J . Phys. Chem. 1990,94, 7549-1555
\
I
\
1
\
I
K
A
I
I
i
8
Wavelenth (nm)
Figure 10. Formation of mixed chalcogenides by exposure of CdS to
H,Se. to achieve maximum contrast, and the results clearly show that the presence of the CdS is correlated with the particulate structure, which averages 2-4 nm. While a cluster of 25 CdS (predicted from the distribution diagram, Figure 3), should be considerably smaller than this, the TEM film samples are extremely thin and can quickly equilibrate with water from the air. These samples were handled in air prior to obtaining the images in Figure 8. Hence, it is likely that ripening occurred to produce much larger particles than are formed under dry conditions. Fluorescence Spectra of Q-CdS in NaJion. The fluorescence spectra of bulk CdS, a 50% sample exposed to aqueous sulfide, a 100%gas-phase sample, and a 90% gas-phase sample (in descending order of emission maxima) are shown in Figure 9. The excitation wavelength is 260 nm. Spectra obtained with emission maxima at lower wavelengths were unreliable as emissions in these regions were observed even in the clean N a f i ~ n . One ~ ~ can see that the emission maxima blue shift corresponds with the blue shifting of the absorption onset. (35)
Lee, P. C.; Meisel, D. J . Am. Chem. Soc. 1980, 102, 5477.
7549
CdS$el, Mixed Q-State Particles in Nafion. We have observed that the exposure of Q-state particles of CdS in Nafion to H2Se results in exchange of sulfide in the lattice by selenide. The standard free energy (AGO) of reaction for the exchange is -9 kcal/mol with bulk CdS and CdSe. As expected, CdSe in Nafion is essentially unreactive toward H2S. Upon exposure of CdS to H2Se, the shift of the spectrum to that of CdSe is gradual. Hence, quenching of the reaction prior to complete exchange results in the formation of mixed chalcogenides. The spectrum of pure CdS shows an absorption onset of about 520 nm (Figure IO). Exposure of the sample to H2Se (1 atm) for 10 min resulted in the mixed chalcogenide, yielding a spectrum with an onset at 580 nm. Exposure of the same sample for 10 h to H2Se yielded a spectrum with an onset at 650 nm. Neither further exposure to H2Senor exposure of the CdSe material to H2S had an effect on the absorption spectrum. The absorption onset of the CdSe spectrum in Figure 10 is blue shifted from the bulk value by 0.20 eV. Possibly, the CdS particles were of a size intermediate between Q-state particles and bulk CdS. Exchange of the sulfide for selenide resulted in particles of similar size but with smaller effective electron and hole masses, pushing the system deeper into the Q-state regime. Further studies on mixed Q-state particles in Nafion are in progress.
Conclusions A simple method has been devised to synthesize molecular clusters of CdS and CdSe in a cation-exchange membrane by controlling the number of sites available in the ionomer clusters of Nafion by blocking exchange sites with Ca2+. Ostwald ripening can be controlled by dehydrating the film and hampering intercluster diffusion. In principle, this technique, involving the dilution of the cation used in the synthesis, could be applied to many types of reactive cations exchanged into Nafion. Acknowledgment. Thanks are due to Professor L. K. Patterson (Notre Dame University) for suggesting the idea of the ion-dilution technique, Dr. M. Schmerling (University of Texas a t Austin) for obtaining the EDS data, and Dr.Carolyn Hoener for many helpful suggestions. This research was supported by the Gas Research Institute.
Aggregation and Solvent Interaction in Nonionic Surfactant Systems with Formamide Mikael Jonstromer,**+Marie Sjoberg,*,sand Torbjorn Warnheid Physical Chemistry 1, Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden: Department of Physical Chemistry, Royal Institute of Technology, S- I O 0 44 Stockholm, Sweden: and Institute for Surface Chemistry, P . 0 Box 5607, S- 1I4 86 Stockholm, Sweden (Received: October 25, 1989: In Final Form: February 28, 1990) The self-association and solvent interaction of some polyethylene glycol alkyl ether surfactants (C,E,) in formamide have been studied via determinationsof phase diagrams and NMR self-diffusion measurements. For CIZE3and CI2E4,small micelles but no liquid crystalline phases form. Increasing the alkyl chain length to hexadecyl (C16E4,CI6E6,and CI6Es),mesophase formation occurs analogously to the corresponding aqueous system. No aggregate growth occurs in the micellar phase, neither at high temperatures and high surfactant concentrations nor when approaching the lower consolute temperature. The solvent diffusion was analyzed within the cell diffusion model, and a concentration-independent amount of 1-5 and probably not more than 3 formamide molecules was found to interact with each ethylene oxide group. Furthermore, the calculations indicated a polymer-like state of the micellar headgroup shell, with a slight decrease of the formamide content therein at a raised temperature. In conclusion, the behavior of C,E,/formamide systems is qualitatively similar to that of the corresponding aqueous systems.
Introduction The aggregation of surfactants in nonaqueous, polar solvents has during the past few years been intensely scrutinized.'*2 It To whom correspondence should be addressed.
Lund University. *Royal Institute of Technology. I Institute for Surface Chemistry.
0022-3654/90/2094-7549$02.50/0
has been established that amphiphiles such as lecithin3s4 and, recently, also normal single-chain surfactants5-' form liquid (1) Friberg, S. E.; Liang, Y.C. In Microemulsionr; CRC Press: Cleveland, OH, 1988; Chapter 3, p 79. (2) Evans. D. F. Langmuir 1988, 4, 3. (3) Moucharafieh, N.; Friberg, S. E. Mol. Cryst. Liq. Cryst. 1971,49,231. (4) BergenstAhl, 8.; Stenius, P. J . Phys. Chem. 1987, 91, 5944.
0 1990 American Chemical Society
7550 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
crystalline phases in other solvents than water. This occurs for surfactants with a sufficiently large hydrocarbon moiety in solvents of sufficient p ~ l a r i t y . However, ~ the solvent properties needed to promote surfactant aggregation have not been completely pinpointed,'+ and further experimental and theoretical work along these lines is anticipated. In addition, the question of aggregation in the solution phase remains controversial. While many results on micellization have been reported,'OJ1their validity has repeatedly been q~estioned.~"~~ In some cases, methods have been inappropriate: conductivity measurements have shown breakpoints suggested to indicate micelle while more detailed investigations have failed to reveal conclusive proof of proper micelle formation in several of these cases.13,14*16 Also, in recent investigations surfactant aggregates are found, but different methods suggest different sizes of the aggregates. For example, NMR relaxation rate measurements on hexadecyltrimethylammonium bromide indicate that the surfactant forms aggregates of comparable size in water and formamide at 60 OC.l7,l8 In contrast, X-ray small-angle scattering suggests considerably smaller aggregates in formamide close to the suggested critical micelle concentration.lg This leads to the view that while aggregation certainly may take place in nonaqueous systems, it is doubtful whether proper micelles form or whether there only is a continuous association process without any cooperative nature. In further studies, it is thus useful to concentrate on methods where the system can be probed in a direct way over a broader surfactant concentration region. Also, other phenomena of fundamental interest have been reported. It has for example been shown that the nonionic surfactants tri- and tetraethylene glycol dodecyl ether display a lower consolute temperature (LCT) in formamide20 and that solubilization of hydrocarbon occurs completely in analogy with the corresponding aqueous systems2] Since the mechanism behind the clouding in water-along with related matters such as aggregate growth and monomer exchange in the vicinity of the LCT-is another controversial topic,22-25it is of considerable interest to compare results for the two different solvent systems. Thus, we have continued the study of nonionic surfactant systems in formamide, concerned with a number of fundamental issues. The aggregation in the solution phase and the formation of liquid crystals over a wide concentration range have been investigated: phase diagrams have been determined, and the (5)Friberg, S. E.;Liang, P.; Liang, Y . C.; Greene, B.; van Gilder, R. Colloids Surf. 1986,19,249. (6)(a) Belmajdoub, A.; Marchal, J. P.; Canet, D.; Rico, I.; Lattes, A. Nouu. J . Chim. 1987,11,415.(b) Auvray, X.;Anthore, R.; Petipas, C.; Rim, I.; Lattes, A. C. R. Acad. Sci., Ser. 2 1988, 306,695. (7)WBrnheim, T.;Jonsson, A. J . Colloid Interface Sci. 1988, 125, 627. (8)Beesley, A. H.; Evans, D. F.; Laughlin, R. G. J . Phys. Chem. 1988, 92, 791.
(9)Lattes, A.; Rico, I. Colloids Surf. 1989,35, 221. (10)(a) Ray, A. Narure 1971,23/,313. (b) Ray, A. J . Am. Chem. Soc. 1969. 91. 6511. (1I ) Singh, H. N.; Salem, S. M.; Singh, R. P.; Birdi, K. S. J . Phys. Chem. 1980,84,2191. (121 Das. K.P.: Cenlie. A.: Lindman. B. J . Phvs. Chem. 1987. 91.2938. (13)Almgren, M.; >warup, S.;Lofroth, J. E.-JJ.Phys. Chem. 1985,89, 4621. (14) Binana-Limbele, W.; Zana, R. Colloid Polym. Sci. 1989,267, 440. (15)Copal, R.; Singh, J. R. Kolloid Z.-2. Polym. 1970,239,699. (16)Alfass, 2.9.; Filby, W. G. Chem. Phys. Lerr. 1988,144. 83. (17)Belmajdoub, A.; EIBayed, K.; Brondeau, J.; Canet, D.; Rico, I.; Lattes, A. J . Phys. Chem. 1988,92, 3569. (18)Sjoberg, M.;Henriksson, U.; Warnheim, T Submitted for publication. (19)Auvray, X.; Petipas, C.; Anthore, R.; Rico, I.; Lattes, A,; Ahmahzadeh Samii, A.; de Savignac, A. Colloid Polym. Sci. 1987,265, 925. (20)Warnehim, T.;Bokstrom, J.; Williams, Y. Colloid Polym. Sci. 1988, 266, 562. (21) Warnheim, T.; Sjoberg, M. J . Colloid Interface Sci. 1989,131,402. (22)Staples, E. J.: Tiddy, G. J. T. J. Chem. SOC.,Faraday Trans. I 1978, 74, 2530. (23)Kjellander, R. J . Chem. Soc., Faraday Trans. 2 1982, 78, 2025. (24)Karlstrom, G. J . Phys. Chem. 1985,89,4962. (25)Nilsson, P. G.;Wennerstrom, H.; Lindman, B. Chem. Ser. 1985,25, 67
Jonstromer et al.
r
P
C
1
~
h
20
d0 WtX
r
i0 C16E6
80
Go
io
I
I'
401
io
4b
W t k C,&
Figure 1. Phase diagrams for (a) C&,/fOn"ide, (b) C16E6/formamide, and (c) CI6E8/formamide. L denotes solution phase, 2L two solution phases in equilibrium, I, cubic phase of close-packed spherical micelles, E hexagonal phase, D lamellar phase, and (S) solid surfactant. The regions for the anisotropic liquid crystalline phases include the two-phase regions with an isotropic phase.
solution phase has been studied with surface tension and N M R self-diffusion measurements. In addition, information on micelle growth and monomer exchange, in particular in the vicinity of the cloud point, as well as solvation of the polar group, has been obtained from self-diffusion measurements. Our aim is to reveal similarities and dissimilarities with the corresponding aqueous systems. Experimental Section Chemicals. Nonionic surfactants, C,E, (Nikko) (where x denotes the length of the alkyl chain and y denotes the number of ethoxy groups in the polar group), and polyethylene glycol ( M , = 20000, Merck, 99.5%) were used as received. Formamide (Aldrich, 99.5%+) was used as received or dried with molecular sieves, and the water content was in all cases below 0.5 wt %. Since formamide is quite hygroscopic, care was taken to avoid exposure of samples to the atmospheric humidity. Care was also taken to avoid long time storage of samples at elevated temperatures, since chemical degradation may occur. All data reported are made on freshly prepared samples. Phase Diagrams. The phase diagrams were determined mainly by visual observation of samples in a thermostated bath and by optical microscopy in a Reichert polarizing microscope with a fitted hot stage. The temperature was raised by no more than 3 OC/min. In addition, small-angle X-ray diffraction with a phase-sensitive detector (Tennelec PSD-100)was used to ascertain the identification of the lamellar liquid crystalline phases and for determination of the repeat distance, d . Surface Tension Measurements. The surface tension was measured with a du Noiiy balance. Self-Diffusion Measurements. Self-diffusion coefficients were determined on a JEOL FX-60 or a Bruker MSL-100 spectrometer with the Fourier transform pulsed gradient spin echo (FT-PGSE) method, as described in detail in ref 26. Temperatures were
Nonionic Surfactant Systems with Formamide
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7551
io
io
ab
do
w t x C,6E4
w t x C,2Ecj
Figure 2. Phase diagrams for (a) C,,E3/formamide (redrawn from ref 2 0 ) and (b) C12E4/formamide. Notations as in Figure I .
1
determined within f0.5 O C by a calibrated copper-constantan thermocouple. Presented self-diffusion coefficients are estimated to have an accuracy of 5% or better.
Results Phase Diagrams. The phase diagrams for three binary surfactant C16Ey/formamidesystems, where y = 4,6,8, were determined and are shown in Figure l . In addition, the phase behavior of C12E,,/formamidesystems, where y = 3,4,has been reported previously2' and is reproduced in Figure 2. For C12E surfactants in a narrow hydrophilic-lipophilic balance (HLBS range, 9.1-1 0.5,21J2observable lower consolute temperatures occur with formamide. This miscibility gap occurs with CI6E4(HLB = 9.2) as well, but the high melting point of the solid, solvated surfactant makes it impossible to observe the LCT at the critical concentration (Figure 1a). Phase diagrams for the corresponding C16Ey/watersystems 0,= 4,6,and 8), redrawn from refs 27 and 28, are given in Figure 3. In contrast to C12Eysurfactants, liquid crystalline phases are observed with a surfactant alkyl chain length of c16. For CI6E4, a lamellar liquid crystalline phase D is stable in formamide between 56 and 75 wt % ' surfactant and up to a temperature slightly above 50 OC (Figure la). With a larger polar group, Le., the C16E6/formamidesystem (Figure 1b), the lamellar phase disappears and a hexagonal liquid crystalline phase E is stable at concentrations between 44 and 70 wt % surfactant and up to a temperature slightly above 40 OC. Finally, with CI6E8a hexagonal phase exists in a similar composition region but is stable up to higher temperatures, maximum 60 OC (Figure IC). A cubic phase occurs around 40 wt % in the CI6E8system. The melting point boundaries for solid, solvated surfactant were difficult to determine without hysteresis for both C16E6 and CI6E8,but the upper limit (Le., determined upon slow heating) has been indicated by dotted lines. The liquid crystalline phases were identified by means of optical microscopy and by X-ray small-angle diffraction. The X-ray measurements can also give the corresponding areas per polar group, S,29calculated from the repeat distance, d, and these are listed in Table I. There are no significant differences between the aqueous and the formamide systems; the area in the lamellar phase in the C16E4/formamidesystem is constant slightly above 40 A2 while S in CI6E4/wateris around 40 A2. This contrasts (26) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1. (27) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; MacDonald, M.P. J. Chem. Soc.. Faraday Trans. I 1983, 79, 915. ( 2 8 ) Tiddy, G.J. T. Personal communication. (29) Fontell, K.; Mandell, L.; Lehtinen, H.; Ekwall, P. Acta Polytech. Scand. 1968, Chapter 111.
wtx C16EII
Figure 3. Phase diagram for (a) C16E4/water(redrawn from ref 2 7 ) , (b) C,,E,/water (redrawn from ref 28), and (c) C16E8/water(redrawn from ref 27). V, denotes reversed bicontinuous cubic phase, N nematic phase, and VI normal bicontinuous cubic phase; otherwise notations as in Figure 1. The I, region in (c) consists of two I, phases, detected by an optical discontinuity in the region. TABLE I: Repeat Distance, d , and Areas per Polar Group, S, in the D Phase of the Systems C1&JFormamide and CI6E4/Water at 40 OC wt % C,,E, d . A S. A' wt % C,,EA d . A S , A 2 in formamide in water 59 63 61 71 15
52 51 51 46 44
43 41 39 41 40
45 65 75
17 64 46
40 39 40
to a marked increase in area per polar group in for example the lamellar liquid crystalline phases of ionic surfactants (Aerosol OT, didodecyldimethylammonium bromide) when replacing water with f~rmamide.~~,~' Surface Tension Measurements. The surface tension of solutions of a nonionic surfactant in formamide is known to display a breakpoint at a certain concentration, which for c1&6and c14E6 has been interpreted as due to micelle formation.j2 Comple(30)BergenstBhl, B.; Jonsson, A.; SjBblom, J.; Stenius, P.; Wirnheim, T. Prog. Colloid Polym. Sci. 1987, 74, 108. (31) Warnheim, T.; Jonsson, A.; SjBberg, M. Submitted for publication. (32) Couper, A.; Gladden, D.; Ingram, B. Discuss. Faraday Soc. 1975,59, 63.
7552 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 TABLE II: Critical Micelle Concentrations Derived from Surface Tension Measurements (cmcd) and Self-Diffusion Measurements As Described in tbe TexP (cmc-)
CI2Ej CIzE4
15.5
25
1.5
40 58 39' 11
C12E4
8o
ClIE, C12E6 c16E~ C16E8
25 25
2.3
25 40
0.56
1.8'
1.4 1.7 2.3 1.9
44 47 63 47
24 20 20 17
0.60
12
40
Jonstromer et al. a A
.
15-
0.065 0.069
b ,
w1 % C12E3
OrH is the hydrodynamic radius of the micelles calculated from N M R self-diffusion data. bFrom ref 50, cmc's in water. 'From ref 32.
mentary measurements on CI2E4.CIIES, and C16E8give very similar results, with sharp breakpoints and a constant surface tension level above a critical concentration. It seems thus likely (in the absence of a visible macroscopic phase separation) that a critical micelle concentration exists; i.e., proper micelles form. The cmc's for different nonionic surfactants in formamide are shown in Table 11, including those collected from the literature3* and compared with (when available) the corresponding values for the aqueous systems. SelfDiffusion Measurements on Surfactant. Self-diffusion coefficients can be used to monitor the formation of surfactant aggregates as well as for measuring solvation and similar quantities.26 To start with the aggregation process, the self-diffusion coefficients of the nonionic surfactant are shown in Figure 4a-d for some selected systems. Typically, all systems show a distinct decrease in the self-diffusion constant at surfactant concentrations of a few percent. Since the decay of all echo amplitudes are single exponential in the NMR FT PGSE experiments, it can be assumed that there is a rapid exchange of the surfactant molecules between the different states in the solution on the time scale of the measurements (typically 100 ms). On this basis, the observed surfactant self-diffusion coefficient, D h , can be used to quantify the aggregation process, using the two-site model for nonassociated and micellar bound surfactant molecules:33
p is the fraction of aggregated surfactant. Within the phase separation model, p can be expressed as (2) P = (Go, - cmc)/Ctot where Ctot is the total surfactant concentration in solution. Assuming a hard-sphere potential between the aggregateswhich is reasonable in the absence of Coulombic forces-the reduced mobility due to micellar obstruction can be corrected for approximately by using34*35 Here 6 is the volume fraction of micellar aggregates and Dmi2 the micelle self-diffusion at 4 = 0. Combining eqs 1-3, it is then possible to obtain values of cmc and Dmi2with a nonlinear curve fit. The best fits, where data up to 10 wt 7% surfactant has been used, are shown as solid lines in Figure 4. The agreement with the phase separation model is indeed very good. Finally, Dmi2can be converted to the hydrodynamic radius rH of the surfactant aggregate via the Stokes-Einstein relation: rH = k T / 6 n q D m i 2
(4) r) is the viscosity of the medium around the micelles, and the rest of the symbols retain their usual meaning. q is taken to be that of pure formamide. The derived aggregate radii, assuming spherical shape of the aggregates, are shown together with the critical micelle concentrations in Table 11. (33) Lindman, B.; Nilsson, P. G.; Stilbs, P.; Wennerstr6m. H. Pure Appl. Chsm. 1984, 281. (34) Ohtsuki, T.; Okanu, K.J . Chem. Phys. 1982, 77, 1443. (35) FaucomprC, B.; Lindman, B. J . Phys. Chem. 1987, 91, 383.
_0
m
50 -
E
40 -
r; r
0
30.
0
20. 10 O - ' ' ' ' . 0 10
'
'
I
"
'
20 Wt
I
30
"
"
0
% C12E4
n
Wt %
CIBE8
Figure 4. Self-diffusion coefficient of the surfactant for varying concentrations. Solid lines denote curves fitted to data according to eqs 1-3. The dotted line in (d) represents the best fit including four formamides per ethoxy group. (a) CI2E3/formamideat 15.5 O C , (b) CI2E4/formamide at 25 OC, (c) C12E4/formamideat 80 OC, (d) C16E8/formamide at 40 O C .
In these calculations, the micellar size has been derived under the assumption that a hard-sphere potential exists between the aggregates and that no formamide is interacting with the polar groups. The validity of the first assumption, even up to high surfactant concentrations ( > l o wt %), is supported from an analysis of NMR self-diffusion data on CI2E8/water with use of eq 3.36 As for the second, we will in the following present clear indications for a nonnegligible amount of formamide in the (36) Nilsson, P.G.;Wennerstrh, H.; Lindman, B. J . Phys. Chem. 1983, 87. 1377.
Nonionic Surfactant Systems with Formamide
The Journal of Physical Chemistry, Vol. 94. No. 19. 1990 1553
I
0
10
20
30
40
50
wt % CxEy
Figure 5. Self-diffusion coeflicients of formamide for the binary systems with C,,E, (15.5 "C), C,,E, (25 "C). and C , & (40 'C) as surfactant.
The solid lines represent the best fit to the data points using eqs 5-7. surfactant headgroup layer. Since this increases 4 for a given surfactant concentration, which will increase the calculated D,:, the derived values of rHshould be treated just as a maximum value of the micellar size. However, for reasonable solvation numbers (fewer than five formamide molecules per ethoxy unit), the decrease in rHis less than 20%. which leaves the values in Table 11 as good approximations. On the other hand, a t high surfactant concentrations the fitted curves become sensitive to the choice of solvation number. as can be seen from the dotted curve in Figure 4d. This curve represents the best fit assuming four formamide molecules per ethoxy group and rH = 34 A (to compare with rH = 40 A. assuming no solvation, for the solid line). A more direct answer to the question of whether or not micellar growth occurs can be provided by IH NMR line width meas u r e m e n t ~ .The ~ ~ measurements gave no indication of any appreciable growth, as the line width at half-height of the peak from the surfactant methylene groups stayed constant at 8 & 1 Hr, independent of surfactant concentration. Therefore, we infer that no or at most a very minor growth of the micelles occurs a t high surfactant concentrations. With reference to Table 11, several trends can be identified. First, the observed cmc values in formamide are more than 2 decades higher than those in the corresponding water systems. (The agreement between cmc values obtained from fitting the surfactant self-diffusion data and from surface tension measurements is quite pleasing). Second. the calculated hydrodynamic radii for the C,,E, systems are just slightly larger than the length of the extended hydrocarbon chain (16.7 A according to ref 37). Taking the volume of the headgroups into amunt, and considering a possible correction of rHdue to solvent binding, it is then reasonable to assume the micellar shape to be spherical or close to spherical. Further, increasing the number of ethylene oxide groups on the C,,E, surfactants, a significant decrease in micellar size occurs, even considering the uncertainty of rH due to solvation effects. The obtained value of rHfor C,& is somewhat too large to be consistent with a spherical shape of the aggregates; however, this is only a minor effect. Self-Diffusion Measuremenfs in Solwnf. Let us now consider the solvation of the surfactant polar group, as derived from the measured self-diffusion data of the solvent. In Figure 5 the formamide self-diffusion for some of the systems discussed above is plotted as a function of surfactant concentration. The slopes of these curves are too large to be explained solely by obstruction from micellar aggregates,18 in particular since the surfactant diffusion indicates a small and therefore probably spherical micelles. We must assume that a significant fraction of the solvent molecules is retarded in their translational motion by interaction with the ethylene oxide chain of the surfactant. To allow for a correct theoretical treatment of solvent diffusion in colloidal solutions, accounting for both specific solute-solvent (37) 1980. (38)
Tanford, C. The Hydrophobic Eflecl, 2nd ed.: Wiley: New York, Nilsson, P. 0.; Lindman. E. 1. Phys. Chem. 1983, 81, 4756.
Figure 6. Cross section of the threeregion cell used for the calculations."
interactions and obstruction effects due to the excluded volume, J6nson et al. developed the sc-called cell diffusion model." This model divides the m a c r m p i c system into equally sized subsystems (cells), which in turn can be divided into as many regions as necessary. Each region is defined by its fraction of the total cell volume and a certain diffusion constant for each type of molecule. Therefore, contrary to earlier approaches, this model takes the mobility of solvent molecules within the surfactant headgroup layer into account, which will have a large effect on the calculated solvation numbers. Further, the results are only dependent on the shape of the colloidal particles and not on their size,)9 which decreases the number of parameters needed for the calculations. Applying this model on a micellar C,E,/formamide system, assuming a uniform distribution of solvent molecules in the surfactant headgroup layer, the formamide diffusion is fully described by a cell, divided as in Figure 6. This cell is built up of a central hydrocarbon core surrounded by a palisade layer containing the ethoxy part of the surfactant plus a concentration C, of interacting solvent molecules, diffusing with a constant D,. The remaining volume consists of nearly pure solvent of concentration C,, diffusing with a constant D, (in the calculations set equal to the value at cmc). The volume fraction occupied by each region is defined merely from the solvent concentrations C , and C,, if the molecular volumes, surfactant concentration, and cmc are known. As mentioned previously, the solution to the cell model is dependent on the aggregate shape, but due to the similarity in solvent obstruction," prolate-shaped micelles as well as small oblates (axial ratio less than 1:3) can be evaluated as spheres without any serious error. On the basis of the small hydrodynamic radius found above, we assume a spherical shape of the micelles, even for C16E8. The effective diffusion coefficient F" for a solvent molecule in a system of immobile cells then become^'^
where 4 is the volume fraction of aggregated surfactant plus interacting solvent and 0 is
However, this expression is correct only when the particle (micelle) inside the cell diffuses negligibly slow compared with the solvent. A semiempirical attempt to correct for the diffusion of the cell (Dee") has been suggested:" D = @(I - P " / D , ) + PI1 (7)
W should here be identified with the micellar diffusion coefficient. Within the model, C, and D, cannot be separately determined and some further assumptions must be made to solve for, e.g., the (39) JOnsson. 6.; WcnncrstrOm. H.:Nilssan. P. G.: Lime, P. Colloid PP lym. Sci. 1986, 264. 77. (40) Jbnsson. E.: Janssan. M. Unrrublished results. See: Jansson. M. Thais. Unvcrril) of Upprala. Lppsaia. 1988. (41) Enksson. P.0.. Lmdblom. G.;Burnell. E. E : Tiddy. G J. T. J. Chrm. Sor.. Foroda, TION. I 19XX. 84, 3129
Jonstromer et al.
7554 The Journal of Physical Chemistry, Vol. 94, No. 19. I990 c1
151
I
I 0
20
60
40
80
D i (70-11 m21s)
c1
151
1
//
1 0,O
j//CI2E4
0,2
0,4
0,6
0,8
I
I 1,0
DiiDo
Figure 7. (a) Concentration of formamide (C,) in the micellar palisade layer, shown as the number of formamide molecules per ethoxy group, as a function of the diffusion coefficient (0,)generated from the solid lines in Figures 5 and eqs 5-7. ( 0 )Self-diffusion coefficients for formamide in polyethylene glycol at 25 OC. (b) Concentration of formamide (C,) in the micellar palisade layer, shown as number of formamide molecules per ethoxy group, as a function of the relative diffusion coefficient @ , / D o ) generated from the solid lines in Figure 5 and eqs 5-7, where Do is the self-diffusion coefficient of formamide at the relevant temperature. (0) Self-diffusion coefficients for formamide in polyethylene glycol at 25 OC.
amount of interacting solvent. Assuming C , and D , to be independent of surfactant concentration, and using volume data for the pure c o m p o n e n t ~ ? ~excellent * ~ % ~ ~ fits of eqs 5-7 to experimental data are obtained. The best fits are shown as solid lines in Figure 5.
The associated values of C, and D , generated from this fit are shown in Figure 7a. The same data are recast in Figure 7b to show C, plotted against DIDo,where Dodenotes the diffusion coefficient of pure formamide a t the experimental temperature. From Figure 7b, it is clear that neither the closeness to the clouding temperature (for CI2E3)nor the length of the surfactant headgroup seems to have any profound influence on dynamics of the formamide incorporated in the palisade layer. The small (but significant) difference between the generated curves is probably due to a minor decrease of the formamide content in the palisade layer when temperature is increased. Assuming a constant value of C, will then introduce an artificial increase of DIDo with increasing temperature. Figure 7b gives a lower limit of the solvation number to around one formamide molecule per ethylene oxide unit, corresponding to totally immobilized solvent ( D l = 0). The upper limit of C, is more difficult to state. However, from purely geometrical considerations of the available space, there should be a maximum content of five formamide molecules per ethoxy unit. Also, considering the mismatch of the fitted curve in Figure 4d at a solvation number of four, a lower value of C, is expected. Therefore, we believe that the micellar palisade layer contains 1-5 and probably not more than 3 formamide molecules for each ethoxy unit. To further characterize the physical state of formamide in the palisade layer, a reasonable approach is to compare it with solutions of polyethylene glycol in formamide. The observed dif(42) Kucharski, S.; Sokolowski, A.; Burczyk, B. Rocz. Chem. 1973, 47, 2045. (43) Handbook of Chemistry and Physics, 62nd ed.; CRC Press: Cleveland, OH, 1982.
fusion coefficient of formamide in polymer solutions, plotted in analogy with the data from the micellar systems, is therefore shown in Figure 7a,b. The qualitative agreement between the curves suggests that the ethoxy group in the micellar palisade layer behaves similarly with respect to solvent interaction and mobility as in a bulk polymer solution. Discussion The aggregation pattern of nonionic surfactants in water and formamide may now be rather generally compared. The discussion is divided into two parts, with first an overview of micellization and phase diagrams and then a more detailed consideration of aggregate dynamics and solute-solvent interaction. The phase diagrams for a number of binary systems of nonionic surfactants and water have been extensively treated by Mitchell et al.27 Using a simple geometric packing model, one can reproduce the general features of the phase diagrams for n0nionics.2~ The curvature of the aggregate is determined by the molecular shape for a given surfactant molecule at a certain composition and temperature, as expressed in the packing index vlal. v is the volume of the apolar part of the molecule, a the area of the aggregate interface, and I the apolar chain length. The balance between the forces at the interface, the repulsive solvation, and steric forces between the polar groups and the interfacial forces which strive to minimize the hydrocarbon/water contact leads to a preferred curvature of the surfactant aggregate. Taking in addition short-range interactions between the aggregates into account (in the absence of a computable potential between the surfactant aggregates) as a simple hard-sphere model, it is possible to mimic many features of the phase diagrams in for example Figure 3. In water, hydrophobic nonionics are swelling surfactants which at low surfactant concentration form a lamellar phase. As an example, consider the CI6E4/water system (Figure 3a). For the same surfactant in formamide, the preferred curvature is retained although the extension of the lamellar liquid crystalline phase decreases and the extension of the solution phase increases (Figure la). When the polarity of the surfactant is increased, the sequence micellar phase hexagonal phase cubic phase lamellar phase occurs. For example, the C~&/Water system shows these features (together with a structure outside the scope of the packing index, Le., a nematic phase N) (Figure 3b). The same surfactant in formamide shows a considerable less complex phase behavior, but the high curvature hexagonal phase still occurs in a similar composition region (Figure 1b). Finally, with sufficient polarity, as in the C16E8/watersystem, the existence region for the lamellar phase decreases and is replaced by the hexagonal phase (Figure 3c). A hexagonal phase occurs with formamide as well, together with a cubic phase at lower surfactant concentration (Figure IC). The main effect of replacing water with formamide is to decrease the existence regions for the liquid crystalline phases and thus the complexity of the phase diagram. This leads to drastic effects on the lamellar phase in the surfactant-rich part of the phase diagram; it has disappeared in formamide for CI6E6(Figure 1b) while it is stable in water even for C,6E12.27 It is evident from a variety of observations, solubility measurements, and thermodynamic considerations37*" that there is a solvophobic interaction in formamide but considerably weaker compared to that in water. This decrease in solvophobicity has been estimated from the cmc measurements on CI2E, and Couper gave a value for the free energy of transfer of a methylene group from formamide to a nonionic micelle, -1.5 kJ/mol, which is significantly lower than the corresponding value for water, -2.9 kJ/m01.~*>~' In formamide, the surface tension and self-diffusion measurements show that an aggregation process of a markedly cooperative nature occurs, but with cmc values which are 1-2 orders of magnitude higher than those in water, at equal surfactant alkyl chain length. In spite of that, the phase separation model
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(44) Sinaoglu, 0.;Abdulur, S . Fed. Proc. Fed. Am. Soc. Exp. Biol. 1965, 24, 5.
Nonionic Surfactant Systems with Formamide offers a good rationalization of the surfactant self-diffusion data. The decrease in the driving forces for aggregation when replacing water with formamide is evident also from the hydrodynamic radii of the micelles. This comparison can be made in different ways. For C12E3and CI2E4hydrodynamic radii of 20-24 A are observed in formamide, while in water self-assembly leads directly to infinite aggregates (lamellar phase). Even for CI2ES the micelle size is markedly smaller in formamide than in water,36 implying lower aggregation numbers and larger areas per polar group a t the interface in formamide. (It is slightly surprising, though, that this trend is not visible in the areas per polar group directly measured in the lamellar phase; cf. Table I.) Also, while aggregate growth occurs readily at higher concentrations of nonionic surfactant in water, in particular for Cl2EXwith x < 6,4594 no or only minor growth seems to occur in formamide. Thus, we definitely can conclude that, under comparable conditions, these nonionic surfactants form smaller aggregates in formamide than in water. The next point relates to the possible change in aggregate size with temperature and when approaching the cloud point. It has been suggested that in order to account for the very low critical concentration for nonionic surfactants in water, down to a few volume percent, aggregate growth has to be invoked,23although alternative views have been offered.47 It has also been clearly demonstrated that aggregate growth may occur as a function of temperature; one example is the water/C12E5system where there is a very large increase in rHwith temperature all from 0 OC to the cloud point at 31 OC!s** However, when increasing the ethoxy chain length to for example CI2E8no or only minor growth is observed in the same temperature The relation between cloud point and aggregate growth for ClzE5could just as well be coincidental; while the cloud point is dramatically displaced upon small additions of ionic surfactant to C,2E5micelles, the aggregate growth with respect to temperature is very similar to that of the noncharged system.* Thus, the decrease in curvature of surfactant aggregates shown to occur in some systems with increasing temperature could be regarded as an intraaggregate effect and occurs if the system is sensitive to small changes in packing, while the phase separation occurs in any case whenever the aggregate interactions become attractive. The self-diffusion data for the formamide systems CI2E3in the vicinity of the cloud point and CI2E4at varying temperature, show no sign of aggregate growth, i.e., neither related to the temperature increase nor to the distance to the cloud point. This is to be expected since that the aggregates are smaller (Le., higher curvature) than in water and, therefore, should be less sensitive to changes in packing-if such effects occur. The exchange of surfactant monomers between aggregates is another phenomenon which affects the self-diffusion rate of the surfactant. It is well-known that the distance to the cloud point can be extremely important for the exchange rate in the aqueous systems. The self-diffusion of C12Esin water at 25 O C decreases somewhat with increasing surfactant concentration, passes through a minimum at low concentrations, and increases somewhat with
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7555 increasing concentration. This minimum has been explained as an additional term to the observed diffusion coefficient due to the exchange of surfactant molecules between colliding miceles.M At a certain surfactant concentration this term starts to dominate over the micellar diffusion, and a minimum in the diffusion coefficient is observed. However, it has been pointed out that the frequency of random collisions between spheres is too low to allow such a molecular contribution to dominate the total diffusional process a t low volume c ~ n c e n t r a t i o n . ~Thus, ~ in the region of spherical micelles, surfactant diffusion becomes slower since exchange between aggregates has a low probability. For example, for C I 2 bat 25 O C , the self-diffusion decreases monotonously with increasing concentration. However, for nonspherical aggregates with less repulsive (or even attractive) micellemicelle potential, as for CI2ESa t 25 OC, a more extensive exchange of monomers is permitted at the more frequent micellar encounters. Considering Figure 4 a 4 , it is clear that exchange effects do not dominate the surfactant diffusional process in formamide. The self-diffusion decreases monotonously with increasing surfactant concentration, and there are no visible effects due to exchange neither for the CIZE3system close to the cloud point nor for CI2E4 when increasing the temperature. However, from the previous arguments it is clear that exchange effects should be of less importance for surfactant self-diffusion in the case of small, spherical aggregates. In addition, the high cmc will considerably increase the contribution to the self-diffusion from monomers. The positive deviation from predictions of eqs 1-3 at high concentrations (Figure 4) indicates surfactant exchange, but the actual contribution is not possible to separate from other mechanisms (negative deviations due to multibody interactions, failure of the phase separation model a t high concentrations, etc.). Let us finally compare the specific solvent-ethylene oxide interactions in water and in formamide. In this paper, the cell diffusion model has been used to quantify the solvation of the polar group, although most analyses available for the aqueous systems have been made using less elaborate models. However, recently water NMR relaxation data on several C12E,,/water systems have been published49 and the water binding discussed analogously to what has been argued in this paper with respect to formamide. The relaxation results appear to be consistent with a compact palisade layer including fewer than five water molecules per ethoxy unit. The solvent content was also shown to be invariant over a large concentration range. This concentration independence was supported from a recalculation of N M R self-diffusion data with use of the cell diffusion model. The analysis further supported a solvent diffusion state in the micellar palisade layer similar to what has been reported for polyethylene glycol/water systems, in full analogy with our results. Acknowledgment. We are grateful to Bengt Jonsson and BjBrn Lindman for helpful discussions and comments on this manuscript and to Gordon J. Tiddy for discussions and unpublished material concerning cubic phases. This work was financially supported by the Research Council at the Swedish Board for Technical Development.
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(45) Brown, W.; Johnsen, R.; Stilbs, P.; Lindman, B. J . Phys. Chem. 1983, 87, 4548. (46) Lindman, B.; Jonstrbmer, M. In Physics of Amphiphile Luyers; Meunier, J., Langevin, D., Boccaca, N., Eds.;Springer-Verlag: Berlin, 1988. (47) Blankschtein, G . ;Thurston, G.; Benedek, G. J . Chem. Phys. 1986, 85, 7268.
(48) Clarkson, M. T.; Beaglehole, D.; Callaghan, P. T. Phys. Rev. Lert.
1985, 54, 1722.
(49) CarlstrBm, G.; Halle, B. J . Chem. Soc., Faraday Trans. I 1989,85, 1049. (50) Nikko Chemicals, Tokyo, Japan, datasheet for nonionic surfactants.
