2098
J. Phys. Chem. 1982, 86,2098-2102
Reversed Micelle of Dodecylpyridinium Iodide in Benzene. Pressure-Jump Relaxation Kinetic and Equlllbrium Study of the Solubilization of 7,7,8,8-Tet racyanoquinodimethane ShoJl Harada’ and 2. A. Schelly” Department of Chemistry, The University of Texas at Arlington, Arlington, Texas 76019 (Received: October 20, 1981; In Fhal Form: January 13, 1982)
Vapor pressure osmometric (VPO) measurements on dodecylpyridinium iodide (DPI) in benzene (with 0.03 % w/w water content) reveal the presence of reversed micelles with the number-average aggregation number of ii = 7 at 25 “C. In the concentration range of 1-5 mM, the aggregation can be described by the equilibrium 7A M, where only the monomer and micelle concentrations are significant, and the overall association constant is K = 8 X loz5M4. The monomer concentration [A] increases with the surfactant concentration. Spectrophotometric studies indicate that 7,7,8,8tetracyanoquininodimethane(TCNQ) is solubilized by the reversed micelle as TCNQ- anion radical. The pressure-jump relaxation method was used to elucidate the mechanism of the solubilization. Accordingly, the solubilizationprocess can be subdivided into several steps, where TCNQ first penetrates the hydrophobic coat of the micelle in a rapid, probably diffusion-controlled,step. For the completion of the electron transfer to TCNQ at the boundary of the pool, apparently the condition for the formation of the water-soluble Is- in the pool must be created by the entrance of a second electron-acceptor TCNQ molecule into the micelle. The transfer of an electron to each of the two TCNQ molecules is very likely a multistep process. The entrance of the second TCNQ and the transfer of electrons seem to be the rate-determining reactions. A micelle with two TCNQ molecules in its hydrophobic coat is crowded and unstable. We assumed that this species is in a steady state. In the final steps, the TCNQ- anion radicals and Is- are redistributed among the micelles. The overall solubilization rate constant Itf was found to be 6.0 X lo7 M-I s-’. Probably a large fraction of the estimated activation energy E, = 3.1 kcal mol-’ is consumed in the electron-transfer step.
Introduction Recently, there has been much interest in the equilibrium c h a r a c t e r i ~ a t i o nand ~ ~ ~the study of the dynamic behavior5 of reversed micelles. Reversed micelles are aggregates that arre spontaneously and reversibly formed by many amphiphilic molecules in nonpolar solvents, yielding homogeneous solutions. In contrast to “normal” micelles in aqueous solution, the structure of reversed micelles is inverted the polar head groups of the surfactant molecules (usually dipping into a water pool6) form the core of the aggregates while their hydrophobic parts face the apolar solvent. Reversed micelles may also differ from the normal ones in several other aspects. Their mean aggregation number in dry solvents is significantly smaller than that of normal micelle^,^*^ and the population distribution function of their aggregates may have a shape3unlike the approximately Gaussian‘ one typically found in aqueous micelles systems. Because of the difference in population distributions and the consequences thereof, the traditional concept of the critical micelle concentration (cmc) as it is used for systems in aqueous solutions is not generally transferable to reversed micelles.8 For the latter, the cmc often has only an operational meaning,3 which in some cases designates the monomer concentration4if it is con(1)R.A. Welch Postdoctoral Fellow. On leave of absence from the Hiroshima University, Japan. (2)Fendler, J. H.; Fendler, E. J. “Catalysis in Micellar and Macromolecular Systems”; Academic Press: New York, 1975. (3)Herrmann, U.; Schelly, Z. A. J. Am. Chem. SOC.1979,101,2665-9. (4)Tamura, K.;Schelly, Z. A. J.Am. Chem. SOC. 1981,103,1013-8. (5)Tamura, K.;Schelly, Z. A. J. Am. Chem. SOC.1981,103,1018-22. (6)The term “water pool” was originally coined to describe reversed micelles containing large amounts of water (Menger, F. M.; Donohue, J. A.; Williams, R. F. J. Am. Chem. SOC.1973,95, 286). Since then, the usage of the term has been extended to describe the interior of aggregates formed in nonpolar solvents, which contain some water even after careful drying. (7)Aniansson, E.A. G.; Wall, S. N. J.Phys. Chem. 1974,78,1024-30. (8) Kertes, A. S.; Gutmann, A. In “Surface and Colloid Science”; Matijevic, E., Ed.; Wiley: New York, 1976;Vol. 8, pp 193-295. 0022-365418212086-2098$0 1.2510
stant over a certain range of the surfactant concentration. In the present paper we report vapor pressure osmometric results on dodecylpyridinium iodide (DPI) reversed micelle in dry benzene (containing 0.03% w/w water), which lead to an equilibrium description of the system. This information in turn, together with spectrophotometric results, is used for the interpretation of the pressure-jump kinetics of the solubilization of 7,7,8,8-tetracyanoquinodimethane (TCNQ) by the micelle. Details of the solubilization mechanism are discussed, and numerical values of equilibrium concentrations, rate and equilibrium constants, and the activation energy of solubilization are reported.
Experimental Section Chemicals. The solvent benzene was distilled over sodium. The water content of the dry benzene was found to be 0.03% w/w by Karl-Fischer titration. The surfactant DPI was prepared from DPCl (Matheson Coleman and Bell) by 2-times crystallization from saturated KI solutions and purified by 3-times recrystallization from water. TCNQ (Fluka) was recrystallized 5 times from acetonitrile. Its purity was ascertained by the absorption spectrum of its acetonitrile ~ o l u t i o n . ~ All of our experiments were performed on freshly prepared solutions that were kept in the dark between manipulations. Optical Spectra. The absorption spectra were recorded in the wavelength range of 280-880 nm on a Cary 219 spectrophotometer. Quartz cells of 0.1-cm path length were used in all experiments, thermostated at 25 “C.To obtain absorption spectra a t high pressure (150 atm), we installed the cell of the pressure-jump apparatus in the cell compartment of the spectrophotometer, and the pressure was maintained constant (A10 atm) during the recording of the spectra. (9) Acker, D. S.; Hertler, W.
R. J. Am. Chem. SOC.1962,84, 337C4.
0 1982 American Chemical Society
The Journal of Physical Chemisfry, Vol. 86, No. 11, 1982 2099
Reversed Micelle of DPI in Benzene
TABLE I:
Summary of the Equilibrium and Kinetic Results for the DPI-TCNQ-Benzene System at 25 "C 108[Tf] X
103 x CDPI,M
104 x [AI, M
104 x M
1.0 1.o 1.o 1.o 1 .o 2.5 2.5 2.5 2.5 2.5 5.0 5.0 5.0 5.0 5.0
1.97 1.97 1.97 1.97 1.97 2.28 2.28 2.28 2.28 2.28 2.54 2.54 2.54 2.54 2.54
1.15 1.15 1.15 1.1 5 1.15 3.24 3.24 3.24 3.24 3.24 6.78 6.78 6.78 6.78 6.78
a Concentration
104x 105 x 105 x CTCNQ,MITCNQ-1, M [ T C N Q f l , M
0.5 1.0 1.5 2.0
3.23 5.84 8.13 9.84
1.77 4.16 6.87 10.2
0.5 1.0 1.5 2.0
4.11 7.97 11.4 14.6
0.89 2.03 3.61 5.40
0.5 1.0
4.39 8.73 12.7 16.7
0.61 1.27 2.27 3.26
1.5 2.0
104 x [Mfl, M 1.15 0.83 0.57 0.34 0.17 3.24 2.83 2.44 2.10 1.78 6.78 6.34 5.91 5.51 5.11
(4[Mfl + 7-l,
s-'
[ T f l ) , M2
0.42 0.71 0.80 1.22
0.62 1.12 1.41 1.72
0.72 1.21 1.93 2.01
1.02 2.02 3.16 4.14
0.91 2.53 3.05 3.75
1.55 3.02 5.05 6.77
of the micelle as A, aggregate.
Vapor Pressure Osmometry. The VPO measurements were carried out on a Hewlett-Packard instrument, Model 302B, at 25 "C. The instrumental calibration and the measurement procedure were the same as described previ0us1y.~~~ Pressure-Jump Apparatus. Our pressure-jump apparatus with optical detection strongly resembles the one described by Knoche and Wiese.lo With the use of 0.004-mm thick steel bursting diaphragm, the pressure jumps were about 150 atm, with a dead time of 150 ps. Because of the large value of the thermal expansion coefficient of benzene (a = 1.225 X per degree at 25 "C),ll a 150-atm isentropic pressure change is associated with a 3.7 "C temperature change12(heating during pressurization and cooling during the pressure drop). Therefore, in order to approximate adiabatic conditions, we paid special attention to performing the pressurization in as short a time as possible (0.3-3 s). The temperature of the sample was controlled at h0.2 "C.
Results and Discussion Spectrophotometric Measurements. Benzene solution of TCNQ shows a single absorption band at 400 nm. The same band is observed in the presence of DPI, but three major new bands appear in the TCNQ spectrum at 680, 750, and 850 nm (Figure l),as well as a minor one at 480 nm. The 480-nm band, however, develops only if the sample solution is kept at ambient illumination for several hours. The intensity of the four new bands increases with the surfactant concentration. The absorption at the three long-wavelength bands has been attributed to the TCNQ solubilized by DPI reversed micelles as TCNQ- anion radical,13and the one at 480 nm to the TCNQ-dodecylpyridinium charge-transfer c0mp1ex.l~ The absorption band at 850 nm has previously been used for the spectrophotometric determination of the cmc of surfactants in both aqueous15 and organic14J6solvents. (10) Knoche, W.; Wiese, G. Rev. Sci. Instrum. 1976, 47, 220-1. (11) Washburn, E. W., Ed. "International Critical Tables"; McGrawHill: New York, 1928; Vol. 3, p 29. (12) The isentropic temperature change can be estimated by the use of the thermodynamic relationship ( d T l ~ 3 p=) ~T a / p C p ,where p is the density and C, is the heat capacity of benzene. p = 0.8734 g cm-3 at 25 "C (cf. ref ll), and C, = 32.4 cal mol-' deg-' at 25 "C ("Handbook of Chemistry and Physics",60th ed.; CRC Press: Boca Raton, FL, 1980; p D- 176). (13) Melby, L. R.; Harder, R. J.; Hertler, W. R.; Mahler, W.; Benson, R. E.; Mochel, W. E. J . Am. Chem. SOC.1962,84,3374-87. (14) Muto, S.; Meguro, K. Bull. Chem. SOC.Jpn. 1973,46, 1316-20.
----
500
150 a i m 1 aim
600
I
I
700
800
Figure 1. Effect of pressure on the absorption spectrum of the M, CTCNO DPI-TCNQ-benzene system at 25 OC. CopI = 5.0 X = 2.0 X M. A = absorbance per centimeter.
Figure 2. Representative pressure-jump relaxation signal at C o p I= 2.5 X lo3 M and C T m = 2.0 X lo4 M in benzene at 25 'C. Vertical axis is proportional to the intensity of the transmitted monitoring light beam (A = 680 nm).
The absorption spectrum of the TCNQ-DPI-benzene system is affected by changes of both pressure and temperature, but in the opposite directions. The absorption peaks of the TCNQ- anion radical increase with pressure (Figure 1)and decrease if the temperature is raised. Both the pressure and temperature effects are reversible. These equilibrium results are in accord with the sign of the relaxation amplitude observed in the kinetic experiments (Figure 2), which indicate that the decrease of pressure during the pressure jump leads to the reduction of the TCNQ- concentration in the subsequent relaxation. (15) Deguchi, K.; Meguro, K. J . Colloid Interface Sci. 1972, 38, 596-600. (16) El Seoud, 0. A.; Da Silva, M. J.; El Seoud, M. I. J . Colloid Interface Sci. 1977, 62, 119-24.
2100
Vapor Pressure Osmometric Results. To establish the equilibrium description of the DPI-benzene system, we carried out VPO measurements in the concentration range - 5.0 X M for DPI. The total solute of 1.0 x concentration C of each solution was obtained by the use of the calibration constant (determined with benzilbenzene solutions), and assuming the activity coefficients to be unity." The results clearly indicate aggregation of DPI (Table I). For the quantitative interpretation of the VPO data, one can use two basically different methods: (a) the empirical (or graphical) method of analysis4-lsand (b) the one based on the optimal choice of chemical equilibria that lead to micelle f o r m a t i ~ n . ~ Of , ~ Jthe ~ many different equilibrium models possible$ we found that the simple monomer-nmer association model gave satisfactory agreement with both the equilibrium and the kinetic data. In the empirical analysis, the mean aggregation number ri of the micelles and the concentration of the surfactant monomer [A] are assumed to be constant. In the monomer-n-mer association model, on the other hand, ri and the equilibrium constant K of the monomer-micelle equilibrium are assumed to be constant. Although the empirical analysis may provide a rough approximate picture of the aggregat i ~ nthe , ~ assumption that [A] is independent of the surfactant concentration seems to be unrealistic. This is especially true if the assumption is applied over a wide concentration range with a system of small ri, as is the case in the present study. The simple monomer-micelle equilibrium model nA
F?
M
K = [Ml/[Al"
(2)
(17) Since the DPI monomer concentration is very low M), md the total solute concentration is less than M, the approximatlon is justified. (18)Kon-no, K.; Kitahara, A. J. Colloid Interface Sci. 1971, 35, 636-42. (19) Lo, F. Y. F.; Escott, B. M.; Fendler, E. J.; Adams, E. T., Jr.; Larsen, R. D.; Smith, P. W. J . Phys. Chem. 1975, 79, 2609-21. ~~
850 nm (with €850 = 4.3 X lo4 M-' cm-1),20the concentrations [TCNQ-] and [TCNQ,] can be calculated. Since [TCNQ-] represents also the concentration of those micelles which are occupied by a TCNQ molecule, [TM], the concentration of micelles free of TCNQ, [M,], can be calculated from [MI = [T-MI + [M,]. The results are summarized in Table I. Relaxation Kinetic Results. The pressure-jump experiments covered the same concentration ranges as the VPO measurements. Single relaxations between 200 ms and 3 s were observed in all DPI-TCNQ-benzene solutions, and no relaxation was found in solutions containing only DPI or TCNQ. A typical relaxation curve is shown in Figure 2. Restricted by the spectral sensitivity of our photomultiplier (IP28), the relaxations were monitored at 680 nm. As expected from the pressure dependence of the absorption spectrum, no relaxation could be seen at 550 nm (see Figure 1). The reciprocal relaxation time 7-l as a function of CDPI and CTCNQ is shown in Table I. The values listed are the average ones obtained in a t least four experiments. The dynamics of the solubilization of TCNQ (henceforth symbolized as T in the equations) and the subsequent electron transfer from I- to TCNQ can be described by the following mechanism that is in quantitative agreement with the kinetic data as well as the equilibrium picture established previously. In the first, essentially diffusion-controlled step TCNQ penetrates the hydrophobic coat of the reversed micelle K,
T+M=TM
(1)
(where M is identical with A,) is more suitable in several respects. I t realizes that the micelle M must be formed in successive aggregation steps, where eq 1 is the sum of the individual steps and K is the product of the individual association constants. The overall thermodynamic equilibrium constant K is, of course, assumed to be independent of CDpI. The model also assumes that only monomer and n-mer are present at significant concentrations. Using the results (for ri, [A], and [MI) of the empirical analysis as initial trial values, one can optimize the values of K and ri for the constancy of K and for the best fit of the experimental and computed solute concentrations C. With the optimal value of ri = 7, the association constant K of the equilibrium 7A s A, was found to be 8 X M4. The monomer concentration, calculated from this model, slightly increases with CDpI. Solubilization of TCNQ. In the presence of TCNQ, to be able to calculate the equilibrium concentrations of the dominant species present in the solution which are also needed for the kinetic analysis, the following assumptions were made: (a) the presence of TCNQ does not affect the values of It and K, (b) only one TCNQ molecule can be solubilized per micelle in a stable form, and (c) TCNQ is present in the system either as TCNQ- anion radical solubilized at the boundary of the water pool or as "free" TCNQf which includes all other possible forms, of which only TCNQ in the bulk benzene phase is a t significant concentration. Since TCNQ- has a strong absorption a t
~~~
Harada and Schelly
The Journal of Physical Chemistry, Vol. 86, No. 11, 1982
(3)
TCNQ is practically insoluble in water; thus, the subsequent electron transfer from I- to TCNQ must take place at the boundary of the pool. The actual electron transfer, which clearly must take place in several steps, can be represented by the stoichiometric equation 4.13 Since we 2T
+ 31-
2T- + I,-
(4)
found that the kinetics are unaffected by I2 added to the solution, 1,- must be formed before I, has a chance to escape the pool and partition between the bulk benzene and the aqueous pseudophase. The need for two TCNQ molecules for the electron transfer1, requires the formation of TZM k
T + T M & T2M k -2
(5)
The electron-transfer process 4 that takes place inside the micelle can also be written as
with the asterisk indicating 1; in the pool. In subsequent steps 7 and 8, TCNQ- and 1; are redistributed among the G
(T-)2M* + M + T-M
+ T-M*
(7)
K
T-M* + M -9 T-M + M* (8) micelles. Reaction 8 may become significant only a t large excess of free micelles. If one assumes that reactions 5 and 6 are the rate-determining steps, with T2M as an unstable intermediate (i.e., (20) The molar decadic extinction coefficient of TCNQ- was deter(Le., eBso = mined by linear extrapolation of the apparent values liml,cDp,--o~sso) obtained at constant CTCN9 and increasing CDPI.
Reversed Micelle of DPI in Benzene
The Journal of Physical Chemistry, Vol. 86, No. 11, 1982
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research, and to the Robert A. Welch Foundation for additional support.
-
7
0
-
v)
v
k.
1
2
3
4
5
6
7
Figure 3. Reciprocal relaxation time 7-l vs. the concentration factor in eQ 12. The solld line represents the least-sauares fit to the data points. , C = 1.0 X 10-3 M (0),2.5 X M (O),5.0 X M (0).
k2,k3 >> k2, k-,) being in a steady state, the reciprocal relaxation time T-' is given by T-'
2101
Appendix In the following we show that under our experimental conditions, to a good approximation, the second term in eq 9 can be neglected. For the analysis one has to distinguish two major cases: (1)where [Mf]is high enough for reaction 8 to occur to a significant extent and (2) where reaction 8 can be neglected. Case 1 . At high [Mf],reactions 7 and 8 go far enough to completion such that [M*] = [T-M]/2
(AI)
can be assumed, and eq 11 becomes K4K5
K45 % [TMl3/(2[(T-)2M*I[Mfl2) (A2)
After substitution of expressions A1 and A2 into eq 10, expression A3 is obtained. A t this point one can distin-
=
Y = [(T),M*l[Mf1(4+ 6[MfI/[T-MlJ (9)
where
('43)
guish three extreme subcases: (la) [Mf] >> [T-MI, (lb) [Mf] > In this case the second term in the braces of expression A3 is much larger than 4, and the expression, with the use of eq A2, simplifies to
[Tw.
Y % 3[TMI2/K45 (A4) in the parentheses of the second K4K5 ~ T - ~ 1 2 ~ ~ * l / ~ ~ ~ T (11) - ~ ~ ~ Using * l ~this, ~ ~the 1 2expression 1 term of eq 9 becomes Under the conditions of our experiments, the second term ([Mfl2/7 + 1)-l (K45[Mf]2/(3[T-M]21 + l)-' in eq 9 can be neglected (see the Appendix for details), yielding the approximate expression 12 for T-' 3 [T-MI2/ (K45[Wl2) (A5) If this result is substituted into eq 9, it is possible to 7-1 = kd[T,1(4[Mfl + [Tfl)) (12) compare the two terms on the right side and to show that where the inequality kf = Kik&,/(k-, + k3) (13) kd[Tf1(4[Mf]+ [Tfl))>> 3kb[yMI2/(K45[Mfl2) (A6) with
%
The experimental reciprocal relaxation times 7-l plotted vs. the concentration factor in eq 12 are shown in Figure 3. The linear plot going through the origin supports the validity of eq 12 and the proposed mechanism. From the slope of the line in Figure 3, kf = 6.0 X lo' M-l s-l can be obtained, which may be considered as the overall rate constant of the solubilization of TCNQ in the reversed micelle. With the assumption that the temperature effect on the concentration factor in eq 12 is negligible, a rough estimate for the activation energy E, of solubilization can be obtained from the temperature dependence of T - ~ . Pressure-jump experiments carried out in the temperature range of 25-45 "C yielded the estimated value of 6.3 kcal mol-' for E,. Since actually two molecules of TCNQ are solubilized in the rate-determining steps 5 and 6, the activation energy per mole of TCNQ is E, i= 3.1 kcal. It is interesting to compare this number with the 2.2 kcal mol-' activation energy of electron exchange between TCNQ and TCNQ- in acetonitrile,21or the 1.4 kcal mol-' in THF.21 If the comparison is justified, one can conclude that a large fraction of the barrier to solubilization is represented by the electron transfer to TCNQ. (21) Haran,
ma-90.
N.;Luz, Z.;Shporer, M. J. Am. Chem. SOC.1974, 96,
used in the text holds. kf in expression A6 symbolizes K1k,k3/(k2 + k 3 ) , and kb stands for k-,k-3/(k-z + k J . Inequality A6 can be rearranged to kfK45/kb >> 3[T-MI2/([Mfl2[Tf1(4[Mfl + [TfI)) (A7) The left side of expression A7 is just the overall equilibrium constant K = n i = t K ,of the steps 3 and 5-8 involved, with the equilibrium expression of K = [T-MI,[ M*] / (IT,],[MfI3) % [T-MI3/ (2 [Tfl,[Mf]3, (-48) The approximate equality is obtained by the use of expression A l . If eq A8 is substituted for the left side of inequality AT, after rearrangement one obtains (-49) 4/[Tfl + 1/[Mfl >> 6/[T-M1 Since l/[Mf] can be neglected, the condition for the validity of inequality A6 at high [M,] is [Mf] >> [T-MI
>> 3[Tf]/2
(-410)
( l b ) [Mf] > 2kb[T-M13/(K&'&13)
(A13)
I.. )-' = 2[(T)2M*]/[TM] = 2[T-M*]/(K4[Mf]) To analyze the inequality kf[Tfl(4[Mfl + [Tf])>> 2kb[TM*l/(K4[MfI) one has to realize that
now, one has to evaluate
resulting in the condition
(IC) [Mf]=
>> [Mf] >> 3[Tf]/4
(A18
[Tm. In this case expression A3 becomes Y
10[(~)2M*I[Mfl
(A16)
and expression A5 changes to ([MfI2/r +
(A231
kfK4/kb = [T-MI [T-M*l /([Tf12[Mf12) (A241
[T-MI / (2 [Tfl2[Mrl3, >> 2 [T-M13/ ( [Mfl3[Tf114[Mf1 + [TflD (A14) [T-MI
(A22)
11-I
%
5/K45
(A17)
and, thus, one must evaluate
>> [T-MI [TM*l/([Tfl2[MfI2) 2~~~*l/~[MfI[Tf1(4+ [ M[TfIN f l (-425) After rearrangement of inequality A25, one obtains 4/[Tfl + 1/[Mfl >> 2/[TMI where l/[Mf] can be neglected. Thus, the condition for the validity of inequality A23 is [Mfl >> [ T M I >> [Tf1/2 (A27) (2b) [Mf]
