J. Phys. Chem. 1987, 91, 4760-4765
4760
Solvent Isotope Effects on Alkyltrimethylammonium Bromide Micelles as a Function of Alkyl Chain Length S. S. Berrt Chemistry Department, University of Virginia, Charlottesville, Virginia 22901 (Received: January 5, 1987)
The effect on micellar structure of changing the solvent from HzOto DzOfor alkyltrimethylammonium bromide [C,TAB; C,,TAB = CJ-IwlN(CH3)3Br, with n = 12,14, and 161 has been examined. The energetics of micellization have been determined by measuring critical micelle concentrations by using surface tensiometry. The micellar structure has been elucidated through the use of small-angle neutron scattering (SANS). It was found that there is a solvent isotope effect that is small for C,,TAB but increases with n. This effect is manifested mainly by an increase in aggregation number and is attributed to solventhydrocarbon interactionsof the dissolved monomers. The fractional charge of the micelle is not altered by the isotopic composition of the solvent. C,TAB micelles are found to be drier than are micelles formed by the corresponding sodium alkyl sulfates, and this results in a larger solvent effect for the quaternary ammonium bromides.
Introduction
D 2 0 has frequently been substituted for H 2 0 in studies of amphiphilic micellar aggregates, most notably in small-angle neutron scattering and nuclear magnetic resonance (NMR) experiments.'-12 It has been recognized for some time that such an isotopic substitution might result in an alteration in the structural properties of the aqueous aggregate. The first empirical evidence of a solvent isotope effect on micellar properties was presented by Mukerjee et al., who showed that CloS04Na and CIzSO4Na(C,,S04Na 1 CnH2,+]S04Na)have lower cmc's in D,O than in H20.13 Since then, a number of studies have investigated the effect of replacing HzO with DzO, in order to achieve a better understanding of the nature of the hydrophobic effect. Several investigators have concluded that changing the isotopic composition of the solvent leads to a change in aqueous micelles, whereas others have concluded that it does not. micelles in salt-free C16TAB(CnTAB CnH2n+lN(CH3)3Br) solutions,' C14TABwith added pentanol in KBr solution^,^^^^^ and C12S04Nawith added NaC1I6 have been found to form larger micelles in DzO than in H20. The isotopic composition of the solvent has been found to affect the structure of micro emulsion^,^^ gel-to-liquid crystalline phase transition temperatures and free energies for this transition for lipid vesicle^,^*^^^ and the lifetime of the cation radical of N,N,N',N'-tetramethylbenzidine in CloS 0 4 N a and CI2SO4Nasolutions.20 On the other hand, no difference was noted by SANS on micelle properties for C12S04Na, C12S04N(CH3)4, and ClzS04Liin HzO and D,O salt-free solution~.~,~ An attempt is made here to clarify the conditions under which solvent isotope effects should be expected. Isotope effects have been examined by surface tensiometry and SANS of a series of solutions of R,TAB ( n = 12, 14, and 16) in water in which the volume fraction of D 2 0 of the solvent ( x ~ , is~varied ) from 1.O to 0.5. It will be shown that the solvent isotope effect is due to small differences between the surfactant hydrocarbon-water interactions in H 2 0 and D 2 0 due to stronger hydrogen bonding between D 2 0 molecules and that these differences magnify with increasing chain length. Thermodynamics
The process of micellization can be represented as
Ns+ + cx-
SNXCZ+
(1)
where S+ and X- represent surfactant monomer and counterion, Work carried out in part at the Chemistry Department, Wake Forest University, Winston-Salem, NC, and in part at the Chemistry and Solid State Divisions, Oak Ridge National Laboratory, Oak Ridge, TN, in partial fulfillment of Ph.D. requirements under the supervision of Drs. R. R. M. Jones, 3M Co., St. Paul, MN, and J. S. Johnson, Jr., Chemistry Division, Oak Ridge National Laboratory.
0022-3654/87/2091-4760$01.50/0
respectively, Z = charge of the micelle, and c = N - Z = number of counterions associated with the micelle. If activity coefficients are neglected, the equilibrium constant for the above process is K =
[SNXCZ+I [S+]N [ x-1'
and the Gibbs free energy is AGO,, = -RT In K. The standard free energy per monomer is AGO = (-RT In K ) / N or
For large values of the aggregation number (>50), the In Also, at [SNXcZ+]/N makes a negligible contribution to cmc. The free energy of micellization the cmc, [S'] N [X-] thus becomes AGO N R T ( l c / N ) In cmc (4)
+
(1) Berr, S. S.; Caponetti, E.; Johnson, J. S., Jr.; Jones, R. R. M.; Magid, L. J. J. Phys. Chem. 1986, 90, 5766. (2) Berr, S. S.; Coleman, M. J.; Jones, R. R. M.; Johnson, J. S., Jr. J. Phys. Chem. 1986, 90, 6492. (3) Bendouch, D.; Chen, S.-H.; Koehler, W. C.; J . Phys. Chem. 1983,87, 153. (4) Tabony, J. Mol. Phys. 1984, 51, 915. (5) Triolo, R.; Magid, L. J.; Johnson, J. S., Jr.; Child, H. R. J. Phys. Chem. 1982,86, 3689. ( 6 ) Zana, R.; Picot, C.; Duplessix, R. J. Colloid Interface Sci. 1983, 93, 43. ( 7 ) Gustavsson, H.; Lindman, N. J . A m . Chem. SOC.1978, 100, 4647. (8) Henriksson, U.; Odberg, L. J . Colloid Interface Sci. 1974, 46, 212. (9) Frenot, M. P.; Nery, H.; Canet, D. J . Phys. Chem. 1984, 88, 2884. (10) Persson, B.-0.; Drakenburg, T.; Lindman, B. J. Phys. Chem. 1979, 83, 301 1. (1 1) Staples, E. J.; Tiddy, G. J. T. J . Chem. SOC.,Faraday Trans. 1 1978, 74, 2530. (12) Lindblom, G.; Lindman, B.; Mandell, L. J . Colloid Interface Sci. 1973, 42, 400. (13) Mukerjee, P.; Kapauan, P.; Meyer, H. G. J . Phys. Chem. 1966, 70, 783. (14) Candau, S.; Hirsch, E.; Zana, R. J. Colloid Interface Sci. 1982, 88, 428. (1 5) Zana, R.; Picot, C.; Duplessix, R. J. Colloid Interface Sci. 1983, 93, 43. (16) Chang, N. J.; Kaler, E. W. J . Phys. Chem. 1985, 89, 2996. (17) (a) Chou, S. I.; Shah, D. 0. J . Colloid Interface Sci. 1981, 80, 49. (b) Chou, S . I.; Shah, D. 0. J . Phys. Chem. 1981,85, 1480. (18) Chen, C.-H. J . Phys. Chem. 1982, 86, 3559. (19) Lipka, G.; Chowdhry, B. Z.; Sturtevant, J. M. J . Phys. Chem. 1984, 88, 5401. (20) Plonka, A.; Kevan, L. J . Phys. Chem. 1984, 88, 6348. (21) An estimation of the effect the term In [SNXCZ']/Nmakes on AGO can be made. The largest effect will be seen for CIzTABdue to its small N N 50. The cmc Y 2.4 X IO4 in mole fraction units. Assume 50% of the surfactant is in the micellar pseudophase at the cmc. Then [SNXCz']= 2.4 X 10-4/(2 X 50) = 2.4 X 10" and In [SNXcZ"]/N= 0.26. From Table I, it is seen that AGO N -8.4 kcal mol-' for CIzTAB. Thus the error in neglecting the above term will be at most -0.26RT = -0.15 kcal/mol or 2%.
0 1987 American Chemical Society
TABLE I: cmc and Calculated AGO Values at 25
n H20
D20
12 14 16 12 14 16
-* I
O C
cmc, cmc, mol AGO, 424 mM fraction In cmc kcal mol-’ AlkyltrimethylammoniumBromides 0.23 0.19 0.16 0.23 0.19 0.16
13.3 3.41 1.00 13S20 3.20 0.82
2.41 6.17 1.81 2.45 5.97 1.48
X X X X X X
lo4 10”
-8.33 -9.69 -10.92 -8.31 -9.73 -11.12
-8.39 -10.16 -12.03 -8.37 -10.20 -12.25
-
n
0
E
\
a
Sodium Alkyl Sulfated6
H20 8 0.275
D20
10 12 14 8 10 12 14
0.275 0.275 0.275 0.277 0.277 0.277 0.277
136 33.6 8.20 2.21 130 31.4 7.60 1.97
2.51 6.11 1.48 4.00 2.40 5.71 1.38 3.56
X 10” X lo4 X lo4 X X X lo4 X lo4 X
-5.99 -7.40 -8.82 -10.13 -6.03 -7.47 -8.89 -10.24
0
R T ( 2 - @)In cmc
t
-6.12 -7.56 -9.01 -10.35 -6.16 -7.63 -9.08 -10.46
If the fractional charge of the micelle is defined as /3 the free energy can be written as AGO
-:I
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4761
Solvent Isotope Effects on C,TAB Micelles
-1 1
0
0
a
-12
Z/N,
-13
+
L++++11
12
13
14
1s
16
17
n
(5)
This provides a convenient means by which free energies of micellization can be calculated if @ and the cmc are known. Although eq 5 has been derived in similar form by other^,'^,^^,^^ its derivation is given here in order to highlight the assumptions and approximations made. If the variation of AGO with respect to the number of carbons in the alkyl chain ( n ) is determined, a free energy of transfer of a methylene unit from water to a micelle (6AGo/6n) can be calculated. Other investigators have determined, using conductivity measurements, that /3 is constant with respect to n (Le., 6/3/6n = 0) for a series of sodium alkyl sulfates (C,S04Na), meaning that 6AG0/6n depends solely upon the change of the cmc with respect to n.I6 This is not the case for alkyltrimethylammonium bromides (C,TAB), as indicated by the results obtained from the analysis of the neutron scattering data presented in this work and from the analysis of electrical conductivity measurements made by Zana.24 If the change in /3 with respect to n is not accounted for, 6AG0/6n will be in error. Instead of assuming that 6AG0/6n = RT(2 - @)6 In cmcldn, 6AG0/6n will be calculated from a plot of AGO vs. n. The slope of the line is equal to 6AG0/6n. The /3 values used for these calculations are those of Zana.24 Although the SANS and emf values are qualitatively similar, the emf values are probably somewhat more accurate. This is because the way in which the SANS data are analyzed here assumes the micellar solution to be a one-component macrofluid; Le., the finite size of the counterions is ignored. This results in a value of PsANsthat is an apparent charge.25
Experimental Section Surfactants. The preparation of C,TAB (n = 12, 14, and 16) was performed in a manner previously described.26 The surfactants were recrystallized 3 times from acetone/ethanol (1 0: 1 v/v) and dried to constant weight under vacuum. The 0.1 M surfactant solutions were prepared with H 2 0 triply distilled from quartz and D 2 0from Aldrich Chemical Co., 99.8 atom % D, used as received. Critical micelle concentrations at 25.0 f 0.1 OC in H 2 0 and D 2 0 were determined by using a Fischer DuNouy tensiometer with a 6-cm platinum-iridium ring as reported previously.’ These values are compiled in Table I along with values for sodium alkyl (22) Mukerjee, P. J. Phys. Chem. 1962, 66, 1375. (23) Phillips, J. N. Trans. Faraday SOC.1955, 51, 561. (24) Zana, R. J. Colloid Interface Sei. 1980, 78, 330. (25) Nagele, G.; Klein, R.; Medina-Noyola, M. J . Phys. Chem. 1985, 83, 2560. (26) Szajdzinska-Pietek, E.; Maldonado, R.; Kevan, L.; Berr, S. S.; Jones, R. R. M. J . Phys. Chem. 1985.89, 1547.
Figure 1. Free energy of micellization (AGO) vs. chain length (n) of R,TAB in H 2 0 (A) and D 2 0 (0). Note that the difference in AGO between the two solvents increases as n becomes larger. Thus, as n increases, more surfactant monomers will reside in the micellar pseudophase in D 2 0 than in H 2 0 . TABLE 11: Analysis of AGO vs. n
slope, surfactant C,TAB C,TAB C,S04NaS C,S04NaS
y
solvent 6AGO /an, kcal/mol intercept 0.755 H2O -0.7925 D20 -0.8 525 1.52 -0.7070 -0.483 H20 -0.440 D20 -0.7175
correlation coeff -0.9996 1.oooo -0.9998 -0.9999
sulfates taken from ref 16. The cmc’s are presented in terms of mole fractions, which have been calculated by taking into account the volume of surfactant present. Using mole fractions allows for the calculation of AGO in the unitary system as the standard state2’such that comparison can be made between C,TAB and C,SO,Na. The calculated AGO vs. n for C,TAB is plotted in Figure 1. It is seen that the difference in free energy of micellization between the two solvents becomes increasingly greater as the number of carbons in the surfactant chain increases, with AGO being more negative in D20. Linear least-squares analysis of the lines for C,TAB in Figure 1 and for C,$04Na were performed. The results are presented in Table 11. The slopes of the lines are equal to 6AGo/6n. Two points should be noted concerning these results. First, the free energy of transfer of hydrocarbon from the bulk aqueous medium to the micelle is more negative in D 2 0 than it is in H 2 0 . Second, the free energy of transfer is greater for C,TAB than it is for C,SO,Na. The difference in 6AG0/6n between D 2 0 and H,O for C,TAB is 60.0 cal/mol, while for C,S04Na it is 10.5 cal/mol. Small-Angle Neutron Scattering (SANS) Measurements. Neutron scattering measurements were performed on the 30-m (source to detector distance) SANS instrument at the High Flux Isotope Reactor of the National Center for Small-Angle Scattering Research (NCSASR) at Oak Ridge National Laboratory (ORNL). The sample to detector distance was 3.0 m for all the runs. The momentum transfer range was 0.025 5 Q 5 0.25 A-’ (Q = 4?r (sin 0 ) / A where 20 is the scattering angle and X = 4.75 A is the neutron wavelength). The samples were contained in cells with a 0.2-cm path length, except for samples containing less than 70 vol % D 2 0 in the solvent, which were held in 0.1-cm cells. The cells were made of Suprasil UV-grade quartz stoppered with tight-fitting Teflon stoppers, sealed with Parafilm. The cell (27) Tanford, C. The Hydrophobic Effect, 2nd ed.; Wiley-Interscience: New York, 1980.
4762 The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4.0
-
Berr
'""1
XOl0
= 1 0"
I
0 00
0 05
0 10
0 15
0 25
0 20
Q(0 Figure 2. ClzTAB as a function of external contrast, which is propor-
tional to the volume fraction of D20(xDIO)in the solvent. The open symbols are experimental data, while the solid curves are calculated by using an elliptical micelle model as described in the text. xDz0is indicated above each of the curves.
Figure 4. Ci,TAB as a function of external contrast. The open symbols are experimental data, while the solid curves are calculated by using an elliptical micelle model as described in the text. xDlois indicated above each of the curves.
in o
0 00
0 05
0 15
0 10
0 25
0 20
Q(A-') Figure 3. CllTAB as a function of external contrast. The open symbols are experimental data, while the solid curves are calculated by using an , ~ above elliptical micelle model as described in the text. x ~is indicated each of the curves.
temperature was maintained at 25.0 0.1 "C by means of an external circulating bath and was monitored by a thermocouple. Scattering intensity from the surfactant solutions was corrected for detector background and sensitivity, empty cell scattering, incoherent scattering, and sample transmission. Solvent intensity was subtracted from that of the sample. The resulting corrected intensities were converted to radial averages vs. Q by using programs provided by the NCSASR. Absolute cross sections, dZ/d9, were computed from calculations based on known scattering from pure H 2 0 . The resulting intensities vs. Q are shown as open symbols in Figures 2-4. The error bars reflect counting statistics. The solid line curves in Figures 2-4 are calculated by using a nonlinear least-squares fitting routine as described in detail below. Analysis ofSANS Data. For a system of elliptical micelles, the scattering intensity Z(Q) is where N p = particle number density (micelles ~ m - ~A) ,= absolute intensity factor which is used as a free-fitting parameter to account for uncertainties in the absolute intensity calibration, B background factor which is another fitting parameter used to account for residual background, and S(Q) interparticle structure factor as calculated from the rescaling version of the now standard procedure of Hayter and P e n f ~ l d . ~ ~ - ~ ~ ~
~
~~~
~
~
~~~
~
~~
~
~~~~~~~~
(28) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. (29) Hayter, J. B.; Penfold. J . J . Chem. Soc., Faraday Trans. 1 1981. 77, 1851.
E CH3(CH2Ii5
Figure 5. Micelle model used in the calculation of F(Q). The core consists of hydrocarbon only and has dimensions A, X A, X E,. A, is the extended length of the portion of the alkyl chain that is in the core. B, increases to accommodate all of the dry hydrocarbon. The Stern layer, of thickness THIK, contains the cationic head groups, associated coun-
terions and water, and possibly some hydrocarbon. The overall dimensions of the micelle are A, X A, X E,. The above diagram is for CI6TAB; the models for C12TABand Ci4TABare analogous. F(Q) is the single particle form factor, here chosen to be an ellipsoidal hydrocarbon core plus hydrated Stern layer, as shown in Figure 5 . The Stern layer contains the trimethylammonium head groups, associated bromide counterions and water, and possibly some "wet" methylene units. The following definitions apply to this model: N = aggregation number (number of surfactant monomers per micelle), Z = micellar charge, @ = Z / N , w number of water molecules per monomer, A, minor axis of the core, AT 1 minor axis of the total micelle, B, = major axis of the core, BT = major axis of the total micelle, THIK thickness of the Stern layer, WET = number of wet methylenes per monomer, and AR BT/A, = the axial ratio (AR turns out to be greater than unity, indicating the ellipsoids are prolate). All lengths are in nanometers and volumes in cubic nanometers. A, is set equal to the extended length2 of the portion of the chain that is in the core, i.e. A, = 0.295
+ 0.127(n - WET)
(30) Hansen, J.-P.; Hayter, J. B. Mol. Phys. 1982, 46, 651.
(7)
The Journal of Physical Chemistry, Vol. 91, No. 18. 1987 4763
Solvent Isotope Effects on C,TAB Micelles
TABLE 111: 0.1 M CllTAB at 25 "C, THIK = 0.90 (h0.02) nm, and WET = 4.3 (A0.1)' N 2, p, w A,, nm AT, nm B,, nm XDzO 1.00 0.90 0.80 0.70 0.60 0.50
49.81 (0.44) 49.04 (0.42) 48.46 (0.42) 48.17 (0.38) 47.38 (0.43) 47.12 (0.50)
+
+
15.2 (0.4) 14.6 (0.4) 14.7 (0.4) 14.7 (0.3) 13.9 (0.4) 13.9 (0.4)
0.31
18.8
1.29
2.19
0.30
19.0
1.29
0.30
19.2
0.30
average
BT, nm
AR
A
B
X
1.71
2.61
1.19
1.68
2.58
1.18
1.29
2.19
1.66
2.56
1.17
19.2
1.29
2.19
1.65
2.55
1.17
0.29
19.5
1.29
2.19
1.62
2.52
1.16
0.30
19.6
1.29
2.19
1.61
2.5 1
1.15
0.02 (0.01) 0.02 (0.01) 0.02 (0.00) 0.04 (0.00) 0.03 (0.00) 0.02 (0.00)
4.1
2.19
1.98 (0.02) 1.94 (0.02) 1.91 (0.02) 1.90 (0.02) 1.95 (0.02) 1.94 (0.02)
0.30
19.2
1.29
2.19
1.66
2.56
1.17
1.94
0.03
3.0 2.5 1.7 1.5 1.1
"0.1 M C,TAB (=C,H2,+1N(CH3),Br in water as a function of volume fraction of D20(xDzo).Fixed parameters are THIK (Stern layer thickness) and W E T (number of methylene units per monomer that reside in the Stern layer). Their associated error in standard deviation units is adjacent to their average value, in parentheses. Fitting parameters are N (aggregation number), Z (overall charge), A (absolute intensity factor), and B (residual background factor). Underneath each of the fitting parameters in parentheses is the associated error. Other micelle parameters determined from this fitting procedure (see Figure 1) are A,, AT, B,, BT ( A denotes a double axis, B denotes a single axis, c = core, and T = overall), AR (the axial ratio of the micelle = &/AT), and w (number of water molecules per monomer). Since WET and THIK are fixed, A , and AT are constants and are determined as described in the text. X describes the agreement between experimental and calculated intensities.'2
TABLE IV: 0.1 M C,,TAB at 25 OC, THIK = 0.79 (+0.02) nm, and WET = 2.3 (+0.1)" XDlO N 2, 6, + w A,, nm A T , nm B,, nm
+
1.00 0.90 0.79 0.70 0.60 0.49
84.10 (0.51) 83.18 (0.43) 82.34 (0.43) 81.57 (0.44) 81.35 (0.44) 80.23 (0.57)
19.5 (0.5) 18.9 (0.4) 19.2 (0.4) 18.8 (0.4) 18.7 (0.4) 18.4 (0.5)
average
BT, nm
AR
A
B
X
0.23
14.5
1.78
2.57
2.17
2.96
1.15
14.6
1.78
2.57
2.14
2.93
1.14
0.23
14.7
1.78
2.57
2.12
2.91
1.13
0.23
14.8
1.78
2.57
2.10
2.89
1.12
0.23
14.8
1.78
2.57
2.09
2.88
1.12
0.23
14.9
1.78
2.57
2.07
2.86
1.11
0.23
14.7
1.78
2.57
2.11
2.91
1.13
0.04 (0.01) 0.04 (0.00) 0.05 (0.00) 0.04 (0.00) 0.03 (0.00) 0.04 (0.00) 0.04
4.0
0.23
1.62 (0.01) 1.57 (0.01) 1.56 (0.01) 1.53 (0.01) 1.53 (0.01) 1.61 (0.00) 1.57
BT, nm 4.43
AR
A
B
X
1.66 1.65
4.34
1.63
4.30
1.62
4.26
1.60
4.19
1.58
4.32
1.62
0.22 (0.01) 0.28 (0.01) 0.33 (0.01) 0.41 (0.00) 0.51 (0.00) 0.50 (0.00) 0.38
4.3
4.39
1.13 (0.00) 1.12 (0.00) 1.07 (0.00) 1.09 (0.00) 1.11 (0.00) 1.11 (0.00) 1.11
2.9 2.4 2.1 1.6 1.5
'See footnote a in Table 111.
TABLE V: 0.1 M C16TABat 25 OC, THIK = 0.65 (A0.04) nm, and WET = 2.6 (A0.2)" XDiO N + b, + w A,, nm A T , nm Bc, nm 1.00 163.51 23.2 0.14 6.89 2.01 2.66 3.78 (0.44) (0.2) 2.66 3.74 6.94 2.01 22.9 0.14 0.90 161.80 (0.40) (0.2) 2.01 2.66 3.69 0.14 6.99 22.3 0.80 159.94 (0.42) (0.2) 3.65 0.14 7.04 2.01 2.66 158.05 22.7 0.70 (0.44) (0.2) 3.61 2.01 2.66 0.15 7.10 156.32 23.3 0.60 (0.40) (0.2) 2.66 3.54 7.20 2.01 0.15 153.21 23.6 0.50 (0.40) (0.2) average 0.14 7.03 2.01 2.66 3.67
z,
2.4 2.3 2.3 1.8 1.3
"See footnote a in Table 111.
B, varies so as to accommodate the hydrocarbon that is present in the core, i.e.
B, = 3V,/4irAC2
nm3), counterion (0.0393 nm3), and solvent (0.0299 + 0.0003xD,~ nm3), respectively. The single-micelle form factor is given by
The other axes are defined then as AT = A , + THIK and BT = B, THIK. The hydration number is determined from the volume in the Stern layer that is not occupied by head groups and counterions:
+
OJ
=
IVT
- Vc - N(WET)VCH>+ VHG + (1 - P)Vc1II/(NVs)
(9) where V,, V,, IfCHI, VHG,VcI, and Vs are volumes of the overall micelle, micelle core, methylene (0.0269 nm3), head group (0.1023
ui = Q [ A ~ +~ ~~ * ~ - , ~u ) ] ~ ( / ~1 where p,, psh,and ps are the scattering length densities of the core, shell, and solvent, re~pectively.~'
4764
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Berr 165
TABLE VI
slope Cl2TAB C1,TAB C,,TAB
5.41 7.29
20.1
y
intercept
correlation coeff
44.3
0.991 0.991 0.994
16.1 143.8
The data were analyzed with N , Z , A , B, THIK, and WET as free-fitting parameters. Under conditions of low contrast, the errors on the parameters became unsatisfactorily large. However, THIK and WET were quite stable with respect to X D ~ Owhen X D ~ O was 10.7,which is to say that there does not appear to be a solvent isotope effect on the Stern layer thickness or on the depth of water penetration into the micelle. Therefore, THIK and WET were fixed at their average values, which are presented in Tables 111-V along with the standard deviations for these values. The data were with N , Z , A , and B as then reanalyzed for all values of xDIO, free-fitting parameters. The results of these fits are also given in Tables 111-V. X gives an indication of the quality of fit.32 It should be mentioned that other micelle models were also tried, including, in particular, a spherical model in which all of the hydrocarbon was placed in a dry core and hydration numbers were assigned to the head group and counterion (1 and 4, respectively). Using the spherical dry-hydrocarbon model resulted in average aggregation numbers that were somewhat larger than those of the ellipsoidal model (18%, 5%, and 4% larger for n = 12, 14, and 16, respectively). Values of @, however, were the same, as were the trends in the variation of N with respect to xDZ0.The fits for the spherical model were not as good as those for the ellipsoidal model as judged by the average values of X (2= 3.4, 3.1, and 4.9 for the spherical model and 3 = 2.3, 2.4, and 2.4 for the ellipsoidal model for n = 12, 14, and 16, respectively). Alkyl Chain Length Variation. As the length of the hydrocarbon chain increases, so does the micelle size. The micelles of C,,TAB and CI4TABare roughly spherical, whereas those of C16TAB,at this concentration and temperature, take on a more pronounced prolate ellipsoidal shape in order to accommodate the extra hydrocarbon in the core. The micelles appear to become drier, both in terms of water content (resulting in a thinner Stern layer) and depth of water penetration (smaller WET) as n increases. Furthermore, as n increases, the fractional charge decreases. The increased bound counterion concentration screens head group repulsions, allowing the head groups to move closer together, resulting in a drier core and a larger possible axial ratio. The aggregation number of 0.1 M C,,TAB at 25 "C in D 2 0 ( N = 163.5) is larger than that for 0.12 M C,,TAB at 50 "C in D 2 0 ( N = 152), which was previously determined by SANS.' This is likely to be due to the decreased solubility of surfactant monomers with decreasing temperature. As more surfactant molecules are forced into the micelle at lower temperatures, there is less room to accommodate the monomers. In order to provide space, the axial ratio can increase and/or the monomers can protrude farther out of the dry core, resulting in an increase in WET. Both appear to occur; at 25 OC, AR = 1.66 and WET = 2.5, while at 50 "C, AR = 1.49 and WET = 0.0. Soluent Isotope Effect. The only facet of the micellar structure that appears to change as a function of the isotopic composition of the solvent is the aggregation number (and hence the micelle size and AR, which are functions of N). Micelles in D 2 0 are larger than those in H,O. This effect has been noted in the past.l.I6 Also, it is consistent with the measured free energies of micellization. The larger magnitude of AGO in D 2 0 indicates that the equilibrium represented by eq 1 lies more to the right in D,O; Le., as the D 2 0 content of the solvent increases, monomers will be (31) Bendedouch, D.; Chen. S.-H. J . Phys. Chem. 1984, 88,648. (32) X ( ~ [ [ I C a l d- Ie,,,i)/ER]2/DF]05,where the sum runs over all the data points. Icalcdand [Iexptl are the calculated and experimental intensities, respectively, ER is the error associated with a particular data point due to counting statistics, and DF = N,,, is the degrees of freedom with N,,, the number of data points and N,,, the number of free-fitting parameters (4 in this case). If X 5 1. the calculated points lie, on the average. within the error of the data.
,
L
140i 2 E
9
c
q
f
0
85
D
m a, L
m m
80
75
55
f
T
0. 5
Vo
I. 0
1u m e F r c c t 1 o n E 2 0
Aggregation number as a function of volume fraction of D,O for C,TAB with n = 12, 14, and 16. The slope of the line is greatest for CI,TAB and least for C,,TAB, indicating that as n increases, the solvent isotopic composition has a larger influence on the micellar aggregation process. Figure 6.
driven from the bulk to the micellar pseudophase, yielding larger and/or a greater number of micelles. When the aggregation number is plotted vs. the volume fraction of D,O, a linear relationship between the two is apparent (Figure 6). A linear least-squares analysis gives the results in Table VI. The y intercept gives the aggregation number in H 2 0 . This number is nearly impossible to obtain directly from SANS measurements due to the negligible contrast between a protiated micelle and H 2 0 . The slopes indicate that the solvent isotope effect becomes progressively larger as the length of the alkyl chain increases. Again, this is consistent with the thermodynamic measurements, which suggest very little difference between CI2TABmicelles in H 2 0 and D 2 0 , but substantial differences between C,,TAB micelles as a function of isotopic composition of the solvent.
Solvent Isotope Effects on C,TAB Micelles
Discussion It has been demonstrated that there is indeed a difference between micelles in H20and D 2 0 and that this difference becomes more pronounced as the length of the alkyl chain increases. The difference revels itself as an increase in the aggregation number with increasing D 2 0 content. These results are in accord with the known differences between H 2 0 and D 2 0 , where D 2 0 is thought to be more structured as is manifested by its higher melting point (3.81 vs. 0.00 "C), higher viscosity (1.1 13 vs. 0.895 cP), larger heat capacity (20.16 vs. 17.99 cal K-l mol-'), and its higher temperature of maximum density (1 1.23 vs. 3.98 DC).33 The alkyl chain, which cannot participate in the hydrogen-bonding network set up by water, would be more disruptive in a more highly ordered structure, e.g., D 2 0 . This causes the surfactant monomer to be at higher free energy in D 2 0 than in H20. SANS results presented here for trimethylammonium bromides, SANS and light scattering results for C14TAB,'4v'5and electrical conductivity and light scattering experiments for sodium alkyl sulfates16 suggest that the fractional charge, and hence the head group interactions, do not change with respect to the isotopic composition of the solvent. The alkyl tail-tail interaction is not expected to change either, because the majority of the hydrocarbon is not in contact with water. Hence AGO will be more negative in DzO as a result of the hydrocarbon of the surfactant monomer in the bulk D 2 0 being at a higher free energy than that of the monomeric hydrocarbon in HzO. This dependence of the isotope effect on the nonpolar portion of the surfactant, and hence the alkyl chain length, explains why the effect has not been observed for sodium dodecyl sulfate, except when large amounts of salt are added to the ~ o l u t i o n . ~It~may ~J~ be that the added salt can screen head group repulsions (which prohibit growth at low salt concentrations but are ineffective at prohibiting growth at high salt concentrations) and allow weak isotope effects to become evident.16 Furthermore, the isotope difference is expected to be larger for C,TAB than for C,S04Na as judged by the larger difference in 6AC0/6n between D 2 0 and H 2 0 for C,TAB (60.0 cal mol-') compared to C,SO,Na (10.5 cal mol-I). The larger magnitude of 6AG0/6n for C,TAB over C,S04Na should be discussed further. Several investigators have determined (33) Nemethy, G.; Scheraga, H. A. J . Chem. Phys. 1964, 41, 680.
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4765
6AG" 6n to be around -700 cal mol-' for C,S04Na in The larger magnitude of transfer for a methylene group for C,TAB ( E -793 cal mol-') suggests that the removal of a surfactant monomer from the bulk water upon micellization is more complete for C,TAB than for CnS04Na,which is to say that alkyltrimethylammonium bromide surfactants have a lower degree of water penetration than do the sodium alkyl sulfates. This conclusion is supported by a number of SANS studies performed on these system^.'^^-^^ Hz0.j2327334-36
Conclusions The isotopic composition of the solvent indeed has an effect on micellar size due to aggregation numbers which increase with increasing D 2 0 content. The Stern layer thickness, depth of water penetration, and fractional charge of the micelle appear to be unaffected by the solvent isotopic composition. The effect of the solvent on micelle size is due to solvent-hydrocarbon interactions and thus becomes less pronounced as the length of the alkyl chain decreases. Alkyltrimethylammonium bromides form micelles that are somewhat drier than those of sodium alkyl sulfates, resulting in more complete removal of a monomer from the bulk aqueous phase upon micellization. This results in a larger solvent isotope effect for C,TAB than for C,S04Na. Acknowledgment. I thank Dr. J. S. Johnson, Jr., of the Chemistry Division of Oak Ridge National Laboratory and Dr. R. R. M. Jones of the 3M Co. for enlightening discussions and their beneficial critique of the manuscript. I also thank Oak Ridge Associated Universities for financial support in the form of a fellowship during the time in which this study was conducted. SANS measurements were carried out on facilities managed by the NCSASR, which is funded by National Science Foundation Grant DMR-77-244-58 through Interagency Agreement 40637-77 with the Department of Energy and is operated by the US.Department of Energy under Contract DE-AC05-840R21400 with the Martin Marietta Energy Systems, Inc. Registry No. C,,TAB, 1 1 19-94-4; C,,TAB, 1 1 19-97-7; &TAB, 5709-0; deuterium, 7782-39-0. (34) Ramadan, M. S.;Evans, D. F.; Lumry, R. J . Phys. Chem. 1983,87, 4538.
(35) Stigter, D. J . Phys. Chem. 1975, 79, 1015. (36) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983, 261, 1022.
