1854
The Journal of Physical Chemistry, Vol. 83, No. 14, 7979
Figure 3 shows the agreement between the model and the experimental data for a different detergent (TTAC1). Assuming an LY = 0.2 f 0.05, one finds that the experimental rate data are adequately represented by a KoHjCl of 0.14 f 0.02. The validity of any model must be examined in the light of its ability to accommodate the experimental behavior of the system under disparate conditions. The simulated curves adequately reproduce the rate data a t two quite different values of OHTover the entire concentration range of detergent studied. Moreover, the failure of previous methods to quantify the binding of OH- to micellar CTAB has led several authors to suggest that OH- binds inefficiently to the m i ~ e l l e . ~Our values for KOHIYindeed confirm that OH- competes inefficiently with both C1- and Br- for sites a t the micelle surface. These considerations provide strong support for the adequacy of the assumptions employed in the treatment of the rate data and for the ion-exchange model in micellar solutions.'
E. J. R. Sudholter and J. B. F. N. Engberts
Pesquisa do Estado de SBo Paulo (FAPESP 77/0285 to F.H.Q. and 76/0401 to H.C.) and the CNPq (7186/75 to H.C.).
References and Notes For paper 1 in this series, see F. H. Quina and H. Chaimovich, preceding paper in this issue. E. J. Fendler and J. H. Fendler, "Catalysis In Micellar and Macromolecular Systems", Academic Press, New York, 1975. In this regard, see ref 4 and references clted therein. C. A. Bunton, K. Ohmenzetter, and L. Sepilveda, J. Phys. Chem., 81, 2000 (1977). L. R. Romstead and E. H. Cordes, J . Am. Chem. SOC.,90, 4404 (1968). 0. Schales and S. S. Schales, J. Biol. Chem., 140, 879 (1941). E. M. Kosower and J. W. Patton, Tetrahedron, 22, 2081 (1966). M. Politi, I. M. Cuccovia, H. Chalmovich, M. L. C. de Almeida, J. B. S. Bonilha, and F. H. Quina, Tetrahedron Lett., 115 (1978). S. Spurlin, W. Hinze, and D. W. Amstrong. Anal. Lett., 10,997 (1977). B. Permutter-Hayman, Prog. React. Klnet., 6, 239 (1972). F. H. Quina, Tese de Livre DocBncia, Universidade de SHo Paulo, 1977. J. M. Politi, J. B. S. Bonilha, H. Chaimovlch, and F. H. Quina, unpublished results. F. H. Quina and V. G. Toscano, J. Phys. Chem., 81, 1750 (1977). Since we have assumed' that cy remains constant
Acknowledgment. F.H.Q. thanks the Conselho Nacional de Desenvolvimento Cientifico e Tecnolbgico (CNPq) and the Financiadora de Estudos e Projetos (FINEP) for fellowship support. M.J.P. is an undergraduate fellow and J.B.S.B. a graduate fellow of the CNPq. This work was supported by grants from the FundaGBo de Amparo 5
!&(rnIc)
= aCD
+ cmc + [OH,] +
Yd
where Yd represents the concentrationof Y which has been displaced upon binding of OH- to the micelle. Thus Yd = [OH,] and [OH,] Yd =! [OH,]. L. R. Romsted, Thesis, Indiana University, Bloomington, Ind., 1975.
+
Salt Effects on the Critical Micellar Concentration, Iodide Counterion Binding, and Surface Micropolarity of I-Methyl-4-dodecylpyridinium Iodide Micelles Ernst J. R. Sudholter and Jan B. F. N. Engberts" Department of Organic Chemistry, University of Groningen, Nijenborgh, 9747 AG Groningen, The Netherlands (Recelved January 22, 1979)
Electrolyte effects on the crnc and iodide counterion binding of micelles of 1-methyl-4-dodecylpyridinium iodide (1) have been investigated by conductance measurements and by UV spectroscopy. The intramolecular charge-transfer (CT) absorption band of the ionic head group of 1 was successfully employed as an intrinsic microscopic medium polarity reporter for the innermost part of the electrical double layer. This micropolarity can be expressed in terms of Kosower's 2 values which demonstrate the reduced polarity near the micellar surface. The applicability of Mukerjee's band-match method reveals that the Stern layer is quite homogeneous. The presence of electrolytes only modestly affects the micropolarity in the Stern layer. Sodium salts decrease the cmc in the order C1- < Br- < NO3- < I- < OTs- (which parallels the lyotropic series for the inorganic anions) and the effect on the cmc follows the Shinoda equation. The above order also applies for the ability of the anions to reduce the iodide counterion binding (B)as shown by the decrease in the molar extinction coefficient of the intramolecular CT band. The association constant for binding of iodide ions to the long-chain pyridinium cations within the micelles was also derived from the optical absorption data. The deviant salt effect of sodium p-toluenesulfonate is briefly discussed.
Introduction A large variety of reactions catalyzed by micelle-forming surfactants have served as valuable model processes for the study of microenvironmental factors which affect the high efficiency of chemical transformations in the biological realm. In this context, the large electrical potential in the Stern layer of micelles composed of ionic detergent molecules as well as medium effects characteristic of the micellar pseudophase have been recognized as integral parts of the catalytic advantages offered to micelle-bound substrates.14 0022-3654/79/2083-1854$01 .OO/O
For a proper understanding of micellar catalysis, knowledge of fundamental micellar properties such as size, shape, stability, counterion binding, and micropolarity in the Stern layer and micellar core is indispensible. In this paper we report a study of the aggregation process of 1-methyl-4-dodecylpyidinium iodide (1) a t 25 OC in water C H 3 ( C H 2)11 G ' - C H a
I-
1
and in several aqueous electrolyte solutions (NaC1, NaBr, 0 1979 American Chemical
Society
Aggregation Properties of 1-Methyl-4-dodecylpyridinium Iodide
The Journal of Physical Chemistry, Vol. 83, No. 14, 1979
1855
TABLE I: Critical Micellar Concentrations of 1 in the Presence of Sodium Salts NaX as Determined by Conductance Measurements (25.0 i 0.2 "C) cmc ( l o 3M )
[NaXI, 103 M
x = c1
X = Br
x =I
X = NO,
X = OTs
0 1.0 2.0 3.0 4.0 5.0 5.9 6.9 7.9 8.8 9.8
2.45 I 0.05 2.40 i 0.05 2.35 t 0.05 2.35 i 0.05 2.35 t 0.05 2.35 i 0.05 2.25 i 0.05 2.25 i 0.05 2.35 I 0.10 2.35 i 0.10 2.25 i 0.10
2.45 i- 0.05 2.25 i 0.05 2.25 i 0.05 2.20 i- 0.05 2.10 i 0.05 2.10 c 0.10 2.00 i 0.05 2.00 i 0.05 2.10 i 0.10 2.10 i 0.10 2.10 i 0.10
2.45 I 0.05 2.15 t 0.05 1.70 i 0.05 1.50 i 0.05 1.30 f 0.05 1.20 i- 0.05 1.05 t 0.10 1.00 I 0.10 0.80 i 0.10 0.80 i 0.10 0.75 i. 0.05
2.45 i 0.05 2.20 i 0.05 2.00 i 0.05 2.00 I 0.05 1.95 i 0.05 1.90 i 0.05 1.90 i. 0.05 1.85 t 0.05 1.85 i 0.05 1.90 i 0.05 1.75 t 0.05
2.45 i 0.05 2.00 i 0.05 1.90 i 0.05 1.45 i 0.05 1.20 i 0.05 1.05 i 0.25 1.05 t 0.35 0.85 I 0.15 0.85 i 0.25 0.95 i 0.35 0.65 i 0.25
NaI, NaN03, and NaOTs) in order to probe into the effects of added salts on the critical micellar concentration (crnc), iodide counterion binding, and micellar surface micropolarity. In a previous we have shown that the first intramolecular charge-transfer (CT) absorption band of the ionic head group of 1 can function as an intrinsic microscopic medium polarity parameter for the region near the surfactant head group in the aggregate. Accordingly, we can avoid the ambiguities associated with studies using extrinsic micropolarity reporters* which result mainly from the disturbance of the micellar structure by the probe mole~ule.~
Experimental Section Materials. 1-Methyl-4-dodecylpyidiniumiodide (1)was prepared as described previou~ly.'~The salts used in all experiments were of the highest grade available (Pro Analysi) and were usually obtained from Baker or Merck A.G. All salts were dried before use over Pz05in vacuo at 100-150 "C for 24 h. The detergent-salt solutions were made by diluting stock detergent solutions with concentrated (ca. 0.5 M) stock salt solutions. The water used was demineralized and distilled twice in an all-quartz distillation unit. The specific conductivity of this water was 0.8-0.9 X lo4 ohm-l cm-l. Methods. The conductivity was measured as "specific conductivity" (ohm-' cm-l) with a Philips conductivity meter PW 9501/01 fitted with a Philips electrode PW 9512/00 (cell constant 0.63 cm-l). The conductivity cell was equipped with a magnetic stirring device. All solutions were thermostated a t 25.0 f 0.2 "C, The absorption spectra were recorded manually with a double-beam Beckman Model 24 spectrophotometer. Optical densities (accuracy fO.OO1) were read from the digital display between 260 and 350 nm at intervals of 5 nm. The solutions in the cell compartment were thermostated at 25.0 f 0.2 "C at least 15 min before the measurements were started. Linear regression analyses by the method of least squares were carried out on a HP-25 calculator. Results Conductance Measurements. The cmc's of 1 (at 25 "C) in water and in several aqueous salt solutions (NaX; X = C1, Br, I, NOs, OTs; OTs = tosylate) were obtained from plots of the specific conductance K vs. [l]. In the surfactant concentration range near the cmc the slopes of these plots underwent an abrupt change.1° The cmc was determined by the intersection of the two lines. Results are listed in Table I. As argued previously,ll there exists no unique experimental definition of the cmc, and its magnitude will be somewhat dependent on the experimental method used. The Krafft point or critical micellar temperature (cmt) of 1 in water was obtained12 by measuring K as a function of
log C M C
0 7
06
i
1 2
I
3
I 4
IoglCMC
I
I
5
6
I
7
I
0
I
9
I
1
0
* [Nsl])
Figure 1. log cmc (of 1) as a function of log (total counterion concentration at the cmc) for added NaCl (I), NaBr (2), NaNO, (3), NaI (4), and NaOTs (5) at 25 OC.
TABLE 11: Linear Regression Analysisa of the Cmc Decrease with Increasing Salt Concentration (NaX)
X-
c1Br-
INO,-0Ts
A
B
rz b
-2.72 - 2.88 -4.75 -3.04 - 5.00
0.04 0.10 0.83 0.15 0.91
0.57 0.73 0.97 0.90 0.94
Obtained by using the Shinoda equation, see text. Coefficient of determination.
a
temperature and was found to be 23.2 f 0.1 "C. The decrease of the cmc with increasing salt concentration follows the total counterion concentration at the cmc (Shinoda e q ~ a t i o n ) , i.e. '~ log cmc = A - B log (cmc + [NaX]) where A and B are constants. Plots of log cmc against log (cmc + [NaX]) are displayed in Figure 1. Results of a linear regression analysis are given in Table 11. Clearly, the salt effect on the cmc becomes more pronounced in the order C1- < Br- < NO3- < I- < OTs-. For X- = I-, the constant B in the Shinoda equation represents the counterion binding to the micelles at the cmc.14 In this case, B = p / N , where p is the number of bound counterions and N is the number of long-chain cations in the micelle. For micelles of 1 at 25 "C, B = 83 f 12%. In the presence of NaOTs the transition from monomer surfactant to micelles occurred over a substantial concentration range, implying that less accurate cmc's were obtained (Table I). Optical Absorption Measurements. In order to check the utility of the first intramolecular CT absorption band
1856
The Journal of Physical Chemistry, Vol. 83, No. 14, 1979
E. J. R. Sudholter and J. 8.F. N. Engberts
TABLE 111: Correlation of the Transition Energies, E T , of 1 in Various Solvents with Kosower's 2 values solvent
2
[1I, 103M
CHCl, CH,Cl, DMF MeCN i-PrOH EtOH
63.2 64.2 68.5 71.3 75.9 79.7
0.74 4.60 4.90 4.90 4.80 5.13
t
ET kcalmol-' 9
h,,
nm
361 k 352 332 i: 322 i: 302 i 288
1
*1
*
2 1 1 2
79.5 81.5 86.4 89.1 95.0 99.6
i: 0.2 i: 0.2
* 0.5
1
0.0 cm-'
i: 0.3 k 0.3 1- 0.7
z
t
r
90
c 2 1 80
r e
t70
1-
O'l 0.01
c
i
250
I= 70
80 90 E T (kcal.mole-'l
100
3 50
300 h(nrn)
Figure 3. The appearance of the first intramolecular CT band of 1 in water at 25 OC with increasing detergent concentratlon: 0.45 (l), 0.93 (2), 1.85 (3), 3.98 (4), 5.70 (5),8.19 (6),and 10.30 (7) mM. I
Flgure 2. The transition energy ETof the first intramolecular CT band of 1 (1) and of 1-methylpyridinium iodide (2) in solvents of different Z values.
of 1 as a measure for micropolarity,15the optical absorption spectrum of 1 was recorded in various media of different 2 values. Concentrations of 1 were chosen sufficiently low to prevent aggregation in the particular solvent.' The absorption maximum (Am, nm) expressed in transition energy E T [ = (2.8690 X 104)X,-' kcal mol-I] showed excellent correlation (1.2 = 0.9981) with Kosower's 2 values15@ (2 = 0.838ET - 3.49) (Table 111). As shown in Figure 2, almost parallel straight lines are obtained upon plotting 2 vs. ET for 1 and 1-methylpyridinium iodide17 (2). In the aqueous solution below the cmc, the CT band of 1 cannot be observed. Since for water 2 = 94.6, we expect Am = 245 nm and ET(monomer) = 117.1 kcal mol-'. Consequently, the CT transition will be hidden under the strong H-H* transition of the heterocyclic R system, even more so since a low molar extinction coefficient is expected in view of the absence of significant amounts of intimate ion pairs in the polar medium. If the concentration of 1 is gradually increased above the cmc, the long-wavelength part of the first intramolecular CT band becomes resolvable (Figure 3) as a result of the reduced polarity in the Stern layer of the micellar aggregate. This reduced polarity will possibly result from a dielectric saturation effect and/or from the proximity of the hydrophobic part of the cation.18 The position of the absorption maximum as well as the optical density of the chromophore within the micelle were determined by means of the band-match method advanced by Mukerjee.18 Applying the well-resolved CT band of 1 in c h l o r ~ f o r min~this ~ procedure, we find for the micelle Ammic = 286 f 1nm and ETmic = 100.3 f 0.3 kcal mol-l. Thus, transferring the pyridinium iodide polarity reporter from bulk water to the Stern layer of the corresponding micelle results in a lowering of the transition energy of the first CT band by 16.8 kcal mol-l. Accordingly, in the Stern layer of the micelle, Z will be about 80.6,
1
(0.0. cm- Im 12
c
2
4
6
8
10
lo3 M Flgure 4. Optical density per centimeter pathlength of the first intramolecular CT band maximum as a function of [l] at different concentrations of NaI: 0.0 ( l ) , 2.0 (2), 4.0 (3), 6.0(4), 8.0 (5),and 10.0 (6) mM.
which may be compared with the 2 value for ethanol as the solvent (2 = 79.7). Our value is in good agreement with the micropolarity a t a micellar surface as estimated previously.18 Upon plotting the optical density (OD) per centimeter pathlength of the maximum [(OD cm-l),] vs. [ 11, straight lines (according to Lambert-Beer's law) with good correlation coefficients are obtained both in the presence and absence of added sodium iodide (Table IV and Figure 4). The intersection of the line with the concentration axis provides the cmc whereas the slope of the line represents
Aggregation Properties of 1-Methyl-4-dodecylpyridiniumIodide
TABLE IV: Effect of NaI on t h e Absorption Spectrum and Counterion Binding of Micelles of 1
The Journal of Physical Chemistry, Vol. 83, No. 14, 1979
TABLE V: Effect of NaX on the Absorption Spectrum of Micelles of 1a t [NaX] t [NaI] = lo-' M [NaXII
0.0 2.0 4.0 6.0 8.0 10.0 75 100
2.47 1.79 1.48 1.20 0.93 0.84 0.36
286 286 288 288 288 290 292 292
1364 1390 1425 1453 1450 1505 1570 1605
80.3 80.3 79.7 79.7 79.7 79.2 78.6 78.6
85 87 89 91 91 94 98 1008
0.9998 0,9991 0.9949 0,9999 0,9999 0.9993 0.9989 0.9967
a ~ 0 . 0 5x M. r l nm. The concentration of 1 was 8.60-9.49 X M. 1 2 0 M-' cm-'. i0.2. e ?r 2%. f Coefficient of determination. See text.
the molar extinction coefficient (E) of the CT band. Because only CT complexes in the Stern layer of the micelle contribute to t, the magnitude of t can serve as a measure for the counterion binding ( B )by iodide ions to the long-chain pyridinium ions in the micellar aggregate. Now we assume that if no iodide counterions are bound ( B = 0%) t will be zero and, in addition, that B will be a linear function of t. Since plots of t values vs. increasing sodium iodide concentration showed saturation behaviorz0 around an E value of 1600 f 20, we suppose that this E value indicates complete counterion binding ( B = 100%). Although some uncertainties are involved in this treatment,21 the B value calculated from t at zero sodium iodide concentration agrees well with that obtained by Corrin's method from conductivity data (vide supra). This provides evidence for the concept that CT interaction in the Stern layer directly reflects counterion binding to the micelles. The data listed in Table IV again demonstrate the lowering of the cmc with increasing [NaI]. Although the decrease of the cmc as measured by the spectrophotometric method closely parallels the decrease in cmc found by the conductometric procedure, the cmc values obtained by the latter technique are smaller (except one) than those determined by the former method. This situation has been encountered beforels and again establishes the notion that cmc values are always arbitrary to some extent. The amount of iodide counterion binding to the micelles at the cmc was calculated by applying Corrin's method14 to the cmc values obtained from the absorption data. This leads to B = 7 3 f 10% (r2= 0.9894). We conclude that B values derived from the effect of sodium iodide concentration on t contain the smallest experimental error ( B = 85 f 2% a t the cmc). In the range [NaI] = 0-0.100 M, B is found to increase from 85 to 100%. In this concentration range, the observed shift of the absorption maximum is Ah, = 6 f 2 nm, corresponding to a lowering in transiton energy of 2.0 f 0.9 kcal mol-' and a reduction in 2 from 80.6 f 0.2 to 78.8 f 0.2. The salt-induced change in micropolarity is relatively small and reflects the enhanced iodide concentration near the surfactant head groups in the micelle. When NaC1, NaBr, NaN03, and NaOTs were added to the micellar solution, a substantial deviation from Lambert-Beer's law was observed, i.e., a plot of (OD cm-l), vs. stoichiometric concentration of 1 gave no linear relationship. This curvature may be best attributed to competition between the two counterions for binding in the Stern layer.22 If [NaX] is kept constant over the whole concentration range of 1, the ratio [NaX]/[ 11 will decrease with increasing [ l ] and less iodide ions are repelled from the Stern layer by X- ions as [ 11 is increased. This implies that different amounts of I- and X- will be bound with varying concentration of 1 and, consequently, the amount of pyridinium-iodide CT complexes in the micelles will not
1857
e,b M-'
h,:
B,'
nm
cm-'
%
rzd
0.50 1.00
103cmc,M 0.85 i 0.05 0.60 r 0.05
289 288
1353 1080
85 68
0.9997 0.9990
Br
0.50 1.00
0.70 + 0.05 0.60k 0.05
288 288
1292 1073
81 67
1,0000 0.9996
NO,
0.25 0.50 0.75 1.00
0.90 i 0.75 i 0.60 i 0.51 f
0.05 0.05 0.05 0.05
290 288 288 287
1372 1212 1104 1002
86 76 69 63
0.9990 0.9987 0.9988 0.9996
OTs
0.25 0.50e 0.75 1.00
0.88 c 0.10 0.10 t 0.10 0.10 f 0.10 0.33 f 0.10
290 290 288 288
1209 830 719 639
76 52 45 40
0.9985 0.9984 0.9996 0.9999
X
[l]
C1
a i 1 nm. f 2 0 M-' cm-'. i2%. Coefficient of deM, cmc termination. e At [NaOTs] + [NaI] = 8.0 X = 0.06 c 0.05 X M, h m = 289 ?r 1 nm, E = 774 i. 20 M-' cm-', B = 48 k 2%, and r z = 0.9967. At [NaOTs] t [NaI] = 5.0 x M, cmc = 0.67 i 0.05 M, h , = 287 i. 1 nm, E = 742 i. 20 M-'cm-', B = 46 i 2%, and r 2 = 0.9987.
be a linear function of the stoichiometric concentration of 1. This, however, may be avoided by keeping the ratio of [X-1 to [ l ] constant.23 However, in that case, the total added salt concentration is increased with increasing [ 11. We have circumvented this problem by adding NaI to the solution so that the total amount of added salt, [NaX] f [NaI], remains constant upon increasing [ 11, We find that under these conditions Lambert-Beer's law is obeyed. The results obtained from plots of (OD cm-l), vs. [l] are summarized in Table V. On increasing the ratio [NaX] / [I] the cmc decreases for all added salts, the effect becoming more pronounced in the order C1- < Br- < NO3< -0Ts. Furthermore, the amount of iodide counterion binding to the micelles is diminished as the ratio [NaX]/ [ I] becomes larger. The magnitude of this effect increases in the series C1- < Br- < NO< < -0Ts. Iodide counterion binding also decreases with decreasing total added salt concentration. The cmc is increased when the total salt concentration is decreased from to 5.0 X M at [NaOTs]/[l] = 0.5. The observed shifts in the absorption maximum (Ah,) are small, indicating that the polarity in the Stern layer is only little affected. Finally, optical absorption measurements allow the calculation of the association constant for binding of iodide ions to the long-chain pyridinium cations within the micelles formed'from 1. If only iodide ions are present as counterions in the micellar solution, the following 1:l association equilibrium is assumed: Pyr+
+ I-
KI
Pyr+.I-
where Pyr+ represents the long-chain pyridinium cation and Pyr+.I- represents a pyridinium iodide CT complex, both within the micelle. The equilibrium constant is KI. Neglecting the effect of sodium cations, we may write [Pyr+-I-] = B(CD - cmc) [Pyr+] = (1- BNC, - cmc) [I-] = (1- B)(CD- cmc)
+ [NaI]
in which B is the counterion binding (vide supra), CDthe stoichiometric concentration of 1, and NaI the added stoichiometric concentration of sodium iodide. In Figure 5 the calculated values for [Pyr+-I-] are plotted against [Pyr+][I-1. The slope of the straight line represents the association constant per long-chain pyridinium cation (KI
1858
The Journal of Physical Chemistty, Vol. 83, No. 14, 1979
5
Y I
I
1
I
I
I
I
I
1
2
3
b
5
6
7
[ @] ( hiz 1 [Pyr'] [I-] plotted vs. calculated values
106 P y r B ] , :I
Flgure 5. Calculated values for
for [IJ~~+.I-].
= 390 f 10 M-l, CD = 9 X M). The obtained value is somewhat greater than the equilibrium constants found by Mukerjee18 for the ionic association of N-dodecylpyridinium iodide in 80% MeOH-H20 (KI = 24 M-l) and of 1-ethyl-4-carbomethoxypyridiniumiodide in EtOH (KI = 185 M-1),15aboth at 25 "C. The association constant of 1-methylpyridinium iodide (KI = 21.2 M-l), determined at X = 290 nm in 80% EtOH-H20, is also smaller.24
Discussion The results presented in Table IV disclose the utility of the first intramolecular CT band of the pyridinium-type head group of 1 to function as a micropolarity reporter in aggregation processes in aqueous media. Thus, the shift of the CT band upon transfer of the surfactant molecule from bulk water to a micelle at 25 "C corresponds to a surface micropolarity expressed by 2 = 80.6 f 0.2 and which is rather similar to the polarity of ethanol on the same solvatochromism scale. Since the CT bands of 1 in micelles and of intimate ion pairs of 1 in chloroform are very well matchable, we conclude in accord with Mukerjee,18 that the Stern layer of the micellar aggregate is quite homogeneous. Earlier work8J6J8J9also revealed reduced polarity in the micelle-water interface. For example, Ferndndez and Fromherzsg estimated a dielectric constant of 32 f 1 for the binding site of two fluorescent pH indicators in Triton X-100 by comparing pK values in bulk water and in the region near the micellar surface. Whereas added salts greatly influence the observed cmc's (Tables I, IV, and V) and probably also affect the micellar size and shape, the position of the CT band of the surfactant molecules in micelles underwent only small changes with salt concentration (Tables IV and V). Therefore the micropolarity in the Stern layer is weakly affected under these conditions. Since this conclusion seems also to be valid for other types of micelles,18 it is suggested that the often large salt effects on micellarcatalyzed reactions4 cannot be rationalized by only invoking changes in micropolarity at the micellar surface. The conductance as well as the optical absorption measurements evidence the decrease of the cmc with increasing concentration of the"sa1ts N a X (Tables I, IV, and V). The order of effectiveness of the anions studied in this work is C1- < Br- < NO3- < I- < -0Ts. The same order applies for the ability of these anions (except I-) to displace I- from the Stern layer of the micelles. These anion results closely parallel the lyotropic series,%originally advanced by Hofmeister,26which represent relative salt effects on precipitation and denaturation processes of proteins. No definite conclusions can be drawn as to the detailed mechanism of the observed salt effects. Nevertheless, it is highly likely that the decrease in cmc with increasing salt concentration is mainly the result of a reduction in
E. J. R. Sudholter and J. B. F. N. Engberts
charge density per surface area of the micelle which leads to a lowering of Coulombic repulsions between the head groups. For the halide ions, the effect on cmc parallels the anion radii.25b The greater the anion radius, the greater the polarizability and the lower the heat of d e h y d r a t i ~ n . ~ ~ Both factors will enhance the attraction between the polarizable pyridinium cation and the added anion and will determine the lowering of the cmc and the tendency of the noncommon anion to repel iodide anions from the electrical double layer. The same order in effectiveness of the halide anions has previously been observed for the lowering of the cmc of dodecyltrimethylammonium for the effect on the activity coefficient of benzene in aqueous salt solutions,2s and for the decrease in the salting-out effect of the hydrophilic part of nonionic detergents.25d The position of an anion in a lyotropic series has also been correlated with Stokes hydrated radii (although the correlation is and with heats of transfer from water to micellar solutions of various detergents.25" We note that the tosylate anion forms a special case because of its hydrophobic bonding proper tie^.^^ Interestingly, a t [NaOTs] / [I] = 1 the optical absorption measurements reveal a small increase of the cmc after an initial decrease in the region [NaOTs]/[l] = 0.25-0.75 (Table V). We submit that this finding reflects the effect of the tosylate anion on the Gibbs free energy for the hydrophobic interaction which constitutes the driving force for micellization. At a higher ratio of NaOTs to 1, the aggregation process will involve relatively many tosylate anions to form some type of mixed micelles in which the favorable Coulombic contribution of the tosylate anions is now partly offset by a decrease in hydrophobic interaction, owing to the relatively small hydrophobic residue of the tosylate In fact, the complete order of anion effectiveness in reducing the cmc of 1, as given above, is in accord with the relative order of the effects of the anions on water ~ t r u c t u r e . ~ Therefore, l-~~ one could argue that the position of an anion within the series corresponds to the effect of the anion on the magnitude of the hydrophobic term in the free energy of micellization. On this basis, several authors have considered salt effects on cmc's both for ionic25cand nonionic detergents.25d However, our optical absorption spectra (A, and e) unambiguously indicate that addition of the sodium salts in question modifies the Stern layer of the micelles in the sense that more counterions are being bound in this region. We conclude, therefore, that the addition of salts primarily increases the thickness of the Stern layer (i.e., the "Debye length") and decreases the electrical part of the standard state chemical potential of the micelle in equilibrium with surfactant monomers. However, the overall effect may be modified by salt effects on the hydrophobic part as suggested by the deviant behavior of sodium tosylate. Acknowledgment. The investigations were supported by the Netherlands Foundation for Chemical Research (SON) with financial aid from the Netherlands Organization for the Advancement of Pure Research (ZWO). This paper is dedicated to Professor E. Havinga on the occasion of his 70th birthday. References and Notes (1) E. H. Cordes and R. B. Dunlap, Acc. Chem. Res., 2, 329 (1969). (2) E. H. Cordes, Ed., "Reaction Kinetics in Micelles", Plenum Press, New York, 1973. (3) I. V. Berezin, K. Martinek, and A. K. Yatsimirskii, Russ. Chem. Rev., 42, 787 (1973). (4) J . H. Fendler and E. J. Fendler, "Catalysis in Micellar and Macromolecular Systems", Academic Press, New York, 1975. (5) D. Pizklewicz, J . Am. Chem. Soc., 99, 1550 (1977). (6) K. L. Mittal, Ed., "Micellization, Solubilization and Microemulslons", Vol. 1 and 2, Plenum Press, New York, 1977.
Fluctuations Near the Critical Point of One-Component Fluids (7) (a) E. J. R. Sudholter and J. B. F. N. Engberts, Red. Trav. Cbim. Pays-Bas, 96, 86 (1977); (b) work to be published. (8) (a) J. Oakes, J. Cbem. Soc., Faraday Trans. 2, 68, 1464 (1972); (b) J. H. Fendler and L. J. Liu, J. Am. Cbem. SOC.,97, 999 (1975); (c) H. Okabayashi, K. Kitrama, and M. Okuyama, 2. Naturforsch. A , 32, 1571 (1977); (d) K. Kalyanasundaram and J. K. Thomas, J . Am. Chem. Sm.,99,2039 (1977); J. Pbys. Chem., 81,2176 (1977); (e) B. B. Craig, J. Kirk, and M. A. J. Rodgers, Cbem. Pbys. Lett., 49, 437 (1977); (f) J. Llor and M. Cortijo, J . Chem. SOC.,Perkin Trans. 2, 73, 1111 (1977); (9) M. S. Fernlndez and P. Fromherz, J. Pbys. Cbem., 81, 1755 (1977); (h) P. Stllbs, J. Jermer, and B. Llndman, J . Colloid Interface Sci., 60, 232 (1977). (9) M. A. J. Rodgers, M. F. da Silva, and E. Wheeler, Cbem. Pbys. Lett., 43, 587 (1976); 53, 165 (1978). (10) P. Mukerjee, Adv. Collold Interface Sci., 1, 241 (1967). (11) C. Tanford in ref 6, Vol. 1, p 119. (12) Y. Moroi, T. Oyama, and R. Matuura, J. ColloidInterface Sci., 60, 103 (1977). (13) K. Shlnoda, Bull. Cbem. SOC.Jpn, 26, 101 (1953). (14) M. Corrin, J. ColloldInterface Sci., 3, 333 (1948). (15) Compare (a) E. M. Kosower and P. E. Klinedinst, Jr., J . Am. Chem. Soc., 78, 3493 (1956); (b) E. M. Kosower, ibid., 80, 3253 (1958); (c) E. M. Kosower, “An Introduction to Physical Organic Chemistry”, Wiley, New York, 1968. ( 16) Employing probe molecules, several workers have previously estimated Zvaiues for_microenvironments in micelles and polymers. See ref 8 b and P. Strop, F. Mike& and J. Kllal. J . Pbys. Cbem., 80, 694 (1976). (17) E. M. Kosower and J. A. Skorcz, J . Am. Cbem. Soc., 82, 2195 (1960). (18) P. Mukerjee and A. Ray, J . Phys. Cbem., 70, 2138, 2144, 2150 (1966).
The Journal of Physical Chemlstty, Vol. 83, No. 14, 1979
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(19) P. Mukerjee, J. R. Cardinal, and N. R. Desai in ref 6, Vol. 1, p 241. (20) Precipitation of 1 occurred above [NaI] > -0.1 M. It is of interest to note that for the CT complex of 1-dodecylpyrldlnium iodlde e is also about 1600, see ref 18. (21) One could imagine that the c values are partly affected by 1:2 donor-acceptor interactions because of the excess of positively charged ions at the CT sites in the Stern layer. However, the fact that the line shapes of the CT bands of ion pairs of 1 in chloroform and in micelles are nicely matchable does not support this possibility. (22)’ L. S. Romsted in ref 6, Vol. 2, p 509. (23) It is assumed that cmc values are negligible as compared wlth stoichiometric concentrations of 1. (24) P. Hemmes, J. N. Constanzo, and F. Jordan, J . Pbys. Cbem., 82, 387 (1978). (25) (a) I. Cohen and T. Vassiliades, J . Pbys. Cbem., 65, 1774, 1781 (1961); (b) E. W. Anacker and H. M. Ghose, ibkf., 67, 1713 (1963); (c) P. Mukerjee, K. J. Mysels, and P. Kapauan, ibu., 71, 4166 (1967); (d) A. Ray and G. NBmethy, J . Am. Cbem. Soc., 93, 6787 (1971); (e) J. W. Larsen and L. J. Magid, ibid., 98, 5774 (1974). (26) F. Hofmeister, Arch. Exp. Patho/. Pbarmacol., 24, 247 (1888). (27) H. L. Friedman and C. V. Krishnan In “Water, A Comprehensive Treatise”, Vol. 3, F. Franks, Ed., Plenum Press, New York, 1973, Chapter 1. (28) W. F. McDevit and F. A. Long, J. Am. Cbem. Soc., 74, 1773 (1952). (29) (a) C. A. Bunton, M. J. Minch, J. Hidalgo, and L. Sepulveda, J. Am. Chem. Soc., 95, 3262 (1973); (b) C. A. Bunton and M. J. Minch, J . Pbys. Cbem., 78, 1490 (1974). (30) J. Steigman, I. Cohen, and F. Spingola, J. Colloid Interface Sci., 20, 732 (1965). (31) M. J. Blandamer, Q . Rev. Cbem. SOC.,24, 169 (1970). (32) T. S. Sarma and J. C. Ahluwalia, Cbem. SOC. Rev., 2, 203 (1973). (33) N. Nishikido and R. Matuura, Bull. Cbem. Sac. Jpn., 50, 1690 (1977).
Fluctuations, Density Gradients, and Interfaces Near the Critical Point of One-Component Fluids 0. K. Rlce Department of Chemistry, University of Nortb Carolina, Chapel Hi//, Nortb Carolina 27514 (Received November 14, 1977)
In this paper we make use of the analogy between boundaries of fluctuations and interfaces between phases. Fluctuations involve an increase in local free energy from the changes in density involved; there is also a contribution to the free energy from the gradient in density and proportional to the square of the gradient. Evidence is now given that these parallel each other, which means that the gradient term contains a factor Eq, where [ is the correlation length and a critical exponent. Interfaces also involve free energies arising from the local density changes and from the gradient; these must be equal to each other. These two terms involve the thickness Az of the interface, but in each case the Az is defined slightly differently. If Az, is the value for the local density part and Az2 for the gradient part, then Azl a: [ and Azz 0: E’”. This factor which occurs in the expression for the gradient free energy in the fluctuations can also be attributed to a similar behavior of the thickness of the boundary layer between fluctuations. It is also shown that various scaling laws for the exponents can be derived from the relation between fluctuations and interfaces. It is indicated that the compressibility depends only on 5, but this is not true for other thermodynamic functions.
1. Introduction
Widom1i2 has pointed out the similarity between the boundaries between fluctuations in density of different direction and the interfaces between phases in equilibrium, and has shown how a number of scaling relations can be obtained from the use of this analogy. We wish to consider this resemblance in somewhat more detail. This will enable us to see some of the scaling relations in a slightly different light, and examine some scaling relations which have not been examined from this point of view. In recent papers we have considered the relationship of fluctuations and thermodynamic properties near the critical point of fluid^.^ Fluctuations are self-limiting, because a fluctuation near the critical point takes the
portion of the fluid in the fluctuation away from the critical region, thus driving it to a condition with much smaller compressibility. The standard formula for the fluctuation 6p in the density p over a volume u where KT is the thermal compressibility, breaks down where the compressibility changes, i.e., where the linearity of the equation-of-state breaks down. The 6p where this occurs can then be substituted back into eq 1and the latter solved for u , giving a value, say, u, = t3, If E, then, is identified with the correlation length, values are found which are very close to optically observed values, and the exponent Y in [ = tot-”obeys standard scaling laws. Here tois a constant
0022-3654/79/2083-1859$01.00/0 0 1979 American Chemical Society
