Langmuir 1990, 6, 244-249
244
Aggregation and Critical Behavior of 2-Butox$thanol in Water Francois Quirion,*?+Linda J. Magid,' and Maurice Driffords INRS-Energie, Varennes, Qugbec, Canada, JOL 2P0,Department o f Chemistry, University of Tennessee, Knoxville, Tennessee 37996-1600, and Dgpartement de Physico-Chimie, C E N de Saclay, 91191 Gif-sur- Yvette, Cedex, France Received March 27, 1989. I n Final Form: J u l y 14, 1989 The critical behavior of 2-butoxyethanol (BE) in water was investigated through dynamic and Rayleigh light-scattering measurements. The critical exponents related to the osmotic compressibility and the correlation length are consistent with the Ising predictions, and they apply over a wide range of temperature. At higher values of momentum transfer (Q),the small-angle neutron scattering (SANS) spectra had to be analyzed with a model that accounts for the critical concentration fluctuations and the presence of aggregates of BE having a radius of about 9 A. The correlation length and the critical intensity at zero momentum transfer obtained by light and neutron scattering are in excellent agreement. The freezing point depression of water in the presence of BE was correlated to the self-association of six BE molecules. Our results are discussed in terms of dry and wet aggregates coupled with concentration fluctuations.
Introduction Although 2-butoxyethanol (BE) is mostly used as a solvent, its behavior in water is similar in many ways to that of long-chain poly(oxyethy1ene) monoalkyl ethers (C,E,). For the past 10 years, this system has been the object of many studies. Still, it is not clear to what extent BE can be considered as a surfactant. Kilpatrick et al.' defined a surfactant as "an amphiphile which aggregates collectively with other amphiphilic molecules to form a surface which separates oil-rich and water-rich domains". In Table I, we present a retrospective of the properties that have been measured for aqueous solutions of BE.1-54 In many of these studies, a sharp change in the properties was observed around XBE = 0.02 and correlated to some kind of self-association of BE in water. From heat capacity measurements, Kusano et al.,, pointed out that BE enhances the structure of water around the alkyl chain to form some kind of clathrate structure. Around XBE= 0.02 Roux et al.26*30 observed a sharp change in the partial molar volumes, heat capacities, and expansibilities of BE in water. They associated it with a microphase transition similar to the micellization of surfactants. From Raman spectroscopy and light scattering, Ito et aL2s3' and Kato40 suggested the coexistence of clathrates of the type g[(H,O),,BE] and
* Author to whom correspondence should be addressed. INRS-Energie.
* University of Tennessee. * CEN de Saclay.
(1) Kilpatrick, P. K.; Davis, H. T.; Scriven, L. E.; Miller, W. G. J . Colloid Interface Sci. 1987,118, 270. (2) Ito, N.;Fujiyama, T.; Udagawa, Y. Bull. Chem. SOC.Jpn. 1983, 56,379. (3) Shindo, Y.;Kusano, K. J. Chem. Eng. Data 1979,24,106. VanDinter, T.; Saunders, J. R. Can. J. Chem. (4) Desrosiers, 0.; 1984,62,56. (5) Pegg, I. L.; McLure, I. A. Mol. Phys. 1984,53,897. (6) Hamano, K.; Kawazura, T.; Koyama, T.; Kuwahara, N. J. Chem. Phys. 1985,82,2718. (7) Bennes, R.;Privat, M.; Douillard, J. M. C. R. Seances Acad. Sci., Ser. 2 1983,296,537. (8) Douillard, J. M.; Bennes, R.;Privat, M.; Tenebre, L. J. Colloid Interface Sci. 1985,106,146. (9) Elizalde, F.;Gracia, J.; Costas, M. J. Phys. Chem. 1988,92,3565. (10) Burczyk, B.; Piasecki, A.; Para, G.; Pomianowski, A. J . Colloid Interface Sci. 1981,80, 123.
0743-7463/90/2406-0244$02.50/0
h[(H,O),BE] in the range 0.02 < XBE< 0.2, where g and h increase with temperature up to the miscibility gap. From ultrasonic properties, Kat0 et al.34applied a double-equilibrium modelss to explain the two relaxation processes observed above the microphase transition of BE. The first process was related to the merging of clathrates, while the second was the self-association of five BE molecules. Nishikawa et a1.33,35analyzed their ultrasonic data with two different models similar to the one of Tamura et al.," and they suggested that more than BE monomers associate to form short-lived aggregate^.^^ Desrosiers et aL4used a mass action model to analyze their 13C chemical shifts, and they reported an aggregation number of 8 a t 32 OC. On the other hand, their T , data could not be fitted with such a model, and they suggested that the aggregates were hydrated, but to a lesser extent than the monomers. Yamashita et al.23 also used a mass action model,@and they obtained aggregation numbers of 14.3 and 8.6 from the apparent molar heat capacities and volumes, respectively. Haak and Engbertsls referred to the microphase transition as a "critical hydrophobic interaction concentration" (CHIC), which they observed from solvent polarity measurements. Fluorescence-probing14 studies and kinetic effects on ester hydrolysis5' in aqueous BE solutions also support the aggregation of BE molecules through hydrophobic interactions. The idea of a microphase transition comes from the occurrence of an upper miscibility gap having a lower critical solution temperature (LCST). The two clath(11) Hamdi, M.; Vanel, P.; Schumann, D.; Bennes, R.J. Electroanal. Chem. 1982,136,229. (12) Sokolowski, A.; Burczyk, B. J. Colloid Interface Sci. 1983,94, 369.
(13) Hansen, C.M. Ind. Eng. Chem. Prod. Res. Deu. 1977,16,266. (14) Bennes, R.; Douillard, J. M.; Privat, M.; Tenebre, L. J . Phys. Chem. 1985,89,1822. (15) Bennes, R.;Douillard, J. M.; Privat, M.; Tenebre, L. C. R. Seances Acad. Sci., Ser. 2 1985,t300, 787. (16) Ross, S.;Nishioka, G. J. Phys. Chem. 1975,79,1561. (17) Ross, S.;Nishioka, G. In Foams Proc. Symp. Akers, R. J., Ed.; Academic Press: London, 1976;p 17. (18) Haak, J. R.; Engberts, J. B. F. N. Rec. Traul. Chim. Pays-Bas 1986,105,307. (19) Schneider, G. M.; Wilhelm, G. 2. Phys. Chem. Neue Folge 1959,20,219. (20) Scatchard, G.; Wilson, G. M. J . Am. Chem. SOC.1964,86,125.
0 1990 American Chemical Society
Langmuir, Vol. 6, No. 1, 1990 245
Aggregation and Behavior of 2-Butoxyethanol in Water Table I. Retrospective of Properties Measured for Aqueous Solutions of 2-Butoxyethanol property
ref
refractive index viscosity and shear viscosity surface and interfacial tension ellipticity foaminess solvent polarity free energy enthalpy density and volume heat capacity expansibility compressibility ultrasonic properties NMR (lH, *H, 13C) PG-FT-NMR (self-diffusion coefficient) fluorescence probing light scattering infrared and Raman spectroscopy small-angle neutron scattering phase diagram electric birefringence
1-3 4-6 1,7-13 8, 14, 15 9, 16, 17 18 19, 20, 21 20-25 1, 3, 5, 24, 26-29 22, 24, 26, 28, 30 26, 29 27, 29, 31, 32 33-35 1, 4, 36, 37 38
Experimental Section
14 2, 6, 14, 15, 38-43, this study 2, 44, 45 this study 2, 9, 19, 46-53, this study 54
Table 11. Literature Values of LCST a n d Critical Composition of Water BE System
+
LCST 47.5 49.1 49.2 44.5 48.8 49.4 49.0 49.0 48.7 48.2 48.0 49.0 48.3 49.8
x c
ref
0.048 0.048
46 49 19 50 48 2 51 9 52 6 53 5 this study 54
0.053 0.054 0.07 0.059 0.058 0.059 0.061 0.048 0.059 0.052 0.051
rate compositions suggested by Ito et aL2v3' are essentially the composition of the coexistent phases of the system at higher temperatures. As the critical point is approached, many properties diverge according to an exponential law which can be predicted through the renormalization group theory (RGT). One of the models used to calculate the critical exponents of binary solutions is the Ising 3D Degiorgio5' observed that the critical exponents obtained for short-chain C,E, agree with the RGT predictions while the higher homologues diverge substantially. Table I1 summarizes the critical compositions and temperatures reported for the LCST of BE in water. The critical exponent related to the shear viscosity of BE in water was obtained e ~ p e r i m e n t a l l y , ~ and ' ~ .it~ is ~ consistent with the RGT prediction. This was also observed for the mutual diffusion coefficient and the e 1 l i p t i ~ i t y .Belll~~~~ ini and D e g i ~ r g i obtained o~~ the critical exponent related to the Kerr constant obtained with electric birefringence measurements, and their value is consistent with those obtained for nonionic micellar solutions.60 In order to get more information on the structure of BE in water, we investigated this system through Rayleigh and quasi-elastic light scattering (QELS) as well as small-angle n e u t r o n scattering (SANS). Corti et al.61mentioned that "data for short chain amphiphiles (C6E,, CsE4,and CsE5) seem to be adequately described by a (D12j6114915
model of small micelles with a short range, temperature dependent, attractive pair potential". For C12E6, Triolo et aL6*expressed this attractive potential by the OrnsteinZernike equation for critical scattering. Our results are analyzed in terms of critical behavior and self-association of BE molecules in water.
B E (Fisher Chemicals, Les Produits Chimiques Shefford Ltd, and Aldrich Chemicals) was distilled a t atmospheric pressure, and the middle fraction was collected. T h e consolute temperatures were determined from the visual detection of the cloud point. For the boiling point diagram, the equilibrium temperature was noted as the solution distilled under atmospheric pressure. Light-scattering measurements were conducted a t the CEA/ CEN of Saclay in France (QELS) and a t the University of Tennessee in Knoxville (QELS and Rayleigh ratios) using an argon ion laser combined with a photomultiplier and digital correlator (Malvern and Brookhaven). T h e incident radiation (wavelength 5145 A) was vertically polarized, while unpolarized scattered light was detected. The sample was placed in a 1-cm cylindrical test tube thermostated in a toluene bath. Mutual diffusion coefficients (D,J were obtained at 25 "C a t a scattering angle of 90" except a t low and high concentrations, where it was measured a t 45" because of the low intensity of scattered light. Rayleigh ratios (R(90)) were calculated from the scattered intensity of the solution relative to the intensity of benzene a t a scattering angle of 90" and a t 25 "C. Both D,,and R(90) were calculated by using standard proceduresF3 For the critical scattering experiment, the temperature dependence of the refractive index and of the Rayleigh ratio of benzene was taken from Arlie e t al.64 Small-angle neutron-scattering spectra were measured on the D16 diffractometer at the high-flux reactor of the Institut Laue Langevin, Grenoble, France. Spectra were recorded a t two angles (6" and 13") on a 16 X 64 multidetector covering values of moment u m transfer (Q) between 0.05 and 0.45 A-1. T h e wavelength used was 4.52 A, and the sample to detector distance was 1.09 m. Samples were contained in 2-mm path length optical quartz cells thermostated at 26 & 1 "C. Spectra were corrected for absorption and detector efficiency, and they were put on an absolute scale by using the incoherent scattering of waterUB5 The spectra were then analyzed from 0.05 to 0.25 A-1 (36 data points) with a nonlinear nonwei hted least-squares fitting program based on Bevington's CURFIT. 6%
(21) Cabani, S.; Mollica, V.; Lepori, L. J. Chem. SOC.,Faraday Trans. 1 1978, 74, 2667. (22) Kusano,. K.:. Suurkuusk.. J.:. Wadso, L. J. Chem. Thermodvnam. i973.5.757. (23) Y i a s h i t a , F.; Perron, G.; Desnoyers, J. E.; Kwak, J. C. T. ACS Symp. Ser. 1986, 311, 79. (24) Oncken, V. U. 2.Electrochem. 1959,63, 321. (25) Anderson, B.; Olofsson, G. J. Solution Chem. 1988, 17, 9. (26) Roux, G.; Perron, G.; Desnoyers, J. E. J . Solution Chem. 1978,
. --".
7, fig9
(27) Rao, N. P.; Verrall, R. E. Can. J. Chem. 1987,65, 810. (28) Quirion, F.; Desnoyers, J. E. J . Colloid Interface Sci. 1987,
115. 76. ~~~
(29i Harada, S.; Nakajima, T.; Komatsu, T.; Nakagawa, T. J.
Solution Chem. 1978, 7, 463.
(30) Roux, G.; Perron, G.; Desnoyers, J. E. J . Phys. Chem. 1978,82, 966. (31) Lara, J.; Desnoyers, J. E . J . Solution Chem. 1981, 10, 465. (32) Swamy, K. M.; Swamy, P. S. Acustica 1983,54, 61. (33) Nishikawa, S.; Kotewaga, K. J. Phys. Chem. 1985, 89, 2896. (34) Kato, S.;Jobe, D.; Rao, N. P.; Ho, C. H.; Verrall, R. E. J. Phys. Chem. 1986,90, 4167. (35) Nishikawa, S.; Tanaka, M.; Mashima, M. J. Phys. Chem. 1981, 85, 686. (36) Howarth, 0. W. J . Chem. SOC.,Chem. Commun. 1974,8, 286. (37) Attanasio, A. 2.Naturforsch. A 1973,28, 504. (38) Kato, T. J . Phys. Chem. 1985,89,5750. (39) Ito, N.; Saito, K.; Kato, T.; Fujiyama, T. Bull. Chem. SOC.Jpn. 1981, 54, 991. (40) Kato, T. J. Phys. Chem. 1984,88, 1248.
246 Langmuir, Vol. 6, No. 1, 1990
120
L
L... +
I + V
A
I
-.
Quirion et al.
4
v
Q
s
V'
-0.8
1.6 LOG(Tc-T) Figure 2. log-log representation of the critical behavior of the system water 2-butoxyethanol at X,, = X, = 0.052. T was taken as 48.3 "C. Data are plotted on arbitrary log Y scales.
I
I
I
+
0.3
0
XBE
Figure 1. Phase diagram of the system water + 2-butoxyethanol (BE) at 1 atm: ( 0 ) H,O + BE; (0)D 0 (95%) + BE; (- - -) from ref 48. Boiling point of H 2 0 + Bb: (A)one liquid phase; (+) two liquid phases. 1, v, 1, + l,, and X, refer to liquid, vapor, two liquid phases, and the mole fraction of BE. e
Results Phase Diagrams. P ~ p p e S, ~~h~n e i d e rand , ~ ~Ellis4' all reported an upper miscibility gap for the system waterBE with a LCST around 48 "C and a UCST around 130 "C. Their experiments were conducted in sealed tubes, which means that their phase diagrams were isochoric and not isobaric. Although the effect of pressure on the UCST is not drama ti^,^^'*^ it has a large effect on the liquid-vapor equilibrium. This is shown in Figure 1, where the phase diagram reported by Ellis4s is compared with our results for the liquid-liquid equilibrium and the boiling point under atmospheric pressure. In the range 0.02 X,, < 0.19, the solutions boil as an unmixed system with a constant boiling point of 98.8 "C. The decrease of the boiling point of water by BE is consistent with the vapor pressure-composition diagrams obtained by Schneider and Wilhelm,lg who reported an azeotrope around X,, = 0.05. The LCST was evaluated by plotting T against IX, X111/3,where XI and X, are the composition of BE in the coexisting phases at the equilibrium temperature T . The intercept gave T , = 48.3 f 0.1 "C, and using the procedure described by Ellis4' we obtained X , = 0.052 f 0.005. Our LCST compares quite well with those reported in Table 11. When H 2 0 is replaced by D,O (95%), the LCST decreases to 41.5 f 0.2 "C while the critical composition remains almost unaffected at 0.055 f 0.003. This has also been observed for nonionic surfactants6' of the same (41) Bender, T. M.; Pecora, R. J . Phys. Chem. 1988,92, 1675. (42) Quirion, F.;Magid, L. J. J. Phys. Chem. 1986,90, 5193. (43) Wakeham, A. Faraday Symp. Chem. SOC.1980,15, 139.
(44) Bribes, J. L.; Maillols, J.; Sportouch, S.;Gaufres, R. C. R. Seances Acad. Sci., Ser 2 1985, t300, 787. (45) Bribes, J. L.; Maillols, J.; Sportouch, S.;Gaufres, R. C. R . Seances Acad. Sci., Ser 2 1984, t298, 335. (46) Poppe, G. Bull. SOC.Chim.Belg. 1935, 44, 640. (47) Schneider, G. M. 2. Phys. Chem. Neue Folge 1963,37, 333. (48) Ellis, C. M. J . Chem. Educ. 1967, 44, 405. (49) Cox, H. L., Cretcher, H. J. Am. Chem. SOC.1926,48, 451. (50) Chakhovskoy, N. Bull. SOC.Chim.Belg. 1956, 65, 476. (51) Guzman, F. Int. Data Ser. B 1980, 105.
family. This isotope effect may be related to the stronger hydrogen bonding of d e ~ t e r i u m . ~ ~ Light Scattering. From the consolute curve, the Rayleigh ratio (R(90)),and the mutual diffusion coefficient (D,,), we obtained the critical exponents p, y , and Y related to the length of the coexisting phases (IX, - XJ), the osmotic compressibility ((aa/ac)-'), and the correlation length ([), respectively, with
- ( a i ~ / a ~ ) - ' ROJT, TI' D l i l - E [olTc TI-"
R(90)
=
=
-
-
(2) (3)
where Xo,R,, and 5, are constants. R(90) and D,, were measured at the critical composition as a function of temperature, and the log-log representation of eq 1-3 is shown in Figure 2. Linearity extends over a wide range of temperature, and the critical exponents are compared with the Ising predictions in Table 111. The agreement is good except for the system with heavy water and for the solution far from the critical composition. The critical behavior of BE in water is in accordance with the behavior of short-chain nonionic ~urfactants.~~.~~ Critical scattering far from the LCST is evidenced in Figures 3 and 4, where R(90)and D,, are plotted against the mole fraction of BE at 25 "C. R(90) is maximum, while D,, is minimum at the critical composition (XBE = 0.054). This supports the idea of a critical line suggested by Corti et aL61for nonionic surfactants. For the system water-BE, the composition defining this line seems to be temperature independent. (52) Kahlweit, M.; Strey, R. Angew. Chem. (Int. Ed. Engl.) 1985, 24, 654. (53) Izumi, Y.; Dondos, A.; Picot, C.; Benoit, H. J. Phys. (Les Ulis, Fr.) 1981, 42, 353. (54) Bellini, T.;Degiorgio, V. Phys. Rev. B 1989, IO, 7263. (55) Tamura, K.; Maekawa, M.; Yasunaga, T. J. Phys. Chem. 1977, 81, 2122. (56) Desnoyers, J. E.; Caron, G.; DeLisi, R.; Roberts, D.; Roux, A. H.; Perron, G. J. Phys. Chem. 1983,87, 1397. (57) Kanerva, L. J. Chem. Soc., Perkin Trans. 2 1983,467.
(58) Stephenson, J. In Physical Chemistry: an advanced treatise; Eying, H., Henderson, H., Jost, W., Eds.; Academic Press: New York, 1978; Vol. 8, Chapter 10. (59). Degiorgio, V. In Physics of Amphiphiles: Micelles, Vesicles, and Mmoemulsions; Degiorgio, V., Corti, M., Eds.; North-Holland: Amsterdam, 1985; p 303. (60) Degiorgio, V.; Piazza, R. Prog. Colloid Polym. Sci. 1987, 73,76.
Aggregation and Behavior of 2-Butoxyethanol in Water
+
Table 111. Critical Exponents of the System Water 2-Butoxyethanol Obtained from Phase Diagrams and Light-Scattering Measurements exponent
property
@
phase diagram phase diagram Rayleigh ratio Rayleigh ratio correlation length
0 y y u
system
this study
H,O + BE 0.322 f 0.003 D,O + BE 0.399 f 0.002 X,, = 0.052 1.20 f 0.02 X,, = 0.150 -0.48 X,, = 0.052 0.688f 0.005
Ising 3D" 0.312 0.312 1.250 1.250 0.643
Reference 58.
250
I.
*z
I
I
.o 1
I
i
T:2 5 "C
0
0
I
0
I
0
I
T
O
XBE
0
'
1
Figure 3. Rayleigh ratios and Debye plot relative to water for the system water 2-butoxyethanol at 25 "C.
+
e T=2 5°C
0
0.3
X BE Figure 4. Mutual diffusion coefficient of t h e system water + 2-butoxyethanol at 25 "C: ( 0 )BE from Fisher Chemicals; (a) BE from Aldrich Chemicals.
For micellar solutions, the Rayleigh ratios are usually expressed as the excess scattering relative to the c ~ c . This procedure applies to systems where the concentration of monomer does not change significantly over the concentration range studied. Using a mass action model, Desnoyers et a1.6s showed that this condition was obeyed for long-chain surfactants but not for short-chain surfactants, where the concentration of monomer is still varying substantially even at 5 times the cmc. This, along with critical scattering contributions, limits the use of the Debye plot for short-chain nonionic surfactants. This is shown in Figure 3, where the reciprocal of the appar-
Langmuir, Vol. 6, No. 1, 1990 247
ent molar weight ((M)ap-') is plotted at low mole fraction. This parameter is calculated with the excess light scattering of BE solutions relative to pure water, and the extrapolation at infinite dilution leads to 103 g mol-' in accordance with the molecular weight of BE (118.2 g mol-'). The negative slope might be caused by attractive interactions and/or continuous aggregation and/or critical concentration fluctuations. There is no definite break around the microphase transition (XBE = 0.018), and it is not possible to analyze safely these data to get the average molecular weight of the aggregates of BE. Kat0 et al.34 have reported very low D,, at low XBE. Bender and Pecora4' obtained similar results which they associated to the presence of impurities forming large aggregates (- 1000 A), and they suggested a chemical source dependency. We also observed very low values of D,,at XBE < 0.014 for samples prepared with BE from Aldrich (data not reported), but we concluded that the effect was not specific to BE because we had observed a similar behavior for solutions of charged amphiphile~.~' Figure 4 shows the trend of D,,obtained with BE from two chemical sources in the range 0.014 < XBE < 0.29. The agreement is excellent, and the extrapolation of D,, to X B E = 0 leads to 7.7 X lo4 cm2 s-', which is in fair agreement with -8.2 X lo4 cm2 s-l extrapolated from the self-diffusion coefficients obtained by Kate.% As the concentration increases, D,,goes through a minimum at the critical composition. Turq et al.70developed a model that accounts for the influence of monomer-micelle exchange on the diffusion of micelles of small-chain ionic surfactant^.^' Such a model does not apply for aqueous solutions of BE, because it does not account for the contribution of critical scattering that is still present even far from the LCST. In the vicinity of the critical composition, D,,reflects the correlation length associated with the critical concentration fluctuations, and it can no longer be associated with the Stokes's hydrodynamic radius. Small-AngleNeutron Scattering. SANS spectra were analyzed in the range 0.05 < XBE < 0.25 A-1 where the critical scattering contribution is attenuated compared to light-scattering experiments. Figure 5 shows the SANS spectra of BE at three compositions in D,O. Below the microphase transition (XBE = 0.01), there is no coherent scattering, and at XBE= 0.04 and 0.09, the trend of the (61) Corti, M.; Minero, C.; Degiorgio, V. J. Phys. Chem. 1984,88, 309. (62) Triolo, R.; Magid, L. J.; Johnson, J. S., Jr.; Child, H. R. J. Phys. Chem. 1982,86,3689. (63) Candau, S. J. In Surfactant Solutions: New methods of inuestigation; Zana, R., Ed.; M. Dekker: New York, 1987;Vol. 22, p 57. (64) Arlie, J. P.; Buzon, J.; Vignes, J. Reu. Inst. Fr. Pet. 1970,25, 174. (65) Harris, N. H. Ph.D. Thesis, Oxford University, 1980. (66) Bevington, P. R. Data reduction and error analysis for the physical sciences; McGraw-Hik New York, 1969;Chapter 11. (67) Benjamin, L.;Benson, G. C. J. Phys. Chem. 1963,67,858. (68) Desnoyers, J. E.; Perron, G.; Roux, A. H. In Surfactant Solutions: New methods of investigation; Zana, R., Ed.; M. Dekker: New York, 1987;Vol. 22,p 1. (69) We observed this phenomenon for aqueous solutions of CTAB at low ionic strength and without added salt. Similar behavior was ~observed ~ for polyelectrolytes. See: Drifford, M.; Dalbiez, J.-P.; Tivant, P. J. Chim. Phys. 1985,82,571. (70) Turq, P.; Drifford, M.; Hayoun, M.; Perrera, A.; Tabony, J. J. Phys. Lett. 1983,44,471. (71) Drifford, M.; Belloni, L.; Dubois, M. J. Colloid Interface Sci. 1987,118,50. (72) Magid, L. J. In Nonionic Surfactants; Schick, M. J., Ed.; M. Dekker: New York, 1987;p 677. (73) Cabane, B. In Surfactant Solutions: New methods of inuestigation; Zana, R., Ed.; M. Dekker: New York, 1987;Vol. 22,p 57. (74) Zulauf, M.; Weckstrom, K.; Hayter, J. B.; Degiorgio, V.; Corti, M. J.Phys. Chem. 1985,89,3411. (75) Zulauf, M.; Rosenbusch, J. P. J. Phys. Chem. 1983,87,856. (76) Perron, G., unpublished data.
Quirion et al.
248 Langmuir, Vol. 6, No. 1, 1990 - . .-
IO
0
0.3
Figure 5. Small-angle neutron-scattering spectra of 2-butoxyethanol in D,O at 26 O C : (B) experimental intensities; (-) fit obtained with a model of spheres + critical scattering. Table IV. Parameters Obtained from Analysis of Small-Angle Neutron-Scattering Spectra with a Model of Spheres Critical Scattering
'
+
X,,
A, cm-le
B,cm-ln
i(0)
[, Ac
0.04 0.09 0.09
0.26 0.39 0.37
0.2258 0.3826 0.3826
27.6b 19.7b 21.7'
17.8 13.7 13.7
Obtained from the Porod limit at high Q. Obtained as a fitting parameter.
R,,
data at low Q to get i(0) from the model. However, since there is good agreement between S(0)sANsand S(O),,.at XBE = 0.09, i(0) was fixed a t the value calculated with the Rayleigh ratio (i(0) = S(O),, - 1). With this procedure, the model gave 5 = 17.8 and 13.7 8, at XBE= 0.04 and 0.09, respectively. These correlation lengths are in very good agreement with the values 15.5 and 12.0 8,calculated with eq 9 using D,, at XBE = 0.04 and 0.09, respectively. The small difference may be due to solvent isotope effects. The consistency between light- and neutron-scattering results suggests that the model used for SANS analysis describes adequately the behavior of BE in water. On this basis, the values of RP can be used to evaluate the aggregation number of BE (nBE) in water. Assuming that the aggregates are dry and using 219 A3 for the molecular volume of BE,26 we obtained nBE = 14.9 and 9.8 at XBE = 0.04 and 0.09, respectively. However, the aggregates are not likely to be dry, and the volume (V,) probably contains a contribution due to the hydration of the oxyethylene group of BE.
P
9.2 8.0 7.9
Calculated with
This equation cannot be solved unless one has a second equation. For instance, the amplitude ( A ) obtained through the fitting procedure can be related to the contrast ( p ) between the aggregates and the solvent
eq 7 and 8.
scattered intensity (1(Q)) is typical of intermicellar attraction or critical scattering by aqueous solutions of nonionic surfactant^.^^^^^-^^ The shape of the spectra could not be fitted with a model that accounts only for the critical concentration fluctuations. Therefore, they were fitted with a model including the form factor ( ( F ( Q ) )of) homogeneous spheres of radius R, coupled to the OrnsteinZernike critical structure factor ( S ( Q ) )
1(Q)= A ( F ( Q ) ) 2 S ( Q+)B ( F ( Q ) )= (3/Q3R?)(sin(QRp)- (QRp)cos (QRp))
(4)
(5)
S(Q)= 1 + i(O)/(l + Q2Z:') (6) where A , B , i(O), and 6 are the amplitude (cm-'), the base line evaluated from the Porod limit72,73(cm-'), the critical intensity at Q = 0, and the correlation length, respectively. i(0) and 5 can be calculated from light-scattering measurements, or they can be obtained as fitting parameters S(OISANS = 1 + i(0)
(7)
(9) Z: = k T / ( 6 ~ D l z ) where S(O), K , M , k , and 17 are the structure factor a t Q = 0, the amplitude factor related to the variation of the refractive index (n) with the concentration (C = g mL-'), the molecular weight of BE, the Boltzmann constant, and the viscosity of the solution. For BE in water, we obtained anlac = 0.1119 mL g-' from the data of Shindo and K~sano.~ Table IV reports the values of A, R,, i(O), and 6 obtained by fitting the model to SANS spectra. At XBE = 0.09, the model gave i(0) = 21.7, which leads to S(0)sANs= 22.7, in fair agreement with 20.7 calculated from the Rayleigh ratio (S(0)Ls). At XBE = 0.04, there are not enough
A = &,VPp21O8
(11)
/s = (nBEbBE + nDzObD20)/vP - PS
(12)
where ,@, ps, and b are the volume fraction of the aggregates, the solvent scattering length density, and the scattering length, respectively. Using this approach, we have to make three assumptions. First we suppose that the scattered intensity is absolute (no corrections needed). Second, we suppose that the water molecules are homogeneously distributed within the aggregates. Third, we have to fix the concentration of the free monomers to evaluate 4, and ps. We chose XBE= 0.018, which corresponds to the microphase transition. These approximations lead to results with a large uncertainty. Nevertheless, the numbers that we get can be regarded as a semiquantitative evaluation of the hydration of BE aggregates. Using eq 10-12, we obtained nBE = 9 and 6 at XBE = 0.04 and 0.09, respectively. In both cases, npZo/ nBE = 5. Although these numbers are only approximations, they suggest that the mole fraction of BE in the aggregates is about 0.17, which corresponds fairly well with the composition of the macroscopic phase that separates a t higher temperatures (XBE 0.18, see Figure 1). This supports the idea of a microphase separation at temperatures below the LCST of BE in water. One must keep in mind that the aggregation numbers that are reported in this paper were obtained only at two compositions, so it is not possible to suggest a trend of nBE with respect to the concentration of BE. These numbers should be regarded as a range of possible values for the state of aggregation of BE in water a t 26 "C. Freezing Point Depression. We also checked if the aggregation of BE was reflected in the freezing point depression of water. The liquid-solid phase diagram of the system water-BE has been measured by Perron et al.'6 It is presented in Figure 6 along with two simulations based on a model that evaluates the activity of water at the freezing temperature. This is done by calculating the monomer concentration with a mass action This model requires values of the cmc and the aggrega-
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Langmuir, Vol. 6, No. 1, 1990 249
Aggregation and Behavior of 2-Butoxyethanol i n Water I
I
Table V. Literature Values of Aggregation Number of 2-Butoxyethanol in Water Obtained with a Mass Action Model
I
property
- 7 0
13C NMR
ultrasonics" ultrasonics" cryoscopy
Y
I-
T,OC
nar
25 25 32 8 25 25 -0
14.3 8.6 8 5.6
ref
5
23 23 4 4 34 35
6
this study
>4
" Second relaxation process. -50 -64
0
XBE
1
Figure 6. Liquid-solid phase diagram of the system water + 2-butoxyethanok ( 0 )experimental freezing temperature; (A) experimental eutectic temperature; (--) ideal freezing temperature; (-) freezing temperature assuming an aggregation number of 6 and a microphase transition at X,, = 0.018.
tion number. The simulation with cmc = X,, = 0.018 and n B E = 6 is compared with the ideal behavior of the freezing point depression. This experiment shows that the strong deviation from ideality can be explained by the formation of aggregates. In Table V our value for nBEis compared with literature values obtained with a mass action model for BE in water.
Conclusion The analysis of small-angle scattering data of BE in water must be conducted with care since both the critical behavior and the presence of aggregates must be accounted for.
The critical behavior of BE in water is in accordance with the Ising predictions, and the critical exponents are valid over a wide range of temperature below the LCST. The structure factor at zero Q ( S ( 0 ) )and the correlation length (5) obtained by light- and neutron-scattering measurements are in excellent agreement. When X,, > 0.018, BE molecules aggregate collectively to form spherical micelles having a radius of about 9 8.Assuming wet aggregates, we suggest that the micelles contain about seven molecules of BE, each hydrated by five molecules of water. These results support the idea of a microphase transition that occurs at temperatures below the miscibility gap. Acknowledgment. It is a pleasure to thank the Institut Laue Langevin for giving us the opportunity to use their neutron facilities. We also wish to thank Dr. James Tabony, who adapted the D-16 diffractometer for SANS and Dr. Arnaud Degeyer, who put the SANS spectra on an absolute scale. F.Q. is indebted to the FranceQu6bec exchange program for the award of a fellowship and to the Natural Sciences and Engineering Research Council of Canada for financial support. L.J.M. acknowledges support from the National Science Foundation (CHE-8611586). Registry No. BE, 111-76-2; H,O, 7732-18-5.
