1472
J . Phys. Chem. 1990, 94, 1472-1417
is suggested by the two-stage diffusion model and the paramagnetic contact shift mechanism postulated here. It may be that the distinction of edge versus face CO or the distance to a paramagnetic site may be more important to the interpretation of the NMR data than bridging versus linear. Further experimentation is needed to test the suitability of these additional models. The fact that the shifts recorded here with MAS NMR seem to be less affected by chemical effects than by the morphology of the metal particles or some other factor should not be taken as pessimistic for the prospects of MAS NMR for other adsorbates in catalyst systems. The metals studied here should be viewed as difficult systems since Pd and Pt have relatively large magnetic susceptibilities. Studies using other metals such as Rh or Ru with much smaller magnetic susceptibilities do in fact often show much better resolution in powder spectra and under MAS. Knight shifts are not observed for I3COon highly dispersed Rh and Ru catalysts. In this vein, it is interesting to note that comparison of MAS and static powder spectra for I3CO on Ru and Rh catalysts demonstrates that MAS narrows only a portion of the powder pattern. One might speculate that the portion that does not narrow corresponds to I3COon Rh or Ru clusters large enough to be metallic in nature or to clusters with paramagnetic sites in analogy to the observations made here for I3CO on Pt and Pd particles. Comparison of static and MAS spectra of adsorbed CO may then serve
as a basis for distinguishing different types of clusters of metal atoms in oxide-supported catalystsgbonce the source of the shift distributions is identified. This may also explain the marked differences in the spectra obtained for 'TOon high-dispersiongb versus low-dispersion Ru and Rh catalyst^.^^ Further study of the shift distribution effect on different metals and over a range of dispersions will be useful in evaluating this hypothesis and in determining the structural source of this heterogeneity observed by NMR. Acknowledgment. We acknowledge stimulating discussions with D. L. VanderHart, C. P. Slichter, J. P. Ansermet, and T. M. Duncan during the course of this work. Partial support of this work was provided by the Department of Energy under Grant DE-FG22-85-PC80508 and the National Science Foundation under Grant CHE-85 17584. D.M.H. also acknowledges support by a National Science Foundation Graduate Fellowship. L.B. also thanks the NSF/CNRS for support from the US.-France Cooperative Science Program, which makes possible the collaboration between our laboratories. Registry No. CO, 630-08-0; Pt, 7440-06-4; Pd, 7440-05-3. (48) Wang, P.-K.; Ansermet, J. P.; Rudaz, S. L.; Wang, 2.;Shore, S.; Slichter, C. P.; Sinfelt, J. H. Science 1986, 234, 35.
Simulations of Micelle-Catalyzed Bimolecular Reaction of Hydroxide Ion with a Cationic Substrate Using the Nonlinearized Poisson-Boltzmann Equation Elvira Rodenas, * Cristina Dolcet, and Mercedes Valiente Departamento de Quimica Fisica. Quimica Analitica e Ingenieria Quimica, Universidad de Alcalri, Alcalri de Henares, Madrid, Spain (Received: August 4, 1988; In Final Form: July 20, 1989)
We discuss the validity of the Poisson-Boltzmann nonlinearized equation to explain kinetic results of the basic hydrolysis of crystal violet in cationic micelles. Ion distribution around spherical CTAB micelles is described by considering specific interactions between micelle counterions and micellar surface. Aggregation numbers used in the calculation were determined by fluorescence measurements. This treatment is compared with the pseudophase ion-exchange equilibrium model. The Poisson-Boltzmann treatment provides a clear interpretation of salt effects on the binding of a positively charged substrate to cationic micelles.
Introduction Many papers have been published in recent years showing the effect of micellar systems on different chemical reactions'-' in aqueous solution. Most of the kinetic results are interpreted by using the pseudophase kinetic m ~ d e l ,which ~ , ~ treats micelles as a separate phase, and a mass-action model6 or an ion-exchange equilibrium model' to describe counterion distribution between the two phases for reactive and nonreactive counterions, respectively. Neither treatment satisfactorily fits all the results at high ~ ~ ~ ~ and negasalt concentration for neutral,8 p o ~ i t i v e l ycharged, ( I ) Fendler, J. H.; Fendler, E. J. Caralysis in Micellar and Macromolecular Systems; Academic: New York, 1975. Fendler, J. H. Membrane Mimefic Chemistry; Wiley-Interscience: New York, 1982. (2) Romsted, L. S. In Surfacranrs in Solurion; Mittal, K.L., Lindman, B., Eds.; Plenum: New York, 1984; p 1015. (3) Bunton, C. A.: Savelli, G. Adu. Phys. Org. Chem. 1986, 22, 213. (4) Menger, F. M.; Portnoy, C. E. J . Am. Chem. SOC.1967, 89, 4698. (5) Bunton, C. A. Caral. Reu. Sci. 1979, 20, 1. (6) Martinek, K.; Yatsimirski, A. K.; Osipov, A. P.; Berezin, I. V. Terrahedron 1973, 29, 963. (7) Romsted, L. S. In Micellizarion Solubilizarion and Microemulsions; Mittal, K. L., Ed.; Plenum: New York, 1977; Vol. 2, p 509. (8) Otero, C.; Rodenas, E. Can. J . Chem. 1985, 63, 2892. (9) Ortega, F.; Rodenas, E. J . Phys. Chem. 1986, 90, 2408. (10) AI-Lohedan, H.; Bunton, C. A.; Romsted, L. S. J . Phys. Chem. 1981, 85. 2123.
0022-3654/90/2094- 1472$02.50/0
tively" charged substrates. Additional corrections terms for salt effects on the substrate binding constant to micelles1'J2 are required to fit the kinetic results. Other treatments have been published to interpret kinetic data at high ~ a l t . ' ~ ,One ' ~ invokes an additional pathway across the micellar boundary, in which the reactive ion in the aqueous phase reacts with the micelle-bound substrate.12 Another describes the distribution of two or more counterions with independent equilibrium ~0nstants.I~ This approach fits acetylsalicylic acid and homologues hydrolysis in cationic micelles well but cannot explain all the kinetic data in the l i t e r a t ~ r e . ~ , ~ Ion distribution around ~pherical,'"'~cylindrical, or ellipsoidalls micelles can be described by the Poisson-Boltzmann equation, which has been used succesfully to describe the thermodynamic behavior of ionic micelles. For simple monovalent ions, Monte ~
~~
~
(11) Vera, S.; Rodenas, E. J . Phys. Chem. 1986, 90, 3414. ( 1 2) Nome, F ; Rubira, A. F.: Franco, C ; Ionescu, L. G J. Phys. Chem 1982,86, 1881. (13) Rodenas, E.; Vera, S. J . Phys. Chem. 1985,89, 513. (14) Stigter, D. J . Phys. Chem. 1975, 79, 1008, 1015. ( 1 5 ) Bell, G. M.; Dunning, A. J. Trans. Faraday SOC.1970, 66, 500. (16) Mille, M.; Vanderkooi, G. J. Colloid Interface Sci. 1977, 59, 21 I . (17) Gunnarsson, G.; Jonsson, B.; Wennerstrom, H. J . Phys. Chem. 1980, 84, 3114. (18) Bratko, D.; Dolar, D. J . Chem. Phys. 1984, 80, 5782
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1473
Bimolecular Reaction of OH- and Cationic Substrate TABLE I: Micellar Aggregation Numbers at Different CTAB and Salt Concentrations system [CTAB], M [salt], M N CTAB CTAB CTAB CTAB/NaOH CTAB/NaOH CTAB/NaOH CTAB/NaOH CTAB/KBr CTAB/KBr CTAB/KBr CTAB/KBr CTAB/KBr CTAB/KBr
0.005 0.01 1 0.021 0.01 1 0.011 0.061 0.06 1 0.005
0.01 1 0.01 1 0.01 1 0.02 1 0.03 1
1.6
I
I
Nz44
44 55
0.0 IO 0.050 0.010 0.050 0.100 0.030 0.100 0.300 0.100 0.100
75 60 65 76 76 57 65 68 72 71 71
Carlo simulation gives similar results. The simp.- PoissonBoltzmann treatment fails with multivalent ions,19and a modified treatment (MPB) must be used.20q21 However, the simple Poisson-Boltzmann treatment does fit kinetic data in micellar solutions of reactive counterion surfactants such as CTAOH and CTACN.22 In this paper we discuss the validity of the simple PoissonBoltzmann treatment of ion distribution around CTAB micelles and include a specific interaction between micelle counterions, Br, and the micellar surface. The aggregation numbers used in the calculation were determined by fluorescence quenching measurements using pyrene as a probe and cetylpyridinium chloride as a static quencherZ3following widely accepted method^.^^-,^
Experimental Section The surfactant CTAB (Merck) was recrystallized from MeOH/Et,O. Crystal violet (Merck), KBr (Merck), and NaOH (Carlo Erba) were used without further purification. Pyrene (Merck) and cetylpyridinium chloride (Merck) were recrystallized several times, pyrene from methanol and cetylpyridinium chloride from MeOH/Et,O. All the solutions were prepared in MILLI-Q (Millipore) water. All the reactions were run at 25.0 f 0.1 OC in thermostat cuvettes in a Bausch & Lomb Spectronic 2000 spectrophotometer. Reaction was followed at 591 nm, A, of the substrate absorbance in water. The crystal violet concentration was 1.6 X M in all the experiments. The hydroxide ion concentration was always in large excess with respect to the substrate, and the rate profiles fit a pseudo-first-order rate equation, with a cc >0.999. Aggregation numbers were obtained by fluorescence measurements. Steady-state fluorescence measurements were made with a Perkin-Elmer LS-5B spectrofluorometer thermostated at 25.0 f 0.1 OC. Pyrene was excited at 336 nm, and its emission was monitored at 375 and 386 nm, corresponding to the first and third vibronic peaks of pyrene. Aggregation Numbers from Fluorescence Measurements The aggregation numbers were obtained from fluorescence quenching measurements using pyrene as probe and cetylpyridinium chloride as quencher. Literature results show that cetylpyridinium chloride acts as a static quencher. Both the substrate probe and quencher, pyrene and cetylpyridinium chloride, distribute between the aqueous and micellar pseudophase according to the Poisson statistics. ( I 9) Jonsson,B.; Linze. P.; Akesson, T.;Wennerstram, H. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 3, p 2023. (20) Bratko, D.; Lindman, B. J . Phys. Chem. 1985,89, 1437. (21) Levine, S.; Outhwaite, C. W. J . Chem. Soc., Faraday Trans. 2 1978, 74, 1670. (22) Ortega,,F.; Rodenas, E. J . Phys. Chem. 1987, 91, 837. (23) Malliaris, A.; Lang, J.; Zana, R. J. Chem. SOC.,Faraday Trans. 1 1986, 82, 109. (24) T w o , N. J.; Yekta, A. J. Am. Chem. SOC.1978, 100, 5951. (25) Infelta, P. P. Chem. Phys. Lett. 1979, 61, 89. (26) Kalyanasundaram, K. Photochemistry in Microheterogeneous Systems; Academic Press: New York, 1987.
*
0.4 O . 1
/
/
I
Figure 1. Natural logarithm of pyrene fluorescence intensity ratio, In( I o / I ) (I,, = fluorescence intensity in the absence of quencher and I = fluorescence intensity in the presence of quencher), versus quencher concentration. (m, [CTAB] = 0.005 M; 0 , [CTAB] = 0.011 M and [KBr] = 0.03 M; A, [CTAB] = 0.061 M and [NaOH] = 0.01 M).
Therefore, pyrene fluorescence intensity in the absence and in the presence of quencher is related to surfactant and quencher concentration [ Q ] ,which is expressed as In Uo/O = [QIN/[Dnl (1) The aggregation number is obtained from the slope of the In (Zo/Z) vs cetylpyridinium chloride concentration curve. Figure 1 shows the values of In (Zo/Z) for CTAB micelles and CTAB micelles in the presence of KBr and NaOH. Straight lines were also obtained at all other concentrations. The aggregation numbers are listed in Table I. Aggregation number values for other surfactant concentrations are interpolated.
Theoretical Description of This Electrostatic Approach Ion distribution aroound CTAB micelles according to the nonlinearized Poisson-Boltzmann equation can be obtained on the basis of the cell model. The total volume of the micellar solution is divided into cells, each containing one micelle and the amount of water and electrolyte given by the whole concentration of the particular system. Under our experimental conditions, CTAB micelles are considered spheri~al,~’ and the ions are distributed in the region rmC r C r, (rm is the micelle radius and rc is the cell radius) according to the nonlinearized PoissonBoltzmann equation, which for spherical symmetry is expressed as trto(l/r2) d/dr(? d4/dr) = -p = -ZziFci
(2)
If only monovalent ions are present in solution, (2) reduces to the expression ere0( 1/rZ) d/dr(rz d4/dr) = -dc+o exp(-@J/kT) - c-0 expW/kT)I (3) where t, is the relative permittivity, assumed to be constant in the cell with a value of 78.54, to is the vacuum permittivity, Tis the absolute temperature, k is the Boltzmann constant, 4 is the electrostatic potential, p is the charge density, zi is the valency of charged species i, and and c4 are the concentration (mol m-3) of positive and negative ions, respectively, at the point of the solution where 4 = 0. For a micellar solution at equilibrium +(r=rc) = 0 (4) ( d 4 / d r L r C = 4’(r=rc) = 0 (5) and from the electroneutrality of the cell (d4/dr),=,m = 4’(r=rm) = -u/t0tr (6) (27) Young, C. Y.; Missel, P. J.; Mazer, N. A.; Benedek, G. B. J . Phys. Chem. 1978, 82, 1375.
Rodenas et al.
1474 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990
TABLE II: Calculated Values of Micellar Surface Potential, bo and and Fraction of Micellar Head Groups Neutralized with Nonspecifically Adsorbed Bromide Ions [CTABI, M N &A, mV 60,mV mBrNCA
&,A,
0.004 0.010 0.040
0.080
45 60
143.2 134.1 11 1.1 95.0
75 75
213.0 207.0 185.1 168.0
0.420 0.494 0.551 0.562
with the equilibrium condition given by
where u is micellar surface charge per square meter. The parameters c + and ~ ,c are related to the whole number of positive and negative ions in the cell, n+ and n-, by the normalization conditions n+ = c + P A
1:
exp(-e4/kT)(4rr2) dr
(7)
Solution of the Poisson-Boltzmann equation gives the average concentration of bromide ions in a layer of thickness Ar around the micelle. The fraction of micellar head groups neutralized with statistically distributed bromide ions is expressed as
Values of neutralized micellar head groups by considering bromide ions only statistically distributed around CTA+ micelles are given in Table 11. In the calculation, cells have been considered spherical with a cell radius (r,) given by 4 r r d / 3 = N/ 10 3 N ~[ D] ( - CmC)
(10)
where NA is Avogadro's number, [D] is the surfactant concentration, cmc is the critical micelle concentration with a value of 9 X 10" M, and N is the aggregation number. The Stern layer thickness is assumed to be constant, Ar = 4 A. The micellar radius, rm, is obtained from Tanford's expression:28 (4/3)rrm3 = N(27.4
+ 26.9nC)
adsorption of Br ion is described by a Butler-Volmer adsorption eq~ilibrium:~~
(11)
where n, = 15 for CTAB. The nonlinearized Poisson-Boltzmann (eq 3) was solved by using the fourth-order Runge-Kutta, giving initial values to c + ~ and c, and optimizing to a complete solution using the boundary (eq 4 and 5) and normalization conditions (eq 7 and 8). The calculated results are checked by using eq 6 where u = Ne/4rrm2. The numerical integral values in eq 7 and 8 were obtained by Simpson's rule. According to Table I1 values of /3 obtained do not agree with the experimental evidences. For CTAB micelles, /3 values have been determined by different methods such as emP9 and cond u ~ t i v i t y . ~ ~Its* ~value ' is essentially independent of surfactant c ~ n c e n t r a t i o n( ~p ~= 0.8). although some experimental evidence shows that @ increases slightly with surfactant concentration and with added salt.33 The experimental evidence indicates that Br ion adsorbs specifically onto charged surfaces and the amount of ions specifically adsorbed, [BrCA],depends on surface charge, solvent, environment, et^.,^^ and we repeated the calculation by assuming the specific (28) Tanford, C. J. Phys. Chem. 1974, 78, 2469. (29) Zana, R.; Yiv, S.;Strazielle, C.; Lianos, P. J. Colloid Interfuce Sci. 1981, 80, 208. (30) Evans, H. C. J . Chem. Soc. 1956, 579. (31) Hoffmann, H.; Ulbricht, W. Z . Phys. Chem. 1977, 106, 167. Hoffmann, H.; Tagcsson, B. Z . Phys. Chem. 1978, 110, 8 . (32) Sepblveda, L.; Corth, J. J. Phys. Chem. 1985, 89, 5322. (33) Rhcde, A,; Sackmann, E. J. Colloid Intetface Sci. 1979. 70,494: J . Phys. Chem. 1980, 84, 1598.
where [BrNCA]is the nonspecifically adsorbed bromide ion concentration, [B~NcA] = [Br] - [BrCA],and [Br] is the total bromide ion concentration; mB,.(-Ais the fraction of micellar surface neutralized with the specifically adsorbed bromide ions and (1 mg&A) represents the fraction of free micellar surface. The amount of specifically absorbed bromide ions depends on the surface potential, 40, which also depends on the amount of bromide and hydroxide ions distributed around the micelles as described by the Poisson-Boltzmann equation. Equation 3 was solved by use of an iterative method with the fourth-order Runge-Kutta, giving initial values to the micellar surface potential, I # J ~ , c + ~ ,and ,c and optimizing to a complete solution using the boundary (eq 4 and 5 ) and normalization conditions (eq 7 and 8). The calculated results are checked using eq 6 where u = Ne( 1 - mBrcA)/4rrmz.Other Poisson-Boltzmann treatments consider the amount of bromide ions specifically adsorbed as independent of surface p ~ t e n t i a l . ~ ~ . ~ ~ In this case, the total fraction of neutralized micellar head groups is given by
6 = mBrCA + mBrNCA
(1 3)
where mBrNCA is given by eq 9. The bromide ion specific adsorption constant, KB,.(-A,in eq 12, was estimated by taking into account that the CTAB fraction of neutralized micellar head groups in the absence of other ions is nearly constant with a value of p = 0.8. The KBrcA value that best explains these results is 30 M-I, and calculated @ values are given in Table 111. As can be seen, /3 increases with surfactant concentration but the average value is nearly 0.8. Values can be considered correct by taking into account the insensitivity of experimental estimation by different methods. The same calculation has been made for CTAB micelles in the presence of hydroxide ions that can be considered nonspecifically adsorbed onto micellar surface. The cmc value with added salt has been calculated by an empirical equation:" log cmc =
-3.7671 - 0.2133 log ((cmc)o + [NaOH]
+ [KBr])
where (cmc), is the critical micelle concentration in the absence of added salt: 9 X lo4 M. The amount of specifically adsorbed bromide ions has been assumed given by eq 12, where the fraction of free micellar surface has been taken as (1 - mB&A). The fraction of micellar head groups neutralized with O H and Br distributed according to the Poisson-Boltzmann equation can be neglected under our experimental conditions (Table HI), since it is much smaller than the amount of bromide ions specifically adsorbed, mB,.(-A. Solution of the Poisson-Boltzmann equation gives the average concentration of bromide and hydroxide ions in a layer of thickness Ar around the micelle. The fraction of micellar head groups neutralized with statistically distributed bromide and hydroxide ions is expressed as
(34) Bockris, J. OM.; Reddy, A. K. N. Modern Electrochemistry; Plenum: New York, 1970. (35) Bunton, C. A.; Moffat, J. R. J . Phys. Chem. 1986, 90, 538. (36) Almgren, M.; Rydholm, R. J. Phys. Chem. 1979, 83, 360. (37) Bunton, C. A.; Robinson, L. J. Am. Chem. Soc. 1968, 90, 5972.
Bimolecular Reaction of OH- and Cationic Substrate
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1475
TABLE 111: Calculated Values of Micellar Surface Potential, and 64A9 Fraction of Micellar Head Groups Neutralized with Specifically Adsorbed Bromide Ions and Nonspecifically Adsorbed Bromide Ions, Hydroxide Ions, and the Total Fraction of Micellar Head Groups Neutralized,
B
60,mV
[CTAB], M
N
0.004 0.0 10 0.060 0.080
45 60 75 75
76.2 70.5 47.9 43.3
1OOmoH [NaOH] = 0 M 101.6 94.2 67.4 62.3
0.004 0.006 0.010 0.020 0.040 0.060 0.080
45 48 60 75 75 75 75
61.2 64.7 63.2 59.3 50.8 45.2 41 .O
0.004 0.006 0.010 0.020 0.040 0.060
62.8 61.1 59.7 55.7 48.7 43.4 39.5
&A9
mV
0.080
45 48 60 75 75 75 75
Wrl,M
N
64A9 mV
0.005 0.010 0.030 0.050 0.080 0.100
60 60 65 66 67 68
47.2 40.4 27.0 21.2 15.3 12.8
lo0mBrNCA
0.731 0.775 0.824 0.830
0.742 0.787 0.838 0.845
[NaOH] = 0.006 M 96.4 3.0 92.4 2.5 89.0 2.0 83.3 1.4 72.5 1.o 65.7 0.7 60.4 0.6
0.8 0.9 1.o 1.1 1.3 1.4 1.5
0.676 0.701 0.740 0.784 0.805 0.8 16 0.822
0.7 14 0.735 0.770 0.809 0.828 0.837 0.843
[NaOH] = 0.010 M 93.3 4.4 90.1 3.8 86.7 3.1 80.2 2.2 71.0 1.5 64.2 1.2 59.1 1.o
0.7 0.8 0.9 1.1 1.3 1.4 1.4
0.653 0.687 0.728 0.771 0.799 0.81 1 0.8 18
0.704 0.733 0.760 0.804 0.827 0.837 0.843
60,mV 1OOmoH [D] = 0.010 M; [NaOH] = 0.010 M 1.8 69.7 1.4 60.9 43.8 0.8 35.8 0.6 27.7 0.4 24.2 0.4
loomBrNCA
[s]+
(16)
where poSMand posw denote the substrate standard chemical potential in the micellar phase and in the aqueous phase, respectively; [%] and [%] are the effective substrate concentration in the micellar phase and the aqueous phase, related to the analytical concentrations by
where P i s the volume of micellar phase per mole of micellized surfactant. The molar volume is essentially constant according to Tanford's treatment,= and under our experimental conditions, 1 - [ D n ] P - 1. The substrate partition coefficient, Ps, between both phases is given by ps
= ['%I/[%]
= poS expks(6M
- dW)/kTj
(18)
~ B ~ C A
1.4 1.7 2.5 3.0 3.6 4.0
0.774 0.798 0.840 0.862 0.878 0.887
P 0.806 0.829 0.873 0.898 0.918 0.93 1
where Po, = exp(posw - posM)/RT and (4M- 4w) denotes the potential barrier that the substrate must overcome to dissolve in the micellar pseudophase. In this study we have considered this value at the potential given by the Poisson-Boltzmann equation in the point Ar = 4 A where the reaction is supposed to occur. This partition coefficient is related to the substrate to micelle binding constant, K,, by P, = K,/Pas Ks
The total fraction of neutralized micellar head groups is given by (15) 6 = mBrCA + mBrNCA + MOH Values of micellar surface potential and values of 6 are given in Table 111. Above the cmc, substrate distributes between aqueous and micellar phases. The positively charged substrate is assumed to behave ideally in cationic micelles, so that the electrochemical substrate potential in the micellar and in the aqueous phases are equal at equilibrium, and poSM+ RT In [G] z , F = ~ posw ~ R T In z,F&
+
B
1.1 1.2 1.4 1.5
where mOHis the fraction of micellar head groups neutralized with hydroxide ions distributed in the layer between rm and rm+ Ar according to Poisson-Boltzmann. Taking into account that mOH/m&NCA should be equal to the ratio of statistically distributed hydroxide ions to bromide ions, mOHcan be obtained by
+
~ B K A
=
ISMI
/ [SWl iDnl
(19)
This treatment explains that substrate to micelle binding decreases with micellar surface potential drop when micelle and substrate have different charge and concurs with other results in the l i t e r a t ~ r e . ~ ~
Results and Discussion The pseudo-first-order rate constants for the basic hydrolysis of crystal violet at different surfactant and hydroxide ion concentrations are given in Figure 2. The effect of an additional amount of KBr is shown in Figure 3. The experimental results are adapted to the pseudophase kinetic mode14s5and the exchange equilibrium of ions in the micellar surface.' In this treatment, the fraction of micellar head groups neutralized by counterions is constant with a value for CTAB micelles of 6 = 0.8. The pseudo-first-order rate constant is easily derived as
where koH is the second-order rate constant for the reaction between hydroxide ion and crystal violet in aqueous phase, kH [Od] is the first-order rate constant for the reaction with H20, is the hydroxide ion total concentration, kM is the rate constant in micellar pseudophase written in terms of the mole ratio of micellar hydroxide ions bound to micellar head groups, K, is the substrate to micelle binding constant given in eq 19, and [Dn] is the micellized surfactant concentration. The fraction of micellar (38). Miola, L.;Abakerli, R. A,; Ginani, M. F.; Filho, P. B.; Toscano, V. G.;Quina, F. H. J. Phys. Chem. 1983, 87, 4417.
1476 The Journal of Physical Chemistry, Vol, 94, No. 4, 1990
Rodenas et al. TABLE IV: Substrate to Micelle Bindin Constant, K,, and Ion-Exchange Equilibrium Constant, KO(,, Calculated from the Results Supposing Ideal Behavior of Micellar Pseudophase
[Dl, M 0.006
0.004
79 177
161
0.040
0.060
0.080
76 188
63 304
59 379
56 445
63 331
60 406
57 473
70 219
[NaOH] = 0.010 M
PHBr89 K., M-'
0.020
[NaOH] = 0.006 M
PHBr83 Ks, M-I
0.010
83 204
191
79 216
73 252
[KBrl, M 0.005
0.010
0.030
0.050
0.080
0.100
[NaOH] = 0.010 M; [D] = 0.010 M
PHB, 57 0
0 02
f
0 06
004
CTAB
os
0 02
0 04 KBr l M '
Figure 3. Pseudo-first-order rate constants for reaction at different KBr concentrations for [D] = 0.010 M and [NaOH] = 0.010 M. Solid lines are calculated using the pseudophase ion-exchange model, and dashed lines are the calculated values considering the electrostatic model with an ideal behavior of the micellar pseudophase.
head groups neutralized by hydroxide ions, mOH,is described by ion exchange:
and then mOH2
+
mOH
I
[OH1 + PHBr[BrI (KOH& - 1 ) P n I -
48 456
35 769
30 966
25 1214
23 1336
rate constants calculated with these parameter values. The value of the ion-exchange equilibrium constant agrees with other constants in l i t e r a t ~ r e , but ' ~ it is smaller than for other reactions values.2,8-10It should be pointed out that these results are fitted with this treatment by assuming that Ks increases with added salt ion concentration. This effect for additional bromide ion results has been taken into account for the variation in KS$OKs = KOs + 700[KBr], where is the substrate binding constant to CTAB micelles in the absence of additional Br ions. These results can also be simulated using the electrostatic treatment, eq 3-8, 10-12, and 15-18. Calculation of the reaction rate is defined in terms of effective concentration in the micellar phase and in the aqueous phase as
where ti is independent of the micelle aggregation number (eq 11) and surfactant and salt concentration, P = 0.259 M-I; and k, is the second-order rate constant for the reaction in the micellar phase. The pseudo-first-order rate constant is obtained by using eq 22:
\'..
0
350
M
Figure 2. Pseudo-first-order rate constants for reaction at different surfactant and ion concentrations. Solid lines are calculated values with the pseudophase ion-exchange model, and dashed lines are the calculated values considering the electrostatic model with an ideal behavior of the micellar pseudophase (0,[NaOH] = 0.010 M; 0, [NaOH] = 0.006 M).
002c
Ks, M-'
1'
P [ W -- ( P H B r- l)[Dn] 0 (21)
PHBr is the ion-exchange equilibrium constant. The kinetic results are simulated with eq 20 and 21 using known values of the parameters p = 0.8, koH39= 0.201 M-' s-', and kH2039 = 1.94 X s-', and using kM,K,, and PHBr adjustable parameters. The values40 that best fit the experimental results are kM = 0.46 s-', PHsr = 4, and Ks = 70 M-' for hydroxide ion concentration [OH] = 0.006 M and Ks = 90 M-' for [OH] = 0.010 M. Solid lines in Figure 2 correspond to pseudo-first-order (39) Ritchie, C. D.;Wright, D.J.; Huang, D.-S.; Kamego, A. A. J . Am. Chem. Soc. 1975, 97, 1163. (40) Valiente, M.; Rodenas, E. J . Colloid Interface Sci. 1989, 127, 522.
k+ =
kOH[oHl + kHtO + (kmPS - kOH)mOHIDnl (23) 1 + Ps[Dn]a
To fit the results, mOHand +,,A were calculated by the electrostatic treatment given before and (given in eq 18) and k, have been taken as adjustable parameters. The values that best fit these results are P',= 8500 and k, = 0.647 M-' s-'. The calculated values for the pseudo-first-order rate constant are represented by dashed lines in Figures 2 and 3. The aggregation numbers used in the calculation are given in Table 111. The calculated values for do,+ 4 ~ ,the fraction of the neutralized micellar head groups with specifically adsorbed bromide ions (mBcA), the fraction of neutralized micellar head groups with O H and Br ions nonspecifically adsorbed (mOHand mBrNCA), and the total fraction of neutralized micellar head groups are also given in Table 111. The micellar surface potential decreases with surfactant concentration and with the amount of added KBr and is related to the drop in the micellar ionization degree and increase of the substrate binding to micelle. The micellar surface potentials obtained agree with the ones determined experimentally with Lipoid pH indicator^.^' To compare the theoretical treatment of the pseudophase ion exchange with the electrostatic models, we calculated the values of Ks and the ion-exchange constant given by
(eHBr)
KOHBr
= [OHWl [BrMI /[OHM]
lBrWl
(24)
from the values of mOH and mBr(mBr= mBrCA + mSrNCA)given in Table 111. The results, listed in Table IV, show that the Ks increases as (41) Fernlndez,
M. S.;Fromherz, P. J . Phys. Chem. 1977, 81, 1755.
J. Phys. Chem. 1990, 94, 1477-1482 micellar surface potential decreases, whereas the ion-exchange decreases with surfactant and salt equilibrium parameter, PHBr, concentration. We note that Ks was obtained experimentally by ultrafiltration and at low surfactant concentration, and in the absence of salt, K s S 0 = 122 M-I. This value is equivalent to = 8500 in the electrostatic treatment. According to the electrostatic treatment, the second-order rate constant for the reaction in the micellar phase is more than twice the second-order rate constant in water. This means that the micelles produce an authentic catalytic effect on this reaction, while the second-order rate constant for the reaction in the micellar phase, according to the pseudophase ion-exchange equilibrium model, is smaller than the second-order rate constant in water. We conclude that the Poisson-Boltzmann ion distribution
1477
around spherical micelles fits experimental kinetic results assuming a specific bromide ion interaction with the micelle. It improves the pseudophase ion-exchange kinetic model as it predicts that cationic substrate to cationic micelle binding increases with surfactant and ion concentration in solution, according to the experimental evidence, and only two parameters are needed to explain kinetic data: k,, the rate constant in the micellar phase, and Pos, related to the Ar value. According to this treatment, there is a big variation in the ion-exchange equilibrium parameter although we are aware that a constant value of this parameter explains kinetic data at low salt concentration according to the pseudophase ion-exchange model. At this moment, we continue working trying to improve this electrostatic treatment although until now we could not find a better one.
Morphology of Molybdena Supported on Various Oxides and Its Activity for Methanol Oxidation Yoshihito Matsuoka, Miki Niwa,* and Yuichi Murakami Department of Synthetic Chemistry, Faculty of Engineering, Nagoya University, Furo-cho, Chikusa- ku. Nagoya 464-01, Japan (Received: December 5, 1988; In Final Form: August 16, 1989)
This paper describes a method of benzaldehyde-ammonia titration (BAT) that can distinguish surfaces of supports and loaded oxides. Such a method has been found to be effective in examining the morphology of molybdena when held on a variety of supports; the results achieved are corroborated by spectroscopic and electron microscopic studies. A molybdena monolayer of tetrahedral or octahedral coordination was loaded at a surface concentration of
