J. Phys. Chem. 1991,95,6017-6020
6017
Ultrasonic Relaxation Associated with Monomer/Miceiie Exchange of Nonionic Surfactants in Formamide M. A. Thomason, D. M. Bloor, and E.Wyn-Jones* Department of Chemistry and Applied Chemistry, University of Salford, The Crescent. Salford A45 4 WT, U.K. (Received: December 1 7 , 1990)
Excess ultrasonic sound absorption and relaxation has been observed in solutions of some nonionic poly(oxyethy1ene)albyl ether surfactants in formamide. The concentration dependence of the relaxation time and amplitude have been analyzed respectively by using the equations proposed by Aniansson and Wall and also Teubner. In all cases the data are consistent with a multistep aggregation scheme to describe the kinetics in which stable micelles are formed via a series of stepwise bimolecular equilibria of the general form Al
+ A,,
k+
F A , ,
n = 2, 3, 4, ...
where A,, denotes an aggregate made up of n monomers and the k's are the rate constants. From the relaxation data estimates of k+, k-, and the polydispersity of the micelles are obtained. In addition, the kinetics are also consistent with an alternative phenomenological treatment.
Introduction As a result of extensive experimental studies over a long period of time and covering a wide variety of different experimental techniques the relationship between surfactant chemical structure and both micellar and lyotropic liquid crystalline structures is fairly well understood for aqueous systems.'J Recently there has been much interest shown in the fundamental properties of both dilute and concentrated surfactant solutions in nonaqueous polar solv e n t ~ . ~ ~These ' studies are extremely important in the sense that they underpin the current and anticipated developments in the technological use of these systems. In addition, on the molecular level, a range of nonaqueous polar solvents can be used, which enables the experimentalist to gain information on the molecular mechanisms of the so-called "solvo-phobic" effect. At present, the concensus of the published work on the solution properties of various surfactants that have been studied in nonaqueous polar solvents confirms that in dilute solutions aggregation of the surfactant usually takes place; however, it is the mechanism of the aggregation pracess that is the subject of debate and in many cases remains a controversial issue.+'* In some of the systems that have been studied the use of inappropriate ex(1) Wyn-Jones, E.; Gormally, J. Aggregation Processes in Solution; Elscvier: Amsterdam, 1969; Chapters 2, 3, 7. (2) Tiddy, G. J. T. Modern Trends of Colloid Science in Chemistry and Biology; Berkhauer Verlag: 1969; Chapter 7. (3) Fribcrg, S . E.; Liang, Y. C. Microcmulsions;CRC Press: Cleveland, OH, 1988; Chapter 3. (4) Evans, D. F. Longmufr 1988, 4, 3. (5) Backlund, S.;Bergenstah, 9.; Molander, 0.;Warnheim, T. J . Colloid Interface Sci. 1989. 131. 393. (i)Binama-Link, W.; a n a , R. Colloid Polym. Sci. 1989, 267, 440. (7) Ray, A. Nature 1971, 231, 313. (8) Ray, A. J. J. Am. Chem. Soc. 1969, 91,651 1. (9) Singh, H. N.; Salem, S.M.; Singh, R. P.; Birdi, K. S.J . Phys. Chem.
1980,84, 2191. (IO) Das, K. P.; Ceglie, A.; Lindmann, 9. J. Phys. Chem. 1987.91,2938. (1 1) Jopel, R.; Singh, J. R. Kolloid 2.2.Polym. 1970, 239, 699. (12) Belmydonts, A.; El Bayed, K.; Brondeau. J.; Canet, D.; Rico, I.; Lattcs, A. J . Phys. Chem. 1988, 92, 3569. (13) Latter, A.; Rico, I. Colloid Surf, 1989, 35, 221. (14) Almgren, M.;Swamp, S.; Lofroth, J. E. J . Phys. Chem. 1985, 89, 4621. (IS) Alfaw, 2.9.; Filby, W. G. Chem. Phys. Lctt. 1988, 144, 83. (16) Sjobcrg, M.; Henriluson, U.;Wamheim, T. Longmuir 1990,6, 1205. (17) Gharibi, H.; Palepu, R.; Tiddy, G. J. T.; Hall, D. G.; Wyn-Jones, E. J . Chem. Soc., Chem. Commun. 1990, 1 1 5. (18) Jonstromer, M.; Sjoberg, M.: Wamheim. T. J . A y s . Chem. 1990,94, 1549.
0022-3654191 12095-6017$02.50/0
periments have led to ambiguous data, which in turn has generated questions concerning the validity of drawing conclusions from the results. In other cases different experimental approaches have been taken to study a common system still leading to different conclusions. At present the situation with respect to the understanding of the aggregate behavior of ionic surfactants is still unclear; however there seems to be a general pattern emerging concerning the properties of dilute solutions of nonionic surfactants particularly in formamide where micelle formation is now established.18J9 In order to expand on this progress we wish to focus our attention on the dynamic properties of the aggregation behavior of some nonionic micelles in formamide. In this communication we describe our ultrasonic relaxation data on some poly(oxyethy1ene)alkyl ethers in formamide, which represents as far as we are aware the first attempt to investigate the kinetics of micelle formation of surfactants in nonaqueous polar solvents.
Experimental Section A. Materials. The surfactants used in this work were the poly(oxyethy1ene)alkyl ethers C,H2n+l(OCH2CH2)m(C,,EOm) supplied by Nikkol Chemicals (Japan). The surfactants used were C10EO4 (I), CloEO6 (11), CI2EO4 (HI), and C12E06(IV) with stated purities of 98%. The formamide used was a spectrophotometric grade product supplied by Aldrich. B. Ultrasonic Relaxation. The ultrasonic absorption and velocity were measured by using a modified version" of the Eggers resonance technique that covers the frequency range 0.4-18 MHz. The modified version of the Eggers resonance technique utilizes a Hewlett Packard 41 95A network/spectrum analyzer, which is used in its spectrum analysis mode with the whole setup controlled by a microcomputer (Opus), removing the need for many tedious manual repetitive measurements to be made. In order to accommodate formamide as a solvent the procedure used in assembling the mechanical cell also had to be modified. The x-cut crystals were mounted onto the stainless steel cell bcdy in the usual fashion by using silicone rubber as sealant. The (1 9) 63.
Couper, A.; Gladden, D.; Ingram. 9. Discuss. Faraday Soc. 1975,59,
(20) Eggers, F. Acoustica 1965, 19, 3223. (21) Eggers, F.; Funk, T. L.; Richmann, K. H. Reu. Sci. Instrum. 1976. __ 42, 361. (22) Aniansson. E. A. G.; Wall, S. N.; Almgren, M.;Hoffmann. H.;
Kiebran, I.; Ulbricht, W. J.; a n a , R.; Lang, J.; Tondre, C. J. J . Phys. Chem. 1976, 80, 905.
Q 1991 American Chemical Society
6018 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
i x 7 30
10~[s-']
T
2o 15 10
t
A
t
0
t
60
2
t
0.00
/
0,
i
25
Thomason et al.
+
0.10
+
A 0
t c
/
o
0.20 0.30 Total Concentration (C) [mol dm"]
0.40
0.50
0.05
0.00
0.10
0.20
0.15
Total Concentration [mol dm-3 ]
Figure 1. Plot of 1 /T versus total concentration C for nonionic surfactants: ( 0 ) CloEO,; (A) CloE06;(0)C,,EO,; (+) C,,E06.
Figure 2. Plot of (u/f - B ) versus total concentration C for nonionic surfactant CI2EO4: (0) 1.5 MHz; (+) 2.2 MHz; (A)3.0 MHz.
+
narrow circular gap between the x-cut piezoelectric crystal and the cell body is sealed by the silicon rubber and is covered with a coating of silver dag following which the cell was placed in an oven set at 110 O C for 2 h in order to bake the silver dag. This treatment ensured (i) that a good electrical contact was achieved between the gold-plated crystal and the cell body and (ii) that the heat-treated silver dag was resistant enough to formamide as a solvent and at the same time protected the silicon rubber seal from degradation by the solvent.
30
Results In all the solutions investigated in this work an ultrasonic relaxation was observed in the experimental frequency range. For solutions of CIOE04,C,zEO4, and CI2EO6in formamide a welldefined single relaxation exists and the data were analyzed by using the equation
lO*[s-']
T I
5
0
0.0
0.5
1.0
ff
A +B 7 = 1 + V/LJ2
where a is the sound absorption coefficient at frequencyf, A is a relaxation amplitude parameter, fc is the relaxation frequency, and B represents contributions to a/$ that are independent of frequency. The relaxation time 7 and the maximum absorption per wavelength p,,, are given by -I = ZTf,
(3) where u is the velocity of sound through the sample. It should be noted at this point that a relaxation was observed in solutions of CloE06-the amplitude of the process was however very weak and only estimates of T and p,,, are possible. The 1/7 values as a function of total surfactant concentration are shown in Figure 1 for compounds I-IV. In all cases the equilibrium being perturbed by the sound wave gets faster as the surfactant concentration is increased, indicating that at least one of the steps in the equilibrium is bimolecular. An inspection of the concentration dependence of the relaxation parameter p,,, reveals that at lower surfactant concentrations this quantity does not extrapolate to the origin; rather, it extrapolates to a positive value on the concentration axis. This implies that the observed relaxation only occurs when a certain well-defined surfactant concentration is reached and is thus consistent with micelle formation. Indeed, this extrapolation procedure has been used in the past to estimate critical micellization concentrations (cmc), and the method is best illustrated if we plot the excess sound absorption (a/$ - B) against total surfactant concentration for various operating frequencies, as shown in Figure 2. In all cases the excess absorption resulting from the relaxation extrapolate to approximately the same concentration. The observations confirm that the relaxation occurs as a result of the perturbation
1.5 (C
-
2.0
2.5
3.0
3.5
4.0
cmc)/cmc
Figure 3. Plot of l/s versus (C - cmc)/cmc according to eq 4 for nonionic surfactants: ( 0 ) CloE04;(A) CloEO,; (0) CI2EO4;(+) CIIEO6.
of an equilibrium involving the micelles, which we assign to the monomer/micelle process; hence, the cmc can be estimated directly from the ultrasonic experiment. These results are consistent with data from other e q u i l i b r i ~ m 'experiments ~*~~ on the aggregation of poly(oxyethy1ene)alkyl ethers in formamide that confirm the presence of micelles with aggregation numbers in the range 40-60. These experiments involved both sedimentation studies and small angle neutron scattering. In addition, the cmc's that were quoted in these previous works are consistent with those found in this work. On this basis we are justified in analyzing the present relaxation data, using an Aniansson and Wall fast relaxation equation22for the monomer/micelle exchange. Thus (4)
where C is the total surfactant concentration, n the micellar aggregation number, k- the rate constant for the dissociation of a monomer from the micelle, u the width of the micellar distribution, and m , the monomer surfactant concentration in the micellar region. For nonionic surfactants it is well established that once micelles are formed the monomer surfactant concentration remains constant and equal to the cmc of the surfactant. Therefore in the analysis of the above equation (4), 1/7 measured from the ultrasonic relaxation experiment is plotted against (C - cmc/cmc) as shown in Figure 3, for I-IV. The respective values for the slopes ( k - / n ) and intercepts (k-/u2) are listed in Table 1.
e.
(23) Ravey, J. Paper presented at Symposium on Surfactants in Solution, Gainesville, FL, 1990.
Monomer/Micelle Exchange of Nonionic Surfactants
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 6019
TABLE I: Kinetic and Equilibrium Parameters for Nonionic Surfactants (I-IV) Studied in "his Work at 50 O C in Foroumide
param cmc, mol dm-'
ClOEO4
ClOEO6
0.19
CllE04 0.05 f
0.22
0.01
k-In, s-I (eq 4) k-In, s-I (eq 9) k-/$. s-' (eq 4) k-, (q4) (eq 4) k+, mol-' dm3 s-I (eq 4) Q
18.4 X IO6 17.6 X IO6 1.4 X lob
5.5
X
-23.3 X lob -23.5 X IO6 -3.5 X IO6
1.5 X lob 1.8 X lob 1.3 X lob
-7.0 X IO' I4 -3.1 X IO9
6.0 X lo7
-
IO'
20 2.9 X IO9
6.0
C12E06 0.05 0.01 2.8 X lob 2.5 X lo6 0.4 X lo6 11.2 X IO'
CIOEO4
CIOE06
C12E04
$In h 5 )
6.5
-4.0
1.1
(eq 5)
14
-11 -0.74
1
Q
((AHCp/ap- AV)l, m3 mol-' (eq 5 )
1.1
X
10-6
10-6
4.0
1
A
/
1
o
I/
3.0
1 5 1.2 X IO9 2.2 x IO9
TABLE 11: Equilibrium Parameters Derived from Amplitude Analysis for Nonionic Surfactants (I-IV) Studied in This Work at 50 O C in Formmide
param
5.0
R, x IOd[mol dm-'s-'] T
X
1.8 X 10-6
C12E06 1.8 9 1.29 X 10-6
l'oEwy;
0.0
0.00
~
0.05
0.10
0.15
0.20
0.25
((
0.30
C-cmc [mol dm-' ]
Figure 5. Plot of Rd versus (C - cmc) according to eq 9 for nonionic surfactants: ( 0 ) CIOE04;(A)CloEO6;( 0 )CI2EO4;(+) CI2EO6.
are experimental. The resulting values of the two adjustable parameters mentioned above are in Table 11. Kinetic Studies Using the Phenomenological Approach
Finally, we focus our attention to an alternative approach to investigate the kinetic aspects of aggregation phenomena from ultrasonic relaxation experiments. We have shown that the kinetics of any aggregating phenomenon such as micelle formation whose chemical relaxation is characterized by a well-defined single ultrasonic relaxation can be investigated by using a phenomenological treatment. For a monomer/micelle equilibrium that can be represented by a general equilibrium description, e.g. "free" monomer e 'aggregated" monomer (6) the phenomenological equation of interest is 0.0
Y 0.0
I 1.0
2.0
(C
- cmc)/cmc
3.0
4.0
Figure 4. Plot of p,,, versus (C - cmc)/cmc according to eq 5 for nonionic Surfactants: ( 0 ) C&O4; (A)CloEO6; ( 0 )Cl2E04; (+) C12E06. Amplitude Analysis
The expression for the concentration dependence of the relaxation amplitude parameter, the maximum absorption per wavelength (p,) arising from the perturbation of the monomer/micelle equilibrium, has been derived by TeubneP and takes the form of the following expression:
where a = C- m l / m l ,p is the density of solution, and AH and AV the respective thermodynamic equilibrium parameters, enthalpy and volume change associated with the process. Cpis the specific heat at constant pressure, and cu is the coefficient of thermal expansion of the solution. All other terms in eq 5 have been defined previously. With the exception of ref 25, all applications of eq 5 have been confined to aqueous ionic surfactant solutions where the AH term has been neglected. Experimentally p,, p, u, and a are known (ml = cmc), and therefore it is possible to analyze the concentration dependence of the amplitude data with a least-means-square procedure using a two parameter fit in a 2 / n and ( A H C l a p - AV2. A typical set of l a t a are presented in Figure 4, where the solid line represents the results of the fitting procedure and the points (24)Teubner, M.J . Phys. Chem. 1919,83, 2917. (25)Jones, P.;Tiddy, 0. J. T.; Wyn-Jones, E. J . Chem. Soc., Faraday Trans. 2 1987, 83, 2733. (26)Hall, D.G.; Gormally, J.; Wyn-Jones. E. J . Chem. Soc., Faraday Trans. I 1983, 79,645. ( 2 7 ) Wan-Bahdi, W.; Palepu, R.; Bloor, D. M.;Hall, D. G.; Wyn-Jones, E. J . Phys. Chem., submitted for publication.
r
I
-' where Rl is the reaction forward (= backward) rate for (6) at a specified surfactant concentration C. In eq 7 are known from the relaxation data and the term in brackets is a constant and has been evaluated from the analysis of eq 5; thus a t any surfactant concentration C in the micellar range, Rl can be evaluated. As we have shown previously, once RI is known, one can apply conventional kinetic considerations to investigate the dynamics of the aggregation process. In these circumstances let us consider the backward step in (6) involving the dissociation of a monomer from the micelle. This would be expected to be a first-order process whose rate is proportional to the amount of micellar surfactant. Thus Rd = kd( c - CmC) (8)
or if we are to compare this approach directly with the treatment of the relaxation equation (4), the molar concentration of micellar material must be taken into account (i.e., the molecular weight of the micelles). Thus (9) If eq 9 holds, a plot of Rd against (C- cmc) should be a straight line passing through the origin with a slope of k-/n. As shown in Figure 5, this simple kinetic treatment works, and the values of k-In agree very well with the values found by using the conventional approach to relaxation kinetics via eq 4. Summary
The following is a summary of the noteworthy features associated with the present results: 1. As far as we are aware, the relaxation parameters of the nonionic surfactant in micellar solutions of formamide at 50 OC behave in exactly the manner predicted by the relaxation equations derived on the basis of the Aniansson and Wall theory for the fast
6020
J. Phys. Chem. 1991,95,6020-6027
relaxation time in micellar kinetics. Thus the observed ultrasonic relaxation is associated with the perturbation of the monomer/ micellar equilibrium. The kinetics are also consistent with the phenomenological approach. 2. As a result of 1 above the mechanism describing the formation of micelles from monomers is a multistep bimolecular scheme of the type k'
AI + A w I F A ,
n
= 2, 3, 4,...
In the above scheme, once micelles are formed there are substantial amounts of monomers and micelles present in solution, but the concentration of the intermediate aggregates is assumed to be extremely small and undetectable. However the presence of these intermediate aggregates is a necessary requirement for the formation of micelles via the above scheme. 3. The variation of the relative relaxation times for the different surfactants studied in this work follows the same trends as those of the well-documented ionic surfactants in water in the sense that for the same head group the relaxation is slower for the surfactant with the longer hydrocarbon chain. The influence of changing the head group on the relaxation is not immediately obvious from this work. 4. From the analysis of the concentration dependence of the relaxation parameters via the relaxation equations or the phenomenological treatment, it is possible to get two estimates for both k-/n and u2/n. In both cases the two values of these parameters agree very well, confirming the self consistency in the approach used for the analysis. 5 . In order to evaluate the new micellar parameters k- and u from these studies, information on the micellar aggregation numbers is necessary. As far as we are aware there is one report in the literature on the aggregation number of C12E06micelles in formamide. This has been measured at temperatures that are
lower than those in the present experiments (20-30 "C), and the data suggest that n is apparently not very temperature dependent. On this basis we can assume the "average" value of 40 for CI2EO6. Information on the effect of the alkyl chain length and the size of the EO group on the micellar aggregation number is extremely rare. It would appear that the "average" value for the aggregation number of CI4EO6is =60. Furthermore at a recent conferencen a value of -40 was quoted for C12E03in formamide. On the basis of this externally limited information we will assume that the aggregation numbers are independent of the EO size and decrease with chain length. Thus for CIOE04and CloE06we will assume n i= 30, and for CI2EO4and CI2EO6n i= 40. By use of these rough values, the estimates of k- and u are quoted in Table I. If we now proceed further by using the equation k + / k - = 1/cmc, it is possible to get the order of magnitude of k+, the rate constant describing the association of a monomer with the micelle. Values of lo9 mol-' dm' s-I are obtained as shown in Table I, indicating that this step is almost diffusion controlled in line with the same conclusions obtained from earlier experiments on ionic surfactants in water. 6. Finally we comment on the concentration behavior of the maximum absorption per wavelength pm displayed in Figure 4. Once micellization occurs, pm increases sharply with surfactant concentration, reaches a maximum value that is dominated by the thermodynamic term in brackets in eq 5 . At surfactant concentrations in excess of this maximum value the concentration dependence of pm is governed by the mI term in eq 5 . In the case of nonionic surfactants m lis expected to be constant and equal to the cmc, which is entirely consistent with the observed leveling off of p,,, in this region.
-
Acknowledgment. We thank the SERC for a research grant and fellowship (M.A.T.) and also the University of Salford Research Committee for equipment funds.
Structure of Mixed Short-Chain Lecithin/Long-Chain Leclthln Aggregates Studied by SmaiCAngie Neutron Scattering Tsang-Lang Lin,* Chi-Chang Liu, Mary F. Roberts:
and Sow-Hsin Cbent
Department of Nuclear Engineering, National Tsing- Hua University, Hsin- Chu, Taiwan 30043, ROC (Received: January 9, 1991; In Final Form: March 20, 1991) Small-angle neutron-scattering measurements with extensive internal and external contrast variations have been made to determine the structure of the small aggregates formed spontaneously by mixing 20 mM dipalmitoyl-PC (PC = phosphatidylcholine) with 5 mM diheptanoyl-PCin aqueous solutions at 30 OC. The radii of gyration of the head groups, the hydrocarbon tails of DPPC, and the hydrocarbon tails of diC,PC in the small aggregates are determined to be 81.4, 72.3, and 67.1 A, & .:peee;;t The Kratky-Porod plot shows that these small aggregates have disklike structure with a bilayer thickness of The polydisperse unilamellar vesicle model does not fit the measured neutron-scattering spectrum very well. Instead, a polydisperse disk micelle model with a Gaussian size distribution of radii fits the measured neutron-scattering spectrum very well. The mean radius of the disk micelles is found to be 92.3 A, and the half-width at half-maximum of the Gaussian distribution of the radii is 18 A. The thickness of the disk micelle as determined by the fitting is equal to 45 A. It is concluded that these small aggregates are most likely to be disklike mixed micelles.
Introduction Many amphiphilic molecules form small aggregates in aqueous solutions. Depending on the relative size of hydrophobic and hydrophilic parts of the molecule, the aggregates can be micelles, either rodlike or disklike, or vesicles, either unilamellar or multilamellar. Short-chain phosphatidylcholine molecules (fatty acid chain lengths 6-8 carbons) form micelles in aqueous solutions.'" 'Department of Chemistry, Baton College, Chestnut Hill, MA. *Department of Nuclear Engineering. Massachusetts Institute of Technology; Cambridge, MA. Correspondence should be addressed to: Professor Tsang-Lang Lin.
Dihexanoyl-PC forms globular micelles while diheptanoyl-PC and dioctanoyl-PC form rodlike micelles." When gel-state long-chain phospholipids are dispersed in aqueous solutions, they form large (1) Lin, T.-L.; Chen, S.-H.; Gabriel, N. E.;Roberts, M. F.J . Am. Chem. Soc. 1986, 108, 3499. (2) Lin, T.-L.; Chen, S.-H.; Gabriel, N. E.; Roberts, M. F.J . Phys. Chem. IPR'I. - - - . , -91.406. ., . - - . (3) Lin, T.-L.; Chen, S.-H.;Roberts, M. F. J. Am. Chem. Soc. 1987, 109, 2321. (4) Tausk, R. J. M.; Overbeek, J. Th.G. J . Colloid Inlerface Sci. 1976, 2, 379. (5) Tausk, R. J. M.; Karmiggelt, J.; Oudshoorn, C.; Overbeek. J. Th. G. Biophys. Chem. 1974, I , 175.
0022.365419 112095-6020302.50/0 0 1991 American Chemical Society
