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Tailoring Membrane Nano-Structure and Charge Density for High Electrokinetic Energy Conversion Efficiency Sofie Haldrup, Jacopo Catalano, Mogens Hinge, Grethe V. Jensen, Jan S. Pedersen, and Anders Bentien ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b07229 • Publication Date (Web): 15 Jan 2016 Downloaded from http://pubs.acs.org on January 18, 2016

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Tailoring Membrane Nano-Structure and Charge Density for High Electrokinetic Energy Conversion Efficiency Sofie Haldrup†, Jacopo Catalano†, Mogens Hinge†, Grethe V. Jensen‡,§, Jan S. Pedersen‡, and Anders Bentien†,* †

Department of Engineering, Aarhus University, Hangoevej 2, 8200 Aarhus N, Denmark ‡

Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, 8000 Aarhus C, Denmark. ABSTRACT

The electrokinetic energy conversion (EKEC) of hydraulic work directly into electrical energy has been investigated in charged polymeric membranes with different pore charge densities and characteristic diameters of the nano-porous network. The membranes were synthesized from blends of nitrocellulose and sulfonated polystyrene (SPS) and were comprehensively characterised with respect to structure, composition, and transport properties. It is shown that the SPS can be used as a sacrificial pore generation medium to tune the pore size and membrane porosity which in turn highly affect the transport properties of the membranes. Furthermore, it is shown that very high EKEC efficiencies (> 35 %) are encountered in a rather narrow window of the properties of the nano-porous membrane network: i.e pore diameters of circa 10 nm and pore -3 charge densities of 4.6·102 - 1.5·103 mol SO m for dilute solutions (0.03 M LiCl). The high

absolute value of the efficiency combined with the determination of the optimal membrane

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morphology make membrane-based EKEC devices a step closer to practical applications and high-performance membrane design less empirical.

KEYWORDS Electrokinetic energy conversion, nitrocellulose, sulfonated polystyrene, transport properties, membrane morphology.

In nano-porous ion-conductive membranes the electrokinetic effect and energy conversion are consequences of the interactions between the hydrated mobile counter-ions and the fixed surface charges on the pore walls.1, 2 In the simplest case the pore is a straight circular channel, with uniformly distributed negative fixed surface charges, that as an example has identical LiCl electrolyte solutions at each end. If a pressure difference is applied across the channel the solution is forced through and due to electrostatic interactions in the channel the Cl- ions are, to a varying degree, excluded (Donnan exclusion) and mainly Li+ ions will permeate. If each side of the channel is electrically open circuited this will lead to an accumulation of positive Li+ charges on the low pressure side that are balanced by negative Cl- charges on the high pressure side. This charge accumulation evolves on a time-scale of seconds and it can be measured as an electric streaming potential difference using suitable electrodes. The electrokinetic effect can be utilized for direct conversion of potential or kinetic energy into electrical energy, i.e. conversion of the energy contained in pressurised liquids and gases into electricity (see Figure 1).


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Figure 1. Schematic of a membrane-based electrokinetic energy conversion device. A pressure difference drives an electrolyte solution (e.g. aqueous LiCl) through a thin (50-100 µm) cation exchange membrane (CEM). The solution transport (Jv) in the membrane together with the membrane permselectivity, which allows manly Li+ ions to permeate, induces an electrical/ionic current density (j) that can be harvested with proper electrodes (e.g. Ag/AgCl) and used for electrical work in an external circuit.

In reverse mode, supplying an electrical potential difference to the electrodes leads to migration of hydrated ions across the membrane that can be used for pumping or gas compression.3 The main advantage of electrokinetic energy conversion (EKEC) devices with respect to electromagnetic generators or pumps is the absence of moving parts and can in particular be used for micro-scale applications. Indeed the efficiency of conventional electrical generators and motors decreases with size and for effects below 10 W it diminishes down to values (~50%4) that can be reached, and possibly overcome, by EKEC if properly engineered materials are employed.


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The initial theoretical foundation of EKEC was based on the phenomenological transport equations and the maximum conversion efficiency = on the electrokinetic figure-of-merit ( =

∙

) only.5,

6

was shown to be dependent

Here , , and are the streaming

potential coefficient, the ion conductivity, and the hydraulic permeability, respectively. The main point here is that the goodness of a specific material for EKEC applications can be evaluated experimentally from the measurements of the three independent transport coefficients. Cleanroom fabricated nano-channels have shown efficiencies in the range of 1 to 10%, nonetheless the application of these materials is challenged by their high fabrication cost.7-13 As an alternative we have in previous work investigated the EKEC properties of polymeric ion conductive membranes which may possibly prove to be a more cost-effective alternative because of their high flexibility with respect to structural design, optimization, and upscaling.14-16 Typically in polymeric cation exchange membranes the pores form a random interconnected network of channels of non-uniform radii with fixed charges of covalently bonded SO groups that are uneven distributed in the walls.17 Nonetheless, the principles of the electrokinetic effect still apply to this structure although data analysis and theoretical modelling is more complicated.18,

19

Previous studies performed on commercially available membranes have

revealed maximum EKEC efficiencies ranging from 5.5% for an uncharged Nuclepore membrane up to 18% for Nafion 117.1, 14 Recently, we showed that high ≈ 46 % can be achieved in membranes with a specific composition of nitrocellulose and sulfonated polystyrene (SPS).16 This type of membrane (in the following referred to as C-SPS membranes) have been chosen as a proof-of-concept system due to their flexibility in tuning the pore network characteristics and hence the transport properties and their exceptionally high streaming potential coefficients. 4 ACS Paragon Plus Environment

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C-SPS membranes were first investigated by Neihof20 and later by Tasaka et al.21 who reported a remarkably high streaming potential coefficient =0.58 µV Pa-1 obtained with a membrane containing 5 wt % SPS. This value of is about 150 times larger than that of Nafion and since

enters squared in the figure-of-merit it underlines the potential for reaching high EKEC efficiencies with the C-SPS membranes. The present article is a comprehensive study of the EKEC properties of C-SPS membranes where different nitrocellulose/sulfonated polystyrene compositions have been systematically investigated with respect to structure, membrane and transport properties, and evaluated with focus on their EKEC performances. It is shown that the SPS can be used as a sacrificial medium to increase the membrane porosity and tune the pore size. To the best of the authors’ knowledge, experimental studies of the effect of the pore size and charge density on the EKEC properties has not been reported in the literature and this study is the first of its kind. It is found that increasing is a trade-off between pore size and pore charge density and that the highest is found for membranes with the highest hydraulic permeability that still remain almost ideally permselective.

Results and Discussion In the following the membranes will be referred to as C-SPSX where X is a number between 0 and 7, that represents the amount in g L-1 of SPS added to the casting solution of that particular membrane. Data for the pure nitrocellulose (C-SPS0) and the C-SPS5 membranes have previously been published, while data for Nafion® 117 is included as a reference. 14, 16 Pore generation and membrane structure


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Figure 2. (a) Upper panel: ion exchange capacity measured with ion selective electrodes (iecNH4+), NMR (iecNMR) and from synthesis data iecsyn (dashed line) as a function of CSPS. Lower panel: volumetric faction of SPS leached as function of CSPS calculated from both iecNH4+ and iecNMR. In the cases where iecNMR> iecsyn it is assumed that the leached SPS equal zero. (b) Main panel: and number of water molecules coordinated per sulfonic group () in 0.03 M LiCl solutions as function of CSPS. The dashed lines are guides for the eyes. The inset shows the inplane (diameter, ∆Ø⁄Ø) and out-of-plane (thickness, Δ$ ⁄$ ) linear dilations. (c) Average pore diameter (dp) measured with SAXS in the dry state. The dp in the wet state was estimated as %&,()* = %p ∙ ,1 . ∆/⁄/ ) from the measured dp and the dilation data of the (*) 1 anisotropic, ∆/⁄/ = ∆Ø⁄Ø, and (**) isotropic matrix swelling, ∆/⁄/ = ∆0⁄0 . 1 2 1. The inset shows the relative increase of the pore diameter of the C-SPS membranes with respect to the pure nitrocellulose membrane (C-SPS0) as a function of the leached SPS. Data for the CSPS6 membrane is not included because it degraded before the SAXS experiments. (d) Mechanism of pore generation in nitrocellulose and sulfonated polystyrene membrane. The membranes are cast from nitrocellulose and sulfonated polystyrene (SPS) which work as the fixed charge polymer and the sacrificial pore generating medium. Above a solubility limit, SPS (> 4 g L-1), the weekly entangled SPS domains present in the membrane matrix are partially leached out resulting in membranes with higher porosity and pore size.

The SPS content in the membranes measured as the ion exchange capacity (iec in meq g-1), which represents the equivalent of exchangeable cations per dry weight of polymer, was determined by 1H-NMR (iecNMR) (see SI for details) and with NH4+-ion selective electrodes


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(iecNH4+). The resulting iec values are shown in Figure 2a which also includes the expected theoretical value (iecsyn) calculated from the mass balances of the added SPS in the syntheses. The slightly higher value of iecNMR compared to iecNH4+ is expected since 1H-NMR detects all the SPS in the membrane while the electrode measurements rely on an ion exchange process where not all the fixed charges may be accessible (e.g. void and cavities).ǁ Both iecNH4+ and iecNMR increase with CSPS and follow the theoretical trend of iecsyn up to 4 g L-1. Above this latter value iecNH4+ and iecNMR decrease and is a clear indication that a significant fraction of the SPS is not present in the cast membranes after swelling. The lower part of Figure 2a shows the calculated volumetric fraction (3454 ) of the SPS leached from the cast membranes with respect to the total membrane volume as a function of CSPS. Above the threshold value of CSPS = 4 g L-1, it is seen that increasing fractions of SPS are leached from the membrane. Figure 2b shows the water uptake ( ) as a function of CSPS. In comparison to literature, the

values of are somewhat larger than the ones obtained by Neihof20 where = 0.1

gH2O/gdry,mem for a membrane containing 2.5 g L-1 SPS. On the other hand they are significantly lower than the values reported by Tasaka et al.21 where values up to = 12.9 gH2O/gdry,mem for a membrane containing 1.5 g L-1 SPS was found. The reasons for these large discrepancies have not been specifically addressed in the present work, however, it is known that differences in the molecular weight of the polymers, casting conditions, and post-treatment procedures considerably affect the properties of cast membranes.22 As shown in Figure 2b is an increasing function of CSPS with an evident change in the functional dependence for membranes having CSPS < 4 g L-1 and CSPS > 4 g L-1. The monotonic trend of with CSPS also for membranes characterized by a low iec (i.e. membranes C-SPS6 and C-SPS7) suggests the presence of increasing fractions of weakly- and un-bounded water molecules in membranes


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synthetized with CSPS > 4 g L-1. To highlight this concept also the number of water molecules coordinated per sulfonic group () is reported in Figure 2b. is approximately constant for membranes having CSPS < 4 g L-1 with values ranging between 30-50 molH2O/molSO3H while it increases exponentially with CSPS for membranes where the SPS leached (CSPS > 4 g L-1). The presence of such high coordination numbers suggests that the membranes have more porous and open structures and that the water molecules occupy the voids created by the SPS leached from the membrane matrix. The characteristic pore diameters (dp) of the membranes in the dry state were measured by Small Angle X-ray Diffraction (SAXS) (for details see SI) and are shown in Figure 2c as a function of . The same figure reports the dp values in the wet state estimated from the measured dp and the data of the anisotropic and isotropic matrix swelling. As seen increases dp from 5.0 nm for C-SPS0 to almost 10 nm for C-SPS5. The inset in Figure 2c shows, as expected, that dp is an increasing function of the amount of SPS leached from the membrane matrix (3454 ), with exception of C-SPS7. The leaching of the SPS for CSPS > 4 g L-1 suggests that the solubility of SPS in nitrocellulose is about 4 g L-1 of SPS (0.18 gSPS/gnitrocellulose) and when more SPS is added to the mixture it aggregates during the membrane casting. As a consequence the membrane no longer consists of a homogenous blend of nitrocellulose and SPS but contains SPS domains with different entanglement strength in the nitrocellulose matrix (see Figure 2d). When the membranes are immersed in water and swell the SPS-domains that are only weakly entangled are leached into the aqueous phase resulting in a lower iec and a more porous membrane with larger pore size. To ensure that defects or other inhomogeneities in the membranes do not play a role on the measured properties, the permselectivity of the membranes was measured. It has been quantified by calculating the cation transport number (t+) from measurements of the membrane potential


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and it is included in Table 1. At low concentration (0.01/0.02 M LiCl) it is seen that all the membranes are almost ideally permselective (t+~ 1) and that defects do not affect the measured properties. If defects were present this would result in a low or no permselectivity since the defects would function as a shuttle for permeation of Cl- anions.#

Table 1. Main results for the membranes studied in the present work measured in 0.03 M LiCl solutions, except for the membrane potential measurements, and at ambient temperature. Δ0 0

iecNH4+

dp

t+ 0.01/0.02 M LiCl a

t+ 0.1/0.2 M LiCl a

[-]

[meq g-1]

[nm]

[-]

[-]

0.069 0.143 0.187 0.210 0.298 0.583 0.765 1.072

0.06 0.19 0.27 0.402 0.36 1.19 N/A 2.32

0.0 0.16±0.03 0.25±0.04 0.39±0.07 0.43±0.08 0.27±0.02 0.12±0.01 0.036±0.04

5.1 ± 0.4 5.7 ± 0.1 6.7 ± 0.2 6.4 ± 0.2 7.9 ± 0.2 9.1 ± 0.3 N/A 5.9±0.3

N/A 0.96 1.0 0.98 1.00 0.98 0.93 0.93

N/A 0.98 1.0 1.0 1.0 0.75 N/A 0.84

0.330a

0.66

N/A

4.8 b

0.98c

0.9c

Membrane

C-SPS

[g g-1]

0 1 2 3 4 5 6 7 Nafion

Cm [mol SO3m-3] N/A 1.10·103 1.34·103 1.88·103 1.45·103 4.59·102 1.55·102 3.31·101 2.76·103 d (3.10·103) e

ηmax [-] 1.0·10-7 0.032 0.223 0.218 0.350 0.455 0.223 0.240 0.180 a

Notes: a the error in between experiments is below 2% for all the membranes; b Nafion 120 from ref. 17 for which the Bragg spacing in fully hydrated conditions has been considered; c Nafion 117 from ref. 14; d calculated from ref. 14 in 0.03 M LiCl; e measured in 0.05 M NaCl from ref.23 for Nafion 120.

Some further considerations about the nano-porous network structure can be drawn from the analysis of the linear dilation data in the inset of Figure 2b. Normally solution-cast membranes do not lead to preferred orientations of the polymer matrix and pores, and the anisotropic swelling is somewhat unexpected. Nonetheless, because of the soft nitrocellulose matrix it is suggested that during the drying process the pores collapse in the out-of-plane direction and when wetted again they expand in the same direction. If this is the case, the presumed membrane structure in the swollen state is a network of water nano-channels with a rather low tortuosity factor (ϑ). Considering the limiting case in which all the pores are parallel to the out-of-plane 9 ACS Paragon Plus Environment

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direction (ϑ = 1), the swelling in that direction would be of the same order of magnitude as the linear expansion of the sole nitrocellulose matrix of C-SPS0 (1–2% see SI). This is not the case, for instance the swelling in the out-of-plane direction for the C-SPS7 membrane is around 120% whereas the in-plane only is 25%. With 7Li pulse-field gradient (PFG) NMR spectroscopy a low experimental tortuosity value (ϑ = 0.043) was found for membrane C-SPS5.16 Together this supports the hypothesis that the pores in the membranes have a low tortuosity factor with preferred orientation along the in-plane direction. In a summary of the structural properties of the membranes, it has been shown that in blends of nitrocellulose/SPS, the SPS works as a sacrificial pore generator in the nitrocellulose matrix at concentrations above the solubility limit of circa CSPS = 4 g L-1 (0.18 gSPS/gnitrocellulose). At this concentration the SPS domains are partially leached during the swelling procedures of the cast membranes which results in a more open nano-porous structure. By varying the composition of the SPS both the iec and pore size can be tuned, and hence the pore charge density. Tuning these parameters is of particular interest with respect to EKEC because they are the primary parameters that determine the conversion efficiency and power density. Transport properties


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Figure 3. (a) Measured hydraulic permeability ( ) and calculated intrinsic hydraulic permeability in the absence of electroviscous effects (∗ = ∙ ,1 . 7) as function of water uptake ( ). The inset is an example of raw volumetric flux data in the steady state for membrane C-SPS4. (b) Streaming potential coefficient (), as function of . The upper inset are raw data of the measured electric potential (8) as function of the time (t). When a pressure difference of 140 kPa is applied at t = 0 an instantaneous increase in 8 is observed. This is followed by a monotonic increase related to concentration polarization which has a characteristic √: dependence as shown in the lower inset. (c) Ion conductivity () as a function of . As an example of the raw data, the inset shows the measured electric potential (U) as function of the applied current (I) for membrane C-SPS4. All data have been retrieved in 0.03 M LiCl solutions at room temperature. The data for C-SPS5 is previously published16 and for comparison the data for Nafion measured in 0.03 M LiCl solution has been included.14 (d) Relationship between the intrinsic hydraulic permeability (∗ ) and the electroosmotic permeability (), for all the membranes tested in the present work. Data for Nafion in 0.03 M LiCl solution is added for comparison. The solid line represents the theoretical curve having a slope of 1 F (96485 C mol-1).


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A detailed description of the procedures and data analysis for the measurement of the hydraulic permeability (κ ), streaming potential () and ion conductivity () can be found in previously published work.14, 16 The main results are shown in Figure 3a,b and c. The inset of Figure 3a is an example of the raw data used for obtaining for membrane C-SPS4. The volume flux (Jv) is determined at several transmembrane pressure differences (∆p) as the linear regression of the permeated volume of solution, normalized per membrane surface area (V/A), versus time. The linear dependence of the volumetric flow with time guarantees that the measurements are carried out under steady state conditions and that the membranes are mechanically relaxed. is calculated from the linear regression, constrained to pass through the origin, of Jv as function of the applied ∆p and normalized to the membrane thickness. The results for all membranes are shown in the main panel of Figure 3a as a function of . spans over three orders of

magnitude and for membranes with ≥ 0.2 gH2O/gdry,mem systematically increases with

while membranes synthetized with CSPS 1 g L-1 and 2 g L-1 are characterised by a lower with respect to the pure nitrocellulose membrane. These results can possibly be

explained by a denser matrix and less interconnected channel network for membranes C-SPS1 and C-SPS2 with respect to C-SPS0. It is noted that shows the same dependence on

(Figure 3b) and is a good indication that the measured is intrinsic and not related to e.g.

pinholes or other defects in the membranes. The high (and ) value for the C-SPS7 membrane may appear contradictory with the data reported for dp (6 nm). However, the higher hydraulic permeability and streaming potential values can be a consequence of a higher ϑ of CSPS7 because of the markedly large volume swelling of this particular membrane.¤ Figure 3a also includes the intrinsic hydraulic permeability in the absence of the electroviscous effects, ∗ = ∙ ,1 . 7, which has been calculated from the measured values of and .3 12 ACS Paragon Plus Environment

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The upper inset of Figure 3b is an example of the streaming potential measurements for membrane C-SPS4. At time t = 0 a transmembrane pressure difference of 140 kPa is applied resulting in an instantaneous increase in the potential which corresponds to the intrinsic streaming potential. This is followed by a monotonic increase of φ with time that is related to the concentration polarization on each side of the membrane. The intrinsic streaming potential (∆φ) can be obtained by extrapolating φ versus √: to t = 024 as shown in the lower inset of Figure 3b.

Finally, has been determined from the linear regression of ∆φ as function of ∆p constrained to

pass through the origin. The results for all the membranes are plotted as a function of in the main panel of Figure 3b. Here spans over almost two orders of magnitude and for membranes

C-SPS0, C-SPS5 to C-SPS7 is larger than Nafion but markedly lower than the 0.58 µV Pa-1 previously reported for a C-SPS membrane by Tasaka et al.21 The insert of Figure 3c shows the electric potential as function of applied current for the CSPS4 membrane. The resistance (=) of a membrane equals the slope of the curve and is found from the linear regression constrained to pass through the origin. The ion conductivity is calculated from = = ,$/?7, where $/? is the geometrical factor of the wet membrane. The

results are shown in the main panel of Figure 3c as a function of . Calculation of both

and from raw experimental data includes the geometrical factor while is an intensive variable and independent of $/?.

Electroviscous effects and data consistency. Comparison of Figure 3a with Figure 2c shows that there is no simple power law dependence between and dp as expected from the Hagen– Poiseuille equation. This may be explained by the coexistence of two effects. The first (i) is the presence of a high pore pore charge density (e.g. C-SPS3 and C-SPS4) which results in a thicker Stern layer of immobile water molecules on the pore walls. This suppresses the hydrodynamic


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slip length and as a consequence also .25 The second (ii) is the electroviscous effect due to the increase of the apparent viscosity because of the electrostatic forces between the fixed charges in the membrane, the counter ions, and the solvent. This is experimentally observed as a decrease in , which is quantified by ∗ = ∙ ,1 . 7, where and ∗ are the hydraulic permeability with and without electroviscous effects, respectively.3 Because of significant experimental challenges related to direct measurements of ∗ , it is only that have been measured directly in the present study. The electroviscous effect increases with since it is a measure of the degree

of coupling between the solvent and the counter ions. As seen from Figure 3a, the electroviscous effect contributes significantly for the membranes C-SPS2 to C-SPS7 with C-SPS5 having a ∗

about 7 times larger than .

The Poisson−Nernst−Planck equations can describe the electrokinetic transport in a pore with both slip flow and electroviscous effects. In this case becomes a complex function of the size and surface charge density of the pores.13, 18, 26-28 Nonetheless, it is possible to check the internal consistency of versus ∗ if is rewritten as an extensive variable. Here a good choice is the

electroosmotic permeability (@ = ) which is one of the cross terms entering in the

phenomenological transport equations.1,

29

Assuming electro neutrality conditions along with

constant ion concentration profiles in the solution inside the pores, it is possible from the capillary model to obtain

AB1 ∗

= ∗ = CD ,

18, 23, 29

where F is the Faraday’s constant and Cm

represents the charge density in the volume of the pore which is determined experimentally from the iec. Figure 3d shows the experimental values of /D versus ∗ . Considering the crude model and that the data spans over four orders of magnitude it tracks the theoretical slope (F) very well and the maximum deviation for C-SPS7 is only a factor of five. This also includes CSPS2 to C-SPS4 that appear as outliers in the plots of κH and ν in Figure 3a and 3b. For 14 ACS Paragon Plus Environment

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membrane C-SPS1 the lower /D is probably a consequence of the large D value calculated from the iec, which also is seen in the case reported for Nafion in NaCl solutions.18, 23 For the membranes C-SPS6 and C-SPS7 the deviation increases and here the assumptions in the model E may not fully apply. Nonetheless, all thermodynamic requirements29, in particular ∗ 2 @ F

0, are fulfilled for all the membranes, which substantiates that the experimental transport data are

intrinsic. EKEC efficiency and power density. From the measurements of , , and the

electrokinetic figure-of-merit () and maximum EKEC efficiency , 7 are calculated and are

shown in Figure 4a. Considering, that reported experimental conversion efficiencies are of the order 10 %,7-13 it is remarkable that all the membranes in the range C-SPS2 to C-SPS7 have above 20 %. The highest value, ~46%, is found for C-SPS5 which is a trade-off between several parameters: a network of pores with rather large diameters of about 10 nm, moderate iec but still retaining a high permselectivity in dilute LiCl solutions.

Figure 4. (a) The figure–of-merit () and the maximum EKEC efficiency (ηmax) as a function of the water uptake ( ). The inset shows the empirical dependence of versus the dimensionless pore diameter (%H I ) where a Debye length of 1.74 nm is used. (b) Hydraulic (P/A)hy and electrical power (P/A)el density for power generation. In the calculations of the power density it has been assumed for all the membrane ∆p = 1MPa and a thickness of 50 µm. Data of Nafion are from ref.14. 15 ACS Paragon Plus Environment

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The relation between and the dimensionless pore diameter (%& J 7, where J is the inverse

Debye length, is shown in the inset of Figure 4a. An approximate linear relation between and

%H I is found. To the best of the authors’ knowledge this relation is not predicted theoretically. In most continuum models6,

30-33

the maximum is obtained at %& J ~ 1–3, however, in the

present work is record high and increases with the dimensionless pore diameter up to at least %& J ~6. These intriguing results may suggest that there may exist regions in the electrokinetic

parameter space, currently not predicted by the continuum based formalism, where very high EKEC efficiencies can be obtained. Besides high energy conversion efficiency an equally important property for EKEC is the M

power density LNO, which is the hydraulic or electric power per unit area inserted or extracted M

from the membrane. For power generation the maximum hydraulic power density LNO M

to the membrane is LNO M

M

from LNO = LNO )T

PQ M

PQ

=

RH RS

M

PQ

applied

∙ L1 . E O.3 The electrical power density LNO can be found )T

∙ and it is seen that both high and increases the power density.

Figure 4b shows LNO

PQ

M

and LNO assuming a membrane thickness of 50 µm, similar to the ones )T

M

synthetized in the present study, and a trans-membrane pressure difference of 1MPa. LNO

PQ

increases as function of CSPS for membranes with CSPS > 2 g L-1. However, more interesting is M

the LNO

)T

since this is the electrical power density that can be extracted from the membrane

during power generation. It increases as a function of CSPS and has a value of ~1.7 W m-2 for the C-SPS5 up to ~13 W m-2 for the C-SPS7 membrane. These latter values compare well to the corresponding values of membrane-based technologies that convert chemical energy of salinity


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gradients e.g. pressure retarded osmosis (PRO) and reverse electrodialysis (RED) for which values of about 4-40 W m-2 and 0.8-1.8 W m-2 have been reported, respectively.34, 35 On the other hand membrane-based EKEC power densities are still well below the values obtained in fuel M

cells and redox flow batteries (RFB) where L O ~10U 2 10V W m-2 are about three orders of M

N )T

magnitude higher. Nonetheless, L O can be increased in EKEC processes by (i) an increased N )T

transmembrane pressure difference or the use of thinner membranes (ii) identification of membranes that maintain the efficiency but with enhanced , i.e. membranes with increased ϑ

or %& . Ultimately, the maximum %& is limited by %& J , but as was seen from the inset of Figure

4a, the maximum is not found for %& J ~ 1–3, but is still increasing for %& J F6. This is encouraging with respect to identifying efficient membranes with larger pores and it is M

anticipated that L O ~ 10 W m-2 is realistic for an optimised membrane/electrolyte system. N )T

Conclusions This study is the first in the literature where the effect of both the pore diameter and pore charge density on the EKEC properties has been investigated experimentally. Ion conductive membranes have been synthesized from nitrocellulose solutions with a content of sulfonated polystyrene (SPS) ranging between 0 to 7 g L-1. Above the solubility limit of SPS in nitrocellulose, ~0.18 gSPS/gnitrocellulose, the SPS partially was leached from the matrix resulting in membranes with a larger pore size and porosity. The intrinsic EKEC efficiencies for these membranes have been determined from the figure-of-merit in 0.03 M LiCl solutions at ambient temperature and remarkably high values of 35% and 46% have been reached for the membranes with 4 and 5 g L-1 SPS, respectively. These membranes have the largest pore diameters (~8-10 nm) and remain highly permselective (t+F0.98) in dilute LiCl solutions. The corresponding pore 17 ACS Paragon Plus Environment

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charge densities for these two membranes are

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-3 D = 1.45·103 and 4.59·102 mol SO m

respectively, and are moderate values compared to Nafion. At the same time it shows that the highest efficiency is not obtained for membranes with the highest D or iec. The results presented here ultimately show the importance of tailoring the membrane nanostructure and charge density for achieving high EKEC efficiencies. Higher power densities can be obtained by synthetizing membranes with higher degree of order (W ⟶ 1) and by reducing the membrane thickness.

Materials and Methods Chemicals and Materials. Nitrocellulose (Collodion solution 4–8 % in ethanol/diethyl ether, CAS: 9004-70-0, Sigma Aldrich). The nitrocellulose was dried at 35 ºC prior to use. Sulfonated polystyrene (SPS) (30 % w/v aq. soln., CAS: 28210-41-5, M.W 75,000, Alfa Aesar). Before use the SPS was first dried and then dissolved in ethanol. The rest of the chemicals were used as received. Lithium chloride (CAS: 7447-41-8, VWR), ammonium chloride (NH4Cl > 99.5%, CAS: 12125-02-9, Sigma Aldrich), sodium chloride (CAS: 7647-14-5, VWR), potassium chloride (≥99.0, CAS: 7447-40-7, Sigma Aldrich), potassium chloride solution (for Ag/AgCl electrodes ~3 M KCl, CAS: 7447-40-7, Sigma Aldrich), ethanol absolute (99.8 %, CAS: 744740-7, VWR), and diethyl ether (CAS: 60-29-7, Sigma Aldrich). The membrane support in the experimental cell was a porous glass slide with nominal pore size 160-250 µm and a thickness of 2.8 mm (VWR) and the silver wire used for electrode fabrication had a diameter of 0.25 mm (≥99.99 Ag metal basis, Sigma Aldrich). Membrane synthesis and characterisation. The membranes were synthesized from dissolved nitrocellulose (3 wt%) in ethanol and ether (50/50wt%). After dissolution an alcoholic solution


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of sulfonated polystyrene (SPS) was added drop wise with a content varying from to 0–7 g L-1 (1.3–23 wt% SPS) and the solution was stirred until a homogeneous mixture was obtained. The membranes were solution cast and dried under atmospheric conditions at 35 °C for several days in closed glass petri dishes. The dried membranes (thickness ranging between 37 to 53 µm) were carefully removed from the petri dishes by adding a few droplets of deionized (DI) water. The membranes were then placed in 0.5 M LiCl solution to exchange the H+ counter-ions with Li+ ions followed by rinsing with DI water, and afterward stored in 0.03 LiCl solutions. Before each measurement the membrane samples were carefully rinsed several times in LiCl solutions with the same concentration as the one used in the experiments. The water uptake, , was gravimetrically determined and expressed as mass gain upon swelling overnight in 0.03 M LiCl as function of the dry mass measured after drying in an oven at 50 ºC overnight. The low thermal stability of the nitrocellulose prevented the use of temperatures above 50 ºC, and negligible amounts of bonded water (∼1–2 H2O molecules per fixed charge) could still be present in the membranes.16,

36-38

The linear dilation of the

membranes were determined, both in-plane (∆Ø⁄Ø) and out-of-plane (Δ$ ⁄$ ), by measuring the width and the thickness of the membrane samples in the dry state and after immersion in 0.03 M LiCl. The ion exchange capacity (iecNH4+) was determined by exchanging the counters-ions in the membrane with NH4+ by immersion in a 0.5 M NH4Cl solution that was changed daily for several days. This was followed by placing the membrane in DI water that was changed daily for three days to wash out any residual NH4+. To exchange the NH4+ ions the membranes were placed in a 0.5 M NaCl solution for one day. The ion exchange capacity was then determined by measuring the NH4Cl concentration in the NaCl solution using an ammonia selective electrode


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(NH3-selective gas electrode, Metrohm). A calibration curve for the electrode was made by using different concentrations of NH4Cl in 0.5 M NaCl in the concentration range found in the iec experiments. The pore charge density was calculated as D =

YZ[\]^ ∙ _`ab,cdc ∆e ⁄e

.

The SPS contents of the membranes were determined by 1H-NMR. The resulting spectra were deconvoluted into separate peaks using ACD Lab 1D NMR Processor software and the areas were used to calculate the ion exchange capacity (iecNMR). The NMR spectra were acquired on a Bruker AVANCE III HD spectrometer running at 400 MHz for 1H. For additional details the reader is referred to SI. The volumetric fraction of leached SPS (3454 = qYZ[rps YZ[itu v∙wxyx zzz

∙

_`ab,cdc _xyx

efgf,hijklim enin,mop

) has been calculated from 3454 =

where iecexp is either iecNMR or iecNH4+, {454 the molar mass of one

SPS unit, and |454 and |}~Q,) the density of SPS and the dry membrane, respectively. It has been assumed that the leached SPS equals zero if iecNMR > iecsyn. The membrane potential was measured in a homemade concentration cell consisting of two identical chambers separated by the membrane. The chambers were filled with LiCl solutions with a concentration ratio of 1:2. The membrane potential was measured using Ag/AgCl reference electrodes (Ag/AgCl reference electrodes, Schott) which were placed in separated beakers filled with saturated KCl solution connected to each compartment in the concentration cell by salt bridges. From the membrane potential the cation transport number (t+) was calculated

using the Nernst equation : = E ∙

n

∗

j^ ∙ ∗∗ j^

. 1 where φm is the membrane potential, F the

Faraday constant, R the gas constant, T the absolute temperature, and ∗ and ∗∗ the activity coefficients of the two solutions.39


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Small-angle X-ray scattering (SAXS) data were collected on a modified Nanostart instrument from Bruker with a rotating Cu anode, giving Kα radiation with a wavelength of λ = 1.54 Å, and a HiSTAR gas detector at a sample-detector distance of 65 cm.40 Scattering intensities were collected at q values from 0.0085 Å-1 to 0.35 Å-1, where q, is the magnitude of the momentum transfer given by q = 4π sin θ/λ, and 2θ is the scattering angle. A model describing a randomwalk structure of polydisperse spheres were used to fit the data (see SI). The polydisperse spheres in the model describe the pores in the membrane. As the polydispersity determined for the various samples are very similar (∼ 20%) the average sphere diameter represents the pore diameter, dp. The measurements of the three transport properties, , and , were done following the methods developed in previous works.14-16 More elaborate definitions of the transport coefficients and the influence on the measurement conditions are given in ref. 3. This setup can reproduce values of , , and within 5–10 % for Nafion 117 membrane samples. However, due to uncertainty about the geometrical factor it is anticipated that the systematic errors can be up to 25 %. Nonetheless, in the evaluation of the figure-of-merit = E ∙ ⁄ , the geometrical factor cancels out and it is expected that total experimental error here is about 10 %.


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Supporting Information The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org. Corresponding Author *

[email protected]

Present Addresses §

Grethe. V. Jensen is now a postdoctoral fellow at Niels Bohr Institute, University of

Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark. Funding Sources Villum Foundation (grant number: VKR022356, Young Investigator Programme), and The Aarhus University Research Foundation Notes ǁ

This interpretation is supported by the observation that the relative difference between iecNMR

and iecNH4+ is larger for the more dense membranes with lowest hydraulic permeability (see Figure 3a), while for the more porous and permeable membranes, CSPS > 4 g L-1, iecNH4+ values approach iecNMR. #

Additionally the transport numbers can be used for supporting the structure data reported

before. For nano-porous ion conductive membranes in general, permselectivity is increased by small pore diameters, large iec and low electrolyte concentration. Within experimental uncertainty the highest permselectivities are obtained for the membranes with CSPS up to about 4 g L-1 which is in qualitative agreement with the experimental data of the dp and iec. For all


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membranes t+ decreases with increasing LiCl concentration and is most significant for membrane C-SPS5, where it decreases from t+ = 0.98 in 0.01/0.02 M LiCl to t+ = 0.75 in 0.1/0.2 M LiCl. The large decrease for this membrane is most likely a consequence of a relatively large dp combined with a relatively low iec. ¤

The presence of a high tortuosity factor for membrane C-SPS7 is corroborated by the large

water uptake and consequently

porosity of this specific membrane (see eg. Burggerman

relationship between tortuoristy factor and porosity in Verbrugge, M.W.; Hill, R.F. J. Electrochem, Soc., 1990, 137, 886—893). Additionally an indirect indication of the high tortuosity factor of membrane C-SPS7 is experimentally provided by its high σ despite the low charge density of the pore walls.

References 1. Bentien, A.; Okada, T.; Kjelstrup, S. Evaluation of Nanoporous Polymer Membranes for Electrokinetic Energy Conversion in Power Applications. J. Phys. Chem. C 2013, 117, 1582— 1588. 2. Kjelstrup, S.; Bedeaux, D. Non-Equilibrium Thermodynamics of Heterogeneous Systems. World Scientific: Hackensack, NJ, 2008; pp 148—154 3. Catalano, J.; Bentien, A.; Østedgaard-Munck, D. N.; Kjelstrup, S. Efficiency of Electrochemical Gas Compression, Pumping and Power Generation in Membranes. J. Membr. Sci. 2015, 478, 37—48. 4. Waide, P.; Brunner, C. U. Energy-Efficiency Policy Opportunities for Electric MotorDriven Systems; OECD Publishing: 2011; pp 1—128. 5. Morrison, F. A.; Osterle, J. F. Electrokinetic Energy Conversion in Ultrafine Capillaries. J. Chem. Phys. 1965, 43, 2111—2115. 6. Gross, R. J.; Osterle, J. F. Membrane Transport Characteristics of Ultrafine Capillaries. J. Chem. Phys. 1968, 49, 228—234. 7. Daiguji, H.; Yang, P. D.; Szeri, A. J.; Majumdar, A. Electrochemomechanical Energy Conversion in Nanofluidic Channels. Nano Lett. 2004, 4, 2315—2321. 8. van der Heyden, F. H. J.; Bonthuis, D. J.; Stein, D.; Meyer, C.; Dekker, C. Electrokinetic Energy Conversion Efficiency in Nanofluidic Channels. Nano Lett. 2006, 6, 2232—2237. 9. van der Heyden, F. H. J.; Bonthuis, D. J.; Stein, D.; Meyer, C.; Dekker, C. Power Generation by Pressure-Driven Transport of Ions in Nanofluidic Channels. Nano Lett. 2007, 7, 1022—1025.


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Table of Contents The achievement of highly efficient membrane morphology for electrokinetic energy conversion applications revolves around three axes: relatively low surface density, pores on the ten nanometers scale and almost ideal permselectivity.

Graphical Abstract


Tailoring Membrane Nanostructure and Charge ... - ACS Publications

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