J . Phys. Chem. 1989, 93, 4261-4216
4267
Correlations in Micellar Solutions under Shear: A Small-Angle Neutron Scattering Study of the Chain Surfactant N-Hexadecyloctyldimethylammonium Bromide J. KaIus,* H. Hoffmann, Experimentalphysik I und Physikalische Chemie I of the University of Bayreuth, 0 - 8 5 8 0 Bayreuth, F.R.G.
S.-H. Chen, Department of Nuclear Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39
and P. Lindner Institute Laue-Langevin, Grenoble, France (Received: October 10, 1988; In Final Form: December 13, 1988)
Rodlike micelles formed by surfactant N-hexadecyloctyldimethylammoniumbromide (C 16-C8DAB) in aqueous solutions were aligned by shear gradients r of up to 12000 s-l. Small-angle neutron diffraction patterns of a 50 mM solution were recorded for different shear gradients. The quiescent solution shows a single pronounced peak in the scattering intensity distribution at a wave vector of 0.28 nm-’ and a shoulder at -0.51 nm-’. With increasing shear gradients the shoulder transform into a second correlation peak at 0.51 nm-I. Both correlation peaks become more intense and change shape with increasing r while their position remains the same. The scattering data are explained on the asis of formation of two types of aggregates which are in equilibrium with each other. One type of micelles, probably consisting of short, rodlike micelles, is weakly aligned, whereas the other type, appearing above a threshold shear rate, shows strong alignment even at low shear rate. The relative concentrationsof these two species changes with the shear rate. We thus have the evidence of a shear-inducedtransformation of the micellar aggregates.
1. Introduction
Information on the orientational distribution of anisotropic micellar particles at relatively short time scales can be obtained from small-angle neutron scattering (SANS) measurements when an instrumentation which is capable of two-dimensional data acquisition is used.] In our experiment the micellar particles in heavy water are aligned by means of a “mechanical” force, namely, by a shear gradient applied to the system.2 C16-C8DAB micelles have the shape of rods at 50 mM concentration. The change of the diffraction pattern with increasing shear rates enables us to analyze both the structural and the dynamical behavior of the micelles which are responsible for the anisotropy in the scattering patterns. Eventually we hope to study the influence of the interaction between (charged) micelles on the angular distribution of the rod axes. The interaction is responsible for peculiar macroscopic properties of some of the micellar solution~.~ Theoretical work on the distribution of the axes of rodlike particles immersed in a sheared liquid is a ~ a i l a b l eand ~ , ~can be used to describe the anisotropic diffraction pattern. However, the theory does not take into account the interaction between micelles. The interaction itself depends in a complicated manner on the distribution function of the rod axes. When the rods carry electric charges, a strong nearest-neighbor order will be established in the system. The nearest-neighbor order shows up as a strong correlation peak in the scattering experiment. The structure factor S(Q-.O) in such systems can be very low. (Q is the magnitude of the scattering vector of the radiation.) At present, it is very difficult to calculate the orientational distribution function of rods when charge density on the rods is evenly distributed. Schneider et aL6 have made calculations for a simplified interaction in which ( I ) Schmatn, W.; Springer, T.; Schelten, J.; Ibel, K. J . Appl. Crystallogr. 1974, 7, 96.
(2) Herbst, L.; Hoffmann, H.; Kalus, J.; Thurn; H. Neutron Scattering in the Ninefies; IAEA: Vienna, 1985. ( 3 ) Hofmann, H. Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 1078. (4) Boeder, P. Z . Phys. 1932, 75, 258. (5) Herbst, L.; Hoffmann, H.; Kalus, J.; Thurn, H.; Ibel, K.; May, R. P. Chem. Phys. 1986, 103, 431. (6) Schneider, J.; Karrer, D.; Dhont, J. K. G.; Klein, R. J . Chem. Phys. 1987,87, 3008.
0022-3654/89/2093-4267$01.50/0
charge of the rods was concentrated at certain positions along the rods. These calculations show that neighboring rods try to arrange perpendicular to each other. In the past, we mostly chose systems, for the measurements with shear, in which enough excess salt was ,added to suppress the correlation peak.2 Under these conditions we were able to determine the orientational distribution function of the rods under shear. SANS experiments with solutions of rodlike micelles having correlations have been reported by Hayter and Penfold and by Kalus and Hoffmann.’~~In both experiments the position of the correlation peak did not shift under shear. In the present investigations we carry out S A N S measurements, under shear, of semidilute rodlike systems having a strong correlation peak. We shall analyze the scattering curves in detail. The evaluation of the exact shape and size of anisometric micellar aggregates in the semidilute concentration range becomes very difficult because of the presence of a strong correlation peak. The major dimension of the micelles is usually hidden under this correlation peak. The situation can become even more complicated by the presence of two or more different structures which could be in equilibrium with each other. In such a situation it becomes rather hopeless to analyze the scattering pattern in an unambiguous way. We have therefore looked for ways to improve the evaluation of the data in order to get meaningful physical quantities. In cases in which two types of aggregates are simultaneously present, it is conceivable that their effective rotational diffusion constants are different. In this case it seems attractive to orient one type of the structure while leaving the other type in an isotropic, unoriented or in a weakly oriented state. This would provide additional information for the evaluation and determination of the structure. Surfactant solutions with rodlike and disklike micelles in coexistence have been predicted on the basis of a theoretical consideration by McMullen et aL9 Yet the experimental existence of such an equilibrium situation has never been proven, possibly due to the lack of a suitable technique to distinguish between rods and disks in the semidilute state. In (7) Hayter, J . B.; Penfold, J. J . Phys. Chem. 1984, 88, 4589. (8) Kalus, J.; Hoffmann, H. J . Chem. Phys. 1987, 87, 714. (9) McMullen, W. E.; Ben-Shaul, A,; Gelbart, W. M. J. Colloid Interjace Sci. 1984, 98, 523.
0 1989 American Chemical Society
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The Journal of Physical Chemistry, Vol. 93, No. 10, 1989
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previous papers2*10we have shown that an additional information can indeed by obtained when the rodlike micelles are aligned by a shear. It seems possible, for instance, to extract the lengths of the rods from these experiments even in the presence of a strong correlation peak. Our first measurements were made on cetylpyridinium salicylate (CPS), a system which forms rodlike micelles in isotropic solutions at concentrations for which the isotropic phase borders on a liquid crystalline, hexagonal phase. In this instance we found no evidence of an equilibrium between two different structures. In this study we use the surfactant N-hexadecyloctyldimethylammonium bromide. For this system, an isotropic phase, in which rodlike micelles were shown to exist, borders on a liquid crystalline phase. The two-phase region begins at a surfactant concentration of about 80 mM. In the isotropic solution before the two-phase region there is an evidence for the existence of different types of structure^.^ Electric birefringence measurements on a 50 mM solution show that there are at least three different relaxation times, at the time scales of the order -5 p, -500 bs, and -50 ms. The amplitude of the shortest process has a negative sign and a time constant between 1 and 10 ws with increasing concentration while the signals of the longer processes are of positive sign. The intermediate relaxation time increases rapidly with increasing concentration from a few microseconds to about 1 ms. If the processes of the different relaxation times are due to different species it would seem conceivable that the particle with the longest relaxation times would be aligned at moderately high shear field while the smaller aggregates would still remain in the nonaligned state. We shall now look at the S A N S results under shear. Our paper is organized as follows. In section 2 we describe the sample preparation and other experimental details. Section 3 is dedicated to the experimental results. In section 4 we describe the theoretical framework for an evaluation of the S A N S cross section and the equation of motion of rods in experimental data are given for the anisotropic ring and the peaked structure, respectively. A semiquantitative description and conclusions are given in section 7 .
2. Sample Preparation and Scattering Apparatus A . The Sample. The sample is a 50 mM solution of Nhexadecyloctyldimethylammonium bromide (Cl6H3,C8Hl7N(CH3)2Br)dissolved in D20. The compound was received as a gift from the Hoechst Co. in Gendorf, FRG. The compound has a melting point of 146 f 1 OC. The purity was checked by surface tension measurements. Solutions did not give a minimum of the surface tension at the cmc. Information on the micellar solution has been reported]' as well as data of the phase diagram of the compound in D20.4 Conductivity data in the isotropic solutions reveal three transition concentrations at temperature 25 OC used for the present experiment: the critical micelle concentrations (IO) Neubauer, G.; Herbst, W.; Hoffmann, H.; Ibel, K.; Kalus, J. Mater. Sci. Forum 1988, 27/28, 147. ( I 1) Neubauer, G.;Hoffmann, H.; Kalus, J.; Schwandner, B. Chem. Phys. 1986, 110, 247.
50
150
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Figure 2. The extinction angle x and the index of birefringence An as a function of the shear rate I?.
cmc = 0.17 mM/L, a first transition occurs at concentration C,, = 0.8 m M / L and a second at Ct2= 10.9 mM/L. Solutions with concentrations between Ct2 and the liquid crystalline phase boundary, at a concentration of -80 mM/L, show three electric birefringence signals with time constants which can be up to 4 orders of magnitude different. In the concentration range between 10 and 50 mM the viscosity at 25 OC is increasing from 1 mPa-s to about 300 mPa.s. The dynamic viscosity q* for a 50 mM solution as a function of the frequency is shown in Figure 1 . The storage and loss module G'and G"are also given in this figure. They cross at an angular frequency w = 35 SKI.This shows that the system has a structural relaxation time of about 29 ms (UT = 1). If the structural viscosity would be due to this relaxation process only we could expect a strong decrease of the dynamic viscosity for higher frequencies. This is not the case as is evident from Figure I . We also looked at the flow birefringence of the solution. The angle of extinction x and the birefringence An are plotted against the shear rate r in Figure 2. The curve for x is very unusual in comparison with data which were obtained in other systems. The angle of extinction x begins to decrease already at rather modest shear rates, suggesting the presence of particles with a rotational diffusion time constant 7 of around 0.03 s. Normally we would expect that x approaches the angle zero when r7 >> 1. This, however, is not the case. The curve does not follow the theoretically expected behavior but levels off at an angle considerably larger than zero. This is an indication that the material is not well aligned. Previous S A N S and SAXS measurements have indicated the presence of rodlike micelles.'1~'2 From measurements at high Q values we derived the radius R of the rods: R = 1.93 f 0.03 nm." Information on the length L was more difficult to obtain. The neutron diffraction measurements1' give evidence that L, as compared with the radius R , is large, probably around 21 nm. At least the S A N S measurements can be interpreted in such a way that this length fits the data. But one has to be aware that this length may be something like an effective length and the real structure of the micellar solution can be quite different from the simple model we assume. It is also important to note that the mean distance between micelles is smaller than the length of the rods: i.e., the system is in the so-called semidilute overlap regime. The micelles are charged. These charges originate from dissociation of the negatively charged bromide ion. The degree of dissociation (Y is about 0.23, as determined from conductivity measurements.' I B. The Shear Apparatus. Alignment of the rods was made in a shear apparatus described in detail in ref 13. The sample volume was 4.5 mL. The neutron beam crossed 2 times a gap width of 0.5 mm. The shear rate r was varied between 0 and 12000 cm-I. C. The Small-Angle Scattering Apparatus. Experiments were carried out at a neutron small-angle diffraction instrument D11 at the Institute Laue-Langevin in Grenoble with neutrons of wavelength X = 1 and 0.5 nm. The wavelength resolution is (12) Magid, L. J.; Martin, C. A.; Caponetti, E. Proceedings of the Conference on Magnetic Resonance and Scattering on Surfactant Systems, Miami 1985; Plenum Press: New York, 1985. (13) Lindner, P.: Oberthiir, R. C. Reo. Phys. Appl. 1984, 19, 7 5 9 .
Correlations in Micellar Solutions under Shear I
The Journal of Physical Chemistry, Vol. 93, No. 10. 1989 4269 130000
30000
a
*
Figure 3. Isometric plot of the measured scattering intensity of C16C8DAB with a shear gradient of r = 0 s-l. The momentum transfer is
130000
given in units of nm-I.
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Figure 4. Same as Figure 3, but r = 50 s-': (a) experimental results; (b) theoretical intensities for type I micelles.
typically Ah/X = 0.09 fwhm.I4 The distance between sample and detector was 360 and 260 cm, respectively. The measurements showed that it was possible to obtain extremely anisotropic scattering patterns even at low shear gradients. Temperature during the measurements was kept constant at 25 f 0.5 "C.
3. Experimental Results Figures 3-9 show isometric plots and contour plots of the scattering intensities at low scattering angles for a neutron wavelength of 1.O nm. The sample-detector distance was 3.6 m. The r values are 0, 50, 100, 200, 400, 1000, and 2000 s-I, respectively. Between r = 2000 and 12 000 s-l only a minor change was found. An isometric plot for high scattering angles and r = 2000 is shown in Figure 10. In that case the neutron wavelength was changed to 0.5 nm and the sample-detector distance to 2.6 m. The figures denoted (a) are the experimental results, whereas (b) is the result of a fit according to a theory described in the next section. The figure denoted as (c) shows the difference between (a) and (b). The sharp peaks in (c) increase in intensity by increasing r, but no narrowing with increasing shear rate is observed up to I' = 2000 s-I. For convenience (d) shows the same result as (c), but as a contour plot. The magnitude of the scattering vector Q of the sharp correlation peaks are Q, = 0.284 f 0.001 nm-' and Q2 = 0.510 f 0.005 nm-I. It turns out that Q2/Q, = 1.80 is near 3Il2, which could be an indication that a hexagonal structure of parallel rodlike micelles is formed under shear. But (14) Ibel, K. J . Appl. Crysr. 1976, 9, 296.
I
I
0 5 nm-'
I 1 Figure 5. Same as Figure 3, but r = 100 s-*: (a) experimental results, (b) theoretical intensities for type I micelles, (c) is the difference between (a) and (b) giving the contribution of type I1 micelles. (d) is the same as (c), but shown as a contour plot. The scales for the contour plots are 500, 1500, 2500, 3500, 4500, and 5500, respectively.
we have to caution that for such a structure to exist we have to expect a further peak at a wave-vector transfer to Q3 such that Q3/Ql = 2. This peak is, as shown below, hidden unter the high Q tail of the Qz peak. An inspection of the measured intensity plots in Figures 3-9 supports the suggestion that the intensity distribution can be subdivided into two parts. The first part shows a ringlike structure showing an anisotropy at higher shear rates r. A second part, giving rise to a peaked structure superimposed on the first one, indicates a high degree of alignment even at lower values of the shear rate I'. This peaked structure can be first observed at a shear rate of r = 100 s-l and is absent for r = 50 or lower. We mention here that the index of bkefringence An as a function of the shear rate I? shows an anomaly in this r region. We call, for the subsequent discussion, the micelles responsible for these two parts in the scattering pattern "type I micelles" and "type I1 micelles". A closer examination shows that along the lines A-A' and B-B' (see Figure 6 for definition) the ringlike structure shows change
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The Journal of Physical Chemistry, Vol. 93, No. 10, 1989
Kalus et al.
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in intensity but only minor change in shape with increasing r, B-B’ is a cut nearby the narrow peak but avoiding any contribution from this peak. Especially the position of the maxima stay constant for all r values. This behavior is shown in Figure 11 for the measured I’ values. This finding indicates that no substantial change of the correlation between these charged rodlike micelles (type I micelles) as function of shear rate can be found in our scattering experiment. A further indication is that the amount of monomers bound in these micelles decreases slowly with increasing shear rate, as found from an analysis explained in the next chapter. The missing monomers of the rodlike I micelles show up in the sharp peaked micellar structure mentioned above (type I1 micelles). The shape of the micelles responsible.for the sharp peaked structure is not evident. We assume that they are rodlike too; but then these micelles can be quite long and are organized quite differently from the other ones; it is conceivable that these micelles can,build even a network or that they are arranged more like in a crystal as we assumed in an analysis described in the next section. In spite of the uncertainty about the exact shape we assumed, it is certain that both type I and type I1 micelles are long, rodlike micelles showing a strong nearestneighbor order, describable by a phenomenological structure factor.
-05
Figure 7. Same as Figure 5, but I’ = 400 s-I. The scales for the contour plots are 500, 2500, 4500, 6500, 8500, and ‘IO500, respectively.
4. SANS Cross Section and Equation of Motion The scattering intensity I @ ) of an ensemble of identical, centrosymmetric particles measured in a small-angle scattering experiment can be written aslS N N
I(Q> = cc
CF(Q,JJ
k=lj=l
F(Q,iij) COS [ Q < R k
- $j)]
(1)
Here Zk is a vector specifying the orientation of the particle k in space. In our case, ii gives the orientation of the rod axis. The sum runs over the ,N particles in the solution. The value of the scattering vector IQI is given by 4?r sin (8/2)/X, where X is the Tavelength and 8 the scattering angle of ;he scattered neutrons. Rk is the position vector of particle k. F(Q,iik) is the form factor of particle k depending on the scattering vector, the orientation, (15) Fournet, G. In Hundbuch der Physik XXXII; Flugge, S., Ed.; Springer: Berlin, 1957.
The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 4271
Correlations in Micellar Solutions under Shear 1
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Figure 9. Same as Figure 8, but
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the length L, and the radius R . For theoretical evaluation of the form factor R = 1.93 rim and L = 21 nm were assumed. C incorporates the intensity of the neutron beam, the solid angles, the detector efficiency, and the shape of the sample. In reality we can only observe the mean intensity. Therefore we have to calculate the ensemble-averaged values of the first and second term of eq 2. The mean value of the first term is
cp(!(&*u'k) = cp(6,u'k) k = Zk : J p ( e , G k ) k
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Figure 10. Isometric plot for Q range has changed.
r = 2000 8. In contrast to Figure 9a, the
detailed information is available in ref 7.) (1) We neglect any correlation between the_orientation distribution of the particles and the distajces (Rk- RJ ( 2 ) We assumed that the correlation between F(Q,Ck)and F(Q,Zj) can be neglected, giving
F(6,Gk) F(6,u'j) =
For the model calculations we made severe simplifications. (More
Then eq 2 can be written as
( F ( o , u ' k ) )(F(6,"'j))
(5)
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The Journal of Physical Chemistry, Vol. 93, No. 10, 1989
I ( Q ) = CN((F2(Q)+ ) p ( F ( Q ) ) * Jm
cos (&P)[P(F)- I ] d d (6)
is the number density and P(r‘) is the pair correlation function between the centers of gravity of the micelles, which in the sheared solution may depend o n j h e vector 7. ,In the case of a strong correlation between F(Q,iik) and F(Q,ii,) in the sense :hat neighboring micelles are more or less parallelly aligned, ( F ( Q ) ) 2 in eq 6 has to be replaced by ( F ( Q ) )giving , p
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+p
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A further simplification introduced is the assumption that P(7) - 1 is isotropic and independent on the shear rate r. In fact, we fitted G(Q) = pJ” cos (Qr‘) [P(r’)- 11 dr‘to the measured S A N S intensities for r = 0 and used this special C(Q) for an analysis
of all measured curves. An intriguing point is indeed the experimental fact that the peak position of the ringlike structure is independent of the shear rate. By the phenomenological assumption that C(Q) is independent of r and equal to the function of r = 0, we found that this behavior is quite well reproduced by the simulations for r values up to 1000 s-l. Typical cuts along the lines A-A’ and B-B’, as shown in Figure 6, are given in Figure 1 1 together with fit results according to the theory outlined below in the next chapter. W e have to mention that the agreement between experimental results and the results based on theory is much better for eq 7 than for eq 6. This is shown in Figure 12. This might be a hint that neighboring micelles are preferentially aligned parallel. But one has to be cautious with this statement, because eq 6 and 7 are b$h the resul_ts of severe simplifications. ) need the knowledge For a calculation of ( F ( Q ) )or ( F ( Q ) we off(;), the distribution function of the rod axis in the sheared state. For noninteracting particles Peterlin and Stuarti6calculated the time dependence ofAf(t), using a Fokker-Planck equation:
aVu(8)sin 8 ) sin 0 80
w(0) = o(p)
-sin2
cp
+
-aVu(cp)) } e acp sin
(8)
sin 8
= 0.25 sin 2cp sin 28
8 is the angle between rod axis and z axis of an orthogonal x,y,z system. The velocity of the vector is directed parallel to the x axis and has the value c‘ = r y . cp is the angle between the x axis and the projection of the rod axis into the x-y plane.
5. Discussion of the Anisotropic Ring Equation 8 is governed by two parameters, r and D. D is a rotational diffusion coefficient. For a steady-state situation, as in o y experiment,) is the only unknown parameter. We fitted ( F ( Q ) ) and ( F ( Q ) )and therefore the anisotropic scattering intensities according to eq 6 and 7 to the experimental results by calculatingfwith D as a fit parameter. f w a s calculated either by series expansionI6 or by a numerical solution of the equation of motion (8). The results of these fitted values for the rotational diffusion coefficients are shown in Figure 13 and Table I. In this table and in Figure 14 we also present the fitted values of the intensity, I ] , which is a number proportional to the amount of monomers bound in the micelles of type I. The intensities along the cuts A-A’ and B-B’ (see Figure 6), calculated with the help of the fitted D values, are shown in Figure 1 1 and compare up to r = 1000 s-I quite well with the measured intensity profiles. Beginning with r = 2000 s-l the agreement is less satisfactory. ( I 6) Peterlin, A.; Stuart, H. A. In Hand- und Jahrbuch der Chemischen Physik; Band 8, Abschnirr I B Eucken, A,: Wolf, K. L., Eds.; Akademie Verlagsgesellschaft Becker und Euler: Leipzig, 1943.
Kalus et al. Looking at the F dependence of D we can remark that, contrary to the theory (see eq 8), D is not constant. Therefore we call this value D e , , . This means that either the theory has to be improved by the introduction of terms describing the interaction between the micelles or that the system, Le., the micelles of type I, changes with shear rate r. At the moment we cannot decide which of these possibilities is more probable. It is quite remarkable that Deff,l increases with increasing shear rate r, showing eventually a above r 400 s-l. This constant value around D e , , 30 SKI behavior is in qualitative agreement with the strange result of the birefringence measurements, mentioned above. If Deff,iincreases, the relaxation time T = 1 / ( 6 D ) decreases and the alignment in a sheared solution decreases too. This is exactly seen in Figure 2. The large error bars of Deff,]for large r values is due to the fact that the distribution functionfis well peaked at these shear rates and that an increase in r under these circumstances alters the shape only weakly. It is possible to analyze the result of the measured angles of extinction x (see Figure 2) by assuming a length-distribution function according to Lin et al.” and length-dependent rotational diffusion parameters according to Gans.l* This can give excellent fits to Figure 2 (Thurn, H., private communication). We tried, in accordance with our SANS data evaluation, another simpler model, assuming that D depends on r. With such a model effective rotational diffusion coefficients DCff,*are obtained (see Table I). W e can see that both D e , ,and Deff,?increase with increasing shear rate. We see that Deff,l# Dea2,but the difference is not large. It turns out that Deffis very temperature dependent. A change in temperature of 1 OC gives for example, a change of 20% in Deff.Therefore it might be that a substantial part of the discrepancy stems from a difference in temperature in the actual measurements performed for determination of the extinction angle x on the one hand and for the S A N S measurements on the other. Apart from this one has to keep in mind that the influence of the type I1 micelles is not subtracted in the x determination, because there is no way to do this, and that for both measurements the extraction of Deffare quite different. I n another model one assumes, following Doi and Edwards,19 that the rods are strongly entangled and that therefore the rotational diffusion constant depends on the distribution function which depends on r. Following Doi and Edwards19 we tried to see whether their model
-
-
Deff= D ? r 2 / ( 4 S f ( i i ) f ( i i ’ )sin (ii,ii’) dii dii’)*
(9)
fits our result. This expression should give a shear-independent value D which is equal to Deffat r = 0. sin (ii,ii’) means the sine of the angle between ii and ii’ The evaluation of eq 9 is quite difficult to do in practice. We believe that the numerical accuracy is only better than a few percent. In Table I, from the Defl/Dvalues it is seen that the shear dependence is by far not sufficient to fit the experimental results. Our conclusions are that other factors as those imposed by the Doi and Edwards model are important for a proper explanation of the shear dependence of Dep: A length distribution or a shear-induced change in shape or the change in the interaction between the micelles or a combination of all these possibilities. 6. Discussion of the Peak Structure For the peaked structure, we assume that the micelles of type I1 again are of rodlike shape with the same radius R of 1.96 nm as determined for the r = 0 micellar solution. In a x,y,z coordinate system, where the velocity vector of the sheared solution is in x direction, the rods are aligned more or less parallel to this direction. For noninteracting rods we know that the maximum of the ori(17) Lin, T. L.; Chen, s. H.; Gabriel, N. E.; Roberts, M . F., J . Phys. Chem. 1987, 91, 406. (18) Cans, R. Ann. Phys. 1928, 86, 628. (19) Doi, M.; Edwards, S. F. J. J . Chem. SOC.,Faraday Trans. 2 1978, 918.
Correlations in Micellar Solutions under Shear
The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 4273 C
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0 50
Q
Figure 12. Same as Figure IO, but for r = 200 s-' and for an evaluation according to eq 6 : measurements ( O ) , calculations (X). entational distribution functionf(u') for higher and higher shear rates r goes closer and closer to the x axes and that the widths off becomes narrower and narrower. This general behavior is expected to hold for interacting micelles too. We observed that for I' < 50 s-' no scattering of type I1 micelles is observed. For r > 100 s-I we observe for the first time the scattering intensity related to these micelles, but we observe too that the widths of the sharp scattering peaks do not alter at all up to r = 2000 s-l. This was shown by fitting a peak of Gaussian shape along a line DD', as indicated in Figure 7 and documented in Table I. There is nothing but a change in intensity with r. For r > -4000 s-I
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The Journal of Physical Chemistry, Vol. 93, No. IO, 1989
Kalus et al.
TABLE I: Rotational Diffusion Coefficients Ddl,,,DeR,*, and DeR/Dand the Amount of Monomers I I and Ill Fixed in the Micelles of Type I and 11"
rls-1
Deff,l/s-I
DeKalS-'
DefflD
5 16 22
1 .oo 1.07 1.08 1.11 1.16 1.59
0 50 I00 200 400 1000 2000 4000 6000 8000 10000 I2000
10.4 (1.1) 19.5 (1.5) 29.9 (2.7) 37 (7) 21 (8) 32 ( 1 1 )
w2/nm-l 100 96 (1.5) 94 (2) 86 (3) 76 (5) 72 (4) 70 69 67 62 64
2.8 (0.5) 6.4 (0.5) 13.3 (OS) 23.5 (0.5) 28 (1) 30 (1) 31 (1) 37 (1) 38 (1) 36 ( 1 )
0.041 0.039 0.043 0.041 0.042 0.046 0.047 0.054 0.055 0.052
(I) (1)
(1) (I) (1) (2) (3) (3) (4) (4)
0.062 0.064 0.059 0.057 0.055 0.062 0.070 0.072 0.079 0.072
(25) (9) (6) (2) (2) (4) (7) (7) (7) (7)
" For r = 50 s-] II was set to 100%. W , and W2 are the full width at half-maximum of the sharp peaks along line C-C' and D-D', as shown in Figure 7. Beginning with r = 2000 s-' the intensities of Ill were scaled to the value determined at r = 2000 s-l, taking into account the half-widths Wl and the peak intensities of Ill. This is the reason why we omitted to give errors for II beginning with r = 4000 S - I .
0
2wo
l a
m
r IS-']
Figure 15. Intensity of the SANS pattern related to type. I1 micelles.
On
the right-hand side a scaling in percentage is shown. See text for more details. intensity peak along line EE' in Figure 7 is independent of r too, but higher as along the line DD'. These values are noted in Table I too. It seems that type I1 micelles are quite large. Then it is understandable that the alignment can be quite perfect even at low shear rate. In Table I and Figure 15 we show the SANS intensity below the peak Ill related to type I1 micelles. This intensity is a direct measure for the amount of monomers bound in these micelles. This statement follows from the fact that for Q values larger than 2 a / L (this condition is fulfilled in our experiment) the form factor squared of a cylinder, p,is proportional to a function of R and Q times ( l / L ) . The intensity I of the scattered neutrons is proportional to F P N . Vis the volume of one micelle and N is the number concentration of the micelles. Finally one sees that I is proportional to N L , since V = aR2L. N L is the sum of lengths of all micelles in unit volume and is therefore proportional to the amount of monomers bound in these micelles. Comparing intensity curves I , and Illwe see that, while II becomes lower, 111becomes larger with increasing r. In fact, we can attribute a percentage scale to these curves, as shown on the right-hand sides of Figures 14 and IS, which give the percentage of monomers bound to type I or type I1 micelles. This percentage scale is defined in the following way: For the II curve 100% is attributed to the highest intensity; this is the value for r = 50 s-I. For the Ill curve we attributed to the intensity at r = 2000 s-' a percentage of 28, which is the percentage missing in the II curve at r = 2000 8. As mentioned above, only minor changes in the intensity profiles were found between r = 2000 and 12000 s-'. It seems that for these shear rates only the structure related to type I1 micelles changes, whereas a change of the intensity profiles related to type I micelles cannot be found, because the intensities in sensitive regions of the Q space are extremely low for these micelles. It turns out that for all r values below 2000 s-' the sum of II + I,,in the percentage scale is near loo%, which gives some confidence that this scaling might be correct. As is seen in Figure 14, there is a discontinuity in the I1 curve between r = 0 and 50 s-l. I t seems that below the threshold shear rate rswe have some change in micellar size and shape, which might be different from that above rs.
c
[
P.rI
Figure 16. Profile along H-H' from Figure 10. The depression of intensity near Q = 0 is due to the beam stop. The widths of the highest peaks are resolution limited. -0- for F = 2000 s-I; -X- for r = 0.
It was mentioned that the position defined by the value of the scattering vector Q, of the second sharp peak was nearly 3'/2times the position of the first one. This can be a hint that a hexagonal structure might be present. If this is true, the question is how this structure might look like. First of all, the alignment is quite perfect. If we assume a powder of a two-dimensional hexagonal structure of very long parallel aligned rods with rod axes parallel to the velocity of the sheared liquid, we would expect to see Bragg and so peaks at Q values spaced according to 1:31/2:41/2:51/2:71/2: on. (Generally speaking the value of a vector of the reciprocal ), u is the lattice is given by 4a(n2 + m 2 - n m ) ' / 2 / ( 3 1 / 2 uwhere distance between the rods and n,m are integers.) The intensity of such a reflexion would be I
- P(Q)2pexp(-2w)
(10)
where F(Q)2is the form factor squared related to the cross section of the rodlike micelle. p is the multiplicity and w a Debye-Waller factor. We assume some random static displacement u' of the rod axes with respect to an ideal two-dimensional lattice and get w = ( u 2 ) @ / 4in the usual way. F(Q)is given by (2Jl(QR)/(QR))2, where J I is the Bessel function of first order and R is the rod radius. In the Q region of interest, F ( Q ) is near one and the Q dependence of this factor can be neglected. Therefore, we have to conclude that the Debye-Waller factor is responsible for the strong decrease in intensity between the first and the next peaks at Q2 = 3'/'Q1, Q3 = 2Ql, and Q4 = 7II2Q,. Making this assumption we were able to fit the intensity (see Figure 16) along the rim of the SANS intensity profile (see cut H-H' in Figure 10) quite reasonably. Especially, the first and second peak were reproduced nearly perfectly. It turned out that the second peak around Q 0.51 nm-' is a superposition of two peaks with Q2 = 31/2Q1and Q3 = 4 1 / 2 Q ]where , Q , is the Q value of the first peak. The intensities I t ( ' , Ilr2,and Ii13of these peaks were fitted and III1/ZII3 we to be approximately 1:0.40:0.21. From Z11'/11~2 calculated ( u ~ ) ' / ~ 3.4 and 3.6 nm, respectively. This can be compared with the distance u between the rods, which is calculated according to QI = 4a/(3Il2a)= 0.284 i 0.001 nm-I. a then has
-
-
Correlations in Micellar Solutions under Shear
a
[nm’l
I
0.201
0.30 0’25\@) I
-
\ U /
0.35L -0.05
0
~~nm-’]
0.05
Q,,[nni’l
b
0.201
0.30 0’25-
fj
W
0.351
-0.05 0
!
-~i[nm’l
0.05
~[nm’l
c
0.201
0’25: 0.30
@
Figure 17. Contour plot of the sharp peak of Figure 9d in better resolution: (a) experimental result, (b) the expected result for perfectly aligned micelles. In (c) an orientational distribution of liquid crystalline aggregates is taken into account. The intensities of the contour lines are 4000, 8000, 12 000, 16 000, 20 000, and 24 000, respectively.
a value of 25.0 f 0.1 nm. The intensity of a fourth Bragg peak at Q4 = 71/2Qlis then calculated, taking into account the Debye-Waller factor, to be 10%of the first one. The multiplicity factor for this reflection is twice the value of the other reflections. This low intensity explains qualitatively the shoulder marked by S in Figure 10. (The peak intensity of this peak is even lower than 10% because the width of the peaks increases with increasing Bragg angle. The reason for that is the wavelength distribution AX/X = 0.09 of the neutrons.) It was shown by a molecular dynamics calculation20*21 for interacting globular micelles that a phase transition occurs above a threshold value of r. The new phase showed a hexagonal structure, as in our system too. This theoretical results gives some support to our interpretation of the S A N S scattering curves. A closer analysis of the main peak of the type I1 micelles is shown in Figure 17. Figure 17a shows an enlarged view of Figure 9d. Figure 17b is a simulation for perfectly aligned micelles, taking into account the wavelength distribution, the divergency of the neutron beam, and the sample size. The agreement is not good. Therefore, it was supposed that well-aligned rods build regions of hexagonal structure, but that these regions are misaligned. The misalignment of these regions was described with a Gaussian distribution according to exp(-(a/ao)2), where a = 0 means alignment in the flow direction. For a. a value of 0.105 f 0.005 was found to fit quite nicely the experimental result, as shown in Figure 17c. We could not find any extra broadening in the Q,,direction not having its origin in Ah/X and the divergency of the neutron beam. Therefore we have to assume that the correlation length [, which is the size of the liquid crystalline (20) Erpenbeck, J. J. Phys. Rev. Lett. 1984, 52, 1333. (21) H a s , 0.; Weider, T.; Loose, W.; Hess, S.,to be published in Physica B (Amsterdam).
The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 4275 structures perpendicular to the direction of the rod axes, has to be quite large. Probably is of the order of 10 times the distance a = 25.5 nm between the rods, ore more.
7. Conclusions Analysis of S A N S data for the system C16-C8DAB in D,O under shear leads to strong evidence for the existence of two different types of micelles. Micelles with a small axial ratio are responsible for the ringlike scattering pattern and the larger micelles give rise to the sharply peaked structure in the scattering pattern. A comparison between the experiment and the calculation shows that, upon shearing, a redistribution of monomers between micelles occurs. The main features of the scattering patterns are as follows: appearance of a pronounced anisotropy; increase of the peak intensity with increasing shear rate r; decrease of the amount of micelles responsible for the ringlike pattern with increasing shear rate; appearance of an additional narrow peak structure above a shear rate of -50 s-l. The results can be understood semiquantitatively on the basis of a simple model which considers two types of micelles in equilibrium with each other and the equilibrium shifts with increasing shear to the larger micelles. The electric birefringence and the flow birefringence data are consistent with the existence of two different types of aggregates. A considerable portion of the surfactants is present as small anisotropic aggregates (Type I). This type of aggregates is only weakly aligned at shear rates of up to 2000 s-I. They are responsible for the anisotropic ringlike structure in S A N S patterns and in electric birefringence measurements which probe relaxation processes in the time domain of T = (1/6)D N 5 to 30 ms. The largest relaxation time which is maintained by both electric birefringence and the dynamic rheological measurements in the quiescent solution is about 30 ms. It is therefore likely that this largest relaxation time is monitored by SANS and is responsible for the anisotropic ringlike structure. The micelles of type I1 should, taking into account the very high degree of alignment even at r = 50 s-l, show relaxation times in the domain of seconds or even minutes. With increasing shear rates, monomers from type I micelles are converted into the type I1 micelles (shear-induced state). The extinction angle x does not approach zero at the highest shear rate but rather approaches a larger angle. This is due to the fact that this angle is determined by the average orientation of the micellar structures which are aligned around an angle near 45’ and by part of the material which is more or less completely aligned. The type I1 micelles are much larger than the type I, and for this reason, they can be aligned at lower shear rates. The results of the birefringence measurements are now much better understood, because S A N S measurements gave a strong r dependence of Deff. Type I1 micelles are responsible for the pronounced peak in the aligned structure in the S A N S experiment. The S A N S experiments furthermore show that the type I micelles are rods. At higher shear rates, the shape of the correlation peaks along the rim of the ringlike S A N S pattern can be described quite well. It seems likely that the type I1 micelles are of the same general shape and are formed from type I micelles by an aggregation process. The equilibrium between type I and type I1 is controlled by shear rate and is shifted toward type I1 at higher shear rate. There are indications that type I1 micelles form a hexagonal two-dimensional lattice with distortion described by a Debye-Waller factor. The short relaxation times which are monitored in electric birefringence measurements correspond to the rodlike micelles M. which begin to form at the concentration C,, = 1.5 X Above this concentration, the electrostatic interaction between the micelles is strong. This gives rise to a strong correlation peak. There is considerable positional, and probably orientational, correlation between the micelles and it is conceivable that the micelles actually form domains the size of which are much larger than the size of the individual micelles. These structures might give rise to a relaxation time in the region of seconds and determine
4276
J . Phys. Chem. 1989, 93, 4216-4282
the rheological properties of the solution as well as the shape of steadv-state (and not measured transient) SANS Drofiles. Acknowledgment. We thank the Institute Laue-Langevin for Droviding the neutron beam facilities and W. Griessl for his as&stance in computer work. This work has been supported by the
Bundesministerium fur Forschung und Technologie Grant No. 03-KAIBAY-0. Part of the suDD0r-t of S.H.C. came from the Alexander von Humboldt Stiftu-n*gand from the U S . National Science Foundation. Registry No. C16-C8DAB, 107004-19-3
Binding of Alkynes to Silver, Gold, and Underpotential-Deposited Silver Electrodes As Deduced by Surface-Enhanced Raman Spectroscopy Hannah Feilchenfeld*.’ and Michael J. Weaver* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: October 13, 1988)
Surface-enhanced Raman (SER) spectra of acetylene and simple alkynes adsorbed on silver, gold, and gold covered with a monolayer of underpotential-deposited silver were determined in electrochemical systems at room temperature. Multiple bands were observed in the triple bond region (1900-2200 cm-I), in addition to a feature at 1800 cm-I and an intense peak at 1500-1600 cm-I. No =C-H stretching vibrations were detected. The spectra on gold and silver-coated gold electrodes are essentially potential independent. The intensities of the bands obtained on silver, stronger than on the other metals, exhibit clear and reversible potential-related changes. In particular, the I SOO-cm-’ band decreases and the 1550-cm-I band increases at negative potentials. The u(C=C) frequencies of different alkynes on the same metal surface are almost identical, suggesting the formation of similar metal-adsorbate bonding for all compounds. The spectra in the triple bond region closely resemble the vibrational spectra of bulk-phase metal-alkyne complexes. They were therefore assigned to UT alkyne-metal complexes formed on the surface, in which the triple bond lies flat on the metal. The resemblance between the SER frequencies on silver and on gold is due to the similar electronic configuration of the two metals. In contrast, the more electron-deficient silver-covered gold surface exhibits higher v(C=C) frequencies. The 1550-cm-’ band is assigned to sp2 rehybridized forms of the adsorbates. The strongly downshifted 1800-cm-’ band, present on silver at positive potentials, may be due to the presence of polarized or ionic molecular species, stabilized by the electropositive surface.
The adsorption of alkynes at metal surfaces is of fundamental interest for understanding the nature of the bonding involved as well as of practical significance in heterogeneous catalytic processes. In view of the high degree of unsaturation of the alkynes, their surface bonding is anticipated to be very sensitive to the interfacial conditions. Several recent studies have used surfaceenhanced Raman spectroscopy (SERS) as a vibrational structural probe, both in cryogenic ultrahigh-vacuum (UHV)2s3 and at room-temperature e n v i r ~ n m e n t s , ~including -~ electrochemical system^.^^^ Most of these studies involve silver surfaces, although other substrates (usually Group IB metals) have been While the significant frequency shifts of the -C=C- and EC-H vibrations obtained upon adsorption indicate partial rehybridization, the acetylenic moiety appears typically to remain intact. Vibrational studies of acetylene and related alkynes on transition- or near-transition-metal surfaces by electron energy loss spectroscopy (EELS) yield significantly different results.’ The carbon-carbon frequencies, as well as the absence of the EC-H stretching vibration, usually suggest complete rehybridization to sp2 or even sp3, the alkyne being pictured as chemisorbed to the metal by UT or u 2 r bonding. An X-ray absorption investigation of acetylene on copper8 at 60 K confirms the anticipated ( I ) On sabbatical leave from the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel. (2) (a) Moskovits, M.; DiLella, D. P. In Surface Enhanced Raman Scattering; Chang, R. K., Furtak, T. E., Eds.; Plenum: 1982; p 243. (b) Manzel, K.; Schulze, W.; Moskovits, M. Chem. Phys. Lett. 1982, 85, 183. ( 3 ) (a) Pockrand, I.; Petterkofer, C.; Otto, A. J. Electron Spectrosc. Relat. Phenom. 1983, 29, 409. (b) Bobrov, A. V.; Kimel’fel’d, J. M.; Mostovaya, L. M. J . Mol. Struct. 1980, 60, 431. (4) (a) Parker, W. L.; Siedle, A. R.; Hexter, R. M. J . A m . Chem. S o t . 1985, 107, 264. (b) Parker, W. L.; Siedle, A. R.; Hexter, R. M. Langmuir 1988. 4 , 999. ( 5 ) Patterson, M. L. Weaver, M. J. J . Phys. Chem. 1985, 89, 5046. ( 6 ) Abrantes, L. M.; Fleischmann, M.; Hill, I. R.; Peter, L. M.; Mengoli, M.; Zoti, G.J . Electroanal. Chem. Interfacial Electrochem. 1984, 164, 177. ( 7 ) Sheppard, N . J . Electron Spectrosc. Relat. Phenom 1986, 38, 175. ( 8 ) Arvanitis, D.; Wenzel, L.; Baberschke, K. Phys. Rec. Lett. 1987, 59. 2435.
0022-3654/89/2093-4216$01.50/0
lengthening of the C-C bond upon adsorption. On the other hand, EELS of acetylene on silver does reveal a 9 - H band, suggesting the presence of weakly bound acetylene on the surface, but yields no detectable carbon-carbon vibrational modesg The latter can be accounted for in terms of surface selection rules.9 In a recent study from this laboratory, S E R S was used to examine the bonding of a number of alkynes at the gold-aqueous i n t e r f a ~ e .In~ contrast to the partial rehybridization observed for the other alkynes, acetylene exhibited spectra characteristic of complete formation of sp2 bonds, consistent with a surface reaction forming a polymeric specie^.^ Almost identical spectra were reported in ref 4a for acetylene on alumina-supported rhodium in the gas phase, but were interpreted in terms of the formation of a “cluster complex” in which acetylene is u 2 r bonded to three rhodium atoms.4 It is therefore evident that the nature of alkyne surface bonding is far from clarified. The study presented herein contains a comparison of SER spectra of acetylene and several derivatives obtained at silver and gold electrodes and at surfaces formed by underpotential deposition (upd) of a silver monolayer on gold, labeled hereafter “upd silver/gold”. All these surfaces provide suitable substrates for SERS.I0 The results show that under appropriate conditions all the alkynes yield stable adsorbates in these surface environments, forming sp to sp2 hybridized species. Experimental Section
Acetylene, obtained from Arco, Inc., was purified as outlined in ref 1 1; remaining traces of acetone were removed with a pair of traps at approximately -75 O C . 2-Butyne, 1- and 2-pentyne, and phenylacetylene were obtained from Aldrich; 1-butyne came (9) (a) Stuve, E. M.; Madix, R. J.; Sexton, B. A. Surf. Sci. 1982, 123,491. (b) Madix, R. J . Appl. Surf. Sci. 1982-83, 14, 41. (IO) Leung, L.-W. H.; Gosztola, D.; Weaver, M. J. Lungmuir 1987,3, 45. ( I I ) (a) Conn. J. B.; Kistiakowski, G.B.; Smith, E. A. J . Am. Chem. Soc. 1939, 61, 1868. (b) Perrin, D. D.; Armarego, W. L. F.; Perrin, D. R. In Purification of Laboratory Chemicals, 2nd ed.; Pergamon: New York, 1980; p 83.
0 1989 American Chemical Society
