Interactions between Sodium Polyacrylate and Mixed Micelles of

Dec 21, 2012 - Hsueh-Wen Tseng , Po-Chia Chen , Hung-Wei Tsui , Chieh-Hsiang ... Tianxiang Yin , Miao Qin , Yan Yang , Peizhu Zheng , Dashuang Fan ...
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Interactions between Sodium Polyacrylate and Mixed Micelles of Dodecyltrimethylammonium Bromide and Sodium Bis(2-ethylhexyl) Sulfosuccinate Peizhu Zheng,† Dongxing Cai,‡ Zhiguo Zhang,† Yan Yang,† Tianxiang Yin,† and Weiguo Shen*,†,‡ †

School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China

‡

ABSTRACT: The interactions between sodium polyacrylate (PANa) and mixed micelles of dodecyltrimethylammonium bromide (DTAB) and sodium bis(2-ethylhexyl) sulfosuccinate (AOT) were studied by isothermal titration calorimetry (ITC), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). It was found that the interaction mechanism varies with the titration order. For titration of PANa/AOT by DTAB, DTAB monomers first participate in the formation of AOT/DTAB mixed micelles, then bind to polymer individually, and subsequently result in the polymerinduced micellization characterized by two endothermic peaks. Only one endothermic peak was observed for titration of PANa by AOT/DTAB mixed micelle, corresponding to binding of the mixed micelles to the polymer. Exothermic peaks were observed for both types of titration characterizing the cross-link of the polymer chains. These interaction mechanisms were also interpreted by a thermodynamic model and confirmed by the measurements of SEM and TEM.

1. INTRODUCTION Interactions between polyelectrolytes and oppositely charged surfactants have attracted a great deal of attention due to their scientific interest and widespread applications.1−9 It has been known that various factors determine the type of organization of surfactant ions in conjunction with the charged polymer chains in aqueous solutions. The most important ones among them are (a) the charge of polyion,10−12 (b) the charge of the surfactant micelle,13,14 (c) the properties of the hydrophobic chains,15 and (d) the chemical nature of their ionizable groups.16 It was found that surfactant binds onto the polyelectrolytes through the electrostatic attraction after its concentration exceeds a so-called critical aggregation concentration (cac) and releases some counterions of the polyelectrolyte and the surfactant with the associated gain in entropy.17 The driving forces commonly make binding considerably more favorable than formation of the free micelle, as is illustrated by the fact that the cac is orders of magnitude below the critical micelle concentration (cmc). The interaction at such low bulk surfactant levels is often discussed in terms of the binding of individual surfactants. This binding may possibly be followed by the polymer-induced micellization at a certain concentration of the surfactant and finally stops at the second critical concentration C2, where the surfactant concentration reaches a value that the available polymer chains are completely saturated with the surfactants; thus, the additional surfactants are thought to form free micelles. Poly(acrylic acid) (PAA) is a weak polyelectrolyte and has surprisingly strong affinity with cationic surfactants. This © 2012 American Chemical Society

system has potential applications such as control of chemical reactivity, drug delivery, and nonspecific binding of DNA with basic protein and may be used as a simplified model for elucidating the behavior of biological systems.18,19 Extensive studies of linear sodium polyacrylate (PANa) have shown12,20−25 that the interaction between the polyion and the surfactant is chiefly electrostatic, and the flexible polyacrylate tends to collapse around a charged sphere resulting in the complex of low net charge. Wang and co-workers reported a series of calorimetric and light scattering results of the interactions in the PANa/dodecyltrimethylammonium bromide (DTAB) system19,26 and suggested that in the initial stage of the titration the cationic headgroups of the surfactant individually bound to the anionic carboxylate groups on the polymer chains due to electrostatic attraction; when the surfactant concentration reached a critical value, the micellization of polymer-induced surfactant occurred, resulting in the formation of insoluble polymer/surfactant complexes. The calorimetric measurements have confirmed that the electrostatic binding is an endothermic process driven by entropy, and the binding is postponed to higher surfactant concentrations in the presence of background electrolyte, serving to emphasize the dominating role of electrostatics. Similar results were found with methacrylic acid/ethyl acrylate copolymers.27 The phase behavior of the aqueous solutions of polyacrylate (or its copolymer) and the cationic surfactant has been investiReceived: April 19, 2012 Revised: October 6, 2012 Published: December 21, 2012 247

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gated,12,20,25,28−31 and it was found that when a charged surfactant was mixed with an oppositely charged polyelectrolyte, the two-phase region centered around 1:1 charge ratio of surfactant to polymer; remarkably, a one-phase region was reached again at high surfactant excess. It suggested that the principal factor governing coacervation or precipitation should be electroneutrality of the polyelectrolyte−micelle complexes. Fluorescence-probe and dye solubilization studies by Ananthapadmanabhan et al.32 suggested that the redissolution process could be considered as a micellar solubilization. Bereet et al. found that the amount of polyelectrolyte charges always exceeded that of opposite charged surfactants in the poly(acrylic acid)-b-poly(acrylamide)/DTAB complexes.33,34 Besides the electrostatic interaction, in an aqueous solution of polyelectrolyte and oppositely charged surfactant, the hydrophobic interaction between the polymer backbone and the alkyl tail of the surfactant is also important; both of the electrostatic and the hydrophobic interactions drive the selfassembly of surfactant molecules to form ordered structures inside the polymer/surfactant complex. Kabanov et al.35 proposed a lamellar structure for PANa gel−CnTAB complexes. Ilekti et al.21,28 found cubic, hexagonal, and lamellar phases in a phase diagram of stoichiometric complexes between PANa and cetyltrimethylammonium bromide (CTAB). A structure of face-centered cubic packing of undulated cylinders was proposed for the complex of PANa/DTAB by Antonietti.36 Hansson37 also found a cubic structure that fits with the space group Pm3n, which probably involves six micelles in a unit cell. A phase progression of Pm3n cubic ↔ hexagonally close-packed cylinders (hcpc) ↔ lamellar was observed as osmotic pressure and charge density were increased in the system of poly[(acrylate)-co-acrylamide]/cetyltrimethylammonium (PAAm/ CTA+) by Leonard et al.38 The actual resulting structure type (cubic, lamellar, or cylindrical and their coexistence) for such a polyelectrolyte−opposite surfactant complex was believed to be determined by the charge ratio, the spontaneous curvature of the surfactant on the interface, and several other factors related to the molecular geometry of both the surfactant and the polyelectrolyte.36,38−40 Dubin and co-workers41−46 studied the association behavior in the system of poly(diallyldimethylammonium chloride) (PDADMAC) and oppositely charged mixed micelles of sodium dodecyl sulfate (SDS) and polyoxyethylene tert-octyl phenyl ether (TX100). They demonstrated that the strength of electrostatic interaction between polyelectrolyte and oppositely charged surfactant can be attenuated by neutral surfactants TX100, and the interaction of them only takes place when the critical mole fraction of ionic surfactant in a mixed anionic/ nonionic micelle is reached, implying that the electrostatic potential is critical for binding the entire micelle to the polymer chain. To the best of our knowledge, all of the studies of polyelectrolytes and mixed surfactants are limited in the systems of ionic−nonionic mixed surfactants.18,47−51 It is known that the synergy is enhanced in mixtures of oppositely charged surfactants in which strong electrostatic interactions between the head groups alter the aggregation process and lead to new states of aggregation, which may affect the complex behaviors in a system of polyelectrolytes/mixed surfactants. In this paper, we examine the aggregation behaviors of the system of PANa/DTAB−sodium bis(2-ethylhexyl) sulfosuccinate (AOT) using isothermal titration microcalorimetry (ITC), scanning electron microscopy (SEM), and transmission

electron microscopy (TEM). Two types of titration experiments are performed with ITC to investigate the interaction mechanism, and the ITC results are further explained by a pseudophase model and evidenced by SEM and TEM measurements.

2. EXPERIMENTAL DETAILS 2.1. Materials. The polyelectrolyte used in this study is poly(acrylic acid) (PAA, 25% solution from Alfa Aesar Chemical Co.), which has an approximate average molecular weight of 2.58 × 105 determined by static light scattering measurements in our laboratory. The cationic surfactant and anionic surfactant are dodecyltrimethylammonium bromide (DTAB, from J&K Chemical LTD, ≥99% mass fraction) and sodium bis(2-ethylhexyl) sulfosuccinate (AOT, from Sigma, ≥99% mass fraction), respectively. Sodium bromide (NaBr, ≥99.0% mass fraction) and sodium hydroxide (NaOH, ≥96% mass fraction) are purchased from Sitong Chemical Company (Tianjin, China) and Tianjin Chemical Company (Tianjin, China), respectively. All materials were used without further purification. Twice distilled water was used in preparations of the samples. 2.2. Sample Preparation. To prepare a typical mixture of polyelectrolyte and NaBr, poly(acrylic acid) was first converted to sodium polyacrylate (PANa) by adding an appropriate amount of NaOH. Then NaBr was added, and the solution was diluted with water and stirred rigorously. The aim of addition of NaBr is to weaken the interaction between PANa and DTAB to obtain more interaction information. Finally, more NaOH was added to adjust pH of PANa/ NaBr solution to a value larger than 9 (about 9.7) to ensure almost complete ionization of PANa.11,26 The concentrations of the carboxylate groups and NaBr in the solution were 6.93 and 40.0 mM, respectively. 2.3. Isothermal Titration Microcalorimetry (ITC). The isothermal titration data were obtained by using the TAM 2277-201 microcalorimetric system (Thermometric AB, Järfäfla, Sweden), which has a 4 mL sample and reference cells. In study of the interactions between the polyelectrolyte and the mixed surfactants, the titrations were carried in two ways. In “type I” titrations, DTAB aqueous solution was added to 2.2 mL of AOT in NaBr solution or PANa/ AOT in NaBr solution with a certain AOT concentration. “Type II” titration corresponds to the addition of AOT/DTAB mixed micelles with a certain molar ratios to 2.2 mL NaBr solution with or without PANa. The stirring speed in the sample cell was set at 60 rpm, and the experiment temperature was 25.00 ± 0.02 °C. The values of the observed differential enthalpy (ΔHobs) for various concentrations of surfactants were obtained by the integral of the areas under the calorimetric peaks and normalized by the small amounts of injected surfactants. 2.4. Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). Each of the samples was prepared by adding a surfactant or mixed surfactant aqueous solution to a PANa in NaBr solution or PANa/AOT in NaBr solution under stirring condition. The stirring was continued for 2 h after white flocculates appeared, and then the sample was kept 3 days before the SEM experiment or 2 weeks before the TEM experiment. The flocculate complexes were examined by a JSM-6360LV SEM with an accelerating voltage of 15 kV. The measurements of the selected-area electron diffraction (SAED) were conducted with a Tecnai G2 F30 TEM operating at 300 kV.

3. RESULTS AND DISCUSSION 3.1. Interactions between PANa and Single Surfactant. Dilution Curves. We first determined the enthalpy curves (the plots of observed enthalpy ΔHobs vs the concentration of surfactant) titrating 70.0 mM DTAB and 14.0 mM AOT into 40.0 mM NaBr aqueous solutions, respectively, which are named as dilution curves and shown by the blank symbols in Figures 1a and 1b. Both the dilute curves have the sigmoid 248

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dilute one. As shown in Figure 1a, C1 is the onset of peak A where the binding curve and the dilution curve start to separate; C′ and C″ are the onsets of peaks B and C, respectively, and C2 is designated as the point where the binding curve starts to merge with the dilution curve. The critical concentrations are summarized in Table 1. As reported Table 1. Critical Concentrations for Titration of DTAB into PANa in NaBr Solution with Different AOT Concentrations CAOT (mM)

C1 (mM DTAB)

C′ (mM DTAB)

C″ (mM DTAB)

C2 (mM DTAB)

0 1.4 5.6 14.0

0.63 1.54 4.72 7.87

4.72 3.47 8.57 13.33

7.16 8.61 14.54

9.32 15.13 15.71

by Wang,26 peak A corresponds to the binding of the cationic headgroups of DTAB molecules to the negatively charged carboxylate sites along the polymer chains. As shown in Figure 1a, the value of ΔHobs starts to be larger than that of the dilute curve at the DTAB concentration being 0.63 mM and increases rapidly with further addition of DTAB, indicating that more and more amount of DTAB monomers bind onto the polymer. The peak B occurring at C′ (4.72 mM DTAB) corresponds to the micellization of DTAB molecules bound on the polymer chains. Although the bulk concentration of DTAB at C′ is below the cmc of DTAB in the solution without polymer, the local concentration of DTAB on the polymer chains is high enough to induce the micellization. Peak C is believed to represent the cross-link of the polymer chains, which releases the heat resulting in the enthalpy curve below the dilution one. When AOT was added into PANa in NaBr solution, it was found that the binding enthalpy curve significantly departs from the AOT dilution curve even if the AOT concentration is only 0.06 mM (see Figure 1b), indicating that the interaction of AOT and PANa is very strong. It may be explained that when a small amount of AOT is titrated into PANa in NaBr solution, the AOT micelles demicellize into monomers, and the monomers are adsorbed to the polymer chains immediately to form PANa/AOT complexes, resulting in large exothermic enthalpy. It is different from the binding mechanism of the formation of PANa/DTAB complexes; the latter absorbs large amount of heat and is assumed to occur through the entropydriven ion exchange. The enthalpy curve in PANa/AOT system is similar to that in hydrophobically modified poly(acrylamide) (HMPAM)/AOT system,54 where binding of AOT to the apolar segment of HMPAM is enthalpy favorable. The enthalpy-driven bindings are even observed in some polyelectrolyte/oppositely charged-surfactant systems such as bind of DTAB to PAA with a lower degree of neutralization19 and bind of AOT onto polycation poly(diallydimethylammonium chloride).9 The enthalpy increases with further addition of AOT into the polymer solution, but the change rate decreases since more AOT adsorbed to the polymer, the stronger electrostatic repulsion and steric hindrance between them, hindering the further adsorption and resulting in the increase of the amount of the AOT monomers in bulk solution. As the binding curve encounters the dilution curve at C, the value of ΔHobs reaches the maximum. Further addition of AOT causes the decrease of ΔHobs similar to the profile of the dilution curve, but the values of ΔHobs are significantly larger than that of the dilution curve, which may be explained by the formations

Figure 1. (a) Enthalpy changes for titrating 70.0 mM DTAB into NaBr solution (□) and PANa in NaBr solution (■). (b) Titrating 14.0 mM AOT into NaBr solution (○) and PANa in NaBr solution (●).

shapes with abrupt decreases at threshold concentrations corresponding to the micelle formations, allowing identifications of the critical micelle concentrations (cmc) by extrapolations of the initial portions and the rapidly decreasing portions of the curves. Meanwhile, each of the enthalpies of the micellization (ΔHmic ° ) can be determined from the difference of the ΔHobs between the two linear segments of the plot at the cmc.52,53 It was found that the values of ΔH°mic of AOT and DTAB are −2.16 and −2.67 kJ/mol, respectively, but the value of cmc for AOT is only 0.60 mM, nearly a tenth of that for DTAB (5.91 mM). It may be attributed to that the hydrophobicity of AOT is much stronger than DTAB; thus, AOT is more easily to form micelles. The nonzero enthalpy values of the dilution curves even at high concentrations of surfactants reflect the heats of mixing the aqueous solutions with the NaBr solutions, which show that the heat effect of mixing an AOT aqueous solution and a NaBr aqueous solution is much stronger than that of mixing a DTAB aqueous solution and a NaBr aqueous solution. Binding Curves. The enthalpy curve for titrating 70.0 mM DTAB or 14.0 mM AOT into the PANa in NaBr solution is named as the binding curve and shown by the filled symbols in Figures 1a and 1b, respectively. When DTAB was titrated into a PANa in NaBr solution, the enthalpy curve exhibited three peaks (see Figure 1a): two endothermic peaks A and B and one exothermic peak C. The two endothermic peaks A and B were detected by Wang et al.,26 but the exothermic peak C at higher DTAB concentration has never been reported. There are four critical points shown in Figure 1a which can be clearly identified by the comparison of the binding curve with the 249

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mM according to the previous investigations.9,55 When DTAB micelles are added into the solutions, the DTAB micelles disassociate into monomers, and then a part of them enters the AOT aggregates through the electrostatic attraction and forms AOT-rich mixed aggregates. For CAOT = 1.4 mM, as the concentration of DTAB monomers increasing close to the concentration of AOT, the electric charges neutralize each other to yield the precipitation, which results in an abrupt increase of enthalpy. With further increase of CDTAB, the precipitation is redissolved and the enthalpy levels off; finally the DTAB-rich mixed micelle forms. For CAOT = 5.6 mM, the enthalpy decreases initially with CDTAB, resulting from the participation of DTAB to form the AOT-rich vesicles, which are spheres with radius being about 110 nm detected by TEM. However, after CDTAB reaching about 2 mM, the enthalpy increases and the larger aggregates are detected, and then the precipitation appears when CDTAB reaches about 3.8 mM. Further addition of DTAB makes the enthalpy decrease, corresponding to the redissolution of the precipitation. The enthalpy then levels off, which suggests the formation of the DTAB-rich aggregates. When DTAB concentration reaches about 15.6 mM, the enthalpy increases slightly, possibly indicating the formation of the aggregates with different structures.56−58 For CAOT = 14.0 mM, the decrease of enthalpy continues until CDTAB reaches about 7 mM, corresponding to the participation of the added DTAB to form the AOT-rich aggregates. Further addition of DTAB makes the enthalpy increase and then level off at the DATB concentration being about 8 mM, where the precipitation emerges. The enthalpy increases again at the DTAB concentration being about 10.5 mM, representing the further aggregation of the partly neutralized mixed aggregates. When the concentration is larger than 14.5 mM, precipitation redissolution occurs. Binding Curves. Each of the binding curves in Figure 2 has two endothermic peaks A and B, and an exothermic peak C except for the sample with AOT concentration being 14.0 mM. The critical concentrations can be clearly identified as shown in Figure 2b, which are summarized in Table 1. Taking the system with the concentration of AOT being 5.6 mM as a sample, the binding curves may be divided into four regions as typically indicated in Figure 2b, and the turbidities and phase behaviors of some samples in the corresponding regions are shown in Figure 2d. In the first region, the concentration of DTAB is smaller than C1 (∼5 mM) and the binding curve coincides with the dilution curve, indicating that no interaction occurs between DTAB and PANa. When DTAB is added into the PANa/AOT in NaBr solution, the DTAB micelles demicellize into monomers, and a part of DTAB monomers stay in the bulk solution, while the others participate in the AOT/DTAB aggregates, and the solution corresponding to point a is translucent (see the bottle a in Figure 2d). The deviation of the binding curve from the dilution curve is found at C1 and the process enters region 2. In this region, first ΔHobs increases rapidly with DTAB concentration and then slows down to form peak A, and the solution become opaque (see the bottle b in Figure 2d), indicating that a significant amount of DTAB electrostatically bind to the PANa chains. The enthalpy increases sharply again with DTAB concentration when the concentration of DTAB reaches C′, where another endothermic peak B starts to be detected, which indicates that the bound surfactant molecules start to aggregate through hydrophobic interaction and form PANa/DTAB mixed micelles; the process enters region 3. In region 3, more and more mixed micelles are

of both the free AOT micelles and the PANa/AOT complexes. The binding enthalpy curve merges with the dilution curve at C2, suggesting that the polymer chains are fully saturated with surfactant molecules, and further addition of AOT only increases the concentration of the free AOT micelles. 3.2. Interactions between PANa and Mixed Surfactants. a. Titrating DTAB into PANa/AOT in NaBr Solutions (“Type I” Titrations). In these titrations, 70.0 mM DTAB was added to the AOT in NaBr solutions or PANa/AOT in NaBr solutions with the concentrations of AOT (CAOT) being 1.4, 5.6, and 14.0 mM. The plots of ΔHobs vs DTAB concentration (CDTAB) are shown in Figure 2, where the dilution curves are denoted by the blank symbols while the binding curves are denoted by the filled symbols.

Figure 2. Enthalpy changes for titrating 70.0 mM DTAB into PANa/ AOT in NaBr solution. (a) CAOT = 1.4 mM: (□) dilution curve, (■) binding curve; (b) CAOT = 5.6 mM: (○) dilution curve (●) binding curve; (c) CAOT = 14.0 mM: (△) dilute curve, (▲) binding curve. (d) The turbidities and phase behaviors of polymer/surfactant solutions with various DTAB concentrations denoted by letters corresponding to that in (b).

Dilution Curves. As shown in Figure 2, the shapes of the three dilution curves are different, and the natures of them depend on the mutual influence of AOT and DTAB. From the results above, it is known that the concentrations of AOT in the sample cells for the three titrations are all above its cmc in 40.0 mM NaBr aqueous solutions; thus, AOT aggregates and AOT monomers are coexistent in the solutions. AOT vesicles are possibly formed in the samples with CAOT being 5.6 and 14.0 250

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Figure 3. SEM images of the flocculates in the samples corresponding to the points of the “type I” titration curve in Figure 2b; (a) point d, (b) point e, inset shows a magnified view, (c) point f, (d) point f after being kept at 4 °C for 3 months.

Figure 4. Binding mechanism and structure change of polymer/surfactant complexes in “type I” titration.

form large-size clusters, and thus more flocculates may be observed (see the bottle e in Figure 2d) due to neutralization. However, the large-size clusters may be destructed and partly unfolded after more positive charged DTAB is added. Finally, the binding curve coincides with the dilute one at the end of region 4, indicating that the polymer chains are saturated. The solution becomes cloudy again (see the bottle f in Figure 2d), which suggests that the added DTAB participate in redissolution of the flocculates by reorganizing the complexes and unfolding the cross-links of the different polymer chains to yield a larger amount but smaller sized particles in the solution.

produced; thus, ΔHobs increases with DTAB concentration and then levels off; the solutions become more and more opaque (see the bottle c in Figure 2d). Finally ΔHobs turns to decrease and approaches the dilution curve. When CDTAB reaches a certain concentration, the opaque solution becomes clear, but some PANa/DTAB mixed micelles aggregate to form the flocculates suspending on the surface of solution (see the bottle d in Figure 2d). As DTAB concentration increases to C″, an exothermic peak C appears, and the process enters region 4. The exothermic peak C may be explained by that a large amount of polymer chains bound with micelles cross-link to 251

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SEM Measurements. To further insight into the transformation of morphology of the polymer/surfactant complexes before and after peak C in Figure 2, the SEM measurements were carried out. Figure 3a shows a SEM image of the flocculate sample corresponding to the point d of the enthalpy curve in Figure 2b. As can be seen from Figure 3a, the particles have fractal dendritic structures. The individual dendrite consists of a long central trunk with relatively short secondary and tertiary sharp branches. The morphology of the flocculate sample at point e (the minimum of peak C) in Figure 2b is shown in Figure 3b, which seems to be an assembly of the fractal dendrites with the large-scale reticular structure, corresponding to the cross-link of the polymer chains. The inset to Figure 3b shows a magnified image of a dendrite, in which both the trunks and the side branches appear to comprise of grainy clusters, which is believed to be composed of polymer/surfactant complexes. Each branch is parallel to each other in the same plane and perpendicular to the trunk. Figure 3c shows the morphology of the flocculates in the sample with the concentration represented by point f of the titration curve in Figure 2b, in which the dendrite arms split along the direction of tip propagation and grow in a disorderly fashion like seaweed growth. This may be caused by unfolding of the polymer chains. The reticular structure of the fractal dendrites was reorganized, and the fractal dendritic structure was slowly recovered. Figure 3d shows the morphology of the sample at point f after being kept at 4 °C for 3 months; the seaweed growth changes to the fractal dendritic structure like that in Figure 3a but with larger scale, which illustrates that the reorganization is very slow. From the above discussion, the binding mechanism and structural change of polymer/surfactant complexes in “type I” titration are deduced, which are illustrated in Figure 4. Thermodynamic Model. As seen in Table 1, the critical concentrations increase with AOT concentrations, which may be interpreted by that the more AOT are, the more DTAB interact with them and only DTAB monomers may bind to PANa through the electrostatic attraction. This interpretation was rechecked by four simple titration measurements where two NaBr solutions with or without PANa, and two AOT in NaBr solutions with or without PANa were titrated by 5.0 mM DTAB aqueous solution, respectively, instead of 70.0 mM one to ensure that no pure DTAB micelles existed in the system. Comparison of the titrations of NaBr solution and PANa in NaBr solutions with 5.0 mM DTAB gave the value of 0.66 mM for C1, which was consistent with 0.63 mM obtained from the titrations with 70.0 mM DTAB. However, in the case of the titrations of AOT in NaBr solutions with and without PANa by 5.0 mM DTAB, C1 was failed to be detected, which may be reasonably attributed to that the significant amount of the added DTAB participated in AOT/DTAB mixed micelles, and thus the concentration of the free DTAB in the solution was lower than the requirement for start to bind it to the polymer. To further examine this explanation and understand how the concentration of AOT affects the interactions in PANa/AOT/ DTAB system, a pseudophase model was used to analyze the experimental results. As discussed above, before the concentration of DTAB reaches point C1, there exists the equilibrium of DTAB between water phase and AOT/DTAB mixed micelle phase; this equilibrium can be thermodynamically characterized by aq mic μDTAB = μDTAB

⎛ C aq ⎞ aq aq * μDTAB = μDTAB + RT ln⎜ DTAB ⎟ ⎝ S ⎠

(2)

⎛ C mic ⎞ mic mic * ⎟ μDTAB = μDTAB + RT ln⎜ DTAB mic ⎝ CAOT ⎠

(3)

where μaq * and μmic * are the chemical potentials when the DTAB DTAB mic mic concentration variables Caq DTAB/S and CDTAB/CAOT equal to 1, and DTAB in the bulk solution and in the surfactant mixture mic has the behavior in an ideal dilute solution; Caq DTAB, CDTAB, and mic CAOT are the concentrations of DTAB in the water phase, the micelle phase, and AOT in the micelle phase, respectively; S = 1 mM is used to normalize the concentration Caq DTAB. Because the cmc of the mixed micelles is very low, we neglected the existence of the AOT monomers in the water phase and on the polymer; thus, concentration of AOT in the micelle phase Cmic AOT can be substituted by the total concentration of AOT (CAOT) in the system. Combination of eqs 1−3 gives mic ⎡ μ aq * − μ mic * ⎤ C DTAB /CAOT DTAB ⎥ ⎢ DTAB exp = = K1 aq C DTAB /S RT ⎢⎣ ⎥⎦

(4)

where K1 is the equilibrium constant for the equilibrium of DTAB between water phase and AOT/DTAB mixed micelle phase; thus, Cmic DTAB is expressed by mic aq C DTAB = K1CAOTC DTAB /S

(5)

The total concentration of DTAB (CDTAB) in the system can be written as aq mic aq aq C DTAB = C DTAB + C DTAB = C DTAB + K1CAOTC DTAB /S

(6)

Assuming that as the concentration of DTAB in the water phase reaches a certain value at point C1, the binding of DTAB monomers to the polymer immediately occurs; a plot of CDTAB vs CAOT at point C1 yields a straight line as shown in Figure 5a. A linear least-squares fit gives the slope aC1 = 0.57 and the intercept bC1 = 0.94, respectively, from which K1 was calculated to be 0.61 according to eq 6. When the total concentration of DTAB is above C1, a significant amount of DTAB bound to the polymer; therefore, one more equilibrium exists in the system, and the phase equilibriums can be characterized by poly aq mic μDTAB = μDTAB = μDTAB

(7)

with ⎛ C poly ⎞ poly poly * μDTAB = μDTAB + RT ln⎜⎜ DTAB ⎟⎟ ⎝ Cpoly ⎠

(8)

where μpoly DTAB is the chemical potential of DTAB bound on the polymer, μpoly * is the chemical potential when the concenDTAB tration variable Cpoly DTAB/Cpoly equals 1 and the DTAB on the polymer surface has the behavior in an ideal dilute solution, and Cpoly DTAB and Cpoly are the concentrations of DTAB bound on the polymer and the carboxylate groups of the polymer in the system, respectively. Substituting eq 8 into eq 7 gives

(1) 252

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with the value of 2.21 obtained at C′, while the latter characterizes the extent of the neutralization of the opposite charges which causes the cross-link of the polymer chains. We used the same method to calculate K2 and Cpoly DTAB/Cpoly at the point of the minimum of peak C (Cmin), the values of which are 2.14 and 0.77, respectively. poly poly The values of Caq DTAB, CDTAB, CDTAB/Cpoly, K1, and K2 at critical points C1, C′, C″, and Cmin are summarized in Table 2. poly poly Table 2. Values of Caq DTAB, CDTAB, CDTAB/Cpoly, K1, and K2 at Critical Points C1, C′, C″, and Cmin Calculated by the Pseudophase Model

Figure 5. Plots of CDTAB vs CAOT at points (a) C1, (b) C′, and (c) C″. The dots are the experimental results, and the lines represent the leastsquares fits. mic C DTAB /CAOT poly C DTAB /Cpoly

⎡ μ poly * − μ mic * ⎤ DTAB ⎥ = exp⎢ DTAB = K2 RT ⎢⎣ ⎥⎦

(9)

(10)

The total concentration of DTAB in the system can be written as aq poly mic aq poly C DTAB = C DTAB + C DTAB + C DTAB = C DTAB + C DTAB poly + K 2CAOTC DTAB /Cpoly

Caq DTAB (mM)

C1 C′ C″ Cmin

0.94 1.40 2.80 2.73

Cpoly DTAB (mM)

Cpoly DTAB/Cpoly

K1

K2

0.61 2.38 4.09 4.55

0.38 0.69 0.77

2.21 2.45 2.14

As shown in Table 2, K2 is confirmed to be a constant independent of the concentrations in the system; the amount of DTAB bound to polymer and the ratio of Cpoly DTAB/Cpoly increases in the titration process. It was observed that the maximum amount of flocculates appears at Cmin, where it was commonly accepted that the opposite charges completely neutralize each other, but the ratio of positive charge to negative charge in the system is about 1.5 in our investigations, and the value of Cpoly DTAB/Cpoly is only 0.77 as listed in Table 2, both of which are significantly departures from 1 but consists with the result reported by Bereet.34 b. Titrating AOT/DTAB into PANa in NaBr Solution (“Type II” Titrations). In “type II” titrations, PANa in NaBr solutions was titrated by AOT/DTAB mixed micelles, in which the concentration of DTAB is 70.0 mM, while the concentration of AOT is 3.5, 7.0, and 14.0 mM for each of the three individual titrations. The observed enthalpy is plotted vs the total concentration of the surfactant (Cst) as the binding curves for each of the three titrations and shown in Figure 6, and the dilution curves are also presented in Figure 6 for comparisons. Dilution Curves. The dilution curves are shown in Figure 6 denoted by the blank symbols for the three titrations. The abrupt changes of ΔHobs in the initiate parts of the two titration curves with AOT concentrations being 3.5 and 7.0 mM are detectable, and the corresponding points may be determined as first critical micelle concentration (cmc1); however, for the sample with AOT concentration being 14.0 mM, ΔHobs decreases continuously from the first titration point, indicating that the mixed micelles are formed at very low concentration (cmc1 is less than 0.38 mM). The second critical micelle concentrations (cmc2) were detected to be 7.40 and 14.46 mM for the samples with the concentrations of AOT being 3.5 and 14.0 mM, respectively, indicating that the mixed micelles change to other modality.57,58 It is worth to note that ΔHobs at the beginning of the three titration curves increases from 1 to 2 kJ/mol as the concentration of AOT in the system increases from 3.5 to 14.0 mM, which indicates that addition of AOT enhances the stability of the micelles. The dependence of the critical concentration Cm of an ideal mixture of two surfactants on their individual critical concentrations Cm1 and Cm2 of the two pure surfactants can be expressed in terms of Clint’s equation59

with K2 being the equilibrium constant for the equilibrium of DTAB between polymer phase and AOT/DTAB mixed micelle phase, and thus mic poly C DTAB = K 2CAOTC DTAB /Cpoly

critical points

(11)

At various critical points, the volumes of the systems with different CAOT were not exactly the same in our titration experiment, and the values of Cpoly and Cpoly DTAB varied slightly with CAOT. However, the difference was estimated to be less than 5% and will be ignored in the following discussion. Assuming that the concentration variable Cpoly DTAB/Cpoly reaches a certain value at points C′, the polymer-induced micellization immediately occurs; a plot of CDTAB vs CAOT at point C′ yields a straight line as shown in Figure 5b. A linear least-squares fit gives the slope aC′ = 0.85 and the intercept bC′ = 3.78. The combination of eqs 5 and 10 gives Caq DTAB = aC′S/K1 and then Cpoly DTAB = bC′ − aC′S/K1, which allow us to calculate K2 and poly Cpoly DTAB/Cpoly at C′. We obtained K2 = 2.21 and CDTAB/Cpoly = 0.38 at which the polymer/surfactant mixed micelles formed. When the total concentration of DTAB reaches C″, the cross-link of polymer chains occurs. A plot of CDTAB vs CAOT at point C″ for different AOT concentrations yields a straight line as shown in Figure 5c. A linear least-squares fit gives the slope aC″ = 1.70 and the intercept bC″ = 6.89. The values of aC″ and bC″ allow us to estimate the total concentration of DTAB, at which the cross-link of the polymer chains would occur for the system with the AOT concentration being 14.0 mM. This total concentration was found to be about 22.88 mM, which is over our experimental range; thus, the absence of an exothermic peak C in Figure 2c is not surprising. The values of aC″ and bC″ were used to calculate K2 and Cpoly DTAB/Cpoly at C″ and found to be 2.45 and 0.69, respectively. The former is in good agreement 253

dx.doi.org/10.1021/ma300793m | Macromolecules 2013, 46, 247−256

Macromolecules

Article

in a very lower value of cmc; thus, before the DTAB monomer reaches its critical binding concentration, the DTAB-rich AOT/ DTAB mixed micelles are formed first and directly bind to the polymer chains. This is the reason why each of the binding curves of “type II” titrations only exhibits one endothermic peak. In “type II” titrations, the binding curve and dilution curve for each of the three titrations are close to each other at the first titration point; then the binding curve departs from the dilution one rapidly, and the solutions display slight milk-white, indicating the formation of the PANa/AOT/DTAB complexes. Further addition of the mixed micelles, the enthalpy increases first, then levels off, and decreases subsequently; the milkywhite color of the solution becomes more and more intense, indicating that the concentration of PANa/AOT/DTAB complexes continuously increases. At the onsets C″ of the exothermic peaks B of the binding curves in Figures 6a and 6b, corresponding to the total concentrations of the surfactants being 9.54 and 10.26 mM, respectively; the flocculates were found for both of the binding curves, and thus the exothermic peaks may be attributed to the formation of the flocculates resulted from the partly cross-linking of the polymer chains due to the neutralization of the opposite charges. The flocculates were also found at the total concentration being 12.09 mM for the titration with the concentration ratio of AOT to DTAB being 14:70 shown in Figure 6c; however, the exothermic peak was not detected. It may be interpreted by that the exothermic peak was possibly hided by the heat effects from the formations of PANa/AOT/DTAB complexes and free micelles. It was found that the concentration of DTAB at which the flocculates form increases linearly with the concentration of AOT, which demonstrates that AOT suspends the cross-link of the polymer chains because it neutralized the opposite charges of DTAB. As the mixed surfactants are further added, the binding curve merges with the dilution curve at C2; however, it was found that addition of more surfactants results in the redissolution of the flocculates. The SEM image of PANa/AOT/DTAB complexes corresponding to point a of the binding curve in Figure 6c is shown in Figure 7, which reveals the irregular branched morphology, but the dendrite has no obvious main trunk. It may be interpreted by that the existence of a significant amount of AOT in the mixed micelles plays a role of the impurity which leads to a sequential deflection of the tips of growing dendrites and displays a disordered growth in the orientation.60

Figure 6. Enthalpy changes for titrating AOT/DTAB mixed micelles into PANa in NaBr solutions. The mixed micelles have the molar ratios of CAOT:CDTAB: (a) 3.5:70 (□) dilution curve, (■) binding curve; (b) 7:70 (○) dilution curve (●) binding curve; (c) 14:70 (△) dilute curve, (▲) binding curve. Insets show magnified views of the dilution curves.

1 α 1−α = + Cm Cm1 Cm2

(12)

where α is the mole fraction of AOT in the mixture. The values of Cm for the mixed surfactant AOT/DTAB were calculated by eq 12 and are compared with the measured values of cmc1 in Table 3. Table 3. Values of Cmc for AOT/DTAB Mixed Surfactant Systems at 298.15 K CAOT (mM):CDTAB (mM)

Cm (mM)

cmc1 (mM)

cmc2 (mM)

3.5:70 7:70 14:70

4.15 3.27 2.38

1.47 1.03