energies
Article
Power Generation from Concentration Gradient by
Reverse Electrodialysis in Dense Silica Membranes
for Microfluidic and Nanofluidic Systems
Sang Woo Lee, Hyun Jung Kim and Dong-Kwon Kim *
Received: 28 October 2015; Accepted: 12 January 2016; Published: 15 January 2016
Academic Editor: Ling Bing Kong
Department of Mechanical Engineering, Ajou University, Suwon 443-749, Korea;
sadf21@ajou.ac.kr (S.W.L.); hyunkim@ajou.ac.kr (H.J.K.)
* Correspondence: dkim@ajou.ac.kr; Tel.: +82-31-219-3660; Fax: +82-31-219-1611
Abstract: In this study, we investigate power generation by reverse electrodialysis in a dense silica
membrane that is between two NaCl solutions with various combinations of concentrations. Each
silica membrane is fabricated by depositing a silica layer on a porous alumina substrate via chemical
vapor deposition. The measured potential-current (V-I) characteristics of the silica membrane are
used to obtain the transference number, diffusion potential, and electrical resistance. We develop
empirical correlations for the transference number and the area-specific resistance, and present the
results of power generation by reverse electrodialysis using the fabricated silica membranes. The
highest measured power density is 0.98 mW/m2 . In addition, we develop a contour map of the power
density as a function of NaCl concentrations on the basis of the empirical correlations. The contour
map shows that a power output density of 1.2 mW/m2 is achievable with the use of silica membranes
and is sufficient to drive nanofluidic and microfluidic systems. The dense silica membrane has the
potential for use in micro power generators in nanofluidic and microfluidic systems.
Keywords: power generation; reverse electrodialysis; silica membrane; concentration gradient
1. Introduction
Energy sources are increasingly important for nanofluidic and microfluidic systems that are used
in applications such as environmental monitoring with wireless sensor networks and implantable
medical devices [1]. Therefore, considerable effort over several decades has been devoted to the
investigation of energy conversion devices for nanofluidic and microfluidic systems [2,3]. These
devices were developed not only by miniaturization and improvement of conventional energy
conversion machines, but also by the application of truly novel methods of energy conversion [2].
Miniaturized conventional devices include miniaturized heat engines, micro fuel cells, microreactors,
miniaturized gas turbines, and microbatteries. Whalen et al. [4] developed a micro heat engine in
which a piezoelectric membrane extracts power from two-phase working fluids. Choban et al. [5]
presented a microfluidic fuel cell that utilizes the occurrence of microscale multistream laminar
flow to keep the fuel and oxidant streams separated but in diffusional contact. On the other hand,
novel methods to convert energy using microscale fabrication include generation of streaming
potential through a nanochannel and biologically inspired methods. Van der Heyden et al. [6]
investigated power generation by a streaming potential produced by pressure-driven transport of
ions in nanochannels. Tanaka et al. [7] developed a microspherical heart-like pump, which can convert
chemical energy flowing into cells to mechanical energy of a fluid stream. Chang and Yang [8]
derived an exact expression for the figure of merit to calculate the electrokinetic energy conversion
efficiency and power of an ion-selective nanopore. They found that the highest efficiency for a
Energies 2016, 9, 49; doi:10.3390/en9010049
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Energies 2016, 9, 49
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non-slip cation-selective nanopore is 9.7%. They also theoretically and numerically investigated the
electrokinetic energy conversion in short-length nanofluidic channels, taking into account reservoir
Energies 2016, 9, 49 resistance and concentration polarization effects [9]. These studies focused on conversion from
hydrodynamic,
chemical,
and thermal
energy
to electricalnanopore energy. is 9.7%. They also theoretically that the highest efficiency for a non‐slip cation‐selective The
Gibbs
free
energy
of
mixing
can
be
converted
to electrical energy for nanofluidic and
and numerically investigated the electrokinetic energy conversion in short‐length nanofluidic channels, taking into account reservoir resistance and concentration effects These studies microfluidic systems using inorganic membranes. Accordingpolarization to reference
[10],[9]. inorganic
membranes
focused on conversion from hydrodynamic, chemical, and thermal energy to electrical energy. can be divided into two structural categories, dense and porous inorganic membranes, which
The Gibbs free energy of mixing can be converted to electrical energy for nanofluidic and can have a significant impact on their performance as separators. Dense membranes are free of
microfluidic systems using inorganic membranes. According to reference [10], inorganic membranes discrete,can be divided into two structural categories, dense and porous inorganic membranes, which can well-defined pores or voids, as shown in Figure 1a. In contrast, porous membranes show
well-defined
straight or tortuous pores across the membrane thickness, as shown in Figure 1b. In the
have a significant impact on their performance as separators. Dense membranes are free of discrete, pores or voids, as shown in Figure 1a. nanopores
In contrast, throughout
porous membranes show porous well‐defined inorganic membrane,
an aqueous
solution
fills the
the membrane,
and
straight or tortuous pores the membrane thickness, in Figure to
1b. become
surface well‐defined ionization, ion
adsorption,
and
ion across dissolution
cause the
surfaceas ofshown the nanopores
the porous inorganic membrane, an aqueous solution fills the nanopores throughout the chargedIn [11].
These surface charges draw counter ions toward the surface and repel co-ions (Figure 1a).
membrane, and surface ionization, ion adsorption, and ion dissolution cause the surface of the On the other hand, the dense inorganic membrane consists of an irregular atomic network with fixed
nanopores to become charged [11]. These surface charges draw counter ions toward the surface and anionic repel co‐ions (Figure 1a). On the other hand, the dense inorganic membrane consists of an irregular or cationic groups [12]. These groups have an affinity for counter ions that can be adsorbed at
ionic sites
within the membrane [13]. When an electrolyte concentration gradient is applied to either
atomic network with fixed anionic or cationic groups [12]. These groups have an affinity for counter type of ions that can be adsorbed at ionic sites within the membrane [13]. When an electrolyte concentration membrane, counter ions are transported through the layer much more easily than co-ions,
gradient applied migration
to either type of membrane, counter ions are transported through the layer resulting
in a netis charge
of ions
(Figure 1b)
[14]. Therefore,
the Gibbs
free energy
of mixing,
much more easily than co‐ions, resulting in a net charge migration of ions (Figure 1b) [14]. which forces ion diffusion, can be converted into electrical energy. This energy conversion process is
Therefore, the Gibbs free energy of mixing, which forces ion diffusion, can be converted into called reverse
electrodialysis.
electrical energy. This energy conversion process is called reverse electrodialysis. (a) (b) Figure 1. Power generation from concentration gradient by reverse electrodialysis: (a) in a dense Figure 1. Power generation from concentration gradient by reverse electrodialysis: (a) in a dense silica
silica membrane; and (b) in a porous membrane. membrane; and (b) in a porous membrane.
Recently, nanopores and nanofluidic channels have been widely investigated as porous inorganic membranes for use in reverse electrodialysis. Kim et al. [15] showed that silica nanochannels, Recently, nanopores and nanofluidic channels have been widely investigated as porous inorganic
fabricated by a standard semiconductor manufacturing process, can harvest energy by reverse membranes for use in reverse electrodialysis. Kim et al. [15] showed that silica nanochannels, fabricated
electrodialysis. They experimentally investigated the power generated by 4 nm, 26 nm, and 80 nm by a standard
semiconductor manufacturing process, can harvest energy by reverse electrodialysis.
high nanochannels that were between two KCl solutions with various combinations of concentrations. They experimentally
investigated the power generated by 4 nm, 26 nm, and 80 nm high nanochannels
The highest power output measured was 2.89 pW. Ouyang et al. [16] conducted a proof‐of‐concept experiment a nanofluidic of packed silica nanoparticles. They achieved power power
that were
between using two KCl
solutions crystal with various
combinations
of concentrations.
Thea highest
of 1.18 nW with their prototype Kim et al. [17] investigated the potential of alumina using a
output output measured
was
2.89
pW.
Ouyang
et cell. al. [16]
conducted
a proof-of-concept
experiment
nanopores for reverse electrodialysis. Yeh et al. [18] performed numerical simulations based on the nanofluidic
crystal of packed silica nanoparticles. They achieved a power output of 1.18 nW with their
full Poisson–Nernst–Planck (PNP) equations to investigate reverse electrodialysis in negatively prototype
cell.
Kim et al. [17] investigated the potential of alumina nanopores for reverse electrodialysis.
charged conical nanopores, and showed the maximum power conversion efficiency reaches 45%. Yeh et al.
[18] performed numerical simulations based on the full Poisson–Nernst–Planck (PNP)
On the other hand, reverse electrodialysis in dense inorganic membranes has not been investigated equations
to investigate reverse electrodialysis in negatively charged conical nanopores, and showed
yet. These membranes are suitable for use in micro power generators and microbatteries where they can generate power more reliably because they do not On
shrink swell in response to their the maximum
power
conversion
efficiency
reaches
45%.
the and other
hand,
reverse electrodialysis
environment [19]. In addition, the performance of dense membranes is not as affected by biofouling in dense inorganic membranes has not been investigated yet. These membranes are suitable for use
as porous membranes [20]. In particular, because dense silica membrane can be fabricated by the in micro power generators and microbatteries where they can generate power more reliably because
standard complementary metal‐oxide‐semiconductor (CMOS) process, it has the potential for use in they do not shrink and swell in response to their environment [19]. In addition, the performance of
2
dense membranes is not as affected by biofouling as porous membranes [20]. In particular, because
dense silica membrane can be fabricated by the standard complementary metal-oxide-semiconductor
Energies 2016, 9, 49
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(CMOS) process, it has the potential for use in nanofluidic and microfluidic devices. This led us
to investigate the potential of dense silica membrane for the use in reverse electrodialysis systems.
We can expect that a dense silica membrane can be used for reverse electrodialysis, because the
ion-selective properties of glass/electrolyte interfaces were recognized early in the 20th century, and
glass electrodes have been used since then for measurements of pH and the activities of alkali ions [21].
However,
the maximum power densities that can be achieved using a dense silica membrane, and
Energies 2016, 9, 49 the conditions under which these densities are achieved, are unclear. This lack of clarity is due to
nanofluidic and microfluidic devices. This led us to investigate the potential of dense silica the fact that, to the best of our knowledge, there have been no previous studies focused on power
membrane for the use in reverse electrodialysis systems. We can expect that a dense silica membrane generation
bybe reverse
electrodialysis
in a dense
silica membrane
located
between
solutions having
can used for reverse electrodialysis, because the ion‐selective properties of two
glass/electrolyte different interfaces were recognized early in the 20th century, and glass electrodes have been used since then concentrations.
for measurements of pH and the activities of alkali using
ions [21]. However, the maximum by
power In this
study, we investigated
power
generation
dense
silica membranes
placing a
densities that can be achieved using a dense silica membrane, and the conditions under which these silica membrane
between two NaCl solutions with various combinations of concentrations. The silica
densities are achieved, are unclear. This lack of clarity is due to the fact that, to the best of our knowledge, membrane
was fabricated by depositing a silica layer on a porous alumina substrate via chemical
there have been no previous studies focused on power generation by reverse electrodialysis in a vapor deposition. We measured the potential-current (V-I) characteristics of the silica membrane
dense silica membrane located between two solutions having different concentrations. from which we
obtained
theinvestigated transference
number,
diffusion
potential,
electrical
resistance.
In
In this study, we power generation using dense silica and
membranes by placing a addition,silica we developed
empirical
for with the transference
numberof and
the area-specific
membrane between two correlations
NaCl solutions various combinations concentrations. The silica membrane was fabricated by depositing a silica layer on a porous alumina substrate via resistance.
Finally, we studied power generation by reverse electrodialysis using a silica membrane
chemical vapor deposition. We power
measured the potential‐current (V‐I) characteristics of the on
silica and developed
a contour
map of the
output
density as a function
of concentrations
the basis
membrane from which we obtained the transference number, diffusion potential, and electrical of the empirical correlations.
resistance. In addition, we developed empirical correlations for the transference number and the area‐specific resistance. Finally, we studied power generation by reverse electrodialysis using a 2. Materials and Methods
silica membrane and developed a contour map of the power output density as a function of concentrations on the basis of the empirical correlations. For the
experiment, we used a porous alumina substrate (Anodisc 47, Whatman Inc., Marlborough,
MA, USA), 47 mm in diameter and 60 µm thick. Figure 2 shows the scanning electron microscope
2. Materials and Methods (SEM) images of the top and cross section of the alumina substrate that had a nominal pore radius
For a the experiment, we used ofa 1.2
porous substrate (Anodisc Whatman 9 cm2 . An
of 100 nm and
nominal
pore density
ˆ 10alumina undoped
1 µm47, thick
silica Inc., layer was
Marlborough, MA, USA), 47 mm in diameter and 60 μm thick. Figure 2 shows the scanning electron deposited on the substrate by plasma-enhanced chemical vapor deposition (LAPECVD, Plasma-Therm,
microscope (SEM) images of the top and cross section of the alumina substrate that had a nominal ˝ C, with SiH , He, and N O as
Saint Petersburg,
FL, USA) at a deposition rate of 10.2 Å/s and
150
9 cm
2. An undoped 1 μm thick silica 4
2
pore radius of 100 nm and a nominal pore density of 1.2 × 10
the processing
gases. The silica layer was deposited on the front side of the substrate only. Figure 3
layer was deposited on the substrate by plasma‐enhanced chemical vapor deposition (LAPECVD, Plasma‐Therm, Saint Petersburg, FL, USA) at a deposition rate of 10.2 Å/s and 150 °C, with SiH
4, He, shows the
SEM images of the top and cross section of the smooth and dense fabricated silica
layer on
and N
2O as the processing gases. The silica layer was deposited on the front side of the substrate top of the
porous
alumina substrate. In Figure 3, the alumina substrate has a nominal pore radius
only. Figure 3 shows the SEM images of the top and cross section of the smooth and dense of 100 nm.
As shown in Figure 3a, a well-defined pore structure is not observed in the top view of
fabricated silica layer on top of the porous alumina substrate. In Figure 3, the alumina substrate has the silicaa layer.
Therefore, we can conclude that this layer is a dense silica membrane. The fabricated
nominal pore radius of 100 nm. As shown in Figure 3a, a well‐defined pore structure is not silica membrane
was placed at the center of a two-cell apparatus, a schematic diagram of which is
observed in the top view of the silica layer. Therefore, we can conclude that this layer is a dense silica shown inmembrane. Figure 4 [22,23].
Two Ag/AgCl
reference
were
fabricated
by first
coating
The fabricated silica membrane was electrodes
placed at the center of a two‐cell apparatus, a silver
schematic diagram of which is shown in Figure 4 [22,23]. Two Ag/AgCl reference electrodes were mesh (05-1806-02,
40935, Nilaco Corp., Tokyo, Japan) with Ag/AgCl ink (011464, ALS Co. Ltd., Tokyo,
fabricated by first coating silver mesh (05‐1806‐02, 40935, Nilaco Corp., Tokyo, Japan) with Ag/AgCl Japan), washing
the electrodes sufficiently with water, and leaving them overnight to dry. After placing
ink (011464, ALS Co. Ltd., Tokyo, Japan), washing the electrodes sufficiently with water, and the electrodes in the two cells, 0.5 L of a concentrated NaCl solution was placed into the desalting cell
leaving them overnight to dry. After placing the electrodes in the two cells, 0.5 L of a concentrated and 0.5 LNaCl solution was placed into the desalting cell and 0.5 L of a dilute NaCl solution was placed into of a dilute NaCl solution was placed into the concentrating cell. The pH of each solution was
5.4 ˘ 0.2.the concentrating cell. The pH of each solution was 5.4 ± 0.2. (a) (b) Figure 2. Scanning Electron Microscope (SEM) photos of the porous alumina substrate: (a) top view Figure 2. Scanning Electron Microscope (SEM) photos of the porous alumina substrate: (a) top view
and (b) cross‐sectional view. and (b) cross-sectional view.
3
Energies 2016, 9, 49
4 of 11
Energies 2016, 9, 49 Energies 2016, 9, 49 (a) (b) (a) (b) Figure 3.
3. SEM photos of the silica layer on the
the porous
porous alumina
alumina substrate:
substrate: (a) top
top view
view and
and Figure
SEM
photos
silica
layer
Figure 3. SEM photos of of
the the
silica layer on onthe porous alumina substrate: (a) (a)
top view and (b) cross‐sectional view. (b)
cross-sectional view.
(b) cross‐sectional view. (a) (b) (a) (b) Figure 4. Experimental setup: (a) enlarged schematic and (b) normal schematic. Figure 4. Experimental setup: (a) enlarged schematic and (b) normal schematic. Figure 4. Experimental setup: (a) enlarged schematic and (b) normal schematic.
An electrometer (2410 Source Meter, Keithley Instruments Inc., Solon, OH, USA) recorded the An electrometer (2410 Source Meter, Keithley Instruments Inc., Solon, OH, USA) recorded the current (I) from the silica layer for various applied voltages (V
app). The current was measured for 2 min An electrometer (2410 Source Meter, Keithley Instruments
Inc., Solon, OH, USA) recorded the
current (I) from the silica layer for various applied voltages (Vapp). The current was measured for 2 min in the steady state, i.e., when the change in the current was less The was
V‐I characteristics current (I) from the silica layer for various applied voltages (V than ). The±1%. current
measured for
in the steady state, i.e., when the change in the current was less app
than ±1%. The V‐I characteristics were measured for various combinations of the concentrations of the dilute solution (cL) and the 2 min in the steady state, i.e., when the change in the current was less than ˘1%. The V-I characteristics
were measured for various combinations of the concentrations of the dilute solution (cL) and the concentrated solution (c
H), as listed in Table 1. We performed each experiment four times. were
measured for various
combinations of the concentrations of the dilute solution (c ) and the
concentrated solution (cH), as listed in Table 1. We performed each experiment four times. L
concentrated solution (cH ), as listed in Table 1. We performed each experiment four times.
Table 1. Transference number, diffusion potential, area‐specific resistance, and maximum power Table 1. Transference number, diffusion potential, area‐specific resistance, and maximum power density for various combinations of NaCl concentrations. Table
1. Transference number, diffusion potential, area-specific resistance, and maximum power
density for various combinations of NaCl concentrations. density for various
oftNaCl
concentrations.
cL (M) combinations
cH (M) + Ediff (mV)
RA (Ω∙cm2) Pmax/A (mW/m2) cL (M) cH (M) t+ Ediff (mV)
RA (Ω∙cm2) Pmax/A (mW/m2) 0.0001 0.001 0.749 ± 0.001 29.2 ± 0.1 14,600 ± 100 0.145 ± 0.00001 2)
29.2 ± 0.1 14,600 ± 100 cL (M)0.0001 t+
Ediff (mV)
RA (Ω¨0.145 ± 0.00001 cm
Pmax /A (mW/m2 )
H (M)
0.0001 c0.001 0.01 0.749 ± 0.001 0.736 ± 0.001 54.7 ± 0.1 12,200 ± 100 0.611 ± 0.00001 0.0001 0.01 0.736 ± 0.001 54.7 ± 0.1 12,200 ± 100 0.611 ± 0.00001 0.1 0.565 ± 0.001 0.117 ± 0.00001 0.0001 0.0001 0.001
0.749 ˘ 0.001 22.2 ± 0.2 29.2 ˘ 0.110,500 ± 100 14,600 ˘ 100
0.145 ˘ 0.00001
0.1 0.565 ± 0.001 22.2 ± 0.2 10,500 ± 100 0.117 ± 0.00001 0.00010.0001 0.01
0.736
˘
0.001
54.7
˘
0.1
12,200
˘
100
0.611
0.0001 1 0.424 ± 0.001 −34.1 ± 0.3 8100 ± 30 0.358 ± 0.00003 ˘ 0.00001
1 0.424 ± 0.001 −34.1 ± 0.3 8100 ± 30 0.358 ± 0.00003 0.00010.0001 0.1
0.565
˘
0.001
22.2
˘
0.2
10,500
˘
100
0.117 ˘ 0.00001
0.796 ± 0.00019 0.001 0.01 0.782 ± 0.004 32.4 ± 0.5 3300 ± 10 0.796 ± 0.00019 0.01 0.782 ± 0.004 32.4 ± 0.5 3300 ± 10 0.0001 0.001 1
0.424
˘
0.001
´34.1
˘
0.3
8100
˘
30
0.358 ˘ 0.00003
0.001 0.1 0.593 ± 0.001 20.9 ± 0.2 2250 ± 10 0.482 ± 0.00003 0.001 0.001 0.01
0.782
˘
0.004
32.4
˘
0.5
3300
˘
10
0.796 ˘ 0.00019
0.1 0.593 ± 0.001 20.9 ± 0.2 2250 ± 10 0.482 ± 0.00003 0.001 1 0.439 ± 0.004 −20.2 ± 1.3 2140 ± 10 0.477 ± 0.002 0.001 0.001 0.1
0.593
˘
0.001
20.9
˘
0.2
2250
˘
10
0.482 ˘ 0.00003
1 0.1 0.439 ± 0.004 0.477 ± 0.002 0.01 0.619 ± 0.003 −20.2 ± 1.3 13.2 ± 0.4 2140 ± 10 443 ± 2 0.976 ± 0.00074 0.001 0.01 1
0.439
˘
0.004
´20.2
˘
1.3
2140
˘
10
0.477 ˘ 0.002
0.1 1 0.619 ± 0.003 13.2 ± 0.4 443 ± 2 0.976 ± 0.00074 0.01 0.1
0.461 ± 0.001 −8.3 ± 0.1 332 ± 3 0.521 ± 0.00002 0.01 0.01 0.619
˘
0.003
13.2
˘
0.4
443
˘
2
0.976
1 0.461 ± 0.001 −8.3 ± 0.1 332 ± 3 0.521 ± 0.00002 ˘ 0.00074
0.1 0.465 ± 0.006 0.01
1 1 0.461 ˘ 0.001 −3.7 ± 0.6 ´8.3 ˘ 0.1 57.6 ± 0.2 332 ˘ 30.591 ± 0.01796 0.521 ˘ 0.00002
0.1 1 0.465 ± 0.006 −3.7 ± 0.6 57.6 ± 0.2 0.591 ± 0.01796 0.1
1
0.465 ˘ 0.006
´3.7 ˘ 0.6
57.6 ˘ 0.2
0.591 ˘ 0.01796
3. Results and Discussion 3. Results and Discussion The setup for this experiment can be represented in terms of basic circuit elements, as shown The setup for this experiment can be represented in terms of basic circuit elements, as shown in Figure 5a. Eredox, Ediff, and R are the potential generated from redox reactions on the electrodes, in Figure 5a. Eredox, Ediff, and R are the potential generated from redox reactions on the electrodes, 4
4
Energies 2016, 9, 49
5 of 11
3. Results and Discussion
The setup for this experiment can be represented in terms of basic circuit elements, as shown
in
Figure
5a. Eredox , Ediff , and R are the potential generated from redox reactions on the electrodes,
Energies 2016, 9, 49 the diffusion potential of the silica membrane, and the electric resistance of the silica membrane,
respectively.
electricof potential
generated
in the
silica
V, is defined
the diffusion The
potential the silica membrane, and the membrane,
electric resistance of the as:
silica membrane, respectively. The electric potential generated in the silica membrane, V, is defined as: V “ Vapp ´ Eredox “ Ediff ´ IR
V  Vapp  Eredox  Ediff  IR (a) (1)
(1) (b) Figure 5. (a) Basic circuit
circuit elements
elements representing
representing the
the experimental setup; and equivalent circuit Figure 5. (a) Basic
experimental
setup;
and
(b)(b) equivalent
circuit
for
for setup in which the source the electrode are considered the load
electrical load Rload thisthis setup
in which
the source
meter meter and theand electrode
are considered
the electrical
Rload connected
connected to the silica membrane to the silica membrane.
Eredox is produced by an unequal voltage drop at the electrode–solution interface in different Eredox is produced by an unequal voltage drop at the electrode–solution interface in different
electrolyte concentrations. The thermodynamic value of E
redox is defined as [21,24]: electrolyte concentrations. The thermodynamic value of Eredox is defined as [21,24]:
RT γ C cH
E redox  RTln γHC cH (2) Eredox “zF lnγ CL cHL
(2)
zF γCL cL
where R, T, z, F, and  are the gas constant, temperature, charge number, Faraday constant, and where R, T, z, F, and γ are the gas constant, temperature, charge number, Faraday constant, and mean
mean activity coefficient, respectively. Another equivalent circuit for this setup is shown in Figure 5b, activity coefficient, respectively. Another equivalent circuit for this setup is shown
in Figure 5b, in
in which the source meter and the electrode are considered the electrical load R
load connected to the which the source meter
and the electrode are considered the electrical load Rload connected to the silica
silica membrane. R
load is defined as: membrane. Rload is defined as:
Vapp
EE
V
redox V V
app ´
redox
Rload
(3) (3)
Rload“
 “ I
I
I I
Eredox here is for the given concentrations of solutions. Therefore, by changing V app , we can
here is for the given concentrations of solutions. Therefore, by changing Vapp, we can Eredox
change the Rload connected to the silica membrane.
change the Rload connected to the silica membrane. Figure 6a shows a typical potential-current (V-I) curve for the silica membrane. The electrical
Figure 6a shows a typical potential‐current (V‐I) curve for the silica membrane. The electrical resistance R of the silica membrane is calculated using the slope of the curve. The potential decreases
resistance R of the silica membrane is calculated using the slope of the curve. The potential linearly as the current increases, emphasizing the ohmic behavior of the silica layer in the conducting
decreases linearly as the current increases, emphasizing the ohmic behavior of the silica layer in the current. This behavior occurs because the concentration profile inside the silica layer is not highly
conducting current. This behavior occurs because the concentration profile inside the silica layer is dependent on the electrical potential and because there is no polarization effect at the surface of the
not highly dependent on the electrical potential and because there is no polarization effect at the silica layer under small electric fields [25,26]. The zero-current potential on the V-I curve is Ediff and is
surface of the silica layer under small electric fields [25,26]. The zero‐current potential on the V‐I determined by the difference between the diffusion fluxes of the positive and negative ions caused by
curve is Ediff and is determined by the difference between the diffusion fluxes of the positive and the ion-selective property of the silica layer. Thus, the cations diffuse more rapidly than the anions
negative ions caused by the ion‐selective property of the silica layer. Thus, the cations diffuse more when the concentrated solution diffuses into the dilute solution through the silica layer because of
rapidly than the anions when the concentrated solution diffuses into the dilute solution through the the ion-selective transport property of the silica layer. This rapid diffusion of cations into the dilute
silica layer because of the ion‐selective transport property of the silica layer. This rapid diffusion of solution makes it positively charged and leaves the concentrated solution negatively charged. Thus, a
cations into the dilute solution makes it positively charged and leaves the concentrated solution double layer of positive and negative charges develops between the two solutions. This results in a
negatively charged. Thus, a double layer of positive and negative charges develops between the difference
in
potential between the two solutions, i.e., Ediff , which is defined as:
two solutions. This results in a difference in potential between the two solutions, i.e., E
diff, which is defined as: RT γCH cH
Ediff “ p2t` ´ 1q
ln
RT zFγ CH cγHCL cL
Ediff   2t   1
ln
zF γCL cL
(4)
(4) where t+ is the transference number for the cations and is defined as the fraction of the electrical current carried by the cations under an applied voltage. It is an index of the ion selectivity of the silica membrane: t+ = 1 for complete cation selectivity, t+ = 0 for complete anion selectivity, and t+ ≈ 0.4 Energies 2016, 9, 49
6 of 11
where t+ is the transference number for the cations and is defined as the fraction of the electrical
current carried by the cations under an applied voltage. It is an index of the ion selectivity of the silica
membrane: t+ = 1 for complete cation selectivity, t+ = 0 for complete anion selectivity, and t+ « 0.4 for
Energies 2016, 9, 49 NaCl
solutions when the membrane is not ion-selective [27]. In Figure 6a, Ediff is positive, i.e., the silica
membrane is cation-selective. Figure 6b shows a typical P-Rload curve of the silica layer. The generated
the silica power
P ismembrane defined as:is cation‐selective. Figure 6b shows a typical P‐Rload curve of the silica layer. The generated power P is defined as: P “ VI
(5)
P  VI Combining Equations (1), (3) and (5) yields:
(5) Combining Equations (1), (3) and (5) yields: Rload
2
P “ Ediff
2
R
2
pRload
load ` Rq
P  Ediff
2
 Rload  R 
Maximum power is generated when Rload = R; thus:
Maximum power is generated when Rload = R; thus: E2
Pmax “E 2 diff
Pmax  diff4R 4R
35
30
(6)
(6) (7)
(7) 3.0
Pmax
Ediff
2.5
25
P (nW)
V (mV)
2.0
20
1
R
15
1.0
10
0.5
5
0
0.0
1.5
0.1
0.2
0.3
0.0
0.0
0.4
0.2
0.4
0.6
Rload=R
I (A)
0.8
1.0
1.2
1.4
1.6
1.8
Rload (M)
(a) (b)
load for the silica membrane; cL = 0.1 mM and Figure 6. (a) V‐I curve and (b) power generation vs. R
Figure
6. (a) V-I curve and (b) power generation vs. Rload
for the silica membrane; cL = 0.1 mM and
c
H = 1 Mm. cH = 1 Mm.
We measured the I‐V curves for various cL and cH and used them to calculate t+, R, Ediff, and Pmax We measured the I-V curves for various cL and cH and used them to calculate t+ , R, Ediff , and Pmax
of the silica membrane for those concentrations. The results are presented in Figures 7–10, of the silica membrane for those concentrations. The results are presented in Figures 7–10 respectively,
respectively, and each characteristic determined by the experimental results is discussed below: and each characteristic determined by the experimental results is discussed below:
(1) Figure 7 shows that t
(1)
Figure 7 shows that t++ strongly depends on c
strongly depends on cHH for various c
for various cLL.. At the high‐concentration limit At the high-concentration limit
(cHH ≈ 1), t
« 1), t++ is almost equal to that of the bulk solution (t
(c
is almost equal to that of the bulk solution (t++ ≈ 0.4). As c
« 0.4). As cHH decreases, t
decreases, t++ increases because increases because
the effect of the fixed anionic groups, which have an affinity for cations, increases as their density the effect of the fixed anionic groups, which have an affinity for cations, increases as their density
increases compared to the bulk ion concentration [28,29]. From the experimental data, we obtained increases
compared to the bulk ion concentration [28,29]. From the experimental data, we obtained an
an empirical correlation for t
+ using a least‐squares fit: empirical correlation for t+ using
a least-squares fit:
t   0.495  0.0715ln cH  0.00873ln cL t` “ 0.495 ´ 0.0715lncH ` 0.00873lncL
(8) (8)
Figure 7 also shows t+ calculated using Equation (8). The calculated values agree well with the Figure 7 also shows t+H and c
calculated
using Equation (8). The calculated values agree well with the
experimental data when c
L are >10 mM. experimental data when cH and cL are >10 mM.
0.90
0.85
0.80
0.75
t+
0.70
0.65
0.60
0.55
cL
0.50 0.1mM
1mM
0.45 10mM
100mM
0.40
1
Experimental data
Eq.(8)
10
100
cH (mM)
1000
the effect of the fixed anionic groups, which have an affinity for cations, increases as their density increases compared to the bulk ion concentration [28,29]. From the experimental data, we obtained an empirical correlation for t+ using a least‐squares fit: t   0.495  0.0715ln cH  0.00873ln cL (8) Figure 7 also shows t
+ calculated using Equation (8). The calculated values agree well with the Energies 2016,
9, 49
7 of 11
experimental data when cH and cL are >10 mM. 0.90
0.85
0.80
0.75
t+
0.70
0.65
0.60
0.55
cL
Experimental data
0.50 0.1mM
1mM
0.45 10mM
100mM
0.40
1
Eq.(8)
10
100
1000
cH (mM)
Figure 7. Transference number for various concentrations of both NaCl solutions. Figure 7. Transference number for various concentrations of both NaCl solutions.
Energies 2016, 9, 49 (2) Figure
8 presents Ediff diff
as as a function of c
a function of cHH6 and c
and cLL. Figure 8 shows that E
. Figure 8 shows thatdiffE is maximized at a (2) Figure 8 presents E
diff is maximized at a
Energies 2016, 9, 49 particular
concentration of the concentrated solution (cHH). This effect is seen in Equation (4) where ). This effect is seen in Equation (4) where
particular concentration of the concentrated solution (c
c
H/c
cLc)L) increases as c
H increases
increases while 2t
+ +− ´
1 decreases. Figure 8 also shows EdiffE
calculated ln(γcHln(
cH cH
/γ
increases
as
c
while
2t
1
decreases.
Figure
8 also
shows
cL
L
H
diff calculated
(2) Figure 8 presents Ediff as a function of cH and cL. Figure 8 shows that E
diff is maximized at a using Equations (4) and (8) and that those values match the experimental data well when c
H and c
L usingparticular concentration of the concentrated solution (c
Equations (4) and (8) and that those values matchH). This effect is seen in Equation (4) where the experimental data well when
cH and
cL
are >10 mM. are >10
ln(mM.
cHcH/cLcL) increases as cH increases while 2t+ − 1 decreases. Figure 8 also shows Ediff calculated using Equations (4) and (8) and that those values match the experimental data well when cH and cL 60
are >10 mM. Ediff (mV) E (mV)
diff
40
60
20
40
0
20
-20
0
-40
-20
Experimental data
Eqs.(4),(8)
0.1mM
1mM
10mM
100mM
cL
Experimental data
cL
Eqs.(4),(8)
0.1mM
1
1mM
10mM
100mM
-40
10
cH (mM)
100
1000
Figure 8. Open circuit voltage for various concentrations of both NaCl solutions. 1
10
100
1000
Figure
8. Open circuit voltage
for various
concentrations
of both NaCl solutions.
cH (mM)
(3) Figure 9 presents the resistance per unit cross‐sectional area multiplied by the total (3)
Figure 9Figure 8. Open circuit voltage for various concentrations of both NaCl solutions. presents the resistance per unit cross-sectional
area multiplied by the total
cross‐sectional area of the membrane, RA, as a function of c
H for various cL. As cH and cL increase, cross-sectional
area of the membrane,
RA,
as alayer function
of cHwhich for various
cR L .to As
cH and R c increase,
the bulk concentration of ions the silica increases, causes decrease. a (3) Figure 9 presents the in resistance per unit cross‐sectional area multiplied by the Lhas total the bulk
concentration
of
ions
in
the
silica
layer
increases,
causes
R
to
decrease.
R
has
a
strong
strong dependence on c
L and a weak dependence on c
H. which
We obtained an empirical correlation for cross‐sectional area of the membrane, RA, as a function of cH for various cL. As cH and cL increase, RA by fitting the experimental data to the following equation: dependence
cL and a weak
dependence
onlayer cH . increases, We obtained
ancauses empirical
the bulk on
concentration of ions in the silica which R to correlation
decrease. R for
has RA
a by
0.705obtained an empirical correlation for fittingstrong the experimental
data
to the
following
dependence on cL and a weak dependence on cH. cWe RA equation:
0.00134
c 0.0891
(9) H
L
RA by fitting the experimental data to the following equation: 0.0891 ´0.705
Figure 9 also shows RA calculated using Equation (9) and that the results agree well with the RA “ 0.00134c´
(9)
H 0.0891 cL0.705
RA

0.00134
c
cL (9) H
experimental data. Figure
9 also shows RA calculated using Equation (9) and that the results agree well with the
Figure 9 also shows RA calculated using Equation (9) and that the results agree well with the 100000
experimental
data.
experimental data. 1000
10000
Experimental data
Eq.(9)
0.1mM
1mM
10mM
100mM
cL
Experimental data
cL
Eq.(9)
2
R A (cm R) A (cm2)
10000
100000
100
1000
10
100
10
0.1mM
1
1mM
10mM
100mM
10
100
cH (mM)
1000
Figure 9. Area‐specific resistance for various concentrations of both NaCl solutions 1
10
100
1000
cH (mM)
(4) Figure 10 shows the maximum power output per unit cross‐sectional area, Pmax/A, as a Figure 9. Area‐specific resistance for various concentrations of both NaCl solutions Figure
9. Area-specific
resistance formaxvarious
concentrations of both NaCl
solutions.
2 when c
function of c
H for various c
L. The highest P
/A measured was 0.98 mW/m
L = 0.1 mM and cH = 10 mM. By combining Equations (4) and (7), P
max is expressed as: (4) Figure 10 shows the maximum power output per unit cross‐sectional area, Pmax/A, as a 



2
2 when cL = 0.1 mM and function of cH for various cL. The highest Pmax2/A measured was 0.98 mW/m
2
2t   1  RT   γCH cH 
cH = 10 mM. By combining Equations (4) and (7), P
max is expressed as: (10) Pmax 
 
  ln
4R  zF   γCL cL 2
2
2
2t   1  RT   γCH cH 
(10) Pmax 
 Figure 10 also shows Pmax/A calculated using Equations (8)–(10) and that the values agree well 
  ln
Energies 2016, 9, 49
8 of 11
(4) Figure 10 shows the maximum power output per unit cross-sectional area, Pmax /A, as a
function of cH for various cL . The highest Pmax /A measured was 0.98 mW/m2 when cL = 0.1 mM and
cH = 10 mM. By combining Equations (4) and (7), Pmax is expressed as:
Pmax
p2t` ´ 1q2
“
4R
ˆ
RT
zF
˙2 ˆ
γC c H
ln H
γCL cL
˙2
(10)
c
Experimental data Eqs.(8)-(10)
cLL
Experimental data Eqs.(8)-(10)
0.1mM
0.1mM
1mM
1mM
10mM
10mM
100mM
100mM
1
10
100
1
10
100
c (mM)
cHH (mM)
1000
1000
Power
generated
Power
generated
byby
anion
selectivity
anion
selectivity
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
Power
generated
Power
generated
byby
cation
selectivity
cation
selectivity
2
2
Pmax
/A/A(mW/m
Pmax
(mW/m) )
Figure 10 also shows Pmax /A calculated using Equations (8)–(10) and that the values agree well
with the experimental data. Power is generated at low concentrations because of the cation selectivity
of
the silica membrane. At high concentrations (cH = 1 M), ion selectivity of the silica membrane is
Energies 2016, 9, 49 Energies 2016, 9, 49 almost
nonexistent, as shown in Figure 7. However, even in this case, a small amount of power can
be
the naturalfrom anion
selectivity
of bulkselectivity NaCl solutions
(t+NaCl « 0.4).
Finally, Figure
11
of generated
power can can from
be generated generated the natural anion anion of bulk bulk solutions (t++ ≈ ≈ 0.4). 0.4). of power be from the natural selectivity of NaCl solutions (t
shows
the
contour
plots
of
P
/A,
calculated
using
Equations
(8)–(10),
as
a
function
of
c
and
c
max
Finally, Figure Figure 11 11 shows shows the the contour contour plots plots of of P
Pmax
max/A, calculated using Equations (8)–(10), as Ha a .
L
Finally, /A, calculated using Equations (8)–(10), as The
figure
shows
that
the
optimal
concentrations
at
which
the
power
output
density
is
maximum
function of cLL and c
and cH. The figure shows that the optimal concentrations at which the power output function of c
2 ) are c H=. The figure shows that the optimal concentrations at which the power output (1.2
mW/m
4(1.2 mM
and c22H) =
50cmM.
Pmax
/A value
corresponds
to/A a power
density is maximum mW/m
are = 4 4 That
mM maximum
and ccHH = = 50 50 mM. That maximum maximum Pmax
max
value L
density is maximum (1.2 mW/m
) are cLL = mM and mM. That P
/A value output
of
2.1
µW
because
the
cross-sectional
area
of
the
membrane,
A,
used
in
the
present
study
was
corresponds to a power output of 2.1 μW because the cross‐sectional area of the membrane, A, used corresponds to a power output of 2.1 μW because the cross‐sectional area of the membrane, A, used 2
2
17.3
cm . This power output is sufficient
to drive low-power circuitry for wireless systems and to
in the present study was 17.3 cm
. This power output is sufficient to drive low‐power circuitry for 2. This power output is sufficient to drive low‐power circuitry for in the present study was 17.3 cm
power
biomedical
implant
devices
[30,31].
Therefore,
dense
silica membranes
have the potential
for
wireless systems and to power biomedical implant devices [30,31]. Therefore, Therefore, dense silica silica wireless systems and to power biomedical implant devices [30,31]. dense use
in
nanofluidic
and
microfluidic
systems.
membranes have the potential for use in nanofluidic and microfluidic systems. membranes have the potential for use in nanofluidic and microfluidic systems. Figure 10. Maximum power generation density for various concentrations of both NaCl solutions. Figure
10. Maximum power generation density for various concentrations of both NaCl solutions.
Figure 10. Maximum power generation density for various concentrations of both NaCl solutions. 100
100
2
Pmax/A (mW/m2 )
Pmax
/A0.00
(mW/m )
0.00
0.150
0.150
0.300
0.300
0.450
0.450
0.600
0.600
0.750
0.750
0.900
0.900
1.05
1.05
1.20
1.20
c <c
cHH<cLL
cLc(mM)
(mM)
L
10
10
1
1
0.1
0.1 1
1
10
10
c (mM)
cHH (mM)
100
100
Figure 11. Contour map of maximum power generation density as a function of cL and cH. Figure 11. Contour map of maximum power generation density as a function of cL and cH. Figure 11. Contour map of maximum power generation density as a function of cL and cH .
(5) Figure Figure 12 12 shows shows the the energy energy conversion conversion efficiency efficiency corresponding corresponding to to the the maximum maximum power power (5) generation for various c
and c
L values. As given in Reference [32], energy conversion efficiency is (5) Figure 12 showsHH and c
the energy
conversion efficiency corresponding to the maximum power
generation for various c
L values. As given in Reference [32], energy conversion efficiency is defined as the ratio of the output energy (electrical energy) to the input energy (Gibbs free energy of generation
for
various
c
and
c
values.
As given in Reference [32], energy conversion efficiency is
H
L
defined as the ratio of the output energy (electrical energy) to the input energy (Gibbs free energy of mixing) [14], as shown in Equation (11): mixing) [14], as shown in Equation (11): VI
VI
ηη 
 γ CH cH 
(11) 
γ
c
(11) ln C H
RT  ln
J J
RT
 γ CH cL   J   J  
 γ CLL cL 
Here, J++ and J
and J−− are cation flux and anion flux through the membrane, respectively. The motion are cation flux and anion flux through the membrane, respectively. The motion Here, J
of cations and anions through the the membrane membrane gives gives rise rise to to a a current. current. The The current current is is expressed expressed by by of cations and anions through Energies 2016, 9, 49
9 of 11
defined as the ratio of the output energy (electrical energy) to the input energy (Gibbs free energy of
mixing) [14], as shown in Equation (11):
η“
VI
˙
γCH cH
pJ` ` J´ q
RT ln
γCL cL
(11)
ˆ
Here, J+ and J´ are cation flux and anion flux through the membrane, respectively. The motion
of cations and anions through the membrane gives rise to a current. The current is expressed by
Equation (12):
I “ zFpJ` ´ J´ q
(12)
The transference number for the cations is defined as the fraction of the electrical current carried
by the cations under an applied voltage, according to Equation (13):
Energies 2016, 9, 49 t` «
zFJ`
J`
“
I
J` ´ J´
(13)
In Figure 6b, we can see that the maximum power is generated when load
Rload
= R. From Equations
In Figure 6b, we can see that the maximum power is generated when R
= R. From Equations (1) (1) and (3), and
Rload = R, the voltage corresponding to the maximum power generation satisfies
and (3), and R
load = R, the voltage corresponding to the maximum power generation satisfies Equation (14): Equation (14):
EE
VV“ diffdiff
(14)
(14) 2 2
Finally, by combining Equations (2) and (11)–(14), we obtain Equation (15), a formula for the
Finally, by combining Equations (2) and (11)–(14), we obtain Equation (15), a formula for the energy
conversion efficiency corresponding to the maximum power generation:
energy conversion efficiency corresponding to the maximum power generation: ´2 1q2
(2p2t
t `
 1)
ηη “ 
2 2
(15) (15)
This equation equation was was also also used used for
As shown shown in in
This for calculating
calculating the
the efficiency
efficiency in
in references
references [15,18].
[15,18]. As Figure 12 and Equation (15), the highest efficiency is achieved when the transference number is the
Figure 12 and Equation (15), the highest efficiency is achieved when the transference number is the greatest. The best efficiency obtained in the present study is 16%.
greatest. The best efficiency obtained in the present study is 16%. Figure 12. Energy conversion efficiency for various concentrations of NaCl solutions. Figure 12. Energy conversion efficiency for various concentrations of NaCl solutions.
4. Conclusions 4. Conclusions
We investigated power
power generation
generation electrodialysis in a dense silica membrane We investigated
byby reverse reverse electrodialysis
in a dense silica
membrane that that was
was between two NaCl solutions with various combinations of concentrations. The highest measured between two NaCl solutions with various combinations of concentrations. The highest measured
power output density
density was
was 0.98
0.98 mW/m2 .2. In
In addition,
addition, the power output density calculated on power output
mW/m
the
power
output
density
waswas calculated
on the
the basis of empirical correlations for the transference number and the area‐specific electrical basis of empirical correlations for the transference number and the area-specific electrical resistance.
resistance. The contour map of the power output density as a function of the concentrations of the The contour map of the power output density as a function of the concentrations of the NaCl solutions
2 is possible, a level that is 2 is of NaCl solutions showed that a power ofoutput density 1.2 mW/m
showed
that a power
output
density
1.2 mW/m
possible,
a level
that is sufficient to drive
sufficient to drive nanofluidic and microfluidic systems. Therefore, dense silica membranes have the potential for use as micro power generators in nanofluidic and microfluidic systems. Acknowledgments: This research was supported by the Nano Material Technology Development Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT and Future Planning (NRF‐2011‐0030285). Energies 2016, 9, 49
10 of 11
nanofluidic and microfluidic systems. Therefore, dense silica membranes have the potential for use as
micro power generators in nanofluidic and microfluidic systems.
Acknowledgments: This research was supported by the Nano Material Technology Development Program
through the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT and Future
Planning (NRF-2011-0030285).
Author Contributions: Sang Woo Lee and Dong-Kwon Kim conceived and designed the experiments;
Sang Woo Lee performed the experiments; Hyun Jung Kim and Dong-Kwon Kim analyzed the data;
Dong-Kwon Kim wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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