Phase Behavior of Salt-Free Polyelectrolyte Gel–Surfactant Systems

Article pubs.acs.org/JPCB

Phase Behavior of Salt-Free Polyelectrolyte Gel−Surfactant Systems Martin Andersson and Per Hansson* Department of Pharmacy, Uppsala University, Box 580, Uppsala SE-75123, Sweden S Supporting Information *

ABSTRACT: Ionic surfactants tend to collapse the outer parts of polyelectrolyte gels, forming shells that can be used to encapsulate other species including protein and peptide drugs. In this paper, the aqueous phase behavior of covalently crosslinked polyacrylate networks containing sodium ions and dodecyltrimethylammonium ions as counterions is investigated by means of swelling isotherms, dye staining, small-angle X-ray scattering, and confocal Raman spectroscopy. The equilibrium state is approached by letting the networks absorb pure water. With an increasing fraction of surfactant ions, the state of the water-saturated gels is found to change from being swollen and monophasic, via multiphasic states, to collapsed and monophasic. The multiphasic gels have a swollen, micelle-lean core surrounded by a collapsed, micellerich shell, or a collapsed phase forming a spheroidal inner shell separating two micelle-lean parts. It is shown that the transition between monophasic and core− shell states can be induced by variation of the osmotic pressure and variation of the charge of the micelles by forming mixed micelles with the nonionic surfactant octaethyleneglycol monododecylether. The experimental data are compared with theoretical predictions of a model derived earlier. In the calculations, the collapsed shell is assumed to be homogeneous, an approximation introduced here and shown to be excellent for a wide range of compositions. The theoretical results highlight the electrostatic and hydrophobic driving forces behind phase separation.

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INTRODUCTION A long standing issue in colloid science is the origin of the poor solubility of oppositely charged polyelectrolyte−surfactant complexes in water.1 The problem is important in many applications where polyelectrolyte−surfactant mixtures are used, e.g., as soluble complexes, liquid crystalline materials, nanoparticles, and insoluble surface coatings. The present paper deals with the related problem of surfactant induced core−shell phase separation in polyelectrolyte hydrogels which is important in, e.g., pharmaceutics and encapsulation technology. Systematic investigations2−6 of aqueous polyelectrolyte− surfactant mixtures, dating back to the 1980s, have established that, above a critical association concentration (cac), the surfactants self-assemble to form polyion-dressed micelles,7−12 a process chiefly driven by the hydrophobic effect and the gain in entropy from releasing polyion counterions.13−16 Soon it was found that the mixtures have a large tendency to phase separate into a dilute phase and a water-poor complex phase. The phase behavior was shown to resemble that of aqueous mixtures of oppositely charged polyelectrolytes.17,18 To simplify interpretations of phase behavior, Piculell and co-workers introduced three-component phase diagrams of water, complex salts, and regular surfactant salts or polyelectrolytes.19−21 They showed that CnTAPAm, complex salts made of alkyltrimethylammonium ions (CnTA+; n = 12,16) and polyacrylate chains (PAm), are insoluble in pure water but may dissolve in the presence of sufficiently large amounts of NaPAm or CnTAX (X = acetate, bromide). The amount needed depends on the nature of the surfactant counterion, the length of the surfactant tail, and the degree of polymerization (m) of PAm. Other features of the © 2017 American Chemical Society

phase behavior, including the importance of hydrophobic attraction between the polyion and the micelles,22 the effect of other additives,23 and the microstructure of the phases, have also been investigated; for a recent summary of the field, see ref 1. A key to understanding the phase behavior is that complex salts gain less entropy than regular surfactant salts by distributing uniformly in a system because polymerized counterions have lower translational freedom than monovalent ones.24 Even weak attractions should then be enough to stabilize a concentrated phase of the complex salt, and more so the larger the degree of polymerization of the polyion. The very low water content and ordered microstructures (e.g., micellar cubic and hexagonal) of the phases have been attributed to polyion-mediated attractions between the micelles, where polyion−polyion correlation and/or bridging attractions are believed to be important.21 Several features of the phase behavior, including the dependency on the degree of polymerization and charge density of the polyion, were captured by a theoretical model by Hansson.25 The results on linear complex salts have been important for the development of the neighboring field of covalently cross-linked polyelectrolyte gel−surfactant interactions.26 Here the so-called volume phase transition (VPT) taking place when surfactant accumulates in the gel27−30 leads to the formation of waterpoor complexes, often with ordered microstructure.31−40 The Received: March 9, 2017 Revised: May 4, 2017 Published: May 25, 2017 6064

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The Journal of Physical Chemistry B

we have chosen to investigate systems containing C12TAPA, NaPA, and water, where the PA chains form one covalently cross-linked spherical network of macroscopic size. Omitting salt makes the phase behavior easier to interpret both since the number of components is reduced and since only water is free to partition between the gel and the liquid. We also investigate how the phase behavior is influenced by osmotic stress and by variation of the micellar charge in the latter case by forming mixed micelles with the nonionic surfactant octaethyleneglycol monododecylether (C12E8). The results are compared with literature data on preswollen NaPA gels binding C12TA+ from solutions in the traditional way and with theoretical model calculations. For the latter purpose, we use a thermodynamic model derived earlier 56 in which we make a useful approximation that markedly simplifies the calculation of core−shell phase equilibria.

driving forces are essentially the same as those for phase separation in mixtures of surfactants and linear polyelectrolytes. The cross-links are of minor importance for the stability of the complexes in the collapsed state and have small effects on the microstructure even in highly cross-linked gels.41 However, they have large effects on the mechanism of VPT and on the properties of gels with coexisting swollen and collapsed phases. In a series of papers from our laboratory, we have shown that biphasic gels with core−shell structures appear as intermediate states during VPT in reservoir solutions of surfactants.28,29,42−45 The shell consists of the collapsed phase which grows at the expense of the swollen core as the phase transformation proceeds. In spherical gels, the mechanism appears to be quite general for VPTs taking place not too far from the critical conditions.46 The current understanding is that nucleation of a new phase in the bulk of a (macroscopic) gel is effectively suppressed by shear deformation energy,47 but if the phase forms a thin shell (surface phase), the transition can start without deforming the network in the swollen part (core).48 The penalty for that is the free energy needed to deform the shell network from the unperturbed isotropic state; the deformation is a consequence of the requirement that the core and the shell networks are equally stretched in the two directions parallel to the interface between the phases. The deformation is largest when the shell first appears, which explains why the core−shell state is never stable when gels are in contact with reservoir solutions of surfactant.28,29,43,45 Moreover, the coexistence cost is larger for swelling than for collapse transitions,48−50 which gives rise to a hysteresis in the VPT.30,49 Stable core−shell states have been observed when the amount of surfactant in the system is smaller than that required to reach the fully collapsed state.28,29,36,39,44,51−55 The core− shell separation induced by C16TA+ in NaPA gels39 has many features in common with the above-mentioned biphasic mixtures of linear complex salt C16TAPA30 and NaPA30. Thus, the surfactant is almost exclusively partitioned to the shell, and the shell has a similar composition and microstructure as the concentrated phase in the linear system. However, the equilibrium state of a gel is a function also of the elastic free energy of the network.39,44,49,56 When the shell has a finite thickness, both the shell and the core are perturbed from their preferred states. The network in the shell is highly anisotropic and has a higher elastic deformation energy than an isotropic phase of the same composition. The tendency to lower the energy gives rise to contractive elastic forces which tends to make the isotropic core network less swollen than what it would be without the shell.39 This in turn affects the partitioning of the network and the other species between the phases, and makes the composition of the phases functions of the relative amounts of them in the gel, a feature not present in systems without elastic effects. Our theoretical results on core− shell phase separation show that, at equilibrium, the collapsed phase forms the shell, even when the volume fraction of the swollen phase is small.56 So far, this has not been falsified by experiments. However, as far as we are aware of, all gels in stable core−shell states in the literature result from experiments where surfactant ions have entered preswollen networks from the solution. To investigate if the final state depends on the way of preparation, we study in this work slightly hydrated gel− surfactant complexes that are allowed to absorb water until reaching osmotic equilibrium with pure water. Inspired by the work on three-component systems by Piculell and co-workers,

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THEORY The gel is described as a mixture of water (w), anionic polymer network (p), surfactant micelles (mic), cationic surfactant monomers (s), and simple cations (+). To calculate the equilibrium distribution of the different species, we use a model derived earlier,56 taking into account the free energy of mixing (Gmix), the electrostatic free energy of the interaction between charged species (Gel), the standard free energy of transferring N surfactant monomers from water to micelle (Gtrans), and the elastic free energy of deforming the network (Gdef). The total free energy of gel is G = Gmix + Gel + Gtrans + G def

(1)

mix

G is calculated assuming ideal mixing corrected for counterion binding to the network and excluded volume interactions between the micelles. In the absence of nonionic surfactant Gmix = Nw ln x w + N+f ln x+ + Ns ln xs + Nmic ln xmic kT ⎛ 4⌀ − 3⌀ 2 ⎞ HS + Nmic⎜ HS − 1⎟ 2 ⎝ (1 − ⌀HS) ⎠ (2)

with kT being the thermal energy, Ni and xi the number and mole fraction of species i, respectively, and ⌀HS the effective hard-sphere volume fraction of micelles. The polymer chains have no translational entropy and are therefore not included in eq 2, except in the calculation of the mole fractions, for which we have

∑ xi = 1 i

i ∈ {w, s, +, mic, p} (3)

Counterion binding is handled in an approximate way by assuming that only a fraction ξ−1 of the simple ions (+) are free to translate inside the gel (i.e., Nf+ = ξ−1N+); the other fraction is treated as bound to the network and has no translational entropy. Here, ξ is the Manning−Oosawa57 charge density parameter equal to lB/b, where b is the linear separation between charges on the polyion and lB is the Bjerrum length; lB = e2/(4πε0εrkT), with e being the elementary charge and ε0εr the permittivity of the medium (water). The correction improves the quantitative agreement between theory and experiments mainly by reducing the swelling of micelle-lean regions. In previous papers, the nonlinear Poisson−Boltzmann model was used for the same purpose.49,56 Other more detailed 6065

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1920 kJ/mol corresponding to −13 kT per molecule, obtained by setting ΔGhc = −39 kJ/mol, γ = 0.018 J/m2,65 N = 60, and a = 62 Å2. Here, ΔGhc is taken from a study of C12TAB by means of the Poisson−Boltzmann theory.66 The other parameter values are suitable for this surfactant.16,66 For example, N has been found to vary between 54 and 69 in the dense shells of PA gels.36 For a spherical gel, the deformation of each volume element is characterized by the two principal strains λθ (circumferential direction) and λr (radial direction). In a volume element located at a distance r from the center, we have r λθ = (6) R

treatments of counterion binding than the one used here can be found in the literature.58,59 No correction is made for the surfactant monomers; the rationale behind this will be given in the discussion. The last term in eq 2 is the correction for deviations from ideal mixing due to excluded volume interaction between micelles, deriving from the Carnahan− Starling hard-spheres equation of state.60 As in previous work, ϕHS is treated as an effective volume fraction related to the actual volume fraction of micelles ϕ by ⎛r + = ⎜ mic ϕ ⎝ rmic

ϕHS

d⎞ ⎟ ⎠

3

(4)

where rmic is the radius of the micelle and d is the effective thickness of the polyion layer surrounding it calculated from the electrostatic model (see below). The electrostatic interactions are described by means of a model of the interaction between charged spheres and oppositely charged polyions used earlier to model surfactantinduced volume transition in gels with results in semiquantitative agreement with experiments. Gel is given by Gel =

Nmic 2πσ 2rmic 3 ⎛ d(L) ⎞ ⎜ ⎟ ε0εr ⎝ rmic + d(L) ⎠

d(L) = Lc(1 − e−L / Lc)

Lc =

2rmic Z

λθ 2 λ r =

Cp* Cp

(7)

where R is the position of the volume element in the unstrained reference state of the gel (see Figure 1), Cp* is the concentration

(5a) (5b)

(5c)

with σ and Z being the micelle surface charge density and the charge number, respectively, and 2L the distance between the surfaces of neighboring micelles. As discussed elsewhere,49,61,62 eqs 5a and 5b are a generalization of an expression for the electrostatic energy between planar surfaces, giving results in good agreement with Monte Carlo (MC) simulations63 in a wide range of electrostatic coupling strengths. 2Lc describes the range of the counterion-mediated attraction between spheres due to ion−ion correlations. The attraction exists at short separation between micelles where the counterions tend to form one correlated “layer” between neighboring micelles rather than separate layers at each micelle. For monovalent counterions, this is the situation when 2L is smaller than the distance between neighboring charges on the surface of a micelle. By letting this define the decay length of the attraction, and with the area per surface charge taken as the area of a circle with diameter 2Lc, one obtains eq 5c. With increasing distance between micelles, the function d(L) approaches asymptotically the value Lc, which can be interpreted as an effective thickness of the electric double layer surrounding a single micelle. The model was recently shown44 to give results in good agreement with MC simulations on charged spheres in oppositely charged networks.64 Gtrans is the nonelectrostatic part of the standard free energy of transferring N surfactant molecules from water to a micelle. Due to the hydrophobic effect, this contribution provides the driving force for the formation of micelles. By including the free energy change of transferring one hydrocarbon chain from water to the micelle interior ΔGhc and the free energy of creating a contact area a per surfactant molecule between water and hydrocarbons at the micelle surface, we have Gtrans = N(ΔGhc + aγ), where γ is a proportionality constant with the units of surface tension. In all calculations, we have used Gtrans =

Figure 1. Gel geometry in the homogeneous reference state (left) and in the heterogeneous core−shell state (right).

of polymer network segments in the reference state, and Cp is the concentration of polymer network segments at r. The elastic energy is calculated from the Wall theory of rubber elasticity.67 The free energy per unit volume of the unstrained reference state is Cp* ⎛ g def ⎞ 1 = − ⎜ln λθ 2λr − (2λθ 2 + λr 2 − 3)⎟ ⎝ ⎠ kT p 2

(8)

with p being a parameter related to the number of segments between cross-links. The total elastic deformation energy of the gel is Gdef =

∫0

R0

g def 4πR2 dR

(9)

with R0 being the radius of the gel in the reference state. Core−Shell Coexistence. With reference to Figure 1, we let ri denote the position of the inner phase boundary between the core and shell and Ri the corresponding position in the reference state. By introducing the scaled radius, R̂ = R/R0, the fraction of network located inside R becomes equal to R̂ 3. The fraction qC of network in the core becomes ⎛ R i ⎞3 3 qC = ⎜ ⎟ = R̂ i ⎝ R0 ⎠

(10)

The elastic free energy of the shell is 6066

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∫R̂

1 3

APS solution. The synthesis was performed in a water-in-oil suspension. Oil density gradients were prepared by the addition of two different oils (1.06−1.09 g/mL) to 2 mL of Eppendorph tubes. For the gel synthesis, 150 μL of the reaction solution was added to each tube, which were then sealed and placed in a water bath at 65 °C for 20 h. The poly(acrylic acid) gel spheres were dialyzed against excess volumes of slightly acidic water (pH 3) for 7 days and thereafter dried at room temperature on a sterile nonstick surface. The water content (11 wt %) was determined by weighing the gel spheres before and after drying at 105 °C for 48 h. The gels were stored in a tightly sealed container prior to use. Preparation of C12TAOH. C12TAB was converted to C12TAOH by means of ion exchange. A 5 g portion of C12TAB was dissolved in 30 mL of water and added to approximately 200 mL of OH-charged anion exchange resins packed on a column. After 5−10 min, the surfactant was eluted by rinsing with water. The process was repeated three times. From the specifications of the ion exchanger (1.2 mequiv/mL of resin), the process was expected to leave a negligible fraction of Br− in the end product. The product (300 mL) was concentrated by evaporating off water in a N2 saturated atmosphere at 22 °C. In order to avoid Hofmann degradation, the process was terminated before the product was completely dry. The surfactant concentration in the paste (57 wt %) was determined by titrating a portion of the paste dissolved in 500 mM NaCl with HCl. Preparation of Gel Samples. To describe the composition of the gels, we define the surfactant-to-polyion charge ratio (β) and the nonionic-to-ionic surfactant ratio (y)

2

gSdef R̂ dR̂

i

(11)

By letting CpS denote the local concentration of polymer segments in the shell and by using eq 7, gdef S can be written as 2 ⎛ ⎞ Cp* ⎜ CpS 1 ⎛⎜ Cp* ⎞⎟ 3⎟ 2 ln = + λθ S + − kT p ⎜ Cp* 2⎟ 2λθ S 4 ⎜⎝ CpS ⎟⎠ ⎝ ⎠

gSdef

(12)

The core network is isotropic and characterized by a single ⎛ Cp* ⎞1/3 strain λC = ⎜ C ⎟ , where CpC is the polymer concentration ⎝ pC ⎠ in the core. The elastic free energy of the core is NpC ⎛ GCdef 3 2 3⎞ 3 ⎜ln λ = λC − ⎟ C + kT p ⎝ 2 2⎠

(13)

where NpC is the number of polymer segments in the core. Calculation of Core−Shell Equilibrium. Exact calculations are rather involved, since the strains and the compositional variables in the shell vary with the distance from the center. In general, finding the free energy minimum requires advanced numerical procedures; a method for finding the equilibrium distribution of molecules by minimizing the total free energy of gel + liquid (here pure water) is given elsewhere.56 However, the results from our previous calculations show that the composition of the shell formed in C12TA+/PA gels is largely independent of the deformational state of the network.49 Therefore, without introducing large errors, the compositional variables and the strains can be treated as independent of each other in the shell. In particular, the composition can be treated as uniform while the strains are allowed to depend on the position in the shell. By making that approximation, the equilibrium state can be calculated analytically. This is a novel approach that should be useful also in other applications of the theory. In the present paper, we determine the equilibrium state by using the condition that the chemical potential of all electroneutral components must be the same in the core and the shell. Since it is the only species allowed to partition between the gel and the surroundings, the chemical potential of water must also be equal to that of pure water. The chemical potentials of all components and the homogeneous shell approximation are described in detail in Supporting Information S1.

β=

y=

[C12TA+]gel [A−]gel

(14)

[C12E8]gel [C12TA+]gel

(15)

with [...]gel denoting the molar concentration inside a gel bead and A− representing polyacrylate charged groups. Three main series of samples were investigated. In series A, β varied from 0 to 0.98 in the absence of C12E8 (y = 0); in series B, y varied from 0 to 2 at constant β = 0.50; in series C, y varied from 0 to 5 at constant β = 0.35. In all three, dehydrated poly(acrylic acid) (PAA) gels (ca. 0.02 g/bead) were allowed to absorb a liquid containing a mixture of water, C12TAOH, NaOH, C12E8 (series B and C), and oil orange. The added amount of the hydroxide salts was always equal to the amount of acrylic acid equivalents, and the concentration of oil orange was small (∼1 per 250 surfactant molecules). In series A, each gel was placed in a container with 400 μL of liquid solution. During the process of absorption of the liquid, the two hydroxide salts (C12TAOH and NaOH) reacted with the cross-linked PAA in the gel to form water, C12TAPA, and NaPA, the latter two in proportions specified by the composition of the initial mixtures. In an attempt to produce homogeneous gels, the volume of the reaction mixture was kept small. As a side effect, the liquid to be absorbed by the gels initially contained undissolved surfactant. This was mainly a technical problem, as it gradually dissolved as surfactant was reacting with the gel. The reaction was allowed to go to completion, and the gels were allowed to equilibrate. After an incubation period, the gels with β > 0.33 were still in contact with liquid and therefore considered to be in swelling

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EXPERIMENTAL SECTION Chemicals. Acrylic acid (Aldrich), N,N′-methylene bisacrylamide (Sigma-Aldrich), TEMED (tetramethylethylene-diamine) (Sigma), ammonium persulphate (Sigma-Aldrich), C12TAB (Sigma), silicon oil (Fluka), octaethylene glycol monododecyl ether C 12 E 8 (Nikko Chemicals), NaOH (Sigma-Aldrich), oil orange ss (o-tolueneazo-β-naphtanol) (Sigma), and anion exchange resins SBR LC NG (Dowex) were all used as received. All aqueous solutions were prepared with Millipore water. Gel Synthesis. Polyacrylic acid gels were synthesized using free radical polymerization (FRAP). The reaction solution contained acrylic acid (AAc), cross-linker (BIS) (1.8 wt%), radical initiator ammonium persulphate (APS), reaction propagation agent (TEMED), and water in the following amounts: 30 g of water, 3.9 g of AAc, and 0.15 g of BIS. To this solution was added 90 μL of TEMED and 1.5 mL of a 0.18 M 6067

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The Journal of Physical Chemistry B equilibrium with pure water. For gels with lower β, additional pure water was added. Before the addition, these gels appeared to be without internal phase boundaries, as deemed by visual inspection. For series B and C, the same procedure was used but the initial volume of the reaction mixture (including also the nonionic surfactant) was small enough to be completely absorbed by all gels. The gels in series B and C were incubated for 3 months, after which all gels were without internal phase boundaries as judged by visual inspection of intact gels. This was confirmed also by cutting up control gel samples prepared in the same way. After that, each gel was allowed to absorb small aliquots of water (volume much smaller than the gel volume) until reaching maximum swelling in pure water, which was taken as the state where the gel did not fully absorb the last given aliquot. This procedure allowed us to calculate accurately the composition of the gels simply from the amount of each substance added to the system. For all series, gels were equilibrated for another 2−10 months prior to examination. Sample Analysis. After equilibration, all gels were weighted and their diameter determined. Gel volumes were calculated from the determined masses using a density of 1.0 g/mL for all samples, as justified by the results of a previous study.36 Subsequently, a razor blade was used to cut the gels in two halves and to remove a 1 mm thick slice from the flat side of one of the halves. The appearance of intact gels and slices was documented by photography, and the internal structure was examined with special attention to the number of different domains, their position, coloration, and texture. For gels in series A, confocal Raman spectroscopy (cRS) was used to probe the relative amounts of surfactant and polymer present in different regions. For series B and C, small-angle X-ray scattering (SAXS) was used to investigate the microstructure. Confocal Raman Spectroscopy (cRS). The Raman spectra were recorded with a confocal Renishaw micro 2000 spectrometer using an argon-ion laser operating at 514 nm. The power of the laser was set to between 0.2 and 1 mW and concentrated with objectives to a laser spot of approximately 3 μm diameter. Lower laser intensities were also applied to certify that no heat-induced effects occurred in the measured data. SAXS. Small-angle X-ray scattering was performed at the Dutch-Belgian Beamline BM26B of the European Synchrotron Radiation Facility (ESRF) in Grenoble. The synchrotron experiments were executed at a wavelength of λ = 0.775 Å. A two-dimensional (2D) multiwire gas-filled detector was placed at 1.5 m from the sample after an evacuated tube. Data were accumulated at room temperature for 60 s with the samples being presented in a rubber ring, sandwiched between thin mica sheets. The sandwich construction was kept together in an aluminum frame, which ensures a sample thickness of 1 mm. The SAXS patterns were normalized to the intensity of the incoming beam, measured by an ionization chamber placed downstream from the sample, and corrected for the detector response prior to azimuthally averaging the isotropic data using the homemade software ConeX.32. Finally, the patterns were corrected for the scattering due to the empty setup, taking into account the sample and sample holder transmission.

Figure 2. Pictures of intact gels (upper row) and slices through the center of each gel (lower) at three different surfactant-to-polyion charge ratios (β) as indicated; y = 0. Micelle-rich regions are stained red by the presence of small amounts of oil orange in all gels. Left column: Slice showing an inner shell rich in micelles separating micelle-lean outer and inner regions. Middle: Micelle-lean core encapsulated by a micelle-rich shell containing a third domain of brighter color. Right: Fully collapsed (one-phase) gel. The pictures are not shown to scale.

slices through the center of each gel in the upper row. The red color is due to the presence of a small amount of the hydrophobic dye oil orange, added to reveal the location of micelle-rich domains. A complete set of pictures of gels at all charge ratios studied is given in Supporting Information S2. The two gels with the lowest charge ratio in Figure 2 clearly contain more than one domain. Since the border between domains is sharp, these gels are considered to be multiphasic but not necessarily in equilibrium. The gel with β = 0.98 is not completely homogeneous, as judged by the distribution of red colored dye. It is possible that this is caused by the different diffusivities of the penetrating species, including the dye. Keeping in mind that the samples were incubated several months, this indicates that inhomogeneity can remain for long times. However, since the gel contains no sharp internal boundaries, we classify it as monophasic. We stress that when determining the phase state we have taken into account the results from SAXS, cRS, and qualitative analyses of the texture of different domains. The resulting number of separate domains for each investigated gel is indicated in Scheme 1, showing a graphical phase map based on all experiments of the present study. Please note that the cartoons of gels in Scheme 1 are drawn to scale and intended to be accurate representations of the dimensions of different gels relative to one another, as well as of shells, cores, and other internal structures. All samples with y = 0 from series A, B, and C are shown in the vertical row with β increasing from top to bottom as indicated. It is possible to distinguish between three regimes: For β < 0.2, the gels are highly swollen, monophasic, and micelle lean; for β values between 0.2 and 0.66, the gels are multiphasic, with sharp borders between micelle-rich and micelle-lean domains; for β ≥ 0.66, the gels are collapsed, monophasic, and micelle-rich. The division into three regimes is supported by measurements of volume. The ratio of the gel volume to that of the volume of the surfactant-free gel (V/V0) for series A is shown as a function of β in Figure 3a. The result shows that the major volume change takes place in the multiphasic region where micelles are clearly present in distinct surfactant-rich domains. In the monophasic range at low β, where the concentration of

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RESULTS Surfactant-to-Polyion Charge Ratio (β) as a Variable. Examples of pictures of gels from series A are shown in Figure 2. The gels contain PA-network, C12TA+, Na+, and water (y = 0). The upper row displays intact gels and the lower row thin 6068

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More surprisingly, C12TA+ was found also in the colorless areas in the outer regions of these gels; see Supporting Information S4. Osmotic Pressure as a Variable. To investigate, qualitatively, how the phase behavior is influenced by osmotic stress, a gel bead from series B with β = 0.50 (y = 0) was dehydrated in steps by exposing it to air with relative humidity less than 100% (osmotic pressure Π > 0). Pictures of the gel in equilibrium with pure liquid water (Π = 0) and in two partly dehydrated states (Π > 0) are included in Figure 4 (see also

Scheme 1. Graphical Presentation of the Phase State of All Samples Investigated

Figure 4. Pictures of intact gels (upper row) and slices through the center of each gel (lower). Pictures to the right of the vertical bar show gels with β = 0.5 in equilibrium with pure water (Π = 0) at different nonionic-to-cationic surfactant ratios (y) as indicated by the number under each column. Pictures to the left of the bar show two different gels with β = 0.5 and y = 0 after drying (Π > 0). The gel to the far left was dried for the longest period; both gels were initially in equilibrium with pure water. Micelle-rich regions are stained red by the presence of small amounts of oil orange in all gels.

micelles appears to be very low, the volume change is small. In the monophasic range at high β, where the gels are highly collapsed and micelle rich, the volume change is likewise small in absolute numbers. However, the relative volume change in this range is quite large and nonmonotonic, as evident from Figure 3b, showing the concentration of polymer charged groups (obtained from the mass of the dry gel material and the volume V0 of the gels with β = 0) and the concentration of surfactant in the gel. A similar behavior has been observed earlier, and the reswelling can be attributed to excluded-volume repulsions between micelles.68 We note in passing that the concentration of PA in the surfactant-free gel (87 mM) is in reasonably good agreement with the value of 80 mM obtained for PA gels with the present degree of cross-linking determined by interpolation of data in ref 69. The domains in multiphasic gels with β = 0.42 and 0.45 were investigated with confocal Raman spectroscopy. As expected, C12TA+ was detected in the red colored regions and in the more dense inner shells but not in the unstained core-regions.

Figure S5). The water content is lowest in the leftmost picture where the gel is homogeneous. Prior to drying, the gel was in a “regular” biphasic state displaying a micelle-rich dense shell surrounding a micelle-lean swollen core (Figure 4: Π = y = 0). During dehydration, the shell did grow and the diameter of the core decreased. The transition between the core−shell and monophasic states was observed in a narrow range of water contents, suggestive of a discrete transition between two states with slightly different water content at a unique osmotic pressure. Please note that in Figure 4 (and Figure 2) the shells

Figure 3. (a) Relative gel volume and (b) concentration of C12TA+ and PA plotted vs β for gels without nonionic surfactant in series A (y = 0). V is the actual gel volume, and V0 is the volume for the same gel with β = 0. The dotted lines in part a are approximate indications of the borders between single and multiphasic regions. The dashed curves in part b are just guides to the eye. 6069

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In series C (β = 0.35), the gel with only cationic surfactant (y = 0) displayed an intensely colored “ring” separating a weakly colored core from an outer shell with even weaker color (Figures 2 and S6). The interpretation is that the gel was captured in a biphasic state with the two swollen domains belonging to the same phase (see below). At y = 0.25, the colors of the swollen domains had approached each other (Figure S6), and at y = 0.5, phase separation appeared to be suppressed, since no sharp internal boundaries could be observed. Additional samples from the same series were examined with the gels in a semihydrated state. These gels had absorbed all of the liquid (400 μL) added to the initially dry networks and after that additional amounts of water but not enough to saturate the gels. All gels were monophasic (Figure S6), except the one with y = 0 which displayed a micelle-lean shell. The microstructure of gels with β = 0.5 (series B) was investigated with synchrotron SAXS. At all compositions, the resulting spectra contained one rather broad peak (see Supporting Information S3). The corresponding d-spacing is interpreted as the correlation distance between micelles. With a uniform distribution of globular micelles, the product d3(y + 1)β/N should be proportional to the volume per polyion charged group (neglecting the concentration of free surfactant monomers). Included in Figure 5 is a plot of d3(y + 1) vs y. Since β is fixed, the nearly linear relationship indicates that N is nearly constant. This means that the variable y can be related to the average charge Z of micelles in a simple way: Z = N/(y + 1), where the denominator is the inverse of the mole fraction of cationic surfactants in the micelles.

are thicker on the pictures of the sliced sections than in the intact gels. This is because, after preparation, the part of the slice belonging to the shell spontaneously contracted and became positioned out of the plane of the core piece. Importantly, tests with repeated hydration/dehydration cycles indicated that the phase transition was reversible in the sense that it was possible to go back and forth between core−shell and homogeneous states just by regulating the water content of the gel. The reversibility is an indication that swollen core− collapsed shell is the equilibrium distribution of phases. However, during hydration, a collapsed shell was formed only when sufficiently small aliquots of water were added in steps near the transition point. When a partly dehydrated monophasic gel was placed directly in a large volume of water, a swollen shell appeared at the surface. Interestingly, a swollen shell was observed also for the gel with β = 0.35 and y = 0 in series C (Figure S6). Nonionic-to-Cationic Surfactant Ratio (y) as a Variable. Pictures of gels from series B (β = 0.50) containing mixtures of the nonionic surfactant C12E8 and C12TA+ at different molar ratios (y) are shown to the right of the vertical bar in Figure 4; the full series is given as Supporting Information (Figure S5) and also depicted in Scheme 1. All gels were originally in a semihydrated, monophasic state. At the lower y-values, the fully hydrated gels displayed a core−shell structure similar to the one at y = 0. With increasing y, the volume of the shell increased relative to that of the core. Fully hydrated gels with y > 0.25 remained monophasic, as exemplified by the gel with y = 1 in Figure 4. Figure 5 shows

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THEORETICAL RESULTS In this section, the results from theoretical model calculations of the phase behavior are presented together with an analysis of the thermodynamic driving force for core−shell phase separation. All results were obtained with the input parameters given in Table 1, chosen to match the properties of the Table 1. Model Parameters N rmic Gtrans/N p C*p b lB vw

Figure 5. Data for gels with β = 0.50 given as functions of y. Left hand axis: Gel volume (diamonds) and volume of nonionic surfactant carbon tail (squares) per moles of network charges. Right hand axis: d3(y + 1) (circles); d = spacing from SAXS measurements.

60 1.7 nm −13 kT 28 1.5 M 0.25 nm 0.714 nm 0.030 nm3

components of the experimental systems. In the calculations, the gels were allowed to be monophasic (homogeneous) or biphasic with a collapsed shell and a swollen core (C−S). Two competing homogeneous states with markedly different water content were found. These will be referred to as swollen homogeneous (SH) and collapsed homogeneous (CH), respectively, β as a Variable. Figure 6 shows the dif ference in free energy (per polyion charge) between the C−S state and the homogeneous gel states, calculated as functions of β (y = 0) (thick curves). A negative difference means that C−S is the thermodynamically favored state. Going from lower to higher β, it can be seen that the C−S state becomes available at β = 0.023, but SH remains the most favorable state up to β = 0.35.

how the gel volume (V) per mole of charged groups in the network (np) depends on y. In the monophasic range, the volume increases with increasing y. Shown in Figure 5 is also the contribution to the gel volume from the hydrocarbon chains (351 Å3/chain) of the nonionic surfactant molecules (squares). Since the micelles contribute very little to the gel volume, it is clear that the increase is due to the absorption of water, reflecting a change of the intermolecular interactions in the gel. The volume per polymer charge for the gel with y = 0 is equal to 1.7 M. The value is larger than expected at the same β for the gels from series A in Figure 3b, suggesting that the swelling (and the internal morphology) depends on the sample history in this β-range. 6070

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To clearly display the driving force behind shell formation, the individual contributions to the free energy difference from Gmix, Gel, Gtrans, and Gdef are included in Figure 6 (thin curves). In the narrow range at low β where the SH gels contain no micelles, shell formation is chiefly favored by the hydrophobic effect (ΔGtrans < 0) but to a very minor extent also by the elastic free energy. In this range, it is counteracted by the electrostatic interactions because formation of micelles in the shell means that charged interfaces are created which are not present in the SH state. However, the electrostatic energy in the shell is quite low, since the polyion and micelle charges are in close proximity of each other. This is the major reason why the surfactant concentration required for shell formation (0.97 mM; β ≈ 0.02) is lower than that for micelle formation in the homogeneous state (1.2 mM; β ≈ 0.03). The difference is maintained throughout the C−S range because the fraction of free surfactant monomers is always largest in the SH state (for a given β). This explains why the hydrophobic effect continues to favor the C−S state also at high β. However, the hydrophobic driving force for shell formation decreases somewhat when the major fraction of the surfactant molecules are in micelles in both states; for β > 0.23, the electrostatic interaction is the major factor promoting phase separation. The electrostatic driving force increases in importance with increasing β because the electrostatic free energy per micelle is always lower in the C−S state than in the SH state. Shell formation is counteracted by the free energy of mixing, since a nonuniform distribution of molecules is created in the gels, and since the gel volume is smaller in the C−S state than in the SH state. However, the simple counterions (+) are fairly evenly distributed between the core and the shell, as evident from the inset in Figure 7 showing the concentration of (+) in the core (solid line) and in the aqueous subdomain of the shell (dotted). (Note that the calculation of entropy is based on mole fractions but since the number of water molecules greatly exceeds the number of all other molecules in the shell x+S is essentially proportional to the concentration of + in the aqueous domains.) It is clear from Figure 6 that the electrostatic interactions are responsible for the change of state from SH to C−S at β ≈ 0.35, where the two states have the same free energy. The change of state is associated with a discrete volume change, as evident from Figure 7. In fact, in the C−S state immediately to the right of the transition point, 34% of the network chains are in the shell which occupies 1.5% of the gel volume. A discontinuous change is expected, since the SH and C−S states never have exactly the same composition. In practice, the composition of the system can be very close to, but never exactly, equal to the transition composition. As can be seen in Figure 6, shell formation is also favored by the elastic free energy (Gdef), albeit to a very a minor extent. This is not entirely obvious, since the shell network is in an extremely anisotropic deformational state and more concentrated than in the relaxed reference state. However, while the network in the homogeneous state is equally stretched in all three directions, the shell network is stretched in the two lateral directions and compressed in the radial direction. Even though the compression is considerable, the formation of the shell allows the gel network as a whole to relax. Furthermore, increasing the fraction of chains in the shell increases the excess pressure on the core (ΔP) due to larger restoring elastic forces in the shell, leading to deswelling of the core network. The latter effect contributes to the nonlinear evolution of the gel

Figure 6. Theoretically calculated total difference in free energy (per polymer charge) between core−shell and homogeneous states (thick curves) and the contributions to the difference from Gmix, Gel, Gdef, and ΔGtrans (thin curves) plotted vs the surfactant/polymer charge ratio β (y = 0). Solid curves: GC−S − GSH. Dotted curves: GC−S − GCH.

For β-values between 0.35 and 0.88, C−S is the most favorable state; above that range, CH is the only available state (β > 1 were not investigated). CH is available for β > 0.66 but has higher free energy than SH for β < 0.75. Figure 7 shows how the gel volume (V/V0) of the three competing states varies as a function of β. For a given β, the gel

Figure 7. Theoretically calculated relative gel volume (V/V0) plotted vs β for the swollen homogeneous (SH), core−shell (C−S), and collapsed homogeneous (CH) state (left axis); y = 0. Shown is also the calculated total concentration of surfactant and polyion charges in the gel in the C−S and CH states (right axis). Inset: Calculated concentration of small ions (+) in the core (solid curve) and aqueous regions in the shell (dotted curve).

volume is always smaller for C−S than for SH. The plot also highlights the large difference in swelling between the SH and CH states. The onset of shrinking in the SH state coincides with the appearance of micelles at β ≈ 0.03. In the premicellar range, the gel volume initially increases with increasing β. This is a consequence of allowing only the simple counterions to “condense” on the polyion chains. Thus, replacing the simple ions with surfactant ions increases the fraction of freely mobile ions and therefore the osmotic swelling pressure inside the gel (see below). 6071

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The Journal of Physical Chemistry B volume in the C−S range seen in Figure 7, as shown earlier.25,39,56 Above β = 0.35, C−S remains the most stable state as long as it is accessible, i.e., even for β > 0.75, where CH is the competing state. In the latter range, the electrostatic interactions still provide the dominating driving force for shell formation, as shown by the contributions to the free energy differences between C−S and CH included in Figure 6 (dotted curves). This is explained by the closer packing of the micelles in the shell. However, in this range, C−S is also favored by the entropy of mixing, since the gel volume is larger in C−S than in the CH state (Figure 7) which allows for a larger translational freedom of the mobile species. The price for phase separation is elevated elastic and hydrophobic free energies (the latter because of a smaller fraction of surfactant in micelles). For β > 0.88, where CH is the thermodynamically stable state, the free energy minimum associated with C−S no longer exists. At the transition point, there is a small jump in the gel volume when there is still core left (28% of the gel’s volume). The discontinuity is more clearly seen when the total concentrations of polymer charged groups and surfactant are plotted as functions of β, as shown in Figure 7. A similar transition was recently seen in model calculations of gels binding surfactant from solutions of limited volume.56 It can be noted also that the calculated concentration of surfactant in the shell (not shown) is nearly constant (2.1 M) in the entire C−S range, and very close to that in the CH state. At such a high concentration, a disorder−order transition to a liquid crystalline phase (e.g., micellar cubic) can be expected but was not considered in order to simplify calculations. However, it is encouraging that the concentrations in the CH state (i.e., above the transition) are of the same order of magnitude as observed in the experiments (cf. Figure 3b). Osmotic Pressure as a Variable. The effect of drying was investigated theoretically by calculating the equilibrium state of the gel with β = 0.50 (y = 0) at elevated osmotic pressures (equivalent to decreasing the chemical potential of water below that of pure liquid water). According to our calculations, the core−shell state prevails up to Π/RT = 1.01M (98.2% relative humidity) where a discontinuous transition to the homogeneous state takes place. The major volume change takes place already at much lower osmotic pressures, as shown in Figure 8. Water is almost exclusively removed from the core. In the shell, the micelles are so closely packed that further deswelling is effectively prohibited by the excluded volume interactions. The calculated volume of the competing SH state shows a similar evolution (dotted curve). Figure 9 shows the difference in total free energy between the C−S and the homogeneous state as well as the individual free energy contributions. In both states, the fraction of free surfactant monomers decreases as the gel volume decreases and with that also the hydrophobic motive for phase separation. Therefore, in the entire range, the electrostatics is the major driving force behind shell formation. In the lower osmotic pressure range, phase separation is mainly opposed by the free energy of mixing but that contribution decreases as the volume of the gel decreases, and in the upper osmotic pressure range, it even favors the C−S state. Instead, the resistance from the elastic deformation energy increases and finally becomes large enough to completely suppress phase separation. The mechanism is revealed by Figure 10, showing the concentration of polyion in the core and shell and the concentration of the surfactant in

Figure 8. Theoretically calculated relative gel radius and volume as functions of the osmotic pressure (β = 0.5). Solid curves: core (C) and shell (S) boundaries for C−S gels. Dotted curves: homogeneous gel.

Figure 9. Theoretically calculated total difference in free energy (per polymer charge) between core−shell and homogeneous states (thick curves) and the contributions to the difference from Gmix, Gel, and ΔGtrans (thin curves) plotted vs the osmotic pressure; β = 0.5; y = 0.

Figure 10. Theoretically calculated concentration of polyion charges in shell (CpS), micellized surfactant molecules in shell (NCmicS), simple cations in core (C+C), and simple cations in the aqueous regions in shell (C+S) as functions of the osmotic pressure (β = 0.5).

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The Journal of Physical Chemistry B the shell as functions of the osmotic pressure. Removal of water from the core means that the concentration of polyelectrolyte in the core increases. The gel responds by partitioning more of polyelectrolyte (network chains + counterions) to the shell while maintaining the concentration of micelles in the shell nearly constant (the fraction of network in the shell increases nearly linearly with Π). In this way, the system is allowed to reduce the free energy of mixing while maintaining a low electrostatic free energy but not without a cost in elastic free energy due to the nonuniform deformation of the network in the C−S state. Plots of the counterion concentration in the core and in the aqueous subdomain in the shell are included in Figure 10. They show that the system maintains a fairly uniform distribution of counterions throughout the biphasic range. With increasing osmotic pressure, the shell becomes thicker mainly because it has to adapt to the decreasing size of the core, not because the volume of the shell increases. Micelle Charge as a Variable. To investigate theoretically how the phase behavior depends on the parameter y, the micelles were modeled as spheres of radius 1.7 nm and charge Z = 60/(y + 1). The calculations were made at a fixed micelleto-polyion charge ratio equal to 0.5. To simplify the calculations, we neglected the micelle−monomer equilibrium. The justification of that is that at β = 0.5 the hydrophobic driving force for shell formation is much smaller than the electrostatic driving force (see Figure 6). Thus, the fraction of free monomers is small already in the absence of nonionic surfactant and is expected to decrease rapidly with increasing mole fraction of nonionic surfactant in the micelles. The latter effect, due to the entropy of mixing in the micelles, is a wellknown property of binary surfactant mixtures.70,71 Figure 11

Figure 12. Theoretically calculated relative gel volume (V/V0) plotted vs y for the core−shell state (C−S) and the swollen homogeneous state (SH); β = 0.5. The upper x-axis shows the micelle charge (Z).

tions decrease in magnitude with decreasing micelle charge (increasing y), but the electrostatic driving force for phase separation decreases faster than the entropic resistance and so a transition takes place between the C−S and the SH states once the charge is sufficiently low. A closer look at the data behind the plot reveals that the electrostatic energy (per network charge) decreases with increasing y both for C−S and for SH. In the SH state, where, in the y-range shown in Figure 11, the volume fraction of micelles is low (ϕ ≈ 0.01), the decrease is nearly independent of gel volume, and determined mainly by the decreasing surface charge density of the micelles. In the C− S state, however, the decrease is much smaller than what it would be if it depended only on the charge density. The reason is that the distance between micelles in the shell increases with increasing y because of weaker attraction between the micelles, which in the regime of closely packed micelles leads to an expansion of the electric double layer surrounding the micelles. This gives a positive contribution to the electrostatic free energy, partly compensating for the decrease due to the lowering of the charge density. That the shells swell can be seen in Figure 13, showing the concentration of polyion charges (CpS) and the total concentration of surfactant in micelles (NCmicS) in the shell plotted as functions of y. The effect is not completely self-evident, since, for a fixed micelle-to-polyion charge ratio, the number of micelles in the gel increases with increasing y, which explains why, in the SH state, where the volume change is moderate, the distance between the micelles decreases with increasing y (data not shown). To conclude, the suppression of core−shell phase separation following an increase of y (corresponding to a decrease of the micelle charge) is mainly an electrostatic effect related to the swelling of the shell due to weakened attraction between the micelles. It can be mentioned that the core−shell state is metastable up to y-values slightly above 0.5 (Z ≈ 40), where the free energy minimum associated with it vanishes. Interestingly, the elastic free energy is small in the entire range but still to some degree affects where the transition takes place, since the other two contributions nearly cancel out.

Figure 11. Theoretically calculated total difference in free energy (per polymer charge) between core−shell and homogeneous states (thick curves) and the contributions to the difference from Gmix, Gel, and Gdef (thin curves) plotted vs y; β = 0.5.

shows the relevant free energy differences between the C−S and SH states as a function of y. The curve for ΔGtrans has been omitted, since it equals zero when no free monomers are present. As shown by the curve for the total free energy difference (thick curve), the C−S state prevails for y-values up to ca. 0.14 (Z = 53), where a jump transition to the SH state occurs (see Figure 12). A comparison of the individual contributions shows that the C−S state is favored as long as the electrostatic energy gained by packing the micelles into the shell (ΔGel) overcomes the free energy cost of creating a nonuniform distribution of molecules (ΔGmix). Both contribu-

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DISCUSSION Many important aspects of the interaction between polyelectrolyte gels and surfactants of opposite charge have been 6073

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Figure 13. Theoretically calculated concentration of polyion charges in shell (CpS), micellized surfactant molecules in shell (NCmicS) (right axis), simple cations in core (C+C), and simple cations in the aqueous regions in shell (C+S) (left axis) plotted vs y (β = 0.5).

Figure 14. V/V0 plotted vs β. Symbols are experimental data for NaPA gels with bound C12TA+ from this study and gels with 1.8% crosslinker prepared in the traditional way taken from ref 69. Curves are calculated from theory (same as in Figure 7). The arrow indicates the transition from SH to C−S states calculated from theory.

studied in detail by several groups; see ref 26 and papers cited therein. Common to essentially all previous studies is that the surfactants have been absorbed from solution by preswollen polyelectrolyte gels, either for the purpose of studying equilibrium properties or the dynamics of the binding process, the latter accompanied by release of water and network counterions from the gels. The approach taken here is different in at least three respects. First, with a few exceptions, the gels are initially in a moderately hydrated monophasic state containing the surfactant(s), and are subsequently allowed to approach the final state by absorbing additional water. Second, the present systems are totally free from simple salt (such as NaCl). We emphasize that, because even in aqueous mixtures of polyelectrolytes and surfactants prepared without adding simple salt, salt is generated upon mixing by combination of the surfactant and polyion counterions.17 One motive for removing simple salt is thus to reduce the number of components in order to simplify the interpretation of phase behavior. However, there is the additional advantage that mobile ions will be trapped in the gel, due to the condition of electroneutrality, making it easy to control the compositional parameter β. Third, while previous studies have dealt with either nonspherical (macro-) gels or spherical microgels, the gels used here are spherical with volumes in the order of 1 mL. In the following sections, a comparison of the experimental results of the present study with those for systems prepared in the conventional way and with the theoretical predictions is followed by a discussion of general aspects of phase transitions and phase equilibria in gels. Homogeneous States. The plateau-like region at low β in the experimental swelling isotherm (Figure 3a) and the observation of monophasic gel states for β-values up to, at least, 0.2 (Scheme 1) are interesting, since they suggest that the gels can host non-negligible amounts of surfactant micelles without shrinking or undergoing phase separation. The behavior resembles that of preswollen NaPA gels placed in dilute C12TAB solutions without extra added salt reported in an early study.69 The swelling isotherm for gels with 1.4% crosslinker, taken from that study, is shown in Figure 14 together with the one obtained here. The system is suitable for comparison with the present ones, since the amount of NaBr is so small at all compositions that it should have marginal effects

on the interactions inside the gels. Importantly, cooperative binding could be detected in the plateau region at a welldefined surfactant concentration, and the presence of micelles was confirmed by molecular probing. For a gel with 1.8% crosslinker (as in the present study), the critical micelle concentration inside the gel would be ca. 0.5 mM (β ≈ 0.01), as determined by interpolation of data in ref 69. Similar to what is observed here, no significant volume change could be detected until β reached ca. 0.07, and no shells or collapsed phases were observed until β reached much higher values. A similar behavior was recently reported also for spherical PAmicrogels equilibrated in microscopic liquid droplets at an ionic strength of 10 mM.44 In that case, no dense surfactant-rich domains could be detected for β < 0.2, and intact shells were observed only for β > 0.35. From the comparison of the systems, it can be concluded that swollen monophasic states with non-negligible amounts of micelles are reached independently of the way of preparation of the system, and therefore likely represent equilibrium states in this range. In the same region, the theoretically calculated swelling isotherm (Figure 7) has a local maximum instead of a plateau. As already noted, it derives from treating the surfactant monomers as freely mobile while a fraction of the simple counterions are “condensed” on the polyion. This asymmetry has been introduced to account for the fact that PA gels prefer Na+ over C12TA+ in the premicellar range.69 A weak maximum has been observed in a related system,29 but the absence of a maximum in the swelling isotherm in Figure 3a and in ref 69 (see Figure 14) seems to indicate that the effect is either not modeled in a correct way or that it is overestimated or masked by other effects not taken into account in the calculations. In the theoretical calculations, the gel volume starts to decrease immediately above the critical micelle concentration in the gel, in conflict with the results in ref 69. Quite generally, the replacement of Na+ for micelles is expected to lower the swelling pressure in the gel and should therefore promote deswelling of the gel. One explanation to the discrepancy could be that the inhomogeneity of real networks allows a limited number of micelles to form without giving rise to elastic responses observable on the macroscopic scale. 6074

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behavior reported for C16TA+ interacting with PA-gels, where well-defined shells have been observed for β < 0.1 and collapsed domains at very low β (∼0.01) in nonspherical gels. Clearly, C16TA+ has a larger hydrophobic driving force for micelle formation than C12TA+, as evidenced by a 2 orders of magnitude lower critical association concentration in solutions of linear PA.45 Importantly, the theoretical analysis provided in previous sections shows that the hydrophobic interactions also promote phase separation, since shell formation allows a larger fraction of the surfactant to form micelles. Thus, while C16TA+ induces a transition from the SH to the C−S state at a very low β, the much less hydrophobic C12TA+ requires a higher β where also the electrostatic driving force has become sufficiently strong (Figure 6). This is one of the major new findings of the present paper. According to theory, the electrostatic attractions are responsible for the dense packing of the components in the CH state and in the shells formed in the C−S state. We did not perform any calculations for C−S states with the electrostatic attractions removed, since the approximation in the model is not valid for such swollen shells. However, calculations with the electrostatic attraction removed were made for homogeneous gel states. The result shows that there is a driving force for phase transformation also in the absence of polyion-mediated attractions between the micelles, mainly due to the hydrophobic effect, as has previously been demonstrated by others.73 The mechanism is appealing because it is simple but must be rejected, as it cannot account for the low water content of the dense phases observed in experiments. The calculations are described in Supporting Information S5, together with some other theoretical predictions for SH and CH states of equal free energy. Another feature resulting from the model calculations is the nearly uniform distribution of counterions (+) between the core and the shell (Figures 7, 10, and 13). The results and a detailed discussion are included in Supporting Information S5. In the biphasic range, the volumes of the present gels are significantly smaller than those of gels prepared in the traditional way (Figure 14). Because of the large difference in swelling of the collapsed and swollen domains, the latter gives the largest contribution to the gel volume for most compositions. However, the swollen domains are expected to be less swollen than if they were not coexisting in the same gel with the collapsed domain. Theory suggests that the “regular” arrangement with the collapsed phase forming a shell outside the swollen core has a lower free energy than other arrangements of the phases, and also that it gives rise to the smallest deformation of the swollen domain.56 On the basis of this, we argue that the samples with the dense domain forming an inner shell embedded in the swollen matrix are not in equilibrium with respect to the spatial arrangement of the phases. Furthermore, the gel volume should be smaller for those gels than for a regular C−S gel, since, in particular, the swelling of the outer swollen domain is expected to be strongly affected by the presence of the collapsed inner shell. This can explain why the volume of the present biphasic gels is smaller than that for the traditionally prepared ones, and why the theory, which assumes a regular C−S arrangement, is in better agreement with the traditionally prepared ones. The gels with β = 0.42 and 0.45 displayed a surfactant-rich collapsed inner shell separating a swollen core and a swollen outer shell. With cRS, we were able to detect surfactant in the outer shell but not in the core. Furthermore, the outer shell but

The theoretically calculated value of the critical micelle concentration is 1.2 mM (β ≈ 0.03), which is only slightly larger than the experimental value obtained in ref 69 (∼0.5 mM). Similar to the critical micelle concentration in solutions of ionic surfactants with monovalent counterions, it results from a competition between the hydrophobic interactions on the one hand and the free energy of mixing and the electrostatic interactions on the other (Figure 6). The good agreement between the calculated and experimental values suggests that the electrostatic and mixing free energies are reasonably well described by the model. Important here is that the value of the parameter Gtrans/N (−13 kT), describing the hydrophobic driving force, stems from independent data for the surfactant in polyelectrolyte-free solutions (see above). Also, at the highest β-values, the present gels appear to reach the same collapsed state as the ones prepared in the traditional way (Figure 14). In these dense homogeneous states, the crosslinks have no or little effect on the swelling. This is evident from comparison with the swelling of the complex salt in the binary water−C12TAPA6000 system, where the latter component consists of dodecyltrimethylammonium ions and linear polyacrylate with 6000 repeating units in the chain. According to Svensson et al.,19 the water content of the complex phase in equilibrium with pure water is 53 wt %. This corresponds to a surfactant concentration of 1.6 M, in excellent agreement with the concentration in the gel with β = 0.98 (Figure 3b). (Note, the pure complex salt corresponds to the parameter set {β = 1; y = 0} in our work, and the corresponding hydrated gel is a two-component system in the ideal case of a fully connected network.) In the theoretical model, the small influence of the cross-links is explained by the balance of forces in the collapsed phase (β = 1), which is found to be completely dominated by the electrostatic attraction and the excluded volume interaction between the micelles; the influence of elastic forces is very small. Note also that the “mesh size” of the network used in the experiments, which could affect the distribution of, e.g., proteins in gels,72 is not expected to be important for the equilibrium properties of the present systems because the surfactant can redistribute as monomers. Biphasic States. Earlier theoretical work has dealt with the common situation where the surfactant and other mobile ions are free to distribute between the gel and the liquid. Gernandt and Hansson56 showed that the C−S state can only be observed at equilibrium when the total amount of surfactant in the system is limited. For a (free) gel in equilibrium with a reservoir surfactant solution, C−S is never a stable state, but near the critical surfactant concentration, it is observed as an intermediate state during transitions between the SH and CH states.28,29,43,45,49 However, when there is not enough surfactant in the system to reach the CH state, the C−S state can become stable. This is in agreement with the present experiments where the gels in the range 0.2 ≤ β ≤ 0.55 contain both swollen and surfactant-collapsed domains (Scheme 1). For the moment, we will treat them as biphasic, although some of them contain more than two domains. This will be justified later. Furthermore, it will be assumed that they are in chemical equilibrium with respect to the partitioning of components between phases but not necessarily with respect to the spatial distribution of the phases in the gel. The most striking experimental results are the following: (1) The biphasic state only exists in a rather narrow β-range. (2) The transition from the swollen monophasic to the biphasic state requires a substantial amount of surfactant. These findings contrast the 6075

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fluids, the shape of a dispersed phase (e.g., emulsion droplets) is largely determined by the interfacial tension. In gels, the elastic energy is expected to have a larger influence, possibly explaining the shape of the internalized collapsed phases. Another difference vis-a-vis dispersions in fluids is that all phases in a concentric spherical gel, except the core, are by necessity inhomogeneous. This is a consequence of the elastic coupling between the phases. Clearly, in the samples having a dense inner shell, the swollen core and the swollen outer layer are subject to different constraints at their boundaries. This leaves them in different states of deformation and at slightly different compositions, but they can still constitute one phase. The principles governing the phase equilibrium in polymer gels resemble those of coherent phase equilibrium in binary alloys.79 In both cases, the equilibrium conditions contain the relative amount of the phases as variables, due to the elastic coupling between the phases. This means that, in addition to the n + 2 − p potentials that must be specified in order to define the equilibrium state according to Gibbs’ phase rule, pg − 1 phase fractions must be specified for each phase in the gel. Here, n is the number of components, p is the number of phases in the system, and pg is the number of phases in the gel. In the present systems, where p = pg + 1, the number of degrees of freedom becomes n + 2 − p + (p − 2) = n. Thus, the number of potentials that can be varied independently without changing the number of phases is not limited by the number of phases present. At constant temperature and pressure, the number becomes n − 2. Under those conditions, the two-component system characterized by β = 1 and y = 0 has zero degrees of freedom. The gel in this case is homogeneous (pg = 1; p = 2), and the result is in agreement with the phase rule. This is expected, since, in this case, the relative amount of the phases does not enter into the equilibrium conditions. However, for the three-component systems (β < 1; y = 0), the number of degrees of freedom becomes one (at constant temperature and pressure), in agreement with the observation that one chemical potential can be varied without changing the number of phases, even with three phases present (core and shell + pure water). Here it can be noted that according to Gibbs’ phase rule there should be zero degrees of freedom (n − p = 3 − 3 = 0), meaning fixed composition of all phases, in conflict with the observation that the compositions of the core and the shell are functions of β. Likewise, since the number of degrees of freedom is independent of pg, an interpretation of the multiple domains in the gels at intermediate β-values (y = 0) as coexisting multiple phases would not be in conflict with general principles of phase behavior. Despite that, we still believe that the gels with a dense “shell” separating two swollen phases should be considered as biphasic. However, the gel with β = 0.53 appears to be a special case. The innermost and outermost red-stained layers in this gel have a very similar character but are markedly different from the thin layer separating them (Figure 2). As already discussed, the characteristics of the latter resemble those of a micellar cubic phase and it is possible that the micelle-rich regions are slowly undergoing a transition between an ordered and a disordered micellar structure, or that there are three phases in equilibrium in the gel (except for their spatial position). In the latter case, the system would have a total of four phases but still not violate the phase rule, since the number of degrees of freedom is independent of the number of phases. The observations made here are similar to those by Hirotsu80 in a two-component gel−solvent system, where the relative amounts of collapsed and swollen phases coexisting in

not the core was stained red by oil orange. In principle, these observations can be related to a difference in the swelling. According to the theoretical calculations, the surfactant concentration of micelles in the core is always extremely low. This is in part explained by the favorable environment for the surfactant in collapsed domains but also by the fact that the excess pressure ΔP exerted on the core increases the chemical potential of the micelles in the core (since they have a nonnegligible molar volume). Since the outer swollen shell has a free boundary to the liquid phase, the effect is absent there, and thus, the concentration of micelles should be higher. Micelle Charge. The present experiments show that shell formation is suppressed when the micelle charge is below a value somewhere between 40 and 48 (calculated assuming N = 60). This is in qualitative agreement with expectations from previous studies showing, e.g, that the small globular protein cytochrome C, with a net charge of +7, distributes uniformly in the same type of gel.74 There are few studies on the effect of varying the micelle charge in the gel literature. Ashbaugh and co-workers investigated NaPA gels (0.9% cross-linker) in mixed solutions of C12TAB and C12E8.75,76 In one study, the degree of C12TA+ binding (β) covered a large range but the molar ratio between C12E8 and C12TA+ in the gels (y) was either zero or ≳1. No core−shell separation or similar was reported. For the samples containing C12E8, this was in agreement with the present results for gels in the same y-range (Scheme 1). In their control system without C12E8, very few samples were in the βrange where biphasic gels are observed in the present study, which can possibly explain why no shell formation was reported. Neither was shells observed in experiments where y increased from 0.25 to 0.5 as β decreased from 0.95 to 0.65. Since the β-range was higher than that in the gels studied here containing both surfactants, a direct comparison is not possible, but the results seem to be in agreement with ours (Scheme 1). The mixed micelle approach has been used also by others to show that there is a critical charge density required for the interaction between macroions and linear polyelectrolytes.77 It can be mentioned here that previous theoretical calculations on spherical macroions of varying charge and size show that the charge number is more important than the charge density.78 The present experiments suggest that the minimum charge required for shell formation is closer to that typical of micelles rather than small proteins. The present model calculations suggest that the transition from C−S to SH is caused by weaker polyion-mediated attractions between the micelles. However, the transition takes place at a higher charge (Z = 53) and the volume change in the monophasic state is larger than observed experimentally. According to the model calculations, the swelling of the SH state, in the present range, is determined mainly by the balance between the swelling pressure exerted by the small ions and the contractive pressure due to the elastic deformation energy. Both change rather slowly as a function of gel volume, making calculations of the equilibrium swelling sensitive to the exact form of these expressions. This can explain the deviation between theory and experiments. Phase Rule. As already noted, for some compositions in the middle binding range of the samples in series A (β = 0.20, 0.33, 0.42, and 0.45), the collapsed micelle-rich phase forms a spheroidal layer separating two swollen, micelle-lean domains (see Figure 2 and Scheme 1). That does not necessarily imply that the gels contain more than two phases, since the collapsed phase can be considered as dispersed in the swollen phase. In 6076

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homogeneous state has a metastable branch extending down to β = 0.66 (see Figure 7); i.e., it exists in a range approximately overlapping with that of the collapsed homogeneous state in the experiments.

the same gel were found to change with temperature at constant pressure (n = 2; pg = 2; p = 3), but his interpretation of the phase rule is different from ours. Phase Transformations and Metastability. As already noted, the morphologies observed in the middle β-range show that these gels do not reach the same state as preswollen gels placed in surfactant solutions even after 10 months of equilibration. Other indications are the asymmetrical gel shapes and surface structures displayed by the gels with β = 0.42 and 0.45. This is an indication that the multidomain gels with spheroidal inner shells are in kinetically arrested states, which could also contribute to the scattering of the data in the middle β-range in Figure 3a. Theoretical studies of phase transition dynamics suggest that the new phase in a macroscopic spherical gel should first appear at the surface.48,50 The reason is that the nucleation-and-growth mechanism associated with phase transitions in metastable fluids is prohibited by an insurmountable shear-deformation energy barrier.47 Since phase separation is here induced by the absorption of water, it is likely that a swollen shell has initially formed outside the dense core. That state should be less favorable than one with a collapsed shell outside a swollen core,56 but even if there is a mechanism allowing the dense phase to migrate outward in the form of a shell, the driving force is expected to be small and therefore the process should be slow. This might explain why at β = 0.35 and y = 0 a swollen shell was observed also for a gel not in swelling equilibrium with pure water (Figure S6). Another mechanism leading to the formation of a swollen shell could involve surface instabilities induced during the first stages of water absorption. Before water is added, the dehydrated gels are in equilibrium with air with relative humidity well below 100% (Π ≫ 0). Immediately after each addition, before the gel has absorbed the liquid volume added, the osmotic pressure outside the gel is rapidly quenched to zero. During that stage, the outer layers of the gel may become unstable, in particular at the first additions where the gel is very concentrated. All gel samples, except the ones in series A with β ≥ 0.42, were initially in a hydrated monophasic state before the change to the final state was induced by the absorption of additional amounts of pure water. For these samples, concentration gradients initially formed during the penetration of C12TAOH, NaOH, and water are not expected to have strongly influenced the final state. For the gels with β ≥ 0.42 in series A, the final volume was so small that they did not absorb all water in the 400 μL solution they were in contact with during preparation. This means that the ones with β equal to 0.42, 0.45, and 0.53 became inhomogeneous already during the initial incubation period and therefore that the different penetration rates may have influenced the evolution of the internal morphology. An indication of that is that the volumes of the gels with β equal to 0.45 and 0.53 are smaller than expected from comparison with the sample with β = 0.50 and y = 0 in series B, which was initially in a dehydrated monophasic state. Finally, the theoretically calculated upper limit of the core−shell stability range (β = 0.88) is clearly higher than the experimental one (β ≈ 0.6). However, since the theory is in good agreement with the data for gels prepared in the traditional way, the discrepancy may indicate that the present gels are trapped in less swollen metastable states. Indeed, longlived metastable states and hysteresis are intimately associated with phase transitions in gels. It is interesting to note, therefore, that according to the theoretical model the collapsed

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CONCLUSIONS We have investigated the aqueous phase behavior of covalently cross-linked PA networks with Na+ and C12TA+ as counterions at different ratios. It is the first study of such systems with no other electrolytes present and with the gels approaching swelling equilibrium by absorbing water from a dehydrated state. The experiments show that gels with sufficiently low and high surfactant/polyion ratios reach monophasic states of high and low water contents, respectively. The states are very similar to those observed at the same ratios after the surfactant has entered preswollen NaPA-gels by ion exchange from solution (the traditional route), suggesting that these are equilibrium states. At intermediate ratios, the swollen/micelle-poor and dense/micelle-rich domains coexist separated by sharp borders. The dense phase tends to form a spheroidal shell with sharp borders in the interior of the gels, separating a swollen core from a swollen outer shell. This is a novel feature, contrasting the collapsed shell−swollen core separation resulting from the traditional route. It is suggested that the gels are biphasic but in long-lived kinetically arrested states with the dense phase dispersed in the swollen phase. It is found that gels in swollen monophasic states can host substantial amounts of surfactant without entering the biphasic range, in agreement with C12TA+/PA-gels prepared by the traditional route. This shows that surfactant binding/self-assembly in general do not coincide with phase separation in the gel. It is concluded that phase separation can be suppressed by lowering the micelle charge/charge density by forming mixing micelles with nonionic surfactants, and by lowering the water content of the gels. In the theoretical part, we have investigated, for the first time, the phase behavior of salt-free surfactant−gel systems by means of thermodynamic model calculations. By approximating the shells as homogeneous while maintaining an exact treatment of the deformation of the network structure, we have been able to calculate the conditions for equilibrium between swollen core and collapsed shells by analytical means. The calculations, which are in semiquantitative agreement with the experiments, reveal the interplay between electrostatic and hydrophobic driving forces. While the hydrophobic effect promoting surfactant self-assembly provides the largest driving force for phase separation at low surfactant/polyion ratios, the electrostatic driving force, attributed to polyion-mediated forces between the micelles, increases gradually to become the dominant one only at higher ratios. This can explain why the swollen monophasic state is observed to prevail even at rather high surfactant/polyion ratios, since C12TA+, a molecule which is not extremely hydrophobic, requires the contribution from both. The calculations also show that, within the model, suppression of phase separation upon lowering the micelle charge is explained by weaker polyion-mediated attractions between the micelles. The critical micelle charge is found to be closer to that typical of micelles than that of small globular proteins like cytochrome c and lysozyme. For the suppression induced by the increase of the osmotic pressure, the calculations reveal a more intricate interplay of driving forces, but in the water poor state where the transition takes place, the 6077

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(11) Hansson, P.; Almgren, M. Large C12TAB Micelles Formed by the Interaction with Sodium Polyvinylsulfate and Sodium Dextransulfate. J. Phys. Chem. 1995, 99, 16694−16703. (12) Hansson, P. A Fluorescence Study of Divalent and Monovalent Cationic Surfactants Interacting with Anionic Polyelectrolytes. Langmuir 2001, 17, 4161−4166. (13) Wallin, T.; Linse, P. Monte-Carlo Simulations of Polyelectrolytes at Charged Micelles. 1. Effects of Chain Flexibility. Langmuir 1996, 12, 305−314. (14) Wallin, T.; Linse, P. Monte-Carlo Simulations of Polyelectrolytes at Charged Micelles. 2. Effects of Linear Charge Density. J. Phys. Chem. 1996, 100, 17873−17880. (15) Wallin, T.; Linse, P. Monte Carlo Simulations of Polyelectrolytes at Charged Micelles. 3. Effects of Surfactant Tail Length. J. Phys. Chem. B 1997, 101, 5506−5513. (16) Hansson, P. Self-Assembly of Ionic Surfactants in Polyelectrolyte Solutions: A Model for Mixtures of Opposite Charge. Langmuir 2001, 17, 4167−4180. (17) Thalberg, K.; Lindman, B.; Karlström, G. Phase Diagram of a System of Cationic and Anionic Polyelectrolyte: Tetradecyltrimethylammonium Bromide - Hyaluronan - Water. J. Phys. Chem. 1990, 94, 4289−4295. (18) Thalberg, K.; Lindman, B.; Bergfeldt, K. Phase Behavior of Systems of Polyacrylate and Cationic Surfactants. Langmuir 1991, 7, 2893−2898. (19) Svensson, A.; Norrman, J.; Piculell, L. Phase Behavior of Polyion-Surfactant Ion Complex Salts: Effects of Surfactant Chain Length and Polyion Length. J. Phys. Chem. B 2006, 110, 10332− 10340. (20) Svensson, A.; Piculell, L.; Cabane, B.; Ilekti, P. A New Approach to the Phase Behavior of Oppositely Charged Polymers and Surfactants. J. Phys. Chem. B 2002, 106, 1013−1018. (21) Svensson, A.; Piculell, L.; Karlsson, L.; Cabane, B.; Jönsson, B. Phase Behavior of an Ionic Surfactant with Mixed Monovalent/ Polymeric Counterions. J. Phys. Chem. B 2003, 107, 8119−8130. (22) Sitar, S.; Goderis, B.; Hansson, P.; Kogej, K. Phase Diagram and Structures in Mixtures of Poly(Styrenesulfonate Anion) and Alkyltrimethylammonium Cations in Water: Significance of Specific Hydrophobic Interaction. J. Phys. Chem. B 2012, 116, 4634−4645. (23) Janiak, J.; Piculell, L.; Olofsson, G.; Schillén, K. The Aqueous Phase Behavior of Polyion−Surfactant Ion Complex Salts Mixed with Nonionic Surfactants. Phys. Chem. Chem. Phys. 2011, 13, 3126−3138. (24) dos Santos, S.; Gustavsson, C.; Gudmundsson, C.; Linse, P.; Piculell, L. When Do Water-Insoluble Polyion-Surfactant Ion Complex Salts “Redissolve” by Added Excess Surfactant? Langmuir 2011, 27, 592−603. (25) Hansson, P. Phase Behavior of Aqueous Polyion-Surfactant Ion Complex Salts: A Theoretical Analysis. J. Colloid Interface Sci. 2009, 332, 183−193. (26) Hansson, P. Interaction between Polyelectrolyte Gels and Surfactants of Opposite Charge. Curr. Opin. Colloid Interface Sci. 2006, 11, 351−362. (27) Kokufuta, E.; Suzuki, H.; Yoshida, R.; Kaneko, F.; Yamada, K.; Hirata, M. Volume Collapse of a Cationic Poly(Ethyleneimine) Gel Induced by the Binding of Anionic Surfactants. Colloids Surf., A 1999, 147, 179−187. (28) Nilsson, P.; Hansson, P. Ion-Exchange Controls the Kinetics of Deswelling of Polyelectrolyte Microgels in Solutions of Oppositely Charged Surfactant. J. Phys. Chem. B 2005, 109, 23843−23856. (29) Nilsson, P.; Hansson, P. Regular and Irregular Deswelling of Polyacrylate and Hyaluronate Gels Induced by Oppositely Charged Surfactants. J. Colloid Interface Sci. 2008, 325, 316−323. (30) Sasaki, S.; Koga, S.; Imabayashi, R.; Maeda, H. Salt Effects on the Volume Transition of Ionic Gel Induced by the Hydrophobic Counterion Binding. J. Phys. Chem. B 2001, 105, 5852−5855. (31) Khandurina, Y. V.; Dembo, A. T.; Rogacheva, V. B.; Zezin, A. B.; Kabanov, V. A. Structure of Polycomplexes Composed of CrossLinked Sodium Polyacrylate and Cationic Micelle-Forming Surfactants. Polym. Sci. 1994, 36, 189−194.

homogeneous state is favored by the elastic deformation energy.

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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.jpcb.7b02215. (S1) Chemical potentials and the homogeneous shell approximation; (S2) pictures of gels; (S3) SAXS spectra; (S4) Raman spectra; (S5) additional theoretical results (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +46(0) 184714027. ORCID

Per Hansson: 0000-0002-0895-1180 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the Swedish Research Council (grant no. 621-2011-4325). We thank Prof. Bart Goderis and co-workers for the synchrotron SAXS measurements.

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REFERENCES

(1) Piculell, L. Understanding and Exploiting the Phase Behavior of Mixtures of Oppositely Charged Polymers and Surfactants in Water. Langmuir 2013, 29, 10313−10329. (2) Goddard, E. D.; Hannan, R. B. Cationic Polymer/Anionic Surfactant Interactions. J. Colloid Interface Sci. 1976, 55, 73−79. (3) Hayakawa, K.; Kwak, J. C. T. Surfactant-Polyelectrolyte Interactions. 1. Binding of Dodecyltrimethylammonium Ions by Sodium Dextran Sulfate and Poly(Styrenesulfonate) in Aqueous Solution in the Presence of Sodium Chloride. J. Phys. Chem. 1982, 86, 3866−3870. (4) Abuin, E. B.; Scaiano, J. C. Exploratory Study of the Effect of Polyelectrolyte-Surfactant Aggregates on Photochemical Behavior. J. Am. Chem. Soc. 1984, 106, 6274−6283. (5) Dubin, P. L.; Rigsbee, D. R.; McQuigg, D. W. Turbidimetric and Dynamic Light Scattering Studies of Mixtures of Cationic Polymers and Anionic Mixed Micelles. J. Colloid Interface Sci. 1985, 105, 509− 515. (6) Chu, D.; Thomas, J. K. Effect of Cationic Surfactants on the Conformational Transition of Poly(Methacrylic Acid). J. Am. Chem. Soc. 1986, 108, 6270−6276. (7) Almgren, M.; Hansson, P.; Mukhtar, E.; van Stam, J. Aggregation of Alkyltrimethylammonium Surfactants in Aqueous Poly(Styrenesulfonate) Solutions. Langmuir 1992, 8, 2405−2412. (8) Kiefer, J. J.; Somasundaran, P.; Ananthapadmanabhan, K. P. Size of Tetradecyltrimethylammonium Bromide Aggregates on Polyacrylic Acid in Solution by Dynamic Fluorescence. In Polymer Solutions, Blends, and Interfaces; Noda, I., Rubingh, D. N., Eds.; Elsevier: Amsterdam, The Netherlands, 1992; Vol. 11, pp 423−444. (9) Hansson, P.; Almgren, M. Interaction of Alkyltrimethylammonium Surfactants with Polyacrylate and Poly(Styrensulfonate) in Aqueous Solution: Phase Behavior and Surfactant Aggregation Numbers. Langmuir 1994, 10, 2115−2124. (10) Hansson, P.; Almgren, M. Polyelectrolyte Induced Micelle Formation of Ionic Surfactants and Binary Surfactant Mixture Studied by Time-Resolved Fluorescence Quenching. J. Phys. Chem. 1995, 99, 16684−16693. 6078

DOI: 10.1021/acs.jpcb.7b02215 J. Phys. Chem. B 2017, 121, 6064−6080

Article

The Journal of Physical Chemistry B (32) Khokhlov, A.; Makhaeva, E. E.; Philippova, O. E.; Starodubtzev, S. G. Supramolecular Structures and Conformational Transitions in Polyelectrolyte Gels. Macromol. Symp. 1994, 87, 69−91. (33) Dembo, A. T.; Yakunin, A. N.; Zaitsev, V. S.; Mironov, A. V.; Starodubtsev, S. G.; Khokhlov, A. R.; Chu, B. Regular Microstructures in Gel-Surfactant Complexes: Influence of Water Content and Comparison with the Surfactant Structure in Water. J. Polym. Sci., Part B: Polym. Phys. 1996, 34, 2893−2898. (34) Sokolov, E. L.; Yeh, F.; Khokhlov, A.; Chu, B. Nanoscale Supramolecular Ordering in Gel-Surfactant Complexes: Sodium Alkyl Sulfates in Poly(Diallyldimethylammonium Chloride). Langmuir 1996, 12, 6229−6234. (35) Yeh, F.; Sokolov, E. L.; Khokhlov, A. R.; Chu, B. Nanoscale Supramolecular Structures in the Gels of Poly(Diallyldimethylammonium Chloride) Interacting with Sodium Dodecyl Sulfate. J. Am. Chem. Soc. 1996, 118, 6615−6618. (36) Hansson, P. Surfactant Self-Assembly in Polyelectrolyte Gels: Aggregation Numbers and Their Relation to the Gel Collapse and the Appearance of Ordered Structures in the NaPA/C12TAB System. Langmuir 1998, 14, 4059−4064. (37) Zhou, S.; Burger, C.; Yeh, F.; Chu, B. Charge Density Effect of Polyelectrolyte Chains on the Nanostructures of PolyelectrolyteSurfactant Complexes. Macromolecules 1998, 31, 8157−8163. (38) Zhou, S.; Yeh, F.; Burger, C.; Chu, B. Nanostructures of Polyelectrolyte Gel-Surfactant Complexes. J. Polym. Sci., Part B: Polym. Phys. 1999, 37, 2165−2172. (39) Hansson, P.; Schneider, S.; Lindman, B. Phase Separation in Polyelectrolyte Gels Interacting with Surfactants of Opposite Charge. J. Phys. Chem. B 2002, 106, 9777−9793. (40) Nilsson, P.; Unga, J.; Hansson, P. Effect of Salt and Surfactant Concentration on the Structure of Polyacrylate Gel/Surfactant Complexes. J. Phys. Chem. B 2007, 111, 10959−10964. (41) Yeh, F.; Sokolov, E. L.; Walter, T.; Chu, B. Structure Studies of Poly(Diallyldimethylammonium Chloride-Co-Acrylamide) Gels/Sodium Dodecyl Sulfate Complex. Langmuir 1998, 14, 4350−4358. (42) Andersson, M.; Råsmark, P. J.; Elvingson, C.; Hansson, P. Single Microgel Particle Studies Demonstrate the Influence of Hydrophobic Interactions between Charged Micelles and Oppositely Charged Polyions. Langmuir 2005, 21, 3773−3781. (43) Göransson, A.; Hansson, P. Shrinking Kinetics of Polyacrylate Gels in Surfactant Solution. J. Phys. Chem. B 2003, 107, 9203−9213. (44) Jidheden, C.; Hansson, P. Single Microgels in Core-Shell Equilibrium: A Novel Method for Limited Volume Studies. J. Phys. Chem. B 2016, 120, 10030−10042. (45) Nilsson, P.; Hansson, P. Deswelling Kinetics of Polyacrylate Gels in Solutions of Cetyltrimethylammunium Bromide. J. Phys. Chem. B 2007, 111, 9770−9778. (46) Matuso, E. S.; Tanaka, T. Kinetics of Discontinous VolumePhase Transition of Gels. J. Chem. Phys. 1988, 89, 1695−1703. (47) Onuki, A. Paradox in Phase Transitions with Volume Change. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 2192−2195. (48) Sekimoto, K. Temperature Hysteresis and Morphology of Volume Phase Transitions of Gels. Phys. Rev. Lett. 1993, 70, 4154− 4157. (49) Gernandt, J.; Hansson, P. Hysteresis in the Surfactant-Induced Volume Transition of Hydrogels. J. Phys. Chem. B 2015, 119, 1717− 1725. (50) Tomari, T.; Doi, M. Hysteresis and Incubation in the Dynamics of Volume Transition of Spherical Gels. Macromolecules 1995, 28, 8334−8343. (51) Filippova, O. E.; Makhaeva, E. E.; Starodubtsev, S. G. Interaction of the Low Cross-Linked Gel of Diallyldimethylammonium Bromide with Sodium Dodecylsulfate. Polym. Sci. 1992, 34, 602− 606. (52) Hansson, P.; Schneider, S.; Lindman, B. Macroscopic Phase Separation in a Polyelectrolyte Gel Interacting with Oppositely Charged Surfactant: Correlation between Anomalous Deswelling and Microstructure. Prog. Colloid Polym. Sci. 2000, 115, 342−346.

(53) Khandurina, Y. V.; Rogacheva, V. B.; Zezin, A. B.; Kabanov, V. A. Interaction of Cross-Linked Polyelectrolytes with Oppositely Charged Surfactants. Polym. Sci. 1994, 36, 184−188. (54) Råsmark, P. J.; Andersson, M.; Lindgren, J.; Elvingson, C. Differences in Binding of a Cationic Surfactant to Cross-Linked Sodium Poly(Acrylate) and Sodium Poly(Styrene Sulfonate) Studied by Raman Spectroscopy. Langmuir 2005, 21, 2761−2765. (55) Starodubtsev, S. G. Influence of Topological Structure of Polyelectrolyte Networks on Their Interaction with Oppositely Charged Micelle-Forming Surfactants. Vysokomol. Soedin. Ser. B 1990, 32, 925−930. (56) Gernandt, J.; Hansson, P. Surfactant-Induced Core/Shell Phase Equilibrium in Hydrogels. J. Chem. Phys. 2016, 144, 064902. (57) Manning, G. S. Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties. J. Chem. Phys. 1969, 51, 924−933. (58) Anderson, C. F.; Record, T. M. Polyelectrolyte Theories and Their Applications to DNA. Annu. Rev. Phys. Chem. 1982, 33, 191− 222. (59) Rumyantsev, A. M.; Pan, A.; Roy, S. G.; De, P.; Kramarenko, E. Y. Polyelectrolyte Gel Swelling and Conductivity Vs Counterion Type, Cross-Linking Density, and Solvent Polarity. Macromolecules 2016, 49, 6630−6643. (60) Carnahan, N. F.; Starling, K. E. Equation of State for Nonattracting Rigid Spheres. J. Chem. Phys. 1969, 51, 635−636. (61) Bračič, M.; Hansson, P.; Pérez, L.; Zemljič, L. F.; Kogej, K. Interaction of Sodium Hyaluronate with a Biocompatible Cationic Surfactant from Lysine: A Binding Study. Langmuir 2015, 31, 12043− 12053. (62) Hansson, P.; Bysell, H.; Månsson, R.; Malmsten, M. PeptideMicrogel Interaction in the Strong Coupling Regime. J. Phys. Chem. B 2012, 116, 10964−10975. (63) Moreira, A. G.; Netz, R. R. Binding of Similarly Charged Plates with Counterions Only. Phys. Rev. Lett. 2001, 87, 078301. (64) Edgecombe, S.; Linse, P. Monte Carlo Simulations of CrossLinked Polyelectrolyte Gels with Oppositely Charged Macroions. Langmuir 2006, 22, 3836−3843. (65) Jönsson, B.; Wennerström, H. Thermodynamics of Ionic Amphiphile - Water Systems. J. Colloid Interface Sci. 1981, 80, 482− 496. (66) Hansson, P.; Jö n sson, B.; Strö m , C.; Sö d erman, O. Determination of Micellar Aggregation Numbers in Dilute Systems with the Fluorescence Quenching Method. J. Phys. Chem. B 2000, 104, 3496−3506. (67) Wall, F. T.; Flory, P. J. Statistical Thermodynamics of Rubber Elasticity. J. Chem. Phys. 1951, 19, 1435−1439. (68) Hansson, P. Surfactant Self-Assembly in Oppositely Charged Polymer Networks. Theory. J. Phys. Chem. B 2009, 113, 12903−12915. (69) Hansson, P. Self-Assembly of Ionic Surfactant in Cross-Linked Polyelectrolyte Gel of Opposite Charge. A Physical Model for Highly Charged Systems. Langmuir 1998, 14, 2269−2277. (70) Clint, J. H. Micellization of Mixed Nonionic Surface Active Agents. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1327−1334. (71) Holland, P. M.; Rubingh, D. N. Nonideal Multicomponent Mixed Micelle Model. J. Phys. Chem. 1983, 87, 1984−1990. (72) Eichenbaum, G. M.; Kiser, P. F.; Dobrynin, A. V.; Simon, S. A.; Needham, D. Investigation of the Swelling Response and Loading of Ionic Microgels with Drugs and Proteins: The Dependence on CrossLink Density. Macromolecules 1999, 32, 4867−4878. (73) Tararyshkin, D.; Kramarenko, E.; Khokhlov, A. R. Two-Phase Structure of Polyelectrolyte Gel/Surfactant Complexes. J. Chem. Phys. 2007, 126, 164905. (74) Johansson, C.; Hansson, P. Distribution of Cytochrome C in Polyacrylate Microgels. Soft Matter 2010, 6, 3970−3978. (75) Ashbaugh, H. S.; Lindman, B. Swelling and Structural Changes of Oppositely Charged Polyelectrolyte Gel-Mixed Surfactant Complexes. Macromolecules 2001, 34, 1522−1525. (76) Ashbaugh, H. S.; Piculell, L.; Lindman, B. Interactions of Cationic/Nonionic Surfactant Mixtures with an Anionic Hydrogel: 6079

DOI: 10.1021/acs.jpcb.7b02215 J. Phys. Chem. B 2017, 121, 6064−6080

Article

The Journal of Physical Chemistry B Absorption Equilibrium and Thermodynamic Modeling. Langmuir 2000, 16, 2529−2538. (77) Dubin, P. L.; Thé, S. S.; McQuigg, D. W.; Chew, C. H.; Gan, L. M. Binding of Polyelectrolytes to Oppositely Charged Ionic Micelles at Critical Micelle Surface Charge Densities. Langmuir 1989, 5, 89−95. (78) Gernandt, J.; Hansson, P. Core-Shell Separation of a Hydrogel in a Large Solution of Proteins. Soft Matter 2012, 8, 10905−10913. (79) Liu, Z.-K.; Ågren, J. On Two-Phase Coherent Equilibrium in Binary Alloys. Acta Metall. Mater. 1990, 38, 561−572. (80) Hirotsu, S. Some Exotic Properties of Polymer Gels Associated with the Volume Phase Transition. Ferroelectrics 1997, 203, 375−388.

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DOI: 10.1021/acs.jpcb.7b02215 J. Phys. Chem. B 2017, 121, 6064−6080