1454
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
micellization processes), the chainsolvent hydrophobic interactions would be stronger than for usual hydrocarbon s ~ r f a c t a n t s .Such ~~ a hypothesis agrees with findings from Hildebrand and cow o r k e r ~and ~ ~even the large volume change upon micellization, AV,,,, supports the above interpretation. In fact it is reasonable to assign the large AV,,, change to the high hydrophobic hydration of perfluoromethylene chains and not to the formation of large micellar aggregates. The low number of aggregation, in the case of the perfluorinated surfactants, could be due also to an effect of “space filling con~ t r a i n t ?namely ~ to the large steric hindrance of the -CF2- groups. B . Micelle Size, Shape, and Hydration. The size and shape of micelles, as well as their relation to composition, temperature, and other components, have been widely described in l i t e r a t ~ r e . ~ ~ Close to the lyotropic-nematic phase, some perfluorinated surfactants, such as tetramethylammonium perfluorononanoate, form slightly anisotropic aggregates” and exhibit micelle aggregation numbers of about 150. For LiPFN micellar solutions, we noted a slight increase of viscosity with the overall surfactant content (Table 111). An analysis of our data by eq 6 shows that neither size nor shape transitions occurred up to 0.5 mol kg-’; in fact, no change in the slope of the function log vrel vs. l / m log vrcl was ob~erved.’~ The hydrodynamic volume, @v,q,, obtained from the A value of eq 6, is around 500 cm3 mol-’ and the intermicellar interactions, obtained from coefficient C, seem to be negligible. An attempt to get micellar axial ratios from viscosity data requires drastic assumption. However, if the solute volume fraction is less than 0.1,40 it is possible to reduce the polynomial equation for viscosity to the following
vre, = 1 + Kad*
(13)
where a is a proper constant, K a shape factor, and I$* the solute volume fraction. The phenomenological shape factor, K , obtained in this way allows the determination of the micellar axial ratios, J, according to the equation4I
La Mesa and Sesta molecules bound to micelles behave as a whole kinetic entity with the micelles. It is possible to get hydration numbers by comparing the hydrodynamic volume, &?, of the solute with its partial molar volume according to the empirical equation
where ri is the mean hydration number per surfactant molecule and d, the solvent partial molar volume. The obtained ii values lie in the range 10-12, showing a small but systematic increase upon increasing the surfactant concentration. (According to a classical paper by Mukerjee?* the experimental hydration values by viscosity can be higher than the true ones up to 20-30%; this is a consequence of electroviscous effects, which exert long-range forces on neighboring water molecules.) Such variations can be ascribed to long-range effects on the surrounding water molecules, which depend on the net micellar charge, on the micellar shape and on the solute volume fraction. Conclusions
Systematic studies on lithium and sodium perfluorononanoate aqueous solutions show that micelles formed by the above compounds contain a small number of surfactant monomers and retain an almost spherical shape even a t high concentrations. Such behavior is due to the weak chain-chain interactions of perfluorinated moeities, which reduce the contributions to the hydrophobic effect. Note Added in Proof. It has been discussed by T i d d and ~~~ H ~ f f m a n that n ~ ~the sizes and shape of perfluorinated surfactant micelles are practically independent of surfactant content up to compositions very close to those of the phase separation limits. Acknowledgment. Thanks are due to Prof. H. Hoffman (Bayreuth, FRG) for sending us unpublished results in the field, and to Prof. K. Shinoda (Yokohama, Japan) for suggestions on Krafft point temperature data. Appendix
Equation 12 should be rewritten as These J values lie in the range 1-5, corresponding to those for low micellar anisometry. According to our data and to the general assumption that relates the shape of micelles with the structure of the adjacent lyotropic mesophases, the micelles should have a shape resembling short rods.’ As a result of electrostatic and dipolar effects, micelles are hydrated entities. From a viscometric point of view, the water (35) Mukerjee, P. Kolloid Z . Z . Polym. 1970, 236, 76. (36) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solurions: Van Nostrand-Reinhold: New York. 1970. (37) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. N . J . Chem. SOC., Faraday Trans 2 1976, 72, 1525. (38) Mazer, N . A,; Benedek, G. B.; Carey, M. C. J . Phys. Chem. 1976, 80, 1075. (39) Sesta, B.; La Mesa, C.; Bonincontro, A.; Cametti, C.; Di Biasio, A. Ber. Bumenges. Phys. Chem. 1981, 85,198; 1982, 86, 664. (40) Nagarajan, R.; Shah, K. 0.;Hammond, S. Colloid Surf. 1982, 1, 147. (41) Kuhn, W.; Kuhn, H.; Buchner, p. In Ergesnisse der exakten Naturwissenschaffen: Springer Verlag: Berlin, 195 1; Vol. 2 5 .
In K,, + n In
cT((Y-),,,
+ In cT(Y-’)
- (7-’)) = ( n - 1) In ( Y - ) ~
Above the cmc, y- experimentally obtained as (ya2/(y+)will be ( 7 - 1= ~ (y-)mcm ~
+ (Y-)I(CT
-~
7 )
(1 2a)
where the subscripts m and 1 refer to micellized and monodispersed surfactant ions, respectively. Above the cmc we can introduce the term (%’) = (7-1- (y-)I(cT - c m ) / c T = ( Y - ) m ( C m / C T ) (12c)
The above equation allows us not to take into account the term due to (7JI;in this way, eq 12c gives values taken relative to (yJI. Registry No. LiPFN, 60871-92-3; N a P F N , 21049-39-8. (42) Mukerjee, P. J . Colloid Sci. 1964, 19, 722. (43) Tiddy, G. J. T. Lecture presented at the Sixth International Symposium on Surfactants in Solution, New Delhi, August 18-22, 1986. (44) Hoffmann, H., private communication.
J. Phys. Chem. 1987, 91, 1455-1460
1455
Relaxation Klnetlcs of Sodium Tetradecyl Sulfate Micelles in H20 and D20 Christer Elvingson* Department of Physical Chemistry, University of Goteborg and Chalmers Universidy of Technology, S-412 96 Goteborg, Sweden (Received: April 30, 1986; In Final Form: November 11, 1986)
Kinetic measurements using relaxation techniques have been carried out on solutions of sodium tetradecyl sulfate (STS) micelles in H 2 0 and DzO.The slow relaxation time, characteristic of the formation and disintegration of proper micelles, was found to be several times larger in DzO.The relaxation times were analyzed with use of the theory of mixed micelles, regarding the monomers and the counterions as the two components. If a narrow counterion distribution and a Gaussian minimum in the aggregation space are assumed, the location of the minimum and the concentration of the corresponding aggregates in the two solvents could be determined. Furthermore, by analysis of the relaxation amplitudes it is shown that the pressure dependence of the critical micelle concentration (cmc) and the mean aggregation number are larger in DzO than in HzO.
I. Introduction
be of the greatest interest to study the rate of exchange of monomers in micelles as well as the rate of formation and disinteDuring the past 20 years, much effort has been devoted to the gration of micelles in the two solvents. The experimental techinvestigation of hydrophobic interactions in aqueous solutions.14 nique, which is most sensitive to small changes in the parameters Most of the work published in this area has been concerned with characterizing the micelles and the micelle size distribution, is thermodynamic properties determined by equilibrium measurements. Especially the aggregation of amphiphilic molecules has relaxation measurement^.^^-^^ Up to now there has only been been investigated both the~retically~.~ and e~perimentally.~One method, which has been used in these studies is the substitution ~ many physical of DzOfor H 2 0 as the ~ o l v e n t . ~ - 'Although (1) Nemethy, G.; Scheraga, H. A. J . Phys. Chem. 1962, 66, 1773. properties such as the surface tension and the dielectric constant (2) Tanford, C. The Hydrophobic Effect, 2nd ed;Wiley: New York, 1980. are almost identical in H 2 0and D20, other properties which are (3) Ben-Naim, A. Hydrophobic Interactions; Plenum: New York, 1980. sensitive to the liquid structure are significantly different. The (4) Evans, D. F.; Ninham, B. W. J . Phys. Chem. 1986, 90, 226. viscosity of D 2 0 is 20%higher a t 35 O C and the temperature of (5) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J . Chem. SOC. maximum density is 11.2 OC for D 2 0 compared to 4.0 OC for Faraday Trans. 2 1976, 72, 1525. H20.18 These facts suggest that D 2 0 is a more structured liquid (6) Nagarajan, R.; Ruckenstein, E. J . Colloid Interface Sci. 1979, 71,580. in the sense that the hydrogen bonds are stronger in heavy water. (7) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Carey, M. C. J . Phys. In spite of the fact that the hydrogen bonds are agreed to be Chem. 1983, 87, 1264. stronger in D 2 0 , the change of solvent has not been able to give (8) Mukerjee, P.; Kapauan, P.; Meyer, H. G. J . Phys. Chem. 1966, 70, a clear-cut answer regarding the relative strength of the hydro783. phobic interactions in the two media. The measurements of (9) Emerson, M. F.; Holtzer, A. J . Phys. Chem. 1967, 71, 3320. micellar properties have shown that the cmc is somewhat lower (10) Oakenfull, D.; Fenwick, D. E. Aust. J . Chem. 1975, 28, 715. in DZOs-l0and that the mean aggregation number is always larger (11) Bedb, Z.; Berecz, E. Acta Chim. Acad. Sci. Hung. 1980, 103, 217. in heavy Kinetic measurements of reactions in which, (12) Chou, S. I.; Shah, D. 0 .J . Phys. Chem. 1981,85, 1480. for example, the transition state is stabilized by hydrophobic (13) Chou, S. I.; Shah, D. 0 . J . Colloid Interface Sci. 1981, 80, 49. interactions also indicate that these are stronger in Dz0.10319 (14) Chen, C. H. J. Phys. Chem. 1982,86, 3559. However, when measuring the solubility of different hydrocarbons (15) Candau, S.; Hirsch, E.; Zana, R. J . Colloid Interface Sci. 1982, 88, 428. in HzO and D 2 0 the results are not so unambiguous. While the (16) Serdyuk, A. I.; Mikhalchuk, V. M. Russ. J . Phys. Chem. 1983.57, shorter hydrocarbons have a higher solubility in D2O,Zothe larger 1771. hydrocarbons and those with aromatic rings seem to be more (17) Chang, N . J.; Kaler, E. W. J . Phys. Chem. 1985, 89, 2996. soluble in H20.21 Ben-Naim et al.22923have investigated the (18) Kirshenbaum, I. Physical Properties and Analysis of Heavy Water, solubility of a large number of different solutes in H 2 0 and D 2 0 National Nuclear Energy Series, Division 111, Vol. 4A; McGraw-Hill: New and they find that different hydrophobic substances have different York, 1951. relative solubilities in the two solvents and that a given hydrophobic (19) Plonka, A.; Kevan, L. J . Phys. Chem. 1984, 88, 6348. solute can be more soluble in H 2 0at one temperature while the (20) Kresheck, G. C.; Schneider, H.;Scheraga,H. A. J. Phys. Chem. 1965, situation can be reversed at another temperature. From this it 69, 3 132. seems that, in spite of our increased knowledge of hydrophobic (21) Guseva, A. N.; Parnov, E. I. Radiokhimiya 1963, 5, 507. interactions during the past decades, there still remains work to (22) Ben-Naim, A.; Wilf, J.; Yaacobi, M. J . Phys. Chem. 1973, 77, 95. be done before we have a quantitative theory which can account (23) Marcus, Y.; Ben-Naim, A. J . Chem. Phys. 1985, 83, 4744. for the different types of phenomena which are attributed to the (24) Frenot, M. P.; Ntry, H.; Canet, D. J . Phys. Chem. 1984, 88, 2884. interactions of hydrophobic and amphiphilic solutes in aqueous (25) Cabane, B. J . Phys. 1981, 42, 847. solutions. (26) Tobrakcioglu, C.; Dore, J. C.; Robinson, B. H.; Howe, A.; Chieux, Most of the work cited above has been concerned with equiP. J . Chem. SOC.,Faraday Trans. I 1984, 80, 413. librium measurements and very few with kinetic processes. It is (27) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983, 261, 1022. the purpose of the present paper to present a study of the kinetics (28) Aniansson, E. A. G.; Wall, S. N.; Almgren, M.; Hoffmann, H.; of micelle formation in H 2 0 and DzO. The similarity of the two Kielmann, I.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J . Phys. Chem. 1976, 80, 905. isotopic liquids has led to the substitution of D 2 0 for H 2 0in many (29) Baumiiller, W.; Hoffmann, H.; Ulbricht, W.; Tondre, C.; Zana, R. types of experiments on micelles, e.g. in NMR24*2s and neutron J . Colloid Interface Sci. 1978, 64, 418. s ~ a t t e r i n g . ~Especially ~ * ~ ~ with N M R , dynamical processes as (30) Hoffmann, H.; Platz, G.; Ulbricht,G. J . Phys. Chem. 1981,85, 1418. well as equilibrium properties can be studied.24 Thus, it should (31) Bauernschmitt,C.; Hoffmann, H.; Platz, G. Ber. Bunsen-Ges. Phys.
*Present address: Procter Department of Food Science, University of Leeds, Leeds LS2 9JT, UK.
Chem. 1981,85, 203.
0022-365418712091-1455$01.50/0 0 1987 American Chemical Society
1456
The Journal of Physical Chemistry, Vol. 91, No. 6,1987
one preliminary investigation3)using DzOas the solvent concerning the fastest of the two processes observed in relaxation measurements on ionic micelles, and this did not reveal any great differences between the observed kinetics in the two media when the change in viscosity was taken into account. In the present study, pjump and shock tube measurements on sodium tetradecyl sulfate (STS) micelles are presented. The results show that, although the rate of monomer exchange with the micelles does not show any great difference, the rate of micelle formation and disintegration is approximately three times slower in D20 compared with H2O. In section 11, the stepwise model for mixed micelles is reviewed. In section 111, the experimental details are given and in section IV, the results concerning the equilibrium properties and relaxation times in light and heavy water are presented. In the same section a discussion of the results is given and some conclusions are drawn.
Elvingson It is very sen~itive)~ to the values of the parameters characterizing the narrow passage. Thus a small change in some of these parameters can result in a large change in 7 2 . This is one of the reasons why relaxation measurements are such a powerful method in probing small differences in the equilibrium properties characterizing a micelle solution. In this paper, two different methods of dealing with R will be used in the analysis of the slow relaxation time. We will first consider the expression of Lessner et al.)’
11. The Stepwise Model for Ionic Micelles
The stepwise model for the formation of mixed micelles presented in ref 34-36 can be used to describe ionic micelles if one regards the monomers and the counterions as the two components. If the components are denoted by A and B, the stepwise model can be written
A, and B, are the two monomers while M , , represents a micelle with r monomers of A and s monomers of B. A , , B , , and M,,, will in the following also denote the corresponding concentrations. (We will in the following take A, as the surfactant monomer and B, as the counterion.) Assuming a deep minimum in the aggregate concentrations between the monomers and the region of proper micelles, the so-called narrow passage, the theory predicts two fast relaxation times. Experimentally however, only one is found. The fastest of these relaxation times is probably very fast and therefore not easily detected. Thus assuming that k2 in eq 1 is very large, and also that the counterion distribution is monodisperse for every micelle size, the following expressions for the fast ( 7 , ) and slow ( 7 2 ) relaxation times are obtained for ionic micelles34 1
- = k,( 71
-1= - 1 r2 RC,
1+ 5 + (1 u2
A,
Bl
(2)
(3)
Here
(5)
where amis the dissociation degree and m the size of the aggregates in the minimum. M is a constant which among other things involves the effective width of the narrow passage and the rate constant klmin the minimum and also the equilibrium constant for the formation of the aggregates in the minimum. In the derivation)’ of eq 4 and 5 , the position of the minimum and maximum were fixed in aggregation space. Therefore another approach is also used in this paper for the treatment of the resistance. For a monodisperse counterion distribution, R is given by36 1 R=Cmin kl-( r ) M , The minimum in aggregation space is now assumed to have a Gaussian shape
Mr= @ , m e(r-m)2/2a2m
Here, k , is the average of k,-(r,s)in the region of proper micelles, a is the dissociation degree, n the mean aggregation number, u2 the variance of the micelle distribution, and C,,, the concentration of proper micelles. A bar denotes the corresponding value at equilibrium. Equations 2 and 3 which, as noted above, are special cases of the more general results for mixed micelles were also obtained by Lessner et aL3’ who made the above-mentioned simplifications from the outset. The quantity R introduced in eq 3 can be regarded as a resistance to the flow of aggregates through the minimum in aggregation space during the slow p r o c e ~ s . ) ~ . ~ ~ (32) Angel, M.; Hoffmann, H. Z . Phys. Chem. 1984, 139, 153. (33) Gettins, J.; Jobling, P. L.; Walsh, M. F.; Wyn-Jones, E. J. Chem. SOC.,Faraday Trans. 2 1980, 76, 194. (34) Aniansson, E. A. G. “Aggregation Processes in Solution”, in Studies in Physical and Theoretical Chemistry, Vol. 26, Wyn-Jones, E., Gormally, J., Eds.; Elsevier: Amsterdam, 1983. (35) Wall, S. N.; Elvingson, C. J. Phys. Chem. 1985, 89, 2695. (36) Elvingson, C.; Wall, S. N. J. Phys. Chem. 1986, 90,5250. ( 3 7 ) Lessner, E.; Teubner, M.; Kahlweit, M. J . Phys. Chem. 1981, 85, 1529.
(7)
Here M, is the minimum concentration and u, the width of the minimum. The rate constants k,-(r) in this region are assumed to be independent of r and equal to klm,while fi, m, and M, will, when using eq 6 and 7, be taken as concentration dependent. The concentration dependences were calculated according to eq 7-10 in ref 36. The amplitude U2of the slow relaxation process has also been determined. An equation for U2 for a general two-component system was derived in ref 35. There it was also shown that for a monodisperse counterion distribution the equation reduces to that given by Lessner et aL3’
a
r
a.
X 1-2
r 6 In fi
I
(8)
where X is defined as S2/S1(see eq 12). To be able to fit the experimentally obtained relaxation times and amplitudes, one must also calcualte how A , and B , change with the total concentration of amphiphile. In ref 35 eq 18, an expression was given for
The Journal of Physical Chemistry, Vol. 91, No. 6,1987 1457
STS Micelles in HzO and D 2 0
I 3.0 -
TABLE I: Parameters Obtained from Equilibrium Measurements in STS-H20/Dz0 at 35 O C H20
cmc, mol m-3
2.21
LY
0.20 -28.18 0.35
AGO,
x
kJ/mol
D20
1.94 0.18 -29.1 1 0.34
2.0
-
1.0
-
c .1
-P
t
(8Al/BBI) for a general two-component system when the total concentrations of A and B are equal, Le. when A,, = Bto,. An analogous calculation shows that, when Atot = zB,,, and the counterion distribution is narrow, one obtains (1 - a)-Cm dA I _ dB1
-
z
- a-n2:
z
cm 1 + anz-
B1
(9)
AI If B1 is taken as the counterion, z is the ratio between the valencies of the counterions and the amphiphilic ion. In ref 36 it is shown that the mean aggregation number can be considered as concentration independent for a broad range of parameters characterizing the micelle distribution. Equation 9 can then be integrated and the concentration dependence of the monomer will be given by 2, = cmc[l + aa]-(l-a)/(z+l-a) (10) where a = (A,,, and a is defined by the relation f i 2 / f i 1 = (1 - a)/z,where fiz is the number of counterions associated with a micelle of size For the special case of z = 1, this equation was obtained by Lessner et al.,37having implicitly made the simplification introduced above from the start.
al)/al
111. Experimental Section Materials. The STS used in this study was synthesized by the Synthesis Service at the University of Lund. The purity was verified by the absence of a minimum in a surface tension vs. concentration plot. The DzOused was in most cases Ciba-Geigy, 99.8% isotopic purity. In some measurements heavy water from Merck and Norsk Hydro (Norway) was used, but no significant differences were observed when using other supplies. To further assure that the effects presented are due to the different structure of the liquids and not caused by impurities, such as surface-active substances or electrolytes, the surface tension and conductivity of the pure D 2 0 were measured. The results, however, did not show any detectable amount of any impurities. The last check was to destill a sample of the DzO in a nitrogen gas atmosphere, but this did not affect the results either. Cmc Measurements. The critical micelle concentrations were measured in a constant-temperature water bath at 35.0 OC with a LKB 3216B conductivity bridge. The cell used had a cell constant of 2.05 X lo2 m-I. Relaxation Measurements. The fast relaxation time was measured in a shock tube,38 by conductivity detection. The slow relaxation time was measured in a p-jump apparatus39(DIALOG) and also in this case, conductivity was used as the detection method.
IV. Results and Discussion Cmc Measurements. The critical micelle concentrations for STS in HzO and D 2 0 are shown in Table I. It is seen that the cmc is lower in heavy water by 12%. This is in the same range as found in ref 17 and 20 for STS and dodecylpyridinium iodide but a little more then found for SDS in ref 8. By using the following relation for the free energy of micellization" AGO = (2 - a)RT In cmc (11) (38) Platz, G.; Hoffmann, H. Ber. Bunsen-Ges. Phys. Chem. 1972, 76,491. (39) Gruenewald, B.;Knoche, W. In Techniques and Applications of Fast Reactions in Solution, Gettins, W. J., Wyn-Jones, E., Eds.; Reidel: Dordrecht, 1979; NATO Adv. Study Inst. Ser., Ser. C, Vol. 50. (40) Anacker, E. W. In Cationic Surfactants, Jungermann, E., Ed.; Marcel Dekker: New York, 1970; Surfactant Science Series, Vol. 4.
r
Ib -
I
2.0
60
4.0
[STSI (mol mi3)
Figure 1. Reciprocal time constant 1 / of~ the~ fast relaxation process vs. total concentration of STS at 35 O C : (0) H,O; (0) D 2 0 . TABLE II: Parameters of the Fast Relaxation Times in STS-Hz0/D20 at 35 OC' H@
k l x 10-5, s-I U
7.00 f 0.20 10.4 f 2.6
D,O 5.16 f 0.24 11.9 f 4.2
"The errors given in Tables 11-IV are the standard deviations of the individual parameter estimates.48 the values in Table I were calculated. They show that micelle formation is favored in D 2 0 when,compared with H 2 0 . The degree of dissociation was calculated from4' Here SIand S2are the slopes of the conductivity vs. concentration plots before and after the cmc. In H 2 0 ADNa+ is426.15 X m2 R-' mol-' at 35 O C and to obtain XoNa+ in D20, Walden's rule was used to give 5.14 X low3mz 0-'mol-'. The mean aggregation number for STS in HzO is3780 and since ri seems to be somewhat larger in Dz0,1S917 we will from now on take riDZ0 to be 90. This value is not critical for any of the results presented. For example, taking ADZO to be 80 or 100 instead changes the value of k l by 10%. All other parameters would change between 0.1 and 5%. Using the values given for the different parameters in eq 12 aH20 becomes 0.20 and aDz0 0.18. It seems likely that the dissociation degree should be. somewhat lower in D20. This is because simple salts are generally less soluble in heavy water and the free energy of transfer of, for example, the alkali ions from H 2 0 to D 2 0 is positive.43 The value of a in HzO is less than that which has been obtained37by the method of C ~ r r i n . However, ~~ it can be noted that for sodium dodecyl sulfate (SDS) a decreases from 0.33 to 0.20 when the activity coefficients are taken into account according to the method outlined by Hall45when using the Corrin equation. The latter value is also obtained from light scattering measurem e n t ~ . The ~ ~ dependence of a on the method used for its determination is further discussed in ref 47. The Fast Relaxation Process. In Figure 1 the reciprocal of the fast relaxation time vs. total concentration of STS is shown. As predicted by eq 2, kl/a2 and k l / f ican be obtained by fitting of the experimental points. When the same values of fi were used as in the calculation of a, the kl and a presented in Table I1 were obtained. The width of the micelle distribution seems to be (41) Evans, H. C. J . Chem. SOC.1956, 579. (42) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworth: London, 1959. (43) Arnett, E. M.; McKelvey, D. R. In SoluteSolvent Interactions, Coetzee, J. F., Ritchie, C. D., Eds.: Marcel Dekker: New York, 1969. (44) Corrin, M. L. J . Colloid Sci. 1948, 3, 333. (45) Hall, D. G. J . Chem. SOC.,Faraday Trans 1 1981, 77, 1121. (46) Nishikido, N.; Shinozaki, M.; Sugihara, G.; Tanaka, M. J.Colloid Interface Sci. 1980, 74, 474. (47) Elvingson, C.; Wall, S. N. J . Colloid Interface Sci., submitted for publication.
Elvingson
1458 The Journal of Physical Chemistry, Vol. 91, No. 6,1987
6.01i
TABLE III: Parameters of the Relative Amplitude of the Slow Relaxation Process in STS-H20/Dz0 at 35 OC'
(a In cmc/8p)104,bar-' (8 In it/8p)105,bar-'
4.0
U
H20
D20
1.25 f 0.10 -2.94 f 0.46 10.7
1.60 f 0.05 -4.22 f 0.20 11.7
"The values of u have been calculated from the first zeros of the experimental curves in Figure 2. TABLE I V Parameters of the Slow Relaxation Times in STS-H,O/D,O at 35 O C 20
30
40
M am
m
Figure 2. Relative amplitude Uzof the slow relaxation process vs. total surfactant concentration at 35 OC: (0) HzO;( 0 )DzO.
somewhat larger and kl somewhat smaller in D20. The increase in u is in accordance with the increased stability of the micelles in heavy water noted earlier. This will be further discussed in connection with the slow relaxation time. It should, however, also be mentioned that, for sodium octyl sulfate (SOS) and decyltrimethylammonium bromide (DTAB), Gettins et found that u decreased when going from HzO to DzO. However, as the authors noted, the short-chain surfactants used in their study do not have as well defined cmc's as those found for longer chain molecules, e.g. STS, and since u is rather sensitive to the value of the cmc, their data are somewhat uncertain. Furthermore, when comparing the value of u obtained from the relaxation times and amplitudes in ref 33, there is quite a large difference, whereas the value of u determined from r1 and U, (see next section) in this paper are almost identical and show that u is probably slightly larger in heavy water compared to light water. The decrease in kl can be understood from the following considerations. In the derivation of eq 2 and 3 it is assumed that the counterion distribution is so narrow that every amphiphile aggregation number r corresponds to one counterion aggregation number s. Thus, if r is known s can be calculated from the degree of dissociation. Equation 1 can then be written
Taking the concentrations of M,, and M, in the micellar region to be approximately equal leads to kl-(r) = kl+(r)Al (14) To get an estimate of the ratio k1(H20)/k1(D20),we perform the calculation at the cmc using the values in Table I. The rate constants k l + have been shownz9to be of the same magnitude as for a diffusion-controlled reaction, although the temperature dependence is too large49 for this to be strictly true. However, if kl+(r)is assumed to be essentially diffusion controlled, it should be approximately 20% higher in H 2 0 compared to D 2 0 due to the increased viscosity in heavy water. The ratio above then becomes 1.37 which is in reasonable accordance with the data in Table 11. In order to make a better prediction of how k l + and k,- should change between the two media, one should have a molecular t h e ~ r y ~for * -the ~ ~ rate constants in eq 13. The Amplitude of the Slow Relaxation Process. The experimental values of U, shown in Figure 2 were fitted to eq 8, and in Table 111 the resulting values for 8 In cmc/ap and a In ii/ap (48) Bard, Y. Nonlinear Parameter Estimation; Academic: New York, 1974. (49) Hoffmann, H. Prog. Colloid Polym. Sci. 1978, 65, 140. (50) Aniansson, E. A. G.; Almgren, M.; Wall, S. N. In Chemical and
Biological Applications of Relaxation Spectrometry, Wyn-Jones, E., Ed.; Reidel: New York, 1975.
HZ0
D2O
615 f 25 0.32 f 0.04 44 f 3
276 f 7 0.32 f 0.02 31 f 1
are given. The values in HzO are in agreement with other determinations using the same method3' but d In cmc/ap is somewhat less than the value of 2.45 X IO4 bar-' obtained by Kaneshina et aLsl from the pressure dependence of the cmc. From Table 111 it is seen that both the cmc and the mean aggregation number are more sensitive to pressure changes in DzO than in HzO at the temperature used in the experiments. This can qualitatively be understood by considering D 2 0 as light water at a lower t e m p e r a t ~ r e . At ~ ~ atmospheric pressure the partial molar volume change on micelle formation (AV,) decreases with increasing t e m p e r a t ~ r e . ~From ' the following relation for Arm
AV,,, = ( 2
-.)..(-a,) a In cmc T
a In cmc/ap should increase when going from HzO to D20which is also what is observed. Concerning the mean aggregation number, it is known that fi decreases with increasing pressure at low and moderate temperatures and that the decrease is faster the lower the t e m p e r a t ~ r e . Thus, ~ ~ again regarding DzO as H 2 0 at a lower temperature, explains why a In fi/ap is more negative in heavy water than in light water. It should also be mentioned (see discussion above concerning 7 ' ) that from the first term in eq 8 we can determine u2/i2 from the first zero of the amplitude in Figure 2. The result is shown in Table 111 and is in very good agreement with the values obtained from the fast relaxation time. The Relaxation Time of the Slow Relaxation Process. The results obtained from the slow relaxation time are most interesting. In Figure 3 we can compare 1/r2vs. the concentration of STS in light and heavy water. The curves are fairly similar in shape but the D20 curve seems to be displaced downward approximately by a factor three. Since cmc, ii, and u only differ by 10-20%, the last factor in eq 3 cannot explain the difference in rzrso it must be due mainly to differences in the resistances. It should also be mentioned here that preliminary experiments on sodium dodecyl sulfate and tetradecylpyridinium sulfate also showed the same difference in 72 between light and heavy water. Thus the large difference in the slow relaxation time between HzO and D 2 0 seems to be a general feature of both anionic and cationic surfactants. In ref 35 and 36 the factors affecting R were investigated and it was found that R is very sensitive to several of the parameters characterizing the narrow passage, e.g. its position and depth. The connection between these and the experimental data will be discussed presently. For the moment however, eq 4 will be used to fit the experimental data. The resulting values are shown in Table IV and for H 2 0 the results can be compared to those of ref 37. The values of m are almost identical while both cy, and M are larger in ref 37. However, this can be explained by the use of different values of cy. A further discussion on how the (5 I ) Kaneshina, S.; Tanaka, M.; Tomida, T. J . Colloid Interface Sci. 1974, 48, 450. (52) Katz, J. J. Am. Sci. 1960, 48, 544. (53) Dawson, D. R.; Offen, H. W., Nicoli, D. F. J . Colloid Interface Sci. 1981, 81, 396.
STS Micelles in H 2 0 and D 2 0
10
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
30
20
[STS]
(mol
40
-
i3)
Figure 3. Reciprocal time constant 1 / i 2 of the slow relaxation process vs. total concentrationof STS at 35 "C: (0)HzO; ( 0 )DzO.The fitted curves are calculated according to eq 4.
concentration dependence of 7 2 depends on the method used for the determination of CY is given in ref 47. It is seen in Table IV that the greatest difference between H 2 0 and D 2 0 is in M . Furthermore, CY, is in both cases larger than CY but the small difference between the degree of dissociation in light and heavy water remains. Although part of the difference in M can be attributed to the difference in rate constants, most of the change has to come from the factors determining the properties of the aggregates in the narrow passage. Since the concentration of these aggregates must be very much less than for the proper micelles, there is at present no way to get direct information from equilibrium measurements about these aggregates. However, in order to get a better understanding of the factors which cause the large change in T~ when going from light to heavy water, the relaxation times have also been analyzed by use of eq 6 and 7 . When using these equations, the rate constants klmwere chosen somewhat larger than the k, for the proper micelles but the ratio klmH20/klmD20 was taken to be the same as the ratio determined for kl,H20/kl,D20. During the analysis of the experimental data according to eq 4 it was seen that a, was quite stable with respect to changes in, for example, the cmc, while m was more sensitive. Thus, when calculating the relaxation curves by combining eq 3 and 6-7, a, = 0.32 was used, but different values of m were tried. The calculations were started at a total concentration of 2.50 mM and to be able to compare the relaxation times computed in this way to the experimentally determined values, the M, were chosen such that the relaxation times agreed at the starting concentration. It was seen that also here the position of the minimum had a significant effect on the results. In Figure 4 the calculated values are compared with the experimental results. The values for m shown are those which place the minimum in the middle between the monomers and the proper micelles, and those which give the best fit to the experimental data. It is seen that for mHZ0= 52
10
20
30
[STS]
(mol
1459
40
G3)
Figure 4. As in Figure 3 but the curves are calculated according to eq 3 and 6-7. The following values of the parameters are used: (a) cmc = 2.21 mol m-3, ii = 80, a! = 0.20, u = 10.40, klm= 1.00 X lo6 s-', ril = 40, a, = 0.32, u,,, = 7.0, A?, = 1.02 X 10" mol m-3; (b) the same as (a) but A = 52; (c) cmc = 1.94 mol m-3, A = 90, a = 0.18, u = 11.91, klm = 8.25 X lo5 s-l, m = 38, a, = 0.32, u, = 7.0, = 5.27 X lo-' mol m-3; (d) the same as (c) but = 45. For A, riz, and AT,, the values apply at 2.50 mol m-3.
n,,,
and mDZO= 38 the agreement with the experimental points is very good and this procedure thus makes it possible to get direct information about (1) the concentration of the aggregates in the narrow passage and (2) the location of the minimum. Furthermore, although we have taken the mean aggregation numbers to be concentration dependent during this analysis, the variations of both ti and m for the total concentrations used are only approximately 5%. This is in agreement with the results obtained in ref 36 for a narrow counterion distribution. From the results shown in Figure 4 it can be deduced that the concentration of aggregates in the minimum is about lo6 times less than the monomer concentration. Furthermore, although the values for f i obtained by using eq 4 and eq 6 differ, the best agreement between the calculated and the experimental points , o 0.50 and ( m / f i ) ~ ~ This is in agreement with what was found for STS in H,O in ref 37 but it differs from the value of m = 7 found in ref 2 8 . In the latter paper, however, the counterions were not explicitly taken into account. By including the counterions into the expression for the resistance in ref 28, m will increase from 7 to about 6 0 which actually is a little larger than found in this paper. The observed changes in m and M, between light and heavy water can be explained by realizing that the micelles are more stable in D 2 0 than in H 2 0as shown by the AG values in Table I. Since the hydrocarbon chains of the small aggregates in the narrow passage will be more exposed to water than in the micelles proper, the larger micelles will be more stable relative to the aggregates in the narrow passage in heavy water compared to light water. Thus the concentration in the minimum should decrease while the width of the distribution of the proper micelles should increase
1460
J . Phys. Chem. 1987, 91, 1460-1465
when going from HzO to DzO and this is also what is observed. A way to further investigate how the location of the minimum is changed should be to measure rz for a large perturbation, e.g. by stopped-flow measurements. According to Wall et an asymmetrically placed minimum will give a time-dependent relaxation time, i.e., the quantity (1 /s)(ds/dt) is a function of time. Here s can, for instance, be the relative deviation from equilibrium of the monomer concentration. The success of the method outlined above for the analysis of the resistance might suggest that it can be used for the investigation of related problems. It has been shownS5 that a few percent (54) Wall, S. N.; Aniansson, E. A. G. J . Phys. Chem. 1980, 84, 727.
dodecanol changes the cmc for SDS micelles by 10% while rZ is changed from 5 to 15 ms at 15 “C. Thus extending the above procedure to include another component could appear to be most valuable for the understanding of e.g. the influence of long-chained alcohols on the slow relaxation process in micellar systems. Acknowledgment. The author thanks Dr. Staffan Wall for helpful comments on the manuscript. Financial support from the Swedish Science Research Council is gratefully acknowledged. Registry No. STS, 1 19 1-50-0. ( 5 5 ) Folger, R.; Hoffmann, H.; Ulbricht, W. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 986.
Interaction between a-Poly(y-methyl+-glutamate) and 5- and 16-Doxylstearic Acids: A Monolayer and ESR Study P. Baglioni,*+M. Carla,* L. Dei,+ and E. Martinit Dipartimento di Chimica and Dipartimento di Fisica, Universitci degli Studi di Firenze, SO1 21 Firenze, Italy (Received: May 7 , 1986; In Final Form: September 29, 1986)
Two-dimensional mixtures between a polypeptide, poly(y-methyl-L-glutamate) in the a-conformation, and two nitroxide spin probes, 5-doxylstearic acid and 16-doxylstearic acid, were studied at the water-air interface in the 15-30 O C temperature range. The interactions between each spin probe and the polypeptide were investigated by analyzing the parameters obtainable from the spreading isotherms. It was shown that the position of the nitroxide group along the hydrophobic chain notably affected the interactions of the probe with the polypeptide. In particular, the two spin probes were miscible, in monolayers, with the polypeptide; but when the oxazolidine ring is near the carboxyl group (Sposition) the Gibbs free energy of mixing, AG,,, was positive, whereas when the nitroxide group is far from the carboxyl group (16-position) AGmiXwas negative or zero. The analysis of ESR spectra made on the collapsed monolayers fully confirmed the results obtained via the monolayer study.
Introduction The use of nitroxide spin probes in studying biomembranes, vesicles, liposomes, and multibilayers is very useful and wellknown,’,* and the interactions among the spin probes and the substances constituting those oriented systems are often investigated by studying pure and mixed monomolecular films at the water-air i n t e r a ~ e . ~ . ~ There are two main problems related to the use of spin probes or labels in styding these systems. The first is how and where the probe interacts with the compounds constituting the membrane or the oriented system: in fact, only when the probe location is known it is possible to correctly evaluate the information obtained from the ESR of fluorescence spectra. The second problem is related to the possible perturbations that could arise from introducing a foreign molecule in a membrane or membrane mimetic system. There are some findings4xsabout the perturbation caused by the presence of a typical amphiphile spin probe in a membranelike environment. For example, in a scanning electron microscopy study of red cells it has been shown that the spin probe, in the usual concentrations, caused morphological changes6.’ On the other hand, a monolayer study has shown that doxy1 fatty acids perturb a monolayer spread at the water-air interface to a greater degree than the analogous fluorescence probes.s These perturbations are often correlated to the different values of the order parameters obtained via ESR or ‘HNMR, even if possible *To whom correspondence should be addressed. Dipartimento di Chimica, Universiti degli Studi di Firenze, via lyino Camoni 9. 50121 Firenze. Italv. fbipartimento di Fisica, Unhersiti degli Studi, Largo Enrico Fermi 2, 50125 Firenze, Italy.
0022-3654/87/2091-1460$01.50/0
explanations of these differences could be considered, i.e. the time scale of ESR and ’H N M R differs more than a factor 100.6v9,10 It is generally accepted that the perturbation caused by the introduction of a foreign molecule in a system is tolerable as long as the “site” of the probe interaction and the extent of such perturbation are known. A possible way to evaluate the interactions between the spin probes and the substances of biological interest and the location of the nitroxide group is to study the behavior of their mixed monomolecular films spread at the water-air or water-oil interface.” In this approach the monolayer is assumed to represent a model membrane system: the structural difference between a monolayer and a membrane is ~ e l l - k n o w n , but ’ ~ it is considered (1) Devaux, P. F.; Seigneuret, M. Biochim. Biophys. Acta 1985,822, 63, and references therein. ( 2 ) Fung, L. W. M.; Johnson, M. E. Curr. Top. Bioenerg. 1984, 13, 107-157. (3) Cadenhead, D. A,; Muller-Landau, F. Biochim. Biophys. Acra 1973, 307, 279. (4) Cadenhead, D. A.; Muller-Landau, F. Ado. Chem. Ser. 1975, No. 144, 294. (5) Seelig, J.; Neiderberger, W. J . Am. Chem. SOC.1974, 96, 2069. ( 6 ) Schreier, S.;Polnaszek, C. F.; Smith, 1. C. P. Biochim. Biophys. Acta 1978, 515, 375. (7) Bieri, V. G.; Wallach, D. F. H.; Lin, P. S. Proc. Narl. Acad. Sci. U.S.A. 1974, 71, 4797. (8) Cadenhead, D. A,; Kellner, B. M. J.; Muller-Lardau, F. Biochim. Biophys. Acta 1975, 382, 253. (9) Smith, I. C. P.; Stockton, G. W.; Tulloch, A. P.; Polnaszek, C. F.; Johnson, K. G. J . Colloid Interface Sci. 1977, 58, 439. (10) Seelig, J. Q.Reu. Biohys. 1977, 10, 353. ( 1 1) Pyter, R. A,; Ramachandran, C.; Mukerjee, P., J . Phys. Chem. 1982, 86, 3206. 1982, 86, 3189. 1982, 86, 3198.
0 1987 American Chemical Society
