Influence of Anion Hydrophilicity on the Conformation of a

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Influence of Anion Hydrophilicity on the Conformation of a Hydrophobic Weak Polyelectrolyte Brush Timothy J. Murdoch,† Joshua D. Willott,† Wiebe M. de Vos,‡ Andrew Nelson,§ Stuart W. Prescott,∥ Erica J. Wanless,† and Grant B. Webber*,† †

Priority Research Centre for Advanced Particle Processing and Transport, University of Newcastle, Callaghan, NSW 2308, Australia Membrane Science and Technology, Mesa+ Institute for Nanotechnology, University of Twente, Enschede 7500 AE, Netherlands § Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW 2234, Australia ∥ School of Chemical Engineering, UNSW Australia, UNSW Sydney, NSW 2052, Australia ‡

S Supporting Information *

ABSTRACT: The conformation of a hydrophobic, weak cationic poly(2-diisopropylamino)ethyl methacrylate (PDPA) brush was studied using neutron reflectometry as a function of aqueous solution pH, ionic strength, and anion identity. In pH 4, 10 mM potassium nitrate the brush is highly charged, resulting in an extended, dilute conformation; at pH 9 the uncharged brush collapses to a single, dense layer. The brush response to added salt at constant pH (4.5) for varying concentrations of the potassium salts of acetate, nitrate, and thiocyanate revealed ion-specific conformations of the brush. At low ionic strength (0.1 mM) the brush was collapsed, independent of salt identity, while at higher ionic strengths (up to 500 mM) the conformation was dependent on counterion identity. The brush exhibited extended conformations in the presence of kosmotropic acetate counterions, while collapsed conformations were retained in the presence of strongly chaotropic thiocyanate counterions. The brush showed a richer set of behaviors in the solutions containing the weakly chaotropic nitrate anion, being similar to acetate (swollen) at intermediate concentrations but similar to thiocyanate (collapsed) at high salt concentrations. Numerical self-consistent field (nSCF) simulations indicate that the response of the brush to pH changes is dominated by the hydrophobicity of the polymer at pH values near the pKa. Furthermore, the simulations reveal that the addition of a single Flory−Huggins interaction parameter analogous to the hydrophilicity of the counterion is sufficient to replicate the observed specific anion response of a hydrophobic weak polyelectrolyte brush.

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(SCF) theories, scaling theories,22 and Monte Carlo23 and molecular dynamics (MD)24,25 simulations. Mahalik and coworkers were able to qualitatively reproduce the volume fraction profile of a poly(2-dimethylamino)ethyl methacrylate brush in aqueous solution determined by neutron reflectometry (NR) using numerical SCF theory.26 Good agreement between NR fits of poly(acrylic acid) and predictions from analytical SCF theories was achieved by Sudre et al.27 For the polyacid at pH 2, the brush is uncharged, and the volume fraction profile was well approximated by theoretically predicted parabolic28 and hyperbolic tangent forms,29 while a Gaussian form30 was a better fit for the charged, swollen brush at pH 9. A key consequence of many theories for weak polyelectrolyte brushes is that the charge distribution throughout the brush is nonuniform due to unfavorable electrostatic repulsion between ionized acid and base moieties in close proximity.14,19 There is

INTRODUCTION Polymer brushes are films of end-grafted polymer chains at a sufficient areal density to force self-interaction.1 Stimuliresponsive brushes are of wide interest as their physicochemical properties and conformation can be tuned through environmental triggers like temperature, ionic strength, and mechanical confinement.2−7 Control over polymer conformation makes responsive brushes ideal for chemical gating and microfluidic applications.8 Brushes formed from weak polyelectrolytes (composed of ionizable monomers) show particularly rich behavior with the solvent quality affected by both pH and ionic strength.9 The swelling behavior of hydrophilic polyelectrolyte brushes in simple 1:1 electrolytes has been well characterized, and close agreement between experiment and theory is possible.10 However, recent experiments show that these theories are incomplete, with brush behavior found to be strongly dependent on the hydrophobicity of the polymer and the identity of the anion used.11,12 Weak polyelectrolyte brushes have been studied theoretically using analytical13−15 and numerical16−21 self-consistent field © XXXX American Chemical Society

Received: August 30, 2016 Revised: November 23, 2016

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DOI: 10.1021/acs.macromol.6b01897 Macromolecules XXXX, XXX, XXX−XXX

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observed in potassium acetate solutions whereas no swelling is seen at any concentration of potassium thiocyanate for the most hydrophobic (PDPA) brush.11 We proposed that the minimal collapse of the polybasic brush at high concentrations of the acetate anions was a result of their low affinity for the brush. Conversely, the increasing extent of collapse at high concentrations of chaotropic anions was attributed to their high affinity for the hydrophobic interfaces within the brush40−46 together with the poor hydration of the anions.47 Chaotropes may also be more efficient at screening the charge of weakly hydrated tertiary amine groups.48 The brush behavior in potassium nitrate solution was intermediate at all concentrations, reflecting the weakly chaotropic nature of this anion. The origin of the affinity of chaotropic anions for hydrophobic interfaces has received considerable experimental40,45,46,49−52 and theoretical attention.40−46 While no unifying explanation exists, it is clear from these reports that the hydration of both the interface and the anion play an important role in the ion specificity. Binding to hydrophobic interfaces requires dehydration of the anion to occur; this is possible for chaotropes, but a high energetic penalty largely prevents this for kosmotropes.44,50 The hydration of charged residues on the surface relative to that of the ion also influences the extent of anion binding.45,53,54 To our knowledge, the only previous simulations of specific ion effects on polymer brushes were performed by Rodriguez-Ropero et al.55 Their MD simulations of a N,N′-dimethyl(methyl)acrylamide-b-methacryclic acid (DMMAA-b-MAA) diblock copolymer brush showed that the rigidity of the charged MAA block increased with the hardness of the counterion, while ion adsorption in the neutral DMMAA block increased with the hydrophobicity of the anion. Herein, we present a neutron reflectivity study of the conformation of a hydrophobic PDPA brush in aqueous solutions of different dissolved ion identity and ionic strength. These data are compared with theoretical predictions from numerical SCF theory, and we show that addition of a single Flory−Huggins interaction parameter for the counterion is sufficient to describe current and previously reported results, while capturing the essential behavior of chaotropic and kosmotropic anions.

a higher degree of ionization at the brush periphery with a shift of the effective pKa for the interior of the brush to a lower (higher) value for polybases (polyacids) resulting from high local electrostatic potentials. The shift in pKa of the bulk relative to the periphery of the brush has been verified experimentally by Dong et al. for a poly(methacrylic acid) brush.31 Three primary mechanisms exist to compensate for the unfavorable electrostatic repulsion: the acid−base equilibrium can shift to the uncharged state, chains can extend at the expense of conformational entropy, or counterions may be localized within the brush at the expense of translational entropy.19 At low ionic strengths, the first mechanism dominates and weak polyelectrolyte brushes are essentially uncharged. With increasing salt concentration, counterion localization is more favorable, allowing the brush to charge while simultaneously swelling the brush due to the increased osmotic pressure (the osmotic regime). With further increase in salt concentration, the brush is fully ionized and the charge screening effects cause the brush to collapse (salted brush regime). We have recently reported that the hydrophobicity of the monomer significantly alters the pH and salt response of weak polybasic brushes formed from poly(2-dimethylamino)ethyl methacrylate (PDMA) and its increasingly more hydrophobic diethyl (PDEA) and diisopropyl (PDPA) analogues.11,12 Increasing hydrophobicity of the polymer shifted the apparent brush pKa (defined as the pH at half brush swelling response) to lower values and caused the brush to swell over a narrower pH range. At low salt concentrations the brushes were collapsed. Contrary to theoretical predictions,14 no swelling of the brush was observed with increasing ionic strength until a critical salt concentration was reached. The value of this critical concentration increased with polymer hydrophobicity. An increase in monomer hydrophobicity is analogous to a decrease in solvent quality in aqueous solutions. Pryamitsyn et al. have studied the response of a weak polyelectrolyte brush as a function of solvent quality using numerical SCF theory.32 They predicted internal phase separation of the brush into a thin, polymer rich layer near the substrate followed by a dilute tail. Increasing the overall brush charge and ionic strength required a lower solvent quality to induce phase separation perpendicular to the grafting interface. Polyelectrolyte brushes in poor solvents also exhibit nanoscale lateral phase separation with experiment33,34 and theory34−37 showing the formation of aggregates such as bundled cylinders, micelles, and maze-like structures. For weak polybasic brushes bundle formation is favored at pH > pKa and low ionic strength where the brush charge is readily downregulated, allowing hydrophobic backbone interactions to dominate.34,37 We have also observed hydrophobicity-dependent specific anion effects on weak polybasic brushes.11 Specific anion effects concern phenomena that are dependent on the identity of ions in solution, not simply their concentration. Salt anions are generally described in terms of the well-known kosmotropic− chaotropic Hofmeister series.38 One way to describe this series is in terms of the hydrophilicity−hydrophobicity of the anions, which correlates with anion hydration strength.38,39 Kosmotropic anions can be classed as relatively hydrophilic and are strongly hydrated. Chaotropic anions are weakly hydrated and so are relatively hydrophobic. In our previous work we showed that for weak polybasic brushes the extent of brush collapse at high salt concentrations increases with anion hydrophobicity; almost no collapse is

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EXPERIMENTAL METHODS

Materials. Native oxide silicon wafers (100 mm diameter, 10 mm thick) for specular neutron reflectometry experiments were purchased from EL-CAT Inc. (USA). 3-Aminopropyltriethoxysilane (>99%), triethylamine (99%), and 2-bromoisobutyryl bromide (>99%) used during surface initiator functionalization were purchased from SigmaAldrich and used as received. Tetrahydrofuran (Honeywell, >99%) and triethylamine were dried over 4 Å molecular sieves before use. Polymerization reagents 2,2′-bipyridine (≥99%, ligand), copper(II) bromide (99.999%, catalyst), and ascorbic acid (≥99.0%, reducing agent) were purchased from Sigma-Aldrich and used as received. 2(Diisopropylamino)ethyl methacrylate (DPA) monomer was purchased from Sigma-Aldrich; monomethyl ether hydroquinone inhibitor was removed from the DPA monomer by gravity feeding through a 10 cm length and 2 cm diameter alumina column (activated, basic) immediately prior to use. Isopropyl alcohol (Chem Supply Pty Ltd., 99.7%) was used in the polymerization solvent mixture. Aqueous solutions of potassium nitrate (KNO3, Sigma-Aldrich, 99%), potassium acetate (KCH3COO, Alfa Aesar, >99%), and potassium thiocyanate (KSCN, Alfa Aesar, >98%) were prepared and used. Solution pH was controlled at the desired value using a minimum of acidic or basic solution. For the pH adjustments of the nitrate and thiocyanate solutions dilute nitric acid (RCI Labscan Ltd., AR grade) or potassium hydroxide (Chem Supply Pty Ltd., >99%) was used. For the acetate B

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Macromolecules electrolyte solutions, acetic acid (Ajax Finechem Pty Ltd., >99.7%) was used for the pH adjustments. Milli-Q water (Merck Millipore, 18.2 MΩ·cm) was used throughout. Specular neutron reflectivity measurements were performed in solutions prepared with deuterium oxide (D2O). Substrate Preparation and Brush Polymerization. Wafer cleaning and initiator functionalization as well as synthesis of poly(2diisopropylamino)ethyl methacrylate (PDPA) brushes using surfaceinitiated activators regenerated by electron transfer atom transfer radical polymerization (ARGET ATRP) methodology were performed following established protocols.11,12,56 Brush polymerization was performed with a solvent mixture of isopropyl alcohol and water in a 9:1 v/v ratio using an ARGET ATRP recipe composed of DPA monomer/copper(II) bromide/2,2′-bipyridine/ascorbic acid in the molar ratios of 2500/1/10/10. The ratio of solvent to monomer was 1:1 v/v. The lower limit estimate for the grafting density of brushes grown with this methodology has been determined previously to be 0.073 ± 0.01 nm−2 using single molecule force spectroscopy.56 Ellipsometry. The dry PDPA brush was characterized by ellipsometry (Nanofilm EP3 single wavelength 532 nm imaging ellipsometer), and data were analyzed using WVASE software.7,11,12,57 The dry thickness of the brush used in the neutron reflectometry measurements was 147 ± 10 Å (an average of five distinct measurement areas over the brush surface). X-ray Reflectometry. The dry PDPA brushes were also characterized via X-ray reflectometry (Panalytical X’Pert Pro X-ray reflectometer). Specular reflectometry measurements were performed as a function of the scattering vector, Q = (4π/λ) sin θ, where λ is the wavelength (Cu Kα 1.54 Å) and θ is the angle of incidence. Data were analyzed using the MOTOFIT package,58 giving the dry thickness of the brushes. The dry thickness of the brush was 153 ± 1 Å. Neutron Reflectometry (NR). Measurements were performed at the OPAL 20 MW reactor located at the Australian Nuclear Science and Technology Organisation, Sydney, Australia, on the Platypus timeof-flight reflectometer. For full details of the instrumental setup please see ref 59. Specular reflectometry measurements were made at two angles of incidence, 0.8° and 3.8° (0.65° and 3.0° in air), giving useful statistical reflection data over the Q range of 0.009−0.31 Å−1 (0.0075− 0.26 Å−1 in air). An angle of incidence of 0.8° was sufficiently shallow to capture the Si:D2O critical edge in solid−liquid experiments. Standard reduction procedures were used with an overall constant Q resolution of 8.8%.59 The selected PDPA brush had a dry thickness of 149 ± 1 Å, which is comparable to the thickness obtained from the XRR measurement (153 ± 1 Å). Prior to wet characterization, the brush was immersed overnight in 10 mM potassium nitrate at pH 4 as an initial brush hydration step,56,57 before assembly into the fluid cell.59 The fluid cell temperature was fixed at 25 °C with temperature control jackets. The PDPA brush pH response was studied by performing NR measurements at pH 4 and then pH 9 in 10 mM potassium nitrate and repeating the solvent cycle. These pH values correspond to maximum and minimum swelling states as measured by ellipsometry and quartz crystal microbalance with dissipation measurements (QCM-D).12 The pH was monitored at both the inlet and outlet of the fluid cell during fluid exchange. NR measurements were also performed for 0.1, 1, 10, 100, and 500 mM solutions of potassium nitrate, acetate, and thiocyanate at pH 4.5. Experiments were performed for increasing concentrations of a single salt, with nitrate measured first followed by acetate and last thiocyanate. Between all measurements, complete solution exchange was confirmed by monitoring the solution conductivity at the cell outlet. NR data were analyzed using an extension to MOTOFIT,58 with a custom model for polymer brushes described in detail elsewhere.60 The model consisted of a native silicon dioxide layer (whose parameters are known from the dry brush measurement) followed by a small number of slabs (≤4) of uniform scattering length density (SLD) that represent the interior (i.e., closest to the substrate) of the brush. The interface between these slabs was smoothed with a Gaussian roughness term. The exterior region of the brush was represented either by a hyperbolic tangent or parabola with power law “tail”, as described by eqs 1 and 2, respectively.60

ϕ(z ̅ ) =

ϕ0 ⎛ ⎛ Z − z ̅ ⎞⎞ ⎟⎟ ⎜1 + tanh⎜2 0 ⎝ ⎝ 2 H ⎠⎠

(1)

α ⎡ ⎛ z ̅ ⎞2 ⎤ ⎜ ⎟ ⎥ ϕ(z ̅ ) = ϕ0⎢1 − ⎝H⎠ ⎦ ⎣

(2)

where ϕ(z)̅ is the volume fraction at distance z̅ from the start of the tail region of the brush, H is the characteristic thickness of the exterior tail region, ϕ0 is the initial volume fraction at the boundary between the interior and exterior tail regions, and Z0 is the thickness satisfying ϕ(Z0) = ϕ0/2. The total thickness of the tail region was set equal to the characteristic thickness for the parabola with power law, while the hyperbolic tangent tail was truncated at a volume fraction of 0.005. The tail region was discretized into 50 layers of uniform volume fraction with a Gaussian roughness equal to a third of the layer thickness smoothly connecting each layer; 50 layers is sufficient to avoid coarse-graining artifacts in the generated reflectivity profile.60 The SLD of the brush layer was then calculated from the volume fraction weighted sum of each component: ρN (z) = ϕ(z)ρN,PDPA + [1 − ϕ(z)]ρN,Solv (z)

(3)

where ρN,Solv is the SLD of the solvent and ρN,PDPA (0.46 × 10−6 Å−2) is the SLD of the polymer determined by the NR measurement in air. The value of ρN,PDPA corresponds to a bulk polymer density of 1.10 ± 0.02 g cm−3 and is consistent with the value determined by XRR (1.0 ± 0.1 g cm−3). Reflectivity was calculated using the Abeles matrix method.58 The effect of counterion concentration on the bulk SLD was accounted for by allowing ρN,Solv(z) to vary by 10% during fitting; this quantity is sensitive to the position of the critical edge. Localized counterions were assumed to have negligible impact on the SLD profile. This assumption was tested for the case where each monomer has an associated counterion in addition to the bulk concentration; the volume fraction of counterions was estimated by the ratio of monomer:anion volume. Anion SLD’s were estimated from published molecular volumes.61 The impact on the recalculated SLD profile and reflectivity was negligible, indicating the assumption is justified. The adaptable interior layers allow the fitted polymer volume fraction profiles to capture behavior that is not predicted by analytical theories for polymer brushes such as thin, dense layers at the substrate. A combination of interior layers followed by an analytical tail has been applied successfully to model the presence of vertical phase separation of a thermoresponsive poly(N-isopropylacrylamide) brush.60 Each reflectivity data set was analyzed with 1, 2, and 3 interior slabs, with each of the two possible tails at the exterior eqs 1 and 2, as well as 1 to 4 slabs without a tail. The fitted reflectivity curve with lowest χ2 error was chosen for presentation. If multiple fits resulted in similar χ2 errors, the curve with the fewest free parameters was selected. Fitting parameters for each condition are summarized in Tables S1−S4. The effective dry thickness (δ) for each profile was calculated by

δ=

∫0

∞

ϕ(z) dz

(4)

δ must be constant throughout all dry and wet measurements because the polymer is covalently bound to the surface. δ is known from the measurements in air, assuming a dehydrated brush. A Lagrange multiplier approach is used to penalize fits in the swollen state with unreasonable values of δ.60 Lastly, the average brush thickness, Laverage, was calculated as twice the first moment of the volume fraction profile:62 ∞

Laverage = 2

∫0 zϕ(z) dz δdry

(5)

A factor of 2 is used in eq 5 as this corresponds to the thickness of a step-density profile with the same normalized first moment.60 C

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THEORETICAL MODELING APPROACH Theoretical Background. Numerical self-consistent field (nSCF) theories have made several experimentally verified predictions for the structure and scaling behavior of weak polyelectrolyte brushes.26,27,63 These predictions also show excellent agreement with molecular dynamics simulations and additionally are many orders of magnitude more computationally efficient.64 Here, we implement the nSCF lattice model of Scheutjens and Fleer.65 Detailed descriptions of this theory are available in the literature,65−67 so only the essential theory and assumptions used in the current model are discussed below. It is important to mention immediately that there are also limitations to the use of this model. A key downside of latticebased nSCF theory is the lack of chemical detail. Polymers are described as connected monomers with the exact dimension of a lattice site; in fact, all species (ions and solvent molecules) have exactly the shape and size of a lattice site. This means that for more complicated systems, such as the hydrophobic and weakly charged polyelectrolyte brush studied here, the model is not intended to come to an exact match with the experimental data. Rather, the model is intended to predict trends68 and to provide understanding of the behavior of the brush as a function of ionic strength, pH, and solvent quality. Accurate simulation of polymer brushes requires solving the Edwards diffusion equation for polymer chains in inhomogeneous systems:69 ⎞ δG(r, s|1, 1) ⎛ 1 2 = ⎜ ∇ − u(r)⎟G(r, s|1, 1) ⎝ ⎠ 6 δs

Simulation of polyelectrolyte brushes requires the addition of an electrostatic potential term, ψ(z), to the dimensionless segment potential given by Ψ(z) = eψ(z)/kT, where e is the elementary charge. Evaluating this electrostatic potential requires solving of the Poisson equation:70 ∇2 Ψ(z) = −

1 q(z) ε0

(7)

Here, q(z) is the number distribution of charges, where cations add positively and anions negatively to this quantity, and ε0 is the dielectric constant of the solution. It is assumed that the dielectric permittivity is equal to that of water throughout the system. Charged segments in the brush confer an electrostatic contribution to the effective virial coefficient, vel. This contribution is inversely proportional to the concentration of mobile salt ions, φs, and a quadratic function of the charge density α in the brush: vel = α2/φs. The virial coefficient is often negligible compared to the electrostatic contribution. For our weak polyelectrolyte brush, the degree of dissociation is dependent on the pH, ionic strength, and local electrostatic potential.17 This is modeled by a two-state model.69 For a weak basic polycation, such as PDPA, the basic monomer B can exist in a neutral deprotonated state and a cationic protonated state: B + H3O+ ⇌ BH+ + H2O. In this model we assume a monomeric pKa of 7 for symmetry and to limit the influence of pH on the ionic strength. Data have been presented in relative units, pH − pKa, to make comparisons with the different values of pKa found in real systems. The autodissociation of water is implemented as 2H2O ⇌ OH− + H3O+ with a pKw of 14. The degree of protonation, α, at Ka location z then follows from α(z) = + −y(z) , where y(z)

(6)

where the Green’s function G represents the statistical weight of all possible conformations of polymer chains with segment s′ = 1, next to the surface (rz = 1) and segment s′ = s at coordinate r, and u(r) is the dimensionless segment potential. G is closely related to the chain partition function (that is, when s = N = total number of segments) and hence to the free energy of the system. The role of the segment potential is to mimic excluded-volume interactions. This potential also accounts for the solvent quality and, as we will later discuss, describes electrostatic interactions. There are no exact analytical solutions for eq 6, but the equation can be solved numerically using, for example, the lattice approach of Scheutjens and Fleer.65 The Scheutjens−Fleer self-consistent field method generates the statistical weights for all possible and allowed freely jointed chain conformations of the attached polymer chains. By averaging over all possible conformations using their statistical weight, we then come to a brush density profile. In contrast to typical analytical SCF approaches, the current nSCF work makes no prior assumptions concerning the shape of the segment potential. This allows deviations from analytical forms, such as the presence of phase separation,32 to be captured. Typically, the brush is submerged in a molecular solvent (here allowed in three states: H2O, OH−, and H3O+) and in this study also containing cationic and anionic salt ions. The molecular interactions are parametrized by Flory−Huggins interaction parameters χij, while the number of interactions between components i and j is estimated using the Bragg− Williams mean field approximation. The optimal structure of the brush is found after the optimization of the mean field free energy under the constraint that the sum of the polymer, ion, and solvent volume fractions is unity (incompressibility relation).

K a + [H ]e

represents the local electrostatic potential.17 As such, the degree of dissociation can vary perpendicular to the grafting substrate, which is more important at low ionic strengths where the Debye screening length for electrostatic interactions is large. Model Implementation. The model has been implemented on a 1D lattice with key parameters shown in Figure 1.65 The size of a single lattice site has been set at 0.5 nm (0.125 nm3). The brush is composed of polymers with N = 100 and a grafting density (σ) of 0.025 chains per lattice site (0.1 nm−2). This set of parameters is well within the brush regime. A range of polymer solvent qualities were investigated by changing the χpolymer value between 0 (good solvent) and 2.5 (very poor solvent), where χpolymer = 0.5 is the theta condition. The most hydrophilic of the tertiary amine methacrylate analogues, PDMA, has χpolymer ∼ 0.6 at 25 °C, with values >2 achieved when copolymerized with hydrophobic butyl methacrylate.71 Therefore, the chosen range of solvent qualities is reasonable and spans our experimental conditions for PDPA brushes which are expected to be significantly more hydrophobic than PDMA.12 The bulk ionic strength and pH in the system are set by fixing a volume fraction of positively charged co-ions, ϕco‑ion, and H3O+, respectively, while the number of counterions is set by an electroneutrality constraint. To convert from ion volume fraction to the salt molarity, it is necessary to multiply the volume fraction of ions by the molarity of bulk water (55 M). However, this value is a guide only due to the compromises involved in setting the lattice parameters. Specific ion effects were approximated using a Flory− Huggins interaction parameter for the counterion, χcounterion. Values of χcounterion < 0.5 correspond to strongly hydrated kosmotropes, while χcounterion > 0.5 corresponds to increasing D

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charge of the polymer at ϕco‑ion = 0.001 is independent of χpolymer. Salt response calculations were then performed between ϕco‑ion = 10−5 (∼0.5 mM) and ϕco‑ion = 10−1 (∼5000 mM) for χpolymer values of 0, 1, and 2 for χcounterion values between 0 and 2.5. The discussion focuses on χpolymer = 2 as this is analogous to the relatively hydrophobic PDPA.11,12,76 Theories of,34−37 and experiments on,33,34 both strong and weak polyelectrolyte brushes in poor solvents show nanoscale scale lateral phase separation to form structures such as bundled cylinders, micelles, and maze-like structures. Specular NR is only sensitive to SLD changes perpendicular to the interface. If there are lateral inhomogeneities on a smaller length scale compared to the coherence length of neutrons (∼1 μm),77 NR will detect a laterally averaged SLD profile. Therefore, comparison of results from our 1D lattice calculations and fitted volume fraction profiles from NR are valid.

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RESULTS AND DISCUSSION Influence of pH. Raw reflectivity curves presented in Figure 2a confirm that the brush responds reversibly when cycled

Figure 1. Schematic representation of model and coordinate system used for nSCF calculations. The sole relevant coordinate is the z direction, perpendicular to the substrate. Layers parallel to the substrate are defined by a volume fraction of each species (polymer, co-ions, counterions, and water) with the size of the species equal to a cube of the lattice height (0.5 nm). The grafting density is set by the volume fraction of polymer grafting points in the surface layer. Monomer and water can be in a neutral or charged state. The hydrophobicity of the polymer and counterion is set by their respective Flory−Huggins (χ) parameters (χ < 0.5 = hydrophilic, χ > 0.5 = hydrophobic).

chaotropic character. Note that this approach makes no assumption as to the origin of the specific anion interaction, e.g., dispersion forces of the dressed ion or Collins law of matching water affinities.53 Importantly, however, we will show that the addition of a single χcounterion parameter is sufficient to reproduce the experimentally observed variation in hydration of the anions as well as the propensity for strong chaotropes to accumulate at hydrophobic interfaces. The addition of χcounterion builds on previous work of Pryamitsyn et al. that investigated hydrophobicity effects on the swelling behavior of a weak polyelectrolyte brush without considering the nature of the counterion.32 Several NR studies of polyelectrolyte brushes have required thin, dense layers of polymer near the substrate, prior to a diffuse tail, to adequately fit the reflectometry data.72−75 Depending on the system, the origin of this layer is assumed to be electrostatic or hydrophobicity driven. To incorporate this interaction into the current system a solvent quality term for the surface, χsurface, was introduced. The value of χsurface has been set at 2, reflecting the hydrophobic nature of the initiator surface.7 Our calculations show no difference between a hydrophobic surface and a direct attractive interaction between substrate surface and the polymer. Varying χsurface had negligible impact on the average thickness (determined by the first moment of the end points), and charge of the simulated brush, and only serves to test the hypothesis that hydrophobic interactions result in dense, thin surface layers for the polymer brush. We will show that this interaction term is insufficient to replicate the experimental observations. Volume fraction profiles, to compare to the pH-response experiments, were calculated for pH values between 4 and 11 at a fixed ionic strength of ϕco‑ion = 0.001 (∼50 mM) and χcounterion = 0. As discussed below, subsequent salt response calculations were performed at a constant pH value of 4 for which the

Figure 2. (a) Measured (data points) and fitted (solid lines) neutron reflectivity data and (b) model volume fraction profiles for a 149 ± 1 Å PDPA brush (dry thickness) immersed in 10 mM potassium nitrate solution in D2O at pH 4 and pH 9. The height of the data points in (a) corresponds to their uncertainty.

between pH 4 and 9 in 10 mM KNO3. Reflectivity is presented as RQ4, which highlights features arising from surface structures which deviate from the Q−4 decay of a bare interface, as predicted by Fresnel’s law. The large peak around Q = 0.014 Å−1 corresponds to the critical edge between Si and D2O. Reflectivity curves plotted as R vs Q, and SLD profiles are given in Figure S1. The corresponding volume fraction profiles are given in Figure 2b. At pH 4, the brush consists of a dense inner layer and a diffuse tail extending further from the solid substrate, observed previously by neutron reflectometry on weak and strong polyelectrolyte brushes. Dense interior layers E

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The nSCF pH titrations also provide further insight into the relationship between polymer hydrophobicity and pH response as described in our previously published QCM-D and ellipsometry measurements.11,12 These data have been provided in Figure S3 for ready comparison. At high pH, the average thickness of the polymer brush shown in Figure 3a is constant and directly relates to the polymer hydrophilicity with the collapsed thickness being invariant for χpolymer ≥ 1. This is consistent with previous experimental data; the collapsed swelling ratio of the two most hydrophobic analogues (PDEA and PDPA) are identical, while PDMA swells to a greater extent. The data in Figure 3a also show that the apparent brush pKa is shifted to lower values with a concomitant increase in the gradient of the swelling transition with increasing values of χpolymer. Again these qualitatively match previous experimental work with apparent brush pKa values of ∼8.0, 7.5, and 5.5 observed for PDMA, PDEA, and PDPA, respectively.12 Furthermore, both the current work (Figure 3a) and the ellipsometry data (Figure S3a) show a decrease in the maximum brush thickness at low pH values as polymer hydrophobicity increases. The origin of the hydrophobicity-dependent trends in average thickness can be further investigated by considering the average charge of the brush (Figure 3b). At pH ≫ pKa, the polymer is uncharged, and therefore the swelling of the brush is entirely determined by the solvent quality (analogous to the polymer hydrophobicity). At pH ≪ pKa, the polymer is fully charged with a weaker dependence on solvent quality and brush thickness. The brush can neither extend nor collapse indefinitely due to finite chain extensibility and excluded volume interactions, respectively, leading to the constant values for average thickness at pH extremes.78 The change in average brush thickness with decreasing pH near the pKa is best understood by comparing the most hydrophilic (χpolymer = 0) and most hydrophobic (χpolymer = 2.5) cases. For a fixed concentration of counterions, the brush can reduce unfavorable electrostatic interactions by shifting the acid−base equilibrium or by extending the chains to increase the distance between charges.19 Considering the most hydrophilic polymer (χpolymer = 0), as pH is reduced below pH − pKa ∼ 1, the brush begins to charge and swell simultaneously. As the brush is already extended in the uncharged state, it is relatively easy for the brush to become charged as the pH approaches the pKa. However, further ionization of the monomers becomes difficult as the chain resists further stretching, in turn leading to a relatively small increase in brush thickness and charge with decreasing pH. The most hydrophobic polymer simulated (χpolymer = 2.5) also begins charging at pH − pKa ∼ 1, albeit to a lesser extent than χpolymer = 0 as the acid−base equilibrium shifts to minimize electrostatic repulsion between charges in close proximity. In fact, all values of χpolymer have a lower degree of charge relative to a free monomer in solution (dashed line in Figure 3b) depending on the relative proximity of ionizable groups. Despite the significant percentage of charged monomers, no increase in average brush thickness is observed until pH − pKa ∼ −1 for χpolymer = 2.5 where repulsive interactions between charges begin to overcome the effective attractive interactions between the polymer segments. Further decreasing the pH results in a sharp increase in charge and thickness compared to the gradual swelling of the hydrophilic brush. The concomitant sharp increase in average charge on the polymer suggests that the swelling is a synergistic process; lower pH increases the

are associated with low-frequency oscillations in the reflectivity data (e.g., the minima at ∼0.10 Å−1).60,72−75 The gradual decrease in polymer density in the extended tail region is analogous to a rough interface that reduces the reflectivity at intermediate Q values and smears out the presence of any higher frequency oscillations associated with the larger structure. At pH 9, the brush should be substantially uncharged as it is well above the pKa, resulting in a collapsed conformation.12 The collapsed conformation has an interface which is less diffuse, with a greater SLD contrast between the brush, substrate, and solvent. This leads to a more reflective interface for the collapsed state and the presence of Kiessig fringes with minima at 0.035 and 0.077 Å−1, whose spacing is determined by the thickness of the collapsed layer. The average thickness of the brush (eq 5) changes from 630 ± 25 Å at pH 4 to 177 ± 2 Å at pH 9, with confidence intervals given by the standard deviation of the two cycles. The lack of hysteresis in the measured pH response suggests the brush is near equilibrium under these conditions, a requirement for comparison with the nSCF model. The reduction in average thickness between high and low pH for the PDPA brush observed by NR is also seen in the nSCF calculations for χpolymer = 2 presented in Figure 3a. Qualitative

Figure 3. (a) Average brush thickness and (b) charge percentage as a function of pH relative to the pKa determined by nSCF theory for a range of χpolymer. The ionic strength and χcounterion were fixed at 0.001 (volume fraction) and 0, respectively. The dashed line in (b) corresponds to percentage dissociation of an isolated monomer (pKa = 7) in solution.

features of the volume fraction profiles are also consistent for both approaches (see Figure S2). For example, a single collapsed profile is observed at high pH. While the nSCF model predicts an extended brush at low pH, the formation of a thin, dense layer near the substrate is less apparent. The underestimation of the amount of polymer in the dense interior is a feature of all the nSCF volume fraction profiles and is discussed in detail later in the text accompanying Figure 5. F

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Figure 4. Measured neutron reflectivity data (a, c, e) and corresponding volume fraction profiles (b, d, f) for the PDPA brush immersed in 0.1−500 mM solutions of (a, b) potassium acetate, (c, d) potassium nitrate, and (e, f) potassium thiocyanate, all at pH 4.5 (in D2O). Solid lines in (a, c, e) are fits to the experimental data. The height of the data points in (a, c, e) corresponds to the uncertainty of the measurement (±1 standard deviation).

Influence of Salt. The experimentally determined influence of salt identity and ionic strength on the structure of a PDPA brush was studied at a constant pH value of 4.5, corresponding to the state of maximum swelling in 10 mM potassium nitrate (see Figure S3a).12 Reflectivity data and the corresponding fitted volume fraction profiles for ionic strengths between 0.1 and 500 mM of the potassium salts of acetate, nitrate, and thiocyanate anions are provided in Figure 4. Plots of R vs Q and SLD profiles are provided in Figure S5. These anions span the Hofmeister series with acetate being strongly kosmotropic, nitrate being weakly chaotropic, and thiocyanate being strongly chaotropic. The relationship between reflectivity and the volume fraction profiles is consistent with the data shown in Figure 2. At the lowest ionic strength of 0.1 mM the brush adopts a collapsed conformation, independent of the identity of the anion despite the low solution pH of 4.5. This suggests that the large Debye screening length (∼27 nm) dominates the brush behavior as the low degree of screening makes charging the brush unfavorable, leading to a shift in the acid−base equilibrium to the uncharged state.14,19 Indeed, the volume fraction profiles at 0.1 mM are almost identical to the uncharged brush in 10 mM potassium nitrate at pH 9 (Figure 2b). The brush conformations as a function of ionic strengths are different for concentrations greater than 0.1 mM. This result is expected as specific ion effects become more prominent at higher ionic strengths.38 Potassium nitrate is an intermediate salt in most representations of the Hofmeister series, so we start our

charge, causing the brush to swell which favors further charging as electrostatic repulsion between charged monomers is reduced due to their greater separation. Furthermore, the brush is relatively collapsed compared to the hydrophilic case for the same amount of charge, so the chain is easier to extend. Examination of the volume fraction profiles show the brush partitioning into a weakly charged, dehydrated layer near the substrate followed by a strongly charged and hydrated tail (see Figure S4). As the average charge increases, the proportion of the polymer in the tail increases. This is likely driven by the unfavorable dehydration of the counterion and the high local electric field strength that would be required for the charged monomer moieties to remain in the collapsed phase. There is a smooth transition in overall brush behavior for intermediate values of χpolymer as the solvent quality becomes increasingly unfavorable. For example, the shift in the effective pKa to lower values with increasing χpolymer results from a stronger preference for polymer−polymer interactions and the higher degree of charge that the brush can sustain before swelling. At pH values higher than the effective brush pKa, the behavior is dominated by the effective solvent quality. Conversely, the behavior at low pH is charge dominated, with the average charge of the brush independent of χpolymer at pH values lower than ∼4. The average brush thickness has a weak dependence on χpolymer due to the reduced preference for hydration with increasing values of χpolymer. The above analysis confirms that previously reported variations in the pH response in aqueous solution of a series of weak polybasic brushes may be explained by their relative hydrophobicity.12 G

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stretched at low degrees of charge, which limits the degree of additional stretching in the presence of counterions. Simulated volume fraction profiles of a hydrophobic polybasic brush (χpolymer = 2), analogous to PDPA, as a function of χcounterion and ionic strength are presented in Figure 5. For clarity, Figure 5 only presents every fifth simulated ionic

discussion with this electrolyte (Figures 4c and 4d). For concentrations between 1 and 100 mM, the brush forms a swollen structure in potassium nitrate. As previously seen for the pH 4 data, the swollen brush consists of a dense inner layer followed by a well-hydrated tail extending into the solvent. Interestingly, the thickness and degree of hydration of the dense inner layer are largely independent of the ionic strength over this concentration range, while the theory suggests the entire brush should be responsive. The insensitivity of the interior layer to ionic strength parallels the results of Jia et al. for NR experiments on a PDMA brush where the thickness of the dense interior layer was independent of the pH.73 They concluded that the interior region is not involved with the swelling of the brush and may result from preferential interaction with the hydrophobic thiol initiator layer on the substrate, which we discuss in more detail below. In 500 mM nitrate, the electrostatic screening results in a collapsed brush again, which is consistent with the emergence of a Kiessig fringe at ∼0.026 Å−1. The behavior of the PDPA brush in the presence of the strongly kosmotropic acetate anion (Figures 4a and 4b) is similar to that seen for the nitrate anion up to 100 mM. However, in 500 mM potassium acetate the brush remains swollen. Thiocyanate (Figures 4e and 4f) results in starkly different brush behavior to the other salts, with no swelling observed for the entire range of ionic strengths. The collapsed structure leads to the presence of Kiessig fringes with minima at 0.038 and 0.071 Å−1, the amplitude increasing with salt concentration as the structure becomes slightly less diffuse. These observed variations in swelling with salt identity are consistent with our previously published results.11,56 We have previously postulated that the lack of a collapse in the presence of acetate results from a low affinity of the strongly hydrated kosmotrope for the hydrophobic polymer. The thiocyanateinduced behavior was proposed to result from a combination of preferential accumulation of thiocyanate within the brush due to interaction with the hydrophobic polymer and weakly charged tertiary amine as well as the poor hydration of thiocyanate. The origins of the response of the brush conformation to ion identity and ionic strength can be further elucidated using nSCF. Experimental salt ramps on the PDPA brush were performed at pH 4.5 where the brush is in the charge dominated regime, i.e., maximum swelling as a function of pH in 10 mM potassium nitrate. To make the NR and nSCF data sets as comparable as possible, nSCF salt titrations were performed at pH 4 as informed by the pH response shown in Figure 3. Salt titrations were conducted for χpolymer values of 0, 1, and 2 as a function of counterion hydrophilicity (χcounterion values of 0, 1, and 2.5) and ionic strengths (volume fractions of 1 × 10−5 to 1 × 10−1, ∼0.55−5500 mM). The average thickness and charge predicted for each value of χpolymer are provided in Figure S6. For all conditions, the average brush thickness decreased with increasing χcounterion (hydrophobicity); larger values of χpolymer result in a greater sensitivity to χcounterion. The average charge is essentially invariant with χcounterion for χpolymer values of 0 (relatively hydrophilic) and 1 (weakly hydrophobic), suggesting that the hydration of the counterion plays a significant role in the observed changes in overall brush thickness. Variations in both brush thickness and charge as a function of χcounterion are significantly more pronounced for χpolymer = 2. As with the simulated pH titrations, hydrophilic brushes are significantly

Figure 5. Polymer volume fraction profiles as a function of χcounterion and ionic volume fraction for a hydrophobic brush (χpolymer = 2) at pH 4. χcounterion values of (a) 0, (b) 1, and (c) 2.5 represent hydrophilic, weakly hydrophobic, and strongly hydrophobic counterions, respectively.

strength. Values of χcounterion of 0, 1, and 2.5 have been selected for presentation to correspond with a relatively hydrophilic (kosmotropic), weakly hydrophobic, and a strongly hydrophobic (chaotropic) counterion, respectively. At low ionic strength, collapsed profiles are observed for all values of χcounterion. Profiles for the hydrophilic case (χcounterion = 0, Figure 5a) match the experimental behavior in acetate (Figure 4b), with extended profiles observed even at the highest ionic strength studied. As with the potassium nitrate data (Figure 4d), weakly hydrophobic counterions (χcounterion = 1, Figure 5b) form extended profiles at intermediate ionic strengths, with a dense, collapsed structure occurring at the highest ionic strength. The behavior of the strongly hydrophobic counterion H

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Macromolecules (χcounterion = 2.5, Figure 5c) resembles the collapsed profiles observed in thiocyanate at all values of ionic strength (Figure 4f). Stronger agreement is achieved if the combined density of monomer and counterions is considered (Figure S7); a fully charged polymer is limited to a density of 0.5 by the electroneutrality constraint and the fact that all species are the same size. The qualitative features of the volume fraction profiles in Figure 5 show good agreement with those observed by neutron reflectometry (Figure 4). A key difference between the NR and nSCF data is the absence of a dense interior region of polymer in the nSCF profiles for conditions where the brush is highly extended. Previous NR studies have attributed the formation of a dense interior region with preferential interactions with the substrate (e.g., hydrophobic or electrostatic).60,72−75 While PDMA is relatively hydrophilic compared to PDPA,12 the hydrophobic interactions with the substrate resulting in a dense interior layer73,74 are still possible as PDMA is weakly hydrophobic when uncharged, with χpolymer ∼ 0.6.71 The silane initiator layer used in the current work is hydrophobic, and therefore a preferential interaction between PDPA and the surface is probable.7 To account for a hydrophobic interaction with between polymer chains and the substrate in the nSCF calculations, a χsurface parameter was introduced (data shown for χsurface = 2). Increasing the hydrophobicity of the surface (by raising χsurface) resulted in a small increase in the amount of polymer adsorbed at the interface. No dense interior layer was observed by nSCF for conditions where the brush is highly charged, even when the combined density of counterion and monomer are considered. However, for intermediate conditions (between fully collapsed and fully swollen) in the nSCF data, a dense interior region followed by a dilute tail is present (see profiles at an ionic volume fraction of 1 × 10−4 for χcounterion = 0 and 1 in Figure 5). This structural feature results from a phase separation between charged and uncharged regions of the brush and has been previously observed by nSCF for hydrophobic, weak polyelectrolyte brushes.32 The degree of phase separation is shown to increase with decreasing brush charge and increasing χpolymer.32 Moreover, an increase in grafting density is expected to increase the thickness of the collapsed, uncharged region without changing the overall degree of brush solvation.32 Indeed, increasing the grafting density by a factor of 4 for the current system results in a thicker interior region with only a slight increase in the volume fraction of polymer (see Figure S8). A concomitant reduction in the amount of polymer in the tail region suggests variations in grafting density alone are insufficient to replicate the experimental behavior. There are several plausible scenarios for the lack of an adsorbed layer of polymer in the nSCF model. A significant limitation of the nSCF model is that it can only study equilibrium conformations. The experimental observation that the thickness and degree of hydration of the dense interior layer are insensitive to ionic strength suggests that the structure may be kinetically trapped. Dispersity in the chain length is not accounted for in the current model and may also result in a dense inner layer as short chains collapse relative to long chains.79 Furthermore, there is experimental and theoretical evidence that termination in the early stages of SI-ATRP leads to a bimodal molecular weight distribution.80 Average brush thicknesses determined by NR and nSCF are given in Figures 6a and 6b, respectively. The average thickness (eq 5) is weighted toward polymer density at the periphery of

Figure 6. Comparison of average thickness as a function of counterion identity and ionic strength or volume fraction determined by (a) neutron reflectometry of a 149 ± 1 Å PDPA brush and (b) nSCF theory for a hydrophobic brush (χpolymer = 2). Data in (b) were calculated at a constant pH value of 4 with increasing values of χcounterion corresponding to increasing counterion hydrophobicity. The equivalent range of ionic strengths studied by nSCF is approximately 0.55−5500 mM.

the brush, and therefore the absence of a dense interior layer does not affect the agreement between nSCF, NR, and ellipsometry data (see Figure S9). All three techniques show that the maximum thickness decreases with increasing hydrophobicity (chaotropic nature) of the counterion. The absence of a strong reduction in thickness in the average NR thickness in kosmotropic potassium acetate at high ionic strengths results from the significantly higher ionic strength that has been investigated with nSCF with ϕco‑ion = 0.1 corresponding to ∼5500 mM. An increase in the broadness of the maximum average brush thickness with decreasing χcounterion also contributes to the retention of a swollen state in high ionic strength potassium acetate as observed by NR (Figure 6a) and ellipsometry (Figure S9). The good agreement of the NR and nSCF data (Figures 6a and 6b) suggests that the inclusion of the solvent quality χ parameter for the anion (χcounterion) is sufficient to simulate the specific anion response of a hydrophobic weak polybasic brush. As stated above, we have previously proposed increased electrostatic screening through accumulation of chaotropes within the hydrophobic brush, or through stronger interactions with the amine moiety, or weaker ion hydration, as explanations for the reduced swelling in thiocyanate for PDPA.11 A low affinity of the strongly hydrated acetate anions for the brush resulting in a depletion of counterions and reduced electrostatic screening was also proposed for the absence of collapse in potassium acetate solution at high ionic strength. However, no evidence of counterion accumulation or depletion was observed in the nSCF model (see Figure S10 and surrounding discussion). I

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discussion, it would be essential to also experimentally determine the ion concentration both inside and adjacent to the studied polyelectrolyte brushes. While a considerable challenge, small-angle X-ray scattering82 and contrast-matched neutron reflectivity measurements with bulky, deuterated counterions83 have been shown to allow the determination of ion-density profiles in polyelectrolyte brushes.

An alternate hypothesis is that the observed specific ion effects result from the differing hydration strength of the ions.11 The nSCF model cannot explicitly determine the degree of hydration of each counterion as all species occupy the same volume, that of a single site on a 1D lattice. However, a reasonable indication as to the effect of χcounterion on the hydration of the brush can be achieved by calculating the ratio of solvent to charged species, shown for an ionic strength of 0.01 in Figure 7. In the presence of hydrophilic counterions

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CONCLUSIONS Neutron reflectometry (NR) has been used to investigate the conformational response of a hydrophobic PDPA brush to changes in solution pH, ionic strength, and anion identity. Results are compared to nSCF simulations that incorporate an additional Flory interaction parameter between counterion and solvent, χcounterion. Values of χcounterion above 0.5 indicate a relatively hydrophobic anion, while values below 0.5 indicate a relatively hydrophilic anion. The good qualitative agreement between experiment and simulation yields insight into the effect of polymer hydrophilicity on the pH-response of the weak polybasic brush as well as the origin of the specific ion response. Results show that at low pH the brush is substantially charged with the conformation characterized by an extended, dilute tail region. At high pH, the brush is uncharged and its conformation is strongly dependent on the hydrophilicity of the polymer. nSCF simulations show that hydrophilic polymers remain relatively swollen while hydrophobic polymers (χpolymer > 0.5 such as PDPA) form a dense, collapsed phase. Furthermore, the nSCF simulations replicate our previously published observations of an increase in sharpness of the transition between the collapsed and swollen phase with decreasing pH for hydrophobic polymers. Hydrophobic polymers are able to acquire a substantial internal charge without swelling due to a greater preference for polymer− polymer interactions compared to hydrophilic polymers. Once swelling begins, the polymer separates into a dense, weakly charged layer at the substrate followed by a charged, extended tail. The spontaneous formation of the extended, charged region is responsible for the sharp increase in brush thickness with decreasing pH. The conformation of a hydrophobic, weak polyelectrolyte brush, as found by neutron reflectometry, was independent of salt identity at low ionic strength (0.1 mM). In the presence of kosmotropic acetate counterions, the brush showed an extended conformation for ionic strengths between 1 and 500 mM. Similar behavior was seen for ionic strengths up to 100 mM in the presence of weakly chaotropic nitrate anions, with a collapsed conformation observed at 500 mM. Solutions containing the strongly chaotropic thiocyanate anion resulted in a collapsed conformation for all concentrations. NR results were qualitatively matched by nSCF simulations, with the degree of overall swelling reduced when the counterion hydrophobicity was increased. The nSCF simulations show no evidence for the previously proposed accumulation of hydrophobic counterions or exclusion of hydrophilic counterions from the brush. Rather, the specific anion response of a hydrophobic, weak polycationic brush can be explained by the degree of hydration of the counterion. Strongly hydrated counterions result in relatively swollen brush conformations as they cannot easily shed their tightly bound hydration sheath, while weakly hydrated anions can neutralize the brush without resulting in significant swelling. The nSCF model can be readily adapted and extended to investigate, for example, systems of mixed salts or colloid probe interaction with brushes.

Figure 7. (a, b) Volume fraction profiles at an ionic strength of 1.0 × 10−2 for (a) χcounterion = 0 and (b) χcounterion = 2.5. Black lines = total monomer volume fraction, large dashed green lines = charged monomer, short-dashed purple = counterion, and short-dashed red = co-ion (values displayed on left-hand axis). Blue dot-dashed lines = the ratio of H2O:charged species normalized by the same value in the bulk (values displayed on right-hand axis).

(χcounterion = 0), the brush has significant hydration per unit charge throughout the brush (Figure 7a). A higher degree of hydration helps explain the broadness of the transition between increasing (osmotic brush, increasing charge) and decreasing (swollen brush, increased electrostatic screening) average brush thickness (Figure 6b), since the strong hydration of the counterions encourages swelling. Indeed, a potassium acetate solution has a higher osmotic coefficient than a potassium thiocyanate solution of the same concentration.81 Conversely, in the presence of hydrophobic counterions (χcounterion > 0.5), the brush experiences poor hydration per unit charge for each given condition (Figure 7b). Furthermore, the weakness with which counterions hold water is implicit in the higher density of counterions within the collapsed brush; to neutralize a charge, collapsed brush counterions must be able to enter the brush without significantly contributing to the swelling. Therefore, the level of hydration of the counterion is sufficient to explain the observed phenomena. It is important to mention that our discussion above is purely based on the outcomes of the nSCF model. To build on this J

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(10) Guenoun, P. Polyelectrolyte Brushes: Twenty Years After. In Functional Polymer Films; Wiley-VCH Verlag GmbH & Co. KGaA: 2011; DOI: 10.1002/9783527638482.ch6pp219-237. (11) Willott, J. D.; Murdoch, T. J.; Humphreys, B. A.; Edmondson, S.; Wanless, E. J.; Webber, G. B. Anion-specific Effects on the Behavior of pH-Sensitive Polybasic Brushes. Langmuir 2015, 31, 3707−3717. (12) Willott, J. D.; Humphreys, B. A.; Murdoch, T. J.; Edmondson, S.; Webber, G. B.; Wanless, E. J. Hydrophobic Effects within the Dynamic pH Response of Polybasic Tertiary Amine Methacrylate Brushes. Phys. Chem. Chem. Phys. 2015, 17, 3880−3890. (13) Lyatskaya, Y. V.; Leermakers, F.; Fleer, G.; Zhulina, E.; Birshtein, T. Analytical Self-Consistent-Field Model of Weak Polyacid Brushes. Macromolecules 1995, 28, 3562−3569. (14) Zhulina, E.; Borisov, O. Poisson−Boltzmann Theory of pHSensitive (Annealing) Polyelectrolyte Brush. Langmuir 2011, 27, 10615−10633. (15) Zhulina, E.; Borisov, O. Structure and Interaction of Weakly Charged Polyelectrolyte Brushes: Self-consistent Field Theory. J. Chem. Phys. 1997, 107, 5952−5967. (16) Borisov, O.; Zhulina, E.; Birshtein, T. Diagram of the States of a Grafted Polyelectrolyte Layer. Macromolecules 1994, 27, 4795−4803. (17) Israels, R.; Leermakers, F.; Fleer, G. On the Theory of Grafted Weak Polyacids. Macromolecules 1994, 27, 3087−3093. (18) Israels, R.; Leermakers, F.; Fleer, G.; Zhulina, E. Charged Polymeric Brushes: Structure and Scaling Relations. Macromolecules 1994, 27, 3249−3261. (19) Nap, R.; Tagliazucchi, M.; Szleifer, I. Born Energy, Acid-Base Equilibrium, Structure and Interactions of End-Grafted Weak Polyelectrolyte Layers. J. Chem. Phys. 2014, 140, 024910. (20) Von Goeler, F.; Muthukumar, M. Polyelectrolyte Brush Density Profiles. Macromolecules 1995, 28, 6608−6617. (21) Zhulina, E.; Birshtein, T.; Borisov, O. Theory of Ionizable Polymer Brushes. Macromolecules 1995, 28, 1491−1499. (22) Pincus, P. Colloid Stabilization with Grafted Polyelectrolytes. Macromolecules 1991, 24, 2912−2919. (23) Hehmeyer, O. J.; Arya, G.; Panagiotopoulos, A. Z.; Szleifer, I. Monte Carlo Simulation and Molecular Theory of Tethered Polyelectrolytes. J. Chem. Phys. 2007, 126, 244902. (24) Chen, L.; Merlitz, H.; He, S.-z.; Wu, C.-X.; Sommer, J.-U. Polyelectrolyte Brushes: Debye Approximation and Mean-Field Theory. Macromolecules 2011, 44, 3109−3116. (25) Guptha, V. S.; Hsiao, P.-Y. Polyelectrolyte Brushes in Monovalent and Multivalent Salt Solutions. Polymer 2014, 55, 2900−2912. (26) Mahalik, J. P.; Yang, Y.; Deodhar, C.; Ankner, J. F.; Lokitz, B. S.; Kilbey, S. M.; Sumpter, B. G.; Kumar, R. Monomer Volume Fraction Profiles in pH Responsive Planar Polyelectrolyte Brushes. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 956−964. (27) Sudre, G.; Hourdet, D.; Creton, C.; Cousin, F.; Tran, Y. pHResponsive Swelling of Poly(acrylic acid) Brushes Synthesized by the Grafting Onto Route. Macromol. Chem. Phys. 2013, 214, 2882−2890. (28) Milner, S. Polymer Brushes. Science 1991, 251, 905−914. (29) Shull, K. R. Theory of End-Adsorbed Polymer Brushes in Polymeric Matrices. J. Chem. Phys. 1991, 94, 5723−5738. (30) Zhulina, E. B.; Borisov, O. V.; Birshtein, T. M. Structure of Grafted Polyelectrolyte Layer. J. Phys. II 1992, 2, 63−74. (31) Dong, R.; Lindau, M.; Ober, C. K. Dissociation Behavior of Weak Polyelectrolyte Brushes on a Planar Surface. Langmuir 2009, 25, 4774−4779. (32) Pryamitsyn, V. A.; Leermakers, F. A. M.; Fleer, G. J.; Zhulina, E. B. Theory of the Collapse of the Polyelectrolyte Brush. Macromolecules 1996, 29, 8260−8270. (33) Günther, J. U.; Ahrens, H.; Förster, S.; Helm, C. A. Bundle Formation in Polyelectrolyte Brushes. Phys. Rev. Lett. 2008, 101, 258303. (34) Hur, J.; Witte, K. N.; Sun, W.; Won, Y.-Y. On the Origins of the Salt-Concentration-Dependent Instability and Lateral Nanoscale Heterogeneities of Weak Polyelectrolyte Brushes: Gradient Brush

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b01897. Tabulated data from neutron reflectivity brush model, together with complementary neutron reflectivity, ellipsometry, and quartz-crystal microbalance and additional numerical self-consistent field simulation Figures in salt solutions (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; phone +61 2 4033 9067 (G.B.W.). ORCID

Erica J. Wanless: 0000-0003-0869-4396 Grant B. Webber: 0000-0001-8303-6081 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by an Australian Centre for Neutron Scattering program grant (PP4274). T.J.M. thanks AINSE Ltd. for providing financial assistance (PGRA Award). UNSW Engineering is thanked for a Faculty Research Grant supporting S.W.P. The authors thank Prof. Vince Craig (Australian National University) for valuable discussions.

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REFERENCES

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DOI: 10.1021/acs.macromol.6b01897 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.6b01897 Macromolecules XXXX, XXX, XXX−XXX