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Evaluation of nano-porous polymer membranes for electrokinetic energy conversion in power applications Anders Bentien, Tatsuhiro Okada, and Signe Kjelstrup J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp308957q • Publication Date (Web): 07 Dec 2012 Downloaded from http://pubs.acs.org on December 30, 2012

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The Journal of Physical Chemistry

Evaluation of Nano-Porous Polymer Membranes for Electrokinetic Energy Conversion in Power Applications Anders Bentien*1, Tatsuhiro Okada2 and Signe Kjelstrup3

1. Department of Engineering, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark (email: [email protected]) 2. Tsukuba Fuel Cell Laboratory, Inc., National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8565, Japan 3. Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway

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Abstract

Electrokinetic energy conversion for pumping or power generation has for the past decade regained attention with focus on applications within pumping in nano-fluidics or micro generators. Little experimental work has been published and mostly in relation to clean-room fabricated nano-pores. In the present study it is suggested that electrokinetic energy conversion have a potential as future decentralized electrical energy sources, if polymer membranes are used. Based on new electrokinetic measurements and literature data we have made a systematic study of commercially available nano-porous polymer membranes and found a promising first law efficiency of 5.5 % in one polymer-electrolyte system. It is likely that future more rigorous and targeted studies will find even larger conversion efficiencies.

Keywords: Surface charge density, Figure-of-merit, Conversion efficiency, Pore size, Power density


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Introduction Electrokinetic effects take place in membranes and porous materials because there is a coupling between the movement of charges (ions) and noncharged solvent (water).1 Electrokinetic effects can in general be utilised to convert kinetic energy into electrochemical energy or vice versa.2 That is; pumping occurs during electro-osmosis, when an electric (ion) current drags water molecules along, and power generation occurs when a pressure gradient moves water that drags ions along and creates a streaming potential. In general electrokinetic effects are increased in materials with large difference in the mobility of cations and anions. This is in practice observed in selective membranes i.e. materials having narrow pores where immobile surface charges prevent ions of the same sign to enter the pores. From the phenomelogical transport equations and Onsager relations it can be shown2-3 that a common first law efficiency defined for the electrokinetic conversion, , increases with the figure-of-merit, where

∙

through the relation 1 / 1 1 / 1,

is the streaming potential in units of electric potential per unit pressure, is the ion

conductivity and is the hydraulic permeability. In porous materials the main parameters that

determine the transport properties , and are the intrinsic material parameters; surface charge

density ( ), pore size, surface charge type (fixed ions in ion-exchange membranes) together with the external parameters; electrolyte type (e.g. H+, Li+, Na+ etc.) and concentration. Electrokinetic energy conversion was initially studied theoretically in the 1960’s by Osterlee and co-workers2-3 who predicted maximum efficiencies ( ) of the order 1-3 %, and by Burgreen and Nakache4 who predicted efficiencies up to 17 %. For the past 10 years a renewed interest in this topic has emerged, however, most reports focus on the theoretical transport properties of straight



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nano channels with well-defined dimensions,5 with only a few experimental investigations,5a,

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6

where of the order up to 10 % has been measured. Furthermore, there exist few systematic experimental studies of the electroviscous effect on track-etched polymer membranes7 from which an up to 7-8 % can be estimated. Up to now electrokinetic energy conversion has mostly been investigated in regard to micropumps for nano-fluid applications. Besides micro power sources for e.g. vibrational energy harvesting, electrokinetic energy conversion may also have a potential as a future decentralised energy source with output powers in the range from a few watts up to several (hundred) kilowatts, powered by solar or waste-heat created pressure differences. In that range fuel cells, thermoelectric materials and solar cells are competing technologies. An analysis of the feasibility of the different technologies is out of the scope here, but it will require detailed reviews of the application areas in relation to the parameter; conversion efficiency, power density, torque, investment, price of electricity in EUR/kWh etc. We nevertheless remark that proton exchange membrane fuel cells (PEMFC) presently reach a first law efficiency of the order 35 % - 45 % when fuelled by hydrogen.8 Costs related to production and handling of hydrogen has until now prevented their use on a large scale. Liquid powered methanol/ethanol fuel cells have conversion efficiencies of the order 10-25 %.8 The first law conversion efficiency used here is the ratio between the electrical work and the higher heating value of the fuel. It does, however, not account for the considerable amount of lost energy during production of hydrogen or ethanol/methanol. The use of solar cells and thermoelectric materials is hampered by large manufacturing costs, resulting in EUR/kWh prices that are not competitive to existing technologies e.g. wind mills, coal fired or nuclear power plants. Electrokinetic energy conversion may in this context have some potential attractive properties; if based on standard polymer or inorganic membranes the initial system investment and electricity


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cost, in terms of price per kWh, could be low, even if the electrokinetic conversion efficiency is modest. Furthermore, electrokinetic energy conversion is versatile with respect to fuelling, the pressure can be generated by heat or chemical combustion, and have much less costs with respect to production/handling of fuels. The only major challenge is the conversion efficiency which currently is only of the order 10 %. In literature there has been no designated study of electrokinetic energy conversion in porous (polymer) membranes and ion conductive membranes. In the present paper we study some commercial porous membranes with pore diameters (

)

in the range nm to µm with various

electrolyte solutions and concentrations. For the study we present new data along with already published literature data.

Transport coefficients and figure-of-merit Before proceeding with the main results a few notes about the observable transport coefficients and figure-of-merit are made. In the Supporting Information the following simplified phenomenological transport equations are derived

!" #"" $ - #" $

1 &' 1 &* ) #" $ ) A6 % &( % &(

1 &' 1 &* ) # $ ) A7 % &( % &(

Eqs. (A6) and (A7) describes volume flux (!" , in units of ms-1) and current density (-, in units of Am-2) in the presence of pressure difference (&') and electrical potential (&*) across a membrane. The direction and magnitude of the fluxes is determined by the phenomenological transport coefficients (#/0 ) and are coupled through the Onsager relation #" #" .



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The electric conductivity is defined for uniform pressure, as

# -&( 1 2 1 &* 3 %

In stationary state, the electric conductivity can also be measured in the case of zero volume flow, i.e. when the mechanical force is balanced by the electric force. This gives

45 3 1

-&( 2 &* 4

5 3

# #" #" #" #" ∙ 61 7 ∙ 61 7 2. % #"" # #"" #

The hydraulic permeability, , is defined for zero current density (- 0), that is, both sides of the membranes are electrically isolated from each other, and is:

#" #" !" &( #"" 2 ∙ 61 7 3 1 &' 03 % #"" #

Alternatively, the hydraulic permeability can be measured when the two membrane sides are electrically short-circuited (&* 0) by inserting an electrode that allows an ion current that flows along with the water (,3 ) and gives: ,3 1

=

#" #" !" &( #"" 2 ∙ 61 7 &' 3 % #"" #


4

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With only a few exceptions, the experimental conditions for measurements of the ion conductivity and hydraulic permeability of membranes in literature are given by eq. (1) and (3), respectively, and in the following we use these definitions unless stated otherwise. The streaming potential is related to the transport coefficients through:

#" &* 1 2 5 &' 03 # and can be related to the salt (@A ) and water (@B ) transport numbers by @A CA @B CB /D,1

where CA and CB are the molar volume of the salt and water respectively. For the membranes and experimental conditions in the current article @B ≫ @A and it is seen that ∝ @B , that is the streaming

potential increases with increased coupling between water molecules and ions. In literature, the electrokinetic figure-of-merit has been defined in different ways. Osterle3, 9 uses =

G#"" # ⁄#" #" I 1 , while Xuan et al.5d and Kedem et al.5d, 10 uses as figure-of-merit J #" #" ⁄#"" # . For #" #" ⁄#"" # 0, J 0, while for #" #" ⁄#"" # →

1, → ∞ while J → 1. We adopt the notation of Osterle, since it is similar to the wellestablished thermoelectric figure-of-merit11 and since has a simpler relation to the normal

definitions of the ion conductivity, eq. (1), and hydraulic permeability, eq. (3). From the relations between observable and phenomenological transport coefficients, eqs. (1)-(5), expressions for the figure-of-merit in terms of observable transport coefficients can be found. Table 1 summarizes the different notations of electrokinetic figures-of-merit and relation to conversion efficiency. can be evaluated by measuring transport properties that contain the transport coefficients #" e.g. electroosmotic pressure, streaming current, streaming potential etc. together with the



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conductivity terms #"" and # , i.e. hydraulic permeability and ion conductivity. Using the streaming potential together with and , results in

∙

.

Experimental The streaming potential was measured with Ag|AgCl-electrodes in cells with two types of membranes following the procedure outlined in an earlier publication.12 The first was a standard MF-Millipore membranes (Merck Millipore) made from a mixture of cellulose acetate and cellulose nitrate. The second, Fluoropore membranes (Merck Millipore), is a hydrophobic PTFE membrane bonded to a high density polyethylene support. Both membranes have high porosities with less well-defined and random pore structures. The membranes were equilibrated in the solution (0.03M or 0.1M KCl, and 0.03M HCl) prior to the streaming potential measurements. The membranes were inserted between two half cells installed with Ag|AgCl electrodes and two identical solutions on both sides of the membrane. Pressure differences were applied by nitrogen gas, and the streaming potential was determined with an accuracy of 10%. This low accuracy is mainly due to a large flux of liquid in the membranes which is a result of the relatively large pore size and hydraulic permeability. In order to minimize this error, the pressure was pulsed for 3-5 s and the electromotive force (emf) across the membrane was recorded simultaneously. The emf reached values of the order tens to hundreds µV, and the streaming potential was obtained by a linear fit between emf and &' obtained at different pressure differences. Table 2 and 3 summarizes experimental conditions and data of the MF-Millipore and Fluoropore membranes, respectively.

Literature data


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The measured data on the MF-Millipore and Fluoropore membranes were compared to values on the streaming potentials obtained from literature data for a wide range of pore sizes range of Nuclepore (Whatmann) and Cyclopore membranes. These membranes are low porosity track-etched polycarbonate membranes with well-defined pore structure and sizes. Table 4 and 5 summarizes experimental conditions and data for the Nuclepore membranes and are collected from literature data,13 while Table 6 shows the experimental conditions and data for the Cyclopore membranes.14

Calculating the figure-of-merit For all membranes, the hydraulic permeability was calculated from the volume flow rate through the membrane, pressure difference, and thickness (@M ) of the membrane, as given by the manufacturer datasheets. The ion conductivity of the membranes was estimated from the porosity of the membranes and the conductance of single nano-pores15 N where

O QR

P ST

1UV U= ∙ W ∙ X UV

P Y QR

2,

is the pore diameter, UV and U= are the mobilities of the cation and anion respectively, W

the electrolyte concentration and the surface charge density on the inside of the pores. The conductance of a single pore consists of two contributions, the first from bulk conductance inside the pore related to UV U= ∙ W ∙ X, the second from surface conductance related to UV

P Y QR

(assuming a negative surface charge). Such properties are observed in track-etched mica pores and fused silica16, where a significant contributions to the bulk conductance only appears whenever Z ∙

< 10, where Z is the inverse Debye length.

In the estimates of in the membranes it is assumed that the bulk contribution is larger than the

surface contribution and N [

O QR

P ST

UV U= ∙ W ∙ X is used. Considering the porosity and the

thickness of the membranes this results in '\]\^_@` ∙ UV U= ∙ W ∙ X. It is emphasized that

this is a minimum estimate and may be larger, in particular whenever Z ∙


< 10.


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The hydraulic permeability, , can be estimated from the porosity and single pore flow with the Hagen-Poiseuille equation, a

O

c QR

b de ST

∙ &', in a similar manner as the electric conductance. This QR

results in the following equation ,fghf '\]\^_@` ∙ id , where Uj is the water viscosity. e

Results Tables 2-6 contain all transport data, while figures 1-4 show selected data. Starting with figure 1, is plotted as a function of

for pores in the range 10-1000 nm. With exception of the

Fluoropore membranes, it is seen that for each type of membrane shows an approximate

dependence as expected from the Hagen-Poiseuille equation. The MF-Millipore and Fluoropore membranes have hydraulic permeabilities that are approximately an order of magnitude larger than of the Nuclepore and Cyclopore membranes. This is mainly due to the larger porosity of the

MF-Millipore and Fluoropore membranes. Figure 1 also includes ,fghf , and with a few exceptions

the ratio ,fghf / , is in the range 1 to 3.5 for all membranes. This indicates that the (hydraulic)

radius of the pores is larger than the nominal and that also the calculated may be underestimated, since / ∙

should be approximately constant.

Figure 2 shows the corresponding streaming potential as a function of

for all membranes.

They have been measured with different electrolytes (HCl, LiCl, NaCl and KCl) and varying concentrations (5⋅10-5 M to 0.1 M). Among all the membranes, the magnitude of varies 5 orders of magnitude depending on membrane, electrolyte, concentration and pore diameter. In Tables 2-6 is also reported in number of water molecules per faraday transported (@j ). The water transference numbers vary from ∼ 2 for 0.03 M HCl in MF-Millipore membranes to an enormous value of 1.7⋅105 for 5⋅10-5 M LiCl in Cyclopore membranes, again reflecting the large span of .


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Figure 3 shows the figure-of-merit (

∙

) for electrokinetic energy conversion in all

membranes. It is estimated from the measured , manufacturer supplied and calculated . It is

seen that spans over seven orders of magnitude, where the MF-Millipore membrane with 0.03

M HCl electrolyte shows the lowest , while the 50 nm Nuclepore membrane with 2⋅10-4 M LiCl

electrolyte has the highest and reaches = 0.24. This corresponds to ~ 5.5 %. As discussed earlier the calculated is probably underestimated, in particular as Z ∙

approaches unity, since

surface conduction has been neglected and that the (hydraulic) pore diameters are larger than the nominal. Furthermore, the value of is probably overestimated, since the addition of electrolytes to the solution will increase the apparent viscosity, thereby decreasing . Thus values in figure

3 are most likely minimum estimates. The magnitude of the maximum we obtain in the present study is similar to the maximum

that can be estimated from measurements of the electro-viscous effect7 in membranes. The

electro-viscous effect is found from the ratio between the hydraulic permeabilities (Ug /U

,3 / ) measured with &* 0 and - 0 experimental conditions and is related to the figureof-merit through

dlRR dY

1. For 50 nm Nuclepore membranes in ∼1.5⋅10-4 M LiCl solutions

Ug /U = 1.33 is observed 7a and this corresponds to = 0.33 and ~ 7.2 %.

Discussion Most studies of electrokinetic energy conversion has been focused on theoretical transport properties and efficiency of well-defined and straight nanopores2-5, and only a few experimental works have been performed5a, 6. When considering the electrolyte concentration and pore size, a maximum is predicted3,

5d, 5f, 5g, 5i

membranes as a function of Z ∙

.

for Z ∙

~ 1-2.5.

Figure 4 is a replot of for all

It is only the data series for the Nuclepore membranes



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measured in 0.001 M KCl that shows a clear maximum (Z ∙

~ 5)

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and considering low density of

data points, the results are in quite good agreement with theoretical predictions. None of the other measurements show a clear maximum, but this can be explained by the higher Z ∙ least 2.5 for the membranes with smallest

which is at

.

With the exception of data of MF-Millipore membranes in HCl electrolytes, it is seen that both the value, within approximately one order of magnitude, and functional dependence of for all membranes is described by Z ∙

= .

Thus the two most important parameters that determine the

magnitude of are the electrolyte concentration and pore size, as expected from theoretical

modeling. The value of for membranes measured in HCl solutions is probably not well modeled by this plot since the transport mechanisms of H+ includes tunneling. Other parameters,

like the cation type, where the row Li+, Na+ and K+ normally shows a decreasing @j ,17 plays a role along with surface charge density and structural differences. The MF Millipore and Flouropore membranes have less well-defined pore sizes and geometry and this may be a possible explanation for the deviation from the Nuclepore membranes in the range Z ∙

= 10-100. Furthermore, the

deviation of the Cyclopore membranes from the Nuclepore membranes, may possibly be due to lower surface charge densities in Cyclopore membranes than in Nuclepore membranes which in both are relatively low and of the order 10-5 Cm-2 - 10-3 Cm-2. 14, 18

Outlook Theoretical calculations3,

5d, 5f, 5g, 5i

have predicted maximum electrokinetic energy conversion

efficiencies of the order 10 % in low charged nanopores with

~25

nm – 100 nm and Z ∙

~ 1-

2.5. The surface charge densities used are similar to those of Nuclepore membranes and are in the range 0 - 10⋅10-3 Cm-2.3, 5d, 5f, 5g, 5i These results are in good agreement with the estimated maximum ∼ 5.5 % obtained in the present study. The electrokinetic properties of commercially available


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nanopore membranes have neither been fully explored in literature nor in the present study. Considering that our investigation most probably underestimates , the variety of commercially available membranes, the number of experimental variables and possibilities with respect to modifications of surface charge properties of commercially available membranes, it is likely that significantly larger can be reached for this type of membranes. One of the major mechanisms that maintains the (theoretical) conversion efficiency < 10 % is the Stern/diffuse layer that result in a higher counter ion concentration at the pore wall than in the pore center. Due to the laminar flow profile, high flow speed is therefore related to regions with low counter ion concentration, while low/zero flow speed is related to regions with high counter ion concentration. Recent theoretical development has shown that much larger than 10 % may be obtained in pores with slip flow5e, 5g, 5n, whereby the counter ions on the pore wall becomes more mobile or in pores where there is a counter ion layering that displaces some of the counter ions away from the pore wall.5o Both effects increases with the surface charge density5e, 5g, 5n, 5o and it is more likely that enhanced values of can be observed in membrane systems with larger . This could e.g. be ion-exchange polymer membranes where ~ 0.2 Cm-2 - 1 Cm-2 for Nafion19 and is

approximately three orders of magnitude larger than for the uncharged polycarbonate in Nuclepore. Thus, more rigorous investigations of electrokinetic properties of ion-exchange membranes could be an alternative route for possible discoveries of efficient electrokinetic materials. Power densities (m⁄n) can be calculated from the work produced per unit time and area by the

liquid in the membrane, m ⁄n ⁄@M ∙ &' . Using = 1⋅10-14 m2s-1Pa-1 and @M = 6µm for 50 nm

Nuclepore membrane with = 0.24 and assuming a pressure difference &' = 10 bar gives m⁄n ~

0.17 Wcm-2 that is converted to m⁄n ~ 0.091 Wcm-2 electrical energy using ~ 5.5 %. This is

comparable to power densities in fuel cells where m⁄n is of the order 0.5 Wcm-2.8 Even higher power densities can be reached by thinner membranes and higher pressures.



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Summary Electrokinetic energy conversion in polymer membranes has a potential as future decentralized power sources driven by pressure that is build up from solar heat, waste-heat or any fossil fuel. Provided that manufacturing costs of membranes are low enough, even modest conversion efficiencies may be attractive in terms of price per kWh when compared to fuel cell, thermoelectric and solar cell technologies. Up to now there has been no direct study of the electrokinetic conversion efficiency of commercially available nm-sized membranes in literature. Here an initial systematic investigation of the electrokinetic properties of commercially available membranes with pore sizes in the range from 15 nm -1000 nm has been presented. The highest estimated electrokinetic energy conversion efficiency was found to be ~ 5.5 % for 50 nm Nuclepore membrane measured in 2⋅10-4 M LiCl

solution. This is in good agreement with the efficiency ( ~ 7.2 %) estimated from electro viscous measurements on 50 nm Nuclepore membranes in ∼1.5⋅10-4 M LiCl.7a It is likely that significantly higher can be found by more rigorous investigations of this type of membranes. Future work should also include surface charge modifications, different electrolytes and solvents. Furthermore, it is suggested that polymer membranes with higher surface charge density (e.g. ion-exchange like membranes) could reach larger efficiencies.

Acknowledgement AB wishes to thank for financial support to both the Villum Foundation through the Young Investigator Programme and Aarhus University Research Foundation through AU Ideas Programme. SK is grateful to the RENERGI project no. 164466, and the FRIENERGI project no. 197598/V30, both of the Norwegian Research Council.


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Supporting Information Available In the Supporting Information the simplified phenomenological transport equations are derived. The information is available free of charge via the Internet at http://pubs.acs.org. References 1. Kjelstrup, S.; Bedeaux, D., Non-equilibrium thermodynamics of heterogeneous systems. World Scientific: Hackensack, NJ, 2008. 2. Morrison, F. A.; Osterle, J. F., Journal of Chemical Physics 1965, 43 (6), 2111-2115. 3. Gross, R. J.; Osterle, J. F., Journal of Chemical Physics 1968, 49 (1), 228-234. 4. (a) Burgreen, D.; Nakache, F. R., Journal of Physical Chemistry 1964, 68 (5), 1084-1091; (b) Burgreen, D.; Nakache, F. R., Journal of Applied Mechanics 1965, 32 (3), 675-679. 5. (a) Yang, J.; Lu, F. Z.; Kostiuk, L. W.; Kwok, D. Y., Journal of Micromechanics and Microengineering 2003, 13 (6), 963-970; (b) Daiguji, H.; Yang, P. D.; Szeri, A. J.; Majumdar, A., Nano Letters 2004, 4 (12), 2315-2321; (c) van der Heyden, F. H. J.; Bonthuis, D. J.; Stein, D.; Meyer, C.; Dekker, C., Nano Letters 2006, 6 (10), 2232-2237; (d) Xuan, X. C.; Li, D. Q., Journal of Power Sources 2006, 156 (2), 677-684; (e) Ren, Y.; Stein, D., Nanotechnology 2008, 19 (19), 195707; (f) Davidson, C.; Xuan, X., Electrophoresis 2008, 29 (5), 1125-1130; (g) Davidson, C.; Xuan, X., Journal of Power Sources 2008, 179 (1), 297-300; (h) Chein, R.; Chen, H.; Liao, C., Journal of Electroanalytical Chemistry 2009, 630 (1-2), 1-9; (i) Chein, R.; Liao, C.; Chen, H., Journal of Power Sources 2009, 187 (2), 461-470; (j) Chein, R.; Tsai, K.; Yeh, L., Electrophoresis 2010, 31 (3), 535-545; (k) Chang, C.-C.; Yang, R.-J., Microfluidics and Nanofluidics 2010, 9 (2-3), 225-241; (l) Chein, R.; Liao, C.; Chen, H., Nanoscale and Microscale Thermophysical Engineering 2010, 14 (2), 75-94; (m) Wang, M.; Kang, Q., Microfluidics and Nanofluidics 2010, 9 (2-3), 181190; (n) Chang, C.-C.; Yang, R.-J., Applied Physics Letters 2011, 99 (8), 083102; (o) Gillespie, D., Nano Letters 2012, 12 (3), 1410-1416. 6. (a) van der Heyden, F. H. J.; Bonthuis, D. J.; Stein, D.; Meyer, C.; Dekker, C., Nano Letters 2007, 7 (4), 1022-1025; (b) Duffin, A. M.; Saykally, R. J., Journal of Physical Chemistry C 2007, 111 (32), 12031-12037; (c) Duffin, A. M.; Saykally, R. J., Journal of Physical Chemistry C 2008, 112 (43), 17018-17022; (d) Xie, Y.; Wang, X.; Xue, J.; Jin, K.; Chen, L.; Wang, Y., Applied Physics Letters 2008, 93 (16), 163116. 7. (a) Huisman, I. H.; Pradanos, P.; Calvo, J. I.; Hernandez, A., Journal of Membrane Science 2000, 178 (1-2), 79-92; (b) Huisman, I. H.; Pradanos, P.; Hernandez, A., Journal of Membrane Science 2000, 178 (1-2), 55-64. 8. Hoogers, G., Fuel cell technology handbook. CRC Press: Boca Raton, Fla., 2003. 9. Osterle, J. F., Applied Scientific Research Section a-Mechanics Heat Chemical Engineering Mathematical Methods 1964, 12 (6), 425-434. 10. Kedem, O.; Caplan, S. R., Transactions of the Faraday Society 1965, 61 (513P), 1897-1911. 11. Rowe, D. M., Thermoelectrics handbook: Macro to Nano. CRC: Boca Raton, Fl, 2006. 12. Okada, T.; Ratkje, S. K.; Hanche-Olsen, H., Journal of Membrane Science 1992, 66 (2-3), 179-192.



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13. (a) Brendler, E.; Ratkje, S. K.; Hertz, H. G., Electrochimica Acta 1996, 41 (1), 169-176; (b) Diez, L. M.; Villa, F. M.; Gimenez, A. H.; Garcia, F. T., Journal of Colloid and Interface Science 1989, 132 (1), 27-33. 14. Calvo, J. I.; Hernandez, A.; Pradanos, P.; Tejerina, F., Journal of Colloid and Interface Science 1996, 181 (2), 399-412. 15. Smeets, R. M. M.; Keyser, U. F.; Krapf, D.; Wu, M. Y.; Dekker, N. H.; Dekker, C., Nano Letters 2006, 6 (1), 89-95. 16. (a) Westermannclark, G. B.; Anderson, J. L., Journal of the Electrochemical Society 1983, 130 (4), 839-847; (b) Stein, D.; Kruithof, M.; Dekker, C., Physical Review Letters 2004, 93 (3), 035901. 17. Okada, T.; Xie, G.; Gorseth, O.; Kjelstrup, S.; Nakamura, N.; Arimura, T., Electrochimica Acta 1998, 43 (24), 3741-3747. 18. Molina, C.; Victoria, L.; Arenas, A.; Ibanez, J. A., Journal of Membrane Science 1999, 163 (2), 239-255. 19. (a) Koh, W. H.; Silverman, H. P., Journal of Membrane Science 1983, 13 (3), 279-290; (b) Pintauro, P. N.; Tandon, R.; Chao, L.; Xu, W.; Evilia, R., Journal of Physical Chemistry 1995, 99 (34), 12915-12924.


Page 16 of 27

Page 17 of 27

0.1 -1

1E-3

-9

0.01

2 -1

κH (10 m s Pa )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1E-4

MF-Millipore Flouropore Nuclepore Cyclopore

d

2

1E-5 1E-6 10

100 d (nm)

1000

p

Figure 1. Hydraulic permeability ( ) as function of pore diameter (

)

for MF-millipore

membrane (black circles), Flouropore (green triangles), Nuclepore (red squares) and Cyclopore (blue squares). Solid lines show the corresponding calculated permeability (,fghf ). Black dashed

line shows a d2 dependence. Deviations in ,fghf from a d2 dependence are due to variations in the porosity of the membranes.



Cyclopore -5

5.10 M LiCl

10

-3

10 M LiCl Nuclepore -4

2.10 M LiCl

1

ν (µV/Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 27

Nuclepore -2

3.10 M KCl -3

10 M KCl

0.1

-2

3.10 M NaCl

Flouropore

0.01

-2

3.10 M KCl -1

10 M KCl

1E-3

MF Millipore -2

3.10 M KCl -1

10 M KCl

1E-4 10

-2

3.10 M HCl

100 d (nm)

1000

p

Figure 2. Streaming potential () as function of pore diameter (

)

in various electrolyte and

concentrations for MF-millipore membrane (black data points), Flouropore (green data points), Nuclepore (red and dark data points) and Cyclopore (blue data points).


Page 19 of 27

Cyclopore

0.1

-5

5.10 M LiCl -3

10 M LiCl

0.01 1E-3

βEK

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Nuclepore -4

2.10 M LiCl

Nuclepore

-2

d

-2

3.10 M KCl -3

10 M KCl

1E-4

-2

3.10 M LiCl

1E-5

Flouropore -2

3.10 M KCl -1

10 M KCl

1E-6 1E-7

MF Millipore -2

3.10 M KCl -1

10 M KCl

1E-8 10

-2

3.10 M HCl

100 d (nm)

1000

p

Figure 3. Figure-of-merit for electrokinetic energy conversion () as function of pore diameter (

)

in various electrolyte and concentrations for the same membranes as in figure 2.



Cyclopore

0.1

-5

5.10 M LiCl -3

10 M LiCl

0.01

Nuclepore -4

2.10 M LiCl

1E-3

βEK

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 27

-2

Nuclepore

d

-2

3.10 M KCl -3

1E-4

10 M KCl -2

3.10 M NaCl

1E-5

Flouropore -2

3.10 M KCl

1E-6

-1

10 M KCl

1E-7

MF Millipore -2

3.10 M KCl -1

10 M KCl

1E-8 1

-2

3.10 M HCl

10

100

1000

κDdp Figure 4. Figure-of-merit for electrokinetic energy conversion () as function of the inverse

Debye length multiplied with the pore diameter (Z ∙

)

in various electrolyte and concentrations

for the same membranes as in figure 2.


Page 21 of 27

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Symbol Ref. 3, 9

5d, 10

J

Figure-of-merit (phenomenological transport coefficients)

Figure-of-merit (observable transport properties)

1 / 1 1 / 1

#" #" #"" #

,3 $1 )

1 1 J / J

#"" # o 1p #" #"

=

Table 1. Definitions of electrokinetic figure-of-merit expressed in terms of phenomenological transport coefficients and observable transport coefficients related to the streaming potential. Using the definition of figure of merit by Osterlee3,

9

results in a simpler dependence on observable

transport properties when using the normal definition/experimental conditions for the ion conductivity, eq. (1) and hydraulic permeability, eq. (3). .



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

@M

nm

25

50

100

220

300

650

1200

µm

105

105

105

150

150

150

150

70

72

74

75

77

81

82

0.15

0.74

1.5

18

32

140

270

3.8E-14

1.9E-13

3.8E-13

6.4E-12

1.1E-11

5E-11

1.0E-10

1.4E-14

5.6E-14

2.3E-13

1.1E-12

2.2E-12

1.1E-11

3.7E-11

porosity % Flow mLmin-1m-2 Rate

,fghf tw

tw

tw

Page 22 of 27

m2s-1Pa-1 2 -1

m s Pa

-1

0.03 M KCl VPa

-1

7.5E-9

9.3E-9

1.0E-8

1.3E-8

1.5E-8

2.0E-8

1.6E-8

Molecules per faraday

40

50

54

67

81

106

87

Sm-1

0.31

0.32

0.33

0.34

0.35

0.36

0.37

4.8E-4

1.5E-4

9.1E-5

8.3E-6

7.0E-6

2.9E-6

1.0E-6

0.1 M KCl VPa

-1

2.9E-9

3.4E-9

3.0E-9

3.4E-9

5.1E-9

7.6E-9

5.5E-9


15

18

16

18

27

41

29

Sm-1

1.0

1.1

1.1

1.1

1.2

1.2

1.2

2.3E-4

6.6E-5

2.7E-5

2.1E-6

2.6E-6

1.4E-6

3.9E-7

0.03 M HCl VPa

-1


3.9E-10

6.8E-10

7.0E-10

6.6E-10

8.2E-10

5.7E-10

1.4E-9

2.1

3.6

3.7

3.5

4.4

3.0

7.7

Sm-1 0.89 0.92 0.95 0.96 0.98 1.0 1.0 3.7E-6 2.3E-6 1.2E-6 6.5E-8 5.8E-8 6.7E-9 2.3E-8 Table 2: Physical properties and transport properties of the MF Millipore membranes. Membrane

pore diameter (

),

thickness (@M ), porosity and flow rate are obtained from manufacturer data

sheet, while the streaming potential () has been measured with various electrolytes and concentrations. The ion conductivity () has been estimated.


Page 23 of 27

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


nm

200

500

1000

@M

µm

175

175

145

porosity

%

70

85

85

mLmin m

15

40

90

2 -1

m s Pa

-1

6.3E-12

1.7E-11

3.14E-11

2 -1

-1

8.8E-13

6.6E-12

2.7E-11

Flow Rate

,fghf

-1

m s Pa

-2

0.03 M KCl

VPa-1

2.3E-8

1.9E-8

2.0E-8

tw


123

101

106

Sm-1

0.31

0.38

0.38

2.6E-5

8.2E-6

4.8E-6

5.8E-9

5.7E-9

6.9E-9

0.1 M KCl

VPa

tw


31

30

37

Sm-1

1.0

1.3

1.3

5.6E-6

2.5E-6

1.9E-6

-1

Table 3: Physical properties and transport properties of the Flouropore membranes. The notation is the same as for table 2.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 27

nm

15

50

100

200

400

600

1000

@M

µm

6

6

6

10

10

10.2

11

porosity

%

10

10

10

10

10

10

10

1

Flow Rate mLmin m

,fghf

-2

0.1

0.7

4

20

70

115

250

2 -1

m s Pa

-1

1.4E-15

1.0E-14

5.7E-14

4.8E-13

1.7E-12

2.8E-12

6.5E-12

2 -1

-1

7.5E-16

7.8E-15

3.1E-14

1.3E-13

5.0E-13

1.1E-12

3.1E-12

m s Pa

0.03 M KCl

VPa-1

2.2E-8

1.9E-8

2.3E-8

2.0E-8

1.9E-8

1.8E-8

1.6E-8

tw


117

102

123

107

102

96

85

Sm-1

0.045

0.045

0.045

0.045

0.045

0.045

0.045

0.015

0.0016

4.2E-4

3.8E-5

9.7E-6

5.2E-6

1.8E-6

0.001 M KCl

VPa

1.7E-7

9.6E-7

1.16E-6

1.36E-6

1.38E-6

1.4E-6

1.45E-6

tw


909

5132

6202

7271

7378

7485

7752

Sm-1

0.0015

0.0015

0.0015

0.0015

0.0015

0.0015

0.0015

0.030

0.14

0.035

0.0058

0.0017

0.0011

4.8E-4

-1

0.03 M NaCl

VPa

2.5E-8

2.8E-8

2.7E-8

2.5E-8

3.2E-8

2.4E-8

2.5E-8

tw


134

150

144

134

171

128

134

Sm-1

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.017

0.0030

4.8E-4

5.0E-5

2.3E-5

7.8E-6

3.6E-6

-1

13a

Table 4: : Physical and transport properties of the Nuclepore membranes.

The streaming potential

() is obtained from table 1 and 2 in ref. (13a), while the membrane pore diameter (

),

thickness

(@M ), porosity and flow rate are obtained from manufacturer data sheet. The ion conductivity () has been estimated.


Page 25 of 27

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


@M porosity Flow Rate ,fghf tw

Nm µm % mLmin-1cm2 2 -1

-1

m s Pa m2s-1Pa-1 VPa-1 Molecules per faraday Sm-1

50 6 10

100 6 10

200 10 10

400 10 10

0.7

4

20

70

4.8E-13 1.3E-13

1.7E-12 5.0E-13

7.1E-6

9.3E-6

1E-14 5.7E-14 7.8E-15 3.1E-14 2⋅10-4 M LiCl 3.1E-6 5.3E-6 16600

28500

38000

49500

2.4E-4 0.24

2.4E-4 0.12

2.4E-4 0.026

2.4E-4 0.013

Table 5: Physical properties and transport properties of the Nuclepore membranes13b. The streaming potential () has been digitized from Fig 1a in ref. (13b), while the membrane pore diameter (

),

thickness (@M ), porosity and flow rate are obtained from manufacturer data sheet. The ion conductivity () has been estimated.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

nm µm %

@M porosity Flow Rate ,fghf tw

tw

Ls-1m-2 2 -1

-1

100 10 4

200 10 14

400 10 13

600 9 8

800 9 15

1000 9 16

0.5

4

12.17

14.67

33.33

36.67

1.9E-12 9.0E-13

4.3E-12 3.0E-12

4.7E-12 5.0E-12

1.6E-5

2.2E-5

3.1E-5

84000

118000

165000

m s Pa m2s-1Pa-1

7.1E-14 1.3E-14

VPa-1 Molecules per faraday Sm-1

4.9E-6

VPa-1 Molecules per faraday Sm-1

Page 26 of 27

5.7E-13 1.7E-12 1.8E-13 6.5E-13 -5 5⋅10 M LiCl 9.4E-6 1.0E-5

26500

50100

2.4E-5 0.0081

8.3E-5 7.7E-5 0.013 0.0047 0.001 M LiCl 2.2E-6 2.5E-6

4.7E-5 0.0062

8.9E-5 0.010

9.4E-5 0.019

2.7E-6

2.8E-6

3.0E-6

8700

12000

13300

14200

15200

15800

4.6E-4 0.017

0.0016 0.014

0.0015 0.0054

9.2E-4 0.0035

0.0017 0.0033

0.0018 0.0034

1.6E-6

54500

Table 6: Physical properties and transport properties of the Cyclopore membranes14. The streaming potential () has been digitized from figure 3 in ref. (14), while the membrane pore diameter (

),

thickness (@M ), porosity and flow rate are obtained from manufacturer data sheet.

The ion conductivity () has been estimated.


26

Page 27 of 27

Table of Contents - Graphics

EK

Electrokinetic figure of merit (β )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.1

0.01 1E-3

-2

d

1E-4 1E-5 1E-6 1E-7 1E-8 1

10

100

1000

κDdp


27

Evaluation of Nanoporous Polymer Membranes for ... - ACS Publications

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