J . Phys. Chem. 1987, 91, 3565-3571
Static and Dynamical Properties of a Nonionic Surfactant (C,,E,)
3565
in Aqueous Solution
Wyn Brown* and Roger Rymdiin Institute of Physical Chemistry, University of Uppsala, 751 21 Uppsala, Sweden (Received: November 20, 1986)
Data are reported on the C12E6amphiphile in aqueous (D2O) solutions obtained by static and dynamic light scattering, pulsed field gradient NMR, and sedimentation velocity at temperatures between 13 and 45 OC. The concentration range extended up to 18% (0.4 M) for light scattering and up to 31% (0.7 M) for NMR measurements. At 13 OC the micelles are spherical. The three types of measurements confirm the earlier conclusion from dilute solution measurements that there is considerable micellar growth above 20 OC which continues up to the vicinity of the cloud point. Cylindrical micelles are the probable form with increasing asymmetry as the temperature is increased. The inverse osmotic compressibility ( X I / a c ) , , increases strongly with concentration and is responsible for the positive trend in D Q Ewith ~ concentration increase. At temperatures above 40 OC ( ~ 3 I I / d c ) ,decreases ~ rapidly as the critical miscibility temperature is approached. DNMR passes through a minimum at temperatures above 30 OC and increases with increasing temperature due to amphiphile exchange between micelles. The thermodynamic term (1 + 2A2MC+ ...) has been evaluated independently from the ratio DQELS/DNMR and from static light scattering measurements.
Introduction A previous communication' dealt with the properties of the
nonionic amphiphile C12E6 (dodecyl hexa(oxymethy1ene glycol monoether) in dilute solution using several techniques: quasielastic light scattering (QELS), static light scattering, pulsed field gradient N M R (PFG-NMR), and sedimentation velocity. Recently, Kat0 and Seimiya2 reported similar measurements on the same system in dilute solution and directed their attention to the nature of the intermicellar interactions. In broad terms as well as in detail, the results of these studies agree. There have also been several reports dealing with the C12E6 system using alternative experimental approaches. Thus Zana and Weil13 used the fluorescence decay method to study probe (pyrene) migration in the system as a function of temperature and concluded that the micellar aggregation number is nearly independent of temperature below 15 OC but then increases rapidly up to the lower critical solution temperature ( T c ) at about 50 OC. LasiE4used spin-labeling ESR measurements and from the line shape deduced that the CI& micelles are probably rodlike above 35 OC. Blankschtein and co-workers5 have developed and applied a theory of thermodynamic properties and phase separation to data on CI2E6solutions including those of ref 1. Their conclusion is that the data fit is consistent with a one-dimensional micellar growth into locally cylindrical micelles. There is thus a broad consensus from the above references, in addition to those summarized in ref 1, that at temperatures below 20 OC C12E6in an aqueous medium forms spherical micelles with a narrow size distribution. These contain approximately 130 molecules of CI2E6 (mass 450). One might conclude from the above that micellar growth as a function of temperature is no longer subject to debate in this system. However, Corti and Degiorgio6 using light scattering techniques have earlier concluded that critical concentration fluctuations are the cause of the observed changes in scattered intensity as the temperature is raised above 30 OC. Subsequent data from neutron scattering (elastic) measurement^',^ have also been ambiguous in interpretation. Thus, for example, ref 7 and 8 disagree in interpretation. Ravey9 analyzed his elastic neutron (1) Brown, W.; Johnsen, R. M.; Stilbs, P.; Lindman, B. J . Phys. Chem. 1983, 87, 4548. (2) Kato, T.;Seimiya, T. J. Phys. Chem. 1986, 90, 3159. (3) Zana, R.;Weill, C. J . Phys. (Paris) Lett. 1985, 46, L-953. (4) LasiE, D.D. J. Colloid. Interface Sci. 1986, 113, 188. (5) Blankschtein, D.; Thurston, G.M.; Benedek, G. B. J . Chem. Phys. 1986, 85, 1268. (6) Corti, M.;Degiorgio, V. J . Phys. Chem. 1981, 85, 1442. (7) Triolo, R.;Magid, L. J.; Johnson, Jr., J. S.; Child, H. R. J. Phys. Chem. 1982, 86, 3689. (8) Cebula, D. J.; Ottewill, R. H. Colloid Polym. Sci. 1982, 260, 11 18. (9) Ravey, J. C. Colloid Interface Sci. 1982, 94, 289.
0022-3654/87/2091-3565$01.50/0 , I
,
scattering data on C& solutions assuming that the micelles grow into flexible rods, using the persistence length of the rod as an adjustable parameter. Zulauf et a1.I0 recently described elastic neutron scattering experiments on C12E6 solutions in D20. Their results were analyzed in terms of small spherical micelles and a satisfactory fit was found. However, the measurements were restricted to only two temperatures and an analysis in terms of cylindrical particles was not made. Thus these additional data do not unequivocally resolve the on-going debate on the structure of the C12Esmicelle as a function of temperature. The earlier1,2 (and presently communicated) PFG-NMR data provide the strongest evidence that there is such micellar growth since the self-diffusion coefficient is not affected by critical fluctuations which complicate interpretation of light scattering data. Zulauf et al.1° use quasielastic neutron scattering to provide convincing evidence that other nonionic amphiphiles (C8E5,C&) vary little in micellar size as a function of temperature. However, this property seems highly system-specific and such measurements were not extended to the C&6 system. In order to obtain a more complete overview of the interactions in the C&6 system and hopefully to resolve existing uncertainties regarding the size-shape pattern, we have extended the earlier measurement series to substantially higher amphiphile concentrations. As before, a key component is the application of PFG-NMR in addition to the QELS and static light scattering measurements since this technique allows a study of the friction behavior without the complication of thermodynamic parameters and particularly of critical fluctuations which come into play as phase boundaries are approached. Use of these methods thus permits the isolation of the thermodynamic term by combination of the two diffusion coefficients as recently done by Kat0 and Seimiya2 for data obtained in dilute CI2E6sohtions. Experimental Section
Samples. High-purity C& was obtained in crystalline form from Nikko Chemicals, Tokyo and used without further purification. Solutions were prepared by weight in D 2 0 (99.8%) purchased from Stohler Isotope Chemicals, Switzerland. The critical micelle concentration for C12E6in H 2 0 has been given M at 25 O C . The by Balmbra et al." as CO = 8.7 X weighed-in concentrations may thus be used directly in the diagrams without correction for C,. Dynamic Light Scattering. The experimental arrangement has been previously described.12 The light source was a 488-nm Ar (10) Zulauf, M.;Weckstrom, K.; Hayter, J. B.; Degiorgio, V.;Corti, M. J. Phys. Chem. 1985,89, 341 1.
(1 1) Balmbra, R. R.; Clunie, J. S.; Corkill, J. M.; Goodman, J. F. Trans. Faraday SOC.1962, 58, 1661. 1964, 60, 919. (12) Brown, W. Macromolecules 1984, 17, 66.
0 1987 American Chemical Society
3566 The Journal of Physical Chemistry, Vol. 91, No. 13, 1987
Brown and Rymden
Co/.C"/w) Figure 1. Self-diffusioncoefficients obtained by using pulsed field gradient NMR. The values have been normalized by using the solvent viscosity, temperature T and are shown as a function of weight concentration CI2E6at different temperatures. The insert shows the low concentration
qo, at
region enlarged. ion laser and the detector system consisted of an ITT FW 130 photomultiplier, the output of which was digitized by a Nuclear Enterprises amplifier/discriminator system. A Langley-Ford 128-channel autocorrelator was employed to generate the full time correlation function of the scattered light. The solutions were filtered through 0.22-pm Millipore filters into IO-mm N M R tubes which are used as scattering cells and are immersed in a large diameter bath of decalin for refractive index matching. All measurements were made in the homodyne mode. Static light scattering measurements were made simultaneously on the same apparatus by recording the intensity photon counts from two photomultipliers, one monitoring a portion of the incident beam and the other the scattered signal. Instrumental calibration was made using benzene (filtered through a 0.22-pm Fluoropore filter after drying over 3.5 A molecular sieves). The Rayleigh ratio for benzene at 488 nm was taken13 as 34.1 1 X The optical constant, K , is K=
4~'n~,(dn/dc)~ NAX4
where n, is the solvent refractive index, dn/dc the refractive index increment, and X the wavelength. The dn/dc values were interpolated from the data given by Balmbra et a1.I' at different temperatures. (The value for C12E6in H 2 0is practically identical with that for poly(ethy1ene oxide) in H2014at 546 nm.) The small shift (51%) involved in translating to the wavelength 488 nm can be neglected. The inverse osmotic c~mpressibilityl~ was evaluated from the absolute scattered intensity at zero angle as
( W a O , ,= (KC/RB)B=ORT
(2)
previous communication.' The time between the 90" and 180" rf pulses was 140 ms for all 6 values, where 6 is the duration of the gradient pulses. Sedimentation velocity measurements were made in a MSE analytical ultracentrifuge with a schlieren optical system. Since C I & is less dense than D20, the sedimentation coefficients are negative. The partial specific volume of CI2E6in D 2 0 was given in ref 1 = 1.005 X lo-) m3 kg-I).
(r2
Results and Discussion Self-Diffusion (Pulsed-Field-Gradient NMR). Figure 1 shows self-diffusion coefficients, normalized by qo/ T, where qo is the D 2 0 viscosity and T the absolute temperature, as a function of concentration at different temperatures. The infinite dilution values ( D o M N R ) (which are approximately equal to those from dynamic light scattering (DoqELs),see Figure 7) decrease with increasing temperature. This shows that the micellar size becomes greater as was concluded in the previous dilute solution investigation. Furthermore, at low concentrations there is an initial decrease in D N M R which is accentuated at the higher temperatures owing to the increase in the friction coefficient as the concentration becomes greater. It is important to note that, while critical concentration fluctuations may reasonably perturb light scattering data from the viewpoint of extracting size information, the selfdiffusion coefficients have been shown'619 to be largely unaffected by them by experiments in binary liquid mixtures. The indicated increase in the hydrodynamic radius with increasing temperature is unambiguous. This is apparent not only in the range 18-30 O C but also between 30 and 45 OC. It is this latter region where micellar growth has been disputed.6-i0 However, above about 46 "C critical fluctuations will start to dominate the light scattering intensity pattern as demonstrated below and in ref 2. Apparent hydrodynamic radii ( R h )have been estimated by assuming a spherical form using values of the self-diffusion coefficient DNMR in the Stokes-Einstein equation:
As an additional internal standard, intensity measurements were made on dilute solutions of an essentially monodisperse fraction of poly(ethy1ene oxide), A?,+ = 280000, obtained from Toya Soda Ltd., Tokyo. Pulsed Field Gradient N M R Measurements. These determinations were made on protons at 99.6 MHz on a standard JEOL FX-100 Fourier transform NMR spectrometer. An internal D,O lock was used for field frequency stabilization as described in the
The values of Rh are shown in Figure 2 as a function of concentration. The insert depicts the dependence of (Rh)c-o on temperature. This dimension increases from about 40 A below 20 "C to about 110 8, at 45 "C.The value of 40 8, agrees with
(13) Imae, T.; Kamiya, R.; Ikeda, S . J . Colloid Interface Sci. 1985, 108, 215. (14) Polik, W. F.; Burchard, W. Macromolecules 1983, 16, 978. ( 1 5 ) Yamakawa, H. Modern Theory of Polymer Solutions; Harper and Row: New York, 1971.
(16) Hamann, H.; Hoheisal, C . ; Richtering, H. Ber. Bunsen-Ges. Phys. Chem. 1912, 76, 249. (17) Allegra, J. C.; Stein, A.; Allen, G . F. J . Chem. Phys. 1971, 55, 1716. (18) Anderson, J. E.; Gerritz, W. H. J . Chem. Phys. 1970, 53, 2584. (19) Lang, J. C.; Freed, J. H. J . Chem. Phys. 1972, 56, 4103.
The Journal of Physical Chemistry, Vol. 91 No. 13, 1987 3561
ClzE6in Aqueous Solution
~
30 2 %
*-
-t-*-
02
I
I
1
I
10
20
30
LO
.01
02
.03
+-+-+-
0 5 Y o I w/w t 17 8 o/o
"
U
'C 50 I
.OL
+-
0.05
.06
L 6 o/'
.07M 01
LL.2'
2 6 o/' 17 0 o/'
Y
1
2
3
4
5
6
7 q2 10-1L/tn-2
(1sine)a.u
200
L
I
I
c Yo ( w/wl 10
20
30
Figure 3. (A, top) The inverse scattered intensity as a function of the square of the scattering vector, q, at different concentrations and at two temperatures. (B, bottom) The scattered intensity as a function of concentration. Curve A, data at 30 OC; curve B, data at 13 (0)and 18 O C (X); and curve C shows the theoretical line for hard spheres.23
the extended length of the ClzE6molecule (39 A) and this then suggests a spherical form for the micelles in the lower temperature range (i.e., below 20 "C). However, the molecular weight obtained from intensity light scattering measurements (seeref 1 and below) a t this temperature indicates about 130 CIzE6molecules per micelle. This number (N) cannot be arranged in a spherical form unless at least one ethylene oxide unit in each molecule is assigned to the hydrophobic core. Such a viewpoint has been advanced by Robson and DennisZowhen considering the size and shape of Triton-X100 micelles-see also the discussion of Nilsson et The coincidence of the hydrodynamic radius and the extended length of Cl2E6may also be the result of compensating effects, i.e. the ethylene oxide chain may be less than fully extended but the overall dimension increased by solvation. The larger (RJappvalues a t the higher temperatures (insert) demonstrate the micellar growth which continues up to the vicinity of the cloud point. An interesting feature of the self-diffusion data is that while D N M R decreases monotonically with increasing concentration below 20 O C , above 30 OC D N M R increases after passing through a minimum. The latter is displaced to lower concentrations as T is increased. Similar behavior has been documented by Nilsson et for C,2E5 and Cl2E8micellar systems, where DNMRwas measured over extended ranges in concentration. Their suggested qualitative interpretation is that, owing to the low micellar diffusion at high concentration, an exchange of amphiphile molecules between the diffusing entities (20) Robson, R. J.; Dennis, E. A. J . Phys. Chem. 1977,81, 1075. (21) Nilsson, P.-G.; Wennerstrom, H.; Lindman, B. Chem. Scr. 1985,25,
67. (22) Nilsson, P . G . ; Wennerstrom, H.; Lindman, B. J . Phys. Chem. 1983, 87, 1377.
becomes possible. This monomer exchange may contribute significantly to the observed diffusion coefficient, even if the probability for the exchange is low. Elastic Light Scattering. Figure 3A demonstrates that the inverse scattered intensity is independent of the square of the scattering vector (9) where the latter is given by q=
4n
- sin 8/2
x
(4)
Here the scattering angle is 8 and is the wavelength of light. This is the expected result if the micellar size is less than q-', which is apparently the case at both 30 and 44.5 OC over the concentration range examined. These data thus confirm that an angular dependence should only be anticipated in the vicinity of the cloud point ( T c = 48.6 "C). Figure 3B shows the intensity profile as a function of concentration at several temperatures. A comparison is made with the calculated curve for the hard-sphere modeLz3 At low concentrations (13%) the intensity increases linearly with C in the region in which the positions of the scatterers are uncorrelated and their intensities then additive. The data at the lower temperatures (1 3 and 18 "C) agree well with the hard-sphere model prediction in this concentration range. At 30 "C, however, the maximum of the intensity curve is strongly displaced to low C. This is the expected result for strongly asymmetrical particles. Thus these observations provide further support for spherical symmetry at 18 "C and an asymmetric form at 30 "C. From measurements of the absolute scattered intensity one may evaluate the inverse osmotic compressibility (XI/aC)T,pand thus (23) Carnahan, N. F.; Starling, K . E. J . Chem. Phys. 1969, SI, 635.
3568
Brown and Rymden
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987
03-
e> T, P
0.2
-
01 -
5
20
15
10
Figure 4. Plots of the inverse osmotic compressibility, (alI/ac),, vs. concentration at different temperatures. The strong curvature of the isotherms shows that eq 5 is only valid over very limited ranges of concentration in the dilute region. Insert B shows the low concentration region enlarged and C depicts the change in (alI/ac),, as a function of temperature at C = 8% w/w.
obtain a measure of the interactions in the system. In dilute solution, the virial expansion takes the form: (aII/dC),, = F ( 1
+ 2A2MC + ...)
(5)
where A 2 is the second virial coefficient, M the molar mass, and the other symbols have their usual significance. The concentration dependence of ( c ~ I I / ~ Cat ' ) different ~~ temperatures is illustrated in Figure 4. The intercepts at C 0 according to ((an/ aC),,), = R T / M allow a very approximate estimate of the micellar mass at a particular temperature; these values are summarized in Table I and agree well with the estimates previously obtained] in dilute solution. Thus at 18 " C , M N 60000 (133 6 X lo5 (1300 C12& units). molecules) while at 45 OC,A? The size e s t i m a t e at the lower temperature agrees well with the value of Zana and Weil13 ( N N 130). At 45 O C however, there is a substantial discrepancy (Zana and Weill find N = 350). This suggests that the size distribution is narrow below 20 O C but broadens considerably with increasing temperature. Since the aggregation numbers of Zana and Weill are number average quantities while light scattering yields a weight average mass, such a difference may be anticipated (for a discussion of the change in size distribution see ref 2 and also below). The earlier measurements of intensity light scattering had shown] that in dilute solution the second virial coefficient becomes negative in the region close to 21 O C . This change is substantiated here on comparing the curves for (aII/aC)T,pat 18 and 25 "C. However, (aII/ac), increases strongly again as the concentration -+
TABLE I: Valuesc of the Molecular Weight Estimated from Static Light Scattering and the Relationship between D Q U and DNm (Eq 8) and the Concentration Dependence of the Apparent Micellar Mass Obtained from DQBIDNMR with (alI/aC)+,p M x 10-3
18 30 40 45
60 255 580 1050
51 216 516 805
M x 10-3 c, % w t / w t 0.5
1.o
2.6 4.6 6.9 8.6
13 "C 48 46 49 38 42 31
18 "C
30 'C
54 52 53 52 69 89
255 214 307 305 308 310
Static light scattering. Relationship between D Q and~ DNMR. ~ 'The precision of the estimates of M given is low since those under b and in the lower part of the table involve three separately measured quantities. Moreover, DQEs data at 13 and 18 " C are derived from data of comparatively low scattered intensity. is further increased showing that eq 5 with only the A , term is valid over a very limited range of concentration. Below 40 O C ,
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 3569
CI2E6in Aqueous Solution the concentration dependence suggests that excluded volume effects make the major contribution to the increase in D Q E(see ~ below) and that this is the result of the progressive deviation of the micellar shape from a sphere as the temperature is raised. Kat0 and Seimiya2 reached a similar conclusion from their dilute solution data for c&6 in aqueous solution. Over the present range of concentration, the system may potentially be complicated by a change in the aggregation number with concentration. Thus changes in ( d n / d C ) , , may in part reflect this dependence and the virial coefficients in eq 5 may be apparent quantities. The ~ , ~ in the insert to temperature dependence of ( ~ 3 l I / d C ) shown Figure 4 indicates that the repulsive interactions become weaker as the temperature increases. At less than about 4 O C from the cloud point at 48.6 OC there is an accentuated change and finally (dII/dC),, becomes extremely small. This latter region has been investigated for C'& solutions by Corti and Degiorgio6 and by Corti et al.24 for related amphiphiles and they show that, at concentrations close to the critical concentration for phase separation, critical fluctuations dominate the behavior. These conclusions derive support from the recent study of Kat0 and Seimiya2 who conclude that attractive interactions will begin to dominate over the repulsive (excluded volume) interactions at above about 46 OC. Similarities to the behavior of poly(ethy1ene oxide) of low molecular weight in aqueous solution may be anticipated. Polik and Burchard14 used static light scattering to investigate the conformation of this polymer at different temperatures. They found that the average molar mass increased with temperature, reaching a maximum at about 60 O C . Spherical microcrystallites were envisaged. Estimations of Micellar Size and Shape. The measured value for the spherical particle at lower temperatures (120 "C) is approximately 60000 (see Table I) while that estimated in the vicinity of 40 OC is 6 X lo5 (ref 1). While deviations from spherical symmetry may be either sphere-rod or sphere-disk, recent discussion^^^^^^^ have preferred the former possibility. Assuming that particles of 6 X lo5 are cylindrical, one may simply estimate the dimensions. Taking the cross-sectional disk of diameter 2r (with r = 40 A, the experimental radius of the spherical particle) and thickness 8.4 8, (using a value for the head radius of 4.2 A26)leads to 28 C12E6entities per disk with M = 12600. A molecular weight of 6 X lo5 then corresponds to 43 such disks which, with hemispherical ends, gives a total length of 440 A. This will of course be in error to the extent of uncertainty of the dimensions used for C & , , for example, if the ethylene oxide chains are less than fully extended. On the other hand, one may use Perrins' formula27expressing the hydrodynamic radius of a prolate ellipsoid in terms of the axial ratio ( b l a ) . Using Rh = 97 A at 40 "C (Figure 2), one obtains b / a = 6.25. With a = 40 A, b = 250 A. In terms of the corresponding cylinder of length I and radius 40 A one gets 1 = 280
A.
Dynamical Properties-Quasielastic Light Scattering. DqELs values were obtained from the measured correlation function by using both a cumulants fit and a three-parameter fit according to
g 2 ( ~ )= p[exp(-rT)
+ BI2
which expresses the normalized second-order correlation function in terms of a single relaxation rate, I'. Here 0 is an instrumental parameter (about 0.65). The inclusion of a small base line term, B, was desirable owing to a small amount of aggregates/dust in (24) Corti, M.; Minero, C.; Degiorgio, V. J . Phys. Chem. 1984,88, 309, (25) Zulauf, M.; Rosenbusch, J. P. J. Phys. Chem. 1983, 87, 853. (26) Almgren, M.;Swarup, S . J. Phys. Chem. 1983, 87, 876.
(27)
where b and a are respectively the semimajor and semiminor axes of the prolate ellipsoid.
1t
Relative variance
0.3 0.2
10 20 30 Figure 5. The relative variance as a function of concentration at various temperatures (variance obtained from the cumulants fit).
C%(W/Wl
0
I
I
5
10
I
15
20
Figure 6. Plots of diffusion coefficients from dynamic light scattering data, DQELS, at various temperatures. The measurements were made at 0 = 60' and the time correlation functions were close to single exponentials. The values of DqELsare normalized by qo/T where qo is the solvent viscosity at temperature T.
the concentrated solutions. The values of D were approximately 3% larger when using eq 6 than when fit according to the cumulants method. Measurements were initially made as a function of angle over the range 20 to 120' and the decay rate was established to be strictly proportional to q2, denoting a diffusive process. The determinations were thereafter made a t an angle of 60'. The solutions at higher concentrations were also scanned by using a multi-.r autocorrelator to control the possible presence of multiple relaxations. Only a single relaxational decay was found to be significant within the range of sample times available (1 ~s to 1 min simultaneously scanned). We note, however, that the parallel measurements on a low molecular weight fraction of poly(ethy1ene oxide) in water solution showed a clearly bimodal behavior and the existence of molecular clusters (see also ref 12). The relative variance resulting from the cumulants fit is shown as a function of concentration at several temperatures in Figure 5. This quantity increases with C but reaches a plateau at about C = 4%. The variance does not seem to be significantly temperature dependent, which may seem surprising in view of the micellar growth discussed above. Although this would suggest that the size distribution remains narrow, the loss or gain of a C12E6entity with a characteristic time T~ is expected to be a very fast process. This may be deduced from the measurements of Zana and Weil13 who used a fluorescence decay method to follow a micelle-solubilized probe (pyrene) in the system. If we assume that intermicellar migration of a C&6 unit occurs on a similar time scale as pyrene, T~ = 5 X low7s at 40 OC. Thus QELS measurements should probe the motions of the average micelle and will not give a measure of particle polydispersity. In other words, T~
