J. Phys. Chem. 1993,97, 1114-1118
1114
The Internal Structure of a Rodlike Micelle L. Herbst, J. Kalus,' and U. Schmelzer Experimentalphysik Z, Uniuersitiit Bayreuth, Bayreuth, Federal Republic of Germany 95440 Received: April 14, I993
Small-angle neutron scattering (SANS) measurements have been carried out on an aqueous solution of cetylpyridinium salicylate (CPS). The internal structure of the rodlike micelles was determined by the method of external and internal contrast variation. A one-shell model was able to explain all scattering curves.
1. Introduction
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A
In previous small-angleneutron scattering (SANS) studies on aqueous solutions of cetylpyridinium salicylate (CPS, C16H33(NC,Hs)+(CaH40HC02)-), we could show that cylindrical micelles are formed in this system.1-6 In many other systems, micelles of this type are present, For CPS, all measurements could be explained by assuming
that,abovethecriticalmicellarconcentration(cmc) of0.15 mM/L at ambient temperature,rodlike aggregateswere built. The radius R of these rods turned out to be 2.15 f 0.02 nm and depends within the quoted error margins not on the CPS concentration.2 The radius was determined assuming cylindrical, long rods with a homogeneous scattering length density p inside the micelles. The length 1 of the micelle is much longer than R . 1 depends strongly on CPS concentration and an accurate determination was not possible, because of the appearance of a correlation peak in the scattering curve at small Q values. Q is the momentum transfer of the scatterd neutrons and is related to the scattering angle 29 and the wavelength X of the neutrons via Q = ( 4 sin ~ q)/X. Only for a solution with low concentration (3 mM/L) the correlation peak was not present. In this case, a length 1 of -32 nm was quoted.' For higher concentrationsthe length increases. The SANS intensityZ(Q) of an isotropic solution can be written as
(P) is the mean squared form factor of the micelle and S(Q) is the structure factor. S(Q) is related to the interaction between the micelles and describes the correlation peak mentioned above. Unfortunately, no simple theory exists for the calculationof S(Q) for a liquid with rodlike aggregates. Therefore, throughout this paper, fits for the evaluation of the radius R or the internal structure were made always at high Qvalues, where the structure factor S(Q) is equal to 1. For the convenience of the reader we show a plot of In (ZQ) against Q2 as dashed curve for the CPS sample in Figure 6, showing a rather good agreement between measured and fitted values using a constant scattering length density p inside the micelle. This agreement has its origin basically in the fact that the solvent was D2O. Then in CPS the contrast Ap, which is the difference of the scattering length density p s of D20 and the scattering length density p of the micelle, is large. Even if there is still some variation of p within the micelle the scattering curve is not much influenced. Nevertheless, the assumption of a constant scattering length density inside the micelle seems to be oversimplified. Therefore,we started contrast variation measurements to get more insight into the internal structure of the micelles. 0022-3654/93/2091-1114~04.00/0
6
--
4
--
2 0
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IOOX D,O
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70% D,Q
-SOX D,O ___p,=_ _ 1.47 10'Ocm-l _ _ _ _ _ ___ _D,O_ _ _ _ - - - . 30% --
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15% D,O OX D,O
core 4
shell 1
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Internal Structure of a Rodlike Micelle
The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7775
-15
0
1
2
3
L
Q'l n m' Figure4. Same as Figure 2, but for partly deuterated CPDSD.The Dz0 content of the solution was (from top to bottom and at Q2 = 2 n m 2 ) 10096, 70%, 5046, 40%, 301,and 0%.
Besides the method of external contrast variation, described above, the internal contrast variation is an other useful method. In that case isotopic substitutionof atoms of the micellarmolecules is performed. We used both methods. Figure 2. Scattering intensities for contrast variation experimentson a 20 mM solution of CPS in water. The DzO content of the solution was (from top to bottom) loo%,70%, 50%, 30%, 0% (2), 10%(3,and 15% (8). The numbers in the parenthesis indicate the number of units the
curves are shifted down with respect to the uppermost curve. Notice the In (le)versus Q3 plot. The solid lines are due to a fit made simultaneously for all experimental points in this figure. Missing points have negative values. Error bars with an arrow indicate that the endpoint of this bar has a negative value, too.
-151 0
I
'
1
2
,
I
3
I
L
a'/ nm-' Figure 3. Same as Figure 2, but for partly deuterated CPDS.The D20 content of the solution was (from top to bottom at Qz= 2 n m Z ) 10046, 70%,50%, 4076, 36%, 3096,1556, and 0%. The model for the internal
structure is shown in Figure 1. data of the present experiment. We tried models which were even more complicated than the one-shell model, but we were able to explain all experimental data with such a simple model. In a constrast variation experiment a series of measurements with different scattering length densities pa of the solvent is performed. We mention here that one can always find Q values where the intensity of all members of such a series stays at the same value. These special Q values are given by the condition d(da/dQ)/dp, = 0 (6) It is easily seen that for the model described by eq 5 this happens when J1(QR1)= 0. Notice that da/dQ # 0 for these special Q values. (Only for homogeneous long cylinders, where the scattering intensities are described by eq 3 or 4 it turns out that du/dQ = 0 for these special Q values.) A more general proof is given in the Appendix, showing that such special Q values can be found always for long rodlike micelles whatever the internal scattering length density p(r) is. This fact can be used to check the reliability of the measurements. The first Q value, where eq 6 is fulfilled, was around Q12 = 3.4 nm-2 in our case as can be seen in Figures 2-4. Sometimes the correct subtraction of a constant background is a problem. Then the law according to eq 6 might be helpful. We come back to the background subtraction in section 4.
3. The Samples The CPS solutions were prepared as described in ref 13 by ion exchange procedure from cetylpyridinium chloride solutions or by dissolving cetylpyridinium salicylate which had been synthesized. Four differently deuterated samples were examined:
4. The Scattering Apparatus
The scattering measurements were performed at the high flux reactor of the Institute Laue-Langevin (ILL) in Grenoble. We used the instrument D 11, which is equipped with a twodimensional detector array with about 3800 active detector elements of 1 cm2 area each.14 The wavelength of the neutrons was 1 nm. The wavelength distribution has a full width at halfmaximum Ah/X = 0.09 and shows a triangular shape.14 This distribution was taken into account in the data evaluation. Tests have shown that any further smoothing of the scattering curves coming from the finite pixel size of 1 X 1 cm2 of the detectors as well as coming from the cross section of the neutron beam (1.6 X 1.6 cm2) can be neglected, because AX/X is relatively large. The sample to detector distance was chosen to be 1.2 m. For each of the micellar samples, we always measured the transmission as well as the scattering intensity of the related pure solvent too. As soon as H20 is present the latter distribution is dominated by the incoherent scattering and was nearly constant and structureless. These intensities as well as the measured background counts and empty cell contributions were handled according to standard procedures.I2J5 Calibration with respect to the intensity of the incomingbeam and the detector efficiencies and solid angles was performed in the usual way with H20,1sJ6 giving the absolute value of the scattering cross section (which was not used as a fit parameter in our data evaluation). The measured absolutescatteringcross sections for CPS, CPDS, CPSD and CPDSD are shown in Figure 6. We used one type of Helma quartz cells with 1.OO 0.01 mm path length each. Difficulties can arise for some of the measurements when the incoherent scattering of the micellar sample exceeds the coherent scattering by far. This happens if the measurements are done with a H20/D20 solvent near the
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Herbst et al.
7776 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993
TABLE II: Common Fits to Each of the Three Contrast Variation Series. substance CPS CPDS CPDSD
-4'
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'
'
'
'
'
'
50
0
D,O
/
'
'
'
100
%
Figure 5. Results of contrast variation experiments with CPS, CPDS, and CPDSD. Notice, that (1Q)II2is plotted against the D20 content of the aqueous solvent. The solid lines are due to least-squaresfits and cross = 0 at the matching points. the line (1Q)1/2
&/nm
Wnm
pc/l0~O
p1/10'0
cm-2
om-2
x*
1.38f0.09 2.154f0.015 -0.56f0.04 1.6fO.l 1.8 -0.36 f 0.02 4.9 f 0.1 1.8 1.80f 0.03 2.21 f 0.01 -0.44f 0.03 4.8 0.1 2.1 1.61 f O . O 1 2.22f 0.01
The core radius &, the radius of the shell R1, the scattering length densities of the core pc, and the shell p1 at the matching points x , respectively,are presented. x2 is the r e d u d chi-squarevalue;the quoted errors are statistical ones.
exchange of the hydrogen in the OH group of the salicylate and assuming that this hydrogen is occupied by a hydrogen or deuterium in proportion of the H20/D20 content, we found for VOa fair agreement for the CPS and CPDS isotopic substitutes, TABLE I: Value x of the DzO Content of the Solvent at but Vois substantially larger for CPDSD. We mention that these Which the Scattering Intensity Z(Q-4) Disappearsa volumes have to be identical, if there is no different dissociation of the counterions and if deuteration does not change the volume of a monomer. We conclude therefore that at least for CPDSD 0.727 f 0.014 742 f 13 CPS 18.6 f 0.2 the deuteration changes the internal structure of the micelle 1.467 f 0.014 730 f 7 CPDS 29.3 f 0.2 2.042 & 0.007 731 f 3 CPDSD 37.6 f 0.1 definitively. Such an influence was found for other substances too.17 p ( x ) = p, is the scattering length density of the H20/DzO solvent In the course of our evaluation of the HzO/D20 contrast and is equal to the mean scattering length density of the micelle. VOis variation experiments, we included as further ingredients the the volume of one monomer in the micelle. known sum of scattering lengths of the core (which is defined to be built by ClaH33) and the total scattering length of the shell matching point. Then the proper subtraction of the scattering (which for CPS is built by C12HloN03, for example), taking into intensity of the related pure solvent sample can give negative account the known isotopic exchange of the hydrogen of the OH values of the intensities for some regions of scattering angles. group as mentioned above. Therefore, we introduced a further small constant background We made common least-squares fits to each of three series of for all curves corrected as described above as a further fit the seven CPS, eight CPDS, and six CPDSD curves, respectively, parameter in the data evaluation. Furthermore, we tested whether taking into account the different experimental values of p, (see the formerly quoted law given by eq 6 is fulfilled approximately. Table I). The weights of the different measured points were included according to their statistical errors. The results are 5. Experimental Results and Discussion given in Table 11, together with the value of xz, the reduced We performed three external contrast variation experiments chi-square value,ls which gives an indication of the goodness of with CPS, CPDS, and CPDSD. The results are presented in the fits. Figures 2,3, and 4. A linear extrapolation of In (ZQ) versus Q2 It is a well-known fact that absolute intensity measurements for Q 0 was always possible. (Notice that basically for a are accurate to some percent in reality. We had to expect the homogeneous long micelle an extrapolation of ZQ stays finite for same magnitude of errors (and in reality found) by a direct Q 0). In Figures 2-4, we present the measurements and the comparison of the relative intensities of our different samples. To fitted curves. In Figure 2 some scatteringcurves were shifted for overcome this difficulty in the fit procedures, we introduced to reasons of clearity of the graphical representation. Notice the each of these curves an individual prefactor, which was handled expected crossing of all curves with different contrasts a t a value as a free-running fit parameter. As expected, the values of all Q2 = 3.4 nm-*. In Figure 5 we present the values of (ZQ)1/2 these prefactors were around 1. The largest deviation from this extrapolated to Q 0 for the three substances mentioned above. value was 5%. Apart from this, only a background, as mentoned As expected, a linear relationship is found between (ZQ)IIz and before, and the radius Rc and R1 are parameters which have to the DzO content x of the aqueous solvent. By least squares fits be fitted. Having Rc and R1, the values of the scattering length the x-values and related scattering length densities pmfor (ZQ)l/z densities in the core and shell pc and p1 are determined then by = 0 were determined (see Table I). p, is identical to the mean the known scattering lengths of the monomers, the volume VOof scattering length densities of the micelles, which is defined the monomer and the measured values of pm. according to The solid curves in Figures 2-4 are the result of these common fits. The agreement between experiment and the very simple shell model is quite good. This supports a statement that any (7) further modification of the model makes sense only if the accuracy The integral has to be taken over the micellar volume V,. In the of the experiments is improved substantially and if measurements framework of the theory the expression within braces in eq 5 at higher Qvalues7notattained in the present experiment become becomes zero for Q 0 and ps = pm. This gives an interrelation available. Amazingly, the core radius RCchanges drastically on going between PI, PC, RI, and Rc [Rc = RI{(PI- Pm)/(Pl - P C ) ) ~ / ~ I , from CPS to CPDS. Related with this is the large value of pc reducing the number of fit parameters. This interrelation was used for the further data handling. An analysis of the matching for CPS. It is known from other measurement~l~ that the point scattering length density Pm = J p ( i ) d3i/ Vm = J p ( i ) d3?/ VO scattering length density of the tail should be around -0.38 X is the basis for a determination of VO,the volume occupied by a 1Olo cm-z. It seems that for CPS the bad statistics and the monomer in a micelle. The integral has to be taken over the restricted quality of the intensity curves measured near the volume V, of the micelle or the volume VOof a monomer. In the matching point lead to a core radius which is too low in value. latter case, we have J p ( i ) d3i = &, where b, is the known Therefore we used all measured curves of CPS, CPDS, and scattering length of atom i in the molecule. The sum includes CPDSD and made a common fit to these three series, the result all atoms of a monomer. Taking into account the known isotopic of which is shown in Table 111. The core radius & of 1.65 nm
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Internal Structure of a Rodlike Micelle
The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 7777
TABLE IIk A Common Fit to All the CPS,CPDS, and CPDSD Curves Simultaneously’ substance &/nm &/nm p,/1010cm-2 p1/1010cm-2 xz CPS 2.1 k 0.1 CPDS 1.65 kO.01 2.20k0.01 -0.41 k0.01 3.9k0.1 2.7 CPDSD 5.3 kO.1 a Same symbols as for Table 11. pc is the common scattering length density of the cores, whereas p1 are the scattering length densities of the shells for CPS, CPDS, and CPDSD at the matching points x , respectively. I
is now definitely larger than the value we got for the CPS data evaluation above. We conclude therefore that the CPS value of Rc in Table I1 is not reliable and that a core radius around 1.65 nm describes all measurements with reasonable accuracy. Assuming now for CPS the values of Table 111, the smooth curves shown in Figure 2 change shape in such a way, that the position of the minimum for the 0, 10, and 15% curves is shifted slightly to the left. For CPDS the minimum of the 0 and 15% curves in Figure 3 is shifted slightly to the right, whereas for CPDSD nearly no change in the position of the minimum of the 30 and 0% curves in Figure 4 is observed. As seen in Figures 2-4 there exists a QI value, where the intensities of all members of a contrast variation series seem to be nearly the same. According to our simple model (see eq 5), this should happen when J1(QIR1) = 0. Taking the R1 values of Tables I1 or 111, we can estimate for Q1 a value around 1.78 nm-l. This has to be compared with the experimentally determined value of 1.85 nm-1. The discrepancy is not large, but might be a hint that our model, where the scattering length density p(r) changes discontinuously,is oversimplified. A smoothing of p ( r ) might give an improvement. The characteristic features of the shell structure of the micelles are best seen for solvents where ps is near the matching value pm. But then the scattering intensity is notoriously low and the statistical errors become large. One such characteristic feature is the minimum in intensity at a finite Q value in the range of Qvalues measured in the experiment when p, < pm. Theoretically, the intensity should go to zero somewhere, but this zero is washed out by reason of the wavelength distribution of the neutrons of 9%. Such a washing out of the Z(Q) curves can be expected to exist too by the presence of micelles with a distribution of radii Rc and R1. (Each subspecies has its own in general different Q value, where Z(Q) becomes zero.) We cannot conclude from the present results that such a polydispersity exists. We tried to improve the fit quality by the introduction of a possible dissociation CY of the (C6H40HC02) group, which was expected to be around a = 0.09.13 The improvement turned out to be not substantial. Furthermore, we tried whether the attachment of water molecules into the shell (which changes automatically the value of Vo) gives a better fit. This would eventually open the possibility that CPS, CPSD, and CPSDS can be fitted with basically one value of Rc and R1. But again, no substantial improvement was found. Up to now, we have assumed that the core is built by Cl6H33 We tried to shift some parts of the rest of the monomer to this core and vice versa. Again, no substantial improvement in fit quality was observed. In Figure 6 we present the absolute scattering cross section dX/dfl for themicelles with the threedifferent isotopicsubstituted molecules in pure DzO solvent. Apart from absolute values, only minor differences of the shapes are observed in this case. Deviations between fitted and measured curves become obvious at the highest measured Q values. This again is a hint that any improvement of the present very simple model needs measurements at higher Q values as achieved here. Unfortunately, the scattering intensity then becomes low and background subtraction is a serious problem. The fits were made with the values of Rc and R1 quoted in Table 11. For CPSD the same values as for CPDSD are used. We checked whether the measured absolute
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0
2
1
3
Q’lnm”
Figure 6. Absolute scattering crow section for solutions of CPS, CPDS, CPSD, and CPDSD in pure D20. The data are taken from Figures 2-4. For CPSD the same radii are used as for CPDSD (see Table 11). Notice the In (ZQ)versus @ plot. For convenience, CPDS, CPSD, and CPDSD are shifted down with respect to the CPS curve for 1, 2, and 3 units, respectively. The solid linea aurespond to the fitted results of Figures 2 4 . The dashed line for the CPS sample is due to a fit using the model of homogeneous cylinders and shows only some minor deviations from the results of the shell model (solid line).
cross section dX/dfl [cm-I] is in agreement with the calculated one. For CPS we get for a Q value of 0.473 nm-l the values 1.81 f 0.05 and 2.17 f 0.03 cm-l for the measured and calculated values, respectively, which can be considered as a fair agreement. For the calculation the results of Table I11 were used.
6. Conclusions A very simple one-shell model for the internal structure of a rodlike micelle was used to describe the scattering intensity as a function of contrast. The internal structure seems to be independent of the degree of deuteration of some hydrogen atoms of the head groups. Further improvement of the model would be possible only by a substantial increase of the accuracy of the measurements as well as by measurements made for larger Q values. We found, that there exists at least one Q value, where the scattering intensity is independent from the value of the contrast.
Acknowledgment. The financial support from Bundesministerium fiir Forschung und Technologie (BMFT) under Grant No. 03-KA3BAY-7 is gratefully acknowledged. We thank Dr. Illini and Prof. H. Hoffmann for the sample preparation and Dr. K. Ibel and Dr. R. May for assistance during the measuring campagne in Grenoble. Appendix The scattered amplitude related to a micelle v is given by
The index v incorporates different orientation. The integral has to be taken over the volume of the micelle. Formally we are looking for dA,(O)/dp, = 0 = l e x p ( i & ) d3i
(2)
which gives the condition that A, does not depend on ps for a certain value of In general, eq 2 cannot be fulfilled if we have a distribution in orientation of anisometriceqtal particles, because for each subspecies v a different value of Q, fulfilling eq 2, is found. But in the case of long cylinders (the length I of these cylinders exceeds the radius R by far), it is found that A,(& becomes large only if the angle 9 between 0 and the axis ir of the cylinder is near 7r/2, and A , ( a ) depends, apart from geometrical parameters, like 1 and R, only on 9. Therefore, we observe only such subspecies v with 8 = r/;, and for these subspecies in fact eq 2 is fulfilled for a distinct Q
a.
7778 The Journal of Physical Chemistry, Vol. 97, No. 29, 1993 value. (There might be several 0 values for which eq 2 can be fulfilled!) Note that for these special Q values the scattering intensity in general is not zero and that we have tacitly assumed that the scattering length density at the boundary between the surface of the micelle and the surrounding solution changes abruptly. The same kind of arguments can be found for thin platelets like discs, where the disc radius exceeds the thickness by far. Then only subspecies where 0 is parallel to the normal vector to the surface contribute to the scattering.
References and Notes (1) Kalus, J. K.; Hoffmann, H.; Reizlein, K.;Ulbricht, W.; Ibel, K. Ber. Bunsenps. Phys. Chem. 1982,86, 37. (2) Hoffmann, H.; Kalus, J.; Thum, H.; Ibel, K. Ber. Bunsenges. Phys. Chem. 1983,87, 1120. (3) Herbst, L.; Hoffmann, H.; Kalus, J.; Thurn, H.; Ibel, K. Neutron Scatrering in rhe Nineties; IAEA: Vienna, 1985; pp 501-506. (4) Kalus, J.; Chen, S.-H.; Hoffmann, H.; Neubauer, 0.;Lmdner, P.; Thurn, H. J. Appl. Crystallogr. 1988, 21, 777. (5) Neubauer, G.; Herbst, L.; Hoffmann, H.; Ibel, K.; Kalus, J. Mater. Sei. Forum 1988, 27, 147.
Herbst et al. (6) Baumann, J.; Hcrtcl, G.; Hoffmann, H.; Ibel, K.; Jindal, V.; Kalus, J.; Lmdner, P.; Neubauer, G.; Pilsl, H.; Ulbricht, W.;Schmelzer, U. Prog. Colloid Polym. Sci. 1990, 81, 100. (7) Marignan,J.; Appell, J.; Bassereau, P.; Porte, G.; May, R. P. J.Phys. Fr. 1989, 50, 3553. (8) Perchc, T.; Auvray, X.;Petipas, C.;Anthore, R.; Rico, I.; Lattes, A.; Bellissent, M. C. J. Phys. I Fr. 1992, 2, 923. (9) Aldcbert,P.;Dreyfus,B.;Gcbel,G.;Naliamura,N.;Pineri,M.;Volino, F. J. Phys. Fr. 1988,49,2101. (10) Cummim, P.G.;Staples,E.;Hayter, J. B.; Pcnfold, J. J. Chem.Soc., Faraday Trans. 1 1987,83(9), 2773. (11) Chevalier, Y.; Zemb, T. Rep. Prog. Phys. 1990, 53, 279. (12) Kostorz, G. Treatise Mater. Sci. Technol. 1979, I S , 277. (13) Hoffman, H.; Platz, G.; Rehage, H.; Schorr, W.; Ulbricht, W. Ber. Bunsenges, Phys. Chem. 1981,85, 255. (14) Ibel, K. J. Appl. Crystallogr. 1976, 9, 296. (15) Chcn, S.-H.; Lin, T.-L. Merh. Exp. Phys. 1987, 23, Part B, 489. (16) Jacrot, B.; Zaccsi, 0. Biopolymers 1981, 20, 2413. (17) Pilsl, H.; Hoffmann, H.; Hofmann, S.;Kalus, J.; Kcncono, A. W.; Lindner, P.; Ulbricht, W. J. Phys. Chem. 1993, 97, 2745. (18) Bevington,P. R.L&~taReductionandErrorAnaIysesforthePhysical Sciences; McGraw-Hill Book Co.: New York, 1969. (19) Lmdemuth, P. M.;Hammouda, B.;Vcnable, R. L. J. Phys. Chem.
1990,94, 8247.
