1554
Langmuir 1992,8, 1554-1562
Alcohol Partition in a Water-in-Oil Microemulsion from Small-Angle Neutron Scattering E. Caponetti,' A. Lizzio, and R. Triolo Dipartimento Chimica Fisica, via Archirafi 26, 90123 Palermo, Italy
W. L. Griffith and J. S. Johnson, Jr. Oak Ridge National Laboratory, Oak Ridge Tennessee 37831 -6150 Received May 14, 1991. I n Final Form: April 1 , 1992 It is often necessary to add a cosurfactant, typically an alcohol of medium chain length, to water, oil, and surfactant for a microemulsion to form. To gain information on the role of alcohols,we have measured small-angle neutron scattering (SANS) from microemulsions comprised of n-hexadecane, potassium oleate, and water, plus several concentrations of l-pentanol, l-hexanol, l-heptanol, and l-octanol, in two regions of the phase diagram. Several models, including polydisperse spheres interpreted by recently developed equations for the structure function, were tested. Experimental data could be fit successfully with the core-plus-shell monodisperse-oblate-ellipsoids model previously used for similar compositions. Variation of the alcohol chain length had little apparent effect on microemulsion structure, except in 1-pentanol systems, where high intensities at low angles are attributed to critical scattering. At fixed alcohol-to-surfactant molar ratios, particle dimensions increase with alcohol chain length in both regions of the phase diagrams. For a given alcohol, increasing the alcohol-to-surfactant molar ratio decreases particle dimensions. The water phase volume can reasonably be assumed constant, and estimates of the amount of alcohol at the water-surfactant interface were made from the parameters obtained from the fits. At fixed alcohol-to-surfactantmolar ratios, we found a lower fraction of larger alcoholsat the interface, in agreement with the increase of hydrophobicity. For a given alcohol,increasing the alcohol-to-surfactant ratio increased the amount of alcohol at the interface, although the fraction of total alcohol in the particle decreases.
Introduction Previously, we reported' small-angleneutron scattering from microemulsions comprised of n-hexadecane, potassium oleate, water, and cosurfactant at constant ratios (moles per mole of surfactant) of hydrocarbon (5.5) and alcohol (5.0) and a varying ratio of water (as DzO). The alcohols were l-pentanol, l-hexanol, l-heptanol, and 1octanol. We found that a core-plus-shell monodisperse oblate-ellipsoid model reproduced the experimental patterns reasonably well; we concluded that variation in the alcohol chain length modifies the microemulsion structure but little. The droplet sizes were found to increase primarily with the water-to-surfactant ratio; the deviation from a linear trend of the ratio between water phase volume and the total interfacial area was attributed mainly to an increasing amount of alcohol at the water-surfactant interface. The aim of this work is to get quantitative information on alcohol partition between the water interface and the continuous hydrocarbon phase. We have investigated the same system, but with the DnO/surfactant mole ratio held constant and with the alcohol/surfactant ratio varied, in two different compositional regions. On the hypothesis that the interfacial area occupied by each surfactant and alcohol molecule is constant, variations in the interfacial area can be assigned to a variation in the number of alcohol molecules a t the interface. Experimental Section Materials. Potassium oleate was prepared by neutralizing oleicacid (FlukaA.G. product)with potassium hydroxide(Merck Suprapur), following the literature.* Before use, the product was kept under vacuum for 72 h. n-Hexadecane (Fluka A.G. (1) Caponetti, E.; Lizzio, A.; Triolo, R. Langmuir 1990, 6, 1628. (2) Hansen, J. R. J. Phys. Chem. 1974, 78, 256.
product)was storedon molecular sievesand used without further purification. D20 was Carlo Erba 99.8% D. l-Pentanol, l-hexanol, l-heptanol,and 1-octanolwere purified by refluxing reagent grade alcohols (Merck) over calcium hydride for 12 h, followed by fractional distillation. The solutions were prepared by weight in approximately 2mL quantities, by diluting with alcohol stocks prepared from potassium oleate, heavy water, alcohol, and hexadecane, added in that order. The samples were sealed with a Teflon septum cap and stored at 20 "C until use, within 5 days of preparation. Apparatus. SANS experimentswere performed on the H9B small-angle neutron diffraction instrument3,'at the High flux Beam Reactor of Brookhaven National Laboratory, equipped with a cold source. The solutions were placed in quartz spectrophotometer cells of 1 mm path lengths. Temperature was maintained at 25 O C by fluid circulation from an external bath. A position-sensitive detector with 128 X 128 pixels, subtending an area of 50 cm X 50 cm, was used to record the scattered neutrons. The sample-to-detectordistance was 180 cm. The neutron wavelengths were X = 4.30 A (1-hexanolsystem) and A = 4.95 A (other systems),with a spread AX/X = 10%. With these two settings the modulus of the scattering vector Q, defined by the expression Q = 47r(sin 0)/X (20 being the scattering angle), ranged between 0.018 and 0.27 and between 0.016 and 0.23 A-l, respectively. Detector sensitivity,empty cell, sample transmission, background corrections, and the data normalization procedures have been described in the literature.s-6The detector was calibrated for absolute intensities with Porasil B, a secondary standard.' Compositions. The compositionsare listed in Table I and 11. Those in Table I are comprised of 5.5 mol of hexadecane per (3) Schneider, D. K.;Schoenborn, B. P. In Neutrons in Biology;Schoenborn, B. P. Ed.;Plenum: New York 1984; p 119. (4) Schneider, D. K.; Ramakrishnam, V.; Schoenborn, B. P. Physica l986,137B, 214. ( 5 ) Jacrot, B. Rep. h o g . Phys. 1976,39, 911. (6) Wise, D.; Karlin, A.; Schoenborn, B. P. Biophjs. J. 1979,243,473. (7) Russell, T. P.; Wignall, G. D.; Lin, J. S.;Spooner, S.J. Appl. Crystallogr. 1988, 20, 28.
0 1992 American Chemical Society
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Langmuir, Vol. 8, No. 6, 1992 1555
Table 1. Microemulsion Compositions of the First SANS Study (numbers indicate moles of each component per mole of potassium oleate) DzO
C7A C7B c7c C7D C7E
C16H34 5.5 5.5 5.5 5.5 5.5
1-C7OH 4.0 5.4 7.2 9.2 12.2
29.9 29.9 29.9 29.9 29.9
C5A C5B c5c C5D C5E
5.5 5.5 5.5 5.5 5.5
5.5 7.2 9.4 12.0 15.4
30.1 30.1 30.1 30.1 30.1
Table 11. Microemulsion Compositions of the Second SANS Study (numbers indicate moles of each component per mole of potassium oleate) C8a C8b c8C C8d C8e
C16H34 15.0 15.0 15.0 15.0 15.0
1-CsOH 3.0 4.0 5.5 7.2 9.1
Dz0 45.0 45.0 45.0 45.0 45.0
C7a C7b c7c C7d C7e
15.0 15.0 15.0 15.0 15.0
4.0 5.5 7.2 9.3 12.1
45.0 45.0 45.0 45.0 45.0
C6a C6b C6c C6d C6e
C16H34 15.2 15.2 15.2 15.2 15.2
C5a C5b c5c C5d C5e
15.0 15.0 15.0 15.0 15.0
1-c60~ 5.5 7.2 9.3 12.1 15.4
DzO 45.2 45.2 45.2 45.2 45.2
8.9 9.3 12.1 15.4 19.9
44.9 44.9 44.9 44.9 44.9
mole of potassium oleate ( N H ~ ~ Iand K Oabout I ) 30 mol of DzO per ) ; moles of alcohol/moleof mole of potassium oleate ( N w I K o ~the surfactant ( N O H I Kcover O ~ ) almost completelythe range of single phases, i.e., much less or much more alcohol would result in immiscibility. In Table 11,N H ~ ~is~about K O 15 I and NwIKoI about 45; again alcohol additions cover most of the single phase region, and in this series, all the alcohols between pentanol and octanol were included. It is interesting that as the chain length of the alcohol decreases, the range of phase stability moves to higher alcohol contents. The trend is most obvious for alcohol concentrations in mole ratios, but, at least for the compositions of Table 11,the same trend is seen with volume fractions of alcohol, although not so striking.
Results and Discussion ScatteringPatterns. Figure 1showsthe experimental intensities as a function of Q for the 1-heptanol and 1pentanol compositionslisted in Table I, and Figure 2 shows intensities for the 1-octanol, 1-heptanol, 1-hexanol, and 1-pentanol compositions of Table 11. The patterns are qualitatively similar, except for 1-pentanol, particularly for those in Figure 2d. In all cases, there is a trend to lower intensity with increasing alcohol, accompanied by a shift (except for the data of Figure 2d) of the maximum to higher Q. This is consistent with an increase in aggregate
size with decreasing alcohol as more alcohol would be expected to be a t the interface at higher concentrations of alcohol and to increase the effective surfactant concentration. Decreasingparticle size with decreasingwater/ surfactant ratio has been reported frequently (e.g. refs 8 and9). ThelackofapeakforthedataofFigure2dsuggest.a that the composition is in the neighborhood of a critical point and that critical scattering contributes to the high intensities at low angles. Models and Data Analysis. Monodisperse ellipsoids gave the best fit to the patterns in earlier studies.1~9JOJ1 In the model, a core was comprised of water, surfactant carboxylates, K+ or ethanolamine counterions, and OH groups of the shell alcohol; a shell of the surfactant and shell-alcohol hydrocarbon; and a continuous phase of hexadecane and alcohol not in the shell. The equations for the particle function were those given by Hayter12and by Kotlarchyk and Chen.13 The structure function was approximated as that for an equivalent-volume, essentially Percus-Yevick, sphere.12J4 Allowance for penetration of the shell by continuous-phase hydrocarbon and shells of other particles was necessary; a penetration factor, value between zero and 1, multiplied by the volume fraction of the disperse phase in the computation of the structure function, was included in the least-squares fit.15 Also included in the adjustable parameters was a constant, SCALE, multiplied by the intensities of each run, to allow for errors in the absolute intensity calibration (which can be as high as 20% ) without distortion of the other leastsquares parameters to fit the shape of the patterns; if the calibration and model were completely correct, SCALE = 1. A small contribution to scattering intensity, constant with angle and largely determined by the high-Q tails of the patterns, was added to the computed values; this flat contribution arises primarily from incoherent scattering. The equations used, along with further details, can be found in ref 10. By our earlier criteria, a monodisperse-ellipsoid model also gave the most satisfactory fit with these results. However, the use of spheres of volume equivalent to asymmetric monodisperse particles or to the average particles in polydisperse spheres in the computation of structure functions is an approximation, known at least for the polydisperse case to be s e r i ~ u s . ' ~ Although J~ we are not aware of any practical way to avoid this approximation with asymmetric particles, a recent analytic integration1*J9 of expressions of Blum and Stell15 for a Schulz (gamma) distribution of particle sizes allows testing of a polydisperse model free of this difficulty. We have reexamined the applicability of various models to the patterns reported here (except for C5a-e, which scatter strongly at low Q and which will be discussed separately). (8) Kotlarchyk, M.; Chen, S.-H.;Huang, J. S. J.Phys.Chem. 1982,86, 3273. (9) Caponetti, E.;Lizzio, A.; Triolo, R.; Compere, A. L.; Griffith, W. L.; Johnson, J. S., Jr. Langmuir 1989,5, 357. (IO) Caponetti,E.;Magid, L. J.; Hayter, J. B.; Johnson, J. S., Jr. Langmuir, 1986,2, 722. (11) Caponetti, E.;Griffith, W. L.; Johnson, J. S., Jr.; Triolo, R.; Compere, A. L. Langmuir 1988,4, 606. (12) Hayter, J. B. In Physics of Amphiphiles: Micelles, Vesicles. and Microemulsions; Degiorgio, V., Corti, M., Eds.;North Holland Amsterdam, 1985; p 59. (13) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79, 2461. (14) Ashcroft, N. W.; Lekner, J. Phys.Rev. 1966,145,83. (15) Blum, L.; Stell, G. J. Chem. Phys. 1979, 71, 42; 1980, 72, 2212. (16) Vrij, A. J. Chem. Phys. 1979, 71, 3267. (17) van Beurten, P.; Vrij, A. J. Chem. Phys. 1981, 74, 2744. (18) Griffith, W. L.; Triolo, R.; Compere, A. L. Phys.Reo. A 1986,33, nn LlYl. 01
(19) Griffith, W. L.; Triolo, R.; Compere, A. L. Phys.Reu. A 1987,35, 2200.
1556 Langmuir, Vol. 8, No. 6, 1992
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Caponetti et al.
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55 ?
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Qd- 1 1 Figure 1. Scattering patterns from systems whose composition is shown in Table I: (a) 1-heptanol-and (b) 1-pentanol-containing systems. Maximum intensity decreases by increasing the alcohol content. I
I
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Q W )
Figure 2. Scattering patterns from systems whose composition is shown in Table 11: (a) 1-octanol-,(b) 1-heptanol-, (c) 1-hexanol, and (d) 1-pentanol-containingsystem. Maximum intensity decreases by increasing the alcohol content. Table 111. Volume of Groups (A3) CH3
-CH= K+ -OH
54.3 20.6 6.6 17.0
CHz
-coo DzO
26.9 25.4 30.0
Figure 3 compares fits by monodisperse spheres, polydisperse spheres, and monodisperse oblate ellipsoids for an example (C7a) of the relatively low-volume fraction compositions, also having high DzO/surfactant ratios. Figure 4 compares polydispersespheres, monodisperseprolate ellipsoids, and monodisperse oblate ellipsoids for a high-volume-fraction,low DzO/surfactant example (C7A), also containing 1-heptanol. Parameters of these fits are collected in Table IV. Besides SCALE and the incoherent contribution, the varied geometrical quantities are, for monodisperse particles, the radii of spheres having equivalent volume to the core and total particle, and the ratio of the axis about which an ellipse is rotated to generate
the ellipsoid to the other axis (ratioless than one for oblate, unity for sphere, and greater than one for prolate). From these parameters, a shell of constant thickness iscomputed, and in computing its scattering-length density, that part of its volume not filled with surfactant and shell-alcohol hydrocarbon is filled with continuous phase. For polydisperse distributions, the number-average radii and Schulz breadth factors are varied. In all cases, the volume fractions occupied by the particles, including invading solvent, are multiplied by a varied penetration factor, to give the effective volume fraction for structure functions. (The volume fractions listed in the tables are for components intrinsicto the particles, rather than volume fractions including penetrating solvent, used in the fitting computation.) The solubility of potassium oleate in hexadecane is small (0.0002 mol/LzO),and it is reasonable to assume essentially all of it is in the particle, with the head group at the water
Alcohol Partition in Microemulsion
Langmuir, Vol. 8, No. 6,1992 1557
Table IV. Parameters and Derived Quantities from Least-Squares Fits to Scattering Patterns by Various Models C7a (Figure 3)
core radius, & total radius, & penetration factor axial ratio Schulz breadth scale incoherent, cm-l vol. fraction* major axis, core A AGG
shell alcohols fraction total alcohol in shell X
monodisperse sphere 44.8 f 0.4 68.4 f 3.3 0.20 f 0.03
polydisperse spheres 38.1 f 0.2 54.6 f 0.4 0.45 f 0.02
1.02 f 0.03 1.10 f 0.08 0.226
23.9 f 1.1 1.02 f 0.00 0.97 f 0.01 0.236
264 1.76 0.440 98
239 2.20 0.550 9.0
C7A (Figure 4) oblate ellipsoid 47.3 f 0.2 61.5 f 0.6 0.39 f 0.02 0.547 f 0.005
prolate ellipsoid 32.8 f 0.7 43.8 f 0.1 0.60 f 0.07 1.70 f 0.10
1.12 f 0.01 1.00 f 0.02 0.227 116 311 1.83 0.458 19.5
1.10 f 0.03 1.48 f 0.04 0.355 93.4 154 1.59 0.34 25.2
polydisperse spheres 28.0 f 0.3 43.2 f 0.2 0.44 f 0.01 71f6 1.03 f 0.01 1.33 f 0.04 0.376 99 2.05 0.51 20.1
oblate ellipsoid 32.4 f 0.1 43.6 f 0.1 0.58 f 0.01 0.56 f 0.01 1.14 f 0.01 1.25 f 0.02 0.362 78 148 1.75 0.44 10.3
a Ellipsoids, radius of sphere of equivalent volume; polydisperse, number average radius. * Volume fraction comprises all of the water and surfactant, plus shell alcohol; i.e. penetrating matter not included.
3
loo0
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100
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w
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10
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0.10
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0.25
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25
QG-3 Figure 3. Comparison of models in fits to scattering patterns from composition C7a (Table 11),parameters in Table IV (- - -1 monodisperse spheres; (-) monodisperse oblate ellipsoids; (- - -) polydisperse spheres.
interface. 1-Pentanol is sparingly soluble in water, and the higher alcohols are even less soluble. The alcohols consequently can be assumed to be in the shell or continuous phase, but their distribution between these regions is aquestion of interest. From the core dimensions, the volumes of the species, and the ratio of water to surfactant, the number of surfactant molecules/particle AGG =
"me
(NW/KOl vW + vCOO + vK + %%?KO1 'OH) can be computed. Here Vw, Vcoo, VK, and VOHare the molecular volume of the water, of the carboxylate head group, of the potassium ion, and of the alcoholic head group. Values used are listed in Table 111. The volume of water was obtained from standard tables of heavy-water density, and volumes for CH, CHz, CH3, and OH groups were estimated from incremental molar volumes, also available in tables, of series of organic hydrocarbons and
(20) Schott,H.; Chang, Shaw-Lang,C.J . Colloid Interface Sci. 1987, 11 7, 94.
Figure 4. Comparison of models in fits to scattering patterns from composition C7A (Table I), parameters in Table IV (. .) monodisperse prolate ellipsoids; (-) monodisperse oblate ellipsoids; (- - -) polydisperse spheres.
alcohols. The counterion volume is from the compilations of Millero.21 Carboxylate volume was estimated from volumes of series of organic carboxylate salts in aqueous media, also compiled in this reference, by subtracting contributions of the counterions and organic groups; the incremental volumes of organic groups in water are about 10% less than in organic solutions. The symbol NW/KOI represents the stoichiometric molecules of water per mole of potassium oleate. For the quantitiesNs$$KO1, themoles of alcohols/moleofpotassium oleate in the shell, an estimate must be made. If areas of surfactant (SKO1) and alcoholic (SOH) head groups can be assigned, the distribution of alcohol between shell and continuous phase is determined, from the area of the coreshell interface not filled by carboxylates. The core surface is Score = AGG (sKol+ ~$&oiSoH) and can also be computed from the dimensions of the
(21) Millero, F. J. In Water and Aqueous Solutions; Horne, R. A., Ed.; Wiley Interscience; New York, 1972; Chapter 13, p 519.
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1558 Langmuir, Vol. 8, No. 6, 1992
+ 1
1
7 40
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1
n
1
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r
b
8 p
1
100
0
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8
ii 20
50
0
0
0
0
0.05
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0.10
aci -I)
Figure 5. Fits of the experimental SANS data for l-heptanolcontaining system with parameters shown in Table V and whose compositionsare given in Table I: symbols,experimental points; full line, calculated intensity. Maximum intensity decreases by increasing the alcohol to surfactant molar ratio.
0.08
0.12
0.18
ad-*)
Figure 7. Fits of the experimental SANS data for l-octanolcontainingsystem with parameters shownin Table VI and whose compositionsare given in Table I 1 symbols,experimentalpoints; full line, calculated intensity. Maximum intensity decreases by increasing the alcohol to surfactant molar ratio.
30 120
7
0.04
020
lJ\
20
E
I 0
w
U
10
0
0 0
0.05
0.10
0.15
020
atA-1)
Figure 6. Fits of the experimental SANS data for l-pentanolcontaining system with parameters shown in Table V and whose compositionsare given in Table I: symbols,experimental points; full line, calculated intensity. Maximum intensity decreases by increasing the alcohol to surfactant molar ratio. core. The equations can be solved simultaneously for yhell OH/KOI
Cross-sectional areas of alcohols are available from surface pressure measurements with Langmuir balances of alcohols insoluble in water (see e.g. ref 22); values are in the range of 20 A2. The arealhead group of carboxylates can be estimated from the dimensions and degrees of aggregations of micelles formed in water by salts of fatty acids;23these are within f 5 A2 of 60 A2. Similar areas have been deduced for AOT headgroups in waterloil microemulsions not containing alcohol and of moles of water per mole of surfactant comparable to the compositions here24~25 and for SDS headgroups in alcohol(22) Scatchard, G. Equilibrium in Solutions; Surface and Colloid Chemistry; Harvard University Press: Cambridge, MA, 1976; p 239. (23) Johnson, J. S.; Griffith, W. L.; Compere, A. L. Langmuir 1989,5, 1191. (24) Eicke, H. F.; Rehak, J. Helu. Chim. Acta 1976,59, 2883.
0.04
6.08
0.12
0.18
a(A-9
Figure 8. Fits of the experimental SANS data for l-heptanolcontaining system with parameters shownin Table VI and whose compositionsaregiven in Table I 1 symbols,experimentalpoints; full line, calculated intensity. Maximum intensity decreases by increasing the alcohol to surfactant molar ratio. containing microemulsions.26 From the dependence of areas on waterlsurfactant ratios, the dependence of areal head group on curvature is believed to be weak.27 We have used 60 A2 for the arealcarboxylate and 20 A2 for alcoholsin computing the valuesofN8$$Kolhere. Iteration by a Newton-Raphson procedure with these assignments of areas determined values of the number of alcohols in the shell and AGG self-consistent with core areas from dimensions. The scattering length density of the shell for the particle functions was computed for surfactant and shell-alcohol hydrocarbon plus the invading solvent. Coherent scattering lengths for all elements were taken from a standard source.28 Scattering arises primarily from contrast between the core and the rest of the medium; in a typical case, the scattering length density of the core is about 6 X 10-6A-2, that of the shell -0.36 X lo4 A-2, and that of the continuous phase, -0.39 X lo4 A-z. (25) Maitra, A. J. Phys. Chem. 1984,88, 5122. (26) Dvolaitzky, M.; Guyot, M.; Lagues, M.; Le Peeant, J.-P.;Ober, R.; Sauterey, C.; Taubin, C. J. Chem. Phys. 1978,69,3279. (27) Hou, M.-J.; Shah, D. 0. Langmuir 1987, 3, 1086. (28) Kostorz, G.; Lovesey, S. W. Treatise on Materials Science and Technology; Academic Press: New York, 1979; Vol. 15, pp 230-231.
Langmuir, Vol. 8, No. 6, 1992 1559
Alcohol Partition in Microemulsion
0 1-Panhnol 0 l-Hept~ol
0
0.04
0
0.08
0.12
0.18
ad-’) Figure 9. Fits of the experimental SANS data for l-hexanolcontaining systemwith parameters shown in Table V I and whose compositionsare given in Table 11: symbols,experimentalpoints; full line, calculated intensity. Maximum intensity decreases by increasing the alcohol to surfactant molar ratio.
I
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l t 01 0
’
2
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8
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,
,
,
,
,
0
10
12
14
18
18
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1
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I
0.08
20
Figure 11. Alcohol/surfactant molecular ratio in the shell as a function of the stoichiometric alcohols to surfactant molar ratio for microemulsions whose compositionis given in Table I. Curves are eye guides. 8)
\
0
?
o 1-pentanol 0 1-hexanol 4 1-heptanol A 1-octanol
0.16
ad-’1
Figure 10. Fits of the experimental SANS data for l-pentanolcontainingaystemwith parameters shown in Table VI1 and whose compositionsare givenin Table I1 symbols,experimentalpoints; full line, calculated intensity. Maximum intensity decreases by increasing the alcohol to surfactant molar ratio.
It is clear from Figure 3 that monodisperse spheres are not an adequate model for the patterns; oscillationsin the computed intensities for this and the other compositions are outaide what one might intuitivelyexpect to be smeared out by the inhomogeneity of neutron wavelengths, finite size of the scattering sample, and multiple scattering. Prolate ellipsoids, as in earlier studies of water-in-oil microemulsions (in contrast to micelles23),also do not give adequate fits (Figure 4). Least-squares fita by this model were frequently unstable, and attainment of convergence was much more sensitive to starting values of the parameters than with other models. Behavior of this sort is common when models are poor approximations. Converged values sometimes were unreasonable physically, e.g., not enough volume allowed between core and total particle radius to accommodate all surfactant and shellalcohol hydrocarbon. The example shown was physically allowable, but, as in all such cases in which convergence was attained, the prolate ellipsoid model gave a poor fit, in comparison to oblate ellipsoids or (sometimes) to polydisperse spheres. Oblate ellipsoids and Schulz distributions of spheres
,
00
5
10
15
20
25
NOH/KO, Figure 12. Alcohol/surfactant molecular ratio in the shell as a function of the stoichiometric alcoholsto surfactant molar ratio for microemulsionswhosecompositionis given in Table 11. Curvea are eye guides. both gave adequate fits to the low-volume-fraction compositions, as the example in Figure 3 indicates. The polydisperse model looks a little better both in the figure and in the x values of this and other compositions listed in Table 11. ( x is square root of the ((sum of the squares of weighted residuals)/ (number of points minus number of parameters plus l)).)The computed curve for polydisperse spheres in Figure 3 is difficult to distinguish from the points. Oscillationsabout experimental points can be seen in the oblate-ellipsoid curve. However these occur in regions of low intensity, here less than twice the incoherent background, and may well be smeared out in the experimental results. The distribution of species
Caponetti et al.
1560 Langmuir, Vol. 8, No. 6, 1992
Table V. Parameters from Least-Squares Fits to Scattering Patterns from Water-in-Oil Microemulsions (compositions in Table I, oblate ellipsoid model) scale
core radius, A
axial ratio
penetration factor
major axis, A
volume fraction'
AGG
x
C7A C7B C7C C7D C7E
1.14 f 0.01 1.19 f 0.01 1.23 f 0.00 1.20 f 0.00 1.16 f 0.01
32.4 f 0.1 30.0 f 0.1 28.3 f 0.1 26.8 f 0.0 24.3 f 0.0
43.6 f 0.1 40.0 f 0.1 37.5 f 0.0 35.3 f 0.0 32.3 f 0.1
0.565 f 0.005 0.557 f 0.004 0.539 f 0.003 0.512 f 0.003 0.481 f 0.004
0.58 f 0.01 0.59 f 0.01 0.57 f 0.01 0.52 f 0.01 0.42 f 0.00
78 73 70 67 62
0.362 0.359 0.349 0.339 0.332
148 117 97 82 60
10.3 6.7 3.7 2.1 1.4
C5A C5B C5C C5D C5E
1.04 f 0.00 1.04 f 0.00 1.03 f 0.01 0.98 f 0.02 0.98 f 0.05
26.2 f 0.0 24.0 f 0.0 22.4 f 0.1 21.1 f 0.1 19.4 f 0.3
38.6 f 0.0 34.8 f 0.1 32.8 f 0.1 31.2 f 0.1 29.5 f 0.1
0.469 f 0.002 0.496 f 0.005 0.507 f 0.012 0.511 f 0.021 0.484 f 0.039
0.25 f 0.00 0.31 f 0.00 0.31 f 0.00 0.29 f 0.01 0.25 f 0.01
68 61 56 53 49
0.398 0.394 0.383 0.369 0.361
76 57 46 38 29
2.8 3.4 3.4 2.9 2.2
total radius,
Volume fraction includes all water, all surfactant, and shell alcohol reported in Table VIII; no penetrating material.
Table VI. Parameters from Least-Squares Fits to Scattering Patterns from Water-in-Oil Microemulsions (compositions in Table 11, oblate ellipsoid model) scale
core radius, 8,
total radius, A
axial ratio
penetration factor
major axis, 8,
vol. fractiona
AGG
x
0.561 f 0.006 0.570 f 0.006 0.567 f 0.006 0.554 f 0.006 0.536 f 0.006
0.57 f 0.03 0.70 f 0.00 0.71 f 0.02 0.69 f 0.04 0.63 f 0.04
130 123 116 111 108
0.220 0.219 0.218 0.217 0.213
455 391 328 278 248
19.3 19.3 17.2 15.4 14.3
C8a C8b c8C C8d C8e
1.07 f 0.01 1.13 f 0.01 1.17 f 0.01 1.20 f 0.01 1.18f 0.01
53.5 f 0.3 51.1 f 0.2 48.1 0.2 45.6 f 0.3 43.9 f 0.3
*
65.6 f 0.7 61.3 f 0.7 57.8 f 0.6 54.6 f 0.5 52.5 f 0.6
C7a C7b C7c C7d C7e
1.12 f 0.01 1.11f 0.01 1.15 i 0.01 1.18 f 0.01 1.17 f 0.01
47.3 f 0.2 45.6 f 0.2 43.8 f 0.2 42.1 f 0.2 40.4 f 0.2
61.5 f 0.6 57.6 f 0.5 55.2 f 0.4 52.8 f 0.5 50.7 f 0.6
0.547 f 0.005 0.553 f 0.005 0.548 f 0.005 0.538 f 0.005 0.519 f 0.006
0.39 f 0.02 0.57 f 0.02 0.59 f 0.03 0.58 f 0.03 0.53 f 0.02
116 111 107 104 100
0.227 0.224 0.220 0.216 0.210
311 278 246 218 191
19.5 19.8 18.5 15.0 13.7
C6a C6b C6c C6d C6e
1.04 f 0.01 1.07 f 0.01 1.09 f 0.01 1.10 f 0.01 1.05 f 0.01
41.3 f 0.2 40.2 f 0.2 39.0 f 0.2 37.8 f 0.2 36.7 f 0.2
57.5 f 1.3 54.6 f 0.6 52.5 f 0.4 50.4 f 0.4 49.0 f 0.5
0.495 f 0.005 0.511 f 0.005 0.513 0.005 0.506 f 0.005 0.493 f 0.005
0.18 f 0.02 0.32 f 0.02 0.39 f 0.02 0.42 f 0.02 0.40 f 0.02
104 101 97 95 93
0.235 0.229 0.224 0.217 0.209
205 189 171 156 143
18.9 14.0 12.8 11.2 10.0
*
Volume fraction includes all water, all surfactant, and shell alcohol reported in Table IX; no penetrating material.
Table VII. Parameters from Least-Squares Fits to Scattering Patterns from 1-Pentanol System Whose Compositions Are Given in Table I1 (the axial ratio and the penetration factor were fixed at 0.45 and 0.5. reswctively) ~~
C5a C5b c5c C5d C5e
scale 0.76 f 0.01 0.69 f 0.01 0.72 f 0.01 0.75 f 0.01 0.69 f 0.01
major axis' 78.0 & 0.4 77.8 & 0.4 77.9 0.2 77.1 0.4 74.2 & 0.4
*
Q.9"
SCritb
LC"
109 f 1 103 f 1 98.8 f 0.4 96.8 f 0.6 95.6 f 0.8
6.6 f 0.2 2.29 f 0.02 0.90 f 0.02 0.47 f 0.01 0.39 f 0.02
78 f 5 38 f 2 23f1 25f 1 27 f 1
a Units in A. % is twice the total radius of Tables V and VI. Units in cm-'. and the alcohol amount reported in Table IX.
implied by the polydisperse model is not broad, Schulz parameters falling between 15and 25 for the compositions of Table 11; the mean square deviation of radii from the number average is the average radius squared divided by the Schulz parameter plus More systematic differences between the two models are seen for the compositions of Table I (high volume fractions, lower DzO/surfactant). Here oblate ellipsoids clearly give the better fits, as Figure 4 illustrates. Both at low angles and at high angles, the polydisperse model diverges substantially from experiment. The Schulz parameters (35 to 164) for the compositions of Table I would indicate a more modest polydispersity than for those of Table 11. Values of SCALE parameters are unity within uncertainty of calibration of absolute intensity and are not consistently closer to one for either of these models. Consequently, they do not aid choice between the alternatives. Despite the approximation in asymmetric-particle structure function, oblate ellipsoids appear to give a better fit over all compositions, and we conclude they are a more (29)Aragon, S.R.;Pecora, R. J. Chem. Phys. 1976,64, 2395.
volume fractionC 0.260 0.258 0.260 0.245 0.225
AGG 79.5 78.6 79.2 76.7 67.9
Volume fraction includes all of the water, all of the surfactant
likely model for these systems. The fits and estimates of alcohol partition to be presented are based on this geometry. The high low-Q scattering by the 1-pentanolseries CSae (Figure 2d) is not predicted by any of these models. Similar observations in other scattering s t u d i e ~ ~ have ~~~*3l been attributed to the proximity of a critical point. We have followed these interpretations by adding an OrsteinZernike32term
to the structure function; L, is the correlation length, and Scritis the contribution at zero Q to the structure function from critical scattering. To limit the number of parameters, the penetration factor and axial ratio were fixed at values in the range of those obtained for the other compositions. The fits were also carried out slightly differently; varied dimensions were the major axis of the (30)Corti, M.; Degiorgio, V. J. Phys. Chem. 1981, 85, 1442. (31)Triolo, R.;Magid, L. J.; Johnson, J. S., Jr.; Child, H. R. J. Phys. Chem. 1982,86, 3689. (32)Ornstein, L.S.;Zernike, F. Proc.-Acad. Sci. Amsterdam 1914, 17, 793.
Alcohol Partition in Microemulsion
Langmuir, Vol. 8, No. 6, 1992 1561
Table VIII. Alcohol Partition in Water-in-Oil Microemulsions Whose Composition Ie Given in Table I NOHIKOI
X E K o t
F
~
H
I .O
NEKO~
C7A C7B c7c C7D C7E
4.0 5.4 7.2 9.2 12.2
1.8 2.2 2.6 3.0 3.8
0.44 0.40 0.36 0.33 0.31
2.2 3.2 4.6 6.2 8.4
C5A C5B c5c C5D C5E
5.5 7.2 9.4 12.0 15.4
3.4 3.9 4.4 4.9 5.9
0.61 0.55 0.47 0.41 0.38
2.1 3.3 5.0 7.1 9.5
Table IX. Alcohol Partition in Water-in-Oil Microemulsions Whose Composition Is Given in Table I1 NoHIKoi
C8a
MheU OHIKOI
F b H
3.0 4.0 5.5 7.2 9.1
1.2 1.4 1.7 2.0 2.3
0.40 0.36 0.31 0.28 0.25
1.8 2.6 3.8 5.2 6.8
C7a C7b c7c C7d C7e
4.0 5.5 7.2 9.3 12.1
1.8 2.0 2.2 2.5 2.8
0.46 0.37 0.31 0.27 0.23
2.2 3.5 5.0 6.8 9.3
C6a C6b C6c C6d C6e
5.5 7.2 9.3 12.1 15.4
2.8 2.9 3.1 3.3 3.5
0.50 0.40 0.33 0.27 0.23
2.7 4.3 6.2 8.8 11.9
C5a C5b
8.0 9.3 12.1 15.4 19.9
5.0 5.2 5.1 5.2 5.9
0.63 0.56 0.42 0.34 0.28
3.0 4.1 7.0 10.2 14.2
c5c C5d C5e
core and the diameter of the sphere equivalent to the total particle volume. The volume fraction by which the penetration factor was multiplied for computation of structure function was comprised of the core plus surfactant and shell-alcohol hydrocarbon, i.e. did not include penetrating solvent. Because it is the product that is pertinent in the computation, the fit is not affected, but the values of the penetration factor cannot be compared directly with those from the other sets. Results. Fits to the patterns are given in Figures 5-10, and the parameters are summarized in Tables V-VII.Table VI1 also reports the critical parameters derived in the fits to C5a-e. Because its value is irrelevant to the geometry, the incoherent parameter is omitted from Tables V-VII; its converged value was in the expected range 1 cm-' or a little higher. Correlations between parameters confirm the inference from their low statistical error that there is no excessive coupling in the least-squares fit. Two of the compositions listed in Table I are close enough in hydrocarbon and alcohol to series in ref 1 to allow comparison of aggregationnumbers, by interpolation to 30 mol of waterjmol of surfactant. For the heptanolcontaining system, the interpolated value of AGG is 125, in comparison with 117 for C7B. For the pentanolcontaining system, the comparison is 57 to 61 for C5B. Because the compositions are not identical and the earlier analysis assumed half the alcohol to be in the shell, the agreements appear satisfactory. Tables VI11 and IX report the alcoholpartition between the particle and the continuous phase, for the compositions in Tables I and 11, respectively. Discussion. The fits to the scattering patterns indicate
0.0
-
0.8
-
0.7
-
0
0.0
i
I-Pontanol
0 1-Heptanol
i
:::I
GgKO1
C8b C& CBd C8e
I
0
,
,
,
,
,
,
,
,
,
2
4
6
8
10
12
14
16
18
, 20
N ~ ~ / ~ Figure 13. Fraction of the total alcohol in the shell as a function of the stoichiometric alcohols to surfactant molar ratio for microemulsionswhose composition is given in Table I. Curves are eye guides.
I1 ~
O.Q
0.8 0.7
X
0
E
o 1-pentanoi 1-hexanol A 1-heptanol A 1-octanol
-
0
-
0.8
-
0
\0
0.4 0.5
0.3
-
0.1
1
o'2
0.0
1
0
I
I
5
10
15
20
25
NOH/KOL Figure 14. Fraction of the total alcohol in the shell as a function of the stoichiometric alcohols to surfactant molar ratio for microemulsionswhose compositionis given in Table 11. Curves are
eye guides.
that the oblate-ellipsoid model provides a satisfactory interpretation of the results. Polydisperse spheres are at least equally satisfactory at the low volume fractions, but unless different models are adopted for the two concentration ranges, asymmetric particles seem a better choice than polydisperse spheres. Critical scattering provides a satisfactory explanation for high scattering at low angles in the case of C5a-e, although the evidence available does not allow a definitive conclusion. The parameters derived for this case are less certain. Trends in parameter values warrant comment. For each alcohol, increasing the alcohol-to-surfactant ratio, other ratios being constant, decreases the aggregate size, con-
~
~
1562 Langmuir, Vol. 8, No. 6, 1992
sonant with the earlier qualitative inferences from the scattering patterns. This trend is documented impressively by the number of surfactant molecules in each particle (AGG) in Tables V-VII. As we previously noted, it is consistent with earlier observations of decreasing particle sizes with increasing surfactant/water ratio. The axial ratios vary little within each system and decrease slowly from l-octanol to l-pentanol systems; the same trend was previously observed in the study of water/ surfactant ratios with the same microemulsion.’ Within a given set, there is a noticeable decrease (in the direction of greater penetrability) in the penetration factor with decrease in alcohol chain length. This is consistent with a larger fraction of the shell that can be penetrated by solvent and other particles when the cosurfactant is shorter. For a given alcohol, a t fixed ratios of other components, the number of alcohols per surfactant molecule in the shell goes up with total alcohol present (Figures 11and 121, as one expects from the increase in core surface for a given amount of water distributed in smaller particles. The fraction of total alcohol FROHin the shells declines (Figures 13 and 14) with increasing total alcohol. In comparison of different alcohols, the fraction in the shell increases with decreasing chain length of the alcohol. The trend is consistent the more hydrophobic character of the higher alcohols. Consistent with this, aggregate size decreases with decrease in alcohol chain length.
Caponetti et al. The ranges of fraction of alcohol in the shell for the two models at compositions for which both give good fits may be of interest. They are listed for oblate ellipsoid/polydisperse spheres: C8a-e, 0.40-0.25/0.42-0.24; C’la-e, 0.460.23/0.55-0.30; C6a-e, 0.50-0.23/0.68-0.33. Trends are seen to be similar. In conclusion, distributions of alcohols as a function of chain length and concentration appear consistent with the chemical nature of the components.
Acknowledgment. We are grateful to the Biology Department of the Brookhaven National Laboratory for granting the beam time at the low angle biological spectrometer [H-93 of the High Flux Beam Reactor. We appreciate the generous help of Dr. D. Schneider in the course of experiment. This research was sponsored by the “Progetto Finalizzato Chimica Fine 11”of the Consiglio Nazionale delle Richerche (Rome). Participation by Oak Ridge National Laboratory was supported by Advanced Industrial Concepts Division, Office of Conservation & RenewableEnergy, US.Department of Energy under Contract No. DE-AC05-480R21400 with Martin Marietta Energy Systems. Registry No. n-Hexadecane,544-76-3;potaesium oleate,14318-0; l-pentanol, 71-41-0; l-hexanol, 111-27-3; l-heptanol, 11170-6; l-octanol, 111-87-5.
