Ion Activity Coefficients in Ion Exchange Polymers: Applicability of

Article pubs.acs.org/Macromolecules

Ion Activity Coefficients in Ion Exchange Polymers: Applicability of Manning’s Counterion Condensation Theory Jovan Kamcev, Donald R. Paul, and Benny D. Freeman* McKetta Department of Chemical Engineering, Center for Energy and Environmental Resources, and Texas Materials Institute, The University of Texas at Austin, 10100 Burnet Road Building 133 (CEER) Austin, Texas 78758, United States S Supporting Information *

ABSTRACT: Manning’s counterion condensation theory, originally developed for polyelectrolyte solutions, was used to predict ion activity coefficients in charged (i.e., ion exchange) membranes with no adjustable parameters. Equilibrium sodium and chloride ion concentrations in negatively and positively charged membranes were determined experimentally as a function of external NaCl concentration, and ion activity coefficients in the membranes were obtained via a thermodynamic treatment. Theoretical values for membrane ion activity coefficients obtained via Manning’s model were compared with those obtained experimentally. Good agreement was observed between the experimental and theoretical values for membrane ion activity coefficients, especially at higher external NaCl concentrations. However, some deviation between experimental and theoretical values was observed in the dilute regime. Manning’s model was also used to obtain activity coefficients for various electrolytes in ion exchange resins using ion sorption data from the literature, and these values were compared to those obtained experimentally.

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electrostatic interactions between membrane fixed charge groups and ions not bound to the polymer network (i.e., those introduced via sorption from the external solution in contact with the IEM) result in highly nonideal ion behavior in the membrane (i.e., ion activity coefficients not equal to unity).24−27 In the past, these nonidealities have often been ignored in studies of transport phenomena in ion exchange polymers.24,28,29 Developing a better understanding of such nonideal ion behavior in IEMs could be useful for quantitatively describing sorption and transport of ions through charged membranes. Deviations from ideal behavior in solutions, including electrolyte solutions, are quantified using activity coefficients.30−32 A substantial literature on electrolyte activity coefficients in solution is available, and several theoretical treatments (e.g., the Debye−Hückel theory and the Pitzer model) are available to predict electrolyte activity coefficients under various circumstances.30−34 However, for ion exchange polymers, there are few reports of ion activity coefficients in such materials.18,29 Moreover, to the best of our knowledge, no reliable fundamental models exist for predicting these values. Some of the difficulty in developing a fundamental understanding of ion activity coefficients in ion exchange polymers lies in the limited number of well-defined experimental techniques available to obtain these values and, consequently, the limited amount of data. In contrast, numerous techniques were developed for determining electro-

INTRODUCTION Polymeric ion exchange membranes play an important role in applications such as electrodialysis, reverse electrodialysis, fuel cells, and batteries because of their relatively high electrical conductivity and ability to selectively permeate certain ions.1−10 They are also promising materials for applications such as desalination, forward osmosis, and pressure retarded osmosis due to their excellent chemical stability and ability to reject mobile ions.9,11−17 Ion exchange membranes (IEMs) are typically made from polymers having charged functional groups covalently bound to the polymer backbone.18 These functional groups can ionize in polar solvents such as water. Membranes having negatively charged (e.g., sulfonate) groups are cation exchange membranes (CEMs), and those having positively charged (e.g., quaternary amines) groups are anion exchange membranes (AEMs).18 The efficacy of the processes mentioned above depends strongly on controlling solvent and/or solute (mainly ions) transport across the membranes. Development of high performance membrane materials with desirable separation characteristics is important for increasing process efficiencies. However, to do so, fundamental understanding of solvent and solute transport across such membranes and the influence of membrane chemical and physical structure on transport properties are required, and such information is missing or incomplete at this time.19 Ion exchange membranes of practical utility often contain high concentrations of fixed charge groups.18,20,21 Ion exchange capacity (IEC), defined as milliequivalents of charge per gram of dry polymer, is often used to quantify the fixed charge group concentration. Typical ion exchange membranes have IEC values ranging from 1 to 3 mequiv/g.12,19,22,23 Strong © XXXX American Chemical Society

Received: July 24, 2015 Revised: October 7, 2015

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DOI: 10.1021/acs.macromol.5b01654 Macromolecules XXXX, XXX, XXX−XXX

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electrolyte solution, which is not consistent with experimental observations, as will be shown later in this study.43 Later, others criticized the Glueckauf approach as requiring excessively large variations in ion exchanger properties to describe ion sorption equilibrium.38 Previous reports often overlooked similarities in behavior of electrolyte activity coefficients in ion exchange membranes with that in polyelectrolyte solutions. Electrolyte activity coefficients in polyelectrolyte solutions containing added salt have been measured by numerous investigators using electrochemical methods.44−48 In such polyelectrolyte-containing solutions, very low values of mean electrolyte activity coefficients (∼0.1) at low added salt concentrations and electrolyte activity coefficients that increase with increasing added salt, qualitatively similar to observations in ion exchange materials, have been widely reported.44,45,47,48 Ion activity coefficient behavior in the polyelectrolyte field was, at the time, apparently more widely studied than in the ion exchange polymer field. In the polyelectrolyte field, models were developed to describe experimentally observed ion activity behavior, such as the empirical “additivity” rule and the theory of Katchalsky and Lifson.47,49,50 Some investigators recognized similarities between the behavior of ion activity coefficients in ion exchange polymers and polyelectrolyte solutions and attempted to extend the theoretical treatment of Katchalsky and Lifson to systems of ion exchange polymers and use it to predict ion activity coefficients. Mackie and Meares found good agreement between theoretical and experimental values of ion activity coefficients in membranes prepared from sulfonated phenol−formaldehyde resins.51 However, this approach contained several empirical parameters whose values were difficult to determine independently.51 In another study, Lakshminarayanaiah found poor agreement between theoretical and experimental values of ion activity coefficients in sulfonated phenol−formaldehyde resins using a similar approach.24 Another theoretical treatment aimed at describing ion activity coefficients in ion exchange materials was developed by Lazare et al., but the mathematical complexity and difficult computation may have limited widespread investigation.52 In the 1950s and early 1960s, the theoretical framework for describing colligative properties of polyelectrolyte solutions was in its infancy, and more refined theories, such as Manning’s counterion condensation theory, were not yet available, with Manning’s original seminal paper published in 1969.53 In this study, ion sorption measurements in commercially available cation and anion exchange membranes are reported as a function of external salt concentration. Manning’s counterion condensation theory is used to predict electrolyte activity coefficients in these ion exchange membranes, and these values are compared to those obtained experimentally. To place these findings in perspective, the data are also compared to other available activity coefficient models, such as those described above and data from the literature.

lyte activity coefficients in solution (e.g., electrochemical methods, freezing-point depression, etc.).35 Virtually all reports of ion activity coefficients in ion exchange polymers rely on characterization of ion concentrations in ion exchange polymers equilibrated with electrolyte solutions.18,29 Any subsequent thermodynamic analysis of such data depends on the accuracy of the experiments to determine ion concentrations in the materials and the validity of assumptions underpinning the thermodynamic analysis. Because of experimental difficulties and a lack of fundamental models, this approach has led to considerable disagreement in interpreting such results.36−39 Many early studies (∼1950s) of electrolyte sorption equilibrium in ion exchange polymers focused mainly on ion exchange resins. Several investigators observed an increase in mean electrolyte activity coefficients in such resins with increasing external salt concentration, with unusually low values ( ξcrit) and (b) counterion condensation does not occur (i.e., ξ < ξcrit).

neglected, and local segments of a chain are “screened” from distant segments on the same chain. Thus, only local interactions between fixed charges and mobile ions are considered. Because of its reliance on the limiting (i.e., infinite dilution) form of the Debye−Hückle model to describe the electrostatic contribution to the free energy of a polyelectrolyte solution containing added salt, all ions, including fixed charges, counterions, and co-ions, influence the system thermodynamics only due to their number and charge. Chemical specificity, size, and shape of charged groups do not enter the description. The model has a single parameter, ξ, which is defined as the dimensionless linear charge density of the polyelectrolyte chain and is calculated as follows:53 ξ=

λ e2 = B 4πε0εkTb b

where zi is the counterion valence (e.g., zi = 1 for Na+) and zp is the valence of the fixed charges (for the case considered here, zp = −1). Thus, for NaCl in solution around a polyelectrolyte chain having monovalent charges (e.g., sulfonate or quaternary amine groups), the critical value of ξ is one. This theory is built around the phenomenon of “counterion condensation”. A simple illustration of this concept, within the framework of Manning’s model, is presented in Figure 9a, and the meaning of the critical charge density becomes clear. When ξ is at its critical value of one for NaCl in a solution containing polyelectrolyte bearing univalent fixed charge groups, the distances between fixed charges and the Bjerrum length are equal. If ξ is greater than the critical value, the Bjerrum lengths of neighboring fixed charges overlap, and “counterion condensation” occurs.53 Counterions located in regions of overlapping electrostatic fields from neighboring fixed charges will tend to stay in this region and are regarded as “condensed”. In this case, enough counterions will “condense” on the polyelectrolyte chain, essentially screening a sufficient number of the fixed charges to reduce ξ to the critical value (e.g., ξcrit = 1 for NaCl and polymers containing either sulfonate or quaternary amine fixed charge groups).53 If ξ is equal to or less than the critical value, counterion condensation does not occur (cf. Figure 9b).53 Counterion condensation is the trapping (or binding) of counterions in the vicinity of polyelectrolyte chains caused by strong, overlapping electric fields generated by nearby fixed charges on the polyelectrolyte chain. The uncondensed mobile ions are treated in a Debye−Hückel approximation to obtain expressions for the free energy of the system and ultimately derive expressions for ion activity coefficients via standard thermodynamics.53 The existence of a critical linear charge density and onset of counterion condensation in polyelectrolyte solutions have been experimentally confirmed by numerous investigators, and an excellent survey of this literature is given by Manning.69 As indicated above, for a polyelectrolyte system containing a monovalent salt (e.g., NaCl), ξcrit is one. For the vast majority of polyelectrolyte systems considered in the literature, ξ is greater than this critical value.44,53,70 Therefore, counterion condensation plays an important role in the behavior of many polyelectrolyte systems.53,69−71 For the case of a monovalent salt and when ξ > 1, the product of ion activity coefficients, γ+γ−, is given by53

(16)

where e is the protonic charge, ε0 is the vacuum permittivity, ε is the solvent dielectric constant, k is Boltzmann’s constant, T is absolute temperature, b is the average distance between charges on the polyelectrolyte chain, and λB is the Bjerrum length.67,68 Thus, ξ is a ratio of two length scales, one being the distance between neighboring fixed charges and the other being the Bjerrum length, which characterizes the distance away from a fixed charge at which the work required to separate a counterion from the fixed charge is four times that average kinetic energy per degree of freedom (i.e., 2kT). Counterions closer to a fixed charge than the Bjerrum length do not have sufficient thermal energy to readily diffuse away from the fixed charge group and were regarded by Bjerrum as “associated” as opposed to “free” pairs of ions, which are separated by a distance greater than the Bjerrum length.68 Calculating ξ for polyelectrolytes is relatively straightforward based upon knowledge of the polyelectrolyte chemical structure. Assuming full extension of locally unscreened polyelectrolyte chain segments, which is plausible for a line charge model, the distance between fixed charge groups may be estimated geometrically. The dielectric constant is set to that of pure solvent (∼78 for water at ambient conditions). Therefore, ξ is a well-defined parameter depending on molecular properties of the polyelectrolyte chain and the solvent. Typical values for ξ lie between 1 and 4 for polyelectrolyte systems.44,53 The concept of a critical linear charge density, ξcrit, is essential to this theory. This parameter is defined as follows:53 ξcrit =

1 |zizp|

(17) J

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Macromolecules ⎡ − ne ⎤ ⎛ X + 1 ⎞ ⎛ ne + 1 ⎞ ns nξ ⎟ exp⎡ − X ⎤ ⎥=⎜ξ ⎟ exp⎢ γ+γ− = ⎜ nse ⎢ ⎥ n e ⎜ ⎟ ⎢ + 2ξ ⎥ ⎜ +1⎟ ⎣ X + 2ξ ⎦ ⎦ ⎝ X + 1⎠ ⎣ ns ⎝ ns ⎠

approximately 90% of the value of the estimated dielectric constant of the polymer/water mixture. Therefore, the treatment presented in this study is not very sensitive to the dry polymer dielectric constant, as demonstrated in the Supporting Information. The value of ε obtained by this method for CR61 was approximately 42. This value depends slightly on external salt concentration, since the concentration of water in the membrane changed as the external salt concentration increased. The value reported here is based on the pure water uptake (cf. Table 1). Using the estimated values for b and ε in eq 16, a value of 1.83 was calculated for ξ in CR61. The change in water uptake with Css shown in Figure 4 will change the dielectric constant of the water/polymer mixture slightly and, in turn, the value calculated for ξ. However, over the salt concentrations considered in this study, the changes in ξ values were negligible. For example, for CR61, the estimated value for ξ was ∼1.87 at 1 M external NaCl concentration (∼2% change). This approach was also used for the other membranes considered in this study to obtain approximate values for ξ. For cases where ξ could not be calculated in this manner, fitting experimental sorption data to obtain a value for ξ may be considered. In the following discussion, ξ is taken to be a constant, independent of Css. Equation 19 was used to compute values for the product of ion activity coefficients in the membranes as shown below:

(18)

where ne is the concentration of fixed charges on the polyelectrolyte chain, ns is the concentration of salt added to the polyelectrolyte solution, and X = ne/ns. General expressions for individual ion activity coefficients are given in the Supporting Information. Despite the simplicity of the model and lack of adjustable parameters, good agreement between experimental and theoretical values of activity coefficients has been observed for many polyelectrolyte systems.53,70,71 Extension of Manning’s limiting laws to ion exchange membranes, which may be considered as cross-linked polyelectrolytes, requires knowledge of the parameters ξ and X. For charged membranes, we set X = CmA /Cms , where CmA is the concentration of fixed charges and Cms is the concentration of mobile salt (i.e., co-ions for monovalent electrolytes) sorbed in the membrane. These values were measured in the ion sorption experiments presented earlier. Unlike polyelectrolyte systems, estimating ξ for charged membranes is not as straightforward. The assumption of a fully extended conformation of the polymer chain may be questioned, and the presence of uncharged monomers and cross-linkers makes it difficult to obtain a simple expression for the average distance between fixed charges. The membranes considered in this study are believed to be homogeneous. However, the actual distribution of fixed charges along the polymer backbone may not be uniform. Moreover, experimental and theoretical evidence suggests that the dielectric constant of water sorbed into polymers is different from that in bulk water.72,73 Nevertheless, we used the following, albeit crude, procedure to estimate ξ for charged membranes. Knowing the membrane chemical structure, monomer and cross-linker molecular mass, and IEC (mequiv of charge per g of dry polymer), the molar ratio of uncharged to charged monomers was estimated. For example, for CR61, based on the chemical structure of the polymer shown in Figure 2 and the IEC value reported in Table 1, there are 2.2 mmol of charged monomer in 1 g of dry polymer, or ∼0.45 g of charged monomer. Therefore, there are ∼0.55 g (or 4.2 mmol) of noncharged monomer in 1 g of dry polymer. So, CR61 contains approximately 1.9 uncharged monomer units for every charged monomer unit. Assuming the monomer units are uniformly distributed, there are on average, 2.9 monomer units between neighboring fixed charges. Moreover, if the chains were stretched out in a planar zigzag conformation, the projected length of one monomer unit would be approximately 0.25 nm.74 Therefore, the average distance between fixed charges (i.e., b in eq 16) for CR61 is approximately 0.73 nm. An estimate of the water-swollen dielectric constant was calculated as the sum of the dielectric constants of water at ambient conditions (∼78) and dry polymer (∼6) weighted by their appropriate volume fractions.75 The dielectric constant for the dry polymer was chosen based on values typically observed in dry charged polymers. Efforts are underway to determine these values experimentally for the materials considered here, and this will be the subject of future studies. The reported dielectric constants for dry polymers containing polar and/or charged groups appear to vary over a fairly narrow range (∼2− 10).73,76−79 Because of the high water uptake (cf. Table 1) and high dielectric constant of water, the water contributes

⎡ − CAm ⎤ ⎛ CAm + 1 ⎞ m Cm ⎥ ⎢ ⎜ ξC ⎟ γ+mγ−m = ⎜ Cms exp⎢ Cm s ⎥ ⎟ A ⎜ Am + 1 ⎟ ⎢⎣ Csm + 2ξ ⎥⎦ ⎝ Cs ⎠

(19)

where Cms is Cm− for CEMs and Cm+ for AEMs. The fixed charge concentration, CmA , was calculated as the difference between membrane counterion and co-ion concentrations at a given external salt concentration; thus, effects due to osmotic deswelling were included in this calculation. The resulting activity coefficient values, along with those obtained experimentally, are presented in Figure 10. In general, reasonable agreement is observed between the values obtained by

Figure 10. Ion activity coefficients in ion exchange membranes as a function of external NaCl concentration obtained experimentally (CR61 (red ●), AR103 (green ◆), and AR204 (black ■)) and predicted by Manning’s limiting laws (CR61 (red dashed line), AR103 (green dashed line), and AR204 (black dash-dotted line)). K

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describe the experimental values as well as Manning’s model, so we focus primarily on Manning’s model in this study. The relatively good agreement observed between activity coefficients obtained experimentally and those obtained using Manning’s model with no adjustable parameters suggests similarities between the physical phenomena governing the behavior of ions in polyelectrolyte solutions containing added salt and those governing ion behavior in charged membranes. This observation seems reasonable, since most ion exchange materials are, in fact, cross-linked, dense polyelectrolytes.18 Therefore, counterion condensation should also be expected to occur in ion exchange materials. The implications of this observation for sorption and transport of ions in ion exchange membranes are not fully understood, although the occurrence of ion pairing between fixed charges and counterions in charged membranes has been suggested by some investigators.80−82 Moreover, the ability of Manning’s limiting laws to describe electrolyte activity coefficients in ion exchange membranes has significant practical implications in predicting ion sorption in such materials. Findings related to this topic will be reported separately. The applicability of Manning’s counterion condensation theory to ion exchange polymers was further tested using ion sorption data in ion exchange resins reported by Freeman et al.37 Manning’s model was used to estimate values for resin ion activity coefficients, and these values were compared to those obtained experimentally. The results are presented in Figure 12.

Manning’s limiting laws and those obtained experimentally, particularly at more concentrated external NaCl solutions. However, some deviations are observed at low external NaCl concentrations, such as 0.03 and 0.01 M. Moreover, the trend of activity coefficients increasing as external salt concentration increases is qualitatively captured by Manning’s counterion condensation theory. The model predicts that activity coefficients asymptotically approach constant values at low external salt concentrations, which is in contrast to the experimental observations. The reason for the deviation at low external NaCl concentrations is not well understood, and investigations are underway to elucidate this behavior. The disagreement at low external NaCl concentrations could signal a breakdown in one or more of the assumptions used to arrive at the final results. For example, Manning’s model ignores interactions between different chains and distant segments on the same chain, but such interactions may play a larger role at lower external salt concentrations due to low levels of sorbed co-ions at these conditions, which reduce screening between distant charges on the same or neighboring chains. Nonetheless, it is remarkable that Manning’s model, although developed as a “limiting law” for polyelectrolyte solutions, provides a qualitatively reasonable description of the behavior observed for activity coefficient in ion exchange membranes with no adjustable parameters. Other models have been proposed for describing colligative properties of polyelectrolyte systems, and these may also be extended to ion exchange membranes. In this study, we have considered two other models: the “additivity rule” and a model developed by Gueron.47,66 Values for membrane ion activity coefficients obtained by these two models, along with Manning’s counterion condensation theory and those obtained experimentally for CR61 cation exchange membrane, are presented in Figure 11. For the sake of brevity, the expressions for these models and a description of their implementation for membranes are given in the Supporting Information. Like Manning’s model, these other models may be applied with no adjustable parameters. Based on the comparison shown in Figure 11, the “additivity rule” and Gueron’s model do not

Figure 12. Ion activity coefficients for KCl and MgCl2 in cation- and anion-exchange resins (CER and AER), γr+γr− and (γr+)(γr−)2, from a study performed by Freeman et al.37 Circular points denote values obtained experimentally, and dashed lines denote values obtained by Manning’s counterion condensation theory. The ξ value for the CER (ξ = 2.0) was obtained by fitting the experimental data for MgCl2 using a nonlinear curve fit, and the same ξ value was used to predict the data for KCl activity coefficients in the same material. The ξ value for the AER (ξ = 2.5) was obtained by fitting the experimental data using a nonlinear curve fit. The nonlinear curve fitting was performed with Kaleidagraph plotting software.

The Manning expressions for ion activity coefficients for multivalent salts were obtained using the general expressions presented in the Supporting Information. Freeman et al. studied KCl sorption in a cation exchange resin and MgCl2 sorption in both cation and anion exchange resins.37 The authors modified their experimental technique such that the resin and solution phases were never separated, so errors due to

Figure 11. Ion activity coefficients for CR61 determined experimentally (red ●) and predicted by the polyelectrolyte models considered in this study. The black dashed line represents Gueron’s model, the blue dashed line represents the “additivity rule”, and the red dashed line represents Manning’s model. L

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Macromolecules occlusion of electrolyte solution were largely eliminated. Predicting values of ξ for the materials used in their study a priori was impossible because there was insufficient information, such as resin chemical structure and water uptake, about the materials used. Therefore, ξ values were chosen to give the best fit between the model and the data. The values for ξ obtained in this way were reasonable and well within the range of those typically observed in polyelectrolyte systems. Moreover, Manning’s model correctly captured the behavior of ion activity coefficients over the external salt concentration ranges considered. Interestingly, the same value of ξ was used to compute activity coefficients for KCl and MgCl2 in the same cation exchange material. Thus, when ξ cannot be calculated a priori, based on polymer structure and water uptake, it may be fit to experimental data for one salt, and this value of ξ may then be used to obtain reasonably accurate activity coefficient values for other types of salts in the same material. This observation will be further tested in future studies. Additional investigation of materials where chemical structure and membrane properties are accurately known is necessary to validate the capability of Manning’s counterion condensation theory to predict ion activity coefficients in ion exchange polymers.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel +1-512-232-2803; Fax +1-512-232-2807 (B.D.F.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported in part by the National Science Foundation (NSF) Graduate Research Fellowship under Grant DGE-1110007, the NSF Science and Technology Center for Layered Polymeric Systems (Grant 0423914), and by the NSF CBET program (CBET-1160128). This study was also partially supported by the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology. The authors thank Dr. Neil Moe and Dr. John Barber from GE Power and Water for kindly providing the membranes used in this study. Professor Gerald S. Manning provided the equations for the multivalent extension to the univalent activity coefficient model presented in eqs 18 and 19. Professor Manning also generously provided numerous insights regarding counterion condensation and the potential use of this concept in ion exchange membranes.

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CONCLUSIONS Concentrations of Na+ and Cl− ions in one cation exchange membrane and two anion exchange membranes were determined as a function of external NaCl concentration. The concentration of counterions remained relatively constant at or below 0.1 M external NaCl concentration and slightly increased above this concentration due to significant co-ion sorption. The concentration of co-ions increased by about 3 orders of magnitude as external NaCl concentration increased from 0.01 to 1 M due to decreasing Donnan exclusion. Ion sorption data were used to calculate ion activity coefficients in the membrane phase. Membrane ion activity coefficients increased with increasing external NaCl concentration, beginning at rather low values. Manning’s counterion condensation theory was applied to charged ion exchange membranes to calculate ion activity coefficients with no adjustable parameters. These values were compared with those obtained experimentally. The dimensionless linear charge density parameter appearing in Manning’s model was estimated using knowledge of membrane chemical structure and basic properties such as water content and ion exchange capacity. Considering that Manning’s model contains no adjustable parameters when used this way, reasonable agreement between the experimental and model ion activity coefficient values was observed at relatively high external NaCl concentrations, but deviations were observed at dilute NaCl concentrations. Manning’s model was also used to describe ion activity coefficients in ion exchange materials reported in the literature. However, due to insufficient information, ξ was chosen so that good agreement was observed between the values obtained by Manning’s model and those obtained by the Donnan treatment. Nonetheless, Manning’s model captured the behavior of ion activity coefficients obtained by the Donnan treatment reasonably well.

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AR204 ion sorption, ion activity coefficients in membrane, general expressions for membrane activity coefficients from Manning’s counterion condensation theory, influence of dry polymer dielectric constant on ξ, and other polyelectrolyte models for ion activity coefficients (PDF)

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01654. M

DOI: 10.1021/acs.macromol.5b01654 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.5b01654 Macromolecules XXXX, XXX, XXX−XXX