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Aggregate Structure in Aqueous Solutions of Brij-35 Nonionic Surfactant Studied by Small-Angle Neutron Scattering Sa´ndor Borbe´ly† Institut fu¨ r Festko¨ rperforschung, Forschungszentrum Ju¨ lich GmbH, D-52425 Ju¨ lich, Germany Received September 27, 1999. In Final Form: January 31, 2000 The aggregate formation in aqueous solutions of Brij-35 (C12EO23) nonionic surfactant has been studied in the concentration range from 5 to 200 g/L at 20, 40, and 60 °C. The structure of micelles was modeled by a spherical core with tethered polymer chains to the surface, while the intermicellar interaction was described by a hard sphere structure factor. The mean aggregation number was found to increase substantially with both concentration and temperature from 34 (5 g/L, 20 °C) to 64 (200 g/L, 60 °C). The average core radii obtained are between 18 and 19 Å. On the basis of the above two parameters, 35-50% of the core volume is occupied by hydrated poly(ethylene oxide) (PEO) chains. The radius of gyration of tethered chains, Rgc, is in agreement with the theoretical value for Gaussian conformation (11.6 Å) at the smaller concentrations measured but increases significantly with increasing concentration. It reveals considerable stretching of the chains that is attributed to sterical constraints. At higher concentrations Rgc decreases with temperature similarly to the interaction radius. This fact is interpreted as a change in the conformational equilibrium of PEO chains.
Introduction Nonionic surfactants containing PEO chains as hydrophilic moieties (CiEj) are well-known and have been widely used for decades. They found applications in many fields such as cosmetics, pharmaceuticals, paints, and cleaning agents. Moreover, they are routinly used for the solubilization of membrane proteins. These types of compounds are generally prepared commercially by the condensation of ethylene oxide with alcohols to yield a product, in which the hydrophilic portion has a Poisson distribution of chain lengths.1 These commercial products, for example, the Triton X-100, the Brij series, etc., have been intensively studied.2-6 Later, efforts have been made to fractionate the commercial products,7 to synthesize homogeneous compounds, and to characterize them.8 They show very reach phase behavior in aqueous solutions including phases from isotropic micellar to various ordered liquid crystalline ones. Their phase structure is thoroughly studied,9-11 mainly for homologues containing short PEO chains up to CiE12. The poly(ethylene oxide) type nonionic surfactants have an unusual feature, they possess a concentration-dependent lower consolute temperature which in the literature is usually called “cloud point”. The micellar properties † Present address: Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary.
(1) Flory, P. J. J. Am. Chem. Soc. 1940, 62, 1561. (2) Kushner, L. M.; Hubbard, W. D. J. Phys. Chem. 1954, 58, 1163. (3) Becher, P.; Clifton, N. K. J. Colloid Sci. 1959, 14, 519. (4) Heusch, R. Prog. Colloid Polym. Sci. 1978, 65, 186. (5) Heusch, R. Ber. Bunsen-Ges. Phys. Chem. 1978, 82, 970. (6) Heusch, R. Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 834. (7) Kushner, L. M.; Hubbard, W. D.; Doan A. S. J. Phys. Chem. 1957, 61, 371. (8) Corkill, J. M.; Goodman, J. F.; Ottewill, R. H. Trans. Faraday Soc. 1961, 57, 1627. (9) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975. (10) Sjo¨blom, J.; Stenius, P.; Danielsson, I. In Nonionic Surfactants. Physical Chemistry; Surfactant Science Series Vol. 23; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; p 369. (11) Medhage, B.; Almgren, M.; Alsins, J. J. Phys. Chem. 1993, 97, 7753.
have been extensively studied in the vicinity of the cloud curve. In early light scattering experiments the strong enhancement of the turbidity with increasing temperature has been explained by a drastic increase in the aggregation number.12-15 Corti and Degiorgio16-18 proved that the clouding observed is a critical phenomenon which can be described by the mean field theory of critical concentration fluctuations. Previous experimental work proved that the clouds are loose secondary aggregates of small micelles and the secondary aggregation is induced by the increasing intermicellar interaction.19-24 Sato et al.25 have studied the influence of the alkyl chain length on the structure and micellar inner polarity in the series CiE8 (i ) 10, 12, 14). They observed an increase in the aggregation number and the compactness of the micelles and, in consequence, a decrease in the inner polarity with increasing alkyl chain length. Schefer et al.26 have applied small-angle neutron scattering to determine the aggregation number of Brij58 (C16E20) micelles in D2O solutions at 7 °C. A value of 71 was obtained for concentrations less than 1 wt %. The scattering curves have been described by a two-shell (12) Balmra, R. R.; Clunie, J. S.; Corkill, J. M.; Goodman, J. F. Trans. Faraday Soc. 1964, 60, 978. (13) Ottewill, R. H.; Storer, C. C.; Walker, T. Trans. Faraday Soc. 1967, 63, 2796. (14) Robson, R. J.; Dennis, E. A. J. Phys. Chem. 1977, 81, 1075. (15) Paradies, H. H. J. Phys. Chem. 1980, 84, 599. (16) Corti, M.; Degiorgio, V. Opt. Commun. 1975, 14, 358. (17) Corti, M.; Degiorgio, V. Phys. Rev. Lett. 1980, 45, 1045. (18) Corti, M.; Degiorgio, V. J. Phys. Chem. 1981, 85, 1442. (19) Staples, E. J.; Tiddy, G. J. T. J. Chem. Soc., Faraday Trans. 1 1978, 74, 2530. (20) Triolo, R.; Magid, L. J.; Johnson, J. S.; Child, H. R. J. Phys. Chem. 1982, 86, 3689. (21) Zulauf, M.; Rosenbusch, J. P. J. Phys. Chem. 1983, 87, 856. (22) Zulauf, M.; Weckstro¨m, K.; Hayter, J. B.; Degiorgio, V.; Corti, M. J. Phys. Chem. 1985, 89, 3411. (23) Herrington, T. M.; Sahi, S. S. J. Colloid Interface Sci. 1988, 121, 107. (24) Lesemann, M.; Belkoura, L.; Woermann, D. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 695. (25) Sato, T.; Saito, Y.; Anazawa, I. J. Chem. Soc., Faraday Trans. 1 1988, 84, 275. (26) Schefer, J.; McDaniel, R.; Schoenborn, B. P. J. Phys. Chem. 1988, 92, 729.
10.1021/la991265y CCC: $19.00 © 2000 American Chemical Society Published on Web 06/03/2000
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spherical model consisting of a hydrocarbon core surrounded by the shell of hydrated headgroups. Phillies et al.27 have used light scattering combined with multiplesize mesoscopic optical probes to investigate Brij-35 (C12E23) micelles in aqueous solutions. From the concentration dependence of the micellar and optical probe diffusion coefficients, they could determine a single aggregation number valid for the whole concentration range measured. They obtained 40 for 10 °C e T e 50 °C and 64 at 70 °C. From the temperature dependence of the hydrodynamic radii, a conclusion has been drawn about the continuous contraction and dehydration of the poly(ethylene oxide) chains in the temperature range from 25 to 70 °C. In this work an attempt is made to give a detailed structural description of Brij-35 micelles in aqueous solutions using a more sophisticated model in comparison with the two-shell spherical one applied by Schefer et al.26 Experimental Section Brij-35 was purchased from Sigma and was used without further purification. A stock solution having concentration of 200 g/L was prepared dissolving the surfactant in 99.8% D2O. Individual samples in the concentration range from 5 to 200 g/L were made by volumetric dilution of the stock solution with D2O. The solutions were filled into quartz cells (Hellma, Germany) of 2 or 5 mm neutron path lengths depending on the concentration. The cuvettes were placed in a sample holder thermostated from an external bath with accuracy of (0.1 °C. The measurements were performed at 20, 40, and 60 °C on the small-angle neutron scattering (SANS) spectrometer installed at the Budapest Research Reactor. The neutron beam was monochromatized by a velocity selector to 4.15 Å with 13% full width at half-maximum (fwhm). All measurements were carried out at two sample-todetector distances (1.3 and 5.5 m) to cover the widest q-range available with the spectrometer (q is the magnitude of the scattering vector and equal to q ) (4π/λ) sin(θ/2), where λ is the neutron wavelength and θ is the scattering angle). To eliminate the high incoherent background arising from the hydrogen content of the solute (mainly at high concentrations), D2O-H2O mixtures were prepared that contained the same number of hydrogen atoms as the samples and were measured as background samples. The scattering was isotropic; therefore the primary two-dimensional spectra were circularly averaged, corrected for background and detector efficiency, and transformed to absolute scattering cross section using a 1 mm H2O sample as standard incoherent scatterer.
Results and Discussions Scattering curves measured at 20 °C for various concentrations are shown in Figure 1. A charasteristic feature of small-angle scattering from systems of this type is the appearance and strengthening of the interparticle correlation with increasing concentration which is caused by the excluded volume interaction of micelles. The effect of temperature on the aggregation can be qualitatively followed in Figure 2. The increase in temperature alters the innermost part of the scattering curves only. This fact together with the stability of the outermost part suggest that the structural change responsible for the increase in the scattered intensity at low q values takes place at large distances in the real space, probably in the outer shell of the aggregates containing the hydrated poly(ethylene oxide) chains. To obtain quantitative information about the structure of micelles, model scattering curves have been fitted to the measured ones. In the idealized model used, micelles were considered as being polydisperse (27) Phillies, G. D. J.; Hunt, R. H.; Strang, K.; Sushkin, N. Langmuir 1995, 11, 3408.
Figure 1. Experimental (symbols) and model (solid line) scattering curves at various concentrations (T ) 20 °C). The error bars indicate the change in the statistical accuracy of data with concentration. For better visibility the curves have been multiplied by the following coefficients: 5 g/L, 0.1; 10 g/L, 0.5; 50 g/L, 4; 100 g/L, 10; 150 g/L, 50; 200 g/L, 200.
Figure 2. Measured (symbols) and fitted (solid lines) scattering curves at various temperatures (c ) 200 g/L).
spheres with tethered Gaussian polymer chains to their surface. The scattering function for the above structural model was derived and published recently by Pedersen and Gerstenberg.28 The form factor of “hairy spheres” is written as follows
Fmic ) N2aggF2s Fs(q,R) + NaggF2c Fc(q,Rgc) + Nagg(Nagg - 1)F2c Scc(q) + 2N2aggFsFcSsc(q) (1) where Nagg is the aggregation number of micelles and Fs and Fc are the excess scattering lengths of the core-forming portion of the monomer and the tethered chain, respectively. Generally the excess scattering length Fex is defined by the following formula
Fex )
∑i bi - VpF′solv
(2)
where the first term is the sum of the scattering length for the particle, or for a portion of the particle, Vp is the (28) Pedersen, J. S.; Gerstenberg, M. C. Macromolecules 1996, 29, 1363.
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Borbe´ ly
volume the scattering length is summed for, and F′solv is the scattering length density of the solvent. In the case of Brij-35 Fs corresponds to the excess scattering length of a dodecyl chain that is equal to -21.704 × 10-12 cm, while Fc is the excess scattering length for the EO23 moiety, and equal to -81.289 × 10-12 cm. The volumes of dodecyl and poly(ethylene oxide) chains were calculated from their partial molar volumes obtained from high-precision density measurements of nonionic surfactant solutions.29 The values calculated are 322 and 1432 Å3 for dodecyl and EO23 chains, respectively. The Fs(q,R) ) Φ2(q,R) is the normalized form factor of the spherical core and Φ(q,R) is the form factor amplitude.
Φ(q,R) ) 3
sin(qR) - qR cos(qR) (qR)3
F(q,Rgc) ) 2
e
sin(qR) qR
(5) chain31
sin(qR) qR
R ) (1 + 2ηhs)2/(1 - ηhs)4
ηhs R 2
(11)
A ) 2qRhs, where Rhs is the interaction radius. The structure factor depends on two parameters, the interaction radius Rhs and the corresponding volume fraction ηhs, but the latter can be calculated from the concentration as ηhs ) (4π/3)Rhs3n, where n is the number density of aggregates. The polydispersity of the aggregation number was described by Gaussian distribution.
f(Nagg) )
1 1/2
(2π) σNagg
e-(〈Nagg〉-Nagg) /2σNagg 2
(12)
The final form of the fit function was the following
(6)
and x ) q2Rgc2 as before
]
2
(7)
The above formulation of the cross-correlation terms considers the starting point of the chains (the center of the spheres representing them) as lying on the surface of the core, that is, assumes a fixed penetration of chains into the core. According to Monte Carlo calculations the chains are shifted outward relative to the surface of the core. It can be taken into account by moving the starting points of the chains from distance R (that is from the surface of the core) to R + ∆R. It changes the sin(qR)/(qR) term in expressions 5 and 7, instead of R one has to write an increased distance R + ∆R
q(R + δRgc)
β R (sin A - A cos A) + 3(2A sin A + A2 A γ (2 - A2) cos A - 2) + 5[-A4 cos A + A 4{(3A2 - 6) cos A + (A3 - 6A) sin A + 6}] (10)
G(A) )
γ)
1 - e-x ψ(q,Rgc) ) x
sin[q(R + δRgc)]
where ηhs is the hard sphere volume fraction
(4)
where ψ(q,Rgc) is the form factor amplitude of a
[
(9)
β ) -6ηhs(1 + ηhs/2)2/(1 - ηhs)4
where x ) q2Rgc2, and Rgc is the radius of gyration of the polymer. In the micellar form factor (1) the cross correlations between the sphere and the tethered chains and between the chains are also taken into account by the terms Ssc and Scc, respectively, representing the ethylene oxide chains as spheres with radius Rgc in the derivation. These cross correlation terms are written as follows
Scc(q,R,Rgc) ) ψ2(q,Rgc)
1 1 + 24ηhsG(A)/A
and
+x-1 x2
Ssc(q,R,Rgc) ) Φ(q,R)ψ(q,Rgc)
S(q) )
(3)
Fc(q,Rgc) is the scattering function of the attached polymer chains with Gaussian statistics given by the Debye function.30 -x
The interparticle correlation has been taken into account by using a hard sphere structure factor calculated in the Percus-Yevick approximation.32,33
(8)
where δ measures the displacement in Rgc units and can be used as a fit parameter.28 (29) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physico-Chemical Properties of Selected Anionic, Cationic and Nonionic surfactants; Elsevier: Amsterdam, 1993. (30) Debye, P. J. Phys. Colloid Chem. 1947, 51, 18. (31) Hammouda, B. J. Polym. Sci., B: Polym. Phys. 1992, 30, 1387.
∫
∞ dΣ (q) ) n(Nagg) 0 {Fmic(q,Nagg) + dΩ FA2(Nagg)[S(q,Rhs(Nagg)) - 1]}f(Nagg) dNagg + B (13)
where n(Nagg) is the aggregation number dependent number density and FA is the sum of the amplitudes weighted by the excess scattering lengths
sin[q(R + δRgc)]
FA ) FsΦ(q,R) + Fcψ(q,Rgc)
q(R + δRgc)
(14)
Because of the inhomogeneity of the particle the (13) complete formula describes correctly the scattered intensity instead of the simple product of the form factor and the interparticle structure factor.34 The above manner of including the polydispersity in the fit corresponds to the local monodiperse approximation.35 According to the literature36 this method works better for systems with larger polydispersities and higher concentrations than the decoupling approximation.37 Before fitting, the model scattering curves have been convoluted with the resolution function of the spectrometer. The components of the resolution function were approximated by Gaussian (32) Percus, J. K.; Yevick, G. J. Phys. Rev. 1958, 110, 1. (33) Kinning, D. J.; Thomas, E. L. Macromolecules 1984, 17, 1712. (34) Pedersen, J. S. J. Chem. Phys., in press. (35) Pedersen, J. S. J. Appl. Crystallogr. 1994, 27, 595. (36) Pedersen, J. S. Adv. Colloid Interface Sci. 1997, 70, 171. (37) Kotlarchyk, M.; Chen, S. H. J. Chem. Phys. 1983, 79, 2461.
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Langmuir, Vol. 16, No. 13, 2000 5543
Table 1. Best Fit Parameters of the Interacting Polydisperse (Core + Tethered Chains) Modela c, g/L 5 10 25 50 100 150 200
T, °C
〈Naggr〉
20 40 60 20 40 60 20 40 60 20 40 60 20 40 60 20 40 60 20 40 60
34.4(2.3) 38.8(2.3) 41.9(3.0) 35.4(1.8) 38.8(1.8) 43.7(2.0) 45.7(0.8) 47.9(1.0) 52.9(1.2) 47.5(1.6) 50.5(1.9) 55.3(2.1) 51.8(0.6) 54.2(0.6) 59.1(1.6) 55.7(0.6) 58.6(1.0) 62.0(0.9) 58.6(0.8) 60.3(0.9) 64.1(1.1)
σNagg/〈Nagg〉
R, Å
Rgc, Å
0.421 F 0.347 F 0.090 F 0.377 (0.005) 0.322(0.004) 0.278(0.070) 0.291(0.019) 0.309(0.028) 0.291(0.005) 0.255(0.014) 0.278(0.018 0.301(0.027)
15.8(0.8) 16.1(0.7) 18.6(1.3) 16.4(0.6) 18.3(0.7) 18.4(0.7) 18.3(0.2) 18.7(1.0) 19.1(0.3) 17.9(0.5) 18.5(0.7) 19.1(0.7) 18.9(0.3) 18.5(0.3) 18.9(0.8) 18.4(0.1) 18.8(0.2) 18.8(0.2) 19.0(0.1) 19.1(0.2) 19.6(0.3)
12.3(0.8) 11.9(0.7) 11.7(1.0) 11.1(0.5) 11.3(0.6) 11.4(0.6) 15.8(0.4) 14.8(0.4) 14.5(0.4) 16.4(0.6) 15.1(0.6) 15.2(1.7) 17.5(0.6) 16.0(0.5) 15.3(0.6) 17.4(0.4) 16.8(0.6) 15.8(0.4) 18.9(0.7) 17.4(0.6) 16.5(0.7)
Rhs/R
δ, Å
χ2
2.32(0.06) 2.18(0.07) 2.14(0.08) 2.39(0.09) 2.24(0.14) 2.08(0.12) 2.25(0.04) 2.21(0.04) 2.10(0.24) 2.28(0.07) 2.17(0.12) 2.10(0.03) 2.16(0.05) 2.10(0.08) 2.00(0.14)
0.75 F 0.75 F 0.50 F 0.75 F 0.50 F 0.50 F 0.3 F 0.3 F 0.3 F 0.294(0.077) 0.335(0.100) 0.329(0.085) 0.179(0.072) 0.316(0.070) 0.364(0.072) 0.317(0.030) 0.295(0.064) 0.366(0.059) 0.207(0.060) 0.257(0.067) 0.273(0.074)
0.561 0.541 0.546 0.606 0.541 0.551 0.492 0.446 0.609 0.620 0.614 0.667 1.012 0.932 0.742 0.681 0.980 0.799 1.167 0.817 0.967
a The numbers in parentheses correspond to the errors of parameters obtained from the fit. The parameters marked by F were fixed in the fit procedure. Meaning of the parameters: 〈Naggr〉, mean aggregation number; σNagg, standard deviation of the aggregation number; R, radius of core; Rgc, radius of gyration of the tethered chains; Rhs, interaction radius; δ, displacement of the starting points of tethered chains outward of the core surface.
functions.38 The mean aggregation number 〈Nagg〉 and its standard deviation σNagg, the radius of the core R, the radius of gyration of the tethered chains Rgc, the ratio of the interaction radius to the core radius Rhs/R, the parameter describing the displacement of the chains’ starting point away from the core surface δ, and the background term B were the seven free parameters of the fit. At high concentrations (100-200 g/L) excellent fit was obtained using the whole parameter set discussed above. However, a continuous increase in the parameter errors has been obtained at lower concentrations. This can be accounted for by two reasons. First, in consequence of the low scattered intensity, the statistical accuracy of the data (mainly at high q) is much less at low concentrations than at high ones. Because of the lack of a cold neutron source at the Budapest Research Reactor, the flux of 4.15 Å neutrons was low, and a substantial increase of the measurement time, to increase the accuracy for weakly scattering samples, was not possible. The error bars in Figure 1 show the change in the accuracy of measurements with increasing concentration. Second, the weakening of the interparticle interaction at low concentrations decreases the information content of the scattering curves, and seven fit parameters appear to be too many to be determined independently in a fit. Therefore, to decrease the number of free parameters, at 50 g/L concentration the fit was carried out at several fixed values of the parameter describing the polydispersity of aggregation number, and the parameters from the run giving the minimum χ2 were accepted. At even lower concentrations the fit was insensitive to the polydispersity. Therefore, at 25 g/L a monodisperse model was fitted to the measured spectra at various fixed values of the penetration parameter δ. Furthermore, at 5 and 10 g/L the influence of the excluded volume interaction was so weak, that the scattering curves could be equally well fitted with a noninteracting model. For this reason, the latter model requiring fewer free parameters has been used also with fixed values of δ. The best fit parameters and the (38) Pedersen, J. S.; Posselt, D.; Mortensen, K. J. Appl. Crystallogr. 1990, 23, 321.
corresponding normalized χ2 are collected in Table 1. The normalized χ2 is defined by the following formula 2
χ )
1 Nexp - Npar - 1
Nexp
∑ i)1
(Iexp,i - Imod,i)2 σexp,i2
(15)
where Nexp is the number of experimental points, Npar is the number of fit parameters, Iexp,i and σexp,i are the measured intensity and its statistical error, respectively, while Imod,i is the model intensity. In Figures 1 and 2 the fitted spectra are represented by solid lines. The agreement between the measured and model curves is very good. It can be judged also from the χ2 values in Table 1. Because the scattering curves are very sensitive to the particle shape, the good fit proves the spherical shape of micelles in contradiction with the conclusion of an early work, interpreting light scattering from aqueous Brij-35 solutions as originating from rod-shaped aggregates.39 The concentration dependence of the aggregation number at various temperatures is shown in Figure 3. It increases with both concentration and temperature. Two papers have been found in the literature reporting on the aggregation number of Brij-35 in aqueous solutions. In both works, light scattering was used to characterize the micelles and the aggregation number has been obtained from the concentration dependence of the turbidity or the diffusion coefficient. Because the aggregation number is concentration dependent, the values determined in the cited works can be considered as averaged values for the concentration range of measurements. Becher39 has obtained a value of 40, but the concentration range and temperature are not mentioned in the paper. The latter was presumably room temperature. Phillies et al.27 have obtained 40 as well in the concentration range from 2 to 100 g/L at temperatures 10 °C e T e 50 °C and a value of 64 at 70 °C. These aggregation numbers take into account that they are some kind of averaged values fit in the trend obtained in this work. For the polydispersity of the aggregation number, about 30% has been obtained at (39) Becher, P. J. Colloid Sci. 1961, 16, 49.
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Figure 3. Concentration dependence of the mean aggregation number at various temperatures.
Borbe´ ly
Figure 5. Concentration dependence of the radius of gyration of the tethered chains at various temperatures.
gyration can be calculated from the contour length L and the Kuhn statistical segment length b as
Rgc ) (Lb/6)1/2
Figure 4. Concentration dependence of the core radius at various temperatures.
high concentrations where it could be determined. At these concentrations the polydisperse model has given a much better fit than the monodisperse one. The smearing effect of the polydispersity could be observed at the high q part of the spectra, and this is what led to a better fit in comparison with the monodisperse model. The impossibility of obtaining information on the polydispersity at low concentrations is due to the low statistical accuracy of the data at high q values, which is the most sensitive part of the spectra to the above-mentioned smearing effect. The fitted core radius lies between 18 and 19 Å, except for some less accurate values at the lowest concentrations, and does not show marked change with the concentration, as can be seen in Figure 4. The small increase with increasing temperature can be accounted for by the the increase in the aggregation number. Because both the aggregation number and the core radius were fit parameters, from the known volume requirement of the alkyl chains, the filling ratio of the core by alkyl chains can be calculated. The values obtained are between 0.5 and 0.65, which means that approximately from one-third to onehalf of the core volume is occupied probably by the polyoxyethylene chains. The radius of gyration of tethered chains increases considerably with increasing concentration and decreases with temperature (Figure 5). For a polymer chain with Gaussian statistics, the radius of
(16)
From the bond lengths and angles the contour length per one ethylene oxide unit is 3.5 Å, while the Kuhn length for poly(ethylene oxide) is about 10 Å.40 From these values Rgc ) 11.6 Å is obtained. At low concentrations the fitted values are close to the calculated one, from which one can conclude that the chains are probably Gaussian coils. However, the large radii of gyration at higher concentrations probably show substantial conformational change toward a more stretched conformation. For comparison, the radius of gyration of a homogeneous rod with the length equal to the contour length of EO23 and with cross section radius corresponding to the stretched EO chain is 23.2 Å. The interaction radius is 2-2.3 times larger than the core radius. Attributing to the polyoxyethylene chains a mean dimension of 2Rgc, the interaction radius is less than R + 2Rgc even if the chain penetration into the core is also taken into account. It means that in the excluded volume interaction the outer regions of the poly(ethylene oxide) layers are partly interpenetrable. The penetration parameter δ shows a decreasing trend with increasing concentration (Table 1). It would suggest that the tethered chains penetrate deeply into the core, but this is in contradiction with the near constancy (5060%) of the filling of the core by dodecyl chains. To make an approximate estimation, let us consider two spheres with radii R and Rgc. The center of the latter is 0.75Rgc away from the surface of the sphere with radius R. Approximate the common volume by the cap of the sphere with radius Rgc, the cap height in this case is 0.25Rgc. The volume of the cap can be calculated as
Vcap )
πh2(3Rgc - h) 3
(17)
Writing h ) 0.25Rgc after rearrangement, one can get Vcap ) 0.043(4π/3)Rgc3, which shows that approximately 4% of the volume of the sphere determined by the radius Rgc is embedded in the core. Taking Rgc ) 11.6 Å, one can get Vcap ) 281 Å3, which gives together with the volume of the dodecyl chain a 0.53 filling ratio of the core by the (40) Aharoni, S. M. Macromolecules 1983, 16, 1722.
Aggregate Structure of Nonionic Surfactant
hydrophobic chains. This value is close to experimental ones calculated from the fit parameters at low concentrations, and in reality it is even better if we take into account that the common volume in the simple estimation used is slightly overestimated. The above simple calculation suggests that at small concentrations an average portion of 4% of all poly(ethylene oxide) chains is incorporated in the core in its hydrated Gaussian form. At high concentration the above estimation gives an unphysically large penetration volume which does not fulfill the experimentally found 50-60% filling level of the core by dodecyl chains. Therefore the large values of Rgc obtained from the fit are thought to be an indication of significant conformational change of the tethered chains, and this is why the above volume estimation does not work. The change in conformation probably can be attributed to sterical hindrance. With regard to this it has to be mentioned that the aggregation number, that is, the number of attached chains, increases substantially with increasing concentration, but at the same time the radius of the core can be considered almost constant. To understand the effect of temperature on the aggregate structure revealed by the scattering curves in Figure 2, one has to examine jointly the temperature dependence of the radius of gyration of the tethered chains Rgc and the interaction radius Rhs. Both parameter decreases with increasing temperature. In the case of poly(ethylene oxide) chains it reveals a change toward the Gaussian conformation. That seems to be confirmed in Figure 2. As it was pointed out,28 if the assumptions of the structural model used are fulfilled entirely, a power law behavior of the scattering curves can be observed at large q with exponent -2, charasteristic for Gaussian polymer chains. The scattering curves in Figure 2 show a transition from a power law behavior close to the rod scattering (I ∼ q-1) to that which is closer to a random chain scattering (I ∼ q-2) as the temperature increases. This feature could also be observed on other temperature series measured at higher concentrations (50-200 g/L) where the statistical accuracy of the data was sufficiently high. This fact also supports the former assumption that the larger value of the radius of gyration of the attached chains corresponds to a more expanded conformation. The more compact conformation results in the decrease of the overall dimension and, in consequence, in the decrease of the interaction radius. The change in Rhs is not so large, 5.3% at 200 g/L. However, because the volume fraction depends on the third power of the radius, the above small change decreases the hard sphere volume fraction by 15%, which resulted in the weakening of the excluded volume interaction as revealed in Figure 2 at low q values. In the middle 1980s Karlstro¨m41,42 published a theoretical model on the conformational equilibria of poly(ethylene oxide) homopolymer dissolved in different media. A modified mean field theory based on the conformational equilibrium model was able to describe the phase behavior of poly(ethylene oxide) in water, the phase behavior of other nonionic polymers in aqueous and nonaqueous solutions, and, furthermore, the effect of various cosolutes on the phase boundaries.42-45 Karlstro¨m’s work was (41) Andersson, M.; Karlstro¨m, G. J. Phys. Chem. 1985, 89, 4957. (42) Karlstro¨m, G. J. Phys. Chem. 1985, 89, 4962. (43) Sjo¨berg, A° .; Karlstro¨m, G. Macromolecules 1989, 22, 1325.
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initiated by experimental observations46-48 that in polar solvent the conformation of poly(ethylene oxide) is predominantly gauche around the C-C bonds and trans around the C-O bonds. It turned out from model calculations that the experimentally found conformation, despite the fact that it has low statistical weight among the possible conformations because of its rather large dipole moment, is stabilized by the interaction with the solvent and, consequently, becomes highly populated. The increase in the temperature decreases the dielectric constant of the solvent, that is, the dipole moment of the water molecules and, consequently, their stabilization effect on the EO chains. Therefore the statistical weight of more hydrophobic conformers, which seem to be closer to the Gaussian conformation, increases. The temperaturedependent structural change observed in this work at higher concentrations (50 g/L and higher) is believed to correspond to the same phenomenon which was observed by Phillies et al.27 and characterized as coronal contraction and dehydration of the aggregates. The above findings suggest that the conformational change observed in solutions of PEO homopolymers and explained by the Karlstro¨m’s model plays an important role in the microstructure formation of PEO-type nonionic surfactants. Conclusions The time-averaged static picture of the equilibrium dynamic micelle formation obtained from small-angle neutron scattering allows depiction of the following structural evolution of aggregates in Brij-35 aqueous solutions. At low concentrations the micelles can be characterized by a spherical core with tethered polymer chains, conformation of which is close to a statistical random coil. The spherical core is filled by alkyl chains (50-60% of the core volume) and by hydrated poly(ethylene oxide) moieties. On average ca. 4% of each PEO chain is embedded in the core. The increase in the concentration induces an increase in the mean aggregation number, but the core radius increases only slightly. With increasing aggregation number there is not enough space for the attached bulky PEO chains; therefore they adopt a more streched conformation in comparison with the Gaussian one. At higher temperatures the more hydrophobic conformers of PEO chains are favored, which are in less contact with the solvent molecules, their dimension is smaller, and the conformation is closer to that of a statistical coil. The filling ratio of the core with alkyl and PEO chains remains unchanged. The intermicellar interaction reveals partial interpenetrability of the PEO corona. Acknowledgment. The support from the Hungarian National Research Fund Grant T 25747 is gratefully acknowledged. LA991265Y (44) Samii, A. A.; Lindman, B.; Karlstro¨m, G. Prog. Colloid Polym. Sci. 1990, 82, 280. (45) Karlstro¨m, G.; Carlsson, A.; Lindman, B. J. Phys. Chem. 1990, 94, 5005. (46) Viti, V.; Zampetti, P. Chem. Phys. 1973, 2, 233. (47) Viti, V.; Indovina, P. L.; Podo, F.; Radics, L.; Nemety, G. Mol. Phys. 1974, 27, 521. (48) Bailey, F. E.; Koleske, J. V. Poly(ethylene oxide); Academic Press: New York, 1976.
