APPLIED PHYSICS LETTERS 99, 173702 (2011)
Miniaturized concentration cells for small-scale energy harvesting based
on reverse electrodialysis
Ramin Banan Sadeghian, Oxana Pantchenko, Daniel Tate, and Ali Shakouria)
Baskin School of Engineering, University of California—Santa Cruz, 1156 High St., Santa Cruz,
California 95064, USA
(Received 17 September 2011; accepted 3 October 2011; published online 28 October 2011)
We describe experimental and theoretical results that demonstrate the feasibility of power
generation using concentration cells based on ionic concentration gradients and reverse
electrodialysis. A peak power density of 0.2 (0.7) lW cm2 and a maximum energy density of
0.4 (0.4) mJ cm3 delivered in 3 h to a 2 (5) kX resistor were recorded using a microfiltration
(anion exchange) membrane, respectively. A comprehensive model is developed to predict the
evolution of the output voltage with time in relation to the solute concentration in each cell and
C 2011 American Institute of Physics.
derive the power density and efficiency limits. V
[doi:10.1063/1.3656279]
There has been increasing demand for small scale energy
sources capable of powering a wide range of devices spanning
from remote sensors to in vivo electronics. Some examples of
such electronic devices include temperature sensors, pacemakers, neurostimulators, pressure, and pH sensors. Latest
research has shown that such devices require very low operating power. Currently, many electronic devices are being powered by commercially available batteries which contain
substances lethal to organism, and they need to be regularly
replaced. Energy harvesting devices based on temperature
gradient, vibration energy, or ambient illumination have been
developed mostly for ex vivo applications.1–4 Power densities
on the order of nW cm2 to mW cm2 are available depending on the strength of the energy source. These energy harvesting devices do not include storage directly; either
rechargeable batteries or supercapacitors have to be
employed. Concentration cells that utilize reverse electrodialysis (RED) process of ionic gradients such as those between
saline and fresh water can be suitable substitutes,5–7 although
their output power density is comparably low. Large scale systems have been demonstrated in which the concentration gradient between two compartments is kept constant by
replenishing the dilute and concentrated solutions; as a result,
the output power level does not decay with time. Here, we
focus on small scale concentration cells in which each halfcell is not refreshed during the operation. However, this
results in a limited power delivery time of couple of hours to
days but there is no need for pumps, and one can use ionic
concentration differences in nature or inside the body and
extract a large fraction of the stored energy.
Ion exchange membranes (IEMs) have been traditionally used in conventional RED applications. Due to their
fixed charge groups, they exhibit permselectivity for ions
with opposite charge (counter-ions). For instance, anion
exchange membranes (AEMs) which have positive charge
groups are transparent to anions (counter-ions) while inhibit
passage of cations (co-ions).8 Filtration membranes, on the
other hand, allow both anions and cations to pass because
a)
Author to whom correspondence should be addressed. Electronic mail:
ali@soe.ucsc.edu.
0003-6951/2011/99(17)/173702/3/$30.00
they have little or no fixed charges. As a result, the cell voltage is merely due to the diffusion of solute and depends on
the mobility difference of cations and anions in the medium.9
The principal aim of this work, apart from proof of concept
demonstration, is to study the temporal behavior of diffusion
potentials across the membrane and the total power densities
available from miniature concentration cells.
Figure 1(a) shows a schematic drawing of a concentration
cell and a photograph of our prototype. Six cylindrical cells
were fabricated by cast molding two slabs made of
polydimethylsiloxane (PDMS) each having a thickness of
7 mm. The diameter of each cell was 5 mm. Before taking
measurements, the slabs were exposed to air plasma to make
the interior of the cells hydrophilic and thus, prevent
formation of bubbles later when solutions were injected.
Semi-permeable microfiltration-MilliporeTM membranes were
soaked in a 0.01 mol L1 CuSO4 solution for 24 h to rule out
the effect of membrane swelling during the measurements,
rinsed in deionized water, and then placed in between the
slabs. These membranes are used for filtration purposes and
virtually offer no ion exchange capability because they contain only a very small density of negative fixed charges
(Cfix 2 106 mol L1).10,11 In contrast, fumasepV acid
dialysis (FAD) microporous membranes are anion selective
and permeable to SO42 with Cfix 1.7 mol L1. Adhesive
copper straps bonded on microscope slides were used as electrodes. Figure 1(b) shows a photograph of the device. Cupric
sulphate electrolyte of various concentrations (CL ¼ 103 to
0.5 mol L1) was injected into the compartments at one side
(as seen at the top, in Figure 1(b)), and a constant CH ¼ 1 mol
L1 solution was injected into the compartments at the other
side (as seen at the bottom, in Figure 1(b)) immediately after.
The output voltages of each cell were recorded individually.
The curves in Figure 2(a) show the temporal behavior of
the open circuit output voltages (VO.C.) generated at six different concentration ratios. The initial 100 s of data, related
to in-diffusion of electrolyte into the membrane were truncated. Experiments were repeated with resistors connected
to the cells. In RED systems, the output power density, Pload,
is defined as the delivered power per membrane area
(lW cm2) and is given by Pload ¼ Vload/(Rload A), where A is
99, 173702-1
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C 2011 American Institute of Physics
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Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
173702-2
Sadeghian et al.
Appl. Phys. Lett. 99, 173702 (2011)
FIG. 1. (Color online) (a) Schematic illustration of a
concentration cell showing the semi-permeable microporous membrane and one of the copper contacts. (b)
Photograph of device comprised of six individual cells.
High/low concentrations of CuSO4 solution are
discernable.
the area of the membrane.12 Figures 2(b) and 2(c) show the
curves of instantaneous output power density delivered to a
10 kX load using Millipore and FAD membranes, respectively. Figure 2(d) shows the values of Pload at peak delivered to 2 kX and 10 kX resistors versus the starting
concentration ratios. Peak values of Pload measured using
anion exchange FAD membranes are also given in this figure
for comparison reasons. The load resistances were chosen to
be close to the internal resistance of the cells for maximum
output power. The closer the load resistance to the internal
resistance of the cell, the higher the delivered power is. Since
microfiltration membranes are permeable to both cations and
anions, the concentration ratio and the output voltage drop
with time. On the contrary, the output characteristics of FAD
membranes remain flat for longer periods of time.
In the following, we modeled the time-dependence of the
ion concentration gradient. We assume ambipolar transport of
ions. The concentration profiles were calculated by numerically solving the one-dimensional Fick’s equation given as
@
Cðx; tÞ ¼ r DðC;
xÞrC ;
@t
(1)
where C ¼ C(x,t) is the solute concentration and D(C,x)
is the
medium dependent ambipolar diffusivity of undissociated cupric sulphate. The initial condition of Eq. (1), C(x,0), corresponds to the concentration profile immediately after the
dilute, and concentrated solutions were injected into the corre-
sponding compartments. The solute diffusivity in free solution, D0, was obtained from conductivity measurements in
different salt concentrations using the Nernst-Einstein relation
K¼
z2 F2
D0 ðCÞ;
RT
(2)
where K is the molar conductivity, z is the ion valence number, F is Faraday’s constant, R is the gas constant, and T is
the solution temperature. Figure 3(a) shows cupric sulphate
diffusivity versus concentration, and Figure 3(b) shows the
solutions of Eq. (1) along the cell for an initial concentration
ratio of 1 mol L1/103 mol L.1 The flux of individual ions
along the cell is given by the Nernst-Planck equation
dlnðc6 C6 Þ
F du
J6 ¼ D6 C6
6jz6 jC6
;
(3)
dx
RT dx
where C6 is the ion concentration, u is the potential, and D6
and c6 are the individual ion diffusion and activity coefficients.8,13 Contribution of osmosis effect to the membrane
potential is neglected in this study.
At equilibrium, there is no net current flow, therefore
Jþ ¼ J; in addition, C6 ¼ C(x,t) is enforced due to charge
neutrality. In this case, Eq. (3) will be simplified to
@u
RT 1 @C r 1
¼
;
@x
zF C @x r þ 1
(4)
FIG. 2. (Color online) (a) Evolution of open circuit voltages
(VO.C.) with time measured using Millipore membranes at six different starting concentration ratios; the top three area curves, corresponding to CH/CL ¼ 1000, 200, and 100, show the range of
variations of VO.C. among several experiments. (b) and (c) Output
power densities delivered to a 10 kX load using Millipore and
FAD membranes, respectively. (d) Output power densities (Pload)
at peak vs. different concentration ratios; values measured using
Millipore and FAD membranes.
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173702-3
Sadeghian et al.
Appl. Phys. Lett. 99, 173702 (2011)
TABLE I. The ion mobility ratios and diffusivity in free solution and membrane phases.
Free solution
Membrane
FIG. 3. (Color online) (a) Diffusivity of CuSO4 vs. concentration in free solution phase. (b) Simulated plateaus of CuSO4 concentration along the entire cell
for t ¼ 10a s, where a [ {0, 0.5, 1,…, 4}; the membrane is placed at x ¼ 0.7 cm.
where r, the cation to anion mobility ratio, is defined as
r ¼ l þ /l ¼ Dþ/D and depends on the medium. In an ulti¼ 0:67. Equamately dilute solution, r ¼ r0 ¼ lCu2þ =lSO2
4
tion (4) was solved along with Eq. (1) to find the spatial/
temporal profiles of @u/@x. The cell potentials were calculated
by integrating @u/@x along the cell length. Figure 4(a) shows
the simulated VO.C. vs. t characteristics. It is interesting to note
the similarities to the measured VO.C. curves of Figure 2(a).
Table I shows two parameters used in our model to
explain the open circuit behavior within the range of concentration ratios studied experimentally (2–1000). We found
that both r and D(C) were reduced in the membrane phase,
and the reduction factors were calculated by curve fitting
analysis in a similar fashion to the earlier work.14 Although
these factors depend on the concentration in each medium, a
single constant value could fairly explain the measured data.
As long as ionic transport takes place in the near equilibrium regime, it is assumed that the curves of VO.C. can fairly
describe the electromotive potential of concentration cells
and the load voltage can be found using Vload ¼ VO.C. Rload/
(Rint þ Rload), where Rint is the internal resistance of the cell.
Using the concentration plateaus as shown in Figure 3(b),
Rint(t) was estimated by the following integral
ðl
1
dx;
(5)
Rint ðtÞ ¼
rðx;
tÞ
0
where the solution conductivity is given by rðx; tÞ
¼ KðCÞCðx; tÞ=N and N is the Avogadro number. Figure 4(b)
shows the calculated profiles of Rint(t) at different starting concentration ratios. In order to achieve maximum output power,
the load resistance should follow Rint(t).
The output energy densities (energy per total cell volume) were calculated by integrating the instantaneous output
power curves during the first 10 000 s and were 0.4 mJ cm3
on a 2 kX load at CH/CL ¼ 1000, and 0.4 mJ cm3 on a 5 kX
FIG. 4. (Color online) Simulated curves of (a) VO.C. and (b) Rint at different
concentration ratios.
r
D(C)
r0
0.2
D0(C)
0.03 D0(C)
load at CH/CL ¼ 100, for Millipore and FAD membranes,
respectively.
The total Gibbs free energy resulting from mixing the
concentrated and dilute solutions is given by
CH
CL
þ VL CL ln
;
(6)
DGRED ¼ 2RT VH CH ln
CT
CT
where CT ¼ (VHCH þ VLCL)/(VH þ VL), VH and VL are the
volumes of the concentrated and diluate half-cells, R is the
gas constant, and T is the solution temperature.12 For CH
¼ 1 mol L,1 CL ¼ 103 mol L,1 and VH ¼ VL ¼ 0.137 cm3,
Eq. (6) gives a available energy of DGRED ¼ 470 mJ. In comparison, the total energy recovered from the cell containing
FAD membrane, for instance, will be 7.7 (VH þ VL) ¼ 2.1 mJ
which results in an efficiency of roughly 2.1/470 ¼ 0.44%.
This shows that there is room to improve the output power
of the concentration cells. Factors limiting the efficiency are
important parameters which will be the subject of future
studies.
In conclusion, power generation at millimeter scale was
demonstrated for a substantial amount of time using concentration cells comprised of microfiltration and ion exchange
membranes and without refeeding the reservoirs. The nearequilibrium ionic mass transport in the solution/membrane/solution system was modeled with reasonable accuracy. The
dynamics of the open circuit output voltage and the internal resistance were explained using the model. The maximum output
power and energy, and efficiency limits are also discussed.
This work was supported by the Grant No. W911NF-081-0347 from Defense Advanced Research Project Agency
(DARPA)/ARO.
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