Microphase-enhanced Reactions: Simultaneous Effects of Ion

Ind. Eng. Chem. Res. 1999, 38, 4571-4578

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Microphase-enhanced Reactions: Simultaneous Effects of Ion Coupling and Counterion Binding Abul Hasnat† and Sandip Roy* Department of Chemical Engineering, Indian Institute of Technology, Powai, Mumbai-400 076, India

Microphase-induced enhancement of the rate of mass transfer of the reactive species in instantaneous heterogeneous reactions is described by the generalized film theory under quasisteady-state conditions. The diffusive transport of ions which incorporates the ion-coupling phenomenon is represented by the Nernst-Planck equation. The molecular transport is described by the Fickian diffusion. In contrast to the previous investigations, a substantial increase in the relative enhancement factors (about 2 to 6 times) in the two phase reactions (between N,Ndiethyl aniline and HCl in the presence of anionic surfactant sodium lauryl sulfate, and between 2,5-dimethyl phenol and NaOH in the presence of cationic surfactant cetyltrimethylammonium bromide) is observed experimentally. This increase in the rate of mass transfer of the reactive species is shown to be caused by the augmentation of the diffusion coefficients of the reactive species owing to the ion-coupling effect. Also, counterion binding of the reactive species on the micellar charged surface is analyzed within the framework of the ion-exchange equilibrium model. The solution of the resulting ion-exchange expressions in conjunction with mass-transfer model predicts the reduction in enhancement factors by 5-15%. Introduction It is now well understood that the surfactant micelles comprising cationic, anionic, zwitterionic, or nonionic headgroups play an important role in chemical reaction catalysis. Extensive studies on micellar catalysis for slow, medium, and fast reactions have been reported.1-5 The effects are varied, ranging from inhibition to activation of the reactions. Interpretations of these kinetic results are based primarily on the view that the actual reactions occur in the micellar pseudophase. Both the hydrophobic and electrostatic interactions between the substrate and the micelle induce the localization of substrate concentration in the vicinity of the reaction sites. The effect of micellar microphase on very fast or instantaneous heterogeneous reactions, however, has been less well investigated, even though such reactions have considerable industrial and theoretical interest. Using film theory, Janakiraman and Sharma6 have concluded that the micelles are not likely to have any marked effect on the specific rate of mass transfer for such reactions. Janakiraman and Sharma’s conclusion was based on the reasoning that the micellar holdup in the film is negligibly small. Once the dissolved reactant in the micellar pseudophase is used up in the diffusion film, no further enhancement of the reaction rate is possible. More recently, using penetration theory, Mehra7 has also arrived at similar conclusions. Experimental observations in our previous work,8 however, contradict the above-mentioned conclusions. It was observed that simple inert electrolytes as well as cetyltrimethylammonium bromide (CTAB) (as the microphase) micelle exhibit a marked influence on the mass transfer of H+ ions in the instantaneous hetero† Present address: Corporate Technical Services, Reliance Industries Limited, 4-A, Shanti Nagar Industrial Estate, Santacruz(East), Mumbai-400 055, India. Email: Abul [email protected]. * Correspondence concerning this article should be addressed to Sandip Roy. Phone: 022-5767249. Fax: 0225796895. E-mail: [email protected].

geneous reaction between N,N-diethyl aniline (organic phase) and HCl (aqueous phase). This reaction essentially takes place at a reaction plane that is located close to the actual physical interface. The relative enhancement factor showed a moderate increase of 30% in the presence of simple salts to a remarkable 600%, increase in the presence of CTAB surfactant. These observations were explained on the basis of the generalized film theory. The ion-coupling phenomenon was assumed to control the diffusion of ionic species in the film. H+ ion diffuses from the bulk aqueous phase toward the reaction plane and reacts with the N,Ndiethyl aniline (DEA) molecule, which simultaneously diffuses from the physical interface to the reaction plane. The reaction product DEAH+ ion, being ionic in nature, counterdiffuses (with respect to H+ ion diffusion) toward the bulk aqueous phase. The movements of these ions are governed by the electrical potential generated due to the local deviation from the electroneutrality caused by the unequal mobilities of various ionic species present in the system. The nonreactive species such as micelle (carrying an RN amount of charge on its surface) and Cl- ion do not actually diffuse. However, these ions may enhance the fluxes of reactive species by modifying the concentration gradients of the latter primarily through maintaining the local electroneutrality. This analysis of the experimental observations did clarify some important aspects of ion diffusion process. The observed rate enhancement was attributed to a large increase in the ion diffusion coefficients of reactive species rather than to the conventional micellar catalysis. That the micelles behave as inert polyelectrolytes and not as a catalyst in such cases is supported by the fact that simple inert electrolytes also enhance the mass-transfer rates. It was observed further that the ion diffusion coefficients tend to approach the free diffusion coefficients at high surfactant concentrations, and the concentration profiles of ions in the film exhibit a strong nonlinearity. Fundamental principles of the film theory were used to represent an otherwise complicated diffusion-controlled mass-transfer problem in

10.1021/ie9902380 CCC: $18.00 © 1999 American Chemical Society Published on Web 10/29/1999

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a simple way. This mechanism was quite effective in providing a quantitative agreement between theory and experimentally observed trends. The previous work,8 however, did not consider the possible effect of distribution of two or more counterions between the micellar charged surface and the aqueous phase. The reasons cited were as follows. The competitive binding affinity of the counterion Br- for cationic CTAB micelle is much higher than that of the counterion Cl-; hence, no significant ion exchange is expected. Moreover, because both Br- and Cl- ions are nonreactive and have identical mobility, any minor exchange would have little or no influence on the effective masstransfer rates of the reactive species. However, if the reactive ions do participate in competitive binding on the micellar charged surface, the concentration of reactive species in the aqueous phase would significantly decline, which in turn would alter the mass-transfer rate of reactive species. Two approaches to ion binding on micellar pseudophase have generally been adopted in the literature. One uses an electrostatic model with partition coefficient (P) of the substrate of the type: P ) P0 exp(-ψ0e/kT), where P0 accounts for the potential barrier that the substrate must overcome to dissolve in the micellar pseudophase and ψ0 is the micellar surface potential. This surface potential, specifically and nonspecifically distributed ions in and around the Stern layer, may be obtained through the numerical solution of the nonlinear Poisson-Boltzmann equation.9,10 The other approach uses an ion-exchange equilibrium model which assumes that an ion-exchange equilibrium exists between the aqueous phase and the micellar pseudophase.11-13 The present work attempts to exploit the dual behavior of micellar electrolytes on the instantaneous heterogeneous reactions, as an ion-binding agent and as a supporting electrolyte. Two such reaction systems are studied to rationalize the model predictions and to ascertain the extent to which the counterion binding on micellar surface can affect the enhancement factor. The first reaction system involves the protonation of amine by hydrochloric acid according to the following scheme

N, N - diethyl aniline (DEA)

DEA hydrochloride salt

The anionic surfactant, sodium lauryl sulfate (SLS), was used as the microphase in the reaction above. The second reactive system consists of the neutralization of 2,5-dimethylphenol with sodium hydroxide.

2,5-dimethyl phenol (DMP)

that is located in the aqueous phase. The coupled diffusion of ionic species is represented by the NernstPlanck equation. Simultaneous diffusion of ions of unequal mobilities in aqueous solution has been investigated by many workers.14-19 It has been established that the ion-coupling phenomenon has a profound effect on the ion diffusion coefficients and that the magnitude of the effects of unequal diffusivities on the enhancement factor is appreciable. For such systems, the penetration and surface renewal theories have offered improvements over the film theory model. However, the enhancement factor predicted by the film theory model does not differ by more than 3-5% from that predicted by the penetration theory.20 According to Chang and Rochelle,21 the deficiency of the film theory can be removed partially if the diffusion coefficient of each species is corrected by a square root ratio of the species diffusion coefficients to the species on which the masstransfer coefficient is based. Applying the correction factor makes the film theory solution quantitatively identical to the surface renewal theory result. Use of the quasi-steady-state assumption for the film theory, which also takes into account the effect of the progressive movement of the reaction plane within the boundaries of the film, further reduces this discrepancy. In the present study, to elucidate the role of preferential counterion binding on the micellar pseudophase on the rate of mass-transfer of the reactive species, the equilibrium ion-exchange model is used to derive the expressions for ion distributions between the micellar and the aqueous phases. However, ion-exchange effects are considered only for the DEA-HCl-SLS system. Ionexchange effect for the DMP-NaOH-CTAB system is ignored here based on the following reported observations. Rodenas et al.10 studied the OH-/Br- exchange on CTAB micellar surface using both the electrostatic approach and the ion-exchange equilibrium approach. The regressed ion-exchange constant KOH/Br over a range of surfactant concentrations (1-8 mol m-3) averaged 70 at a NaOH solution concentration of 10 mol m-3. Also, the magnitude of specifically adsorbed amount of OHions in the Stern layer of micelle was much lower than the combined magnitude of specifically and nonspecifically adsorbed Br- ions. Further, Paredes et al.22 showed that the relative strength of the binding of anions to the CTAB micelle lies in the order of Br- > NO3- > Cl> OH-. In light of these findings, it is expected that the depletion of OH- ion concentration in the aqueous phase caused by ion exchange would have a negligible effect on the rate of mass transfer of reactive species in the film.

DMP sodium salt

The cationic surfactant CTAB was used as the microphase in the reaction above. Quasi-steady-state film theory is used to model the mass-transfer process occurring in the diffusion film

Experimental Section Measurement of Physicochemical Data. The solubilities of organic substrates (DEA and DMP) and the critical micelle concentrations (CMCs) of SLS and CTAB surfactants in the aqueous phase were determined following the procedures as outlined previously.8 The values of solubilities of DEA and DMP in 100 mol m-3 NaCl solution at 298 K were obtained as 35 and 1.28 mol m-3, respectively. The CMC values obtained by the surface tension measurements were 1.4 and 0.721 mol m-3 for SLS and CTAB surfactants, respectively. Measurement of Overall Reaction Rate. As indicated earlier, the anionic surfactant SLS and the cationic surfactant CTAB were used as the microphases. Toluene was used as a solvent to dissolve DMP. In the

Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4573

DEA-HCl system, N,N-diethyl aniline, which constituted the organic phase, was used in a pure form (i.e., without any solvent). All the chemicals used in the experiment were obtained from firms of repute. The experimental apparatus consisted of a glass reactor (internal diameter, 0.08 m) provided with a sample withdrawal facility. A 0.375 dm3 of aqueousphase solution was first transferred to the reactor. The liquid organic stream of 0.15 dm3 was then fed to the reactor from a reservoir tank through a specially designed perforated circular tube. The locations of perforated holes in the tube were perpendicular to the container wall. This arrangement ensured that the organic liquid drained through the perforated tube and spread rapidly, over the aqueous phase rapidly. The flow rate of the organic liquid was adjusted to prevent it from penetrating deep into the aqueous phase and undergoing any emulsification. To promote adequate mixing during the reaction, the reactor was provided with four equally spaced Teflon baffles. A crucifix-type stirrer was inserted into the aqueous phase to stir the solution. The stirrer speed was adjusted to 60 rpm to avoid the interfacial disturbance while keeping the diffusion film thickness small. The system temperature was maintained at 298 ( 1 K for all runs. Because consumption of the organic molecules at the end of the experimental runs in the present system is very small compared with the total amount present initially, the assumption of constant concentration of the organic reactant at the interface during the reaction period holds true. Method of Analysis. UV Spectrophotometer was used to measure the salt content (DEAH+Cl- and DMPO-Na+) in the samples withdrawn from the reactor at regular intervals. UV calibration curves were used to obtain the salt concentration in each sample. The spectrophotometer was standardized with known concentrations of salts. Good reproducibility of the salt concentration measurement by UV absorption spectra was observed when the salt concentration in the solution was of the order of 1 mol m-3. In the present experiment, as the reaction progresses the salt content of the aqueous solution increases. In such cases, samples withdrawn were suitably diluted to reduce the concentration to about 1 mol m-3. Theory Ion-Exchange Model in the Micellar System. In an equilibrium state between the micellar pseudophase and the aqueous phase, H+, DEAH+ and Na+ ions will bind competitively on the charged sites on the micellar surface. The distribution of ions between the two phases is governed by the magnitude of the individual equilibrium constant. The following assumptions are implicit in developing the model: the ion-ion and ion-micelle interactions are independent of each other and the exchange constant, K, the degree of ionization of micellar surface, R, and the CMC are independent of the variation of surfactant concentrations. Here, H+, DEAH+, and Na+ are designated as B, A, and N, respectively. If the micellar phase is considered to be a distinct, but pseudo phase, Na+/H+ exchange may be represented by the following equation. KN/B

Bf + Nb {\} Bb + Nf with the equilibrium-exchange constant

(3)

KN/B )

BbNf BfNb

(4)

where subscripts b and f refer to bound and free counterions, respectively. Similarly, for Na+/DEAH+ exchange, the equilibrium exchange constant may be written as

KN/A )

AbNf AfNb

(5)

The following relation may be obtained from eqs 4 and 5

KA/B )

KN/B AfBb ) KN/A AbBf

(6)

The following material balances in the micellar and aqueous phases should hold true (the surfactant micelle is designated as M).

MT ) M + CMC

(7)

Nb ) (1 - R)M - Bb - Ab

(8)

Nf ) RM + CMC + Bb + Ab

(9)

Ab + Af + Bb + Bf ) Bi

(10)

where i represents the initial state in the bulk aqueous solution. The expression for Ab may be derived using eqs 6 and 10.

KA/BA2b - (Bi - Bb - Af)KA/BAb + BbAf ) 0 (11) Equation 4 may be resolved for Bb using eqs 8 through 10.

(KN/B - 1)B2b + [(2KN/B - 1)Ab - {(1 - R)M + Bi Af}KN/B - RM - CMC]Bb + {(1 - R)M(Bi - Ab Af) + (Af - Bi)Ab}KN/B + KN/BA2b ) 0 (12) The nonlinear algebraic eqs 11 and 12 can be solved simultaneously to yield the bound concentrations of reactive species on the micellar surface. Mass-Transfer Model: Film Theory. Mass transfer of the reactive species is assumed to occur within the diffusion film of thickness δ located near the physical interface in the aqueous phase (Figure 1). Mass transfer from the organic phase (at x ) 0) occurs by molecular diffusion. Simultaneously, the reactant ions (H+ or OH-) from the bulk aqueous phase (at x ) δ) diffuse toward the interface. The reaction takes place at a reaction plane (at a distance λ from the interface). The concentrations of both H+ (or OH-) and the organic molecule are reduced to zero at reaction plane. The ionic reaction products (see eqs 1 and 2) counterdiffuse toward the bulk aqueous phase under sharp concentration gradients. The nonionic diffusion process is assumed to obey Fick’s law. Ionic diffusion is subject to the influence of ion coupling and is represented by the Nernst-Planck equation. Resistance to the mass transfer in the organic phase is expected to be negligible and therefore is ignored in the present study.

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JS|x)λ ) -JB|x)λ

(20)

where JS is the molecular diffusive flux in the region 0 < x < λ, the expression for which has been provided previously.8 After substituting the expressions for the respective fluxes, the equation above simplifies to

DB

Figure 1. Film theory representation of instantaneous heterogeneous reaction.

The flux of any ion i in the region λ < x < δ as represented by the Nernst-Planck equation is given by

di u dψ + Zii Ji ) -Di dx RT dx

[

]

(13)

(14)

No current condition for the reactive ions may be given by

JA + JB ) 0

(15)

Because the nonreactive microphase or inert ions are not diffusing, their fluxes are set equal to zero, i.e.,

ZiJi ) 0

(16)

The actual flux expression, JB, for the reactive species B and the ordinary differential equations representing the concentration profiles of all the inert ions may be developed by algebraic manipulation of eqs 13-16. Quasi-steady state is assumed to exist in the diffusion film. Thus for the concentration profile of ion B one may write

dJB )0 dx

(17)

The set of coupled ordinary differential equations (eq 17 for the reactive ion B and equations for other ions derived through eqs 13-16) constitutes the boundary value problem (BVP). The boundary conditions available to solve the BVP are

at x ) λ at x ) δ

B)0

{

B ) B0 i ) i0

(18)

}

(19)

where the subscript 0 stands for the bulk aqueous phase. The term i0, which designates the bulk-phase concentrations of the nonreactive species, requires further considerations. Because the nonreactive ions are always conserved, i0 may be taken as the initial concentrations of the components. This assumption does not affect the final solution to the BVP in any significant way. The location of the reaction plane is governed by the fact that at x ) λ, the flux of H+ (or OH-) ion must be balanced by the flux of the organic molecule (designated as S).

(21)

where DS and S* represent the diffusivity and the interfacial concentration for the organic molecule, respectively. To evaluate the bulk concentration of ion B in the aqueous phase, the following material balance is used

dB0 ) aJB|x)λ dt

-V

The electroneutrality in this region is defined by

∑i Zii ) 0

DSS* dB |x)λ ) dx λ

(22)

where V and a are the aqueous phase solution volume and the interfacial area, respectively. The integration of the equation above is carried out with the initial condition

B0 ) Bi

at t ) 0

(23)

The expression for the relative enhancement factor quantifying the effect of the presence of a charged microphase on the rates of the reactive species is defined as the ratio of the flux of reactive ion in the presence of a microphase to that without. Its magnitude is calculated from the results of the numerical solution of the model equations at t ) 0.

φ)

JB

) W

JB

λW λ

(24)

The derivation of the theoretical expressions of the diffusion equations for each of the two reaction systems, following the procedure discussed above, is relatively straightforward. Numerical Treatment. Equation 21 implies that the position of the reaction plane varies with time which essentially renders the system a moving BVP. The solution of a nonlinear moving BVP is usually complex. However, several approximate solution techniques have been proposed.23 For the present problem, the front fixing method was the most suitable solution. Using this methodology, the moving boundary in λ is fixed by the following transformation of the coordinate in the xdirection

η)

x-δ λ-δ

(25)

Using this transformation, the first- and second-order derivatives appearing in ordinary differential equations in the film, the flux balance equation, and the continuity equation in the bulk aqueous phase now are replaced by the derivatives in the new space coordinate (η). The time and space derivatives are then discretized by the finite difference method. The implicit CrankNicholson scheme was used. The differential equations by this procedure are converted into a set of nonlinear algebraic equations. These equations are then solved using the subroutine CONLES24 at each value of ∆t. The subroutine CONLES is particularly useful for this case because it deals with physically constrained variables.

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Figure 2. Variation of H+ ion concentration in bulk aqueous phase with time.

Figure 3. Variation of OH- ion concentration in bulk aqueous phase with time. OHI ) 22 mol m-3.

The algorithm does not allow the physical restrictions to be violated. For example, the solution avoids negative amounts of chemicals or concentrations. The accuracy of solution was checked by varying the grid size, ∆x, and ∆t. A final value of 0.01 was obtained at for both ∆x and ∆t for satisfactory accuracy and stability of the solution. Finally, the model parameters (DA, DB, and δ) are regressed through the minimization of the standard deviation between the experimental data and the simulated values using the Simplex method25 for unconstrained optimization. The unweighted least-squares method was used to calculate the standard deviation. Numerical Parameters. The molecular diffusivities of DEA and DMP molecules were estimated as 5.43 × 10-10 and 6.49 × 10-10 m2 s-1, respectively.26 Solubilities of DEA and DMP in 100 mol m-3 NaCl solution were determined experimentally as 35 and 1.28 mol m-3, respectively. Salting out effects on solubilities due to the ionic strength of solution used, however, are not taken into account. The concentrations of DMP and DEA at the liquid-liquid interface are taken to be their respective solubilities. Further, it is assumed that these concentrations at the interface are invariant with time. The micellar surface charges were calculated from the relation Z ) RN, where R is the degree of ionization and N is the micellar aggregation number. The values of R and N obtained are 0.22 and 62 for the CTAB micelle27 and 0.2 and 67 for the SLS micelle.28 As stated earlier, the equilibrium constant, KNa/H, for Na+/H+ exchange on SLS micellar pseudophase was taken as 1.2,9 whereas for the exchange constant, KNa/DEAH of Na+/DEAH+ exchange, an approximate value of 6 was assumed on the basis of values of similar compounds reported by Bonilha et al.29 The diffusivities of protonated amines, DMPO- and + H ions along with the film thickness are the parameters that are regressed by matching predictions with experimental data. Because δ depends primarily on the hydrodynamic conditions of the system, it is expected to remain constant for all the experimental runs.

Table 1. Comparison of Experimental and Computed Enhancement Factors

Results and Discussions The experimental results on the rate of mass transfer for instantaneous heterogeneous reaction between N,Ndiethyl aniline and HCl in the presence of microphase SLS are shown in Figure 2. Similar data on the neutralization reaction between 2,5-dimethyl phenol and NaOH in the presence of CTAB are displayed in Figure 3. The model predictions are also plotted in the same figures and are represented by solid lines. The

microphase concentration, mol m-3

φmodel

b φmodel

1.895 2.111 2.970 3.27 3.94 4.43 5.23 6.12

1.987 2.286 3.253

CTABa

System: DEA + HCl 6.30 1.905 10.6 2.036 17.4 2.937 2.91 2.91 5.20 4.08 8.00 4.67 10.0 5.39 13.0 6.28

CTAB

System: DMP + NaOH 3.3 3.428 5.9 5.079 13.7 6.111

3.541 5.210 6.302

microphase SLS

a

φexp

Data from ref 8.

close agreement between the simulated and experimental values of the bulk aqueous phase concentration suggests that the diffusion mechanism assumed for the present mass-transfer systems is fairly accurate. The enhancement factor obtained from experimental data and from model predictions (φmodel) are compared in Table 1. The experimental enhancement factors (φexp) were extracted from the ratio of slope (at t ) 0) of the curve of H+ (or OH-) vs t in the presence of a microphase to that of the slope (at t ) 0) in the absence of the microphase. Because manual slope estimations are prone to inaccuracies, it was decided to fit each measured concentration vs t profiles with a polynomial function. The local slopes were then calculated by differentiating the polynomial. In Table 1, the enhancement factors for DEA-HCl systems in the presence of CTAB micelle from the previous work8 are also included for comparison. Inspection of the Table 1 reveals that the CTAB microphase enhances the rate of mass transfer of the H+ ion much more than the SLS microphase. At the same surfactant concentration level, the enhancement factor in the presence of CTAB is about 50% higher than that in the presence of SLS. This difference in the enhancement factor is observed, although both the micellar species contain approximately the same amount of surface charge. Two plausible explanations may be offered for this observation. First, consider the binding of the H+ ion on the micellar surface. Such binding is expected to reduce the amount of free H+ ion available in the bulk aqueous phase. This would lower the local concentration gradient of H+ ion in the diffusion film and hence reduce the overall rate of H+ ion transfer to

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Table 2. Ion Diffusion Coefficients and Film Thickness

microphase none SLSa SLSb CTABc

none CTAB DEA + HCl (SLS) DEA + HCl (CTAB) DMP + NaOH (CTAB) a

microphase concentration, mol m-3 6.30 10.6 17.4 6.30 10.6 17.4 2.91 5.20 8.00 10.0 13.0

DB/DW B

DA/DW A

δ, µm

σ, × 102

1.00 1.30 6.51 7.78 2.42 7.13 8.56 3.56 4.18 4.67 4.76 5.51

65.4 65.1 64.9 65.7 66.1 63.9 65.0 56.1 57.8 54.4 56.6 57.2

3.31 3.78 4.12 5.88 1.63 0.99 2.44 1.39 3.0 0.884 1.06 0.977

66.4 64.1 64.6 63.9

1.93 6.21 8.22 7.10

System: DEA + HCl 1.00 1.09 1.19 1.42 1.15 1.21 1.56 2.83 3.58 3.83 4.03 4.57

System: DMP + NaOH 1.00 1.00 3.3 2.10 1.41 5.9 3.51 3.52 13.7 4.49 4.70 -10 m2 s-1, DW ) 2.78 × 10-9 m2 s-1 DW A ) 1.15 × 10 B -10 m2 s-1, DW ) 1.80 × 10-9 m2 s-1 DW A ) 0.986 × 10 B W -10 -10 m2 s-1 m2 s-1, DW DA ) 4.25 × 10 B ) 6.79 × 10

Counterion binding not considered. b Counterion binding considered. c Data from ref 8.

the reaction plane. Table 1 also enlists the enhancement b ) for DEA-HCl-SLS system calculated on factors (φmodel the basis of the assumption of no counterion binding b on the micellar surface. Comparing φexp with φmodel from Table 1 indicates that the ion-exchange process has reduced the enhancement factor by about 5-10% in the concentration range studied. This effect clearly demonstrates that the ion exchange in the system is partly a contributory factor in explaining the apparent difference. The second factor is the ability of the CTAB micelles to decouple the diffusion of the H+ ion from that of the other ions, thus causing substantial enhancement of the flux of H+ ion. The ion-decoupling effect brought about by SLS micelles, however, is lower than that caused by CTAB micelles. This is distinctly evident from the regressed diffusion coefficients of the H+ ion presented in Table 2. It can be seen that there is a considerable increase of ion diffusion coefficients for H+ and DEAH+ ions in the presence of microphases over those in their absence. With increasing surfactant concentration, the decoupling of the diffusion of H+ and DEAH+ increases, resulting in higher mass-transfer rates. At sufficiently high surfactant concentrations, the ion-diffusion coefficients tend to approach the respective free diffusion coefficients. However, the extent of decoupling of the diffusion of H+ ion from that of the other ions brought about by anionic micelle SLS is considerably weaker than that effected by the cationic micelle CTAB. The ratio of DB/DW B in the presence of CTAB to that in the presence of SLS at the same surfactant concentration is approximately equal to the difference of their corresponding enhancement factors. However, the increase in the diffusivity of reaction product (DEAH+) is of a higher order of magnitude in the presence of the SLS micelle. This implies that the instantaneous accumulation of ion (DEAH+) at the reaction plane due to reaction is electrically balanced by otherwise slow-moving anionic SLS micelle, whereas in the zone λ < x < δ, the H+ ion charge is electrically balanced by the Cl- ion. Consequently, the SLS micelle develops a concentration gradient in a direction opposite to that of the H+ ion

Figure 4. Movement of reaction plane with time and typical concentration profiles of ions. SLS ) 17.4 mol m-3; Hi ) 100 mol m-3.

which impedes the motion of the H+ ion. However, the concentration gradient of the CTAB micelle has the same sign as that of the H+ ion, an effect that augments the mobility of the H+ ion. The regression estimates of δ and values of standard deviations of the experimental data from the model fit are listed in Table 2. The average value of δ from Table 2 is 65.0 µm with a maximum deviation of 2%. Because a constant stirrer speed was maintained in all the experiments, the value of δ is expected to be the same for all the runs. Table 2 confirms this point. Movement of the Reaction Plane (λ-Plane). Figure 4 depicts the shift in the location of the reaction plane with time. This figure is a schematic representation of the actual simulated results. This was done primarily to depict the manner in which the concentration profiles undergo a change with the shifting of the λ-plane. The cross-coupling of ion movement in the film is evident from the figure. As evident from Figure 4, the reaction plane is located very close to the actual physical interface during the initial phases of the experimental run. As the solution concentration of reactive species in the bulk aqueous phase is depleted, the λ-plane gradually travels toward the other boundary of the film at x ) δ. When the solution concentration is reduced to very small values

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Figure 5. Predicted bound concentration of H+ ion on SLS micellar surface.

(