Influence of mixed CTABr–C₁₆E₂₀ nanoparticles on relative counterion binding constants in aqueous solutions of inert salts (2-NaOC₆H₄CO₂Na and NaBr): kinetic and rheometric study

Abstract

A semi-empirical kinetic technique has been used to obtain the ratios of pure CTABr (cationic nanoparticle) and mixed CTABr–C₁₆E₂₀ (cationic–nonionic nanoparticle) micellar binding constants of counterions X and Br, K_X/K_Br (=K^Br_X or R^Br_X) for X = salicylate ion. The values of K^Br_X or R^Br_X for the salicylate ion remain typically independent of the concentration of pure micelles, [CTABr]_T (0.006–0.015 M). These values are also independent of mixed [CTABr]_T–[C₁₆E₂₀]_T micelles under similar conditions. The presence of C₁₆E₂₀ decreases the average values of K^Br_X or R^Br_X from 42 to 16 for salicylate ions. Increase in concentration of cationic and cationic–nonionic nanoparticles at a fixed amount of CTABr reveals the monotonic increase in the value of k_obs, which was explained using the PPM model together with an empirical equation. Rheological characteristics of 0.015 M CTABr solutions in the presence of disodium salicylate indirectly show the presence of branched elongated nanoparticles at 25 °C and 35 °C and [C₁₆E₂₀]_T = 0. Contrarily, such findings reveal the existence of spherical micelles at 25 °C and 35 °C in the presence of ≥0.006 M [C₁₆E₂₀]. The values of K^Br_X or R^Br_X and rheological observations clearly demonstrate that 0.015 M CTABr/M₂X/H₂O (M₂X = disodium salicylate, 2-NaOC₆H₄CO₂Na) solutions contain wormlike and spherical micelles when K^Br_X or R^Br_X values are ≈42 and 16, respectively.

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1. Introduction

Micellar substances are nanoparticles in nature and their molecular, physical and chemical behaviors on the kinetic rates of reactions have been thoroughly investigated for almost sixty years.¹ Despite the fact that experimental and theoretical studies on the structure of mixed micelles have been published for the past 20 to 30 years, details of the reactions have not been well discussed when compared to pure micelles. Studies on the kinetic rates of reactions and the influence of mixed micelles began less than 25 years ago.^2,3 Efforts were made to come up with highlights on the majority of the data using one of the two following models: (i) micellar models of pure surfactant solutions^4,5 or (ii) the combination of (i) and empirical equations.^6,7

Addition of nonionic micelles (C_nE_m) to cationic micellar-mediated reaction mixture lowers a number of counterions at the surfaces of ionic surfactants, and hence reduces the fraction of ionic surfactant coverage (β).^8,9 Moreover, the volume of the micellar pseudophase also increases,¹⁰ which in turn affects the amount of micellized reactant via dilution. The pseudophase micellar model (PMM), coupled with eqn (1), has been used to analyze the data.¹¹

K_S = K⁰_S/(1 + K_X/S[MX]_T) (1)

where K_S is the CTABr micellar binding constant of the anionic reactant S⁻ (and is equal to K_S in the absence of X⁻) and K_X/S is an empirical constant whose value indicates the tendency of X⁻ to alter the micellar affinity of S⁻ from pure CTABr micelles to an aqueous CTABr micellar phase. Therefore, K_X/S should be directly and inversely proportional to K_S and K⁰_S, respectively.¹²

Several efforts have been made to bring reliable clarification(s) to the viscoelastic nature of the micellar systems in the aqueous phase, but almost all the clarifications are insufficient for some systems, such as those of CTABr with certain inert salts.¹³ Moreover, there is a scarcity of quantitative and theoretical evidence(s) to confirm that the addition of these salts in a surfactant solution results in viscoelastic behavior of micelles.

The present study varies from previously published ones^12,14 due to the fact that it is designed with aims as follows: (a) to deal with mixed cationic–nonionic surfactants (CTABr–C₁₆E₂₀) and a bimolecular reaction aimed at providing a quantitative elucidation on how the rate of CTABr–C₁₆E₂₀ micellar-catalyzed organic reactions could be affected by the addition of sodium salicylate, and (b) to use rheological information to ascertain if near-irreversible micellar entrapment of sodium salicylate could be due to the change in the structure of mixed cationic–nonionic surfactants (CTABr–C₁₆E₂₀) from spherical to rod-like micelles under different experimental conditions. The results obtained and their likely elaborations are presented in this manuscript.

2. Experimental

2.1 Materials

Reagent-grade substances, which are commercially available, included the following: phenyl salicylate (PSH), hexadecyltrimethyl ammonium bromide (CTABr), polyethylene glycol hexadecyl ether [C₁₆H₃₃(OCH₂CH₂)₂₀OH·(C₁₆E₂₀)], piperidine (Pip), sodium bromide (NaBr, MX) and sodium salicylate (2-HOC₆H₄CO₂Na, M₂X). The standard solutions of 0.5 M disodium salicylate (2-NaOC₆H₄CO₂Na) were prepared by adding 0.55 M NaOH to a 0.5 M solution of sodium salicylate. Stock solutions of 1.0 M Pip and 0.01 M PSH were prepared using distilled deionized water and acetonitrile, respectively.

2.2 Kinetic method

Spectrophotometric measurements have been carried out to observe the disappearance of ionized phenyl salicylate PS⁻ in a solution containing 0.1 M Pip, >0.03 M NaOH, and NaBr as well as 2-NaOC₆H₄CO₂Na, at 370 nm and 35 °C (in the presence of pure CTABr and mixed CTABr–C₁₆E₂₀ micelles). The rate was monitored at different concentrations of MX and M₂X (MX = NaBr and M₂X = 2-NaC₆H₄CO₂Na) using a UV-visible spectrophotometer. The details and the outcome of the kinetic experiment were described elsewhere.¹⁵

The pseudo first order rate law was maintained throughout by making sure that the ratio of [Pip]_T : [PS⁻]_T was 500 : 1 where [ ]_T stands for the total concentration. Eqn (2) shows the relationship between the absorbance (A_ob) and the reaction time (t) for the reaction.

A_ob = [R₀]δ_appexp(−k_obst) + A_∞ (2)

where [R₀] stands for the initial concentration of PS⁻ (2 × 10⁻⁴ M). This equation was used to calculate δ_app (apparent molar absorptivity), k_obs (pseudo first order rate constant) and A_∞ (=A_ob at t = ∞) by the use of the nonlinear least-squares method. Analyses of the results are described elsewhere.¹⁵

2.3 Determination of ^mK^Br_X or ^mR^Br_X for X (=–OC₆H₄CO₂Na) using the semi-empirical kinetics technique

To determine ^mK^Br_X or ^mR^Br_X, for the reaction kinetics of this study, the semi-empirical kinetics (SEK) method is used, which has been explained elsewhere.¹⁶ Kinetic parameters Kⁿ_X/S for the counterions in question being X⁻ and Br⁻ (test and reference counterions), were determined using the SEK technique at a constant pure [CTABr]_T and temperature. The values of k_obs for the piperidinolysis of PS⁻ were obtained in the presence of pure [CTABr]_T and mixed [CTABr]_T–[C₁₆E₂₀]_T micelles at different concentrations of MX and M₂X (MX = NaBr and M₂X = 2-NaOC₆H₄CO₂Na). Different values of k_obs at various [MX], in the absence of CTABr, are required to use the SEK technique. Details of this technique and explanations of the reaction mechanisms are described in earlier reports.¹⁷

2.4 Rheological measurements

In these measurements, the total volume of the sample used, for kinetic measurements was doubled (i.e. 10 mL). Two different sets of desired samples were prepared: (i) constant volume of >0.03 M NaOH, 0.1 M Pip, 2 × 10⁻⁴ M PSH and 0.015 M CTABr at various [M₂X] (within the range of 0.006 to 0.120 M); (ii) >0.03 M NaOH, 0.1 M Pip, 2 × 10⁻⁴ M PSH and [CTABr]_T–[C₁₆E₂₀]_T (with [CTABr]_T = 0.015 M and [C₁₆E₂₀]_T = 0.006 M) at various [M₂X] (within the range of 0.006 to 0.120 M). The rheological measurements were conducted at 25 °C and 35 °C using an Anton Paar MCR301 rheometer, with a double gap cylinder (DG26.7/T200/SS having 26.661 mm external diameter and 24.656 mm internal diameter). The values of steady-shear viscosity (η), during the flow curve measurement, were obtained within the range of 0.010–1000 s⁻¹ of shear rates. The details of the rheometric measurements were described in the previous study.¹⁸

3. Results

3.1 Effect of mixed CTABr–C₁₆E₂₀ on k_obs for the piperidinolysis of PS⁻ at various [NaBr] and 35 °C

Several kinetic runs were conducted to study the effects of mixed CTABr–C₁₆E₂₀ on k_obs for the reaction of 0.10 M Pip, with 2 × 10⁻⁴ M PSH, in the presence of NaBr (within the concentration range from 0.00–0.700 M) and 0.030 M NaOH. These data were used to obtain parameters required to find the value of K^Br_X or R^Br_X. The experiments were carried out by adding three different [CTABr]_T (=0.006, 0.010 and 0.015 M) at 0.006 M C₁₆E₂₀, 35 °C and 370 nm. Similar observations were obtained by increasing [C₁₆E₂₀] to 0.010 M and 0.015 M. The values of k_obs, are presented in Tables 1–3.

Table 1 Pseudo first order rate constants (k_obs) for the reaction of piperidine with anionic phenyl salicylate (PS⁻) at 0.006 M [CTABr]_T in the presence of 0.006, 0.010, and 0.015 M [C₁₆E₂₀]_T and different [MX] (=NaBr)^a

[MX]^b, M	[CTABr]T^c = 0.006 M		0.006 M		0.006 M
	[C16E20]T^d = 0.006 M		0.010 M		0.015 M
	10^4kobs, s^−1	10^4kcalcd, s^−1	10^4kobs, s^−1	10^4kcalcd, s^−1	10^4kobs, s^−1	10^4kcalcd, s^−1
a [PSH]0 = 0.2 mM, [Pip] = 0.1 M, [NaOH] = 0.03 M, λ = 370 nm and aqueous reaction mixture for each kinetic run contains 2% v/v acetonitrile.b Total concentration of NaBr.c Total concentration of CTABr.d Total concentration of C16E20.e Observed pseudo first order rate constant.f Calculated pseudo first order rate constant.g Error limits are standard deviations.
0.00	25.3^e ± 0.4		31.3 ± 0.5^g		30.1 ± 0.3
0.01	26.7 ± 0.7	25.0^f	39.3 ± 0.4	34.3	32.5 ± 0.3	32.5
0.03	33.0 ± 0.4	29.8	44.9 ± 0.4	39.7	38.1 ± 0.3	37.0
0.06	37.0 ± 0.4	36.1	51.6 ± 0.5	46.3	47.1 ± 0.5	42.9
0.10	40.0 ± 0.7	42.8	52.0 ± 0.4	53.2	48.2 ± 0.2	49.4
0.12	44.9 ± 0.6	45.7	54.9 ± 0.9	56.1	48.5 ± 0.7	52.3
0.15	48.9 ± 0.3	49.5	56.7 ± 0.4	59.9	54.2 ± 0.4	56.1
0.18	51.8 ± 0.5	52.9	61.1 ± 0.4	63.0	61.8 ± 0.4	59.5
0.20	54.8 ± 0.5	54.9	61.7 ± 0.5	64.9	62.2 ± 0.6	61.5
0.25	60.1 ± 0.8	59.2	64.2 ± 0.9	68.9	68.0 ± 0.4	66.0
0.30	65.3 ± 0.8	62.8	75.9 ± 0.6	72.2	69.9 ± 0.5	69.8
0.35	66.7 ± 0.8	65.8	77.5 ± 0.5	74.9	72.8 ± 0.8	73.0
0.40	67.8 ± 0.9	68.4	79.8 ± 1.0	77.1	73.0 ± 0.5	75.8
0.50	71.9 ± 0.7	72.5	81.9 ± 0.6	80.7	78.5 ± 1.0	80.4
0.60	76.1 ± 1.0	75.8	84.8 ± 0.9	83.4	89.1 ± 0.6	84.0
0.70	77.8 ± 1.0	78.3	82.5 ± 0.6	85.6	84.9 ± 0.7	86.9

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Table 2 Pseudo first order rate constants (k_obs) for the reaction of piperidine with anionic phenyl salicylate (PS⁻) at 0.010 M [CTABr]_T in the presence of 0.006, 0.010 and 0.015 M [C₁₆E₂₀]_T and different [MX] (=NaBr)^a

[MX]^b, M	[CTABr]T^c = 0.010 M		0.010 M		0.010 M
	[C16E20]T^d = 0.006 M		0.010 M		0.015 M
	10^4kobs, s^−1	10^4kcalcd, s^−1	10^4kobs, s^−1	10^4kcalcd, s^−1	10^4kobs, s^−1	10^4kcalcd, s^−1
a [PSH]0 = 0.2 mM, [Pip] = 0.1 M, [NaOH] = 0.03 M, λ = 370 nm and aqueous reaction mixture for each kinetic run contains 2% v/v acetonitrile.b Total concentration of NaBr.c Total concentration of CTABr.d Total concentration of C16E20.e Observed pseudo first order rate constant.f Calculated pseudo first order rate constant.g Error limits are standard deviations.
0.00	23.0^e ± 0.4		17.5 ± 0.4^g		28.7 ± 0.3
0.01	24.2 ± 0.4	24.0^f	18.1 ± 0.7	18.0	29.4 ± 0.2	29.0
0.03	26.3 ± 0.6	26.5	20.1 ± 0.3	20.4	30.8 ± 0.4	31.1
0.06	29.8 ± 0.5	29.8	22.8 ± 0.6	23.4	34.0 ± 0.4	34.0
0.10	33.4 ± 0.4	33.3	26.8 ± 0.4	26.6	26.8 ± 0.4	37.6
0.12	34.7 ± 0.5	34.9	28.4 ± 0.3	27.9	38.1 ± 0.3	39.2
0.15	36.5 ± 0.5	37.0	30.3 ± 0.5	29.7	38.8 ± 0.5	41.4
0.18	38.8 ± 0.5	38.8	30.9 ± 0.6	31.2	41.3 ± 0.4	43.4
0.20	39.9 ± 0.4	39.8	31.7 ± 0.3	32.1	44.6 ± 0.4	44.6
0.25	42.1 ± 0.5	42.2	33.6 ± 0.4	34.1	48.2 ± 0.3	47.5
0.30	44.6 ± 0.4	44.2	35.6 ± 0.6	35.7	49.5 ± 0.3	50.0
0.35	46.4 ± 0.5	45.8	37.3 ± 0.5	37.5	51.6 ± 0.5	52.2
0.40	47.0 ± 0.5	47.3	37.7 ± 0.4	38.2	54.4 ± 0.3	54.2
0.50	50.4 ± 0.5	49.6	40.4 ± 0.4	40.0	57.7 ± 0.4	57.6
0.60	50.8 ± 0.7	51.4	41.4 ± 0.4	41.4	59.5 ± 0.5	60.4
0.70	52.5 ± 0.6	52.9	43.3 ± 0.5	44.6	62.6 ± 0.2	62.8

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Table 3 Pseudo first order rate constants (k_obs) for the reaction of piperidine with anionic phenyl salicylate (PS⁻) at 0.015 M [CTABr]_T in the presence of 0.006, 0.010 and 0.015 M [C₁₆E₂₀]_T and different [MX] (=NaBr)^a

[MX]^b, M	[CTABr]T^c = 0.015 M		0.015 M		0.015 M
	[C16E20]T^d = 0.006 M		0.010 M		0.015 M
	10^4kobs, s^−1	10^4kcalcd, s^−1	10^4kobs, s^−1	10^4kcalcd, s^−1	10^4kobs, s^−1	10^4kcalcd, s^−1
a [PSH]0 = 0.2 mM, [Pip] = 0.1 M, [NaOH] = 0.03 M, λ = 370 nm and aqueous reaction mixture for each kinetic run contains 2% v/v acetonitrile.b Total concentration of NaBr.c Total concentration of CTABr.d Total concentration of C16E20.e Observed pseudo first order rate constant.f Calculated pseudo first order rate constant.g Error limits are standard deviations.
0.00	21.8^e ± 0.3		17.9 ± 0.4^g		23.22 ± 0.4
0.01	22.4 ± 0.4	22.0^f	18.4 ± 0.5	18.0	24.18 ± 0.4	23.0
0.03	23.9 ± 0.4	23.9	20.1 ± 0.5	19.4	24.69 ± 0.4	24.8
0.06	26.1 ± 0.3	26.2	20.8 ± 0.6	21.4	27.32 ± 0.4	27.1
0.10	28.8 ± 0.4	28.7	23.8 ± 0.5	23.6	29.30 ± 0.3	29.7
0.12	30.3 ± 0.2	29.7	24.9 ± 0.5	24.6	29.94 ± 0.3	30.9
0.15	30.9 ± 0.3	31.1	26.3 ± 0.6	26.0	32.37 ± 0.3	32.5
0.18	31.8 ± 0.3	32.3	26.8 ± 0.7	27.3	33.82 ± 0.3	33.9
0.20	33.1 ± 0.6	33.0	28.2 ± 0.4	28.1	34.55 ± 0.2	34.7
0.25	34.2 ± 0.6	34.5	29.1 ± 0.5	29.9	37.04 ± 0.2	36.7
0.30	35.7 ± 0.8	35.8	30.5 ± 0.5	31.4	39.14 ± 0.3	38.3
0.35	37.3 ± 0.6	36.8	33.2 ± 0.4	32.8	39.92 ± 0.3	39.7
0.40	38.5 ± 0.6	37.7	34.1 ± 0.2	34.0	40.71 ± 0.4	40.9
0.50	38.9 ± 0.7	39.1	35.8 ± 0.3	36.1	42.56 ± 0.5	43.0
0.60	39.5 ± 0.8	40.2	37.9 ± 0.6	37.7	44.61 ± 0.3	44.6
0.70	40.7 ± 0.8	41.0	38.8 ± 0.5	39.1	44.54 ± 0.3	45.9

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3.2 Effect of [2-NaOC₆H₄CO₂Na] on k_obs for the piperidinolysis of PS⁻ at constant concentration of CTABr and 35 °C

Several kinetic experiments were conducted at 0.006 M [CTABr], 0.1 M Pip, 2 × 10⁻⁴ M PSH, >0.03 M NaOH and various [2-NaOC₆H₄CO₂Na] (0.00–0.14 M). Complementary results were found by increasing the concentration of CTABr to 0.010 M and 0.015 M. The values of k_obs obtained within the [2-NaOC₆H₄CO₂Na] range are presented graphically in Fig. 1.

Fig. 1 Plot of k_obs against [2-NaOC₆H₄CO₂Na] for the piperidinolysis of PS⁻ at 35 °C in the presence of [CTABr]_T/M = 0.006 (●), 0.010 (♦) and 0.015 (▲). The broken curves are sketched via the calculated values of the rate constant (k_calcd). Inset: the plot at magnified scale for the data points at lower values of [M₂X].

3.3 Effect of mixed CTABr–C₁₆E₂₀ on k_obs for piperidinolysis of PS⁻ at various [2-NaOC₆H₄CO₂Na] and 35 °C

In order to study the influence of mixed CTABr–C₁₆E₂₀ micelles ([CTABr]_T = 0.006, 0.010 and 0.015 M + 0.006 M [C₁₆E₂₀]) on the reaction between Pip, PS⁻ and NaOH, different kinetic experiments were conducted in the presence of [2-NaOC₆H₄CO₂Na] (0.00–0.15 M). Similar results were obtained by increasing [C₁₆E₂₀]_T to 0.010 M and 0.015 M. The values of k_obs, are outlined and presented in Fig. 2–4, respectively.

Fig. 2 Plot of k_obs against [2-NaOC₆H₄CO₂Na] for the piperidinolysis of PS⁻ at [CTABr]_T + [C₁₆E₂₀]_T/M = 0.006 + 0.006 (●), 0.006 + 0.010 (♦) and 0.006 + 0.015 (▲) and 35 °C. Broken curves represent the calculated values of the rate constant (k_calcd). Inset: the enlarged plot for the concentrations of M₂X at lower values.

Fig. 3 Plot of k_obs against [2-NaOC₆H₄CO₂Na] for the piperidinolysis of PS⁻ at [CTABr]_T + [C₁₆E₂₀]_T/M = 0.010 + 0.006 (●), 0.010 + 0.010 (♦) and 0.010 + 0.015 (▲) and 35 °C. The broken curves are sketched via the calculated values of the rate constant (k_calcd). Inset: the enlarged plot for the concentrations of M₂X at lower values.

Fig. 4 Plot of k_obs against [2-NaOC₆H₄CO₂Na] for the piperidinolysis of PS⁻ at [CTABr]_T + [C₁₆E₂₀]_T/M = 0.015 + 0.006 (●), 0.015 + 0.010 (♦) and 0.015 + 0.015 (▲) and 35 °C. The broken curves are sketched via the calculated values of the rate constant (k_calcd). Inset: the enlarged plot for the concentrations of M₂X at lower values.

3.4 Rheological behavior of aqueous pure CTABr and mixed CTABr–C₁₆E₂₀ micelles in the presence of various [2-NaOC₆H₄CO₂Na] at 25 and 35 °C

Rheological measurements of solutions (in aqueous form) containing 0.015 M [CTABr]_T, constant 0.1 M Pip, 2 × 10⁻⁴ M PSH and >0.03 M NaOH at different values of [2-NaOC₆H₄CO₂Na] were conducted at the steady-shear rheological response at 25 °C and 35 °C. The values of shear viscosity (η) at various shear rates ([small gamma, Greek, dot above]) were determined at this condition. These results are presented, using log–log plots of η vs. [small gamma, Greek, dot above] at various [2-NaOC₆H₄CO₂Na], in Fig. 5a and b at 25 °C and 35 °C, respectively. Measurements on aqueous solutions containing mixed 0.015 M [CTABr]_T and 0.006 M [C₁₆E₂₀]_T with other conditions similar to those mentioned above were also conducted. The values of η at various [small gamma, Greek, dot above] were also determined. Different observations were obtained at the two different temperatures (25 °C and 35 °C) and the results are presented in Fig. 6a and b.

Fig. 5 Graphs of shear viscosity (η) against shear rates ([small gamma, Greek, dot above]) for the piperidinolysis of PS⁻ containing 0.015 M [CTABr]_T and [2-NaOC₆H₄CO₂Na]/M = (a) 0.006 (●), 0.008 (□), 0.012 (▲), 0.020 (♦), 0.040 (○), 0.08 (◊), and 0.120 (■) at 25 °C and (b) 0.006 (●), 0.008 (□), 0.012 (▲), 0.020 (♦), 0.040 (○), 0.08 (◊), and 0.120 (■) at 35 °C.

Fig. 6 Plots of shear viscosity (η) against shear rate ([small gamma, Greek, dot above]) for the piperidinolysis of PS⁻ containing 0.015 M [CTABr]_T, 0.006 M [C₁₆E₂₀]_T and [2-NaOC₆H₄CO₂Na]/M = (a) 0.006 (♦), 0.008 (○), 0.0120 (▲), 0.020 (●), 0.040 (□), and 0.120 (◊), at 25 °C and (b) 0.006 (♦), 0.008 (○), 0.0120 (▲), 0.020 (●), 0.040 (□), and 0.120 (◊) at 35 °C.

4. Discussion

4.1 Explanation of kinetic observations for the piperidinolysis of PS⁻ in the presence of pure CTABr and mixed CTABr–C₁₆E₂₀ micelles at various [MX] or [M₂X] and 35 °C

The pseudophase micellar model has been used to explain the values of k_obs for the nucleophilic reaction of Pip and PS⁻ in an alkaline medium at 35 °C.¹⁶ The values of k_obs obtained in the presence of a constant concentration of pure CTABr at various [M₂X] (where M₂X = NaOC₆H₄CO₂Na) were related by eqn (3)¹⁹
orwhere k₀ stands for k_obs in the absence of MX or M₂X with [MX]^op₀ or [M₂X]^op₀ ≈ 0, respectively, θ and K^X/S representing empirical constants whose values were calculated from eqn (3) using the nonlinear least-squares relationship by considering k₀ to have a known value. Different k₀ (=k_obs at [MX] or M₂X = 0) values were determined by conducting kinetic experiments at typical [CTABr]_T as well as [CTABr]_T + [C₁₆E₂₀]_T and their values are shown in Tables 1–3. The values of k_obs obtained in the presence of mixed CTABr–C₁₆E₂₀ micelles within the concentration range of 0.006–0.015 M [C₁₆E₂₀] surfactants were also found to fit to eqn (3). The values of fraction of micellized S ion moved from the CTABr micellar phase to the aqueous phase, through the occurrence of ion exchange S⁻/PS⁻, is denoted as F_X/S. The relationship between θ and −F_X/S is expressed in eqn (4).

θ = F_X/Sk^W_obs (4)

where k^W_obs = k_obs (=kⁿ_W[Pip]_T) at different [C₁₆E₂₀]_T (=0.006, 0.010 and 0.015 M) and [MX] = [M₂X] = [CTABr] = 0. The values of K^X/S, presented in Tables 4–6, at various concentrations of pure CTABr micelles as well as mixed CTABr–C₁₆E₂₀ micelles, were determined by the use of eqn (3).²⁰ The values of K_X/S, obtained for pure CTABr micelles (Table 5), were calculated from eqn (5) with the value of K⁰_S as 7000 M⁻¹ obtained from the literature.²⁰

K_X/S = K^X/S(1 + K⁰_S[CTABr]_T) (5)

Table 4 Values of empirical constants ^mθ, ^mF_X/S and ^mK^X/S calculated from eqn (3) and (4) for MX = NaBr at different concentrations of mixed CTABr–C₁₆E₂₀^a

[CTABr]T, M	[C16E20]T, M	10^4k0^d, s^−1	10^3mθ, s^−1	^mK^X/S, M^−1	^mFX/S	^nmK^X/S, M^−1
a [PSH]0 = 0.2 mM, [NaOH] = 0.03 M, [Pip] = 0.1 M, λ = 370 nm and aqueous reaction mixture for each kinetic run contains 2% v/v acetonitrile.b Total concentration of CTABr.c Total concentration of C16E20.d k0 = kobs at [MX] = 0.e Error limits are standard deviations.f ^mFX/S = ^mθ/^mk^Wobs; with ^mk^Wobs = kobs (=k^nW[Pip]T) = 240 × 10^−4, 193.2 × 10^−4 and 184.2 × 10^−4 s^−1 at constant [C16E20]T (0.006, 0.010 and 0.015 M [C16E20]T respectively) and [MX] = [CTABr]T = 0.g ^nmK^X/S = ^mFX/S^mK^X/S.
0.006^b	0.006^c	25.3 ± 0.4	10.1 ± 0.3^e	3.4 ± 0.3	0.4^f	1.4^g
0.006	0.010	31.3 ± 0.5	10.3 ± 0.9	4.4 ± 0.8	0.5	2.2
0.006	0.015	30.1 ± 0.3	11.4 ± 0.6	3.0 ± 0.4	0.6	1.8
0.010	0.006	23.0 ± 0.4	6.6 ± 0.1	3.2 ± 0.1	0.3	1.0
0.010	0.010	17.5 ± 0.4	5.2 ± 0.6	3.7 ± 0.1	0.3	1.1
0.010	0.015	28.7 ± 0.3	8.5 ± 0.1	1.8 ± 0.7	0.5	0.9
0.015	0.006	21.8 ± 0.3	4.8 ± 0.1	3.8 ± 0.2	0.2	0.8
0.015	0.010	17.9 ± 0.4	5.4 ± 0.1	2.1 ± 0.1	0.3	0.6
0.015	0.015	23.2 ± 0.4	5.9 ± 0.2	2.6 ± 0.2	0.3	0.8

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Table 5 Values of empirical constants, θ, F_X/S and K^X/S obtained using eqn (3) and (4) with the [M₂X]^op₀ values for M₂X = 2-NaOC₆H₄CO₂Na at different [CTABr]_T^a

[CTABr]T, M	10^4k0^c, s^−1	[M2X]^op0, M	10^3θ, s^−1	K^X/S, M^−1	KX/S, M^−1	FX/S	K^nX/S, M^−1	K^BrX
a [PSH]0 = 0.2 mM, [NaOH] > 0.03 M, [Pip] = 0.1 M, λ = 370 nm and aqueous reaction mixture for each kinetic run contains 2% v/v acetonitrile.b Total concentration of CTABr.c k0 = kobs at [M2X] = 0.d Error limits are standard deviations.e KX/S = K^X/S(1 + K^0S[CTABr]T), where K^0S = 7 × 10^3 M^−1.f FX/S = θ/(k^nW[Pip]T), where k^nW = kobs at [CTABr]T = [C16E20]T = 0 and [Pip]T = 0.1 M and the values of k^nW, under such conditions is 0.322 s^−1.g K^nX/S = FX/SKX/S.h K^BrX = K^nX/S/K^nBr/S, where K^nBr/S = 25 M^−1.
0.006^b	23.0 ± 0.2	0.007	23.1 ± 0.1^d	39.4 ± 5.6	1694.2^e	0.72^f	1219.8^g	48.8^h
0.010	21.2 ± 0.4	0.011	19.4 ± 0.6	26.4 ± 2.4	1874.4	0.60	1124.6	45.0
0.015	16.4 ± 0.4	0.016	19.6 ± 0.4	13.0 ± 0.6	1378.0	0.60	0826.8	33.1

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Table 6 Values of empirical constants, ^mθ, ^mF_X/S and ^mK^X/S calculated from eqn (3) and (4) with the [M₂X]^op₀ values for M₂X = 2-NaOC₆H₄CO₂Na at different concentrations of mixed CTABr–C₁₆E₂₀^a

[CTABr]T, M	[C16E20]T, M	10^4k0^d, s^−1	[M2X]^op0, M	10^3mθ, s^−1	^mK^X/S, M^−1	^mFX/S	^nmK^X/S, M^−1	^nmK^Br/S, M^−1	^mR^BrX
a [PSH]0 = 0.2 mM, [NaOH] > 0.03 M, [Pip] = 0.1 M, λ = 370 nm and aqueous reaction mixture for each kinetic run contains 2% v/v acetonitrile.b Total concentration of CTABr.c Total concentration of C16E20.d k0 = kobs at [MX] = 0.e Error limits are standard deviations.f FX/S = θ/(k^nW[Pip]T), where k^nW = kobs at [CTABr]T = [C16E20]T = 0 and [Pip]T = 0.1 M and the values of k^nW, under such conditions is 0.322 s^−1.g ^nmK^X/S = ^mFX/S^mK^X/S.h ^nmK^Br/S = ^mFBr/S^mK^Br/S (for MX = NaBr).i ^mR^BrX = ^nmK^X/S/^nmK^Br/S.
0.006^b	0.006^c	24.7 ± 0.5	0.00028	20.8 ± 0.4^e	34.8 ± 2.2	0.87^f	30.3^g	1.4^h	21.6^i
0.006	0.010	27.2 ± 0.5	0.00201	19.9 ± 0.2	28.1 ± 0.9	1.03	28.9	2.2	13.1
0.006	0.015	14.1 ± 0.1	0.00000	21.7 ± 0.5	24.6 ± 1.5	1.18	29.9	1.8	16.6
0.010	0.006	22.9 ± 0.8	0.00000	26.5 ± 0.5	8.82 ± 0.4	1.10	09.7	1.0	09.7
0.010	0.010	25.3 ± 0.4	0.00006	35.0 ± 1.1	4.87 ± 0.2	1.82	08.9	1.1	08.1
0.010	0.015	25.3 ± 0.5	0.00047	32.3 ± 0.5	7.26 ± 0.2	1.75	12.7	0.9	14.1
0.015	0.006	23.6 ± 0.2	0.01085	19.6 ± 0.4	16.8 ± 0.8	0.82	13.8	0.8	17.3
0.015	0.010	24.5 ± 0.3	0.00768	20.6 ± 0.4	16.8 ± 0.9	0.86	14.5	0.6	24.2
0.015	0.015	19.9 ± 0.4	0.00560	18.0 ± 0.4	12.4 ± 0.6	0.98	12.2	0.8	15.3

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The results, at various constant concentrations of pure CTABr, and mixed CTABr–C₁₆E₂₀, in the presence of different [MX] and [M₂X], (MX = NaBr and M₂X = NaOC₆H₄CO₂Na) are presented in Tables 4–6. Symbolic modification of parameters was done to differentiate between those obtained in the presence of pure micelles and mixed micelles. Therefore, k₀, k^W_obs, θ, K_X/S, K^X/S, K⁰_S, F_X/S and Kⁿ_X/S are considered as ^mk₀, ^mk^W_obs, ^mθ, ^mK_X/S, ^mK^X/S, ^mK_S, ^mF_X/S and ^mKⁿ_X/S, respectively. The small letters “m” (superscripts) were used to imply that the parameters are obtained in the mixed micellar solutions throughout the text.

The hydrophilic parts of CTABr in CTABr–C₁₆E₂₀ surfactants mixture are covered within the larger sized hydrophilic C₁₆E₂₀ micellar parts of the same mixed surfactants.²¹ Thus, it appears acceptable that the combination of ionic surfactants (C_nI_m) and nonionic ones (C_nE_m) with n ≤ m is related to incomplete dehydration of the hydrophilic part of C_nI_m (comprising the outermost portion of headgroups), which causes the ion exchange, leading to changes in structure of micelles from spherical to wormlike.²²

It is also clearly demonstrated from eqn (5) that as the concentration of pure CTABr increases, the values of K^X/S decrease provided the values of K_X/S are independent of [CTABr]_T. This prediction coincides well with what is presented in Table 5 (the values of K^X/S = 39, 26 and 13 for 0.006, 0.010 and 0.015 M [CTABr]_T, respectively).

The optimum values of [2-NaOC₆H₄CO₂Na], ([M₂X]^op₀), for the mixed CTABr–C₁₆E₂₀ micelles (Table 6) decreased compared to that of the pure CTABr (Table 5). However, the values of parameters k₀, θ and K^X/S remain independent of whether the micellar system is pure or mixed and it was observed that the lowest value of the concentration of CTABr is more than 20-fold larger than the corresponding value of [M₂X]^op₀ in the presence of 0.006 M C₁₆E₂₀. The values of F_X/S are also independent of the [CTABr]_T and mixed [CTABr]_T–[C₁₆E₂₀]_T. However, these values increased in the mixed CTABr–C₁₆E₂₀ micellar system (Table 6) compared to the pure one (Table 5). The value of ion-exchange constant, K^Br_X or R^Br_X, is empirically related to the normalized values of K_X/S (Kⁿ_X/S = F_X/SK_X/S) and K_Br/S (Kⁿ_Br/S = F_Br/SK_Br/S).¹⁷

K^Br_X = K_X/K_Br = Kⁿ_X/S/Kⁿ_Br/S (6)

The values of K_X/S were calculated using eqn (5) for M₂X (=2-NaOC₆H₄CO₂Na) with K⁰_S = 7000 M⁻¹.

The value of Kⁿ_X/S and the proclaimed value of Kⁿ_Br/S (=25 M⁻¹)¹⁷ give the values of K^Br_X = 48.8, 45.0 and 33.1 at [CTABr]_T = 0.006, 0.010 and 0.015 M, respectively (Table 5). These results are similar to the one presented in the previous study (=44).¹⁹

However, eqn (6) holds only if the values of Kⁿ_X/S and Kⁿ_Br/S are determined in micelles with the same structural behavior. Contrarily, if the micellar structures are different, then K_X/K_Br refers to R^Br_X with the relationship in eqn (7)

R^Br_X = ^nmK^X/S/ⁿK^Br/S (7)

where ^nmK^X/S = ^mF_X/S^mK^X/S (for M₂X = 2-NaOC₆H₄CO₂Na) and ⁿK^Br/S = ^mF^m_X/SK^Br/S (for MX = NaBr). The conditions to use either of the relationships (eqn (6) and (7)) have been reported in detail elsewhere.¹⁹

It can be easily shown, in view of eqn (5), that

^mKⁿ_X/S = ^nmK^X/S(1 + ^mK⁰_S[CTABr]_T) (8)

and

^mKⁿ_Br/S = ^nmK^Br/S(1 + ^mK⁰_S[CTABr]_T) (9)

Eqn (8) and (9) give eqn (7).

The presence of mixed CTABr–C₁₆E₂₀ micelles revealed the increase in the values of F_X/S for M₂X = 2-NaOC₆H₄CO₂Na (Table 5). This is in contrast with the reported study, and could be due to the fact that the concentrations of C₁₆E₂₀ (0.006, 0.010 and 0.015 M) used in the present study are lower than that of the reported one (0.05 M).¹⁹ The results show that the values of K_X/K_S for mixed CTABr–C₁₆E₂₀ micelles are higher than that of pure CTABr. The corresponding values of K_X/S could not be calculated because their K⁰_S values for mixed CTABr–C₁₆E₂₀ micelles are not available.

4.2 Explanation of rheological measurements for the piperidinolysis of PS⁻ in the presence of pure CTABr and mixed CTABr–C₁₆E₂₀ micelles at various [M₂X]

In the presence of pure CTABr micelles, all flow curves in Fig. 5a and b, at 0.012 M 2-NaOC₆H₄CO₂Na at both 25 °C and 35 °C, show the Newtonian fluid behavior at their beginning (except at 0.006 and 0.008 M 2-NaOC₆H₄CO₂Na) and show the shear thinning behavior at the end. This behavior of CTABr surfactant, with a constant concentration in the presence of different [2-NaOC₆H₄CO₂Na], indicates the presence of elongated micelles.^23,24 As the [2-NaOC₆H₄CO₂Na] increases from 0.006 to 0.012 M, the values of critical shear rate γ_cr decrease and also shift to lower values with increase in zero shear viscosity, η₀. However, further increase in [2-NaOC₆H₄CO₂Na] (0.02–0.12 M) increases the values of γ_cr with decrease in η₀. It implies, therefore, the CTABr micellar structure is getting networked to a greater extent and lesser degrees at >0.008 to 0.012 M and 0.02 to 0.12 M ranges of 2-NaOC₆H₄CO₂Na, respectively. This is a typical rheological behavior of wormlike micelles.¹⁸

Almost all of the flow curves in Fig. 6a and b (0.006–0.12 M 2-NaOC₆H₄CO₂Na) at 25 °C and 35 °C, in the presence of mixed CTABr–C₁₆E₂₀ (with fixed concentration of both CTABr and C₁₆E₂₀), show Newtonian fluid systems, but increase in the value of η₀ is observed within the range from 0.012 to 0.12 M [2-NaOC₆H₄CO₂Na]. This behavior might be linked to the presence of the C₁₆E₂₀ surfactant's branched structure.²⁵

The graph of η₀ at [small gamma, Greek, dot above] against [2-NaOC₆H₄CO₂Na] at two temperatures (25 °C and 35 °C) is shown in Fig. 7. Typical single asymmetrical maxima of the graph at [CTABr]_T = 0.015 M, [C₁₆E₂₀]_T = 0 and 25 °C and 35 °C (□ and ◊, respectively) were obtained at the same value of [2-NaOC₆H₄CO₂Na]_sp (=0.02 M, specific concentration of 2-NaOC₆H₄CO₂Na). The values of [2-NaOC₆H₄CO₂Na]_sp at which the maximum viscosity was reached at a constant shear rate remained the same at both the temperatures. This observation agreed with previous studies that the maxima obtained for a solution of cationic surfactant, for instance CTABr, at fixed concentration and various [M₂X] (where M₂X stands for salt with counterion behavior) reveals the existence of wormlike micelles.

Fig. 7 Graph of zero shear viscosity (η₀) at constant shear rate ([small gamma, Greek, dot above]) against [2-NaOC₆H₄CO₂Na] with 0.015 M CTABr in absence of C₁₆E₂₀ at 25 °C (□) and 35 °C (◊), and in the presence of 0.006 M C₁₆E₂₀ at 25 °C (△) and 35 °C (○). M₂X = 2-NaOC₆H₄CO₂Na.

However, no maxima of the graph were obtained at the two different temperatures (△ and ○ respectively) and the same concentration of CTABr in the presence of C₁₆E₂₀. Thus, no significant differences in η₀ values were obtained at various [2-NaOC₆H₄CO₂Na]_sp.

5. Conclusions

It is known from the literature that the CTABr micellar binding constant of phenyl salicylate ion is nearly 100-fold larger in the presence of CTABr micelles compared to that in the presence of C₁₆E₂₀.¹⁴ It is now common belief that the viscoelastic behavior of aqueous CTABr micellar solution containing sodium salicylate is caused by the strong CTABr micellar binding of sodium salicylate. However such perception has never been supported by quantitative determination of such binding constants. The new and interesting finding described in this manuscript is that CTABr/M₂X/H₂O micellar solution (with R^Br_X ≈ 42) contains wormlike micelles, whereas CTABr/M₂X/C₁₆E₂₀/H₂O micellar solution (with K^Br_X ≈ 16) contains spherical micelles, with M₂X = disodium salicylate. This is a quantitative correlation between the magnitude of counterion (X) binding constant with CTABr (R^Br_X) and X-induced CTABr micellar growth. It is also important to note that the structural feature, as well as the viscosity of CTABr/M₂X/C₁₆E₂₀/H₂O micellar solutions, can be manipulated by simply changing the concentration of C₁₆E₂₀.

Acknowledgements

The authors acknowledge the financial support of this research from University of Malaya (UM) and Ministry of Higher Education (MOHE), Malaysia, under the UM.C/HIR/MOHE/SC/07 and RG022/09AFR grants.

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