J. Phys. Chem. 1994,98, 12361-12366
12361
Quantitative Treatment of Ketal Hydrolysis in Aqueous Solutions Containing Polymer-Surfactant Complexes Using a Pseudophase Kinetic Model Angelo Adolfo Ruzza, Sandro JosC Froehner, Edson Minatti, Faruk Nome, and Dino Zanette* Departamento de Quimica, Universidade Federal de Santa Catarina, 88040-900, Florianbpolis, SC, Brazil Received: March 31, 1994; In Final Form: July 12, 1994@
The acid-catalyzed hydrolysis of 2-@-methoxyphenyl)- 1,3-dioxolane and benzaldehyde di-tert-butyl acetal has been studied in the presence and absence of poly(ethy1ene oxide)-sodium dodecyl sulfate (PEO-SDS) solutions. The kinetic data were interpreted in light of the pseudophase ion-exchange (PPIE) formalism by assuming that reaction can occur in three pseudophases, namely, aqueous, micellar, and PEO-SDS complex. The degree of ionization (a)for PEO-SDS complexes was determined from the ratio of the slopes of conductivity against [SDS] above and below the critical aggregation concentration (cac) by the application of Evans equation. Values of 0.25 and 0.41 for SDS micelles and PEO-SDS complexes, respectively, were found. Free micelles are shown to be better catalysts than PEO-SDS complexes because of (i) the lower a value of free micelles and because (ii) second-order rate constants for the acid hydrolysis reactions in SDS micelles are higher than in PEO-SDS complexes.
Introduction The pseudophase model of micellar catalysis successfully treats the effect of ionic micelles upon unimolecular and bimolecular reactions by assuming that the overall rate depends on reactant concentrations and on rate constants in aqueous and micellar pseudophases.1-6 The kinetic interpretations can be simplified for hydrophobic reactants, which bind strongly to micelles and consequently react only in the micellar pseudophase. The model has also been applied to reactions in solutions of analogous systems containing charged interfaces such as microemul~ions,~ reverse micelles,8 and vesicle^.^ Here, we apply pseudophase ion-exchange model principles to the effect of ionic complexes formed by anionic surfactant and nonionic watersoluble polymers. Surfactants and polymers are used extensively in solutions for industrial applications such as several fields of medicine, cosmetic products and food, detergency, textiles, paints, and, recently, enhanced oil recovery. For at least the last three decades, the scientific community has been exploring the physical properties of polymer-surfactant complexes and attempting to interpret the nature and the mechanism of association. Sodium dodecyl sulfate (SDS) interacts strongly with poly(ethy1ene oxide) (PEO), and this system has been extensively investigated'O by using several techniques such as viscometry, surface tension,12,13 dialysis,l4 conductivity,10~12~13,15 NMR s p e c t r o ~ c o p y , ~light ~ . ' ~ scattering, electrophoretic light s~attering,~*.'~ and fluorescence spectroscopy.20 Despite this effort, several doubts and controversies about the mechanism of interaction exist. NMR results indicate that interactions in PEO-SDS complexes involve association or docking of the polymer with micelle-like aggregates of the surfactant, which suggests that the environment of the surfactant alkyl group is similar to that in ionic micelles and that the interaction occurs in the head group region or in the neighborhood of the first carbon of the s u r f a ~ t a n t . ~For ~ . ~ PEO-SDS ~ and PEO-lithium dodecyl sulfate complexes, Dubin et al.18319 assume that counterions play a role in this interaction, by simultaneously coordinating with the polymer oxygens and being electrostatically bound to the @
Abstract published in Advance ACS Abstracts, October 15, 1994.
micelle. The cation in the double layer coordinates with the nonionic polymer to form a "pseudopolycation", which then forms complexes with the anionic micelles. Despite uncertainties about the structure and the mechanism of formation of nonionic polymer-surfactant complexes, important properties of aqueous micelles, such as the degree of ionization and the aggregation n ~ m b e r ,were ~ ~ . estimated. ~~ In general, these complexes are similar in structure to aqueous micelles, but the surfactant aggregates formed on the polymers are smaller than those of free micelles and the degree of ionization is higher.21 Recently, Somasundaran and M a l t e ~ h ~ ~ . * ~ used PEO end-labeled with pyrene to monitor changes in the polymer conformation on association with SDS micelles, and they estimated the aggregation number as a function of various salts. The only parameter affected by an increase in ionic strength was the number of bound surfactant aggregates per polymer chain, and for a given cation there is no effect of either the anion or the salt concentration on the size of the bound aggregate. The authors estimated aggregation numbers for PEO-SDS complexes of about 30 at 0.50 M NaCl, while Lissi et al.24found aggregation numbers of 35 f 5 in the absence and 46 f 5 in the presence of 0.1 M NaCl. Despite the interest in elucidating physical properties of polymer-surfactant complexes, no work has been developed to interpret the effect of these aggregates upon chemical reactions. To investigate the effect of polymer-surfactant complexes on chemical reactivity, we choose poly(ethy1ene oxide) as the nonionic polymer, sodium dodecyl sulfate as the ionic surfactant, and the acid-catalyzed hydrolyses of 2-(pmethoxypheny1)-1,3-dioxolane (p-MPD) and benzaldehyde ditert-butyl acetal (BTBA) (Scheme l), under mildly acidic conditions, pH 5.00 and 6.00.
Experimental Section Material. Sodium dodecyl sulfate, SDS (Sigma, 99%) was used without further purification. The surface tension-surfactant concentration profile was without a minimum, and the critical micelle concentration agreed with that reported in the literature (cmc = 8.0 x M at 25 0C).25The preparation and purification of 2-(p-methoxyphenyl)-1,3-dioxolane @-MPD) has been described,26-28and benzaldehyde di-tert-butyl acetal
0022-365419412098-12361$04.50/0 0 1994 American Chemical Society
Ruzza et al.
12362 J. Phys. Chem., Vol. 98, No. 47, 1994 SCHEME 1
I
'
L
*
(BTBA), n25D 1.4756 (lit.27n25D 1.4752), was prepared according to the proceedings of Fife and Jao.26,27Poly(ethy1ene oxide) (PEO), molecular weight 10 000, was obtained from Aldrich. Succinic acid was used to prepare the buffered solutions, and all other reagents were the best available reagent grade. Methods. The formation of the products p-methoxybenzaldehyde and benzaldehyde was followed spectrophotometrically at 284 and 250 nm, respectively, using a Hewlett-Packard 8452A diode array spectrophotometer. Rate constants, calculated using the HP 89532K kinetic software, for overall kinetic curves, have standard deviations less than 1 x loW5.The temperatures of kinetic runs were maintained at 25.00 and 50.00 f 0.02 "C, by using a water-jacketed cell compartment. Kinetic measurements for the determination of the effect of SDS-PEO solutions on the acid-catalyzed hydrolyses of p-MPD and BTBA were started by addition of 0.005 mL of stock solutions M in acetonitrile) into 2.5 mL of 0.02 M succinate buffer. Conductivity measurements were carried out, at 25.00 and 50.00 "C, in a water-jacketed flow dilution cell with an Analion conductivity meter Model C-701. Conductivity data were stored in a microcomputer using a Microquimica 12 bits AID board. The slopes of the conductivity vs surfactant concentration plots between the experimental break points (Figure 2) were calculated using a standard linear regression routine. The binding constant of p-MPD to SDS (Ksm = 52) was measured by HPLC, following a described procedure.z9
zt 0
3
40
80
0
Id[SDS] ,M
Results and Discussion Kinetics in Aqueous Solutions. For the acid-catalyzed hydrolysis of acetals such as p-MPD, the accepted mechanism involves fast pre-equilibrium protonation of the acetal followed by unimolecular rate-determining decomposition of the protonated intermediate.26 Indeed, for p-MPD, the overall secondorder rate constant for the acid-catalyzed reaction (k24 has been calculated from the slopes of linear plots (not shown) of the observed first-order rate constant (kobs)vs [H30+], giving values of 11.6 and 194 M-' s-' at 25.0 and 50.0 "C, re~pectively.~*** Benzaldehyde di-tert-butyl acetal (BTBA) shows both specific and general acid catalysis.27 A value for the second-order rate constant for the general acid catalysis HA) of the monoanionic form of succinic acid of 0.20 M-' s-l for the hydrolysis of BTBA was obtained from the slopes of the plots (not shown) of the fiist-order rate constant vs succinate buffer concentration, at different pHs (p = 0.50, maintained with KC1). The intercepts of the graphs described above were plotted vs [H30+] to estimate the second-order rate constant for the specific acid catalysis, kZw = 2000 M-' s-'. The slight disagreement between the values in this work and those in the literaturez7 (kHA = 0.237 M-' s-l and k2w = 2950 M-' s-1)27 can be attributed to differences in ionic strength, because Fife et al. reported values at ,u = 1.O. Additionally, Fife et al. used a pKa2 = 5.26, which is different from those reported by others30 and the one used in this work (pKal = 4.21 and pKa2 = 5.69 at 25 "C). Kinetics in Aqueous SDS Micelles. Figure 1A,B shows plots of kobs against [SDS] for BTBA and p-MPD at pH 6.00
B
0
Figure 1. Plot of observed first-order rate constants against [SDS] in the absence of poly(ethy1ene oxide) (PEO) for acid hydrolysis reactions of (A) BTBA in 0.020 M succinate buffer, pH 6.00, at 25.00 "C and (B) p-MPD in 0.010 M acetate buffer, pH 4.50, at 25.00 "C.
and 4.50, respectively. The shapes of the rate-surfactant concentration profiles for both substrates are similar to those of many other bimolecular reactions described in the literature. To estimate the second-order rate constant in the micellar phase, kzm,from the dependence of the observed firstorder rate constant on the [SDS] and hydrogen ion concentration in the aqueous phase [H+Iw, we used eq lderived from the 1,396,7*28
pseudophase ion-exchange (PPIE) model,2 where Cd is the stoichiometric concentration of surfactant forming micelles, related to the total concentration of surfactant ( C T ) by Cd = CT - cmc; V, is the effective volume per mole of micellized detergent, 0.25 r n L / m ~ l K,, ~ ~ ;represents the binding constant of thep-MPD; K m 8 is the ion-exchange constant; the subscripts m and w denote micellar and aqueous phases, respectively; and the brackets indicate stoichiometric molar concentrations. The contribution of the general acid catalysis in the micellar phase on the hydrolysis of BTBA was not considered in the fitting of the data because buffer catalysis at the pH and buffer
Ketal Hydrolysis in Aqueous Solutions
J. Phys. Chem., Vol. 98, No. 47, I994 12363
TABLE 1: Parameters Used To Fit the Experimental Results for p-MPD and BTBA Hydrolyses in the Absence of Poly(ethy1ene oxide) (PEO), pH 4.50 and 5.20, at 0.010 M Acetate and 0.020 M Succinate Buffers, Respectively, at 25.00 "C
/I
t
substrate parameters
p-MPD
BTBA
k2wrM-l S-'
11.6" 0.0055 52 32
2000 0.0025 60 1727
cmc, M
Ksm, M-' kzmrM-' a
S-'
From ref 7.
concentrations used is small, when compared to that of hydronium ion (see above). In addition, only a very small fraction of succinic acid will be micellar bound. Succinic acid is hydrophilic, and at pH 5.20 at least 90% is present in the mono- and dianionic form (see pK values above), and the anionic micellar aggregates should repel hydrophilic anionic species from their surfaces. Reported values of a = 0.253 and K m a = 132were used in all cases, and the best fits (represented by solid lines in Figure 1A,B) were obtained by minimizing the weighted standard deviations. Table 1 shows the parameters used to make the fits. A modest rate enhancement, with k2,lk2,,, 3, is observed for p-MPD, but BTBA shows slightly lower reactivity in the micellar pseudophase than in bulk water. In previous results for p-MPD, a similar enhancement was found when the surfactant was sodium monodecyl phosphate.28 The cmc values for SDS were determined at the buffer concentrations used in the kinetic experiments, the lower values observed being consistent with well-documented salt effects.25 The similarity between the K,, values of p-MPD and BTBA (Table 1) are not surprising. The shapes of the rate-surfactant concentration profiles in Figure 1, parts A and B, are similar. For bimolecular reactions, the shapes of the k,b,-[surfactant] profiles depend on the binding constant Conductivity Measurements of SDS-PEO Solutions. Figure 2 shows conductivity against [SDS] plots at 0.010,0.035, and 0.105 M PEO. These conductivity measurements show that when SDS is added to PEO solutions, a cooperative absorption starts at the first break, denoted here by critical aggregation concentration (cac), which is lower than the critical micellar concentration (cmc) of the surfactant. Micelle-like aggregates begin to form on the polymer above the first conductivity break. Dubin et al. l9 demonstrated from diffusion coefficient and electrophoretic mobility data that PEO-SDS complexes behave like polyelectrolytes, due to the charge density developed on the polymer surface. The polymer saturation point (psp), Le. the second change in slope, is attributed to saturation of the polymer by surfactant molecules. At the psp free micelles start to appear, which coexist with PEO-SDS complexes. It is important to remark that the linearity between cac and psp values is strong evidence that, in the cac-psp range, basically only a single type of aggregate is d e ~ e l o p i n g .The ~ ~ change in slope at the psp indicates that SDS micelles and PEO-SDS complexes have different aggregation numbers and degrees of ionizaTable 2 lists cac and psp values at various [PEO] in 0.020 M succinate buffer, pH 5.20. The results show that psp but not cac values between 0.0022 and 0.105 M PEO are sensitive to polymer concentration. The conductivity data was used to estimate the degree of ionization (a) from the ratios of the slopes of specific conductance above and below the critical aggregation concentration (cac) for PEO-SDS complexes, denoted by al, and below the cac and above the polymer saturation point (psp) for
C 0
3
9
6
IO'[SDS]
1
2
1
5
.M
Figure 2. Specific conductances vs [SDS] at 0.020 M succinate buffer, pH 5.20, in the presence of (A) 0.105 M, (B) 0.035 M, and (C) 0.010 M poly(ethy1ene oxide) (PEO), at 25.00 "C.
TABLE 2: Values of Critical Aggregation Concentration (cac) and Polymer Saturation Point (psp) as a Function of Poly(ethy1ene oxide) (PEO) Concentration at 25.00 "C and at Succinate Buffer, 0.020 M, pH 5.20 103[PE0]
103cac
103psp
103[PEO]
103cac
103psp
105.0 66.0 62.0
2.36 2.58 2.19 2.35 2.15 2.56
38.40 25.35 23.50 15.70 12.50 14.70
28.2 10.0 6.7 5.2 2.2 0.0
2.20 2.20 2.06 2.32 2.32 3.30
11.10 7.20 6.81 7.00
49.0 34.4 35.0
4.00
SDS micelles, a2. The relation between conductance and [SDS] is based on the Evans treatment,34eq 2:
1ooos, = N - m ( 1o0os1- I,)
+ NF - Am
,
nPl3
where S1 and S2 are the slopes of the plots of specific conductance against [SDS] below and above the cac for estimating a for SDS-PEO complexes or below cac and above psp for SDS regular micelles; Ax is the equivalent conductance of the counterion Na+ (A, = 50.11 at 25.00 0C35);and N and m are the aggregation number and number of bound counterions of SDS micelles or PEO-SDS complexes, respectively. Equation 2 is based on the assumption that the aggregate radius is directly proportional to the aggregation number. This assumption works reasonably well for aqueous spherical micelles, and similar assumptions have been made for aqueous micellar solutions of SDS containing butanol, in which aggregates are smaller than in regular SDS micelles.36 The linearity of the cac-psp conductivity plots (Figure 2) is excellent evidence for the formation of PEO-SDS aggregates with a constant al value. Equation 2 is solved for m by using values of N of 65 for SDS micelles3 and 35 iz 5 for PEO-SDS complexes.24 Using these m values and the relation (mlN) = 1 - a, values of a 2 = 0.27 for SDS micelles and a1 = 0.41 & 0.01 for PEO-SDS
Ruzza et al.
12364 .I Phys. . Chem., Vol. 98, No. 47, 1994
/ I
I
0 01 0
100
50
1
150
I03[SDS], M Figure 3. Effect of [SDS] on the observed first-order rate constants (k&) for acid-catalyzed hydrolysis of p-MPD in the presence of 0.105 M poly(ethy1ene oxide) (PEO), in 0.020 M succinate buffer, pH 5.00, and at 25.00 “C.
IO3 [SDS], M Figure 5. Effect of [SDS] on the observed fust-order rate constants (kobs) for acid-catalyzed hydrolysis of p-MPD in the presence of 0.010 M poly(ethy1ene oxide) (PEO), in 0.020 M succinate buffer, pH 5.20, and at 50.00 “C. Inset shows data at low [SDS]. Solid lines are theoretical. Dashed lines are predicted by eq 1, using the same parameters given in Table 3.
SCHEME 2
0.6 I
1
I03[SDS] , M Figure 4. Plot of observed first-order rate constants for the acidcatalyzed hydrolysis of BTBA in aqueous solutions of SDS in the presence of 0.105 M poly(ethy1eneoxide) (PEO), in 0.020 M succinate buffer, pH 5.20, and at 25.00 “C.
complexes were obtained. We note that the a2 value obtained by this method agrees with literature Kinetics in SDS Micelle Solutions in the Presence of PEO. Figures 3 and 4 show the effect of SDS concentration on the observed first-order rate constant (kobs) for p-MPD and BTBA acid hydrolyses, respectively, in the presence of 0.105 M PEO. Despite the difference in reactivity of the substrates (see above), the shapes of the rate constant-surfactant concentration profiles are practically identical. In both cases the rate constants increase toward a plateau at high [SDS], and the most striking feature is that the profiles show a distinct discontinuity at the polymer saturation point (psp). The increase of kobs above the psp shows that micelles formed above this [SDS] are more effective catalysts than PEO-SDS complexes. This conclusion agrees with the results shown in the inset in Figure 5; that is, in the [SDS] range between the cac and the psp (see Table 2 ) , the PEO-SDS complexes show only a slight catalytic effect on the p-MPD hydrolysis. However, above the psp, free SDS micelles increase kobs sharply. These results can be partially explained by the different degrees of ionization estimated in this work, Le., a = 0.25 and 0.41 for SDS micelles and PEO-
SDS complexes, respectively. An increase in the degree of coverage of the charged interface (which corresponds to a lower a value) by counterions Na+ and H30+ results in enhanced catalysis. Another factor contributing to the observed effects is the differential reactivity of the substrate in the different pseudophases (see below). Kinetic Model. The theoretical treatment of the kinetic data for the acid hydrolyses of p-MPD and BTBA in the presence of PEO-SDS complexes is based on the pseudophase ionexchange (PPIE) formalism applied to micro emulsion^,^ but modified to account for known physical properties of polymersurfactant complexes. l-l9 Acid hydrolyses of substrates (S) are bimolecular reactions,26 and the reactants (p-MPD or BTBA and H+) are assumed to be distributed between the aqueous, micellar, and PEO-SDS complex pseudophases (Scheme 2 ) . The observed rate is given by
where kzp is the second-order rate constant in the PEO-SDS complex phase, the subscript p refers to the PEO-SDS complex pseudophase, the [H+] terms are defined as “local” concentrations in each pseudophase, and the other terms are defined
J. Phys. Chem., Vol. 98, No. 47, 1994 12365
Ketal Hydrolysis in Aqueous Solutions above. The mass balance for the total concentration of substrate S is given by kobs
[SI = [SI,
+ [SI, + [SI,
+ Cd,
Ksm = S,
where Cd, and Cd, are defined as the concentrations of surfactant in micelles and bound to polymer, respectively, and Cd, and Cd, are given by Cd, = C, - psp
(7)
Cd, = C, - cac
(8)
Note that eq 8 applies only if CT 5 psp. At surfactant concentrations greater than psp, Cd, is assumed to be constant and equal to psp - cac. The distribution of the substrate between the micellar and PEO-SDS complex phases is governed by a partition coefficient (K,), defined by the ratio Ksm/Ksp. (9) Expressions for the concentrations of S in each pseudophase are obtained by combining eqs 4 and 9 with the Ksm and Ksp expressions derived from eqs 5 and 6 (eqs 10-12):
['Iw = 1 + Cd,K,,
[SI
+ l/Ks,Cd, + K,Cd,/Cd,
(12)
The analytical concentration of Hf is related to the "local" within the molar concentration of the ionic reactant (I?) micellar and PEO-SDS complex pseudophases by the following equations:2
-+ -
W+I,
+
[H Ip - (CpVp Cd,V,) where Vp is the effective volume per mole of polymer and C, is the molar concentration of polymer. The term Cd,Vm, eq 13, denotes the fractional volume of free micelle^,^ while CdpVm CpV,, eq 14, corresponds to the overall fractional volume of the PEO-SDS complex. Substituting eqs 10- 14 into eq 3 gives an expression for the observed rate constant as a function of PEO and SDS concentrations:
+
+
+ CddK,Cd,)
t
k2,[H+IW [H+l + (CpVp+ C%V,)( 1 +k,, l/K,,Cd, + K,(C&/Cd,)) p
(15)
The PPIE theoretical framework2 is used to estimate [H+] in the micellar and PEO-SDS complex pseudophases; that is, the H+ and Na+ distributions are governed by ion-exchange. In the range of surfactant concentrations between cac and psp, the ion-exchange constant (Kma) is based on the equilibrium
+ Na',
H+,
= h" H',
+ Na',
and
where the sodium ion concentrations in the aqueous phase, [Na+Iw,and in the PEO-SDS complex pseudophase, [Na+],, are given by [Na'],
= alCd,
+ cac + [Nil+], +
[Na'],
= (1 - al)Cd, - [H'],
-k [H'],
(18) (19)
and [ N a + l ~is the molar concentration of sodium coming from the buffer. Equations 18 and 19 can be simplified by recognizing that alCd, and (1 - al)Cd, are much greater numerically than [H+],, under our experimental conditions. Finally, substituting the simplified forms of eqs 18 and 19 into eq 17 and assuming that K m a = 1 for both SDS micelles32 and SDS-PEO complexes, one obtains an expression for [H+],:
+ Cd,K,,
[SI
=1
1
(4)
The equilibrium distribution of the substrate between the aqueous, micellar, and PEO-SDS complex pseudophases is given by eqs 5 and 6:
S,
= Cd,V,(
~Z,[H+I, l/K,,Cd,
The same approach can be used to obtain an expression for [H+], from eq 17 and by using assumptions similar to those used for [H+],:
Kinetic Treatments in the Presence of PEO. The solid lines in Figures 3-5 were obtained by fitting the kinetic data using eq 15 and the parameters given in Table 3. The best fits were obtained by setting the partition coefficient Kp equal to unity (see eq 9) for both substrates. This suggests that the organic substrates are statistically distributed between the micellar and PEO-SDS complex pseudophases and that the binding constant Ksmshould be similar to the binding constant to SDS micelles in the absence of PEO (Table 1). Bests fits were obtained with k2p lower than k2m (Table 3) and a = 0.25 and 0.41 for SDS micelles and PEO-SDS complexes, respectively. Thus, both the increase in the degree of coverage of the charged interface and rate constants in free micelles being higher than that in PEO-SDS complexes contribute to the experimental observation that micelles are better catalysts than PEO-SDS complexes. As noted earlier,
Ruzza et al.
12366 J. Phys. Chem., Vol. 98, No. 47, 1994 TABLE 3: Parameters Used To Fit the Kinetic Results for p-MPD and BTBA Hydrolyses in the Presence of PoMethslene oxide) (PEO)
parameters
BTBA 0.105 (Figure 4)
p-MPD 0.105 (Figure 3)
0.010 (Figure 5)
kzm,M-' S-' k2p. M-' S-' hw, M-' S-' cac, M PSP,M Ksm, M-'
2601 f 188 1365 i 143 2000 0.0012 0.038 60
38.0 & 2.8 16.1 f 0.9 11.6 0.0010 0.038 52
463 i 88 51.8 & 22.0 194
0.0005 0.007 25
the sharp increase in rate above the psp in the k,,b,-[SDS] profiles (Figures 3-5) indicates greater catalysis by SDS micelles than PEO-SDS complexes. The smaller Ks value for p-MPD at 50.0 "C (Table 3) can be attributed to an increase in solubility of p-MPD in the aqueous phase. A similar result was found, at the same temperature, for the acid hydrolysis of p-MPD in aqueous solution of SDS in the absence of PE0.37 Best fits were obtained using the psp values measured by conductivity (Table 2 ) and cac values (Table 3) slightly smaller than those determined conductometrically . The latter observation is not unexpected since pseudophase treatments sometimes fail5 near the critical micellar concentration due to the formation of premicelles, or substrate-induced micellization, and probably indicates that kinetically significant aggregates form below the cac. Additionally, premicellar aggregates induce rate enhancements of the acid-catalyzed hydrolysis of 2-(nanoxyphenyl)-l,3-dioxolane.37 The validity of the proposed treatment is supported by the quality of the kinetic fits of the shapes of the profiles (Figures 3-3, obtained by using parameters determined in the presence (Table 3) and absence (Table 1) of PEO and by quality of the fits obtained over a wide range of experimental conditions (temperature, substrate, and pH). As would be expected, since it was not formulated to treat kinetic data in the presence of polymers, the original PPIE model does not fit the data (as an example see dashed line in Figure 5 ) , and although a fit could be obtained by using a "kinetic" cmc for the data in Figure 5, the discontinuities observed in Figures 3 and 4 could be neither treated or rationalized with this model. The advantage of the proposed theoretical framework is that it predicts and explains (on the basis of different rate constants and a values) the discontinuity in the rate constant-surfactant concentration profiles, which occurs approximately at the psp (Figures 3-5). We conclude that eq 15 extends the capabilities of the PPIE model and successfully simulates rate constant-surfactant concentration profiles in the presence of nonionic polymers, such as PEO.
Acknowledgment, We are grateful to CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnol6gico, Brazil), FINEP, and PADCT for the financial support of this work. References and Notes (1) Fendler, J. H.; Fendler, E. J. Catalysis in Micellar and Macromolecular System; Academic Press: New York, 1975. (2) Quina, F. H.; Chaimovich, H. J. Phys. Chem. 1979, 83, 1844. (3) (a) Romsted, L. S. Ph.D. Thesis, Indiana University, 1975. (b) Romsted, L. S. In Surfactants in Solution: Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1015. (4) Berezin, I. V.; Martinek, K.; Yatsimirski, A. K. Russ. Chem. Rev. (Engl. Transl.) 1973, 42, 487. (5) Bunton. C. A,: Nome. F.: Ouina. F. H.: Romsted. L. S. Acc. Chem. Res.'l991, 24, 357. (6) Zanette. D.: Chaimovich. H. J . Phvs. Ora. Chem. 1992, 5, 341 (7) Ricardo, D. R. P.; Zanette, D.; Nome, F. j . Phys. Chem. 1990, 94, 356. (8) El Seoud, 0. A.; Chinelatto, A. M. J . Colloid Interface Sci. 1983, 95, 163. (9) Chaimovich, H.; Bonilha, J. B. S.; Zanette, D.; Cuccovia, I. M. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; p 1121. (10) Goddard, E. D. Colloids Surf. 1986, 19, 225. (1 1) Arai, H.; Horin, S . J . Colloid Interface Sci. 1969, 30, 373. (12) Jones, M. N. J. Colloid Interface Sci. 1967, 23, 36. (13) Schwager, M. J. J . Colloid Interface Sci. 1973, 43, 491. (14) Fishman, M. L.; Eirich, F. R. J . Phys. Chem. 1975, 75, 2740. (15) Fadnavis, N. W.; van der Berg, H. J.; Engberts, J. B. N. F. J. Org. Chem. 1985, 50, 48. (16) Cabane, B. J. Phys. Chem. 1977, 81, 1639. (17) Chari, K. J. Colloid Interface Sci. 1992, 151, 294. (18) Dubin, P. L.; Gruber, J. H.; Xia, J.; Zhang, H. J . Colloid Interface Sci. 1992, 148, 35. (19) Xia, J.; Dubin, P. L.; Kim, Y. J . Phys. Chem. 1992, 96, 6805. (20) Santos, S. de F.; Nome, F.; Zanette, D.; Reed, W. F. J . Colloid Interface Sci. 1994, 164, 260. (21) Zana, R.; Lianos, P.; Lang, J. J. Phys. Chem. 1985, 89, 41. (22) Maltesh, C.; Somasundaran, P. Langmuir 1992, 8, 1926. (23) Maltesh, C.; Somasundaran, P. J. Colloid Interface Sci. 1993,157, 14. (24) Lissi, E. A,; Abuin, E. J. Colloid Interface Sci. 1985, 105, 1. (25) Mukejee, P.; Mysels, K. Critical Micelle Concentrations of Aqueous Surfactant Systems; National Bureau of Standards: Washington, DC, 1971. (26) Fife, T. H.; Jao, L. K. J . Org. Chem. 1965, 30, 1492. (27) Anderson, F.; Fife, T. H. J. Am. Chem. SOC. 1971, 93, 1701. (28) Ruzza, A. A.; Walter, M. R. K.; Nome, F.; Zanette, D. J. Phys. Chem. 1992, 96, 1463. (29) Armstrong, D. W.; Nome, F. Anal. Chem. 1981, 53, 1682. (30) Kortum, G.; Vogel, W.; Andrussow, K. Dissociation Constants of Organic Acids in Aqueous Solution; Butterworths: London, 1961. (31) (a) Shinoda, K.; Soda, T. J . Phys. Chem. 1963, 67, 2072. (b) Mukerjee, P. J . Phys. Chem. 1962, 66, 1733. (32) Bunton, C. A.; Ohmenzetter, K.; Sepulveda, L. J . Phys. Chem. 1977, 81, 2000. (33) Witte, F. M.; Engberts, J. B. F. N. J . Org. Chem. 1987,52, 4767. (34) Evans, H. C. J. Chem. Sac. 1956, 579. (35) Owen, B. B. Physical Chemistry ofElectrolytic Solutions; Reinhold Publishing Corp.: New York, 1958. (36) Rubio, D. A. R.; Zanette, D.; Nome, F.; Bunton, C. A. Langmuir 1994, 10, 1151. (37) Ruzza, A. A. M. Sc. Dissertation, Universidade Federal de Santa Catarina, 1992.
.
