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Small-angle neutron scattering study of sodium hexadecyl sulfate surfactant solutions
Physica B 180 & 181 (1992) North-Holland
PHYSICA 1
519-521
Small-angle neutron scattering study of sodium hexadecyl sulfate surfactant solutions L. Cser”, Sz. Vass”, V.Yu. Bezzabotnov’
S. Borbkly”,
and Yu.M.
Ostanevichh
“Central Research Institute for Physics, H-1525 Budapest 114, P. 0. B. 49, Hungary “Joint Institute for Nuclear Research. 101OOOMoscow, Head POSI O#ice. P.O. B. 79, USSR
The micelle formation in aqueous sodium hexadecyl sulfate solutions is studied by small-angle neutron scattering technique. Measurements are carried out at different concentrations (1.1. 2.2, 3.2, 5.4, 10.9 and 32.8 mM/dm’) and at different temperatures (40, 50 and 60 “C). The monotonous evolution of the interparticle correlation can be observed on the measured scattering patterns. At high concentrations (10.9 and 32.8 mM/dm’) scattering patterns are described by interacting ellipsoids. At low concentrations a satisfactory fit can not be obtained by a simple form factor model. The computation of the distance distribution function proved the ellipsoidal shape at 10.9 and 32.8 mM/dm’, but showed an unexpectedly large particle dimension and structurization of the particle at lower concentrations. An assumption is made on the phase transition in the concentration range studied.
1. Introduction In the last decade small-angle neutron scattering (SANS) has been widely used to investigate the structure of micelles and micellar solutions [ 1,2]. It is due to the possibility of treating scattering patterns arising from both nonionic and ionic micellar solutions. The latter reveals strong interparticle correlation. Because of the dynamic nature of the micelle formation. intermicellar interaction can be eliminated only mathematically in a least-squares fitting procedure but not experimentally (extrapolation to zero concentration as in the case of proteins or other objects). There are two approaches of obtaining structural information from the small angle scattering curves. The first one attributes a definite shape to the particles investigated and fits the appropriate form factor to the scattered intensity pattern. In this procedure one can introduce the effect of interparticle interaction as well [3]. The second approach relates the scattered intensity to p(r), the distance distribution function of the particles [4]. The p(r) function. which bears the structural information can be calculated by inverse Fourier transformation of the experimental scattering curves. 2. Experimental Sodium hexadecyl sulfate surfactant solutions of different concentrations (from 1.1 to 32.8 mM/dm’) were prepared using 99.8% isotope purity D,O. The SANS measurements on these solutions were performed on the time-of-flight SANS spectrometer with axial symmetric geometry installed at the IBR-2 pulsed reactor (Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, USSR). Samples were contained in quartz cells of 1 mm window thickness and 1 or 2 mm neutron path length required 0021.4S26/02/$05.00
0
1992 - Elsevier
by the concentration. The measurements were carried out at 40, 50 and 60 “C. During the exposure the samples were thermostated to &OS “C in the sample holder from an external bath. The sample-to-detector distance was 9.1 m, which covered a q-range from 0.02 to 0.3 A-’ considering the detector dimension and wavelength range of the white beam used. The averaged thermal neutron flux on the sample was 1 X 10’ cm ’ s- ‘_ Raw data were corrected for dead time, absorption, solvent scattering and for incoherent scattering from the solute. All measurements were converted to absolutely scaled cross-section (dB/dR) using a vanadium foil as standard incoherent scatterer [51. 3. Results and discussion The measured scattering patterns show structurization of the solution with increasing concentration (fig. 1). The curves obtained at the lower concentrations (1.1, 2.2, 3.2, 5.4 mM/dm’) look like those characteristic for noninteracting scatterers, but at higher concentrations (10.9, 32.8 mM/dm’) a well pronounced interaction peak appears on the scattering patterns. Therefore, it was expected that curves obtained at the lower concentrations can be modelled simply by a spheroidal form factor, while at higher concentrations one has to take into consideration the interparticle correlation, that is. one has to add a structure factor S(q) to the fitting procedure. The following model has been used to describe the particle form factor. A nonwetted hydrocarbon core was defined containing a certain part of the hydrocarbon chain. Y = (n)&+
Science Publishers B.V. All rights reserved
+ P(l-
I)VcXZ} 3
(1)
S. BorbZly et al. I SANS study of kexadecyl sulfate solutions
520
q(A-‘) Fig. I. Measured
at 40 “C (symbols) and fitted using ellip(solid line) scattering curves for 32.8( * ), 10.9(O), 5.4(M) and 3.2(A) mM/dm’ solutions.
siodal
shape
model
where (n) is the mean aggregation number, p is the portion of chain embedded in the nonwetted core, 1 is the number of carbon atoms in the chain. VcH, and “W are the volumes of the CH, and CH, groups, respectively. The volume of the whole micelle was calculated by eq. (2):
r/;,= (n)[(l + (1
- 0x1 - W,.H2 + Y,g + %gY - cr)(V,, + w,,V,)] + v, 1
(2)
where cr is the effective fractional charge of micelles, V, is the volume of a solvent molecule, V,,, and V,, are the volumes, whg and w,, are the hydration number of head groups and counterions, respectively. The volumes and hydration numbers used were taken from refs. [6,7]. The form factor of a two-shell ellipsoid was computed with the core and micelle volumes defined above [2]. At higher concentrations (scattering curves with peak) computation of the intermicellar structure Table 1 The best fit parameters
and xL for sodium
hexadecyl
sulfate
factor S(q) was introduced into the least-squares htting procedure, using the “One Component Macrofluid” model proposed by Hayter and Penfold [8-IO]. The mean aggregation number (n), the fractional charge LY,the extent of water penetration p. the ratio of axes [. a scaling factor A and a residual background term B were the free parameters. This model allows micelles to have spherical, prolate or oblate ellipsoidal shape depending on the value of [. It was expected that the micelle shape evolutes from a sphere (just above the CMC which is equal to 0.586mMidm’) to an ellipsoid (at higher concentrations), as well as the aggregation number increases with increasing concentration and decreases with increasing temperature as in the case of shorter chain length alkyl sulfates from octyl to dodecyl [ll]. This simple expectation was not proved by the results of the fit. At low concentrations (from 1.1 to 5.4 mM/dm’) the fit was very poor (x’ = 5-10) and the aggregation numbers and axial ratios were surprisingly large. Therefore, we do not present here these unreliable parameters. At higher concentrations (10.9 and 32.X mM/dm’) parameters followed the expected trends and the fit was acceptable. The best fit parameters and xL are shown in table 1. Because of the unexpected aggregation behaviour of the surfactant system investigated we have tried to clarify its structural features using the second approach mentioned above; that is we computed the distance distribution function p(v) from the measured scattering curves (after correction for the fitted S( 4) at high concentrations). The Glatter’s program, which is based on the “Indirect Fourier Transformation” method was used to carry out these computations [12. 13). The p(r) functions obtained from measurements carried out at 4O”C, and normalized to their maximum value are shown in fig. 2. At 32.8mMidm’ p(r) is slightly asymmetric (fig. 3) and the maximum particle dimension is equal to that calculated from the best fit parameters. It is the same for 10.9mMidm.‘. but in this case the p(r) function became slightly structurized. At lower concentrations the maximum dimension is much larger and the course of p(r) differs from that of the known simple shaped particles [14]. The fitted
micellar
solutions
of different
concentrations
at different
temperatures.
TCl
(n)
a
P
i
A
10.9 10.9
40 SO
118.6 + 3.8 110.7 2 3.9
0.18 + 0.04 0.18 ‘- 0.04
0.53 + 0.07 0.62 + 0.08
1.40 t 0.16 1.44 -t 0.17
0.87 t 0.02 0.84 f 0.02
10.9
60
Y8.65 t- 3.2
0.19 t 0.03
0.49 i 0.07
1.45 kO.15
0.88 t 0.02
1.93 2.38
32.X 32.8 32.8
40 SO 60
139.4 + 1.0 130.4 t I .o 111.9+0.9
0.16 k 0.01 0.17 i- 0.01 0.18 k 0.01
0.84 2 0.03 0.73 t 0.03 0.59? 0.02
1.60 + 0.03 1.58 t 0.04 I .s3 2 0.04
0.80 t 0.01 0.83 t 0.01 0.87 t 0.01
2.44 1.47 1.93
Concentration
X2
[mM/dm’] 2.27
521
S. Borbely et al. I SANS study of hexadecyl sulfate solutions
01
0.2
0.3
qW1)
r(A) Fig. 2. Distance distribution functions for aggregates in 32.8(*), 10.9(O), 5.4(U), 3.2(O), 2.2(A) and 1.1(W) mM/ dm’ solutions. Measurements were carried out at 40°C.
Fig. 4. Measured at 40 “C (symbols) and fitted using the p(r) functions (solid line) scattering curves for 32.8( *), 10.9(O),
5.4(O), 3.2(O) and 2.2(A) mMidm3 solutions. tration behaviour of the aggregation process may be due to a phase transition in the concentration range studied. To clarify this hypothesis one needs to carry out more accurate measurements or/and extend investigation by using other techniques.
0” “i
-1
References [II S.H. Chen,
r(A)
Fig. 3. P(r) functions for aggregates in 32.8mMidm’ tion at 40(*), 50(O) and 60(m) “C.
solu-
(on the basis of p(r) function) and measured scattering curves are shown in fig. 4. The x2 obtained are close to unity (0.9-1.3) at all concentrations; this means that the quality of the fit using the p(r) is much better than that with the form factor model. It means that the distance distribution function reflects correctly the information content of the measured scattering curves. The discrepancy between the low and high concen-
Ann. Rev. Phys. Chem. 37 (1986) 351. [21 L.J. Magid, Colloids and Surfaces 19 (1986) 129. and J. Penfold. J. Chem. Sot. Faraday [31 J.B. Hayter Trans. 1, 77 (1981) 1851. in: Small Angle X-ray Scattering, eds. 0. [41 0. Glatter, Glatter and 0. Kratky (Academic Press, London, 1982) p. 130. Yu.M. Ostanevich and [51 V.A Vagov, A.B. Kunchenko, I.M. Salamatin, JINR Report (1983) P14-83/898 Dubna. L61 J.B. Hayter and J. Penfold, Colloid Polymer Sci. 261 (1983) 1022. [71 S.S. Berr, M.J. Coleman, R.R. Marriott Jones and J.S. Johnson, J. Phys. Chem. 90 (1986) 6492. M J.B. Hayter and J. Penfold, Mol. Phys. 42 (1981) 109. L91 J.P. Hansen and J.B. Hayter, Mol. Phys. 46 (1982) 651. ILL Internal Scientific [lOI J.B. Hayter and J.P. Hansen, Report (1982) 82HA14T Grenoble. 1111 L. Cser, Gy. Jbkli, Zs. Kajcsos, Sz. Vass, S. BorbCly, V.Yu. Bezzabotnov, Yu.M. Ostanevich, E. Juhasz and M. Lelkes, in: Surfactants in Solution, Vol. 7, ed. K.L. Mittal (Plenum Press, New York, 1989) p. 197. [12] 0. Glatter, J. Appl. Crystallogr. 10 (1977) 415. [13] 0. Glatter. J. Appl. Crystallogr. 12 (1979) 166. [14] 0. Glatter, in: Small Angle X-ray Scattering. eds. 0. Glatter and 0. Kratky (Academic Press, London, 1982) p. 167.
PHYSICA 1
519-521
Small-angle neutron scattering study of sodium hexadecyl sulfate surfactant solutions L. Cser”, Sz. Vass”, V.Yu. Bezzabotnov’
S. Borbkly”,
and Yu.M.
Ostanevichh
“Central Research Institute for Physics, H-1525 Budapest 114, P. 0. B. 49, Hungary “Joint Institute for Nuclear Research. 101OOOMoscow, Head POSI O#ice. P.O. B. 79, USSR
The micelle formation in aqueous sodium hexadecyl sulfate solutions is studied by small-angle neutron scattering technique. Measurements are carried out at different concentrations (1.1. 2.2, 3.2, 5.4, 10.9 and 32.8 mM/dm’) and at different temperatures (40, 50 and 60 “C). The monotonous evolution of the interparticle correlation can be observed on the measured scattering patterns. At high concentrations (10.9 and 32.8 mM/dm’) scattering patterns are described by interacting ellipsoids. At low concentrations a satisfactory fit can not be obtained by a simple form factor model. The computation of the distance distribution function proved the ellipsoidal shape at 10.9 and 32.8 mM/dm’, but showed an unexpectedly large particle dimension and structurization of the particle at lower concentrations. An assumption is made on the phase transition in the concentration range studied.
1. Introduction In the last decade small-angle neutron scattering (SANS) has been widely used to investigate the structure of micelles and micellar solutions [ 1,2]. It is due to the possibility of treating scattering patterns arising from both nonionic and ionic micellar solutions. The latter reveals strong interparticle correlation. Because of the dynamic nature of the micelle formation. intermicellar interaction can be eliminated only mathematically in a least-squares fitting procedure but not experimentally (extrapolation to zero concentration as in the case of proteins or other objects). There are two approaches of obtaining structural information from the small angle scattering curves. The first one attributes a definite shape to the particles investigated and fits the appropriate form factor to the scattered intensity pattern. In this procedure one can introduce the effect of interparticle interaction as well [3]. The second approach relates the scattered intensity to p(r), the distance distribution function of the particles [4]. The p(r) function. which bears the structural information can be calculated by inverse Fourier transformation of the experimental scattering curves. 2. Experimental Sodium hexadecyl sulfate surfactant solutions of different concentrations (from 1.1 to 32.8 mM/dm’) were prepared using 99.8% isotope purity D,O. The SANS measurements on these solutions were performed on the time-of-flight SANS spectrometer with axial symmetric geometry installed at the IBR-2 pulsed reactor (Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, USSR). Samples were contained in quartz cells of 1 mm window thickness and 1 or 2 mm neutron path length required 0021.4S26/02/$05.00
0
1992 - Elsevier
by the concentration. The measurements were carried out at 40, 50 and 60 “C. During the exposure the samples were thermostated to &OS “C in the sample holder from an external bath. The sample-to-detector distance was 9.1 m, which covered a q-range from 0.02 to 0.3 A-’ considering the detector dimension and wavelength range of the white beam used. The averaged thermal neutron flux on the sample was 1 X 10’ cm ’ s- ‘_ Raw data were corrected for dead time, absorption, solvent scattering and for incoherent scattering from the solute. All measurements were converted to absolutely scaled cross-section (dB/dR) using a vanadium foil as standard incoherent scatterer [51. 3. Results and discussion The measured scattering patterns show structurization of the solution with increasing concentration (fig. 1). The curves obtained at the lower concentrations (1.1, 2.2, 3.2, 5.4 mM/dm’) look like those characteristic for noninteracting scatterers, but at higher concentrations (10.9, 32.8 mM/dm’) a well pronounced interaction peak appears on the scattering patterns. Therefore, it was expected that curves obtained at the lower concentrations can be modelled simply by a spheroidal form factor, while at higher concentrations one has to take into consideration the interparticle correlation, that is. one has to add a structure factor S(q) to the fitting procedure. The following model has been used to describe the particle form factor. A nonwetted hydrocarbon core was defined containing a certain part of the hydrocarbon chain. Y = (n)&+
Science Publishers B.V. All rights reserved
+ P(l-
I)VcXZ} 3
(1)
S. BorbZly et al. I SANS study of kexadecyl sulfate solutions
520
q(A-‘) Fig. I. Measured
at 40 “C (symbols) and fitted using ellip(solid line) scattering curves for 32.8( * ), 10.9(O), 5.4(M) and 3.2(A) mM/dm’ solutions.
siodal
shape
model
where (n) is the mean aggregation number, p is the portion of chain embedded in the nonwetted core, 1 is the number of carbon atoms in the chain. VcH, and “W are the volumes of the CH, and CH, groups, respectively. The volume of the whole micelle was calculated by eq. (2):
r/;,= (n)[(l + (1
- 0x1 - W,.H2 + Y,g + %gY - cr)(V,, + w,,V,)] + v, 1
(2)
where cr is the effective fractional charge of micelles, V, is the volume of a solvent molecule, V,,, and V,, are the volumes, whg and w,, are the hydration number of head groups and counterions, respectively. The volumes and hydration numbers used were taken from refs. [6,7]. The form factor of a two-shell ellipsoid was computed with the core and micelle volumes defined above [2]. At higher concentrations (scattering curves with peak) computation of the intermicellar structure Table 1 The best fit parameters
and xL for sodium
hexadecyl
sulfate
factor S(q) was introduced into the least-squares htting procedure, using the “One Component Macrofluid” model proposed by Hayter and Penfold [8-IO]. The mean aggregation number (n), the fractional charge LY,the extent of water penetration p. the ratio of axes [. a scaling factor A and a residual background term B were the free parameters. This model allows micelles to have spherical, prolate or oblate ellipsoidal shape depending on the value of [. It was expected that the micelle shape evolutes from a sphere (just above the CMC which is equal to 0.586mMidm’) to an ellipsoid (at higher concentrations), as well as the aggregation number increases with increasing concentration and decreases with increasing temperature as in the case of shorter chain length alkyl sulfates from octyl to dodecyl [ll]. This simple expectation was not proved by the results of the fit. At low concentrations (from 1.1 to 5.4 mM/dm’) the fit was very poor (x’ = 5-10) and the aggregation numbers and axial ratios were surprisingly large. Therefore, we do not present here these unreliable parameters. At higher concentrations (10.9 and 32.X mM/dm’) parameters followed the expected trends and the fit was acceptable. The best fit parameters and xL are shown in table 1. Because of the unexpected aggregation behaviour of the surfactant system investigated we have tried to clarify its structural features using the second approach mentioned above; that is we computed the distance distribution function p(v) from the measured scattering curves (after correction for the fitted S( 4) at high concentrations). The Glatter’s program, which is based on the “Indirect Fourier Transformation” method was used to carry out these computations [12. 13). The p(r) functions obtained from measurements carried out at 4O”C, and normalized to their maximum value are shown in fig. 2. At 32.8mMidm’ p(r) is slightly asymmetric (fig. 3) and the maximum particle dimension is equal to that calculated from the best fit parameters. It is the same for 10.9mMidm.‘. but in this case the p(r) function became slightly structurized. At lower concentrations the maximum dimension is much larger and the course of p(r) differs from that of the known simple shaped particles [14]. The fitted
micellar
solutions
of different
concentrations
at different
temperatures.
TCl
(n)
a
P
i
A
10.9 10.9
40 SO
118.6 + 3.8 110.7 2 3.9
0.18 + 0.04 0.18 ‘- 0.04
0.53 + 0.07 0.62 + 0.08
1.40 t 0.16 1.44 -t 0.17
0.87 t 0.02 0.84 f 0.02
10.9
60
Y8.65 t- 3.2
0.19 t 0.03
0.49 i 0.07
1.45 kO.15
0.88 t 0.02
1.93 2.38
32.X 32.8 32.8
40 SO 60
139.4 + 1.0 130.4 t I .o 111.9+0.9
0.16 k 0.01 0.17 i- 0.01 0.18 k 0.01
0.84 2 0.03 0.73 t 0.03 0.59? 0.02
1.60 + 0.03 1.58 t 0.04 I .s3 2 0.04
0.80 t 0.01 0.83 t 0.01 0.87 t 0.01
2.44 1.47 1.93
Concentration
X2
[mM/dm’] 2.27
521
S. Borbely et al. I SANS study of hexadecyl sulfate solutions
01
0.2
0.3
qW1)
r(A) Fig. 2. Distance distribution functions for aggregates in 32.8(*), 10.9(O), 5.4(U), 3.2(O), 2.2(A) and 1.1(W) mM/ dm’ solutions. Measurements were carried out at 40°C.
Fig. 4. Measured at 40 “C (symbols) and fitted using the p(r) functions (solid line) scattering curves for 32.8( *), 10.9(O),
5.4(O), 3.2(O) and 2.2(A) mMidm3 solutions. tration behaviour of the aggregation process may be due to a phase transition in the concentration range studied. To clarify this hypothesis one needs to carry out more accurate measurements or/and extend investigation by using other techniques.
0” “i
-1
References [II S.H. Chen,
r(A)
Fig. 3. P(r) functions for aggregates in 32.8mMidm’ tion at 40(*), 50(O) and 60(m) “C.
solu-
(on the basis of p(r) function) and measured scattering curves are shown in fig. 4. The x2 obtained are close to unity (0.9-1.3) at all concentrations; this means that the quality of the fit using the p(r) is much better than that with the form factor model. It means that the distance distribution function reflects correctly the information content of the measured scattering curves. The discrepancy between the low and high concen-
Ann. Rev. Phys. Chem. 37 (1986) 351. [21 L.J. Magid, Colloids and Surfaces 19 (1986) 129. and J. Penfold. J. Chem. Sot. Faraday [31 J.B. Hayter Trans. 1, 77 (1981) 1851. in: Small Angle X-ray Scattering, eds. 0. [41 0. Glatter, Glatter and 0. Kratky (Academic Press, London, 1982) p. 130. Yu.M. Ostanevich and [51 V.A Vagov, A.B. Kunchenko, I.M. Salamatin, JINR Report (1983) P14-83/898 Dubna. L61 J.B. Hayter and J. Penfold, Colloid Polymer Sci. 261 (1983) 1022. [71 S.S. Berr, M.J. Coleman, R.R. Marriott Jones and J.S. Johnson, J. Phys. Chem. 90 (1986) 6492. M J.B. Hayter and J. Penfold, Mol. Phys. 42 (1981) 109. L91 J.P. Hansen and J.B. Hayter, Mol. Phys. 46 (1982) 651. ILL Internal Scientific [lOI J.B. Hayter and J.P. Hansen, Report (1982) 82HA14T Grenoble. 1111 L. Cser, Gy. Jbkli, Zs. Kajcsos, Sz. Vass, S. BorbCly, V.Yu. Bezzabotnov, Yu.M. Ostanevich, E. Juhasz and M. Lelkes, in: Surfactants in Solution, Vol. 7, ed. K.L. Mittal (Plenum Press, New York, 1989) p. 197. [12] 0. Glatter, J. Appl. Crystallogr. 10 (1977) 415. [13] 0. Glatter. J. Appl. Crystallogr. 12 (1979) 166. [14] 0. Glatter, in: Small Angle X-ray Scattering. eds. 0. Glatter and 0. Kratky (Academic Press, London, 1982) p. 167.