, K. J. Welch, A. B. Pinero, and P. J. Anderson at SCJ for valuable technical assistance.
Acknowledgment. This work was supported in part by N S F Grant PCM-8302893, O N R Grant WR30342, and USUHS
142-82-5.
Registry No. SDS, 151-21-3; benzyl alcohol, 100-51-6; heptane,
Micellar Properties of Sodium Dodecylpoly(oxyethy1ene) Sulfates Claudio Minero,t Edmondo Pramauro,+Ezio Pelizzetti,t Vittorio Degiorgio,*f and Mario Corti$ Dipartimento di Chimica Analitica, Universitri di Torino, 101 25 Torino, Italy, Dipartimento di Elettronica-Sezione Fisica Applicata, UniversitCi di Pauia, 27100 Pauia, Italy, and C.I.S.E. S.p.A., 20134 Milano, Italy (Received: August 14, 1985; In Final Form: November 13, 1985)
Aqueous solutions of sodium dodecylpoly(oxyethy1ene) sulfates with one, two, and four oxyethylene units per monomer have been investigated at various NaCl concentrations by laser-light scattering, tensiometry, and conductometry. The critical micelle concentration, the aggregation number, the hydrodynamic radius, and the micellar hydration are given as functions of the number of oxyethylene units and of the salt concentration. The interpretation of the light-scattering data in terms of DLVO theory permits the derivation of also the electric charge of the micelle and the amplitude of attractive intermicellar forces.
Introduction Polyoxyethylenated surfactants having a sulfate group at the end of the molecule have great technical and economic importance.* Their wide applicability is mainly due to the special properties arising from the presence of the ionic sulfate group adjacent to the oxyethylene groups, thus combining some of the peculiar characteristics of anionic and nonionic surfactants. Despite their interest, only a few on this class of compounds are available concerning physicochemical properties such as critical micelle concentration, solubilization properties, Krafft point, and micellar parameters. In the present paper, compounds of the general formula C,2Hz5(OCHzCH2),0S03Na, w i t h j = 1, 2, 4 (hereafter called SDE,S) have been investigated through tensiometric, conductometric, and laser-light-scattering techniques. As is well-known, static and dynamic light-scattering data contain information not only about individual micelle properties, but also on intermicellar interactions. In order to separate the two contributions, the light-scattering data are analyzed according to the method proposed in ref 4 for sodium dodecyl sulfate (SDS) micelles and subsequently used for other ionic micellar solution^.^ Such a method assumes that, in the investigated range of amphiphile and salt concentration, the micellar properties do not depend on the amphiphile concentration, the pair interaction potential is that of DLVO theory, and the hydrodynamic interactions among the micelles are correctly described by the Felderhof6 (or Batchelor’) formulas. In this paper, however, we depart from previous work by explicitly taking into account micellar hydration in the data interpretation. Experimental Section The SDE,S surfactants were kindly donated by Henkel Co., West Germany, and used without further purification. Surface tension measurements were performed with a Kriiss K10 tensiometer equipped with a platinum blade. The temperature was 25.0 f 0.2 “C. Calibration of the apparatus was checked by measuring the interfacial tension of various pure liquids. Universiti di Torino. di Pavia. gC.1.S.E. S.P.A. 1 Universiti
0022-3654/86/2090-1620$01.50/0
The conductivity of aqueous surfactant solutions was measured with an Amel 123 conductometer, at 25.0 f 0.2 ‘C. The cell constant was determined by using KCI standard solutions. The light-scattering apparatus is the same as described in ref 4 and 8. The light source is a 514.5-nm argon laser. The scattered light intensity and the time-dependent correlation function of the scattered intensity are measured at a scattering angle 0 = 90’. The intensity calibration method used to derive the micellar molecular weights is the same as in ref 8. All measurements have been performed at 25 ‘C. Refractive index increments dn/dc have been measured with a standard differential refractometer. Surface Tension Data. Plots of the surface tension y of SDE,S aqueous solutions against the logarithm of the surfactant molar concentration C show the usual behavior. The plots relative to solutions with no salt added show a minimum which is indicative of the presence of some impurities. The critical micelle concentration (cmc) was taken as the concentration at the point of intersection of the two linear portions of the plots. The maximum surface excess concentration (r,mol cm-*) and the minimum area per molecule at the solution/air interface ( A s ,A2) are calculated from the Gibbs adsorption isotherm by using the following relations
A, = 10I6/NAr (1) Schwuger, M . J . In “Structure/Performance Relationships in Surfactants”; Rosen, M. J., Ed.; American Chemical Society: Washington, DC, 1984; ACS Symp. Ser. 253, p 3. (2) Tokiwa, F.; Ohki, K. J. Phys. Chem. 1967, 71, 1343. Tokiwa, F.; J . Phys. Chem. 1968, 72, 1214, 4331. ( 3 ) Hato, M.; Shinoda, K. J . Phys. Chem. 1973, 77, 378. Shinoda, K.; Hirai, T. J . Phys. Chem. 1977, 81, 1842. Hato, M.; Tahara, M.; Suda, Y. J . Colloid Interface Sci. 1979, 72, 458. Tsujii, K.; Saito, N.; Takechi, T. J . Phys. Chem. 1980, 84, 2287. (4) Corti, M.; Degiorgio, V. J . Phys. Chem. 1981, 85, 711. ( 5 ) Nicoli, D. F.; Dorshow, R. B. In “Physics of Amphiphiles: Micelles, Vesicles and Microemulsions”; Degiorgio, V., Corti, M., Eds.; North-Holland: Amsterdam, 1985; p 429. (6) Felderhof, B. U. J . Phys. A , : Math. Gen. 1978, 1 1 , 929. (7) Batchelor, G. K. J . Fluid Merh. 1976, 74, 1. (8) Degiorgio, V.; Corti, M.; Minero, C. N u m o Cimenro D 1984, 3, 44.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1621
Properties of Sodium Dodecylpoly(oxyethy1ene) Sulfates
TABLE I: Surface Tension Data for S D E S Solutions at Various Salt Concentrationsu
compd SDE,S
added salt (NaCI, M)
cmc x io4,
0.00
42 5.5 2.5 1.5 26 3.4 1.5 0.g5 20 2.5 1.2 0.65
0.10 0.30 0.60 0.00 0.10 0.30 0.60 0.00 0.10 0.30 0.60
SDE,S
SDE4S
r,
As, A2
mol cni2
M
&nc
AGOrnio
1
molecule-'
mN m-l
kJ mol-'
65.8 46.0 44.9 42.4 76.4 51.2 50.5 43.7 86.0 62.5 61.7 48.7
33
-13.6
31
-14.7
29
-15.4
2.5 X 3.6 3.7 3.9 2.2 3.2 3.3 3.8 1.9 2.6 2.7 3.4
"The symbols are defined in the text.
+
where R = 8.314 J mol-] K-I, N A is Avogadro number, f = 1 1/(1 + r ) , and r is the ratio between the molar concentration of added salt (NaCI) and the molar concentration of surfactant in the s o l ~ t i o n . ~ Values of cmc, I?, A,, and IIcmc(defined as Y~~~~~ - -ycmc) are reported in Table I. Electric conductivity measurements were performed only for the solutions with no added salt. Over the range of interest, the plots of specific conductivity vs. surfactant concentration gave two straight lines with a welldefined transition on the cmc region. This latter method gave cmc values 10-15% larger than the former. The cmc values in aqueous solution reported in Table I represent the mean obtained from surface tension and conductivity measurements. Variation of Cmc in the Presence of Added Salt. It is wellknown that the cmc of ionic surfactants decreases upon addition of salts. In the present case, since the added monovalent salt is a sodium salt like the surfactant, it is possible t o correlate the variation of cmc as a function of the total counterion concentration in terms of the fractional charge of the micelles.10 The treatment of the ionic micelle formation equilibrium in the presence of NaCl can be performed by applying the mass action law and assuming the pseudophase model for the charged micelles." From the equilibrium
nS-
+ mNaf
~t
M("-")-
where S- is the anionic surfactant monomer and M is the micelle, the following equation can be derived In cmc = K - (1 - q / n ) In (C,
+ cmc)
1
(3)
where A is an instrumental constant, c is the concentration (g ~ m - ~and ) , II is the osmotic pressure. Equation 3 refers to the case in which both the particle size and the range of interactions are much smaller than the wavelength of the incident light so that (9) Matijevic, E.; Pethica, B. A. Trans. Faraday SOC.1958, 54, 1382. Chattoraj, D. K. J . Phys. Chem. 1966, 70, 2687. ( I O ) Corrin, M. L. J . Colloid Sci. 1948, 3, 333. ( 1 1 ) Corrin, M. L.; Harkins, W. D. J . Am. Chem. SOC.1947, 69, 684. Mukerjes, P.; Mysels, K. J.; Kapouan, P. J . Phys. Chem. 1967, 71,4166.
I
I
I
I
I
0 c
-
-8
-9
-10
I
I
-2.5
-2
I
I
-1.5
-1
I
-0.5 IdCMC +CJ
Figure 1. Dependence of the critical micelle concentration (cmc) on the ionic strength of the surfactant solution. Cs is the molar concentration of NaCI. Dots, squares, and triangles represent, respectively, SDE,S, SDE2S,and SDE4Sdata.
I, does not depend on the scattering angle 8. When interactions , ~ - ' with the molecular weight are negligible, R T ( ~ I I / ~ C )coincides M . If we define the apparent molecular weight as Mapp= RT/(dII/dc),,, to the first order in the volume fraction 6,MaPp-l can be written as
(2)
where Cs is the molar concentration of the added salt, q is the effective charge of the micelle (q = n - m), and n is the number of surfactant molecules per micelle. From plots according to eq 2 an estimate of the degree of ionization a = q / n for the examined compounds in the present ionic strength range can be obtained. The fit to the data shown in Figure 1 gives a = 0.28 f 0.02 for SDE,S, a = 0.29 + 0.04 for SDE2S, and a = 0.31 f 0.05 for SDE,S. A slight increase of a with the number of oxyethylene groups is observed for the investigated compounds. This trend, although less pronounced, is in agreement with previous work* and with the light-scattering results discussed below. Light-Scattering Theory. The average intensity of light scattered by a solution of small and monodisperse particles, in excess of that scattered by the solvent, is
I , = AcRT(dn/dc)T,p-~
-r 0
Mapp-l= M - y l
+ kl$)
(4)
The coefficient kI is proportional to the second virial coefficient. If one considers rigid spherical particles of radius a with a pair interaction potential V ( x ) ,where x = ( R - 2a)/2a and R is the distance between the center of particles, k l is given by4
kl = 8
+ Jmdx 0
(5)
G(x)[l - exp(-V(x)/kgT)]
+
where 8 is the hard-sphere contribution and C ( x ) = 24( 1 x ) * . The collective diffusion coefficient D of a solution of small and monodisperse particles, as measured by quasi-elastic light scattering, can be expressed to the first order in the volume fraction $ by the eqbation D = Do(1
+ k&)
(6) where Do is the translational diffusion coefficient of the individual particle and kD describes the net effect of all interparticle interactions. The coefficient k,, is given by4v6 kD = 1.56 +
s,-
dx F(x)[l - eXp(-v(X)/k~T)]
(7)
where 1.56 is the hard-sphere contribution, and F ( x ) is given in ref 4. The potential V ( x ) ,as in DLVO theory,I2 can be expressed as (12) Verwey, E. J. W.; Overbeck, J. T. G. "Theory of the Stability of Lyophobic Colloids"; Elsevier: New York, 1948.
1622
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986
0.10
0
I 0.01
I
0.02
I
M
I
I
0.03 (c-c,)(g
Minero et al.
0.04
t
01 0
0.10
I
0.01
I 0.02
cm7
Figure 2. Reciprocal of the apparent molecular weight Mappof SDE,S solutions plotted as a function of the micelle concentration at various NaCl concentrations.
I
M
I
I
0.03 (c-c,)(g
0.04
cm7
Figure 3. The same as Figure 2 for SDE,S solutions.
the sum of a repulsive Coulombic part V,(X) and an attractive London-van der Waals part V,(x), v(x) = VR(x) + b ( x )
(8)
We have used for VR and V, the same expressions considered in ref 4. We simply recall here that VR and V, contain as unknown parameters, respectively, the particle electric charge q and the Hamaker constant A . It is important to note that the Hamaker expression for V, makes the integrals which appear in eq 5 and 7 divergent. To eliminate the divergence, one has to impose a lower cutoff xL > 0. The physical origin of x L is that the two particles cannot approach closer than the Stern layer thickness. It is easy to see from the structure of eq 5 and 7 that a purely repulsive interaction potential produces positive kl (and kD), and that kl (and k,) is larger when the amplitude and (or) the range of the repulsive potential are larger. The attractive part of the potential tends to reduce k l (and kD), and may lead, if large enough, to negative values of k , (and k D ) . The validity of eq 5 and 7 is limited to the range of parameters for which the pair correlation function of the suspended particles can be expressed as g(r) = exp[-V(r)/kBU. The relation fails when the range of the potential V(r) becomes comparable with the interparticle distance, that is, when the Debye-Huckel length K-' is large (low salt concentration C,) or when the particle concentration is large. It is, however, possible to use more general expressions which require the numerical calculation of g(r).13 A second limit to the validity of eq 5 and 7 must be set at high salt concentrations whenever the attractive interparticle potential promotes particle aggregation and makes, therefore, the solution polydisperse with a concentration-dependent size distribution of the aggregates. Instead of using eq 6-8, some author^'^,^^ have calculated the dependence of D on by using the continuity equations with an interaction term derived by a Debye-Huckel expansion. As was pointed out in ref 4 (see eq 17 and related discussion) and, more recently, in ref 15, such an approach implicitly assumes that the ionic micelle can be treated as a point charge and that the term exp[-V(x)/kBU can be approximated as 1 - V(x)/k,T. The micelle can be considered a point charge only when the DebyeHuckel length K - ~ is much larger than the radius a, which means very low salt concentrations. The approximation of the exponential term requires very low surface charge of the micelle. Both approximations are invalid for most part of the published studies on micellar and macromolecular solutions. ( 1 3) Cannell, D. S. In "Physics of Amphiphiles: Micelles, Vesicles and
Microemulsions"; Degiorgio, V., Corti, M. Eds.; North-Holland: Amsterdam, 1985; p 202. (14) Evans, D. F.; Mukherjee, S.; Mitchell, D. J.; Ninham, B. W . J . Colloid Interface Sei. 1983, 93, 184. (15) Belloni, L.; Drifford, M.: Turq, P. J . Phys. Lett. 1985, 46. 207.
I
0
00.20
I
1
0.01
0.02
M
1
1
0.03 (c-c,)(g
I
0.04 cm7
Figure 4. The same as Figure 2 for SDE4S solutions.
(c-c,)(g
cm31
Figure 5. Mass diffusion coefficient D of SDE,S solutions plotted as a function of the micelle concentration at various salt concentrations.
Light-Scattering Results. We report in Figures 2-4 the static light-scattering data for SDE,S, SDE2S, and SDE,S, respectively. The quantity Map;' is plotted vs. the micellar concentration c co, where co is the critical micelle concentration, at various NaCl concentrations. The plots are linear at low concentrations. The data points have been fitted with the linear expression M&'
= M-' [ 1
+ kI'(C
- eo)]
The obtained values of the aggregation number n are reported in Table 11. The intensity correlation results are analyzed by performing a polynomial fit to the logarithm of the time-dependent part of
The Journal of Physical Chemistry, Vol. 90, No. 8, 1986 1623
Properties of Sodium Dodecylpoly(oxyethy1ene) Sulfates TABLE 11: Micellar Properties of SDE,S Solutions” [NaCI], M 0.10 0.20
0.30
0.40
0.50
0.60
0.80
121 30.9 4 1.33 12.4 0.120
130 31.0 5 1.25 10.3 0.117
SDE,S
n R H ,A 102r; G,, cm3 g-l nh
dnldc, cm3 g-I SDE2S n
Rn, 8, 1020 cm3 g-’
DM,
nh
dnldc, cm3 g-’ SDE4S
n R H ,8, 1020
o,, cm3 g-’ nh
dnldc, cm3 g-’
146 29.6 10 I .34 7.9 0.115
164 30.2 10 1.27 7.9 0.1 14
177 31.1 10 1.30 7.9 0.113
200 32.3 12 1.28 7.9 0.1 11
126 (29.2) (1.32) (9.6) 0.120
137 29.4 3 1.24 8.0 0.119
148 29.6 4 1.18 6.7 0.117
161 30.0 3 1.12 5.4 0.116
96 29.3 8 1.43 15 0.129
100 29.6 4 1.41 14.4 0.127
105 30.0 3 1.39 14 0.125
112 30.2 2 1.34 12.6 0.123
8
,
168 30.2 4 1.10 5.0 0.1 14 116 30.6 2 1.34 12.6 0.122
OThe aggregation number n, the hydrodynamic radius RH, the fractional variance u, the specific volume of the hydrated micelle O M , and the number of water molecules per monomer nh a r e given for j = 1, 2, and 4 at various NaCl concentrations. The table also gives the refractive index increments dnldc. The estimated percent errors on the reported values are 10% for n, 3% for RM, 20% for u, 20% for nhr and 1% for dnldc. I
I
SDE,S Y
10 /
‘0.50 ‘0.80
M
8
e
0
0.01
0.02
0.03 (c-c&l
0.04 C d )
6
0
0.01
0.02
0.03 (c-l$(a
0.04 cni3)
Figure 6. T h e same as Figure 5 for SDE2S solutions.
Figure 7. The same as Figure 5 for SDE4S solutions.
the measured correlation function.16 Such a fit allows one to derive the average diffusion coefficient D and the fractional variance u. The obtained diffusion coefficients are plotted in Figures 5-7 vs. the micellar concentration c - co at various NaCl concentrations. As expected, the linearity of the plots extends over a concentration range larger for D than for Map;’. The experimental data have been fitted with the expression D = Do[l kD’(c- co)]. From Dothe hydrodynamic radius RH = k,T/ ( 6 ~ t D o )where , 17 is the solvent viscosity, is derived. RH and u are reported in Table 11. The experimental results indicate that n is a decreasing function of the number of ethylene oxide units and is increasing with the salt concentration. The increase is less marked for SDE4S than for SDE,S and SDE2S. The aggregation numbers found for SDE4Sare very similar to those obtained for SDS micelle^.^ The only previous values of n have been given by Tokiwa and Ohki2 by combining sedimentation and free diffusion data. Our results are not in agreement with those of Tokiwa and Ohki. In part the disagreement is due to the fact that the diffusion data of ref 2 are not correct. Indeed the plots in Figure 3 of ref 2 show that D is a decreasing function of amphiphile concentration for C, = 0.1 M NaC1, whereas it is known (at least for SDS micelles) that D increases with c. However, this effect alone cannot explain the
discrepancy. Probably, the difference in the purity of the used samples is the main reason for the discrepancy. It should be mentioned that Triolo et a1.l’ have performed neutron scattering measurements on SDE,S solutions by using the same material employed in our investigation. They obtain very similar values for n. The hydrodynamic radius is found to increase with C, for all three surfactants, whereas the dependence on the number of ethylene oxide units is much less pronounced. Note that R H is larger than that found with SDS micelles, consistent with the fact that both n end the monomer length are larger. We have derived the number of water molecules bound to the micelle per surfactant molecule, n h , as VH - DM/NA NA nh = (9) n 18
+
(16) Koppel, D. E. J . Chem. Phys. 1972, 57, 4814
where VH = (4/3)rRH3is the hydrodynamic volume of the micelle and 0 is the specific volume of the surfactant; d = 0.865 for SDE’S, 0.861 for SDE2S, and 0.852 for SDE4S, as given in ref 2. The obtained values of nh are reported in Table 11. They are in good agreement with those derived by Tokiwa and Ohki2 from viscosity and sedimentation data. Our data confirm that nh changes very little when j goes from 0 to 1 and 2 . It should (17) Triolo, R.; Caponetti, E. J . Solution Chem. 1985, 1 4 , 8 1 5
1624 The Journal of Physical Chemistry, Vol. 90, No. 8,1986
.Miner0 et al.
TABLE 111: The Slopes k , and k o for SDE,S, with j = 0, 1, 2, and 4, at Various Salt Concentrations [NaCI], M 0.1C 0.20 0.30 0.40 0.50 0.60 0.80 SDS 10.3 5.6 3.10 -0.4 25.8 14.3 9.8 2.3 11.8 27.4
6.1 15.0
1.5 3.0
-12.6 -16.2
12.1 24.3
7.2 17.1
4.4 9.2
3.5 6.0
-1.9 -1.0
11.4
7.3 19.9
5.1 15.2
4.2 10.9
3.8 10.6
32.8
3.2 10.5
I
0.10-0.40 0.10-0.30 0.10-0.40 0.10-0.80
0.26 f 0.01 0.30 f 0.02 0.40 f 0.01
Note that eq 9 and 10 imply that the density of water is 1 g / ~ m - ~ . Clearly, k l = klr/iiMand kD = k D r / L ' M . The coefficients k , and kD derived from the experimental results by using eq 10 are reported in Table 111. We now discuss the application of the theory expressed by eq 4-8 to the experimental Map;' and D data in the positive-slope linear-fan region. First, we have modelled the micelles as rigid spherical particles of radius a, independent of the surfactant concentration c. The radius a is taken to coincide with the measured hydrodynamic radius RH. Since the Debye-Huckel inverse screening length is fixed when the salt concentration is fixed, the only free parameter in the expression of the repulsive potential V, is the electric charge q or the fractional charge a = q/n. Concerning the choice of the cutoff xL,we have followed a criterion which is slightly different from that adopted in ref 4. If we consider that the measured R, includes also the Stern layer, it is more convenient to assume that the van der Waals attraction starts at a inner surface having radius R, - d, where d is the Stern layer thickness. This implies that the quantity z = x 2 x appearing in the expression of V, (see eq 11 in ref 4) should be written as
+
+ d + 2(
-) +
ax d a-d We have fixed d = 0.2 mm in our fit, but we have checked that the results are little influenced if d is taken equal to 0.1 nm. We have determined the two unknown parameters, a and A , by fitting the theoretical expressions to the experimental k , and k l . The results relative to kD are shown in Figure 8. The best fit values for cy and A are reported in Table IV. It should be noted that, at 0.1 M NaCI, both k l and k D are very ueakly dependent on A because the electrostatic repulsive barrier prevents the particles from getting close enough to feel the van der Waals forces. Therefore, the fit performed at 0.1 M NaCl allows to determine cy directly. If we now make the assumption that cy and A do not depend on the salt concentration, we can also derive A by fitting the salt concentration dependence of kD (or k l ) . If we do so, we obtain the values of A reported irLTable IV. In the case -)2 ax
a-d
I
I
1
\
'
\
\
'
" r\ \
I
1
I
1
'\ I
1
+
(
I
>I5 IO& 1 6 1 1
however be noted that the aggregation number of the SDE,S micelle is too large for a spherical shape, and the polydispersity of S D E I S micelles is larger than for SDE2S and SDE4S micelles (see the values of u in Table 11) so that the calculation of nh for S D E , S should perhaps also include a form factor. In order to derive the coefficients k, and kD defined in eq 4 and 6, we have to convert the micellar concentration (c - co) into a volume fraction. This can be done by calculating the specific volume of the hydrated micelle, CM, as L'M = L' 18(nhn/M) (10)
z =
I
2.5 10.6
TABLE IV: Fractional Charge a and Apparent Hamaker Constant A for SDE,S Solutions, As Derived from Light-Scattering Data compd range [NaCI], M (Y AlkET SDEIS SDS SDE,S SDEPS
I
I
-14
I
I
i
I
I
0.8 (NaCIIM Figure 8. The slope k D as a function of NaCl concentration for S D S (m), S D E , S (+), SDE,S (A),and SDE$ ( 0 )solutions. The full lines represent theoretical results; dotted lines a r e drawn only to guide the eye through the experimental points.
0
0.2
0.4
0.6
of SDE,S the fit was not satisfactory, and we can only assign a lower bound to A .
Discussion The observed decrease of the cmc of SDE,S solutions when j increases could be interpreted by saying that oxyethylene units give a hydrophobic contribution to the free energy of micellization. If we consider the values of AGO,,, reported in Table I, and compare SDS (AGo,,, = -12.0 kJ mol-') with SDE,S we can calculate a contribution of -1.6 kJ mol-' per oxyethylene group. Note that this contribution is smaller than that introduced by ethylene groups which is about -3.6 kJ/mol-' as calculated from cmc data on sodium decyl and dodecyl sulfates.'* On the contrary, it is well-known that in a nonionic surfactants such as CI2E,,by increasing j we increase the hydrophilic character of the surfactant, although the effect on the cmc becomes less and less important as j becomes larger.*9,20 The cmc is about 100 times larger for SDS than for CI2E, because repulsive interactions are much stronger for ionic groups like the sulfate than for weakly polar groups like oxyethylene units. The insertion of oxyethylene groups weakens the repulsive interaction between sulfate groups because it increases their average distance. It is therefore reasonable to expect that SDE,S presents an intermediate cmc between SDS and Cl,E,. (18) Mukerjee, P.; Mysels, K. J. "Critical Micelle Concentrations of Aqueous Surfactant Systems"; Natl. Stand. Re5 Data Ser. 1971, NSRDSNBS 36. (19) Rosen, M. J.; Cohen, A. W.; Dahanayake, M.; Hua, Xi-yuan J . Phys. Chem. 1982, 86, 541. (20) Degiorgio, V. In "Physics of Amphiphiles: Micelles, Vesicles and Microemulsions"; Degiorgio, V., Corti, M . , Eds.; North-Holland: Amsterdam, 1985, p 303.
J. Phys. Chem. 1986, 90. 1625-1630
1625
The data of Table I show that the addition of a sufficient amount of salt makes the influence of the sulfate group on the cmc very small. Indeed, the cmc of SDE4S with 0.6 M NaCl is about the same as found with C12E,solutions (see Table I of ref 20). The increase of the aggregation number n on going from SDS to SDE,S can perhaps be explained by noting that the reduced repulsion allows a lower area per head a. (measured at the surface of the hydrophobic core) and therefore gives a larger packing parameter V/aol ( V and 1 are, respectively, volume and length of the hydrophobic portion of the surfactant).2' The decrease of n as j grows from 1 to 2 and 4 could be attributed to the increase of a. because of the steric repulsion among the hydrated oxyethylene groups. If it is assumed that a, behaves similarly to A,, the data shown in Table I indicate indeed an increase of the area per head a s j is increased. The same considerations can be applied to the dependence of n on the NaCl concentration. Although the concept of effective electric charge of a ionic micelle is not rigorous and leads to distinct values depending on the utilized experimental technique,22it is widely used because it allows a simple comparison between micellar solutions with different surfactants, different counterions, and different ionic strengths. The obtained fractional charge cy increases from 0.26 for SDS to 0.40 for SDE,S. Since the micelle radius is also increasing with the number of oxyethylene unitsj, we find that the surface charge density is approximately independent ofj. Such a result does not agree with the explanation given by Shinoda and Hirai3 to the dependence of the cmc on j . Those authors suggest that the increase o f j results in a decreased electric potential at the micelle surface.
It should be remarked that the value of cy reported in Table IV for SDS is considerably smaller than that given in ref 4. This is due to the fact that we have repeated the fit by taking explicitly into account the hydration of the micelle. The obtained Hamaker constant is a strongly decreasing function of j (except for j = 1). This could be explained by attributing the origin of the attractive potential to the attraction between the hydrocarbon cores. By increasing the thickness of the oxyethylene layer, such an attraction is screened more and more effectively. However, the numerical value of A for SDS is too high to be only due to dispersion forces, so that the model is still to be improved. The most natural improvement would be to consider that, above a given salt concentration, the micelle aggregation number increases with the amphiphile concentration. Such an increase is probably more relevant for SDS and SDEIS than for SDE2S and SDE4S. If we compare the behavior of k , (and k , ) as a function of C,, we see that the effect of salt addition is less marked when we add to the monomer two or more oxyethylene units. This is in qualitative agreement with the behavior of the Krafft point,3 and suggests the existence of some connection between the two phenomena. Finally, it should be noted that the negative slopes observed for Cs > 0.35 M in the case of SDEIS and for Cs > 0.5 M in the case of SDE2S may not be simply due to the predominance of attractive interactions, but may reflect also the occurrence of micellar growth, similarly to the system SDS-NaC1.4s23
(21) Israelachvili, J. N.; Michell, D. J.; Ninham, B. W. J . Chem. Soc., Faraday Trans. 2 1976, 72, 1525. (22) Gunnarson, G.: Jonsson, B.: Wennerstrom, H. J . Phys. Chem. 1980, 84, 31 14. See also: Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J . Phys. Chem. 1984, 88, 6344.
15826-19-4; NaCI, 7647-14-5.
Acknowledgment. This work was partially supported by Progetto Finalizzato Chimica Fine e Secondaria del C N R and by Ministry of Public Education grants. Registry No. SDEIS, 15826-16-1; SDE,S, 3088-31-1; SDE&
(23) Missel, P. J.; Mazer, N. A.; Benedek, G . B.: Young, C. Y.; Carey, M. C. J . Phys. Chem. 1980, 84, 1044.
Adsorptive and Catalytic Properties of Supported Metal Oxides. 2. Infrared Spectroscopy of Nitric Oxide Adsorbed on Supported Iron Oxides D. G. Rethwischt and J. A. Dumesic* Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706 (Received: August 15, 1985)
Infrared spectroscopy of adsorbed nitric oxide was used to probe the nature of ferrous cations supported at low loadings (ca. 1%) on S O z ,A1203,Ti02, MgO, and ZnO. Ferrous cations on all of these supports gave rise to two mononitrosyl species, which appear in infrared spectra near 1810 and 1750 cm-I. These bands are attributed to ferrous cations of different coordination, with the band at lower frequency due to cations of lower coordination. Dinitrosyl species were observed on silica-supported iron, giving rise to a pair of infrared bands at 1900 and 1790 cm-I. These can be attributed to the adsorption of two NO molecules by a ferrous cation which is highly coordinatively unsaturated. These dinitrosyl species may also be present t o a small extent on titania-supported iron. It is suggested that the coordination number of the supported ferrous cation is lower on oxide supports for which the coordination number of the oxygen anions is lower.
Introduction In the first paper of this series, the chemical state of supported iron oxide samples was studied by using Mijssbauer spectroscopy after treatments in CO/CO, gas mixtures.' In the present paper, nitric oxide adsorption on these supported iron oxide samples is Permanent address: Department of Chemical and Materials Engineering, University of Iowa, Iowa City, IA 52242. *To whom correspondence should be addressed.
0022-3654/86/2090-1625$01.50/0
investigated by using infrared spectroscopy. While Mossbauer sPectroscoPY was used in the first paper to study the intoractions between the iron cations and the support, infrared spectroscopy can be used to probe these interactions by studying the nature of adsorbed species associated with the supported iron cations. The supports employed in this study were S O 2 ,y-A1203,TiOz, MgO, and ZnO. These oxides were chosen as supports for iron (1) Rethwisch, D. G.; Dumesic, J. A. J . Phys. Chem., in press.
0 1986 American Chemical Society
