Phase Behavior and Molecular Thermodynamics of Coacervation in

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Phase Behavior and Molecular Thermodynamics of Coacervation in Oppositely Charged Polyelectrolyte/Surfactant Systems: A Cationic Polymer JR 400 and Anionic Surfactant SDS Mixture Dongcui Li,† Manish S. Kelkar,‡ and Norman J. Wagner*,† †

Center for Molecular and Engineering Thermodynamics, Department of Chemical & Biomolecular Engineering, University of Delaware, Newark, Delaware 19716, United States ‡ The DuPont Company, Experimental Station E304/C323, P.O. Box 80328, Wilmington, Delaware 19880-0328, United States S Supporting Information *

ABSTRACT: Coacervation in mixtures of polyelectrolytes and surfactants with opposite charge is common in nature and is also technologically important to consumer health care products. To understand the complexation behavior of these systems better, we combine multiple experimental techniques to systematically study the polymer/surfactant binding interactions and the phase behavior of anionic sodium dodecyl sulfate (SDS) surfactant in cationic JR 400 polymer aqueous solutions. The phase-behavior study resolves a discrepancy in the literature by identifying a metastable phase between the differing redissolution phase boundaries reported in the literature for the surfactant-rich regime. Isothermal titration calorimetry analyzed within the framework of the simple Satake−Yang model identifies binding parameters for the surfactant-lean phase, whereas a calculation for polymer-bound micelles coexisting with free micelles is analyzed in the surfactant-rich redissolution regime. This analysis provides a preliminary understanding of the interactions governing the observed phase behavior. The resulting thermodynamic properties, including binding constants and the molar Gibbs free energies, enthalpies, and entropies, identify the relative importance of both hydrophobic and electrostatic interactions and provide a first approximation for the corresponding microstructures in the different phases. Our study also addresses the stability and metastability of oppositely charged polyelectrolytes and surfactant mixtures.

1. INTRODUCTION The binding of anionic surfactants onto cationic polyelectrolytes can result in associative phase separation over a broad range of mixture compositions, with the gel-like concentrated phase (coacervate) rich in both polymer and surfactant.1−5 This coacervation phenomenon can result in various microstructures, such as pearl−chain complexes, liquid or solid precipitates, gels, and liquid crystals.6−9 There is a substantial literature of applied research on formulating coacervates for successful applications in food,10 consumer health care products,11,12 and pharmaceutical industries.13−15 Of particular interest is the delivery and controlled release of active compounds (i.e., functional oils and antibacterial agents) via the coacervation of polymer−surfactant mixtures during the use of many consumer health care products.11,12 The successful © 2012 American Chemical Society

design of an appropriate coacervation and delivery process best incorporates a knowledge of the molecular interactions governing such self-assembling systems.6,12,16 Such interactions govern the coacervate physical properties of specific interest to some technological applications (i.e., adhesion to a surface/ interface9 and rheology17). Consequently, the molecular thermodynamics of coacervation continues to be of significant fundamental scientific interest.12,16,18,19 The development of a fundamental understanding of coacervation has proceeded along three general lines of investigation: a classical thermodynamic approach characterized by establishing phase Received: October 3, 2011 Revised: June 10, 2012 Published: June 14, 2012 10348

dx.doi.org/10.1021/la301475s | Langmuir 2012, 28, 10348−10362

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with the binding of a small ligand (e.g., surfactant molecule) to macromolecules (e.g., proteins, DNA, or polyelectrolytes) is directly measured as a function of the solution composition, providing thermodynamic properties. Although modern ITC instruments allow for the rapid, accurate thermodynamic characterization of binding events, the resulting enthalpies are not easily interpreted in terms of molecular interactions in the absence of microstructural details. Consequently, the coupling of thermodynamic data from ITC experiments with molecular structural information is becoming increasingly powerful. This can be achieved when ITC is combined with other methods that elucidate microstructure (i.e., SAXS and SANS).53 The phase behavior of polyelectrolyte/surfactant mixtures can be understood by considering the molecular interactions that act between the polymer and free and micellized surfactants in solution.19,54 For instance, Hansson proposed a thermodynamic theory for an oppositely charged polyion− surfactant ion complex salt in aqueous solution.30 The resulting phase diagram has been shown to be in good agreement with experimental and Monte Carlo simulation data. Allen and coworkers31 demonstrated that many of the features of associative phase separation seen experimentally can be recovered with a Poisson−Boltzmann cell model for macroion solutions (a suspension of spherical surfactant micelles), extended to incorporate a polyelectrolyte component. Testing these approaches requires the determination of both the phase behavior and molecular interactions. An interesting and sometimes problematic feature of the phase behavior of such coacervate-forming solutions is longlived nonequilibrium states. Reaching true equilibrium may require an inordinately long observation time. Such nonequilibrium states often arise by following specific paths of sample preparation. For example, Meszaros et al.55−58 proposed the formation of a kinetically stable (colloidally stable) dispersion of polyelectrolyte/surfactant complexes (PSCs) to explain the observed nonequilibrium states. Another explanation of such nonequilibrium behavior includes the classical metastability associated with systems within the spinodal− binodal phase boundaries. This has been calculated for polyelectrolyte/surfactant coacervation by adapting the Flory−Huggins model to include surfactant micelles as the second polymer component.59 The mechanism of redissolution of polyelectrolyte/surfactant coacervates has been debated by several research groups. It has been shown that the precipitates of high-molecular-weight cationic homopolyelectrolytes and SDS cannot be resolubilized even in very large excesses of surfactant. Waterlike, low-turbidity mixtures may be prepared at high surfactant-to-polyelectrolyte ratios, which are, however, not one-phase systems but charge-stabilized colloidal dispersions.55−58 Even within the complex salt mixing plane, Santos et al.36 demonstrated that the true redissolution of the complex polyelectrolyte/surfactant salt may not be achieved even in a very large excess of the surfactant salt for highmolecular-weight homopolyelectrolytes. The authors revealed that true redissolution (the formation of one-phase systems or a thermodynamically stable solution of the individual PSCs) is favored only for very low molecular weight polyelectrolytes or for charged macromolecules with two binding sites for the surfactant (such as nonionic blocks or hydrophobic blocks in addition to the charge groups). This work has helped elucidate whether a thermodynamically stable solution or kinetically stable colloidal dispersion is formed in the presence of excess surfactant.

boundaries or diagrams; structural analysis of the coacervate itself; and a molecular thermodynamics approach designed to elucidate the molecular interactions governing coacervation. However, the prediction of coacervate phase behavior, microstructure, and coacervate properties (including rheology) from a knowledge of the molecular composition still poses a challenging research goal. Coacervation is controlled by both the concentration and primary structure of each component4,20−24 (e.g., solubility, molecular weight, charge density, and hydrophobicity) and the solution conditions7,25,26 (e.g., temperature, pH, salt or ionic strength, and solvent). The complexation behavior is the result of a complicated balance force among electrostatic, hydrophobic, excluded volume, van der Waals, and other contributions to the overall system stability.27−29 Coacervation is driven by the opposite charge between species in solution. The electrostatic interaction energy stems from the columbic attraction between oppositely charged species but is usually accompanied by a significant entropy gain due to counterion release.30−32 Hydrophobic interactions, arising from the chemical structure, also play a crucial role in the molecular binding, coacervation, and micellization.20,21 These interactions are accompanied by a large, favorable entropy gain due to the liberation of unfavorably organized water molecules surrounding the hydrophobic regions of the molecules upon hydrophobic binding.33 The conventional strategy for investigating oppositely charged polyelectrolyte−surfactant systems is to mix the polyelectrolyte and the surfactant in water and study the phases and structures formed in the conventional mixing plane. However, as discussed by Thalberg et al.,26 such mixtures contains four different ions (e.g., the polyion, the surfactant ion, and their respective counterions) and are more properly described by a 3D pyramidal phase diagram comprised of the four salts and water. The conventional mixing plane corresponds to cutting through this pyramidally shaped phase diagram. Problems arise in identifying the equilibrium compositions in phase-separated samples in the conventional mixing plane because the tie-line end compositions are not generally situated in the conventional mixing plane. As an alternative to the conventional mixing plane, Piculell et al.10,32,34−36 demonstrate the advantages of constructing a truly ternary phase diagram by eliminating one type of salt ion and using the polyion−surfactant ion complex salt mixed with either polyelectrolyte or surfactant (with their respective simple counterions). This restricts the phase behavior and all compositions to lie on one surface of the 3D pyramidal phase diagram. The most common characterization techniques used to measure the molecular or bulk thermodynamic properties of such solutions include surface tension,37 turbidity,38,39 conductivity,39,40 rheology,22,41 small-angle neutron scattering (SANS),9,38 time-resolved fluorescence,42,43 dynamic light scattering (DLS),25,44 cryo-transmission electron microscopy (cryo-TEM),8 nuclear magnetic resonance (NMR),45 and isothermal titration calorimetry (ITC).16,20,21,46−50 In comparison to other techniques, a distinct advantage of ITC is the direct measurement of molecular interaction energies over a wide concentration range. Commonly used to measure biopolymers and biomolecular ligand binding,51,52 ITC has been shown to be a powerful method for probing the interaction between polymers and surfactants in solution.16,20,21,46−50 In this technique, the enthalpy associated 10349


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is normally 1−3 orders of magnitude lower than the surfactant’s critical micelle concentration (CMC*).16 (2) The addition of further surfactant leads to the growth in size of these globular PSCs, which can eventually reach visible sizes and may sediment near the charge-neutralization point of the complexes. In this coacervate phase, for instance, ∼2−4 surfactant molecules are reported to be associated with each charge site of the polymer chain in the mixture of JR400 and sodium lauryl ether sulfate,4 and both charge neutralization and hydrophobic interactions are shown to be possibly responsible for precipitation.24 (3) With further increases in surfactant concentration, the PSCs will undergo net charge reversal because of excess surfactant binding. Free micelles may also be present in solution. With sufficient excess surfactant binding, the PSCs will resuspend into colloidally stable PSCs.4,31 These are often termed polymer−micelle complexes (PMCs) as the adsorbed surfactant is present as adsorbed micelle-like structures.6,56,58 Literature reports16,18,65 also demonstrate the importance of quantifying the entropically driven surfactant micellization process. This can be obtained from the CAC and the CMC*, which can be interpreted in terms of the reduction in the Gibbs free energy associated with the transfer of a surfactant molecule from solution to a polymer-bound micellarlike cluster or micelle, respectively.4,16,18,65 Computational studies of the polymer−surfactant micelles' binding interaction have also been reported.27,28,30 In this article, we will quantify the surfactant binding interactions and transition enthalpies and entropies to analyze the metastable phase and redissolution behavior. To do this, we combined the simple but widely used two-state binding model by Satake−Yang46,64,66−72 with the polymer-bound micellization analysis. This simplified model considers surfactant binding to two types of sites on polyelectrolytes, namely, cooperative and noncooperative binding, and has been used by numerous authors on a wide variety of systems.46,64,66−72 We mainly follow the method for analyzing the cooperative surfactant/polyelectrolyte ITC binding isotherms as demonstrated by Yakov et al.46 Such an analysis is a highly simplified but very useful first approximation for understanding surfactant-binding isotherms, providing direct and useful thermodynamic quantities within the model assumptions. This simplified 1D treatment, however, fails to capture many of the mechanistic aspects of the self-assembly process (e.g., steric constraints, the possible coexistence of highly occupied polymer chains with those that are nearly surfactant-free, polyelectrolyte chain conformation, and surfactant molecular geometry). Note that others have extended the interpretation of this model, such as Hansson,73,74 who considered the reliability of the determination of the surfactant aggregation number from the Satake−Yang model parameters. Furthermore, there are other approaches30,75 based on molecular interaction parameters and more realistic models for the selfassembled molecular structures. Here, we limit our analysis to the Satake−Yang model as sufficient to demonstrate the congruence between the experimentally determined phase behavior and ITC measurements. Future work combining direct molecular measurements of the microstructure can benefit from this more detailed analysis of the ITC results. Moreover, the simple model is justified by considering the stiff polymer JR 400 backbone structure (lp ≈ 6 nm such that the conformational energy loss upon adsorption is negligible), the large linear charge distance of 2 nm (such that the steric effect

The focus of this article is to understand the phase behavior and the relationship to the corresponding surfactant binding interactions in aqueous mixtures of cationic polyelectrolyte JR 400 and sodium dodecyl sulfate (SDS). This well-studied system5,12,33,60−62 is of fundamental interest and is a prototype for technologically relevant formulations. The JR 400 polycation has advantageous conditioning and deposition properties for formulating hair and skin products.31,32 The theoretical considerations and experimental observations indicated in the previous discussion suggest that a careful consideration of the possible path dependence is required to determine the true phase boundary when observing coacervate formation. Indeed, for JR 400/SDS aqueous solutions two different phase diagrams have been reported in the literature and are compared in Figure 1, where significant differences are apparent.60−63 Goddard et

Figure 1. Phase diagram of JR 400 and SDS mixtures at 25.0 ± 0.1 °C as studied in the literature. The black dashed shading represents the data from Goddard et al.61−63 The green solid shading is from Yamaguchi et al.60 The shaded region represents a two-phase region identified by the respective authors. The regions on either side are one-phase regions. The red dashed line represents the chargeneutralized line. (This figure is reproduced from references via converting the weight percentage to the charge equivalence as indicated in Table 1.)

al.61−63 examined the phase boundary via a study of precipitation patterns and measurements of surface tension, foaming, and electrophoretic mobility. Yamaguchi et al.60 studied the phase boundary by visual observation. As expected, phase separation at low surfactant concentrations tracks the equal charge equivalence line for both investigations. This transition represents coacervate formation upon charge neutralization. However, the redissolution boundaries at higher surfactant concentrations are in substantial disagreement. Yamaguchi et al.60 observed the redissolution at much lower SDS concentrations than Goddard et al.61−63 Here, we first investigate this discrepancy via a combination of experimental techniques including a visual study of the phase behavior and an ITC study to provide an interpretation of the surfactant binding responsible for the phase behavior. A survey of numerous publications16,20,21,46−50,64 based on several experimental techniques provides a qualitative description of the binding interaction expected over three major distinct regions of behavior: (1) At low relative surfactant concentrations, surfactants adsorb to the polymer and a critical aggregate concentration (CAC) is apparent where micellar-like polyelectrolyte−surfactant complexes (PSCs) form. The CAC 10350


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0.5, 0.8 mM) with a total of 45 injections. Measurements of the dilution enthalpy for SDS were performed by initially loading the sample cell with deionized water and injecting SDS solution. Measurements of the dilution enthalpy of polymer JR 400 were carried out by initially loading the sample cell with JR 400 solution and injecting DI water. Calibration experiments verified the CMC of the SDS in water (8.6 ± 0.4 mM) with a micellization enthalpy of −4.6 ± 0.5 kJ/mol, in good agreement with the literature76 (details in Supporting Information S.1). Note that a negative heat of injection corresponds to an exothermic process and vice versa. For each experiment, the sample cell was rinsed several times with detergent and then DI water before loading with the appropriate sample volume. Similarly, the ITC syringe was also rinsed with DI water before loading with the desired titrant. The differential heat input, q(t), was measured as a function of time t over all injections, followed by the integration of q(t) over each individual injection to 53 obtain the molar heat of injection, Qj(T, P, ctot s,j ).

is small), and high-molecular-weight polymer chains (with 360 binding sites per chain so that the end effects are negligible). The binding behavior of oppositely charged polyelectrolyte/ surfactant systems exhibits multiple, sometimes competing mechanisms, which is a challenge for interpreting the results. Thus, our approach is to employ a combination of experimental techniques, including thermodynamic measurements (isothermal titration calorimetry (ITC)) and microstructure characterization techniques (dynamic light scattering (DLS), cryotransmission electron microscopy (cryo-TEM), electrophoretic mobility, and atomic force microscopy (AFM)), to provide an interpretation of the association mechanisms that drive coacervation and redissolution. This enables an analysis that combines the results of several techniques to handle the complexity of the problem better.

2. MATERIALS AND METHODS Q j(T , P , cs,totj ) =

2.1. Sample Preparation. Cationic polymer JR 400, supplied by Amerchol Inc. (Dow Personal Care), was further purified via dialysis. This amphiphilic polyelectrolyte, JR 400, is a chloride salt of the N,N,N-trimethylammonium derivative of hydroxyethyl cellulose (HEC). The molecular weight is 360 000 Da (PDI = 1.85), and the nitrogen content is 1.73 wt %, corresponding to an ∼1000 g/mol charge equivalent. Anionic surfactant sodium dodecyl sulfate (SDS) from Sigma-Aldrich (BioXtra, ≥99.0% (GC)) was used as supplied. All of the samples were prepared in deionized (DI) water (conductivity ≥18.3 MΩ). A stock solution of each pure component, JR 400 and SDS, was prepared gravimetrically and stirred for at least 24 h at room temperature to ensure complete dissolution. The SDS stock solution was added to a vial containing the appropriate amount of JR 400 solution, and deionized water was added to make a solution of 5 g total mass. All of the samples were then stirred at room temperature for at least 30 min and then placed in a constanttemperature water bath for further observation. The path dependence of the observed phase behavior was further investigated via preparing two sets of samples following the sample preparation methods of Yamaguchi et al.60 and Goddard et al.61−63 Goddard et al.61−63 added SDS concentrates to stock polymer solutions, similar to our preparation method. However, Yamaguchi added an appropriate amount of surfactant to a glass vial containing the polymer powder, which is the opposite order of gradient addition. 2.2. Phase Behavior Study. Phase behavior studies were performed by observing a set of samples with varying polyelectrolyte and surfactant concentrations in an immersion temperature-controlled water bath. All samples were heated from 25 to 45 °C in steps of 5 °C and equilibrated for at least 48 h. Visual inspection was used to identify the number and character of distinct phases within the sample after 24 and 48 h. If in agreement, the bath was taken to the next temperature. At the end of these measurements, the samples were re-equilibrated at 25 °C and observations were made and compared with the initial measurements at that temperature for each sample to confirm the sample integrity throughout the study. 2.3. Isothermal Titration Calorimetry (ITC). ITC experiments were performed on a Microcal VP-ITC calorimeter. Combined with the phase map, the titration spanned surfactant compositions covering the entire region of phase instability (i.e., from one phase at low SDS concentrations to a two-phase region and back to the one-phase region at high SDS concentrations). Experiments were carried out at 35.0 ± 0.2 °C by initially loading the sample cell with JR 400 (cp = 0.1, 0.5, 0.8 mM) and injecting a titrant of SDS lasting a period of 20 s, with 10 min between each injection. Two separate experiments were performed and combined to cover the desired compositions owing to the volume limitation of the instrument: (1) Experiments at low SDS concentrations were carried out using 8 μL per injection of SDS solution (7 mM) into JR 400 solution (cp = 0.1, 0.5, 0.8 mM) with a total of 35 injections. (2) Experiments at high SDS concentrations were carried out using 6 μL per injection of SDS solution (100 mM) into JR 400 solution (cp = 0.1,

∫t

tj+1

q(t ) dt

j

c injΔV

(1)

For any reversible process, the total cumulative molar heat absorbed by the jth injection, Qtol,j(T, P, ctot s,j ), is obtained by summing the individual heat inputs for each injection: j

Q tol, j(T , P , cs,totj ) =

∑ Q i(T , P , cs,toti ) i=1

(2)

The net enthalpy due to the interaction of JR 400/SDS from the jth injection is obtained by subtracting the dilution enthalpy of both surfactant and polymer from the measured total cumulative molar heat: tot SDS * tot ΔH̅ int , j(T , P , cstot , j ) = Q j(T , P , cs , j ) − ΔH̅ dil, j (T , P , cs , j ) JR400 tot − ΔH̅ dil, j (T , P , cs , j )

(3)

2.4. Dynamic Light Scattering (DLS). DLS experiments were performed on a Brookhaven ZetaPALS instrument using a laser with a wavelength of 633 nm with a scattering angle of 90°. All of the stock solutions were filtered before preparing the samples, but no further filtering was performed prior to measurement. Ten consecutive measurements were made on each sample. The average hydrodynamic radius was calculated from the intensity autocorrelation function using monomodal analysis mode. The zeta potential ζ was determined via electrophoretic mobility measurement on the same instrument directly after measuring the size distribution, where the Debye−Hückel limit was assumed for the calculation of ζ. All quantities were averaged over 10−30 consecutive measurements to obtain statistically significant data. 2.5. Atomic Force Microscopy (AFM). Atomic force microscopy investigations by soft-contact mode imaging in liquid were performed on a Digital Instruments Nanoscope IIIa MultiMode instrument. A fluid cell (Digital Instruments device) was used and cleaned with a water−alcohol mixture and rinsed with Nanopure water between each sample. A Pyrex nitride probe (PNP-TR) is used in this study; it has a silicon nitride cantilever with a very low spring constant (∼0.08 N/m), and the radius of the probe curvature is below 10 nm. All of the cantilevers were cleaned with piranha solution followed by deionized water, and a new cantilever was used for each image. Prior to imaging, each probe was calibrated on the mica surface in deionized water to check the cantilever integrity and condition. A liquid sample was injected after the cell was mounted, and 15 min was allowed to reach equilibrium before engaging the cantilever on the surface. 2.6. Cryo-Transmission Electron Microscopy (Cryo-TEM). Cryo-TEM was carried out to image the PSC particles under liquid conditions. The samples were prepared using a temperature- and humidity-controlled environment vitrification system (FEI co.) at 22 °C and 100% humidity and were supported on copper TEM grids coated with a lacey carbon support film. Thin sample films were 10351


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cstotal = cs + c pΘ(cs)

obtained by quickly plunging the grids into liquid ethane and transferring them to liquid nitrogen to vitrify the sample. A Technai 12 transmission electron microscopy combined with a low-dose CCD camera was used at a 120 kV accelerating voltage for all measurements. 2.7. Theoretical Basis. In the dilute surfactant regime, including the two-phase coacervate region, the surfactant binding behavior can be modeled by a cooperative binding model often known as the Satake−Yang model,77 which is based on the Zimm−Bragg model.34,66,67 For the surfactant-rich redissolution regime, a model considering polymer-bound micelles and free micelles is used to describe the polymer-bound micellar cluster formation. 2.7.1. Satake−Yang Model. In related work by Matulis47 and Lapitsky et al.,46 the lipid-binding behavior in DNA condensation and in polyelectrolyte coacervation was quantitatively modeled using the

(6)

The additional parameters in eq 5 are K, which is the intrinsic binding constant, and u, which is the cooperativity parameter. These parameters can be determined directly from the binding isotherm:66,67

Ku =

1 cs(Θ = 0.5)

(7)

⎛ dΘ ⎞ 2 u = 16⎜ ⎟ ⎝ d ln cs ⎠Θ= 0.5

(8)

46

Lapitsky et al. extended this model to the experimental ITC signal, where the measured molar enthalpy per injection associated with surfactant binding onto the polyelectrolyte was expressed as eq 9. The enthalpy per injection is the product of the fraction of the injected surfactant that is binding to the polyelectrolyte and the average molar enthalpy of binding. Thus,

cp

ΔH̅ int , j(cs, j) =

dΘ(cs, j) d cs

1 + cp

dΘ(cs, j)

ΔH̅ avg, j(cs, j) (9)

d cs

Here, the average molar enthalpy, ΔH̅ avg,j, composed of both the cooperative and noncooperative binding enthalpy is given by eqs 10 and 11.46

ΔH̅ avg, j(cs, j) = (1 − xN , j(cs, j))ΔH̅ C + xN , j(cs, j)ΔHN̅ Figure 2. Molecular structures of (a) JR 400 and (b) sodium dodecyl sulfate (SDS).

xN , j(cs, j) =

Satake−Yang model.66,67,77 As shown in Figure 3, each polyelectrolyte is regarded as a 1D lattice with N sites onto which the surfactant can absorb. Two types of binding sites are considered in this model: cooperative binding, where the neighboring site is occupied by other surfactant molecules, and noncooperative binding, where the adjacent site is not occupied. When the binding indices σi for each site (σi = 0 for a vacant site and σi = 1 for an occupied site) are defined, the ensemble partition function Q(α, γ, N) is66,67 1

N

1

N−1

∑ ····· ∑ exp(α ∑ σi+γ ∑ σσi i + 1) σ1 = 0

σN = 0

i=1

i=1

ΔHN̅ = (4)

where α and γ quantify the molar Gibbs free energies of binding and cooperative hydrophobic interactions normalized by kBT. The average site coverage Θ can be expressed as the sum over all possible binding states weighted by the fractional probability of a given state of occupied sites.66,67 By interpreting the average coverage Θ in terms of experimentally measurable quantities, a binding isotherm is developed as given by eq 5,66,67

⎡ 1⎢ Θ = ⎢1 + 2⎢ ⎣

Kucs − 1 (1 − Kucs)2 +

4Kucs u

⎤ ⎥ ⎥ ⎥⎦

⎛ u ⎜1 + ⎝

Kucs, j Θ(cs, j) u(1 − Θ(cs, j))

1 − Θ(cs, j) ⎞ ⎟ ⎠

2

Θ(cs, j) (11)

In this research, we adapt the basic framework of Lapitsky’s method46 but with a minor change whereby fitting is performed on the cumulative binding heat. One advantage of this fitting protocol is that it better captures the high-surfactant-concentration regime (near the saturation) without overemphasizing the dilute regime. The leastsquares fitting method is illustrated in Supporting Information S.5. Briefly, initial guesses for the binding parameters (Ku, u) were obtained from the CAC and the point of maximum isotherm slope via simultaneously solving four coupled algebraic equations.46 Because the CAC corresponds to the first inflection point and the point of maximum slope corresponds to the crest of the differential enthalpy peak, these can be determined readily from the corresponding plots of the cumulative and differential heats of injection. Using the initial Ku and u, we can estimate the molar enthalpy of noncooperative and cooperative binding in the limit of very low surfactant concentration (ΔH̅ int,j (cs → 0)) and the crest of the peak (ΔH̅ int,j (cs = cs,max)) as shown in eqs 12 and 13.46

Figure 3. Binding sites accounted for in the Satake−Yang binding model.

Q (α , γ , N ) =

Kucs, j

(10)

Kc p + 1 Kc p

ΔH̅ int , j(cs → 0)

ΔH̅ C ≈ ΔH̅ int , j(cs = cs,max )

(12) (13)

With these initial parameters, a reasonable four-parameter fitting loop (Ku, u, ΔH̅ N, and ΔH̅ C) can be defined and is substituted into eqs 9−11 to enable a direct estimation of ΔH̅ int,i. The jth cumulative interaction enthalpy is the sum over all of the heat adsorbed until the jth injection, as given by eq 14. j

ΔH̅cum, j(cs, j) =

∑ ΔH̅ int ,j(cs,j) i=0

(5)

(14)

The initial estimate of the binding parameters is used to start a leastsquares-fitting algorithm of the cumulative enthalpy. The optimal fitting parameters are obtained by minimizing the sum of the error of the cumulative enthalpy as defined by eqs 14 and 15.

where cs is the equilibrium free surfactant molar concentration in solution and the total surfactant in the formulation is given by free and bound surfactants as 10352


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sum of the error =

2

exp model ∑ (ΔH̅cum, j − ΔH̅ cum, j ) j

ΔH̅cum, j(T , P , cs,totj ) = (15)

⎛ Ku ⎞ ΔG̅N = − RT ln⎜ ⎟ ⎝ u ⎠

⎛ zeζ ⎞ 8εkBTn± sinh⎜ ⎟ ⎝ 2kBT ⎠

n± =

∑ zi 2ni , ∞ = NA(α0csbound + cs + cp) i

(16)

Q e

(17)

ΔH̅ cum, j(T , P , cs,totj ) Vj tot = cs, j [(ΔH̅demice,f_w + ΔH̅dilu,f_w + ΔH̅correction,p) cinjΔV +ΔH̅ mic,p_bound − (ΔH̅demice,f_w + ΔH̅dilu,f_w)] =

Vj cinjΔV

cs,totj [ΔH̅ correction,p + ΔH̅ mic,p_bound] (22)

For small ΔV, the low-concentration (eq 21, slope 1 in Table 4) and high-concentration (eq 22, slope 2 in Table 4) portions of the ΔH̅ cum,j (T, P, ctot s,j ) curve can be fit to linear expressions and ΔH̅ mic,p_bound is determined by subtracting the slope of the latter to that of the former. Also, the free micellization concentration in the polymer solution is determined by the intersection point of the intrinsic enthalpy transition, and the enthalpy is determined by ΔH̅ demice,f_p = ΔH̅ demice,f_w + ΔH̅ correction,p, as defined. The standard free energies of aggregation (ΔG̅ mic,p_bound) and micellization (ΔG̅ mic,f_p) are given by eqs 23 and 24, and other thermodynamic properties can be derived accordingly.16

(18)

(19)

ΔG̅mic,f_p = (1 + α0)RT ln(cac 2)

(23)

ΔG̅mic,f_p = (1 + α0)RT ln(cmc*)

(24)

3. RESULTS AND DISCUSSIONS 3.1. Visual Phase Behavior. Small concentrations of SDS (C ≪ CCMC,SDS) added to aqueous solutions of JR 400 are completely miscible, and a clear mixture is observed. Upon further addition of SDS such that the solution is near charge equivalence, turbid solutions are observed that phase separate into a gel-like coacervate minority phase and a clear phase. This coacervate phase tends to adhere to the side of a glass tube. With further addition of SDS, the coacervate phase dissolves back into solution, forming a clear, one-phase mixture within the observation time window (≤48 h). One such path for the mixture is shown in Figure 4. Figure 5 is a comparison of the phase map determined by visual observation in this study and those previously reported in

+ Np α0

(21)

Above the redissolution, polymer-bound micellization occurs such that the energy balance is as shown in eq 22:

where n± is the ionic strength given by eq 19, ε is the dielectric permittivity of the solvent, and e is the elementary charge (1.602 × 10−19 C) and the charge valence zi and number concentration ni,∞ are summed over all free ions in solution, not the polymer surfactant complexes or the micelles themselves. In the above, α0 is the degree of ionization of SDS micelles and has a typical value of 0.2−0.3.78,79 Here we use α0 = 0.25 for all calculations. To use this formula, we approximate the radius of each redissolved PSC as given by the measured hydrodynamic radius, Rh. The number of SDS molecules adsorbed per particle or per single polymer chain is given by eq 20 Nagg,p =

cs,totj [(ΔH̅denuce,f_w + ΔH̅dilu,f_w

− (ΔH̅demice,f_w + ΔH̅dilu,f_w)] Vj tot = cs, j [ΔH̅correction,p] cinjΔV

Finally, the molar entropy associated with each process can be determined from ΔS̅ = (ΔG̅ − ΔH̅ )/T. 2.7.2. Polymer-Bound Free Micelles. The redissolution of the coacervate upon further surfactant addition is examined via preparing a concentration series to resolve the PSC's complexation behavior in the surfactant-rich regime. A combination of several experimental methods such as DLS, soft-contact AFM, and cryo-TEM allows for an approximate estimation of the compositions of the resuspended PSCs. The amount of SDS required to account for the measured increase in ζ is obtained using Gouy−Chapman theory, which enables the calculation of the surface charge density, σ*, for a sphere with a constant surface potential53

σ* =

cinjΔV

+ ΔH̅correction,p)

The standard molar Gibbs free energies of cooperative and noncooperative binding can be estimated from the fitted binding parameters using the following standard expressions (where Ku is in units of inverse surfactant mole fraction):46,66,67 ΔGC̅ = − RT ln Ku

Vj

(20)

where Q = 4πRh2σ* is the net charge on a single particle surface and Np = 360 000/1000 ≈ 360 is the number of charges on a single polymer chain in the absence of adsorbed SDS. The interpretation of the ITC results in the surfactant-rich regime is more complicated because the titrant concentration lies above the CMC whereas the sample cell initially does not. Hence, the enthalpy of demicellization and the dilution of the injected micelle aggregates must be explicitly accounted for. As mentioned earlier, this is accomplished via subtracting the total enthalpy of injecting SDS into deionized water, assuming that the demicellization (ΔH̅ demice) enthalpy of the injected SDS micelle is only weakly dependent on the presence of JR 400. Thus, we include a small correction enthalpy ΔH̅ correction,p to account for the effect of the polyelectrolyte on the chemical potential of the solvent (ΔH̅ demice,f_p = ΔH̅ demice,f_w + ΔH̅ correction,p). This term can be determined by the slope of the cumulative molar heat of injection obtained from ITC prior to the formation of polymer-bound micelles in polymer solutions and in water (shown by eq 21). The polymer-bound micellization enthalpy, ΔH̅ mic,p_bound can be determined from the intrinsic enthalpy transition observed in the data. This is determined by considering the energy balances before and after the transition. The energy balance before the formation of polymerbound micelles is given by

Figure 4. Photograph showing the different observed phase behaviors. From the left, the first photograph is one-phase mixture, and the next two are two-phase samples. The last sample is a one-phase mixture. 10353


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Goddard et al.61−63 and Yamaguchi et al.60 followed different sample preparation methods, where our method is similar to that of Goddard et al.61−63 To explore the possibility that the phase behavior exhibits a path dependence, we prepared additional samples following the preparation method of Yamaguchi et al.60 Indeed, such samples with compositions in the region of disagreement between the two literature studies originally appeared as one phase. However, we find that these samples are not stable after 1 week and a small disturbance can affect the sample stability. In contrast, samples in this region of the phase diagram that are prepared using our method of gradient addition, whereby SDS concentrates are added to JR 400 stock solutions, exhibit rapid phase separation. We further explored this path dependence in more detail as follows. Two samples with different initial phase stabilities were prepared and diluted with either SDS stock solution or JR 400 stock solution in the region of discrepancy (more details in Supporting Information S.3). SDS stock solution was added to sample 1, which was initially at low SDS concentration, to increase the sample to higher SDS concentration such that its final composition lies in the region of discrepancy. Alternatively, sample 2, which started at high SDS concentration, was diluted to lower SDS concentration by adding JR 400 stock solution such that its final composition also lies in the region of discrepancy and is similar to that for sample 1. Sample 1 exhibited immediate phase separation and remained phase separated even after 2 weeks. However, sample 2 appeared to be one phase after dilution but eventually exhibited phase separation within 1 day. These results further validate the path dependence we observed in the region of discrepancy and indicate that is corresponds to a region of metastable phase equilibria. On the basis of these observations, we propose that the redissolution boundary observed by Goddard et al.61−63 and verified by our study is the true equilibrium phase boundary (binodal). However, the phase boundary reported by Yamaguchi et al.60 is thought to correspond to a spinodal phase boundary because samples prepared in the region in between are metastable. Further evidence to verify this hypothesis is provided by selective ITC experiments, described next. 3.2. Spinodal−Binodal Transition. ITC studies were performed along designed paths shown on the phase diagram with an approximately constant JR 400 concentration by incrementing the SDS concentration. Figure 6a shows the enthalpy per injection (ΔH̅ int,j (T, P, ctot s,j )) at 35.0 ± 0.2 °C for a typical path of SDS addition to JR 400 (cp = 0.5 mM). The corresponding visual phase boundaries are shaded by different regions. Any abrupt change in the peak area from one injection to the next in a typical microcalorimetric experiment indicates a significant change in the enthalpy of mixing. Therefore, ITC measurements can reveal changes in solution thermodynamics, such as a phase transition or a change in phase composition, as is demonstrated in Figure 6. The slightly negative (i.e., exothermic) enthalpy evident at low SDS concentration indicates the reversible binding of SDS onto polymers upon approaching the CAC, in agreement with reported ITC studies of similar polymer−surfactant mixtures.46,49,76 The maximum at ctot s = 0.03 ± 0.01 mM corresponds to the CAC. Note that these concentrations are significantly below the CMC for SDS (8.6 ± 0.4 mM in water by ITC here and 8.2 mM in the literature16). Further surfactant addition leads to a strong exothermic response with a maximum (corresponding to a minimum in the plot) at ctot s = 0.37 ± 0.07 mM, which corresponds to the

Figure 5. Comparison of visual-ITC phase behavior for the JR 400/ SDS mixture at 25.0 ± 0.1 °C: phase boundary from this study (solid blue line). Data from Goddard et al.61−63 (open circles) and from Yamaguchi et al.60 (open squares). The dashed line represents the charge-equivalent line. The concentration of JR 400 is given in millimolar charge equivalents (left axis) and weight percent (right axis). (This figure is reproduced from referenced data via converting weight percentage to charge equivalents as indicated in Table 1.)

the literature. (Phase behavior information obtained from ITC measurements is also included and compared in Figure 5. Refer to section 3.2). The specific sample compositions investigated are given in Supporting Information S.2. Our phase diagram is presented in terms of the polyelectrolyte charge equivalence concentration, and phase boundaries from this study are denoted by solid lines. Figure 5 includes a reconstruction of the published phase diagrams recalculated using the average residue molecular weight per cationic charge of the polymer as given in Table 1.60−63 The weight percentages marked on the right y Table 1. Comparison of Polyelectrolytes Used in Each Study

Goddard et al.

Yamaguchi et al. our study

Mw (kDa)

PDI

∼500

N/A

670

∼400

N/A

670

N/A

N/A

∼1000

500

N/A

959

360

1.85

1007

equivalent charge (g/mol)

manufacturing Union Carbide Corporation Union Carbide Corporation Amerchol Inc. (Dow Personal Care) Amerchol Inc. (Dow Personal Care) Amerchol Inc. (Dow Personal Care)

axis correspond to the molecular weight of JR 400 used in this study. The concentration range explored in this study, which encompasses the literature, is between 0.03 and 5 mM charge equivalents for JR 400 and between 0.02 and 40 mM for SDS. The phase-separation boundary at low SDS concentration tracks the charge-neutralization line and agrees with both literature studies. The redissolution boundary is in agreement with that observed by Goddard,61−63 which is at higher SDS concentrations than reported by Yamaguchi et al.60 This phase diagram is independent of temperature over the range studied (25−45 °C). 10354


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in slope (the inflection point) occurs at ctot s = 0.37 ± 0.05 mM, in line with our observed phase-separation boundary. With increasing SDS concentration, ITC shows further transitions at ctot s = 1.4 ± 0.1 and 4.5 ± 0.2 mM corresponding to the redissolution phase boundary observed by Yamaguchi et al.60 and the redissolution boundary of Goddard et al.31,32,56 and confirmed by our study. The last break in slope corresponds to the critical micelle concentration CMC* (ctot s = 8.0 ± 0.2 mM). Therefore, all of the phase transitions observed visually are also evident in our ITC measurements. An interesting result of our analysis is the subtle but consistent change in the ITC binding isotherm at the spinodal line determined from the visual phase and metastability studies. The change in intrinsic enthalpy observed upon crossing this boundary has not been predicted theoretically to our knowledge. Further interpretation of the phase behavior is obtained by quantitative analysis of the surfactant binding isotherm. 3.3. Binding Isotherm Interpretation. Figure 7a,b shows the surfactant binding enthalpy isotherms obtained by ITC for JR 400/SDS mixtures at different polymer concentrations that are investigated. 3.3.1. Binding Interactions at Low and Intermediate Surfactant Concentrations. The surfactant binding behavior up to the metastable regime was analyzed by fitting the

Figure 6. ITC results for the titration of SDS into 0.5 mM JR 400 solution at 35.0 ± 0.2 °C: (a) molar heat of injection and (b) cumulative molar heat due to interaction showing three binding scenarios: charge neutralization in the polymer-rich regime, polymerboundary micelle formation, and free micellization in the bulk solution (plot indicates the ITC path consisting of the CAC, phase separation, the spinodal−binodal redissolution phase boundary, and the metastable regime in the phase map).

phase separation determined visually (ctot s = 0.40 ± 0.01 mM, Figure 5). Further surfactant addition after nominally achieving charge equivalence leads to lesser enthalpy releases in the solution. The location of the redissolution boundaries obtained tot by Yamaguchi et al.60 (ctot s = 1.45 ± 0.39 mM) and us (cs = 4.2 ± 0.4 mM) is also evident in the ITC results in Figure 6a. Details of the correspondence between the features of the ITC binding isotherms and the phase boundaries determined from visual observation can be found in Supporting Information S.8. Finally, the transition at higher SDS concentration ctot s = 8.0 ± 0.2 mM corresponds to the CMC* of SDS in the polyelectrolyte solution. This is followed by a jump that corresponds to subtracting the reference dilution curve of SDS in pure water, which has a CMC at ctot s = 8.6 ± 0.4 mM at 35 °C (Supporting Information S.1). ITC experiments conducted at other temperatures validates that the phase boundary is independent of temperature over the range studied (details in Supporting Information S.4). The enthalpy changes associated with these thermodynamic transitions can be also identified by the transitions on a cumulative enthalpy plot (ΔH̅ cum,j (T, P, ctot s,j )). Figure 6b shows the cumulative plot corresponding to Figure 6a. The phase boundaries determined visually are also indicated on this plot, and comparison shows that they are well correlated with the enthalpic transitions. The CAC is identified as the first transition point (ctot s = 0.03 ± 0.01 mM). The second break

Figure 7. JR 400/SDS ITC study at 35.0 ± 0.2 °C. (a) Molar interaction enthalpy per injection and (b) cumulative molar interaction enthalpy as a function of the total SDS concentration with the best fitting parameters (scatters − enthalpy versus SDS concentration from ITC: (purple circles) 0.1 mM JR 400 (cat. charge), (blue squares) 0.5 mM JR 400 (cat. charge), (green triangles) 0.8 mM JR 400 (cat. charge), and (solid lines) best fit to the Satake−Yang model (fitting parameters in Table 2). 10355


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Table 2. Satake−Yang-Model-Predicted Least-Error Fitting Parameters cp (mM)

Ku (mM−1)

u

cs (cac) (mM)

ΔH̅ C (kJ/mol)

ΔH̅ N (kJ/mol)

0.1 0.5 0.8

15.0 ± 0.1 16.6 ± 0.1 16.6 ± 0.1

5.5 ± 0.1 2.9 ± 0.1 2.9 ± 0.1

0.032 ± 0.005 0.030 ± 0.004 0.030 ± 0.010

−8.4 ± 0.4 −7.5 ± 0.4 −7.5 ± 0.4

−1.0 ± 0.2 −0.6 ± 0.4 −0.8 ± 0.3

cumulative isotherm to the Satake−Yang model, as indicated by the solid lines in Figure 7a,b. The least-squares error-fitting parameters can be found in Table 2. Three characteristic regimes in Figure 7a are identified in this concentration regime: a plateau in the limit of low surfactant concentration, which reflects the noncooperative binding before the CAC. A peak at intermediate concentration (“cooperativity peak”46) is the strong cooperative binding that, as will be shown, is driven by hydrophobic interactions. A plateau at high surfactant concentration indicates the saturation of absorption by these mechanisms. For all of the polyelectrolyte concentrations that have been investigated, the experimental cumulative binding enthalpy data are well described by the Satake−Yang model, suggesting that the results can be interpreted in terms of the model’s interaction parameters (Figure 7b). The molar enthalpy of cooperative binding is found to be ΔH̅ C = −7.8 ± 0.6 kJ/mol and the enthalpy of noncooperative binding is ΔH̅ N = −8.0 ± 0.3 kJ/mol. For reference, the molar micellization enthalpy of SDS in water is ΔH̅ mic,f_w = [−4.5, −5.5] kJ/mol76 (and is also confirmed by ITC as shown in Supporting Information S.1), and the molar electrostatic binding enthalpy for cation binding to DNA in water is estimated to be ΔH̅ +,− ≈ −1.0 kJ/mol 47). Comparison identifies the noncooperative binding enthalpy as comparable to the enthalpies for ionic binding, suggesting that a single anionic surfactant binds to a cationic site on the polymer. The cooperative binding enthalpy is about one and a half times the molar micellization enthalpy, suggesting that cooperative binding has elements of both the ion pairing and hydrophobic interactions characteristic of micellization. Because the amount of free SDS in solution is negligible for this binding step (details in Supporting Information S.6), on average each cationic binding site is associated with two or three total surfactant molecules at the end of this binding stage. Note that Vincent et al.4 also report that approximately two to four surfactant molecules associate with each cationic charge site of the polymer chain for an analogous system. Studies were performed at varying polyelectrolyte concentrations, and the cumulative interaction enthalpies measured for each polymer concentration have been normalized by the corresponding number of cationic sites and are shown in Figure 8. Note that these normalized binding isotherms superpose well and can be expressed by a common normalized Satake−Yang model well into the phase-separated region. This indicates that the interaction is scaled by the total number of cationic charges, namely, the available binding sites, but the intrinsic binding energy per single site is independent of the polymer concentration. Sjostrom et al.29 reveals a two-step binding mechanism of JR400/SDS association. In light of this result, it is likely that following charge neutralization a second type of cooperative surfactant binding to the polymer occurs at high surfactant concentrations beyond the stoichiometric point. The binding site is possibly associated with the hydrophobic domains of the hydroxy-ethyl groups. This binding eventually leads to a charge reversal of the polymer−surfactant complex (termed the

Figure 8. Normalized ITC binding interaction isotherms. The solid line represents the generalized Satake−Yang model.

second CAC2). This is also consistent with the understanding of the ITC results in our study, whereby the differential enthalpy does not completely return to zero after the cooperativity peak. The charge reversal is confirmed by electrophoretic mobility measurements (Table 3 and following discussions). Given that surfactant bound cooperatively to the polymer may not be fully dissociated, it is consistent with the data to speculate that the spinodal phase boundary and the third transition point of the ITC isotherm, which correspond well with each other, may reflect this charge-inversion process. A sufficient excess of bound surfactant will eventually electrostatically stabilize the PCSs in solution, leading to redissolution of the coacervate phase. This redissolution behavior is analyzed further in the following discussion. 3.3.2. Composition and Redissolution of PSCs. The driving force for the redissolution of PSCs is investigated via a combination of dynamic light scattering measurements with soft-contact AFM imaging and cryo-TEM imaging. DLS results for a series of samples with constant polymer concentration and incrementally higher surfactant concentration indicate that the hydrodynamic radius of the PSCs changes from a broad distribution in the coacervation regime to a nearly uniform one in the redissolution regime, as shown in Table 3. This observation is in good agreement with the reported “disorder−order” PSCs transition by Zimm et al. (details in Supporting Information S.7).80 AFM soft-contact-mode imaging and the cryo-TEM images shown in Figure 9 demonstrate the spherical structure of these resuspended “ordered” PSCs. The cross-sectional analysis of these images is in good agreement with the size analysis from DLS measurements. The compositions of these resuspended PSCs were characterized by electrophoretic mobility and DLS measurements as follows. In Figure 10, at surfactant compositions above the redissolution boundary, increasing SDS composition leads to a systematic increase in zeta potential at nearly constant hydrodynamic radius. Similar behavior for the electrophoretic 10356


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Table 3. Hydrodynamic Diameter, Zeta Potential, and Average Number of SDSs per Aggregate Z−1 S/P

cp (mM)

ctot s (mM)

0.04 0.2 0.7 12.0 12.5 13.0 14.0 15.0 16.0 18.0

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.02 0.10 0.35 6.0 6.2 6.5 7.0 7.5 8.0 9.0

Dh (nm) 4800 3970 1920 46.9 44.8 44.4 39.9 41.3 43.5 42.0

± ± ± ± ± ± ± ± ± ±

2410 680 770 1.1 0.9 0.5 0.4 0.7 1.2 0.5

ζ (mV)

−17.7 −24.1 −24.0 −28.3 −31.2 −30.0 −40.1

± ± ± ± ± ± ±

0.5 1.0 1.0 1.0 1.0 1.4 1.3

structure disorder disorder disorder order order order order order order order

Nagg,p (DLS)

1209 1212 1211 1211 1214 1218 1221

± ± ± ± ± ± ±

241 241 241 241 242 242 242

regime, and the results are reported in Table 3. We find that the average aggregation number of SDS per single complex is nearly constant (Nagg,p ≈ 1200). The uncertainty in this value arises from an estimated 10% variation of the assumed degree of dissociation α0. This indicates that the PSCs are saturated by SDS at the redissolution boundary such that further SDS addition primarily leads to the creation of micelles in bulk solution. An approximate but interesting calculation of Nagg,p based on the ITC binding isotherm yields comparable results (Nagg,p ≈ 1300) (methods in Supporting Information S.6). However, note that such a comparison requires caution because it is derived from the simplified Satake−Yang binding model.73,74 Sjostrom et al.29 suggested that the JR400/SDS complexes formed above the redissolution boundary are waterswollen equilibrium structures. This also implies that the calculation of the aggregation numbers on the basis of electrophoretic measurements is only a first approximation because it assumes a compact charged sphere surrounded by a double layer. In reality, the excess charges of the bound surfactant molecules could be largely compensated for within the complexes (i.e., within the shear plane) because of the significant water content. A similar issue also arises in the determination of the aggregation number from the ITC measurements because of the simplified interpretation of the microstructure (Supporting Information S.6). Other calculations from theory or simulations and other experimental characterizations (i.e., time-resolved fluorescence quenching, SAXS, or SANS) of the aggregation number can be found in the literature.30,73,74 3.3.3. Binding in the Redissolution Regime. Figure 11 shows the partial cumulative molar interaction enthalpy ΔH̅ cum,j (T, P,ctot s ) in the redissolution regime, corresponding to the formation of resuspended PSCs. Following the analysis in the previous section, we interpret the abrupt enthalpy change in the cumulative heat plot as the enthalpy of formation of polymerbound micelles in the resuspended complex particles. Table 4 lists the fitting parameters and the calculated molar enthalpies of forming polymer-bound micelles (ΔH̅ mic,p_bound) and free micelles (ΔH̅ mic,f_p). For all of the concentrations that have been investigated, it is shown that the formation of polymerbound micelles is more enthalpically and thermodynamically favorable than micellization in solution. This is consistent with the conclusions in other studies, which also suggest that polymer-bound micelles have lower aggregation numbers as compared to those of the free surfactant micelle in water and are more energetically favorable.30 3.3.4. Overall Picture of Surfactant Binding Interactions. The thermodynamic properties are summarized as follows: above the CAC1, the binding is shown to have both ionic and

Figure 9. Spherical resuspended PSCs in redissolution regime: (a) Soft-contact mode AFM image. (b) AFM cross-section analysis for particle size. (c) Low-magnification cryo-TEM image. (d) Highmagnification cryo-TEM image.

mobility measurements have also been reported for similar systems.55,81 The aggregation number of SDS molecules per single PSC, Nagg,p, is calculated from the surface charge as a function of the charge ratio Z−1 (S/P) in the redissolution

Figure 10. Average aggregation number of SDS per single complex Nagg,p vs charge ratio Z−1 (S/P) (anionic charge/cationic charge). 10357


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solution. Thermodynamics properties such as the molar Gibbs free energy and the molar entropy for each binding stage are given in Table 5. As is typical for SDS aggregation,33 the interactions are shown to be driven by the net entropic gain of the release of water unfavorably structured by hydrophobic regions on the surfactant and polyelectrolyte for this model polymer/surfactant mixture. 3.4. Phase Behavior, Surfactant Binding, and Microstructure. Figure 12 provides a schematic model that summarizes the mechanism of surfactant binding to the cationic polyelectrolyte as deduced from observations of the visual phase behavior, ITC, DLS, and zeta-PALS performed in this study. The various states are the following: (1) The polyelectrolyte is molecularly soluble in water with a characteristic blob dimension of ∼2 nm. (2) With a small addition of SDS, strong associative binding leads to phase separation when the surfactant concentration is close to the charge equivalence concentration. (3) Large clusters with local surfactant/polymer aggregates appear in the solution upon approaching the maximum precipitation state. (4) A metastable state may exist depending on the order of gradient addition (i.e., dilution from higher surfactant concentrations). (5) Further addition of SDS induces the formation of polymer-bound micelles, and with sufficient charge reversal, strong electrostatic repulsions counteract the interchain attractions at the redissolution boundary concentration. (6) Resuspension leads to approximately spherical complexes in the solution as stable colloidal particles, and the further addition of SDS appears in the free solution as monomers or micelles (>CCMC,free). The polymer− micelle complexes correspond to individually discrete polymer chains. This schematic model also helps to explain the observed path dependence of the phase behavior. As illustrated in Figure 12, samples prepared according to gradient addition 1 → 6 follow the verified equilibrium behavior whereas samples prepared according to the opposite gradient addition 6 → 5 → 4 exhibit metastable structures that can be in a long-lived nonequilibrium

Figure 11. Cumulative net enthalpy plot of a JR 400/SDS mixture at 35.0 ± 0.2 °C in the redissolution regime with linear fits.

Table 4. Summary of Polymer-Bound Micelle and Free Micelle Calculations cp (mM)

slope1

slope2

ΔH̅ correction,p (kJ/mol)

ΔH̅ mic,p_bound (kJ/mol)

ΔH̅ mic,f_p (kJ/mol)

0.1 0.5 0.8

−0.43 −0.72 −1.06

−1.58 −3.16 −4.17

−0.18 −0.31 −0.44

−0.5 ± 0.1 −1.0 ± 0.6 −1.3 ± 0.5

−4.4 ± 0.6 −4.3 ± 0.5 −4.1 ± 0.5

hydrophobic contributions. When the CAC2, which is the discussed “spinodal” boundary, is crossed, excess SDS binding is driven by the hydrophobic part of the JR 400 backbone. Because of the excess adsorbed surfactant, these complexes are net negatively charged. The composition of the single-phase solution for surfactant concentrations above the binodal redissolution boundary consists of resuspended PSCs, free surfactant monomer, and free surfactant micelles (>CCMC,free) in Table 5. Summary of Thermodynamic Properties cp (mM) 0.1

ccritical (mM) ΔH̅ (kJ/mol) ΔG̅ (kJ/mol) ΔS̅ (kJ/mol K)

0.5


0.8


I. Satake−Yang binding

II. polymer-bound micellization

III. free micellization

cCAC1 = 0.03 ± 0.02 ΔH̅ C = −8.4 ± 0.4 ΔH̅ N = −1.0 ± 0.2 ΔG̅ C = −34.9 ± 0.2 ΔG̅ N = −30.6 ± 0.6 −TΔS̅C = −26.6 ± 0.6 −TΔS̅N = −29.6 ± 0.8 cCAC1 = 0.03 ± 0.01 ΔH̅ C = −7.5 ± 0.4 ΔH̅ N = −0.6 ± 0.4 ΔG̅ C = −35.2 ± 0.2 ΔG̅ N = −32.5 ± 1.6 −TΔS̅C = −27.7 ± 0.6 −TΔS̅N = −31.9 ± 2.0 cCAC1 = 0.03 ± 0.01 ΔH̅ C = −7.5 ± 0.4 ΔH̅ N = −0.8 ± 0.3 ΔG̅ C = −35.2 ± 0.2 ΔG̅ N = −32.5 ± 1.6 −TΔS̅C = −27.7 ± 0.6 −TΔS̅N = −31.7 ± 1.9

cCAC2 = 4.2 ± 0.4 ΔH̅ mic,p_bound = −0.5 ± 0.1

cmic,f_p = 8.0 ± 0.2 ΔH̅ mic,f_p = −4.4 ± 0.6

ΔG̅ mic,p_bound = −42.5 ± 0.4

ΔG̅ mic,f_p = −39.7 ± 0.5

ΔS̅mic,p_bound = 136.3 ± 1.6

ΔS̅mic,f_p = 114.6 ± 3.6


cmic,f_p = 8.0 ± 0.2 ΔH̅ mic,f_p = −4.3 ± 0.5

ΔG̅ mic,p_bound = −42.2 ± 0.6

ΔG̅ mic,f_p = −39.7 ± 0.5

ΔS̅mic,p_bound = 130.0 ± 2.9

ΔS̅mic,f_p = 114.9 ± 3.2


cmic,f_p = 8.0 ± 0.2 ΔH̅ mic,f_p = −4.1 ± 0.5

ΔG̅ mic,p_bound = −42.1 ± 0.4

ΔG̅ mic,f_p = −39.7 ± 0.5

ΔS̅mic,p_bound = 132.4 ± 2.9

ΔS̅mic,f_p = 115.5 ± 3.2

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Figure 12. Molecular structures and equilibrium, nonequilibrium phase behavior of a JR 400/SDS aqueous solution.

state. Indeed, these metastable polymer surfactant complexes may have kinetic stability in the colloidal sense.55−58 As noted in the Introduction, we recognize that the JR 400/ SDS mixtures studied here lie in the conventional mixing plane of a 3D-phase pyramid. As such, we have investigated just a small region of one slice through what is undoubtedly rich phase behavior of this five-component mixture.26 As noted in the Introduction, isolating and employing the insoluble polyion−surfactant salt enables the development of a systematic description of the broader phase behavior.10,32,34−36 Although we do not pursue this line of investigation herein because our goals are to understand a discrepancy in the coacervation reported in the conventional mixing plane and to investigate a path consistent with the technological use of the model system, we note that such an extended study is warranted in the future to develop a more complete understanding of this model system. However, it is possible to use the behavior of the complex salt mixing plane35 in the dilute regime to aid in understanding coacervation in the conventional mixing plane. By assuming that the vast majority of the polyions are condensed in the coacervate phase that we observe as a complex salt phase (JR 400+DS−) with excess adsorbed surfactant ions (including its counterions) (Na+DS−), we can compare against the phase boundaries observed in the complex salt mixing plane. Figure 13 shows the mapping results for both the redissolution boundary (binodal) and the spinodal line. The phase boundary reported by Svensson et al.35 shows reasonable agreement with our redissolution boundary. Again, the spinodal line lies far below the redissolving line even in the complex salt mixing plane. This agreement further confirms that we have identified the true redissolution boundary in the complex mixing plane.

Figure 13. Binodal and spinodal phase boundaries on the polyion− surfactant ion complex salt/surfactant/water mixing plane. The black solid line is the phase boundary in the complex salt mixing plane reported by Svensson et al.35

surfactant concentrations reported by Goddard et al.61−63 and Yamaguchi et al.60 are found to delineate a metastable regime. These transitions are also evident in the ITC measurements, further confirming the thermodynamic significance of the boundaries. Samples prepared in this metastable region show stability that is time- and path-dependent. This redissolution boundary is also in agreement with the expectation from the results reported for the complex salt mixing plane. The nature of the coacervate phases formed in the unstable and metastable regimes is identified in this work, and future work will explore their mechanical and microstructural properties. The investigation here provides some useful experimental information and an explanation of the observed equilibrium and nonequilibrium phase behaviors in the model mixture. It is possible that such an observation is also of value for the investigation of coacervation in other polyelectrolyte/surfactant systems.

4. CONCLUSIONS Visual phase behavior studies and ITC measurements establish the phase behavior in JR 400/SDS mixtures in the conventional mixing plane and resolve a discrepancy in the literature as to the location of the redissolution phase boundary. The onset of phase separation and coacervate formation occurs approximately along the charge equivalence composition line, in agreement with earlier literature reports. This transition is evident as a strong minimum in the enthalpy per injection obtained by ITC and by the appearance of a minority gel phase. The discrepancies in the redissolution boundaries at higher

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ASSOCIATED CONTENT

S Supporting Information *

Path-dependence experiment and other ITC studies including the ITC temperature-dependence study, least-squares-error fitting protocol, and SDS binding-concentration profile. This material is available free of charge via the Internet at http:// pubs.acs.org. 10359


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AUTHOR INFORMATION

kB K n± ni,∞ N

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

Nagg,p

ACKNOWLEDGMENTS This work was supported by a grant from the Proctor and Gamble Corporation. Scientific discussions with Dr. Beth Schubert (P&G) are gratefully acknowledged, as is assistance with the cryo-TEM experiments from Dr. Y. Chen (Material Science & Engineering, University of Delaware).

Np q(t) Qj Qtot,j Q(α, γ, N) Rh

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NOMENCLATURE degree of ionization of SDS molar Gibbs free energy of binding normalized by kBT average site coverage Θ molar Gibbs free energies of hydrophobic γ interactions normalized by kBT σi binding indices for each site σ* surface charge density of the spherical resuspended PSCs ζ zeta potential of the resuspended PSCs ε dielectric permittivity of the solvent deionized water at 25 °C cp initial ITC cell loading polymer concentration in charge equivalence ctot total surfactant molar concentration in the ITC s,j cell after the jth injection cinj surfactant titrant molar concentration in the syringe cs,j equilibrium free surfactant concentration in solution at the jth injection e elementary charge (1.602 × 10−19 C) ΔG̅ C molar Gibbs free energy of cooperative binding ΔG̅ N molar Gibbs free energy of noncooperative binding ΔG̅ mic,p_bound molar Gibbs free energy of polymer-bound SDS mixed micelles ΔG̅ mic,f_p molar Gibbs free energy of free SDS micelles in polymer solution ΔG̅ mic,f_w molar Gibbs free energy of free SDS micelles in water ΔH̅ int,j net binding enthalpy per mole of injected surfactant at the jth injection ΔH̅ SDS molar enthalpy of titrating SDS into deionized dil,j * water at the jth injection 400 ΔH̅ JR molar enthalpy of titrating deionized water into dil,j polymer solution at the jth injection ΔH̅ cum,j net cumulative binding enthalpy per mole of injected surfactant at the jth injection ΔH̅ avg,j average molar enthalpy of Satake−Yang binding at the jth injection ΔH̅ C molar enthalpy of cooperative binding ΔH̅ N molar enthalpy of noncooperative binding ΔH̅ mic,p_bound molar enthalpy of polymer-bound SDS mixed micelles ΔH̅ demice,f_p molar enthalpy of demicellization of free SDS micelles in polymer solution ΔH̅ demice,f_w molar enthalpy of demicellization of free SDS micelles in water α0 α

ΔS̅C ΔS̅N ΔS̅mic,p_bound ΔS̅mic,f_p ΔS̅mic,p_w T u Vj ΔV xN zi Z−1 (S/P)

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Boltzmann constant (1.381 × 10−23 J/K) intrinsic binding constant ionic strength of the formulation number concentration of ions number of total binding sites on a single polymer chain number of SDS molecules adsorbed per PSC particle number of charges in the absence of adsorbed SDS on a single polymer chain ITC differential heat input molar heat per injection cumulative molar heat after jth injection ensemble partition function hydrodynamic radius of spherical resuspended PSCs molar entropy of cooperative binding molar entropy of noncooperative binding molar entropy of polymer-bound SDS mixed micelles molar entropy of free SDS micelles in polymer solution molar entropy of free SDS micelles in water temperature cooperativity parameter total volume after the jth injection surfactant titrant volume per injection fraction of noncooperatively adsorbed molecules per mole of injected SDS ion valence ratio of anionic charge to cationic charge

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