J. Phys. Chem. 1980,84,3105-3110
3105
Experimental Investigations on the Flexibility of Elongated Cetylpyridinium Bromide Micelles GrQgolrePorte, Centre de Dynamlque des Phases Condensges,7 U.S.T.L. MontpeMer, France
Jacqueline Appeil, Laboratolre de Spectrom6trIe Raylelgh 6rl/louln,t U.S.T.L. Montpelller, France
and Yves Poggl Laboratolre dFlectrostatlqu@,Centre Natlonal de /a Recherche Sclentlflque, Grenoble, France, and Max Planck Instltut iiir Festkorperiorschung, Hoch Feld Magnet Laboratorlum Grenoble, France (Received: March 3, 1980)
Three distinct experimental investigation methods are used here to follow the evolution of cetylpyridinium (CP) micelles in high ionic strength aqueous solutions as a function of tfheadded salt (NaBr, NaC1) concentration. The quasi-elastic,light-scattering (QELS)spectrum yields the hydrodynamic radius (&) of the micelles which reflects their overall size: CPBr micelles are found to grow steadily with increasing NaBr concentration while CPCl micelles retain a minimum size at all NaCl concentrations. Under the same conditions magnetic birefringence provides a measure of the shape anisotropy of the micelles, and the broadening of the proton NMR spectra is indicative of their reorientation relaxation time. The magnetic birefringenceand the NMR broadening are both found to level off under conditions where the evolution of RH indicates a steady growth of the CPBr micelles. These experimental results are discussed and found to provide strong support to a model where the CPBr micelles are elongated semiflexible rods. It is shown that the finite rigidity of the rods mainly arises from short-range intramicellar forces and that it can be conveniently represented by the introduction of an intrinsic elastic bending modulus. This elastic modulus is found quite independent of the ionic strength and of the temperature.
give very different predictions, this procedure is often Introduction successful and generally the prolate model gives a correct It is well established by experimental evidence that, for fit while the disklike shape never gives a satisfactory numerous ionic soaps in aqueous solutions, the initially agreement.gJOHowever, the fits are usually performed by spherical micelles of minimum size can grow up to large assuming complete stiffness for the elongated micelles. aggregates when one adds large amounts of salt to the Although the rigidity of the micelles is indeed an important solution. This size-growing effect strongly affects the mechanical characteristic, very few studies have been macroscopic properties of the solution and is easily deconducted with emphasis centered on this possible flexitected through light-scattering or viscosity measurebility. This eventuality is sometimes suggested to explain m e n t ~ . ~Estimations -~ of the micellar weights of the large the discrepancy between the predictions from the stiff-rod micelles indicat~ean impressive increase of the aggregation model and the experimental result^.^ Stigter had some numbers in some cases: from lo2 to lo4 for cetyltrisuccess in treating the viscosity data of Kushner et ala4with methylammonium bromide in NaBr aqueous solutions, for a flexible-rod model.ll Recently, in their study of dodeexamp1e.l cyldimethylammonium chloride micelles by light-scattering The shape of the large micelles obtained in this way is measurements, Ikeda et al.30have obtained evidence for less obvious to determine: the micelles in the solution are a flexible-rod structure of the micelles at high NaCl conin complete disorder and the structure of individual objects centrations. Actually these results, though indicative, cannot be easily derived from classical diffraction methods. remain ambiguous since other characteristics such as the Actually, the constraints introduced by the length of their wide micellar polydlispersity predicted by Mukerjee' and hydrocarbon chains (hydrophobic tails) make the aggreIsraelachvili et al.6 can a priori account as well for the gated surfactants incapable of retaining spherical shape discrepancy between theory and experiment. Up to now for large aggregation numbers.&* And in fact this theoretical deduction finds much experimental s ~ p p o r t , ' ~ ~ the ~ ~ rigidity of rodlike micelles is still open to question. We here report an experimental investigation of the Within this dimensional constraint several attempts have elongation of cetylpyridinium (CP) salt (chloride and been made to determine whether the shape of the large bromide) micelles with special attention focused on the micelles is prolate (rodlike) or oblate (disklike). The shape of the elongated micelles. We use three distinct classical way to obtain this information is to fit the exmethods of investigation to follow the evolution of different perimental datal (low-angle X-ray scattering: angular characteristics of the! micelles: quasi-elasticlight scattering dissymetry of the scattered light3J0) with the prediction (QELS)provides a measurement of the overall size of the of the different models. Since prolate and oblate models micelles through the obtained values for the hydrodynamic radius RH,magnetic birefringence is indicative of the shape 'Laboratoire associ6 au Centre National de la Recherche Scienanisotropy,12and high-resolution NMR measurements of tifique (LA 233). proton spectral broadening give information on the re1Equipe de recherche associ6e au Centre National de la Recherche Scientifique (ERA 460). laxation time 7 for imicellar re0rientati0n.l~ 0022-3654/80/2084-3105$01 .OO/O
0 1980 American Chemical Society
3106
The Journal of Physical Chemistty, Vol. 84, No. 23, 1980
The measurements are performed over a wide range of micellar sizes (RHin the range 30-650 A) and show that the stiff-rod model must be discarded for the largest micelles ( R H > 200 A). On the other hand, introducing flexibility restores a very comprehensive agreement between data and predictions. Materials and Methods Reagents and Solutions. CPBr was prepared14 by refluxing reagent-grade pyridine with 20% molar excess of redistilled bromohexadecane for 12 h. After cooling, the crude material was recrystallized three times in wateracetone mixtures and redissolved near to saturation in ethanol. Active charcoal was added to this latter solution. After filtration, recrystallization was obtained by the addition of a large excess of ether. The obtained product was recrystallized two more times in water-acetone. After vacuum desiccation the purified surfactant showed 99.3 % purity on bromide analysis and 99.0% purity on carbon mass analysis. Its purity was further verified by thin-layer chromatography. CPCl was obtained by recrystallization of CPBr twice in concentrated NaCl aqueous solution and twice in distilled water. The purification procedure was the same as for CPBr. The quality of the obtained product was verified M) with high by checking that in dilute solution (6 X NaBr addition (0.8 M) the same results were obtained by QELS as for CPBr.3 The added salts, NaBr and NaC1, were reagent grade (Merck Suprapur). Water used in solution was tridistilled. Solutions were prepared by weight and filtered through a 0.22-wm Millipore filter directly into the experimental cells. For NMR measurements, D20 is required rather than HzO. D20was provided by CEA Saclay and used as it was. Otherwise the sample preparation was the same as for the other methods. Magnetic Birefringence. A magnetic field H can induce an average degree of orientation fl over a collection of objects presenting a diamagnetic anisotropy Ax. This phenomenon has already been used to detect the shape anisotropy of m a c r o m ~ ~ e c u ~ eas s ~well ~ J as ~ Jof~ mi~e1les.l~ The degree of orientation may be written12 as
as long as AX@ > (1) condition may be no longer fulfilled
The Journal of Physical Chemistry, Vol. 84, No. 23, 1980 3109
Elongated Cetylpyridinium Bromide Micelles
L 20
:
40
30
6o T ("c ) 7 O
50
Flgure 4. CCMas a function of temperature ( T ) . NaBr concentration = 8 X IO-' M.
geometrical parameters are in fact estimated from theoretical considerations6 rather than from precise experimental measurements, and their evaluation leads to uncertainties. This is one of the reasons that flexibility is cautiously suggested only when a wide discrepancy with the simpler stiff-rod model is ~ b s e r v e d .And ~ indeed an important advantage of the magnetic birefringence method is that we could derive our conclusions with no requirements of such a priori specifications. There is certainly also a matter of sensitivity. The Cotton-Mouton constant is essentially determined by the shape anisotropy of the objects which is more sensitively affected by their actual flexibility than other properties. In order to illustrate this point we calculate in the Appendix this CCMand the gyration radius of flexible objects within the Landau and Lifshitzn approximation for flexible macromolecules.
Acknowledgment. This research was supported in part by ATP contract no. 3032 from CNRS. We thank Dr. G. Maret, Dr. J. Charvolin, and Dr. P. Bernier for fruitful discussions on this subject. We are greatly indebted to Dr. P. Bernier, who performed the NMR measurements. Appendix In this last section we compare the efficiency of lightscattering dissymmetry and magnetic birefringence to detect flexibility in a solution of rodlike objects. To do this comparison we have to derive the mean values over all configurations of the gyration radius R G and ~ of the Cotton-Mouton constant CCMfor flexible objects. We start from the classical results of Landau and Lifshitz in ref 27. The resistance to bending of the flexible objects having uniform structure is characterized by the so-called elastic modulus a, and the thermal averaged value of the angle d(1) between two parts of the object separated by the distance Z measured along the object obeys the relations27
e2(l) = 21/(1)
L L . L
0
L
1
.
3
5
7
L/
9
Flgure 5. Comparison of Rc: and CcMfor a semiflexible rod of length L and persistence length ( I ) as given by eq 11 and 17 to Re2 and C, for a rigid rod (rr) cif same length L as a function of L / ( / ) : (1) R -'= RQ2/RCh2;( 2 )
cos e(l) = exp(-l/(l)) -
(8)
with ( 1 ) = a/kBT, while R2(Z)the average distance (taken along a straight line) between two parts of the object is
-
R2(Z) = 2(Z)2[Z/(2)- 1 + exp(-Z/(l))]
(9)
It can be easily s:hown that for any linear object having uniform density R(:2 is given byzs
R = CCM/CCM,.
because of the temperature-shortening effect on micelle length,7J0p22 and no unambiguous information about a can be obtained in this temperature range. Therefore, the peculiar asymptotic behavior of CCM found in this work unambiguously rules out the rigid-rod shape for CP elongated micelles, and good consistency is found for our experimental results with a semiflexible-rod model with a uniform bending elastic modulus showing no noticeable dependence on the ionic strength and on the temperature. To conclude, it is worthwhile to wonder about the rather little attention paid in the literature to the micellar flexibility which has such a striking effect on the CCMvariations. Actually, few experimental methods are available to detect directly the flexibility. Electric birefringence is indeed simpler thnn magnetic birefringence, but we could not obtain a reliable response at the high salt concentrations of our solutions. On the other hand the interpretation of the results obtained by other classical methods (light scattering, viscosity, etc.) requires quantitative a priori Specifications for the geometry of'the model to be fitted to the data (radius of the rod, for instance). These
( L = overall length of the object). Averaging accordiing to eq 9 and performing the integration (eq 10) one easily obtains
with x = L / ( l ) . It can be verified that this gives @ = R2(L)/6 in the x = 0 ) limit (random coil) and = L2/12 in the x = 0 limit (stiffrod) in agreement with the classical relations28for these two limiting cases. More precisely the limited development of @ in the stiff-rod (sr) limit may be written as
--
RG2
-
RG;(l-
~ / 5 )
(12)
Now to obtain CCM for flexible rods, one needs the mean value .-
S ( I ) = 1/,[3 cos2 e(z) - 11
(13) since Aa and A x arise from polarizability tensors. Just as
31 10
The Journal of Physical Chemistry, Vol. 84, No. 23, 1980
it has been done in ref 27 for cos O ( l ) , one immediately shows that, as long as the fluctuations in the curvature of different sections of the object are statistically independent, we have S(I& - 41) = S(Ih - l21) S(llZ - 111)
(14)
On the other hand for small values of O ( l ) we must have
-
S(1) N 1 - 3$/2
= 1 - 31/(1)
(15)
Equations 14 and 15 imply
-
S(2) = exp(-31/(1))
(16)
Now if a section dl azound the point lo is submitted to a local magnetic field H, it will assume a degree of orientation flo(lo): flo(lo) = ( H % x o / k T )dl where axo is the diamagnetic anisotropy of a unit length of the object. Because of the rigidity, this local degree of order will decreasingly propagate over the whole length of the object, and the contribution of the local field to the optical birefringence Ano(lo)is given by
(6aois the polarizability anisotropy of the unit length of the object). We make the following We assume that - approximation. -the preexisting degree of order induced at ll by the local action of H in lo does not affect the response of ll to the magnetic field. Actually this coupling effect is of the order of H4 and is not taken into account in classical CottonMouton situations (AXH2/kBT
