QUANTITATIVE ANALYSIS OF MICELLAR EFFECT ON THE REACTION RATE OF ALKALINE FADING OF PHENOLPHTHALEIN

Quantitative treatment of the kinetic data of the reaction between phenolphthalein dianion and hydroxide ion in aqueous solutions containing variable concentration of various surfactants is presented. Following surfactants are used: Brij-35 (nonionic), sodium n -dodecyl sulfate (anionic), cetyltrimethylammonium bromide (cationic) and 3-(dimethyl-n -dodecylammonio)-propansulfonate (zwitterionic). The quantitative treat-ment is carried out basing of Piszkiewicz’s, Berezin’s, and Pseudophase Ion-Exchange (PIE) models. It is revealed that the Berezin’s model is a more applicable one for describing the effect of nonionic, anionic, and zwitterionic micellar systems. The values of the corresponding kinetic parameters are discussed. The effect of cetyltrimethylammonium hydroxide on the reaction is also examined and quantitatively described by the PIE model. The research of systems based on a cationic surfactant shows previously unknown effect called by us as “diverting influence”.


Introduction
This paper is a continuation of our previous studies [1][2][3] and is devoted to the quantitative treatment of the experimental data of the rate constants of the reaction between phenolphthalein, PP 2-, and hydroxide ion in solutions of surfactants of various types: non-ionic (Brij-35), anionic (sodium n-dodecylsulfate, SDS), cationic (cetyltrimethylammonium bromide, CTAB and cetyltrimethylammonium hydroxide, CTAOH), and zwitterionic (3-(dimethyl-n-dodecylammonio)-propanesulfonate, DMDAPS).The reaction scheme is shown below: Here 1 k is the rate constant of the carbinol ROH 3-formation; 2 k is the rate constant of the reverse reaction.As a qualitative conclusion of the previous observations it can be stated that the addition of any surfactant, the rate of the direct reaction decreases [1][2][3].
It is important to gain insight into the mechanism of the above mentioned influence of the surfactants on the rate constant and to test the applicability of the models to similar systems.

Experimental part
Materials, preparation of solution and the experimental procedure were as described previously [1][2][3].The NaOH solution was carbonate-free.
Apparatus.Spectrophotometer Hitachi U-2000 UV-visible and photocolorimeter KFK-2M were used for kinetic measurements at 25 and 35 o C. The KFK-2M device was equipped with cuvette https://doi.org/10.26565/2220-637X-2018-30-02holder through which thermostated water was continuously circulated.Zetasizer Nano ZS Malvern was used for the study of the colloidal particles size via dynamic light scattering (DLS) at 25 o C.
Procedure of the rate constants determination.The rate constants of the reaction were determined spectrophotometrically under pseudo-first order conditions at 35 °C for SDS, CTAB, Brij-35, and DMDAPS systems, and at 25 °C for CTAOH.The hydrophobic PP was initially dissolved in 96 % aqueous ethanol, therefore in all working solutions the alcohol content was 1.2 vol %.In all systems under study, the PP and NaOH concentrations were 1.810 -5 and 0.041 M, respectively.Under these conditions the reaction between PP 2-and HO -is reversible.The neutral and monoanionic forms of phenolphthalein are practically absent at this concentration of the alkali, judging by the thermodynamic values of the indices of thermodynamic dissociation constants of PP at 25 o C, a1 pK = 8.97 and a2 pK = 9.73 [15].The second-order rate constants, 1 k , were calculated by Eq. ( 1) [1][2][3]. Here is pseudo-first order rate constant; K is the equilibrium constant given by (2).
Here 0 A , and А  are the absorbance at time zero, and equilibrium, respectively.The values of the sum 1 2 k k   were obtained as the slopes of the dependences of ln( ) Here t А is the absorbance at time t.In water, the following values were obtained: 1 k = 2.2510 -2 M -1 s -1 , 2 k = 6.5010 -4 s -1 , K = 34.6 (ionic strength I = 0.041 M, 1.2 vol % ethanol, at 35 o C).Using the above K value and the thermodynamic value of the ionic product of water at 35 o C, 2.08910 -14 [18], and calculating the activity coefficients by the Debye-Huckel equation (second approach), a thermodynamic value of a3 pK = 12.37 for the reaction R 2-= ROH 3-+ H + may be estimated.A value a3 pK = 11.73 was determined spectrophotometrically under equilibrium conditions at I = 0.2 M (KCl), at 25 o C, using the pH values in the activity scale [15].Re-calculation to the thermodynamic value by estimating the activity coefficients via the Davies equation leads to a3 pK = 12.42.

Results and Discussion
Figure 1 shows the dependences of rate constants of the interaction of PP 2-with hydroxide ion on concentrations of surfactants: Brij-35, CTAB, DMDAPS and SDS, taken from previous papers [1][2][3]; some experimental data in the micellar region were added within the course of the present study.
Observed rate constants indicate that an increase in surfactants concentration leads to a decreasing in the rate constant reaching a plateau, where the further addition of the surfactant practically does not influence the rate constant.The ratio of the rate constants corresponding to plateau and water (k plateau /k w ) equals 0.81, 0.57, 0.075, and 0.74 for SDS, CTAB, DMDAPS, and Brij-35, respectively.The surfactants show influence from concentrations: 8×10 -5 , 3×10 -3 , 1×10 -5 , 8×10 -5 M for CTAB, DMDAPS, Brij-35, and SDS, respectively.
As shown in our previous paper, the hydrophobic poorly water-soluble phenolphthalein is to high extend bound in molecular form by surfactant micelles [2].Under such conditions, the reaction will proceed in both phases according to Scheme 1.  5), solid line (for c(surfactants) > kinetic CMC) is drawn using results of calculations according to Eq. ( 9) with  = +59 mV (see below).
For a complete interpretation of the micellar effect, it is necessary to determine the reaction rate constants in the micellar pseudophase and to evaluate the binding of the reagents to the micelles.Berezin's, Piszkiewicz's, and Pseudophase Ion-Exchange models were used for this purpose.

Application of the Piszkiewicz's model
Piszkiewicz proposed a simple model for describing the effect of micellar surfactant on the rate constant, based on the idea of a so-called catalytic micelle [11][12][13].The advantage of this model is that it is capable of describing the effect of premicellar region surfactant.According to this model, the second-order rate constant at low surfactant concentrations is given by Eq. ( 4).
[ ] [ ] Here k w is the reaction rate constant in the absence of surfactant; n is a number of surfactant molecules, which aggregate to form a catalytic micelle; K D is the dissociation constant of this micelle back to its free components; k m is the reaction rate constant in the catalytic micelle.
Parameters of Piszkiewicz's model obtained by fitting the experimental data via Eq.( 4) are presented in Table 1.Such treatment of experimental points is characterized by high values of the determination coefficients (r 2 ).However, the standard errors exceed K D value, which indicates a statistical insignificance of the influence of this parameter on the reaction rate.The calculated k m values are lower than the corresponding k w value.
The obtained non-integer values of the n parameter reflect the usual result when using Eq. ( 4).According to Piszkiewicz [11][12][13], the non-integer values imply multiple equilibria in the formation of a catalytic micelle.This raises doubts about the validity of the formalism used in the derivation of the equation.

Application of the Berezin's model
The general equation of Berezin's theory for a bimolecular reaction is normally simplified, with respect to the values of partition coefficient of the reagents between water phase and micellar pseudophase, P [12].The partition coefficient of the dye, 2 PP  P , should be much higher than unity due to the (probable) hydrophobic interaction.The value of the partition coefficient of hydroxide ion, HO P  , may be estimated by Eq. ( 5) [6,12].
Here HO P  is the partition coefficient of hydroxide ion; F is the Faraday constant;  stands for the difference between the electrical potentials of the phases; T is the absolute temperature; and R is the gas constant.
Values of HO P  , calculated using the literature  values, are presented in Table 2.According to these HO P  values, for SDS, DMDAPS, and Brij-35, Eq. ( 6) is applicable.
For CTAB system, HO P  >1, therefore: Here obs k is the observed second-order rate constant; m k and w k are the corresponding constant in the micellar pseudophase and in surfactant-free system, respectively; V is the molar volume of the surfactant, which equals to 1.064 M -1 for Brij-35 [17], 0.314 M -1 for DMDAPS [18], 0.364 M -1 for CTAB [19], and 0.246 M -1 for SDS [17]; [ ] n D is the concentration of the micellized surfactant, which equals the total surfactant concentration from which CMC is subtracted;

K
and HO K  are the bind- ing constants of the reagents, expressed in framework of Berezin's model [14] in the following way This assumption is quite firmly entrenched by introducing the concept of "kinetic CMC" [20,21].Indeed, the DLS data give evidence for the presence of colloidal species in the solution of 1×10 -5 M PP and CTAB beginning from c = 2×10 -4 M of the surfactant (Figure 2).Accordingly, for SDS, the aggregates appear at 2×10 -3 M, as determined by the DLS method.Since the  values depend on the ionic strength of the aqueous phase and did not coincide as determined using different molecular probes, calculations using three HO P  values for CTAB solutions were carried out (Table 2) [22,23].The obtained values of r 2 show that for this system, a more appropriate value of  is +59 mV, in comparison with the values of +118 and +124 mV.

Application of the Pseudophase Ion-Exchange model by Bunton and Romsted
Among the surfactant systems considered, the PIE model is applicable only to the treatment of the influence of CTAB micelles.In terms of PIE model for such reactions, in the case of cationic micelles the counterions (Br -) compete with reactive hydroxide ions in the Stern layer [4,5], HO + Br HO + Br value is equal to 15, as determined in our recent paper [24], has been used in calculations.Equation ( 10) of the dependence of the observed pseudo-first order rate constant of bimolecular reaction on surfactant concentration is written in terms of the local concentration of micellar-bound HO -   Here 2 PP m K  is the constant of the binding of the dye anion by the micellar aggregate; V is the molar volume of Stern layer (V = 0.14 M -1 [25,26]).
The molar ratio Here β is the fraction of micellar surface charge that is neutralized by counterions (usually β is around 0.8 [4,27]).
The effect of CTAOH micelles was also investigated within the framework of the PIE model.It is of interest because this is a surfactant with reactive counterions.For such type of surfactant, the value of HO m  is equal to β.The dependence of the pseudo-first order rate constant of reaction between PP 2- and hydroxide ion on the concentration of CTAOH in the presence of 0.02 M NaOH is shown in Figure 3.The reaction practically does not proceed in this system without addition of sodium hydroxide.The increase in surfactant concentration leads to acceleration of the reaction reaching a plateau.Consequently, the dye binding by micelles shifts PP 2-to a medium with a higher concentration of HO - ions.The value of local concentration of micellar-bound HO -is estimated as β/V, i.e. ~5.7 M [5].Considering this value, it is not clear how to explain in the framework of PIE model that the reaction does not occur in the system without added NaOH and why an increase in the total HO -concentration causes the possibility of the reaction to proceed.Treatment by the PIE model is characterized by high values of the determination coefficient only for CTAOH system.Parameters of the PIE model obtained by fitting the data for CTAOH system by Eqs. ( 9) and ( 10) are presented in Table 3.The high values of k are lower, than the value of the rate constant in water.The observed acceleration in the CTAOH system according to the PIE model is a consequence of the excess of the contribution of the change in the HO -concentration, which increases 275-fold, over the change in the rate constant (decreased by 60-fold).The same result was obtained by Bunton et al. for the reaction of malachite green, MG + , with HO - [28], but the PIE model does not give a clear explanation of the reason for the change in the rate constant.As shown in our previous article, the factors influencing the value of the rate constant in cationic micelles are high ionic strength and low polarity.The sign and the magnitude of the salt effect and the polarity effect are determined by the signs of the charge of the reacting ions.Therefore, they are not suitable for explaining the decrease in the rate constants of both reactions: MG + and PP 2-with HO -.Table 3. Results of the fitting experimental data to Eqs. ( 10) and ( 11 Probably, the reason of the decrease in the rate constant of the second order reaction on going from the aqueous phase to the micelle is a difference between the reactivity of the hydroxide ion in the aqueous phase and the Stern layer.As a possible reason, we expect a "diverting" effect of cationic head groups: сounterions, including the reactive ones, are closely electrostatically associated with the head groups of micelle.An association constant of this process can allow determining the concentration of HO -ions capable of reacting with the dye.Added NaOH to CTAOH system leads to the com-pression of the diffuse part of the double electrical layer around the CTAOH micelle and thus the increase in the local HO -concentration.This is a possible reason for the fact that the reaction with PP in the CTAOH system proceeds only on addition of 0.02 M NaOH.This effect, however, is not presumed in the common PIE model. The dependence of the pseudo-first order rate constants of reaction between PP 2-and HO -on the concentration of CTAB in the presence of 0.041 M NaOH was treated by Eqs. ( 10) and ( 11 K  .The obtained r 2 value is very low (r 2 = 0.2), that shows the discrepancy between the experimental points and theoretically calculated by Eqs.(10) and (11).

Summary
Comparison of Piszkiewicz's and Berezin's models has shown that in the general case the Berezin's model gives a more satisfactory treatment of the experimental data.The high values of partition coefficient of the dye indicate a strong binding of dye with different charge type micelles, which is consistent with the concept of hydrophobicity of phenolphthalein.The values obtained for m k are lower, than the value of the rate constant in surfactant-free system.This indicates that binding of the dye by micelles leads to a decrease in the observed rate constant due to the low value of m k .Taking into account the fact that molecules containing hydrophilic and hydrophobic groups are located in the surface layer of the micelle, the decrease in the rate constant upon the transfer of reagents from water to the micellar pseudophase is a consequence of a decrease in the polarity of the microenvironment of the reagents accompanying it, according to the Hughes-Ingold rule.

Scheme 1 .Figure 1 .
Scheme 1. Proceeding of the reaction in the presence of micelles.
of derivation of the relation between K and P leads to K = PV.The value of surfactant concentration at which the change in the rate constant begins was used as the CMC value, for calculate [ ] n D values.

Figure 2 .
Figure 2. Size distribution by number, volume, and intensity in CTAB + PP solution; concentrations 2×10 -4 and 1×10 -5 M, respectively, 0.041 M NaOH.Parameters of Berezin's model obtained by fitting the data by Eqs.(6) and (7) are presented in Table 2. Treatment of experimental points by Eqs.(6, 7) is characterized by high values of the determination coefficients and satisfactory values of standard errors.


are the HO -concentrations in aqueous phase and micellar phase, respectively; are the Br -concentrations in aqueous phase and micellar phase, respectively;[HO ]

Figure 3 .
Figure 3. Dependence of the pseudofirst order rate constants of reaction between PP 2-and HO -on the CTAOH concentration at 25 0 C, 0.02 M NaOH.Solid line is drawn using values calculated according to Eq. (10).

K
 indicate a strong binding of the dye by CTAOH micelles.The values obtained for m