University of Virginia 102 Engineers Way, P.O. Box Charlottesville, VA USA

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1 Supporting Information for Water and salt transport properties of triptycenecontaining sulfonated polysulfone materials for desalination membrane applications Hongxi Luo, 1 Joseph Aboki, 2 Yuanyuan Ji, 1 Ruilan Guo, 2 Geoffrey M. Geise 1, * 1 Department of Chemical Engineering University of Virginia 102 Engineers Way, P.O. Box Charlottesville, VA USA 2 Department of Chemical and Biomolecular Engineering University of Notre Dame 205 McCourtney Hall Notre Dame, IN USA *To whom correspondence should be addressed: geise@virginia.edu (Tel: , Fax: )

2 S1. Diffusive Water Permeability and Water Diffusion Coefficient Calculations and Analysis using Flory-Huggins Theory The conversion of measured hydraulic permeability, P " #, to diffusive permeability, P " $, requires information about water sorption and thermodynamic non-ideality: P $ # " = P &' *+, ) " ( ) - where K " is the water sorption coefficient (effectively the volume fraction of water sorbed by the polymer at equilibrium, c.f., Eq. (6) in the main text), R is the gas constant, T is the absolute temperature, and V " is the partial molar volume of water in the polymer (taken to be the molar volume of water, 18 cm 3 /mol), 1 and δ is a thermodynamic factor that describes the relationship between the volume fraction of water sorbed by the polymer, φ ", and the thermodynamic activity of water in the polymer, a " 3, at equilibrium. 2 The thermodynamic factor is defined as: 2 (S1) δ 5678 ) 5679 : ) : 9); (S2) 3 where a "< is the activity of water in the polymer at the upstream (or high pressure) polymersolution interface. In many studies, the thermodynamic factor and the convective frame of reference term, 1 K ", in Eq. (S1) are set equal to unity, which is a reasonable assumption if K " 1 and mixing between water and polymer can be considered thermodynamically ideal. 2 Evaluating δ can be accomplished by either measuring water sorption isotherms as a function of water activity or by using a suitable equation of state. One approach reported in the literature is to use Flory-Huggins theory to evaluate δ. 1-2 Flory-Huggins theory describes the relationship between the activity of water and the volume fraction of water sorbed in the polymer using an interaction parameter, χ: 3-4 ln a" 3 = lnφ " + 1 φ " + χ(1 φ " ) F (S3) The water sorption coefficient, K ", is effectively equivalent to φ ", 5 so δ can be evaluated using Flory-Huggins theory as: 2 δ = * (*+, ) ) *+FG, ) (S4) Thus, if the Flory-Huggins interaction parameter for water and a polymer of interest is known, the diffusive water permeability can be calculated from the measured hydraulic water permeability and sorption coefficient as: 6-7 S1

3 P " $ = P " # &' ( ) [ 1 K " F 1 2χK " ] (S5) 2, 6, 8 The water diffusion coefficient, D ", can then be calculated as: D " = L ) M, ) (S6) As discussed in the main text, the use of Eq. (S5) to calculate the diffusive water permeability will only be accurate if Flory-Huggins theory accurately describes the relationship between water sorption and the activity of water. Water sorption isotherms as a function of water activity are not available for many polymers of interest, and this lack of experimental data prevents the direct calculation of δ using Eq. (S2) or validation of whether Flory-Huggins theory is an appropriate model for the system. As such, attempts have been made to estimate the Flory-Huggins interaction parameter using a single point fit of the Flory-Huggins model (typically made using the pure water sorption data for the polymer). 1-2 While this approach yields a value of δ for use in Eq. (S5), it is possible that the approach could introduce an artifact if the Flory-Huggins model does not accurately describe water sorption in the polymer. In the main text, the analysis was performed by setting the interaction parameter in Eq. (S1) equal to unity. Here, the diffusive water permeability is calculated using two alternate cases: 1) the single point fit using Flory-Huggins theory and Eq. (S5) and 2) the low water content approximation where the convective frame of reference term, 1 K ", is neglected and δ is taken as unity: 2, 9 P" $ # = P &' " (S7) ( ) Interaction parameters, diffusive water permeability values, and water diffusion coefficients calculated using the single point Flory-Huggins fit and Eqs. (S5) and (S6) are provided in Table S1 for the polymers discussed in this study. Water sorption isotherms presently are not available for the TRP-BP, BPS(H), or BisAS polymers discussed in this study, so the applicability of Flory- Huggins theory (or the single point fit) to these materials is not currently known. S2

4 Table S1. Water transport properties and Flory-Huggins interaction parameters for the polymers discussed in this study. Previously reported data for the BPS(H) polymers and the BisAS polymers are included for comparison. Experimentally measured (using a dead-end cell pressurized to 400 psig at room temperature) hydraulic water permeability data are also provided. Material P W H (L µm/m 2 h bar) χ a D W b ( 10-6 cm 2 /s) P W D c ( 10-7 cm 2 /s) TRP-BP 1:1-35-acid 2.8± ± ±0.6 TRP-BP 1:1-35-salt 0.55± ± ±0.3 TRP-BP 2:1-35-acid 2.9± ± ±0.3 TRP-BP 2:1-35-salt 0.75± ± ±0.4 TRP-BP 1:1-50-salt 3.8± ± ±0.6 BPS BPS BPSH BPSH BisAS ± ± ±0.2 BisAS ± ± ±1.3 a Calculated via a single point fit using pure water sorption data and Eq. (S3) b Calculated using Eqs. (S5) and (S6) c Calculated using Eq. (S5) Figs. 2, 6, 7, and 9 from the main text were adjusted using the values reported in Table S1 to prepare Figs. S1, S2, S3, and S4, respectively. Comparing Fig. S1 to Fig. 2 (main text) and Fig. S2 to Fig. 6 (main text) reveals qualitative similarity between the data. This similarity suggests that the method of analysis does not appreciably affect the qualitative results that water diffusivity in the TRP-BP materials is suppressed at a given water content compared to the BPS(H) and BisAS materials (Fig. S1 and Fig. 5) and that salt diffusivity is more sensitive to water content compared to water diffusivity in the TRP-BP materials (Fig. S2 and Fig. 6). S3

5 Fig. S1. Water diffusivity, D W, as a function of 1/K W for the TRP-BP ( ), BPS(H) ( ) 1, and BisAS ( ) 10 materials. The D W values (Table S1) were calculated using Eqs. (S5) and (S6). S4

6 Fig. S2. TRP-BP water diffusivity (D W,, from Table S1 calculated using Eqs. (S5) and (S6)) and salt diffusivity (D S,, calculated from P S and K S values using Eq. (14) from the main text) as a function of 1/K W. S5

7 Fig. S3. Diffusion selectivity, D W /D S, as a function of D W for the TRP-BP 1:1 ( ), TRP-BP 2:1 ( ), BPS(H) ( ) 1, and BisAS ( ) 10 materials. The D W values (Table S1) were calculated using Eqs. (S5) and (S6). S6

8 Fig. S4. Trade-off between water/salt permeability selectivity, P $ " P R, and diffusive water permeability, P $ ", for the TRP-BP 1:1 ( ), TRP-BP 2:1 ( ), BPS(H) ( ) 1, and BisAS ( ) 10 $ materials. P " values were calculated using Eq. (S5). As observed in Figs. S3 and S4, using the single point Flory-Huggins fit to calculate values of the diffusive water permeability and water diffusion coefficients gives a qualitatively different picture of the material selectivity properties compared to the discussion in the main text. The water/salt diffusivity selectivity of the TRP-BP materials is suppressed relative to the other sulfonated polysulfones (Fig. S3), and the acid-form TRP-BP materials have water/salt permeability selectivity values that are comparable to those values for the other sulfonated polysulfones (Fig. S4). Since the sulfonated polysulfone materials are glassy polymers, it is not S7

9 clear whether the single point fit Flory-Huggins theory-based analysis of the diffusive water permeability and water diffusion coefficient introduces an artifact due to the way that the thermodynamics of the system are handled. This alternate analysis, though, is provided in contrast to the main text results to provide a comparison that is similar to other approaches that 1, have been described in the literature. When the diffusive water permeability and water diffusion coefficient are calculated using Eqs. (S7) and (S6), i.e., neglecting both the convective frame of reference and thermodynamic correction terms, the water/salt diffusivity and permeability selectivity plots can be updated accordingly (Figs. S5 and S6). This method of analysis suggests that the water/salt diffusivity (Fig. S5) and permeability (Fig. S6) selectivity properties of the TRP-BP materials are higher or comparable to that of the other sulfonated polysulfones. This analysis also is provided as other reports in the literature have taken this approach to analyze water transport data. 13 The three different approaches (one in the main text and 2 presented here) yield different quantitative results, and are provided in the interest of completeness. S8

10 Fig. S5. Diffusion selectivity, D W /D S, as a function of D W for the TRP-BP 1:1 ( ), TRP-BP 2:1 ( ), BPS(H) ( ) 1, and BisAS ( ) 10 materials. The D W values were calculated using Eqs. (S7) and (S6). The dashed line represents an empirical tradeoff frontier reported for desalination membranes. 13 S9

11 Fig. S6. Trade-off between water/salt permeability selectivity, P $ " P R, and diffusive water permeability, P $ ", for the TRP-BP 1:1 ( ), TRP-BP 2:1 ( ), BPS(H) ( ) 1, and BisAS ( ) 10 $ materials. P " values were calculated using Eq. (S7). The dashed line represents an empirical tradeoff frontier reported for desalination membranes. 13 S10

12 S2. Further Discussion Related to the Supression of Water and Salt Diffusion Coefficients upon Incorporation of Triptycene into Sulfonated Polysulfone The main text suggests that the TRP moieties in the TRP-BP polymers may affect the distribution of free volume in the TRP-BP polymers compared to the other sulfonated polysulfones in a manner that could be consistent with the idea of increasing the effective tortuosity of the transport pathways in the TRP-BP polymers. To further support the suggestion that triptycene incorporation in sulfonated polysulfone might effectively introduce more transport pathway tortuosity compared to the other sulfonated polysulfones, the salt transport properties of two set of sulfonated styrenic pentablock copolymers (spbc) are compared to the sulfonated polysulfone data (Figs. S7 and S8); Figs. S7 and S8 correspond to Figs. 3 and 4 in the main text, respectively. S11

13 Fig. S7. Salt sorption coefficient, K S, values as a function of the water sorption coefficient, K W, for the TRP-BP ( ), BPS(H) ( ) 1, BisAS ( ) 10, and spbc ( ) 14 materials. S12

14 Fig. S8. Salt permeability, P S, as a function of 1/K W for the TRP-BP ( ), BPS (H) ( ) 1, BisAS ( ) 10, and spbc-b ( ) 15 materials. The data are compared to a general representation (solid line) of uncharged hydrogel data reported by Yasuda et al. 16 This comparison was made due to the lack of random copolymer data where the tortuosity of the transport pathways was systematically varied. The pentablock copolymers micro-phase separate into hydrophilic and hydrophobic micro-domains. 17 Therefore, the pentablock copolymers have some element of transport pathway tortuosity. The salt sorption properties of the spbc materials are similar to the sulfonated polysulfones as a function of polymer water content (Fig. S7). Salt sorption data are not available for the spbc-b materials discussed here, so further analysis is focused in terms of salt S13

15 permeability as opposed to salt diffusion coefficients. If the salt sorption coefficient properties of the spbc-b materials are similar to the spbc materials, which may be a reasonable assumption given the chemical similarity between the materials, then discussion of salt permeability would be analogous to a discussion of salt diffusion coefficients. In Fig. S8, the TRP-BP materials appear to establish a functional relationship between P S and 1/K W that appears to be largely coincident with the spbc-b materials. While this observation does not confirm that triptycene affects the structure of the TRP-BP materials in a manner that is consistent with micro-phase separation in a block copolymer, the observation does suggest that micro-phase separation and tortuous transport pathways also tend to suppress salt permeation properties of micro-phase separated materials relative to non-micro-phase separated materials at comparable water content. This discussion is presented in terms of salt permeability due to the availability of published data for comparison. A similar situation and discussion might be expected for water transport properties as both water and salt transport in the materials are described by the solution-diffusion model. Therefore, the incorporation of triptycene into sulfonated polysulfone may influence the polymer chain configurations (and/or the free volume distribution) in the materials in a manner that suppresses rates of water and salt permeability and diffusion. S14

16 S3. References 1. Xie, W.; Cook, J.; Park, H. B.; Freeman, B. D.; Lee, C. H.; McGrath, J. E., Fundamental salt and water transport properties in directly copolymerized disulfonated poly(arylene ether sulfone) random copolymers. Polymer 2011, 52 (9), Geise, G. M.; Paul, D. R.; Freeman, B. D., Fundamental water and salt transport properties of polymeric materials. Prog. Polym. Sci. 2014, 39, Flory, P. J., Thermodynamics of high polymer solutions. J. Chem. Phys. 1941, 9 (8), Huggins, M. L., Solutions of long chain compounds. J. Chem. Phys. 1941, 9 (5), Geise, G. M.; Freeman, B. D.; Paul, D. R., Sodium chloride diffusion in sulfonated polymers for membrane applications. J. Membr. Sci. 2013, 427, Wijmans, J. G.; Baker, R. W., The solution-diffusion model: a review. J. Membr. Sci. 1995, 107 (1), Paul, D. R., Relation between hydraulic permeability and diffusion in homogeneous swollen membranes. J. Polym. Sci., Polym. Phys. Ed. 1973, 11 (2), Paul, D. R., Reformulation of the solution-diffusion theory of reverse osmosis. J. Membr. Sci. 2004, 241 (2), Lonsdale, H. K.; Merten, U.; Riley, R. L., Transport properties of cellulose acetate osmotic membranes. J. Appl. Polym. Sci. 1965, 9, Cook, J. Fundamental water and ion transport characterization of sulfonated polysulfone desalination materials; Ph.D. Thesis, The University of Texas at Austin: Sagle, A. C.; Ju, H.; Freeman, B. D.; Sharma, M. M., PEG-based hydrogel membrane coatings. Polymer 2009, 50, Ju, H.; Sagle, A. C.; Freeman, B. D.; Mardel, J. I.; Hill, A. J., Characterization of sodium chloride and water transport in poly(ethylene oxide) hydrogels. J. Membr. Sci. 2010, 358, Geise, G. M.; Park, H. B.; Sagle, A. C.; Freeman, B. D.; McGrath, J. E., Water permeability and water/salt selectivity tradeoff in polymers for desalination. J. Membr. Sci. 2011, 369 (1-2), Geise, G. M.; Falcon, L. P.; Freeman, B. D.; Paul, D. R., Sodium chloride sorption in sulfonated polymers for membrane applications. Journal of membrane science 2012, 423, Geise, G. M.; Freeman, B. D.; Paul, D. R., Characterization of a sulfonated pentablock copolymer for desalination applications. Polymer 2010, 51 (24), Yasuda, H.; Lamaze, C. E.; Ikenberry, L. D., Permeability of solutes through hydrated polymer membranes. Part I. Diffusion of sodium chloride. Makromol. Chem. 1968, 118 (1), Choi, J.-H.; Willis, C. L.; Winey, K. I., Structure-property relationship in sulfonated pentablock copolymers. J. Membr. Sci. 2012, , S15