Langmuir 1989, 5, 357-363
357
Effect of Composition on Sizes of W/O Ethanolamine-Oleic Acid Microemulsions by Small-Angle Neutron Scattering E. Caponetti, A. Lizzio, and R. Triolo Zstituto Chimica Fisica, V. Archirafi 26, 90123 Palermo, Italy
A. L. Compere, W. L. Griffith,* and J. S. Johnson, Jr. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -6150 Received January 27, 1988. I n Final Form: November 10, 1988 Small-angle neutron scattering from water-in-oil microemulsions comprised of DzO,oleic acid, ethanolamine, 1-pentanol, and hexadecane was measured over a wide range of compositions. The fraction of oleic acid neutralized was varied with the mole ratio of ethanolamine to oleic acid ranging from 0.3 to 1.5. Moles of water/mole of oleate varied between 17 and 68. Microemulsions having fixed ratios of nonhydrocarbon components were prepared by diluting aqueous stock solutions up to a factor of 4 with hexadecane or diesel fuel. Several compositions (including some reported previously) were measured over a wide enough angle range to allow discrimination between models. The model previously inferred appears applicable: monodisperse oblate ellipsoids, having an aqueous core surrounded by a shell of surfactant and alcohol hydrocarbon, penetrated by hydrocarbon from the continuous phase or other particles. At high dilutions, high intensities at low angles suggested contributionsof critical scattering. Other compositions, measured over limited angle ranges, were fit with limited sets of parameters, the less critical parameters selected from fits to compositions measured over wide angle ranges. Dimensions were also characterized in terms of Guinier radii. Unneutralized oleic acid had little effect on particle dimensions. The primary determinant of size was the ratio of water to oleate. Microemulsions made up of fuel components (soy fatty acid instead of oleic acid, 1-butanol instead of 1-pentanol,and diesel fuel instead of hexadecane) had particles of about the same size as analogous compositions from reagents.
Introduction We report here further small-angle neutron-scattering (SANS) studies of water-in-oil microemulsions stabilized by oleate. The components are those in compositions investigated by Shah and c~-workers'-~-potassium oleate, 1-pentanol, water and hexadecane-except that here and in the previous paper the oleate cation is the ethanolammonium ion, rather than potassium. In the first paper: in which the literature was reviewed, we reported that SANS patterns indicated formation of aggregates a t water/potassium oleate ratios that some previous authors had concluded were molecularly dispersed solutions. We found that the model (Figure 1) giving best fits to the scattering patterns was monodisperse oblate ellipsoids of modest axial ratios, the particles having an aqueous core surrounded by a shell of surfactant and alcohol hydrocarbon; it was necessary to allow for penetration of the shell by hydrocarbon of the continuous phase or other particles. In a second paper,5 ethanolammonium was substituted for K+, and the effect of degree of neutralization of the oleic acid present was investigated. For the same compositions, the change in cations had little effect. To a good first approximation, only the neutralized fraction of total oleate was important in determining the particle sizes; for example, a composition containing half the concentration of fully neutralized oleate gave a pattern similar to a composition comprised of the full concentration, half-neutralized. Here we investigate the trends in particle size as a function of several compositional variables. In addition (1) Shah, D. 0.; Hamlin, R. M. Science (Washington, D.C.) 1971,171, 483. (2) Falco, J. W.; Walker, R. D.; Shah, D. 0. AIChE J . 1974,20, 510. Bansal, V. K.; Hsieh, W. C. In Improved Oil Recovery (3) Shah, D. 0.; by Surfactant and Micellar Flooding; Academic Press: New York, 1977; D 293. (4) Caponetti, E.; Magid, L. J.; Hayter, J. B.; Johnson, J. S., Jr. Langmuir 1986,2, 722. ( 5 ) Caponetti, E.; Griffith, W. L.; Johnson, J. S., Jr.; Triolo, R.; Compere, A. L. Langmuir 1988,4, 606.
to a more extensive set of degrees of neutralization, the effect of dilution by hexadecane of compositions fixed in the ratio of water and cosurfactant to neutralized surfactant is reported for several of these ratios. Most of the patterns were taken on the 10-m instrument a t the Oak Ridge Research Reactor and cover a limited momentumtransfer [ K = 4 ( ~ / h sin ) 0, where 20 is the scattering angle and X = 4.75 A is the wavelength of the neutrons] range from about 0.01 to 0.12 A-'. Consequently, they do not carry enough information to evaluate all the parameters describing the particles: aqueous core radius, total particle radius, shell penetration, and axial ratio. We do have, however, a number of patterns over a much wider K range, some reported in ref 5 and some introduced here, at the extremes of the water/surfactant ratios for several of the compositional sets. The model of the previous papers also appears to be a good approximation for the new compositions. We have followed trends in size of those compositions for which patterns over only limited K ranges are available in two ways. Core radii were determined from fits with the complete scattering equations with fixed values of the axial ratio, the ratio of the size of the total particle to the core, and the parameter for penetration of the shell. These fixed values were estimated from the fits to the patterns covering a wide range of angles; those with a high volume fraction of disperse phase were weighted heavily in the selection, because of their greater sensitivity to these parameters. The other procedure was by Guinier radii. At low volume fractions of the disperse-phase components, high intensities are frequently observed at low angles. These are not computed well by the monodisperse ellipsoidal model. Because these compositions are often near phase boundaries, it seems possible that there is a contribution from critical scattering, frequently postulated to explain high intensities in light scattering,6 as well .as in 10W-K SANS.7 We find here that agreement between (6) Corti, M.; Degiorgio, V. J . Phys. Chem. 1981, 85, 1442.
0 1989 American Chemical Society
358 Langmuir, Vol. 5, No. 2, 1989
Caponetti et al.
Table I. Stoichiometries and R, Values (ComposiFion a s Moles/Mole of Neutralized Oleic Acid) R,I*
fraction neutralized 0.33 0.33 0.33 0.49 0.49 0.49 0.49 0.53 0.53 0.53 0.68 0.68 0.68 0.68 0.84 0.84 0.84 0.84 0.99 0.97 0.99 Id
0.99 0.95 0.95 0.95 0.97 le
D20
1-pentanol 17.8 17.8 17.8 12.1 12.0 12.0 12.1 22.1 22.1 22.1 8.6 8.6 8.6 8.6 6.9 6.9 6.9 6.9 5.8 5.8 5.8 5.8 12.1 12.3 12.3 12.3 12.2 5.8
53.1 53.1 53.1 35.2 35.2 35.2 35.2 67.6 67.6 67.6 25.9 25.9 25.9 25.9 20.6 20.6 20.6 20.6 17.5 17.5 17.5 17.3 35.9 37.2 37.2 37.2 36.4 17.3
C16HM 15.7 23.3 37.9 10.8 15.7 24.4 44.8 18.2 26.2 41.4 7.8 11.1 19.3 31.5 6.4 9.3 14.5 25.1 5.4 8.5 12.0 21.9 9.4 14.6 23.8 29.6 38.5 5.5
limited parametersf 54 53 51 30 35 38 34 64 54 52 22 25 28 28 18 21 23 23 17 21 20 21 28 36 35 36 35 18
R,, Table I1 or ref 5
27.2
35.9 60.0
17.0 20.1 27.3
33.3 17.3
range 0.025-0.05 0.025-0.05 0.025-0.05 0.08-0.10 0.08-0.10 0.08-0.10 0.08-0.09 0.03-0.06 0.03-0.06 0.03-0.06 0.075-0.10 0.075-0.10 0.075-0.10 0.075-0.10 0.09-0.11 0.08-0.11 0.08-0.11 0.08-0.11 0.14-0.16 0.08-0.11 0.08-0.11 0.12-0.16 0.09-0.11 0.08-0.11 0.08-0.11 0.08-0.11 0.08-0.11 0.14-0.16 K
eq 6 47 48 49 28 27 27 30 51 52 51 21 23 25 25 17 19 22 21 15 16 18 17 24 28 26 28 28 16
A full fit, eq 7
notes
28 31 52
15 18 23
29 15
Cloudy. *From ref 5. See Table 11. Excess ethanolamine, 0.05 mol. e Excess ethanolamine, 0.48 mol. /The following parameters fixed in fit to full pattern: Rat = 1.5RWIe;P F = 0.4; axial ratio = 0.4; shell alcohol = 0.5 total alcohol; incoherent = 1.0. #Critical parameters included in full fit.
Acore Water
that may be realized are lower emissions,8extension of fuel by natural products,9a4 and decreased fuel explosivity.'" Analyses of scattering from several formulations including components likely to be of practical importance, soy fatty acid, 1-butanol, and diesel fuel, are included here. The Guinier approach allows inferences about systems containing components whose scattering power is not accurately known.
Experimental Section $0
@=-Lo@ =Ethanolamine
-OH L == o
Sur tac t ant 's tai I
=Alcohol's tail
I F i g u r e 1. Microemulsion model.
experimental and computed values can be obtained by including in the structure function a contribution from critical scattering. As we mentioned in ref 5, the substitution of ethanolamineloleic acid for potassium oleate and the extension of concentration ranges are motivated by our desire to obtain information pertinent to development of microemulsion fuels. Dispersion of components in microemulsions greatly increases options in modifying compositions beyond what can be attained if additives are limited by solubility. Interest in this approach is evidenced by several recent publications."'" Some of the advantages (7) Triolo, R.; Magid, L. J.; Johnson, J. S., Jr.; Child,H. R. Phy: Chem. 1982,86, 3689. (8) Davis, M. E.; Sung, R. L. US. Patents 4,561,861 and 4,565,548, 1985.
Materials. Hexadecane-da4, 96% D, was obtained from Cambridge Isotope Laboratories and D20 from Aldrich. nHexadecane was from Aldrich. Oleic acid and ethanolamine were from Eastman. 1-Pentanol and 1-butanol were Fisher certified reagents. Amoco premier diesel fuel base, prepared without surfactant, was used. Solutions were prepared by weight in approximately 1-mL quantities by diluting stocks (prepared from water, oleic acid, alcohol, and ethanolamine, added in that order) with n-hexadecane. The samples were sealed with a Teflon septum cap and stored a t 20 "C until use, within 72 h of preparation. The compositions with oleic acid are listed in Table I. They are grouped according to the fraction of surfactant acid neutralized by ethanolamine. Because we found earlier5 that to a good approximation only neutralized acid was effective as surfactant, the compositions of other components are given as the ratio of their moles t o the moles of neutralized acid. To illustrate, the first composition of Table I can alternatively be written as 1 mol of oleic acid, 0.331 mol of ethanolamine, 5.88 mol of 1-pentanol, 17.6 mol of D20, and 5.19 mol of C16H34. (9) (a) Pryde, E. H. JAOCS, J.Am. Oil Chem. SOC.1984,61,1609. (b) Ziejewski, M.; Kaufman, K. R.; Schwab, A. W.; Pryde, E. H. JAOCS, J. Am. Oil Chem. SOC.1984, 61, 1620. (c) Goering, C. E.; Fry, B. JAOCS, J. Am. Oil Chem. SOC.1984,61, 1627. (d) Schwab, A. W.; Pryde, E. H. US. Patents 4,526,586 and 4,557,734, 1985. (10) Weatherford, W. D.; Naegeli, D. W. J. Dispers. Sci. Technol. 1984, 5, 159.
Langmuir, Vol. 5, No. 2, 1989 359
Effect of Composition on Microemulsion Sizes SANS Measurements. Neutron-scattering measurements were performed on the Oak Ridge Research Reactor 10-m or High Flux Isotope Reactor 30-m instruments. The 10-m camera has a fixed 10-m source to detector path and provides 4.6 m between the sample and detector, while the 30-m variable-length instrument provides sample to detector distances of 1.4-19 m. Both were provided by the National Center for Small-Angle Scattering Research (NCSASR) at Oak Ridge National Laboratory. Momentum transfer is in terms of K , previously defined. Momentum transfer for the 10-m instrument ranges between 0.01 and 0.12 A-1; for the 30-m instrument, the range is 0.003-0.35 A-1. The samples were contained in quartz spectrophotometer cells of 0.1-cm path lengths, and temperature was maintained at 25 "C by fluid circulation from an external bath. Scattering from samples was corrected for detector background, empty cell scattering, sample transmission, and detector sensitivity. Radial averages were obtained by software provided by NCSASR. Contributionsfrom inelastic scatteringwere considered negligible"bb and ignored. Absolute intensity calibrations, based on standards provided by NCSASR, are estimated to be within
mined by the dimensions and volume fraction of the microemulsion droplets, whose distribution is also related to the interaction potential. With increasing K , S(K)oscillates about 1 with a quickly damped amplitude. P(K)is a function of K varying between the square of the contrast and zero. Hence, strongly interacting particles show an interaction peak owing to the product of P ( K )and S(K). The left side of the peak is mainly determined by S ( K ) , whereas the portion to the right of the peak becomes coincident with N,VP(K). Obviously, big particles will give contributions to I ( Kstronger ) (larger than the contributions of small particles. For a given size, the intensity depends linearly on the number density of the scatterers. For weakly interacting particles, S(K) 1 except in the very low K region. This is the case for systems with uncharged particles a t small values of N or at higher concentrations at larger K , when S ( K )has cfecayed essentially to unity. When the condition is met
v)
-
*15%.
F(k) =
Cbj exp(ik.r;)
(1)
where Ikl = K . The scattering intensity is proportional to the product of F(k) times its complex conjugate, F*(k). For centrosymmetrical particles, as here, F(k) is real, and
(2) where CY is a calibration constant depending on the incident neutron flux and the geometry of the experiment. Hence Z(k) = a p ( k )
I(k) = cuCjClb,blexp(ik-rjl)
(3)
with rjl = r ' - rl. If the scattering unit is itself a collection of objects (e.g., microemulsion droplets or micelles), the summations of eq 3 me to be taken for all the pairs j,l both within the particles (intraparticle contribution) and between the particles (interparticle contribution). It is therefore convenient to group these contributions into two categories. After averaging over all the possible orientations of the particles with respect to k, one obtains the intensity as a function of K as I ( K=) N , ~ L [ ( F ( K+) ~ ( F) ( K ) ) ~ ( S-( K111 ) or I(K)
= Npv[P(K)S(K) +
6(K)]
(4)
where P ( K )= ( F ( K ) ' )is the self-portion of the scattered intensity (particle form factor), S(K)is the interparticle structure function (Fourier inverse of the particle-particle correlation function g(r)),Npis the number density of the particles in volume V, 6 ( ~ )= ( F ( K ) ' ) ( F ( K )is) ~a term (usually small) which depends on the shape of the particles (0 for monodisperse spheres), and ( ) indicates thermal averages. Let us consider the various contributions to I(K). In the limit K 0, S ( K )is proportional to "osmotic" compressibility (or activity gradients with concentration). It then goes through a maximum whose position is related to the average distance between the scattering particles, deter-
-
(11) (a) Wignall, G. D.; Bates, F.
s.J.Appl. Crystallogr. 1987,20, 28.
(b) Caponetti, E.; Triolo, R.; Johnson, J. S., Jr. J.Solution Chem. 1987, 16, 295.
= N,v(F(K)')
I(K)
Interpretation With the exception of critical scattering, which we shall discuss later, the equations we have used (and their source) have been given in ref 4. The scattering amplitude of a collection of objects of scattering length b; located by the vector rj is given by
For spherical particles, the phase factor exp(-ik.r.l) of eq 3 can be replaced by cos (k-rjl). For other monodisperse distributions of centrosymmetric particles such as ellipsoids, it can be evaluated similarly, from a set of equivalent spheres generated by integrating over all orientations of the particle with respect to the direction of the beam. In the expansion of cos (ker), squared and averaged over all orientations, into a power series, the term up to K' is the same as for expansion of an exponential. I(K)
[I - (K2R,'/3)
-
+ ...I
exp (-K'R,' / 3)
(5)
(6)
On this basis, Guinier suggested his well-known approximation,12 that for sufficiently small K~ a plot of In I ( Kvs) K~ should be linear, and the Guinier radius R, can be evaluated from the slope. We have evaluated by a procedure outlined in the Appendix the accuracy of this approximation for oblate ellipsoids, the shape of interest here, as a function of scattering angle. Guinier identified R, with the gyration radius, scattering contrast being substituted for mass.13 Analysis of intensities by eq 4, when results over a sufficient K range are available (at least to a maximum K about 27r/rmin,rminbeing the smallest distance between scattering centers for which one needs information), allows inference not only of the size but also of the structural details. However, if one is interested only in size, one can analyze using either eq 5 or 6; a smaller range of K is required. As we mentioned earlier, for several of the series of concentration dependencies reported here, we have patterns over wide K ranges for the highest and lowest ratios of hexadecane to active surfactant. From analysis by the models of ref 4 and 5 and by the forms of eq 3 detailed in ref 4,we can show that the model previously outlined is applicable over the compositional ranges; it appears reasonable to assume that it also applies in the other cases. Approximate values of the parameters likely to vary little with composition can be selected from the values obtained at high volume fractions of the disperse phase and fixed in fitting the patterns covering limited ranges of angles. Further, the complete fits determine the structure functions and dimensions of the extremes of the compositional ranges and therefore allow estimates of the lower K limit for which eq 5 or 6 is valid ( S ( K ) 1). The values of R,
-
(12) Guinier, A. Ann. Phys. 1939, 12, 161
Caponetti et al.
360 Langmuir, Vol. 5, No. 2, 1989 1
1
-1I
30
120 10
”
0
003
0.06 k
aos
n
0
012-
0.03
(8-0
k
Figure 2. SANS patterns as a function of degree of neutralization: (a) 0.33 mol of ethanolamine per mole of oleate; (b) 0.49; (c) 0.68; (d) 0.84; (e) 0.98. obtained by eq 5 or 6 can be compared with those computed from the dimensions obtained by the complete fits (ref 13, p 26) R, = A([2 + ( B / A ) 2 ] / 5 ) o . 5
(7)
B being the semiaxis of rotation and A the other semiaxis, with the axial ratio E = B / A . In the cases here, D20 is the only deuterated component, and consequently there is little contrast between the she1 and the continuous (mainly hexadecane) phase. Consequently, the values of R, will refer primarily to the core. Critical Scattering. We referred previously to high intensities, not predicted by the model, observed at low K with some low volume fraction microemulsions. We have tested here whether they are consistent with what might be expected from critical scattering, by including in S(K) an Ornstein-Zernike term where L, is the critical correlation length.
Results Patterns. Two trends in scattering in composition will be illustrated. Figure 2 compares patterns from microemulsions having about 8 mol of CI6Hs4,17 mol of D20, and 6 mol of pentanol per mole of total oleic acid and oleate, as a function of degree of neutralization of oleic acid (mole ratio of ethanolamine to total oleic). It can be seen that the maxima move to lower K as neutralized oleate decreases, and the intensities a t low angle become higher. This is in agreement with earlier conclusions5that only the salt form of the surfactant is active, because the size of the particles increases with the ratio of water to a m ~ h i p h i l e . ~ Figure 3 shows the effect of dilution of the particles by hydrocarbon (the main component of the continuous phase) for the case of half-neutralized oleate, about 35 mol of D 2 0 and 12 mol of pentanol per mole of neutralized oleate. The maxima move to lower K with increasing dilution, as one expects from the effect on S(K)of lower volume fraction of disperse phase (comprised of particles). The high 10W-K intensities at high dilutions indicate onset of critical scattering. Wide K Coverage. Compositions in ref 5 were very close to some of those at the extreme of the series analyzed here by the Guinier method. In particular, the full concentration fully neutralized set (FCFN) of ref 5 corresponds to the fully neutralized sample here having 17.5 waters and (13) Guinier, A.; Fournet, G. Small-Angle Scattering of X-rays; Wiley: New York, 1955; p 24.
0.06 ti-’)
0.09
0.12
Figure 3. SANS patterns as a function of dilution by hexadecane for a half-neutralized system containing about 35.2 mol of D20 and 12 mol of pentanol per mole of oleate: (a) 44.8 mol of hexadecane per mole of oleate; (b) 24.4; (c) 15.7; (d) 10.8. Table 11. Parameters from Fits to SANS Patterns of Dilute Microemulsions (Monodisperse Oblate Ellipsoid Model) fraction of oleic acid neutralized item 0.49 0.97 1.00 DZO
1-pentanol
C16H34
Compositiono 35.2 36.4 12.1 12.2 44.8 38.5
17.3 5.8
21.9
Parameters scale incoherent RC,,,! A RSF,
A
SC,,,
LC axial ratio penetration factor
RTOT,A number of shell alcohols aggregation number
0.92 f 0.02 1.04 f 0.00 35.9 f 0.4 74.6 f 5.9 3.6 f 0.2
69.2 f 3.4 0.44 f 0.01 0.26 f 0.09 45.4 5.2 154
0.79 f 0.04 1.01 f 0.01 33.3 f 1.3 37.5 f 31.8 10.3 f 1.7 113. f 8.0 0.44 f 0.02 0.10 f 0.10 42.1 5.2 120
1.01 f 0.02 0.9 f 0.00 20.1 f 0.2 37.5 f 1.4 11.7 f 0.3
80.7 f 2.2 0.37 f 0.01 0.29 f 0.06 26.8 2.9 50
Moles/mole of neutralized oleic acid.
5.8 alcohols per oleate, the full concentration half-neutralized set of ref 5 (FCHN) to the half-neutralized set here having 35 waters and 12 alcohols per oleate, the half-concentration fully neutralized set of ref 5 (HCFN) to the fully neutralized composition with 36 waters and 12 alcohols per oleate, and the half-concentration half-neutralized set of ref 5 (HCHN) to the half neutralized composition with 68 waters and 22 alcohols per oleate. For three of these series (FCFN, FCHN, and HCFN), we have previously unreported results covering wide ranges of K at the other extremes of hydrocarbon/oleate. It is for these low volume fraction disperse phases that inclusion of a contribution of critical scattering in S(K)is necessary for good fits in the 10W-K range. Fits are given in Figures 4-6, and the parameters are listed in Table 11. The fits indicate that the model is applicable over the range of results. The values of RSfand of the penetration factor are not well determined for the dilute (high hydrocarbon) compositions, particularly the fully neutralized composition with 38.5 hexadecanes/oleate. The insensitivity arises from the low volume fraction of the disperse phase. A computation for this composition with the poorly determined factors fixed in the range of those of ref 5 (RBf= 1.5RCore; penetration factor, 0.4; axial ratio, 0.4; and incoherent, 1.0) gave about as good fit, with R, = 32.4 f 0.4, scale = 0.86 f 0.02, SOcrit = 9.9 f 0.4, and L, = 97 f 4, within uncertainties of those in Table 11. Limited K Coverage. Fits to the patterns for which only a limited range of angle was available were carried out with
Effect of Composition on Microemulsion Sizes
Langmuir, Vol. 5, No. 2, 1989 361
:I
mo eo 0 500 h
aE
400
=>. 0 -
I.
DIESEL FUEL R A N G E S FOR S I M I L A R C O M P O S I T I O N S E T H A N O L A M I N E OLEATE
30
v)
C
1
1
300
20 0 10 0
lo
00
t
0 ’ 0
I
I
I
I
I
1
I
10
20
30
40
50
60
70
moles 0 2 0 / m o l e o l e a t e
Figure 4. Fit to the SANS pattern of a fully neutralized system containing 17.3 mol of DzO, 21.9 mol of hexadecane, and 5.8 mol of 1-pentanol per mole of oleate. The fit used the system parameters given in Table 11. Solid line, least-squares fits; dotted line, S ( K ) dashed ; line, P(K).
250.0 15.0 p
200.0
E s
h
,z .-
150.0
-2
100.0
25 v,
10.0
E
50 50.0
0.0
0.0 00
01
02
03
04
05
k (k’) Figure 5. Fit to the SANS pattern of a fully neutralized system containing 36.4 mol of DzO, 38.5 mol of hexadecane, and 12.2 mol of 1-pentanol per mole of oleate. The fit used the system parameters given in Table 11. Solid line, least-squares fits; dotted line, S ( K ) dashed ; line, P(K).
-
4.0
-
3.0 h
Y
v
v,
-
2.0
-
1.0
00
00 00
01
02
03
04
05
k &.’)
Figure 6. Fit to the SANS pattern of a half-neutralizedsystem containing 35.2 mol of DzO, 44.8 mol of hexadecane, and 12.1 mol of 1-pentanol per mole of oleate. The fit used the system parameters given in Table 11. Solid line, least-squares fits; dotted ; line, P ( K ) . line, S ( K ) dashed
the same fixed parameters used above for the 38.5 hexadecanesloleate and with pentanol distributed equally between shell and continuous phase. The values of core
Figure 7. Comparison of Guinier radii of ethanolamine oleate and diesel fuel microemulsions.
radius are listed in Table I. At the dilute end, critical parameters were also included as variables; the runs for which this was done are indicated. The core radii obtained for those runs covering wide K ranges computed with limited and complete sets of varied parameters are fairly close; the values for the narrow angle ranges should be good enough to allow comparison of compositional effects. Although there is considerable scatter in the core radii of the various compositional sets, the increase in core radius with increasing waterloleate mole ratios is clear. Guinier Analysis. The values of R, obtained from eq 6 are listed in Table I, along with the K ranges used in evaluating them. Measured intensities include a contribution flat with K from incoherent scattering; it is necessary to allow for this, particularly at high K , to prevent distortion of the slopes of In I vs K~ in evaluation of the Guinier radius. This correction could be estimated by a leastsquares fit of eq 6 over the selected K range, with variables I,=,,, R, and an incoherent term, invariant with angle, added to the computed intensity. Although in most cases the results obtained in this way were not much different from those we shall report, the values of background intensity obtained with the runs of the limited K range of particular interest for Guinier analyses were frequently different, sometimes by a factor of 2, from those expected from the incoherent cross sections of the microemulsions. There are other contributions to flat background, but it appears that the values derived as least-squares parameters were not adequately determined in limited-n patterns. Consequently, to avoid distortion of the dimension parameter, we arbitrarily selected a value of 1cm-’ for the incoherent contribution. This is approximately what is obtained by least-squares analysis of patterns with wide K ranges. The most difficult aspect of Guinier analyses is the selection of K limits, or in some cases, the determination of whether or not there is any K range in a given case for which eq 5 gives a useful approximation. Because the Guinier equation takes no account of interparticle interactions, one should in principle not use angles below those at which S(K) has decayed essentially to unity; in practice, this may be is oscillating around unity. relaxed somewhat when S(K) From our model fits to full K ranges, we can infer values for safe lower limits of K . The upper limit of validity of eq 6 is frequently stated to be K = l/R,, apparently based on series convergence; were this limit strictly applicable, few of our runs would have a useful range above S ( K ) 1. However, the series expansions for the cosine and the exponential are both convergent, and the pertinent question is the difference
-
362 Langmuir, Vol. 5, No. 2, 1989
Caponetti et al. emulsions on this basis and the corresponding values of Guinier radii are given in Table 111. In computing moles of hydrocarbon per oleate, diesel fuel is assigned the molecular weight of hexadecane. Although an approximation, the effect is not important in Guinier analysis of this system.
-C
1
0.01
-_
---- Guinier Approximation
0.1
EI -
I
I
1
1
1
I
0
2
4
6
8
10
12
Exact Expansion I
,
I
14
16
18
20
(KA?
Figure 8. Comparison between the exact expansion and the Guinier approximation for several values of the axial ratio.
Table 111. Guinier Radii of Diesel Fuel Microemulsions (Composition as Moles/Mole of Neutralized Soy Fatty Acid)O fraction neutralized 0.20 0.42 0.51 0.54 0.56 0.73 0.82 0.99
D20 1-butanol diesel fuel 69.5 33.5 54.0 25.8 24.1 19.3 17.3 13.7
18.8 9.2 7.2 6.9 6.6 5.4 4.7 3.7
28.4 13.2 14.8 11.3 47.8 8.0 6.9 5.9
R,, A
K range 0.025-0.05 0.08-0.11 0.03-0.06 0.075-0.10 0.075-0.10 0.08-0.11 0.08-0.11 0.08-0.11
54 26 41 25 23 21
17 14
O In computing stoichiometries, molecular weight of soy fatty acid was taken to be the same as that of oleic acid and the molecular weight of diesel fuel the same as that of hexadecane.
in intensity computed by them as a function of angle. For some anisotropic particles (and polydisperse distributions), terms in eq 6 up to K4 can be inc1~ded.I~By the method outlined in the Appendix, we have evaluated the form factors (proportional to intensity) for oblate ellipsoids as a function of axial ratio; enough terms were included to make truncation errors negligible. These allow a quantitative comparison of the dependence of the logarithm of intensity on K ~ with A ~the exponential approximation (Figure 8). It can be seen that differences in the slopes are small for the axial ratios of interest here and the K ranges from which values of R, in Table I were evaluated. A more precise comparison can be made from least-squares straight-line fits to the logarithm of the form factor vs K ~ . For axial ratios of 0.4 and values of R, in Table I (and Table 111, discussed below), we have generated form factors for selected compositions, including the worst cases, with eq 7 and the series in the Appendix. From the slopes over the K ranges in the table, we have evaluated R,; most of the values are only 5-10% lower (at most, 13%) than those obtained from the experimental patterns by the Guinier approximation, eq 6. Compositions of Practical Microemulsion Components. The stoichiometries of the diesel fuel micro~
~~
(14) Porod, G. In Small-Angle X-ray Scattering; Glatter, O., Kratky, K., Eds.; Academic Press: New York, 1982; p 25.
Discussion The most striking correlation in Table I is the increase of R, with the ratio moles of water/mole of oleate ions. That dimensions of water-in-oil microemulsions stabilized by strong-electrolyte surfactants are greater at higher moles of waterjmole of surfactant ratios is known.15 The dependence here on the concentration of oleate ions rather than on total oleate plus unneutralized oleic acid confirms that the effect of oleic acid is small, confirming our previously reported5 conclusion that unneutralized oleic acid was not a determinant of particle size. For a given water/oleate and alcohol/oleate ratio, there appears to be a slight trend to larger size as the microemulsion is diluted with hydrocarbon, both in the values obtained by eq 6 and 7. Although the increases cannot be said to be definite, they would not be surprising. With dilution, if the distribution coefficient of 1-pentanol and oleate between particles and continuous phase is constant, amphiphile/mole of water in the particles would decrease. From the dependence of R, on this ratio, larger cores would be expected. The Guinier radii for compositions of diesel fuel components (Table 111) and for reagents (Table I, ranges given for sets with the same moles of water/mole of oleate) are compared in Figure 7, plotted against moles of water/mole of oleate. It is apparent that the sizes are not affected significantly by the substitution of the practical components. The reagent compositions therefore provide good models for study of the structure of the practical compositions. The same trend occurs with other microemulsion fuel compositions. Weatherford16 reports measurement of water vapor partial pressures over microemulsions somewhat similar in composition to the simulated fuel samples here. His interpretation, based on surface curvatures of the particles, also gives sizes that increase with water/ amphiphile ratios. The sizes he infers are about 1 5 3 0 % larger than those we obtain for comparable water/surfactant ratios. The higher intensities at low K than predicted by the model of Figure 1 seem consistent with the presence of a critical point not far from the compositions in question. An important compositional variable about which we cannot make inferences from these results is the amount and type of alcohol. Substitution of 1-butanol for l-pentanol did not have any observable effect, in contrast to a substantial difference seen for 1-hexanol and 1-pentanol in ref 4. Further work is required to clarify this difference. The influence of the amount of alcohol is also an important parameter needing attention. Acknowledgment. This research was sponsored jointly by the U.S. Department of energy under Contract No. DE-AC05-840R21400 with Martin Marietta Energy Systems and the “Progetto Finalizato Chimica Fine e Secondaria” of the Consiglio Nationale delle Ricerche (Rome). We gratefully acknowledge partial support for (15) Nicholson, J. D.; Clarke, J. H. R. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1985; Vol. 111, p 1663. (16)Weatherford, W. D. J. Dispersion Sci. Technol. 1985, 6, 467.
363
Langmuir 1989, 5 , 363-369
E. Caponetti as a NATO Senior Fellow (Bando n. 217.18/03).
Appendix Although the intraparticle form factor given by ( F ( K ) ) for ellipsoidal particles has been expressed in integral form,12J7 no explicit analytical expression permitting analysis and easy computation is available. We have obtained a power series for this expression which permits us to make a direct comparison with the Guinier expansion in eq 6. Although we intend to publish this result sepa(17)Kotlarchyk, M.;Chen, S.-H. J. Chem. Phys. 1983, 79,2461.
rately, the series is of the form 2 A 2 ~4-2 A 2 e 2 ~ 2 3 A 4 ~ 4 ~44A 4 ~ 2+~84A 4 ~-4 115 875 20A6e6~' 2 4 A 6 ~ 4 ~ 36 2 A 6 ~ 24-~ 6 4 A ' ~ ~ ... 165375 As shown in Figure 8 and suggested by Guinier,12differences between intraparticle form factors and the Guinier exponential expression given in eq 6 are minimal for axial ratios, e z 0.4. This allows us to extend the use of eq 6 for our samples to K values several times those appropriate for spheres with acceptable error. Registry No. n-Hexadecane, 544-76-3; 1-pentanol,71-41-0; 1-butanol, 71-36-3; oleic acid, 112-80-1;ethanolamine, 141-43-5.
+ +
+
+
+
Polyelectrolyte Ultrafiltration of Multivalent Ions. Removal of Cu2+by Sodium Poly(styrenesulfonate) K. James Sasaki,t Susan L. Burnett,? Sherril D. Christian,*?+Edwin E. Tucker,+ and John F. ScamehornS Institute for Applied Surfactant Research, The University of Oklahoma, Norman, Oklahoma 73019, Department of Chemistry, The University of Oklahoma, Norman, Oklahoma 73019, and School of Chemical Engineering and Materials Science, The University of Oklahoma, Norman, Oklahoma 73019 Received August 29, 1988. In Final Form: November 8, 1988 Ultrafiltration and equilibrium dialysis methods, using the polyelectrolyte poly(styrenesulfonate) (PSS), have been used to investigatethe removal of Cu(I1) from aqueous streams. Separations have been measured at mole ratios of styrenesulfonate to total copper varying from 101 to 3:1, at NaCl concentrations varying from 0 to 80 mM. Retention ratios (i.e., ratios of the total concentration of copper in the retentate to that in the permeate) as large as lo3 have been measured for solutions containing large PSS:Cu(II) ratios. Retention ratios are shown to increase, at fixed PSS:Cu(II) ratios, as the total concentration of copper decreases. The ultrafiltration and dialysis results are well correlated by an ion-binding model proposed previously (ref 1).
Introduction Previou~lyl-~ we showed that micellar-enhanced ultrafiltration (MEUF), utilizing ionic surfactant micelles, can be an effective method for concentrating and/or removing divalent ions from aqueous streams, in the presence and in the absence of added 1 : l electrolyte. Experimental techniques have been described for using MEUF14 and equilibrium dialysis or semiequilibrium dialy~isl"-'~ to study the removal of both organic and ionic species. We have developed an ion-binding model to predict the concentrations of ions that will pass through an ultrafiltration or dialysis membrane when known concentrations of an ionic surfactant are present in micellar form in an aqueous stream, together with known concentrations of the oppositely charged multivalent and monovalent ions.' The model utilizes a two-phase theory developed by Oosawa" to determine the fraction of each counterion that will be either "bound" to the polyelectrolyte or "free" in the bulk aqueous solution. An important feature of the model is the assumption that the activity of a neutral electrolyte passing through the ultrafiltration or dialysis membrane
* Author
*
to whom correspondence should be addressed. Department of Chemistry. School of Chemical Engineering and Materials Science.
0743-7463/S9/2405-0363$01.50/0
will equal the equilibrium activity of that electrolyte in the retentate solution. By use of this assumption, together (1)Christian, S. D.; Bhat, S. N.; Tucker, E. E.; Scamehorn, J. F.; El-Sayed, D. A. AZChE J. 1988,34, 189. (2)Scamehom, J. F.;E l l i i n , R. T.; Christian, S. D.; Penney, B. W.; Dunn, R. 0.; Bhat, S. N. AICHE Symp. Ser. 1986,250,48. (3)Scamehom,J. F.;Christian, S. D. In Surfactant-Based Separation Processes; Scamehorn, J. F., Harwell, J. H., Eds.; Marcel Dekker: New York; 1989;Chapter 2. (4)El-Sayed, D. A.; Scamehom, J. F.; Christian, S. D., in preparation. (5)Leung, P. S. In Ultrafiltration Membranes and Applications; Cooper, A. R., Ed.; Plenum: New York, 1979; p 415. (6)Dunn, R.0.; Scamehom, J. F.; Christian, S. D. Sep. Sci. Technol. 1985, 20, 257. (7)Dunn, R.0.; Scamehom, J. F.; Christian, S. D. Sep. Sci. Technol. 1987, 22, 763. (8) Bhat, S. N.; Smith, G. A.; Tucker, E. E.; Christian, S. D.; Smith, W.; Scamehorn, J. F. Znd. Eng. Chem. Res. 1987,26, 217. (9) Scamehorn, J. F.; Harwell, J. H. In Surfactants in Chemical/ Process Engineering; Wasan, D. T., Shah, D. O., Ginn, M. E., Ede.; Marcel Dekker: New York, 1988; p 77. (10)Christian, S. D.; Smith, G. A.; Tucker, E. E.; Scamehorn, J. F. Langmuir 1985, 1, 564. (11)Smith, G.A.;Christian, S.D.; Tucker, E. E.; Scamehorn, J. F. J. SolutLon Chem. 1986, 15, 519. (12)Smith, G.A.;Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. Langmuir 1987,3, 598. (13)Smith, G.A. Ph.D. Dissertation, University of Oklahoma, 1986. (14)Higazy, W.; Mahmoud. F. 2.:Taha, A. A,; Christian, S. D. J. Solution Chem. 1988,17, 191.
0 1989 American Chemical Society
