Quantitative correlation between counterion (X) binding affinity to cationic micelles and X – Induced micellar growth for substituted iodobenzoates (X)

2.1 Materials

Chemicals such as cetyltrimethylammonium bromide (CTABr; purity ⩾99% from Fluka), phenyl salicylate (PSaH; purity ⩾98% from Fluka), piperidine (Pip; purity ⩾99% from Merck), 2-, 3- and 4-IBzH with BzH representing C₆H₄CO₂H (2-IBzH; purity ⩾99% from Merck, 3-IBzH; purity 98% from Aldrich and 4-IBzH; purity ⩾98% from Merck) and NaOH (purity ⩾99% from Merck) were commercial products with highest available purity. The details of the preparation of the stock solutions of organic salts (MX = 2-, 3- and 4-IBzNa) and PSaH were the same as described earlier (Yusof and Khan, 2011). Because of the extremely low water solubility of PSaH, the stock solutions (0.01 M) of PSaH were prepared in pure acetonitrile.

2.2 Kinetic measurements

The rate of reaction between piperidine (Pip) and ionized phenyl salicylate (PSa⁻) was studied spectrophotometrically by monitoring the disappearance of PSa⁻ as a function of reaction time (t) at a constant wavelength of 350 nm by using UV-visible spectrophotometer equipped with electronically controlled thermostatic cell compartment set at 35 °C. The details of the kinetic procedure and product characterization study were the same as described elsewhere (Khan and Kun, 2001). Nonlinear least-squares technique was used to calculate kinetic parameters k_obs (pseudo first-order rate constant), δ_ap (apparent molar absorptivity of the reaction mixture) and A_∞ (absorbance at t = ∞) from Eq. (1) (Khan and Kun 2001).

2.3 Rheometric measurements

The rheological study was carried out using a Brookfield R/S+ rheometer with double gap coaxial cylinder (CC–DG) and an external temperature controller fixed at 35 °C. The concentrations of all additives except CTABr of a rheological sample were same as maintained in the kinetic measurements. The concentration of CTABr was kept constant at 0.015 M. The sample was thermally equilibrated at 35 °C for at least 15 minutes. The shear rate ( $\dot{\gamma }$ ) range was fixed at 0.5–15 s⁻¹ and 1–1000 s⁻¹ for respectively the total time of 2400 s and 8000 s, for the rheological measurements. The total number of data points was 30 for the first set and 100 for the second set.

2.4 Determination of ${\text{K}}_{\text{X}}^{\text{Br}}$ or ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 2-, 3- and 4-IBz⁻ by the use of SEK method

The semi-empirical kinetic (SEK) method for the determination of ${\text{K}}_{\text{X}}^{\text{Br}}$ or ${\text{R}}_{\text{X}}^{\text{Br}}$ requires the use of a reaction kinetic probe which involves the kinetic study on the effects of the concentrations of the inert salts of counterions (such as [MX] where MX = 2-, 3- and 4-IBzNa) on k_obs for the cationic micelle-catalyzed semi-ionic bimolecular reaction with the ionic reactant representing as the counterion of cationic micelle. The reaction kinetic probe that has been used in the present study, involves the nucleophilic reaction of Pip with PSa⁻. The details of the SEK method including the reaction kinetic probe used in the present study are described in a recent report (Yusof and Khan, 2010; Khan, 2010).

3.1 Effects of the concentrations of 2-, 3- and 4-IBzNa (Bz⁻ = C₆H₄CO₂⁻) on the rate of piperidinolysis of PSa⁻ at a constant [CTABr]_T and 35 °C

Several kinetic runs were carried out at different concentrations of MX (= 2-, 3- and 4-IBzNa) within [MX] range 0.0 – ⩽0.30 M at 0.005 M CTABr, 0.1 M Pip and 2 × 10⁻⁴ M PSa⁻. The values of [NaOH], under such conditions, varied from 0.03 to 0.06 M for 2-IBzNa and 0.03 to 0.04 M for 3- and 4-IBzNa. The values of pseudo-first-order rate constants (k_obs), at different [MX] are shown graphically in Fig. 1 for MX = 3-IBzNa and Figs. S1 and S2 of Supplementary Data (SD) for respective MX = 2 and 4-IBzNa. Similar observations were obtained at 0.006, 0.007, 0.01 and 0.015 M CTABr for MX = 2-IBzNa while for 3- and 4-IBzNa, the observed data could be obtained only at ⩽0.01 M CTABr. The values of k_obs at different [MX] and at a constant 0.015 M CTABr, for MX = 3- and 4-IBzNa could not be obtained because the reaction mixture, even at the lowest value of [MX] (= 0.002 M), became jelly at the reaction time t = 0. As a consequence, the reaction mixtures under such conditions became highly viscous and inhomogeneous as well as observed data, A_ob vs. t, did not fit to Eq. (1). The values of k_obs at different [MX] and [CTABr]_T are also shown graphically in Fig. 1, S1 and S2 for MX = 3-, 2- and 4-IBzNa, respectively.

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Figure 1

Plots showing the dependence of k_obs upon [MX] (MX = 3-IBzNa) for piperidinolysis of PSa⁻ at 2 × 10⁻⁴ M PSa⁻, 0.1 M Pip, ⩽0.06 to >0.03 M NaOH, 35 °C and [CTABr]_T/M = 0.002 (●), 0.005 (▴), 0.006 (■), 0.007 (○) and 0.01 (Δ). The dashed lines are drawn through the calculated data points using Eq. (2) with kinetic parameters (k₀, θ and K^X/S), listed in Table 1 of manuscript, at [MX]₀^op = 0. The solid lines are drawn through the calculated data points using Eq. (2) with kinetic parameters (k₀, θ and K^X/S), listed in Table 1 of manuscript, at [MX]₀^op/M = 0.0044 (●), 0.0045 (▴), 0.0046 (■), 0.0050 (○) and 0.0094 (Δ). Inset: The plots at magnified scale for the data points at the lowest values of [MX].

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3.2 Effects of [MX] (MX = 2-, 3- and 4-IBzNa) on k_obs for the reaction of Pip with PSa⁻ in the absence of CTABr at 35 °C

Although benzoate and substituted benzoate ions are nonreactive toward nucleophilic cleavage of PSa⁻, these inert salts might affect rate of piperidinolysis of PSa⁻ through specific salt/ionic strength effect. In order to find out this probable salt effect on k_obs, a few kinetic runs were carried out at 0.1 M Pip, 2 × 10⁻⁴ M PSa⁻ and within [MX] (MX = 2-, 3- and 4-IBzNa) range 0.0–0.3 M in the absence of CTABr. The values of [NaOH] varied within its range 0.03–0.06 M. The least-squares calculated values of kinetic parameters, k_obs and δ_ap reveal that the values of k_obs are almost independent of [MX] within its range 0.0–0.2 M for MX = 2-IBzNa, 0.0 – 0.10 M for MX = 3- and 4-IBzNa. Mean values of k_obs (i.e., k_obs^mean) are (316 ± 13) × 10⁻⁴, (323 ± 10) × 10⁻⁴ and (311 ± 14) × 10⁻⁴ s⁻¹ for MX = 2-, 3- and 4-IBzNa, respectively. The value of k_obs at 0.3 M 2-IBzNa is ∼10% lower than the mean value of k_obs (= (316 ± 13)) × 10⁻⁴ s⁻¹). The values of δ_ap remain independent of [MX] within its range 0.0 – 0.3 M and mean values of δ_ap (i.e., δ_ap^mean) are 6866 ± 106, 6769 ± 107 and 6871 ± 178 M⁻¹ cm⁻¹ for MX = 2-, 3- and 4-IBzNa, respectively.

3.3 Rheological properties of CTABr micellar solutions containing constant concentrations of PSa⁻, Pip, MX and >0.03 to ⩽0.04 M NaOH

Rheological behaviors of CTABr/2-IBzNa, CTABr/3-IBzNa and CTABr/4-IBzNa were studied at 33.9 ± 1.6 °C under steady-shear rheological response. Aqueous surfactant (CTABr) solutions containing 2% v/v CH₃CN and a constant concentration of all additives (2 × 10⁻⁴ M PSa⁻, 0.1 M Pip, ⩽0.06 M NaOH) including 0.015 M CTABr as well as different concentrations of MX (= 2-, 3- and 4-IBzNa) were used to obtain shear viscosity (η) at different shear rates ( $\dot{\gamma }$ ) within its range >0.4 – 1000 s⁻¹. The log–log plots of η vs. $\dot{\gamma }$ at different values of [MX] are shown graphically by Fig. 2 for MX = 3-IBzNa and respective Figs. S3 and S4 of (SD) for MX = 2- and 4-IBzNa. Similar observations were also obtained at 0.005 M CTABr for 4-IBzNa simply for comparison purpose because the values of η, at shear rates 10 and 1000 s⁻¹ and within [4-IBzNa] range 0.003 – 0.02 M at 0.005 M CTACl and 30 °C, are available from a recent report (Ge et al., 2008). The values of η vs. $\dot{\gamma }$ are shown graphically as log–log plots in Fig. S5. The plots of Fig. 2 and Figs. S3–S5 represent shear thinning which is a typical characteristic of the presence of rodlike micelles (RM)/wormlike micelles (WM) in the surfactant solutions (Lin et al., 2009a; Lin et al., 2009a; Lu et al., 2008; Raghavan and Kaler, 2001).

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Figure 2

Plots showing the dependence of shear viscosity (η) upon shear rate ( $\dot{\gamma }$ ) for samples where [PSaH] = 2 × 10⁻⁴ M, [NaOH] = 0.03 M, [Pip] = 0.1 M, [CTABr] = 0.015 M and [3-IBzNa]/M = 0.01 (Δ), 0.03 (▴), 0.05 (■) and 0.1 (□).

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The values of η at $\dot{\gamma }=2.5{\text{s}}^{-1}$ , i.e. ${\mathrm{\eta }}_{2.5\dot{\gamma }}$ , 0.015 M CTABr and different [MX] are shown graphically in Fig. 3 for MX = 2-, 3- and 4-IBzNa. The plot of ${\mathrm{\eta }}_{2.0\dot{\gamma }}$ vs. [4-IBzNa] at 0.005 M CTABr is also shown in Fig. 3. A remarkable rheological feature of adding salt (MX) to aqueous surfactant solutions is the maximum shown by the plot of ${\mathrm{\eta }}_{\dot{\gamma }}$ vs. [MX]. Although this behavior is no longer unusual for long wormlike micellar systems (Rehage and Hoffmann, 1991; Schubert et al., 2004; Croce et al., 2005; Ali and Makhloufi, 1997; Davies et al., 2006), the mechanism, at the molecular level for the occurrence of such maximum, is still a matter of debate (Davies et al., 2006; Dreiss, 2007).

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Figure 3

Plot of shear viscosity (η) at $\dot{\gamma }$  = 2.5 s⁻¹ vs. [MX] ([MX] = [2-IBzNa] (×), [3-IBzNa] (▴) and [4-IBzNa] (●)) at 0.015 M CTABr as well as the plot of η at $\dot{\gamma }$  = 2.0 s⁻¹ vs. [MX] (MX = 4-IBzNa) (○) at 0.005 M CTABr, 2 × 10⁻⁴ M PSa⁻, 0.03 M NaOH and 0.1 M Pip and ∼35 °C.

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4.1 Determination of ${\text{K}}_{\text{X}}^{\text{Br}}$ or ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 2-, 3- and 4-IBz⁻

It is evident from Fig. 1 and Figs. S1 and S2 that the values of k_obs are more than 10-fold smaller at [MX] = 0 and [CTABr]_T ≠ 0 than those at [CTABr]_T = 0, and at different [MX] within its range 0 – ⩽0.2 M. Thus, the nonlinear increase in k_obs with the increasing values of [MX] at a constant [CTABr]_T cannot be explained in terms of ionic strength effect. The most plausible cause for the nonlinear increase in k_obs with the increase of [MX] is the transfer of micellized PSa⁻ (i.e., PSa⁻_M with subscript ‘M’ indicating micellar pseudophase) to the bulk water phase (i.e., PSa⁻_W with subscript ‘W’ indicating water phase) through the ion exchange process X⁻/PSa⁻. The values of k_obs, at different [MX] (MX = 2-, 3- and 4-IBzNa) and at a constant [CTABr]_T, were treated with Eq. (2) (Khan and Ismail, 2007; Khan, 2010).

The plots of Fig. 1 as well as Figs. S1 and S2, where dashed lines are drawn through the least squares calculated rate constants using Eq. (2) with kinetic parameters (θ and K^X/S) listed in Table 1, reveal significant systematic negative deviations of the observed data points from dashed lines at the lower values of [MX]. The reason for these significant negative deviations of the observed data points from the corresponding calculated data points with the decreasing [MX] at its extreme lower values as well as higher values of [CTABr]_T has been attributed to the significant effects of the ion exchange processes X⁻/HO⁻ and X⁻/Br⁻ on k_obs under such typical reaction conditions (Khan and Ismail, 2007; Yusof and Khan, 2010; Khan, 2010). The consideration of these independent ion exchange processes has led to Eq. (3) (Khan and Ismail, 2007; Khan, 2010)

The effective occurrence of ion exchange process X⁻/S⁻ in the related reaction systems has been found to decrease K_S with the increasing [MX] through an empirical relationship (Khan, 2006)

In view of Eq. (2), the values of θ should be independent of [CTABr]_T. Relatively more reliable calculated values of θ (Table 1) are almost independent of [CTABr]_T for MX = 2-, 3- and 4-IBzNa. Mean values of F_X/S, calculated from Eq. (5) with k_W^MX[Pip]_T = 32.7 × 10⁻³ s⁻¹ at 0.1 M Pip, for X = 2-, 3- and 4-IBz⁻, (Yusof and Khan, 2010) are shown in Table 2.

The values of K_X/S at different [CTABr]_T were calculated from Eq. (6) with the reported value of K_S⁰ (= 7 × 10³ M⁻¹) (Khan, 2006). These calculated values of K_X/S, at different [CTABr]_T for X = 2-, 3- and 4-IBz⁻, are shown in Table 1. Relatively more reliable values of K_X/S are almost independent of [CTABr]_T within its range 0.005–⩽0.015 M (Table 1) and this is a requirement for the validity of Eq. (4). It has been concluded in the recent reports (Khan and Ismail, 2007; Khan, 2010) that the normalized K_X/Sⁿ (= F_X/S K_X/S) and K_Y/Sⁿ (= F_Y/S K_Y/S) values are empirically related to the ratio K_X/K_Y, through the relationship: R_X^Y = K_X/K_Y = K_X/Sⁿ/K_Y/Sⁿ with K_X = [X_M]/([X_W][D_n]) and K_Y = [Y_M]/([Y_W][D_n]). The values of K_X/Sⁿ (Table 1) and the reported value of 25 M⁻¹ (Yusof and Khan, 2010) for K_Br/Sⁿ (with Br = Y) give the values of ${\text{K}}_{\text{X}}^{\text{Br}}$ or ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 2-, 3- and 4-IBz⁻. These results are also shown in Table 1. The mean values of ${\text{K}}_{\text{X}}^{\text{Br}}$ or ${\text{R}}_{\text{X}}^{\text{Br}}$ , obtained within [CTABr]_T range 0.005–⩽0.015 M for X = 2, 3- and 4-IBz⁻, are summarized in Table 2.

Perhaps it is noteworthy that the value of K_Br/Sⁿ (= 25 M⁻¹) has been derived from kinetic parameters obtained in the presence of spherical CTABr micelles (Khan et al., 2000). But the values of K_X/Sⁿ may be obtained, depending upon the structural features of X, in the presence of either spherical or nonspherical micelles. Thus, the value of ${\text{R}}_{\text{X}}^{\text{Br}}$ becomes usual/conventional ion exchange constant ( ${\text{K}}_{\text{X}}^{\text{Br}}$ ) if the value of K_X/Sⁿ is obtained in the presence of spherical micelles.

The cationic micellar structural transition from spherical to rodlike micelles (RM) and RMs+ vesicles is shown to accompany by significant increase in the degree of counterion (X = Br) binding (β_X) (Ono et al., 2005; Rodriguez et al., 2009). However, although β_X values for CTACl/4-XBzNa (with X = F, Cl, Br, I) systems vary only slightly with the change of X from F to I, cryo-TEM images for 0.005 M CTACl/0.003 M MX reveal the presence of only spherical micelles for X = 4-FBz⁻ while mixed spherical + long RM of different natures for X = 4-ClBz⁻, 4-BrBz⁻ and 4-IBz⁻ (Ge et al., 2008). The values of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 3-ClBz⁻ (Khan and Ismail, 2009), 4-BrBz⁻ (Yusof and Khan, 2011) and 4-IBz⁻ (Table 2) are many folds larger than that for X = 4-FBz⁻ (Yusof and Khan, 2010). Similarly, the values of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 3-BrBz⁻ and 3-IBz⁻ are larger by respectively 1.4- and 2.8-fold than that for X = 3-ClBz⁻ (Khan and Ismail, 2009). The increase in electronegativity and polarizability of the substituent of counterions X is expected to decrease and increase the values of ${\text{K}}_{\text{X}}^{\text{Br}}$ or ${\text{R}}_{\text{X}}^{\text{Br}}$ , respectively. The increase in the steric requirements of X is also expected to possibly decrease the values of ${\text{K}}_{\text{X}}^{\text{Br}}$ or ${\text{R}}_{\text{X}}^{\text{Br}}$ . Thus, ∼10-fold larger value of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 4-IBz⁻ than that for X = 4-FBz⁻ may be ascribed to the combined effects of electronegativity, polarizability and steric requirements of F and I.

4.2 Rheological behavior of aqueous solutions of CTABr containing 2-, 3- and 4-IBzNa

Generally, shear viscosity (η) vs. shear rate ( $\dot{\gamma }$ ) plot of wormlike micellar solutions reveals four distinct regions, i.e. Newtonian, shear thinning, shear thickening and shear thinning (Ge et al., 2008). The initial Newtonian regions of Fig. 2 and Figs. S3–S5 (SD) appear to be missing presumably because these Newtonian regions are expected to appear at very low shear rates (<0.4 s⁻¹). The rheometer used in this study could not measure the shear viscosity at $\dot{\gamma }$ < ∼1.0 s⁻¹ for MX = 2-IBzNa and $\dot{\gamma }$ < ∼0.4 s⁻¹ for MX = 3- and 4-IBzNa at 0.015 M CTABr. Although the plots of Fig. 2 and Figs. S3–S5 do not show the distinct presence of shear thickening regions, most of these plots do indicate regions of very low gradients (within $\dot{\gamma }$ range ∼25–200 s⁻¹, Fig. S3, and ∼6–30 s⁻¹, Fig. 2 and Figs. S4 and S5), between two different shear thinning regions at some values of [MX]. The regions of very low gradients are more apparent with MX = 2-IBzNa (Fig. S3) than those with MX = 3- and 4-IBzNa (Fig. 2 and Figs. S4 and S5). It is also evident from the plots of Fig. 2 and Figs. S3 and S5 that the plots representing initial shear thinning regions have significantly larger absolute values of gradients for MX = 2-IBzNa than those for MX = 3- and 4-IBzNa. This may be attributed to the presence of short RM for MX = 2-IBzNa and long flexible RM/WM for MX = 3- and 4-IBzNa. The flow curve at 0.01 M 2-IBzNa exhibits shear thickening while shear thickening does not exist under essentially similar conditions for MX = 3- and 4-IBzNa. Shear thickening, similar to one at 0.01 M 2-IBzNa in Fig. S3, is also exhibited by the flow curve at [MX] = 0 in Fig. S4. It is known from the literature that the aqueous solution containing <∼0.2 M (Rao et al., 1987) and <∼0.1 M CTABr Geng et al., 2005) contains only spherical micelles. Perhaps it is relevant to note that the flow curve at 0.01 M 2-IBzNa (Fig. S3) is very similar to what one would see if Taylor vortices (an unstable flow that occurs in Couette flow of low viscosity fluids at high shear rates) were present. These observations reveal the presence of spherical micelles at 0.01 M 2-IBzNa and RM (rodlike micelles) at 0.01 M MX with MX = 3- and 4-IBzNa. Nearly 13-fold smaller value of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 2-IBz⁻ than those for X = 3- and 4-IBz⁻ is the most probable cause for the presence of short RM for MX = 2-IBzNa and long flexible RM for MX = 3- and 4-IBzNa.

It seems noteworthy that the shapes of the flow curves (i.e., the plots of η vs. $\dot{\gamma }$ ) at different [MX] for MX = 2-, 3- and 4-IBzNa are significantly different from the corresponding plots for MX = 2-, 3- and 4-BrBzNa (Yusof and Khan, 2011) as well as 3- and 4-FBzNa (Yusof and Khan, 2010). The flow curves at 0.01 M MX show the presence and absence of RM for respectively MX = 3-IBzNa (Fig. 2) and 3-BrBzNa (Yusof and Khan, 2011). This distinct difference is attributed to 2-fold larger value of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 3-IBz⁻ than that for X = 3-BrBz⁻ (Yusof and Khan, 2011). The characteristic differences between the flow curves for MX = FBzNa (Yusof and Khan, 2010), BrBzNa (Yusof and Khan, 2011) and IBzNa may be attributed to significantly large differences in the magnitudes of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = FBz⁻, BrBz⁻ and IBz⁻ (Table 2).

The presence of two maxima in the plot of ${\mathrm{\eta }}_{2.5\dot{\gamma }}$ vs. [4-IBzNa] at 0.005 M CTABr (Fig. 3) is comparable with a recent study on rheological behavior of 0.005 M CTACl solutions mixed with [4-IBzNa] in the range 0.003–0.02 M (Ge et al., 2008). However, the plot of ${\mathrm{\eta }}_{2.5\dot{\gamma }}$ vs. [4-IBzNa] at 0.015 M CTABr exhibits the presence of only one maximum (Fig. 3).

Cryo-TEM image for CTACl/4-IBzNa system at 0.005 M CTACl and 0.02 M 4-IBzNa has long flexible and entangled rodlike micelles (RM) (Ge et al., 2008). Thus, it may not be unreasonable to propose that CTABr/3-IBzNa and CTABr/4-IBzNa systems have long linear and entangled RM at both 0.005 and 0.015 M CTABr. For the CTACl/4-FBzNa system at 0.005 M CTACl and 0.02 M 4-FBzNa, the cryo-TEM image has spherical and some short stiff RM (Ge et al., 2008). The value of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 4-FBz⁻ (Yusof and Khan, 2010) is only slightly larger than that for X = 2-IBz⁻ (Table 2). The near similarity of ${\text{R}}_{\text{X}}^{\text{Br}}$ values for X = 2-IBz⁻ and 4-FBz⁻, nearly 13-fold larger value of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 4-IBz⁻ than that for X = 2-IBz⁻ and characteristically different natures of the plots of Figs. S3 and S5 may be attributed to the probable presence of short stiff RM in CTABr/2-IBzNa system at 0.015 M CTABr and different concentrations of 2-IBzNa. It is evident from the plots of Fig. 3 that the aqueous solutions of CTABr/MX contain large number of long linear RM even at 0.003 M CTAX (X = 4-IBz⁻).

4.3 Relationship between the magnitudes of ${\text{R}}_{\text{X}}^{\text{Br}}$ and X-induced micellar growth

Since 1976, the attempts of finding new viscoelastic additives have relied upon the qualitative perception that unusually strong counterionic (X) binding to ionic micelles is the main cause for the X-induced viscoelastic wormlike micellar behavior of aqueous ionic surfactant solutions containing counterionic salts (MX) (Lu et al., 1998; Bijma and Engberts, 1997; Ali et al., 2009; Vermathen et al., 2002; Davies et al., 2006; Gravsholt, 1976; Oelschlaeger et al., 2010; Abezgauz et al., 2010; Takeda et al., 2011; Penfold et al., 2004). Relatively more reliable values of ${\text{R}}_{\text{X}}^{\text{Br}}$ for X = 2-, 3- and 4-IBz⁻ (Table 2) indicate, perhaps for the first time for these counterions (X), a quantitative correlation between the values of ${\text{R}}_{\text{X}}^{\text{Br}}$ and X–induced formation of short RM for X = 2-IBz⁻ as well as long linear and entangled RM for X = 3- and 4-IBz⁻ at the constant [CTABr] (= 0.005 or 0.015 M) and varying values of [MX]. The value of [MX]_sc represents the specific value of [MX] at which maximum density of entangled RM occurs at a constant [CTABr] (= 0.015 M) in the plot of ${\mathrm{\eta }}_{\dot{\gamma }}$ vs. [MX]. It may be noteworthy that the values of [MX]_sc remain unchanged with the change of $\dot{\gamma }$ from ∼2 to 1000 s⁻¹. Thus, if the density of entangled RM formation increases with the increase of the ionic micellar binding constants of counterions (X) at a constant [CTABr] then the values of [MX]_sc should decrease with the increase of ${\text{R}}_{\text{X}}^{\text{Br}}$ . The listed values of [MX]_sc vs. ${\text{R}}_{\text{X}}^{\text{Br}}$ of Table 2 for X = 3-, 4-FBz⁻, 3-, 4-BrBz⁻ and 3-, 4-IBz⁻ support this conclusion.