Modulation of PolyelectrolyteâMicelle Interactions via Zeta Potentials

Article pubs.acs.org/Macromolecules

Modulation of Polyelectrolyte−Micelle Interactions via Zeta Potentials Yaxun Fan,*,†,§ Matthias Kellermeier,‡ Amy Y. Xu,† Volodymyr Boyko,‡ Sebastian Mirtschin,‡ and Paul L. Dubin*,† †

Department of Chemistry, University of Massachusetts at Amherst, Amherst, Massachusetts 01003, United States Advanced Materials and Systems Research, BASF SE, Carl-Bosch-Str. 38, D-67056 Ludwigshafen, Germany § Key Laboratory of Colloid and Interface Science, Beijing National Laboratory for Molecular Sciences (BNLMS), Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China ‡

S Supporting Information *

ABSTRACT: The onset of soluble complex formation between polycations and nonionic/anionic mixed micelles was found to occur at well-defined micelle surface charge density, σc, which could be modulated via Y, the mole fraction of anionic surfactant in the mixed micelle. Critical values of Y were detected by precision turbidimetry for two polycations, each combined with any of the four mixed micelles formed from two anionic and two nonionic surfactants. The values of Yc observed for each of the resultant eight ternary polycation/ anionic−nonionic combinations were used as surrogates for polycation binding affinity: for a given polycation and a given value of Y, micelles with Yc < Y will bind, while those with Yc > Y will not. The polycation affinity of micelles correlated with their “zeta potentials” (ζ), measured by electrophoretic light scattering, and their average surface potentials (ψ0), measured by potentiometric titration of a comicellized probe. For a given polycation at a fixed ionic strength, we found that the critical zeta potential (ζc) measured at Yc was independent of the surfactant pair chosen. This potential at the micelle “shear plane” is thus interpreted as the potential experienced by a bound polycation. The binding affinity was furthermore found to be stronger for polycations with higher linear charge density as well as for micelles with higher axial ratio, attributed respectively to an increase in the number of micelle-bound charged polycation repeat units and to the higher surface potential for micelles with lower surface curvature.

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INTRODUCTION

presence and nature of charges on the polymer and the surfactant; and (3) the presence or absence of (nonionic) cosurfactants. When polymer and at least one surfactant carry opposite charge, the dominance of electrostatic forces is evident. However, an important distinction must be made between long-range interactions involving ionic micelles and the “ion pairing” of polyelectrolytes (PE) to oppositely charged surfactant monomers, which may be cooperative through hydrophobic surfactant−surfactant effects.10−13 The latter, however, is essentially irrelevant when the overall surfactant concentration is very large compared to the CMC. Thus, while systems involving ionic surfactants and oppositely charged polyelectrolytes in general often show complex phase (separation) behavior, especially at low salt and above the CMC,5,14−16 it is of great importance to avoid conflating micelle−PE systems with systems below the CMC.

Given the breadth of applications for polymer−surfactant systems in e.g. laundry, personal care, coatings, electronics, and pharmaceutics,1−4 it is not surprising that the large number of polymers and surfactants formulated in multiple combinations1−8 can lead to properties and phase behavior difficult to predict from molecular structures alone. The self-assembly of such systems, capable of forming many different phases with a variety of structures,5−9 has been an ongoing subject of recent investigations. Because of the variety of states for the surfactant alone, the range of relevant interactions is extensive and dependent on chemical structures, so that the techniques applied and the questions raised largely depend on the type of system. The vast literatures on polymer−surfactant systems can be classified with respect to the types of interactions between the two species according to the following aspects: (1) surfactant concentration, which determines whether the polymer is interacting with micelles or surfactant monomers (depending on the critical micellization concentration, CMC); (2) the © XXXX American Chemical Society

Received: March 18, 2017 Revised: June 13, 2017

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DOI: 10.1021/acs.macromol.7b00584 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

etry. Thus, the nonionic surfactants did not suppress association but rather solubilized precipitates. Furthermore, equilibria involving free surfactant monomers, mixed micelles, and complexes of surfactant monomers with polyelectrolytes all had to be considered; this was also the case for systems investigated by Miguel and co-workers.28 Schillén et al.9,15 studied the interaction of nonionic surfactant micelles with counterion-free complex salts of hexadecyltrimethylammonium (C16TA+) and polyacrylate (PA−). They obtained thermodynamically stable solutions of the polyanion/mixed surfactant nanoassemblies in equilibrium with nonionic surfactant micelles and free uncharged surfactant monomers. Resolubilization was explained by the enhanced hydrophilicity of polymer/surfactant nanoassemblies in contrast to the insoluble complex stoichiometric salt in the absence of nonionic surfactant. Ternary systems including mixtures of anionic and cationic surfactants were studied by Shen and co-workers.29 All these studies are in contrast to the present work, in which bulk surfactant concentrations always exceed the CMC of the mixed micelles by a factor of 100 or more, so that surfactant monomer activities are negligible. As a result, the PDADMAC/SDS/TX100 system is dominated by interactions between mixed micelles and polycations. It appears to be one of the few in which micelle surface potential and/or polyelectrolyte linear charge density has been quantitatively related to micelle− polyelectrolyte binding affinity.21,30 The use of PDADMAC appears to be particularly advantageous because it (1) is “quenched”, i.e., not pH-dependent; (2) is commercially available over a range of molecular weights; (3) is not hydrophobic by any known criterion; and (4) has a charge spacing of 0.7 nm (the Bjerrum length in water), which empirically appears to facilitate coacervation as opposed to precipitation.20,21 The PDADMAC/SDS/TX-100 system has served as a “reference system” providing a foundation for similar studies exploring effects of e.g. polymer persistence length,31 micelle shape and size,32 and chemical structure of the nonionic surfactant.33 This system is a paradigm not in the sense of “typical”, but rather as a model demonstrating multiple phase transitionswhich exist but may not be equally well resolved in other polyelectrolyte/mixed micelle systems. Indeed, a much broader variety of polymer−surfactant systems can be imagined. In order to test the broad relevance of the “reference” system, we chose here as a comparison a commercially relevant system, in which all three components differed strongly from those in the reference system: thus, PDADMAC, SDS, and TX-100 are replaced by respectively poly(2-methacryloxyethyltrimethylammonium chloride) (PTMAEMC), sodium dodecyl dioxyethyl ether sulfate (SLE2S), and undecaoxyethyltridecyl ether (C13E11). In order to understand the roles of the three components, we investigated all eight possible combinations of polycation and anionic and nonionic surfactants. Our goal was to identify differences in micelle−polyelectrolyte affinity and relate these to the corresponding molecular structures of the two polyelectrolytes and four surfactants. To that end, we characterized the phase behavior of the ternary systems by turbidimetric titrations, analyzed the size and shape of the several mixed micelles via dynamic light scattering, and measured their surface potentials by means of potentiometric titration and electrophoresis.

Given the many variables in polyelectrolyte−micelle systems beyond the chemical nature of polyelectrolyte and surfactants (e.g., PE molecular weight and chain stiffness, surfactant:PE stoichiometry, micelle composition, ionic strength, and temperature), we previously performed systematic variations within one particular system where all those other parameters could be adjusted.17−22 That work focused on the ternary system comprising the strong (“quenched”) polycation poly(diallyldimethylammonium chloride) (PDADMAC) and oppositely charged nonionic/anionic mixed micelles formed from Triton X-100 (TX-100) and sodium dodecyl sulfate (SDS). A wide range of studies using turbidimetry,17,20−22 dynamic and static light scattering,20,21 viscosimetry,23 and electrophoretic light scattering20 revealed a progression of several states corresponding to the following evolution of micelle−polycation interactions with increasing mole fractions of anionic surfactant in the mixed micelles (Y) leading to (A) noninteracting solution of free micelles and polyelectrolyte, (B) soluble PE− micelle complexes, (C) liquid−liquid phase separation (coacervation), (D) redissolution of coacervate, and (E) liquid−solid phase separation (precipitation). In contrast to the B → C and C → D transitions, the A → B transition (occurring at critical mixed micelle composition, Yc) depends solely on ionic strength (not subject to mass action). In contrast, coacervation is dependent on polyelectrolyte−micelle stoichiometry and is exquisitely sensitive to temperature,17 while the process of precipitation for the micelle−polyelectrolyte system is the least well understood. While not directly affecting the micelle−PE affinity, the bulk ratio of surfactant and PE controls the microscopic stoichiometry (mixed micelles bound per PDADMAC chain) and hence the overall charge of the polyelectrolyte−micelle intrapolymer complex, which in turn controls intercomplex association and consequent phase separation. The latter process is also influenced by PE molecular weight, with larger polymers enhancing intercomplex association and consequently expanding the coacervate regime. The main subject of the present work, however, is micelle−PE affinity, which may be viewed as the resistance of micelle−PE complexes at a given Y to dissociation by an increase in salt concentration I. Alternatively, it may be considered as the resistance to complex dissociation at fixed I by the addition of nonionic surfactant. Thus, micelles with high PE affinity can be defined as those having low Yc values. Before adopting the conclusions from refs 17−20 as a general framework for other polyelectrolyte−colloid systems, it is necessary to question the broad relevance of that work to the closely related systems with different polyelectrolyte and surfactant combinations, in particular establishing a consistent interpretation of Yc. Deviations from the behavior of the PDADMAC/SDS/TX100 “reference system” would refine our understanding of related systems. Among the relatively few papers on polymer−mixed surfactant systems are several that reflect different viewpoints due to (1) the nonequilibrium behavior observed if the sequence of addition results in precipitation at some stage of mixing and (2) the variation of the chemical potentials of the two surfactants if the system is below CMC. For example, Mészáros and co-workers24−27 investigated the effect of the nonionics n-dodecyl-β-D-maltoside (C12G2) and n-dodecylhexaethylene glycol (C12E6) on the association of PDADMAC and SDS in the dilute surfactant regime. The initial binding of monomeric anionic surfactant to polycation led to soluble or insoluble species depending on surfactant−polymer stoichiomB


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Figure 1. Chemical structures of the polycations (PDADMAC and PTMAEMC), anionic surfactants (SDS and SLE2S), and nonionic surfactants (TX-100 and C13E11) used in this work.

Figure 2. (a) Turbidity of the PDADMAC/SDS/TX-100 system as a function of Y in 0.40 M NaCl. (b) Plots of the derivative define transition points with greater precision for Yc and Yφ1. The definition of Yp is problematic when precipitation and coacervation regions overlap (vide inf ra). Inset is the determination of the Yc from both turbidity (black) and DLS (red) results.

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nonionic surfactant (i.e., TX-100 or C13E11) and 0.4 M NaCl, with an initial polymer concentration of 1 g/L. In this way, the solution was adjusted to different mole fractions of anionic surfactant in the mixed micelles, Y, defined as

EXPERIMENTAL SECTION

Materials. Commercial samples of poly(2-methacryloxyethyltrimethylammonium chloride), sodium dodecyl dioxyethyl ether sulfate, and undecaoxyethyltridecyl ether (abbreviated as PTMAEMC, SLE2S, and C13E11) were provided by BASF SE (Germany). Poly(diallyldimethylammonium chloride) (PDADMAC) was prepared by free radical aqueous polymerization of diallylmethylammonium chloride.34 The weight-average molecular weight (Mw) of PTMAEMC was determined by gel permeation chromatography as 1.0 × 105 Da; the PDADMAC sample had a Mw of 7.0 × 105 Da (from static light scattering) and a number-average molecular weight (Mn) of 4.6 × 105 Da (from osmometry). Triton X-100 (TX-100) and sodium dodecyl sulfate (SDS) (purity > 99%) were purchased from Aldrich. NaCl was obtained from Fisher. The molecular structures of the components used in this study are shown in Figure 1. All of them were used without further purification. All solutions were prepared with Milli-Q water. Turbidimetric Titrations. High-precision turbidimetric titrations were carried out by adding 60 mM anionic surfactant (i.e., SDS or SLE2S) in 0.40 M NaCl under continuous stirring to solutions of cationic polymer (i.e., PDADMAC or PTMAEMC) in 20 mM

Y=

[anionic surfactant] [anionic surfactant] + [nonionic surfactant]

Note that Y is proportional to the average mixed micelle surface charge density. Turbidity, reported as 100 − %T (linear with τ = −ln Abs at % T > 80), was measured using a Brinkmann PC 800 colorimeter (λ = 420 nm) equipped with a 2.0 cm path length fiber-optics probe. Turbidity values were recorded when the meter response was constant for 2 min at room temperature, although equilibrium was attained in less than 10 s in the absence of macroscopic phase separation. Duplicate titrations gave reproducible results. Dynamic Light Scattering (DLS) and Zeta Potential Measurements. DLS and zeta potential (ζ) measurements were carried out on solutions of polycations and anionic/nonionic mixed micelles after filtration (Millipore, 0.22 μm) using a Malvern Instruments Zetasizer Nano ZS system, which was equipped with a 633 nm He−Ne laser and operated at a scattering angle of 173° and a C


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Figure 3. Turbidimetric titrations for the eight possible combinations of four mixed micelles (SDS/TX-100, SLE2S/TX-100, SDS/C13E11, and SLE2S/C13E11) and two polycations (PDADMAC and PTMAEMC). Each pair in (A) represents a given type of mixed micelle; each set of four curves in (B) represent a given polycation. temperature of 25 °C. The measurement duration was 10−12 s. Distributions of the mean apparent translational diffusion coefficients (D) were determined by fitting the DLS autocorrelation functions using non-negative constrained least-squares (NNLS). Apparent hydrodynamic radii Rh were obtained from the diffusion coefficients via the Stokes−Einstein relation

R h = kT /6πηD

radius a. Since the Zetasizer performs both electrophoretic and dynamic light scattering, a is obtained directly as the hydrodynamic radius (Rh). For samples with electrokinetic properties between the Smoluchowsi and Hückel limits of f(κa) = 1.5 and 1, respectively, the Ohshima equation was used to calculate intermediate f(κa) values.35 Potentiometric Titrations. The micelle surface potential was obtained using atitratable probe according to a procedure described elsewhere.36 Dodecanoic acid, C11COOH, was used as a micellesolubilized probe at a molar ratio of 1:20 with respect to 20 mM nonionic surfactant. pH titrations were performed in polymer-free solutions of varying Y using a temperature-compensated Orion 811 pH meter and a model 91-00-02 combination electrode. To determine the apparent and the intrinsic dissociation constant (pKa and pK0) of the micelle-solubilized probe, the relationship between pH and the degree of ionization (α) of the C11COOH probe was measured in nonionic surfactant solutions with and without anionic surfactant. Because of the low solubility of the carboxylic acid form, C11COONa was added

(1)

where k is the Boltzmann constant, T is the absolute temperature, and η is the solvent viscosity, here approximated as that of water. ζ was calculated from the mobility μ0 measured with the same instrument in the electrophoretic light scattering (ELS) mode using

μ0 = 2εζf (κa)/3η

(2)

where ε and η are taken as the dielectric constant and viscosity of pure water, respectively, and f(κa) is the Henry’s function with the Debye− Hückel parameter κ (reciprocal length) and the particle (micelle) D


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Macromolecules to the other components at pH 11 and 40 °C. After complete dissolution, the solution was cooled and titrated at room temperature with 0.500 N HCl. Inflection points in the titration curve were observed at α = 1 and α = 0.31,36 The mean value of pH + log[(1 − α)/α] between α = 0.2 and α = 0.8 was used to determine pKa (pK0 in the case of SDS-free solutions). The surface potential of the mixed micelles, ψ0, was then calculated via pK a − pK 0 = − 0.434eψ0/kT

procedures of Figure 2 to the plots in Figure 3 leads to the values of Yc, Yφ, and Yp assembled in Table 1. Yφ here Table 1. Critical Conditions for Systems Based on Two Different Polyelectrolytes (PDADMAC or PTMAEMC) and Four Different Types of Mixed Micelles (SDS/TX-100, SLE2S/TX-100, SDS/C13E11, and SLE2S/C13E11)a

(3)

where kT/e = 25.6 mV at 24 °C.

PDADMAC

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RESULTS AND DISCUSSION The turbidimetric titration curve for the reference system PDADMAC/SDS/TX-100, as shown in Figure 2, discloses five regions with respect to micelle surface charge density: (1) noninteracting solution at low Y < Yc, followed by (2) the formation of soluble complexes with positive net charge at Yc ≤ Y ≤ Yφ1; (3) biphasic liquid−liquid state (coacervate) at Yφ1 ≤ Y ≤ Yφ2; (4) redissolved soluble complexes of negative net charge at Yφ2 ≤ Y < Yp; and (5) dense biphasic state (precipitate) at Y ≥ Yp. For the reference system these stages have been characterized by multiple techniques.17,20,21 However, in the other PE−micelle system here, overlap of coacervation and precipitation regions (see Figure 3B), also observed visually, complicates precise identification of Yp, which is reported here with appropriate caution. The possible coexistence of fluids and solids in region 5 is the subject of a separate study.37 Yc, the critical mole fraction where soluble complexes start to form, corresponds to the first change in dτ/dY (τ = 100 − %T) and can be determined with high precision and reproducibly to ±0.02 units of Y, equivalent to the theoretical critical colloid surface charge density for polyelectrolyte binding. The slope dτ/dY is essentially zero at Y < Yc, suggesting that complex formation may be a first-order phase transition, as supported by theoretical studies on polyelectrolytes interacting with oppositely charged surfaces.38 In contrast to other transitions, Yc depends exclusively on ionic strength (i.e., it is not subject to mass action) for any given mixed micelle/polyelectrolyte system.20 Dependence on other variables is however seen for subsequent events beyond Yc where micelle:PE stoichiometry becomes important. At Yφ1, soluble complexesinitially positively charged due to a deficiency of bound anionic micellesapproach charge neutrality and form a coacervate, with an abrupt (and reversible) change in turbidity consistent with a true first-order liquid−liquid phase transition. The subsequent maximum in turbidity corresponds to (on average) charge-neutral complexes,20,21 the solubility of which is influenced by factors like surfactant:polymer stoichiometry and polymer molecular weight.17 The following drop in turbidity coincides with coacervate redissolution at Yφ2, yielding soluble complexes of net-negative charge. This stage is followed by a second phase separation process at Yp. The nature of this second dense phase can be complicated37,39 and is the subject of parallel investigation. Here, however, we focus on two different polycations, and the polycation binding affinity of a series of mixed micelles, which is mainly reflected in the Yc parameter. Figure 3 shows the results of turbidimetric titrations for all eight possible combinations of the two polymers and four mixed micelles, organized so as to facilitate comparisons between polycations for a given micelle (Figure 3A) or among micelles for a given polycation (Figure 3B). Applying the

PTMAEMC

SDS/TX-100 SLE2S/TX-100 SDS/C13E11 SLE2S/C13E11 SDS/TX-100 SLE2S/TX-100 SDS/C13E11 SLE2S/C13E11

Yc

Yφ

0.23 0.25 0.28 0.30 0.15 0.23 0.25 0.26

0.28 0.31 0.35 0.36 0.23 0.29 0.34 0.35

Ypb 0.50 0.36 0.52 0.48 0.33 0.34 0.38 0.40

± ± ± ± ± ± ± ±

0.02 0.04 0.02 0.02 0.04 0.04 0.04 0.04

a Values were obtained from the data shown in Figure 3 using the procedure defined in Figure 2. Yc is determined to ±0.01 (see Figure 2 inset) and Yφ to ±0.02 (Figure 2). bEstimates of Yp are approximate and depend on the degree of overlap of coacervation and precipitation regions (see Figure 2).

corresponds to Yφ1 only because Yφ2 (corresponding to coacervate redissolution) is not as clearly observed as in the reference system. For a given polyelectrolyte, Yc and Yφ values increase in the order of SDS/TX-100, SLE2S/TX-100, SDS/ C13E11, and SLE2S/C13E11, while for a given mixed micelle, the Yc, Yφ, and Yp values of the PDADMAC systems are larger than those for the PTMAEMC systems. It can be stated that regardless of polyelectrolyte, the SDS/TX-100 micelle complexes with highest affinity and also coacervates most readily, but the tendency to precipitate is more dependent on the polyelectrolyte, happening more readily for PTMAEMC (Table 1). Herein our primary interest is Yc which, as described above, is the experimental equivalent of the critical surface charge density σc required for the binding of one polymer sequence to a plane or a single sphere of oppositely charge as treated in theory and simulations.40−42 Similarly, the process defining Yc is the binding of a single micelle (n = 1). Since Yc does not depend on micelle:PE stoichiometry, there is no effect on Yc for n > 1. We propose to use it as a surrogate for interaction strength: differences in Yc among several mixed micelles for a given polycation indicate that factors other than the actual mole fraction of ionic surfactant (Y) contribute to the binding affinity. Thus, at Y = 0.26 for example, SDS/TX-100 micelles would bind to PDADMAC, while SLE2S/C13E11 micelles would not (Table 1); i.e., the former mixed micelle has a higher polycation binding affinity than the lattera difference seen even more amply for PTMAEMC. The values of Yc, Yφ, and Yp for each PE:micelle system plotted in Figure 4 demonstrate the correlation of Yφ with Yc but the complete lack of correlation for Yp. Yc controls micelle charge, which in turn determines polycation binding affinity, thus controlling the number of micelles bound per polymer chain, n. The liquid−liquid phase separation at Yφ depends on complex net charge ZT = nZm + ZP (Zm and ZP represent the micelle and PE charge, respectively) and thus occurs at ZT ∼ 0. On the other hand, precipitation at Yp involves the desolvation of the liquid phase is correlated with the release of tightly bound cations from the micelle surface at large Y. It seems likely that nature of these bound counterions is highly sensitive to micelle surface charge density, leading to E


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responsive probe, for example, dodecanoic acid or 4heptadecyl-7-hydroxycoumarin (HHC).31 Since measurements with the fluorescent probe HHC would be complicated by the fluorescence of TX-100, potentiometric titrations were carried out with the titratable probe dodecanoic acid at Y = Yc, yielding the values of Ψ 0,c shown in Figure 6 and also given in Table S1. Previous potentiometric titrations using the same probe for the SDS/C12E631 at critical binding conditions in the system SDS/ C12E6/PDADMAC31 gave Ψ 0,c values ranging from −9 to −12 mV. It is important to consider that these potentials correspond to the average position of sulphate groups, higher than the potentials experienced by polycation units at the average location of the bound polymer segments, and are therefore larger than the potentials at the “shear plane”. More information can be gained by analyzing the distribution of micelle ζc and Ψ 0,c binding to the two polycations, as most clearly shown in Figure 6. At critical conditions for binding to either PDADMAC or PTMAEMC, the range of values is more narrow for ζ than Ψ 0. That is, the data for ζ is much more coherent (qualitatively smaller standard deviation) than that for Ψ 0. For both polycations, the clustering of the results for ζ, in comparison to the wider range of results for Ψ 0, supports the following statement: all micelles measured at their respective Yc’s in the presence of either PDADMAC or PTMAEMC have nearly the same zeta potentials. A similar statement is less valid for the surface potentials where the ranges are much wider. Furthermore, the values obtained follow the same order as for the binding affinity given by Yc in Table 1: SDS/TX-100 > SLE2S/TX-100 > SDS/C13E11 > SLE2S/C13E11. Thus, zeta potentials correlate better with polycation affinity than “surface” potentials. We can therefore state that all mixed micelles with ζ values more negative than −5.6 mV will bind to PTMAEMC, while binding to PDADMAC requires higher absolute zeta potentials of |ζ| > 6.7 mV. Put differently, the zeta and surface potentials of the mixed micelles at Yc are almost independent of surfactant monomer structure. Furthermore, ζ is a better indicator of polycation binding affinity than the bulk mole fraction of anionic surfactant, even though it arises from the measured mobility which is subject to hydrodynamic drag. While the precise location of the “shear plane” (tautologically defined as the location of the zeta potential) is in general not well-defined, it seems likely that the polycation segments in the bound state reside near this plane. According to Table 1, PTMAEMC shows higher micelle binding affinity (lower Yc) than PDADMAC. The most obvious explanation for this behavior is the lower linear charge density of PDADMAC,43 for which the spacing between charges is about 6 Å compared to ca. 3 Å for PTMAEMC (cf. Figure 1), leading to a larger energy difference between the free and bound states of PTMAEMC. Generally, the binding energy depends on the number of cooperatively bound polycation segments (z) multiplied by the zeta potential. The smaller values of z for PDADMAC can be compensated for by larger values of ζ at critical binding conditions. We can also visualize a polyelectrolyte “surface” potential binding micelle guests. Direct measurement of polyelectrolyte “surface” potential is possible for chains with titratable ionophoresfrom the work of Nagaswa et al.44as related to the work of moving H+ from the polymer surface (even though the notion of a polymer “surface” may be controversial).45 While only measurements of the ζ potential are available for nontitratable polyelectrolytes, Cleland et al. obtained a relationship between μ0 and ζ using hyaluronic

Figure 4. Correlations of Yc against Yφ (black) and Yp (red) for each PE:micelle system are represented. Since Yc is determined with highest precision, error associated with Yc is not presented for better visualization. Dashed line represents the linear fit of Yφ data.

highly nonmonotonic dependence of Yp on Yc, unrelated to net charge of complex.37 Also, the determination of Yp values is complicated due to the overlap of coacervation and precipitation region; this could potentially lead to the poor correlation between Yc and Yp. To understand the higher polycation affinity of e.g. mixed micelles with TX-100 compared to those with C13E11, we measured, for mixed micelles formed by different combinations of anionic and nonionic surfactants, the zeta potential (ζ) at different Y values (Figure 5 and Table S1) and the surface potential (ψ0,c) at Yc (Table S1).

Figure 5. Zeta potential (ζ) of mixed micelles formed by different combinations of anionic and nonionic surfactants (SDS/TX-100, SLE2S/TX-100, SDS/C13E11 and SLE2S/C13E11) in 0.40 M NaCl as a function of Y. Error bars from two independent measurements. The shape of the Y dependence of the original electrophoretic mobilities of all micelle:PE systems is identical before and after the application of Henry’s equation used in conversion to zeta potential.

The zeta potential of mixed micelles generally increases with increasing Y, passing through a maximum at values well beyond Yc for the TX-100-containing systems but continuing to increase for C13E11-containing systems. Since ζ is obtained from the electrophoretic mobility and thus might be influenced by friction-dependent diffusivity, an alternative measurement for the electrostatic field around a (mixed) micelle can be obtained by potentiometric titration using a co-solubilized pHF


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Figure 6. Absolute values of zeta potential ζ (left, open bars) and surface potentials Ψ (middle and right, shaded bars) measured at Yc for different types of mixed micelles in the presence of PDADMAC (PD, red) or PTMAEMC (PT, black) (from Table S1). Gaussian curves reflect the standard deviations of limited data in Table S1 (vertical bars in the figure) and are mainly to guide the eye. The zeta potentials for the four different micelles measured at Yc are more coherent than the surface potentials (see text).

acid.46 Thus, the following equation36 can be used to obtain “surface” potential from zeta potential: ψ0PE = 6ημ0 /D = 4ζεf (κa)

volumes and length of the hydrophobic segment.47 Values of a are virtually identical for the two nonionics, but the large value of v/l for the hydrophobic “tail” of TX-100 leads to low curvature and larger size. Therefore, micelles formed with SDS are more elongated than those formed with SLE2S. For both mixed micelles, the maxima in micelle size at intermediate Y can be explained by the Y-dependence of the effective sulfate headgroup of anionic surfactant. The radius increases with Y at low Y because when SDS headgroups are far apart, we have an absence of electrostatic effects. We are left with only the small geometric size of the sulfate headgroups compared to the nonionic ones, and this geometric effect leads to lower curvature and larger micelle size.47 When SDS headgroups are closer at large Y, they repel each other, leading to higher curvature, i.e., smaller size. Figure 8 portrays the effects of polycation linear charge density and micelle anisotropy. The binding affinity (as given by diminution of Yc) SDS/TX-100 > SLE2S/TX-100 > SDS/C13E11 > SLE2S/C13E11 can be correlated with micelle size (Figure 7).

(4)

While the electrostatic potential at the shear plane is not necessarily equal to that experienced by the micelles upon binding, we can empirically test the correlation between ζPE and the micelle binding affinity as given by Yc. The values obtained for ζPE in 0.4 M NaCl are +19.2 ± 0.8 mV for PDADMAC and +24.0 ± 1.6 mV for PTMAEMC (i.e., ∼25% larger for PTMAEMC). The value of Yc is ∼25% larger for PDADMAC, thus compensating for its lower charge density and ζPE. Visualizing the sequence of cooperatively bound polycation residues as the guest on the micelle host surface, we recognize the importance of micelle surface curvature. Size and axial ratios of the mixed micelles were determined by dynamic light scattering, with results shown in Figure 7 and Table S2. Mixed micelles formed with TX-100 are significantly larger and less spherical than those based on C13E11. From geometric considerations, micelle curvature decreases with v/al, where a is the effective headgroup area and v and l are the effective

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CONCLUSIONS Comparisons among four different anionic/nonionic mixed micelle systems show that both the potentiometric “surface potential” and the electrophoretic ζ potential of the micelle correlate with the degree of polycation binding deduced from turbidimetric titration. Our results suggest that ζmicelle is a more consistent indicator of its polycation affinity and that vice versa ζPE serves at least as a qualitative measure for the micelle affinity of a given polycation. In addition to its behavior near Yc, the “reference system” PDADMAC/SDS/TX-100 as well as its variants serves as a model demonstrating multiple phase transitionswhich exist but may not be equally well resolved in other polyelectrolyte/mixed micelle systems. The roles of the nonionic surfactants in the interaction between mixed micelles and polyelectrolytes are complex, ranging from steric hindrance to the approach of the polyelectrolyte toward the locus of the anionic surfactant headgroups and to modulations of micelle surface charge density via changes in micelle geometry. Predicting the influence of the hydrocarbon surfactant moieties would require a better model for the packing parameters in mixed micelles.

Figure 7. Hydrodynamic diameters (Dh) of mixed micelles (SDS/TX100, SLE2S/TX-100, SDS/C13E11, and SLE2S/C13E11) in 0.40 M NaCl as a function of Y. G


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Macromolecules

Figure 8. Schematic depiction of the localized micelle binding of polycation segments with different linear charge density (PTMAEMC and PDADMAC). In this schematic we somewhat arbitrarily show the charged moieties of the polycation in the bound state residing at the interface between the bulk solvent and the EO termini. This interface is distal to the average location of the anionic surfactant headgroups, a more proximal interface whose “surface potential” is probed by dodecanoic acid.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00584. Tables S1 and S2 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(P.L.D.) Tel (413) 577-4167; Fax (413) 545-4490; e-mail [email protected]. *(Y.F.) E-mail [email protected]. ORCID

Yaxun Fan: 0000-0003-0057-0444 Amy Y. Xu: 0000-0002-4071-1750 Paul L. Dubin: 0000-0002-4643-8169 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The support of BASF SE and NSF CBET-1133289 is gratefully acknowledged. REFERENCES

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