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Small-angle neutron scattering studies on the size distribution of mixed micelles
ELSEVIER
Physica B 241 243 (1998) 993-995
Small-angle neutron scattering studies on the size distribution of mixed micelles T.-L. Lin a'*, Y. H u a, W.-C. Liu a, J. S a m s e t h b Department c?]'Engineering and System Science, National Tsing-Hua UniversiW, Hsin-Chu, 30043, Taiwan, ROC b lnstituttfor Energiteknikk, P.O. Box 40, N-2007, Kjeller, Norway
Abstract diC6PC and diCvPC mixed micelles are investigated by small-angle neutron scattering. The size distribution of the mixed micelles is determined from the SANS data by using the indirect transform method and is found to have only a single distribution peak. This indicates that the diC6PC and diCTPC do not segregate to form two size groups of micelles. The size distribution peak of these mixed micelles is also found to change from broad to narrow as the percentage of diC6PC is increased, indicative of changing from polydisperse rod-like micelles to globular micelles. ,i> 1998 Published by Elsevier Science B.V. All rights reserved. Kevwords." Small-angle neutron scattering; Mixed micelles; Indirect transform method
1. Introduction Mixed surfactant systems are widely used in many applications. Some mixed micellar systems have been studied by experiments [1]. However, the size distribution of the mixed micelles is seldom investigated experimentally. Here we are interested in studying the mixed dihexanoylphosphatidylcholine (diC6PC) and diheptanoylphosphatidylcholine (diC~PC) mixed micelles, diC6PC is known to form globular micelles while diCTPC forms polydisperse rod-like micelles in aqueous solutions [2,3]. Previously, we developed a thermodynamics theory for ideally mixed rod-like micelles and the theory is in good agreement with the dynamic light scattering *Corresponding author. Tel.: + 886 3 5742 671; fax: + 886 3 5728 445; e-maih [email protected].
results for the mixed diC6PC and diCTPC micelles [4]. However, it is more difficult to accurately determine the size distribution of the mixed micelles by dynamic light scattering. Combining the indirect transform method (ITM) and the small-angle scattering method [5], it is possible to determine the size distribution of mixed micelles.
2. Experimental section diC6PC and diCTPC were obtained from Avanti Biochemicals. Small-angle neutron scattering measurements were carried out at the Institutt for Energiteknikk, Kjeller Norway. The samples were kept at 25°C during the measurement. The measured neutron scattering intensities were corrected and normalized to obtain the normalized
0921-4526/98/$19.00 ~: 1998 Published by Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 7 7 7 1
T.-L. Lin el al. , Plo'sica B 241 243 (1998) 993 995
994
scattering intensity per unit sample volume, I(Q), in units of 1/cm. Here Q is the scattering vector.
3. The analysis of SANS data by the indirect transform method Here we will show briefly the method of analyzing the SANS data of mixed rod-like micelles by the indirect transform method to determine the size distribution [5]. The scattering intensities from polydisperse mixed rod-like micelles formed by surfactant 1 and surfactant 2 molecules can be given as
I(Q) = ~ c x l ( N ~ A p ~ V~ +
N2Ap2V2) 2
{1)
Here it is assumed that the mixing ratio within each micelle is the same in order to simplify the calculations. This is a reasonable assumption as long as surfactant 1 and surfactant 2 molecules have close similarities in their structures and scattering length densities. CN is the concentration of surfactants forming micelles with aggregation number N, where N = Nl + N2. P'(Q, R, L) is the normalized form factor of cylindrical rods with radius R and length L. Ap is the scattering length density difference between the surfactant molecule and the solvent. V is the volume of one surla, ctant molecule. CN can be expanded into n cubic B-spline functions 4,,.(N):
CN = ~ C,.~,.(N). v
{2}
1
Then, I(Q) can be written as It
I(Q) = ~ C,.T,.[Q), v
(3)
1
where
1 ~P,.(Q) = ~ 4,,.(N)~ [Xlap1V 1 -}-
N2Ap2V2) 2
N
x P'{Q, R, L}.
(4)
The coefficient C,. can be determined by minimizing
[l(Qi)
c, 7*,,(Qi)]2 -a2(Qi)
i=1
v=l tl
1
+ l~ ~ It,.+, - C,t 2. r-1
P'(Q, R, L).
4. Results and discussion
N
x P'~,(Q, R, L).
Here a{Qi) is the statistical uncertainty associated with each scattering intensity l(Qi) and fl is a stabilizing parameter. The ratio of aggregation number N to its rod length L is denoted as and the radius of gyration across the cross-sectional area of the rod-like micelles is denoted as R~. Both ~ and R~ can be determined by plotting ln(I(QIQ 2) versus Q2 or by estimation. The radius of the rod-like micelles R can be related to R~ by R = Rex:"2. R and L are needed in computing
15)
Fig. 1 shows the SANS spectra of the mixed diC~,PC and diCTPC micelles at different diCAPC diCTPC concentration ratios. The total surfactant concentration is 25 mM for each sample. The scattering intensity decreases with the increase of diCAPC concentration percentage. Since the total concentration is the same, the decrease in scattering intensity implies that the mixed micelles become smaller when diCTPC molecules are replaced by diC~,PC molecules. For samples with high percentage of diCvPC, the scattering intensity decreases rapidly with increasing scattering vector Q. This is typical for a system containing long rod-like particles. As the concentration percentage of diC,,PC is increased, the scattering intensity decreases slowly with increasing scattering vector Q, which is typical for short rods, or globular particles. it can be inferred that the mixed micelles change gradually from long rods to short rods or globular particles. Fig. 2 shows the size distribution of the mixed micelles as determined by ITM. The scattering intensities corresponding to the recovered size distributions are plotted in Fig. 1 and they fit the SANS data very well. All the size distributions have a distribution peak, indicating that diCAPC and diCvPC do not segregate in the mixed system. The size distribution becomes less broad as the percentage of diCAPC increases. The point separating the broad-size distribution cases to the narrow-size distribution cases is estimated to be around 40-50% diC~,PC.
T.-L. Lin et al. Physica B 241 243 (1998) 993 995
o
995
C6/C7 = 0/25 C6/C7 = 5/20
[3
C6/C7 = 12.5/12.5
A
C6/C7 = 20/5
v
C6/C7 = 25/0
A
0
0.05
0.1
0.15
0.2
o (l/A) Fig. 1. The measured small-angle neutron scattering intensity distribution for the mixed diCrPC and diCTPC micellar solutions at a total concentration of 25 raM. The curves fitted by indirect transform method are also shown.
Acknowledgements
4.0xlO 16
--C6/C7--0/25 ] --C6/C7=5/20 / ........C6/C7= 12.5/12.5/ ....C6/C7=20/5 1 ....C6/C7=25/0 /
,,--., tw3
3.0xlO 16
This work was supported by the National Science Council of ROC, grant NSC 86-2113-M007-026. We would also like to thank the Institutt for Energiteknikk for using its SANS spectrometer.
!J!i,~ i~ '~',
"~ 2.0x1016
References ~
- ,...t
1.0x1016
i
i '~
[1] H. Pilsl, H.
..... = 7 , 7
O.OxlOo
. . . . . . . . . . .
,
0
[2] 20
40
60
80
100
120
aggregation number Fig. 2. The size distributions of the mixed micelles, determined by the indirect transform method from the SANS data, are plotted as a function of aggregation number.
[3] [4] [5]
Hoffmann, S. Hoffmann, J. Kalus, A.W.
Kencono, P. lander, W. Ulbricht, J. Phys. Chem. 97 (1993) 2745. T.-L. Lin, S.H. Chen, N.E. Gabriel, M.F. Roberts, J. Am. Chem. Soc. 108 (1986) 3499. T.-L. Lin, S.H. Chen, N.E. Gabriel, M.F. Roberts, J. Phys. Chem. 91 (1987) 406. T.-L. Lin, Y. Hu, W.-J. Liu, Langmuir 13 (1997) 1422. T.-L. Lin, C.S. Tsao, J. Appl. Crystallogr. 29 t1996) 170.
Physica B 241 243 (1998) 993-995
Small-angle neutron scattering studies on the size distribution of mixed micelles T.-L. Lin a'*, Y. H u a, W.-C. Liu a, J. S a m s e t h b Department c?]'Engineering and System Science, National Tsing-Hua UniversiW, Hsin-Chu, 30043, Taiwan, ROC b lnstituttfor Energiteknikk, P.O. Box 40, N-2007, Kjeller, Norway
Abstract diC6PC and diCvPC mixed micelles are investigated by small-angle neutron scattering. The size distribution of the mixed micelles is determined from the SANS data by using the indirect transform method and is found to have only a single distribution peak. This indicates that the diC6PC and diCTPC do not segregate to form two size groups of micelles. The size distribution peak of these mixed micelles is also found to change from broad to narrow as the percentage of diC6PC is increased, indicative of changing from polydisperse rod-like micelles to globular micelles. ,i> 1998 Published by Elsevier Science B.V. All rights reserved. Kevwords." Small-angle neutron scattering; Mixed micelles; Indirect transform method
1. Introduction Mixed surfactant systems are widely used in many applications. Some mixed micellar systems have been studied by experiments [1]. However, the size distribution of the mixed micelles is seldom investigated experimentally. Here we are interested in studying the mixed dihexanoylphosphatidylcholine (diC6PC) and diheptanoylphosphatidylcholine (diC~PC) mixed micelles, diC6PC is known to form globular micelles while diCTPC forms polydisperse rod-like micelles in aqueous solutions [2,3]. Previously, we developed a thermodynamics theory for ideally mixed rod-like micelles and the theory is in good agreement with the dynamic light scattering *Corresponding author. Tel.: + 886 3 5742 671; fax: + 886 3 5728 445; e-maih [email protected].
results for the mixed diC6PC and diCTPC micelles [4]. However, it is more difficult to accurately determine the size distribution of the mixed micelles by dynamic light scattering. Combining the indirect transform method (ITM) and the small-angle scattering method [5], it is possible to determine the size distribution of mixed micelles.
2. Experimental section diC6PC and diCTPC were obtained from Avanti Biochemicals. Small-angle neutron scattering measurements were carried out at the Institutt for Energiteknikk, Kjeller Norway. The samples were kept at 25°C during the measurement. The measured neutron scattering intensities were corrected and normalized to obtain the normalized
0921-4526/98/$19.00 ~: 1998 Published by Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 7 7 7 1
T.-L. Lin el al. , Plo'sica B 241 243 (1998) 993 995
994
scattering intensity per unit sample volume, I(Q), in units of 1/cm. Here Q is the scattering vector.
3. The analysis of SANS data by the indirect transform method Here we will show briefly the method of analyzing the SANS data of mixed rod-like micelles by the indirect transform method to determine the size distribution [5]. The scattering intensities from polydisperse mixed rod-like micelles formed by surfactant 1 and surfactant 2 molecules can be given as
I(Q) = ~ c x l ( N ~ A p ~ V~ +
N2Ap2V2) 2
{1)
Here it is assumed that the mixing ratio within each micelle is the same in order to simplify the calculations. This is a reasonable assumption as long as surfactant 1 and surfactant 2 molecules have close similarities in their structures and scattering length densities. CN is the concentration of surfactants forming micelles with aggregation number N, where N = Nl + N2. P'(Q, R, L) is the normalized form factor of cylindrical rods with radius R and length L. Ap is the scattering length density difference between the surfactant molecule and the solvent. V is the volume of one surla, ctant molecule. CN can be expanded into n cubic B-spline functions 4,,.(N):
CN = ~ C,.~,.(N). v
{2}
1
Then, I(Q) can be written as It
I(Q) = ~ C,.T,.[Q), v
(3)
1
where
1 ~P,.(Q) = ~ 4,,.(N)~ [Xlap1V 1 -}-
N2Ap2V2) 2
N
x P'{Q, R, L}.
(4)
The coefficient C,. can be determined by minimizing
[l(Qi)
c, 7*,,(Qi)]2 -a2(Qi)
i=1
v=l tl
1
+ l~ ~ It,.+, - C,t 2. r-1
P'(Q, R, L).
4. Results and discussion
N
x P'~,(Q, R, L).
Here a{Qi) is the statistical uncertainty associated with each scattering intensity l(Qi) and fl is a stabilizing parameter. The ratio of aggregation number N to its rod length L is denoted as and the radius of gyration across the cross-sectional area of the rod-like micelles is denoted as R~. Both ~ and R~ can be determined by plotting ln(I(QIQ 2) versus Q2 or by estimation. The radius of the rod-like micelles R can be related to R~ by R = Rex:"2. R and L are needed in computing
15)
Fig. 1 shows the SANS spectra of the mixed diC~,PC and diCTPC micelles at different diCAPC diCTPC concentration ratios. The total surfactant concentration is 25 mM for each sample. The scattering intensity decreases with the increase of diCAPC concentration percentage. Since the total concentration is the same, the decrease in scattering intensity implies that the mixed micelles become smaller when diCTPC molecules are replaced by diC~,PC molecules. For samples with high percentage of diCvPC, the scattering intensity decreases rapidly with increasing scattering vector Q. This is typical for a system containing long rod-like particles. As the concentration percentage of diC,,PC is increased, the scattering intensity decreases slowly with increasing scattering vector Q, which is typical for short rods, or globular particles. it can be inferred that the mixed micelles change gradually from long rods to short rods or globular particles. Fig. 2 shows the size distribution of the mixed micelles as determined by ITM. The scattering intensities corresponding to the recovered size distributions are plotted in Fig. 1 and they fit the SANS data very well. All the size distributions have a distribution peak, indicating that diCAPC and diCvPC do not segregate in the mixed system. The size distribution becomes less broad as the percentage of diCAPC increases. The point separating the broad-size distribution cases to the narrow-size distribution cases is estimated to be around 40-50% diC~,PC.
T.-L. Lin et al. Physica B 241 243 (1998) 993 995
o
995
C6/C7 = 0/25 C6/C7 = 5/20
[3
C6/C7 = 12.5/12.5
A
C6/C7 = 20/5
v
C6/C7 = 25/0
A
0
0.05
0.1
0.15
0.2
o (l/A) Fig. 1. The measured small-angle neutron scattering intensity distribution for the mixed diCrPC and diCTPC micellar solutions at a total concentration of 25 raM. The curves fitted by indirect transform method are also shown.
Acknowledgements
4.0xlO 16
--C6/C7--0/25 ] --C6/C7=5/20 / ........C6/C7= 12.5/12.5/ ....C6/C7=20/5 1 ....C6/C7=25/0 /
,,--., tw3
3.0xlO 16
This work was supported by the National Science Council of ROC, grant NSC 86-2113-M007-026. We would also like to thank the Institutt for Energiteknikk for using its SANS spectrometer.
!J!i,~ i~ '~',
"~ 2.0x1016
References ~
- ,...t
1.0x1016
i
i '~
[1] H. Pilsl, H.
..... = 7 , 7
O.OxlOo
. . . . . . . . . . .
,
0
[2] 20
40
60
80
100
120
aggregation number Fig. 2. The size distributions of the mixed micelles, determined by the indirect transform method from the SANS data, are plotted as a function of aggregation number.
[3] [4] [5]
Hoffmann, S. Hoffmann, J. Kalus, A.W.
Kencono, P. lander, W. Ulbricht, J. Phys. Chem. 97 (1993) 2745. T.-L. Lin, S.H. Chen, N.E. Gabriel, M.F. Roberts, J. Am. Chem. Soc. 108 (1986) 3499. T.-L. Lin, S.H. Chen, N.E. Gabriel, M.F. Roberts, J. Phys. Chem. 91 (1987) 406. T.-L. Lin, Y. Hu, W.-J. Liu, Langmuir 13 (1997) 1422. T.-L. Lin, C.S. Tsao, J. Appl. Crystallogr. 29 t1996) 170.