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Direct prediction of the desalination performance of
porous carbon electrodes for capacitive deionization†
Cite this: Energy Environ. Sci., 2013, 6,
3700
S. Porada,ab L. Borchardt,c M. Oschatz,c M. Bryjak,b J. S. Atchison,d K. J. Keesman,ae
S. Kaskel,c P. M. Biesheuvelaf and V. Presser*dg
Desalination by capacitive deionization (CDI) is an emerging technology for the energy- and cost-efficient
removal of ions from water by electrosorption in charged porous carbon electrodes. A variety of carbon
materials, including activated carbons, templated carbons, carbon aerogels, and carbon nanotubes, have
been studied as electrode materials for CDI. Using carbide-derived carbons (CDCs) with precisely tailored
pore size distributions (PSD) of micro- and mesopores, we studied experimentally and theoretically the
effect of pore architecture on salt electrosorption capacity and salt removal rate. Of the reported CDCmaterials, ordered mesoporous silicon carbide-derived carbon (OM SiC-CDC), with a bimodal distribution
of pore sizes at 1 and 4 nm, shows the highest salt electrosorption capacity per unit mass, namely
15.0 mg of NaCl per 1 g of porous carbon in both electrodes at a cell voltage of 1.2 V (12.8 mg per 1 g
of total electrode mass). We present a method to quantify the influence of each pore size increment on
desalination performance in CDI by correlating the PSD with desalination performance. We obtain a high
correlation when assuming the ion adsorption capacity to increase sharply for pore sizes below one
nanometer, in line with previous observations for CDI and for electrical double layer capacitors, but in
contrast to the commonly held view about CDI that mesopores are required to avoid electrical double
layer overlap. To quantify the dynamics of CDI, we develop a two-dimensional porous electrode modified
Donnan model. For two of the tested materials, both containing a fair degree of mesopores (while the
total electrode porosity is 95 vol%), the model describes data for the accumulation rate of charge
(current) and salt accumulation very well, and also accurately reproduces the effect of an increase in
Received 1st July 2013
Accepted 13th August 2013
electrode thickness. However, for TiC-CDC with hardly any mesopores, and with a lower total porosity,
the current is underestimated. Calculation results show that a material with higher electrode porosity is
not necessarily responding faster, as more porosity also implies longer transport pathways across the
DOI: 10.1039/c3ee42209g
electrode. Our work highlights that a direct prediction of CDI performance both for equilibrium and
www.rsc.org/ees
dynamics can be achieved based on the PSD and knowledge of the geometrical structure of the electrodes.
Broader context
Capacitive deionization (CDI) is one of the most important small-scale and low-energy alternatives to reverse osmosis for the desalination of brackish water. Key
components of this electro-kinetic method of water treatment are porous carbon electrodes with well-developed porosity. However, until now, the exact
correlation between CDI performance and material parameters of the electrodes has largely remained unknown. To guide the ongoing research and development, quantitative methods to predict the equilibrium and dynamic behavior of CDI cells are essential. For direct practical implementation, predictive tools
have to include the salt adsorption capacity and desalination rate as functions of the pore size distribution of the carbon electrode material, and of the
geometrical measures of the electrodes, such as interparticle porosity. We present such a method based on a two-dimensional porous electrode theory, in
combination with a predictive salt adsorption capacity analysis based on the pore size distribution. A high correlation between salt adsorption and pore size data
for more than 15 different carbon materials presents evidence that sub-nm micropores are essential to achieve a high salt storage capacity. The reported work
serves as an important step in making CDI a predictable electro-kinetic method, presenting clear guidelines for electrode materials' choice, synthesis, and
electrode design.
a
Wetsus, Centre of Excellence for Sustainable Water Technology, Agora 1, 8934 CJ
Leeuwarden, The Netherlands
e
b
Department of Polymers and Carbon Materials, Faculty of Chemistry, Wroclaw
University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland
f
c
g
Department of Inorganic Chemistry, Dresden University of Technology, Bergstraße
66, 01069 Dresden, Germany
d
INM-Leibniz-Institute for New Materials, Energy Materials Group, 66123
Saarbrücken, Germany. E-mail: volker.presser@inm-gmbh.de
3700 | Energy Environ. Sci., 2013, 6, 3700–3712
Biomass Renery & Process Dynamics, Wageningen University, Bornse Weilanden 9,
6708 WG Wageningen, The Netherlands
Department of Environmental Technology, Wageningen University, Bornse
Weilanden 9, 6708 WG Wageningen, The Netherlands
Saarland University, Campus D2 2, 66123 Saarbrücken, Germany
† Electronic supplementary
10.1039/c3ee42209g
information
(ESI)
available.
See
DOI:
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1
Introduction
Providing access to affordable and clean water is one of the key
technological, social, and economical challenges of the 21st
century.1–3 For the desalination of water, commercially available
methods include distillation,4 reverse osmosis,5 and electrodialysis.6 Novel approaches include ion concentration polarization in microporous media,7 systems based on batteries,8,9
forward osmosis,10 and capacitive deionization (CDI).11–15
CDI is based on an electrochemical cell consisting of an
open-meshed channel for water ow, in contact with sheets of
porous electrodes on both sides. Upon applying a cell voltage
between the two electrodes, ions become immobilized by an
electrosorption process, that is, cations move into the cathode
(the electrode into which negative electrical charge is transferred), while anions move into the anode (Fig. 1). Aer some
time, when the electrodes reach their adsorption capacity
(which depends on cell voltage), a discharge cycle is initiated by
reducing or reversing the cell voltage, thereby releasing the salt
as a concentrated stream. In the discharging step of the cell,
energy recovery is possible.16,17
Salt immobilization by CDI is considered an energy-efficient
method for the desalination of water.15,18 Though typically
applied to the desalination of brackish water sources, seawater
can also be desalinated by CDI.19 In combination with ionselective membrane layers placed in front of the electrodes, CDI
can be used to selectively remove a certain ionic species from a
mixture of salts or to harvest compounds such as acetic acid,
sulphuric acid, insulin, and boron.20–26 Such separation
processes may nd use in the treatment of wastewater from
agriculture (mining), industry, and hospitals.
Various congurations for the design, stacking, and water
management of CDI cells are possible. Most studies consider a
design where the salt water is directed parallel to two equal
electrodes, while a constant cell voltage is maintained, see
Fig. 1.13,27,28 However, stacks of electrodes do not necessarily
have to consist of symmetrical cells and, instead, varying the
carbon mass between the two electrodes provides the possibility
to optimize the usable voltage window.29 Another approach
Fig. 1 Schematic illustration of desalination via capacitive deionization (CDI).
Upon applying a cell voltage between the two electrodes, anions and cations are
electrosorbed within highly porous carbon electrodes to counterbalance the
electrical charge. This immobilization of ions decreases the salt concentration in
the flow channel, and results in the production of freshwater.
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Energy & Environmental Science
utilizes carbon rods (called wires) which are sequentially dipped
and taken out of the water, instead of using lm electrodes
forming a stack through which the water ows.30 Instead of
using bare carbon electrodes, improved energy efficiency has
been reported for membrane-CDI (MCDI), where ion-exchange
membranes are placed in front of one or both of the electrodes.26,31–34 Further modications are the use of constant
current operation,33,35 directing the water ow straight through
the electrodes,13,28 or the use of owable electrode suspensions.19 Recently, CDI electrodes have also been used to produce
energy from the controlled mixing of river and seawater, based
on a reversal of the CDI process.36–42
Electrosorption of ions is an interfacial process and in order
to have a maximum contact area between the electrode and the
water, CDI employs high surface area porous carbon electrode
materials. At the water–carbon interface, electrical double layers
(EDLs) are formed in which ions are electrosorbed. It has been
stated that for optimum performance, pores should be large
enough to have only a weak EDL-overlap, that is, mesopores are
to be preferred over micropores.43–45 However, some microporous carbons, such as activated carbons14,46 and carbide-derived
carbons47 actually outperform mesoporous carbons. Recently,
Porada et al.47 reported that CDI desalination capacity positively
correlates with the volume of pores in the range below 1 nm,
while obtaining a negative correlation with the total pore
volume, or with the BET specic surface area (BET SSA, ref. 48).
The importance of pores <1 nm has also been demonstrated for
the capacitance of EDL-capacitor electrodes,49,50 for H2 gas
storage,51 and for CO2 gas removal capacity.52 These results
relate to equilibrium conditions, and micropores (<2 nm) and
especially ultramicropores (<0.8 nm) can pose severe limitations to ion transport in CDI ow cells. Thus, porous electrodes
that combine a large micropore volume (for a high deionization
capacity) with a network of mesopores (between 2 and 50 nm)
and macropores (>50 nm) may yield a highly efficient deionization process.43,53,54
For an optimum performance, the design of the various
components of the CDI system must be tuned to achieve both
high salt electrosorption capacity and fast kinetics at the same
time. Desalination by porous electrodes is by nature a non-linear
phenomenon. Classical transmission-line models applied to
CDI are unsatisfactory as they predict zero salt electrosorption
and assume a constant ionic resistivity in the electrode.15,55
Instead, when ions are being electrosorbed in the EDLs formed
in intraparticle pores (within carbon particles), the interparticle
pores (the pores in between the carbon particles) are subjected to
ion starvation and the ionic conductivity will drop dramatically
during desalination. This phenomenon results in an internal
ionic electrode resistance that is much higher than expected on
the basis of the performance derived for high salinity electrolytes, as common in EDLC research. EDLCs are specically
designed to operate at large salt concentrations to have a high
ionic conductivity and maximum capacity. Such a free choice of
electrolyte is obviously not possible for water desalination. Note
that the effect of ion starvation and the temporal increase in
local resistivity to ion transport in the interparticle pores is
included in the porous electrode theory of our paper.
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A variety of carbon materials, including activated carbons,
carbon aerogels, carbon xerogels, and carbon nanotubes, have
been studied for desalination by CDI.15,18 New developments of
advanced CDI electrode materials include asymmetric electrodes made of activated carbon coated with alumina and silica
nanoparticles,56 reduced graphene oxide and activated carbon
composites,57 graphene electrodes prepared by exfoliation and
reduction of graphite oxide,58 carbon nanotubes with polyacrylic acid,59 carbon ber webs obtained from electrospinning,60,61 and mesoporous activated carbons.62 Templated
carbons, although they require a more elaborate synthesis, are
of particular interest as they provide additional means to
precisely tailor the pore network, in order to combine a high
electrosorption capacity with fast salt removal rates. A particularly high level of pore size control has been documented for
carbons synthesized by selective etching of metal carbides with
chlorine gas, called carbide-derived carbons, or CDCs.63 Lately,
templated CDCs have been reported60,61 that combine a large
micropore volume with hierarchic mesopores. Compared to
conventional CDCs, templated ordered mesoporous CDCs (OM
CDCs) show signicantly larger specic surface areas
(3000 m2 g 1) and total pore volumes (2 mL g 1).64
Furthermore, using foam-like CDCs, synthesized by the “high
internal phase emulsion” (HIPE) approach, it is possible to
obtain control over macropores. The resulting material has both
high surface areas of up to 2300 m2 g 1 and extremely large pore
volumes of up to 9 mL g 1.65
Despite many studies on various kinds of porous carbons,
describing both equilibrium salt adsorption and the dynamics
of the process, tools are not yet available to directly predict the
performance of a certain carbon material and CDI design. The
present work is aimed to be a rst step towards a method for
direct prediction of desalination performance in CDI. Our
approach consists of two main routes.
(1) To extract data of the equilibrium salt adsorption and
kinetics of CDI for carbon materials with precisely tailored and
designed pore architectures. With these data we demonstrate
Paper
how we can directly predict the desalination performance of a
carbon material based on its pore size distribution (PSD).
(2) To use a two-dimensional porous electrode CDI transport
model to predict the actual salt electrosorption kinetics. This
model demonstrates how desalination kinetics depend not only
on the intraparticle pore morphology, but also on the electrode
thickness and interparticle porosity.
In the next sections we briey describe the porous electrode
transport theory, and discuss the synthesis of carbon materials
and electrode architecture. We describe the salt adsorption
performance in terms of equilibrium adsorption and kinetics,
present a method to correlate equilibrium adsorption with PSD,
and compare the dynamics of ion adsorption with theoretical
predictions.
2
Theoretical section
To describe salt electrosorption and electrical current in porous
carbon electrodes forming a CDI cell, we extend existing onedimensional porous electrode theory to two dimensions, to
consider both the ow direction of the aqueous solution
through the spacer channel, and the movement of salt in and
out of the electrodes. Within the electrodes, we consider
simultaneously ion transport through the space between the
carbon particles, that is, the large transport pathways across the
electrode (interparticle pore volume), and the electrosorption of
ions inside carbon particles (intraparticle pore volume). To
describe the latter, a powerful and elegant approach is to
assume that the EDLs inside the intraparticle pore volume are
strongly overlapping and, therefore, that the potential in these
pores does not vary with position in the pore. This is the
common “Donnan” approach for charged porous materials.
The electrical potential in the intraparticle pore volume is
different from that in the interparticle pore volume (the transport pathways) by a value Dfd. The direct Donnan approach is
modied29,31,47 to consider the Stern layer located in between the
electronic and ionic charge, and to include a chemical
Fig. 2 Schematic view of the time-dependent two-dimensional porous electrode model, combining a sequence of sub-cells in the flow direction, with ion fluxes into
the electrode. A symmetric CDI geometry is assumed, thus only half of a cell is depicted. The electrode contains an electrolyte-filled volume allowing for ion transport,
and carbon material in which ions and charge are stored. Electrical current (denoted by “+”) flows through the conductive carbon material.
3702 | Energy Environ. Sci., 2013, 6, 3700–3712
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attraction energy for the ion when it transfers into the intraparticle pores, described by a term matt.66 The modied Donnan
(mD) model equals the limit situation of the Gouy–Chapman–
Stern (GCS) theory when approaching full EDL overlap in
micropores where the Debye length is of the order or larger than
the pore size. In addition to GCS theory it includes the nonelectrostatic adsorption energy matt that reects that also
uncharged carbons adsorb some salt. A difference between the
mD and GCS model is that in the mD model, EDL properties are
described per unit pore volume, whereas in the GCS model
charge and salt adsorption are described as functions of pore
area. Numbers in either denition can be converted when the
pore area/volume ratio is known.
To describe the dynamics of ion transport and charge formation, we set up a two-dimensional porous electrode theory for a
CDI cell consisting of two porous electrodes placed in parallel,
with a at planar slit, or transport channel, or spacer, in between.
In the direction of ow, this transport channel is mathematically
divided into M subsequent sub-cells, see Fig. 2.34 In the porous
electrode, two coupled partial differential equations describe the
salt concentration in the interparticle pores, the electrostatic
potential there, f, the charge density, and the salt electrosorption
in the intraparticle pores as a function of time and depth in the
electrode. The porous electrode transport theory requires various
geometrical measures as inputs (thickness, porosity) that can be
calculated from electrode dimensions. Besides, it requires an
estimate of the diffusion coefficient of the ions in the macropores,
which may be lower than the corresponding value in free solution.
There are no other tting functions. The present model neglects a
transport resistance between interparticle pores and intraparticle
pores, which can be incorporated, but requires an additional
transport coefficient. Further details of the mD and transport
model are provided in section 5 of the ESI.†
Fig. 3
3
Experimental section
Electrodes from three different CDCs were prepared and
compared to establish a basis of reference materials for further
analysis of the salt electrosorption capacity. Details of material
synthesis, electrode manufacturing and CDI testing are given in
the ESI.† The synthesis methods are summarized in Fig. 3 for
titanium carbide-derived carbon (TiC-CDC, Fig. 3A), ordered
mesoporous silicon carbide derived carbon (OM SiC-CDC,
Fig. 3B), and HIPE SiC-CDC (Fig. 3C).
Electrodes were prepared from these powders following the
procedure outlined in ref. 47. A carbon slurry was prepared by
mixing 85 mass% of CDC, 5 mass% of carbon black (Vulcan
XC72R, Cabot Corp., Boston, MA), and 10 mass% of polyvinylidene uoride (Kynar HSV 900, Arkema Inc., Philadelphia,
PA); the latter was previously dissolved in N-methyl-2-pyrrolidone. Thus, the nal electrode contains 85 mass% of porous
CDC carbon. Electrodes were prepared by painting of the
carbon slurry directly on one or both sides of a graphite current
collector, taking care that approximately the same mass was
coated on each side. Results for thickness and total electrode
mass density are provided in Table S5.† Together with openmeshed porous spacer materials (thickness dsp ¼ 350 mm) the
current collector/electrode layers are stacked together forming
three parallel cells (i.e., one stack).29,47 The ow of salt solution
through the stack is kept constant, owing rst into a housing
around the stack, entering the spacer layers from all four sides,
and leaving via a centrally placed outlet to ow along a
conductivity meter placed in-line.
An array of activated carbons and other carbon materials (see
ESI†) were investigated along with the CDC materials for
comparison. These materials were not painted, but prepared by
a wet-casting technique following the procedure explained in
Schematic illustration and SEM images of the synthesis of (A) TiC-CDC, (B) OM SiC-CDC, and (C) HIPE SiC-CDC.
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Paper
ref. 47. In addition, carbon onions were tested as a representative of the class of fully graphitic, dense carbon nanoparticles
(Fig. S9, ESI†) with no intraparticle porosity. The synthesis of
carbon onions is based on the vacuum treatment of nanodiamonds at 1750 C as outlined in more detail in the ESI.†
Ion electrosorption occurs when applying a cell voltage Vcell to
each of the three cells, dened as the voltage difference between
the positively and negatively polarized electrodes. At the end of
the salt electrosorption step, the cell voltage is reduced to zero
and ion desorption begins. The electrical current running from
the cathode to the anode is measured and is integrated over time
to provide a measure for the total charge transferred between the
electrodes. This total charge is divided by the total electrode
mass in the stack, mtot, to obtain the charge expressed in C g 1,
see Fig. 5A, 7A and 8A. From the conductivity of the effluent
solution, the salt concentration is calculated and, thus, by
integrating over time, the salt electrosorbed, Gsalt, is calculated,
see ref. 15 and 47. For each new experiment, the salt electrosorption/desorption cycle was repeated several times until the
differences between cycles became negligible. We like to stress
that in this work, the salt removal data are not obtained from the
rst cycle aer a new condition has been applied, but instead are
obtained when the system has reached the limit cycle, also called
dynamic equilibrium (DE). This is the situation that the same
amount of salt is electrosorbed during the adsorption step as is
being removed in the desorption step of the cycle, as will be
typical during practical long-term operation of a CDI system. All
experiments were done using a cN ¼ 5 mM NaCl-solution
(290 ppm, 550 mS cm 1).
4
Results and discussion
4.1
Structure of the porous carbons
The CDC materials used for this study are produced from
selective etching of silicon or titanium atoms out of a carbide
precursor (SiC or TiC), a procedure which results in a material
with a high BET SSA which, in the case of OM SiC-CDC, is as
high as 2720 m2 g 1 (Table 1). Fig. 4 displays the cumulative
pore volume of these materials, together with the salt adsorption capacity, or z(s)-curve, which is discussed below.
All CDCs investigated in this study are predominantly
amorphous, as evidenced by the broad D- and G-bands observed
Table 1 Pore volume, specific surface area (SSA; calculated with the BET equation48 and quenched solid density functional theory, QSDFT72), average pore size
and local pore size maxima of the three CDC-materials. The average pore size is
the volumetric average, i.e., half of the total pore volume is associated with pores
larger or smaller than this value and not reflect, for example, the bimodal pore
size distribution in OM SiC-CDC
Carbon
material
Total pore
volume
(mL g 1)
BET SSA
(m2 g 1)
QSDFT SSA
(m2 g 1)
Average pore
size d50 (nm)
TiC-CDC
OM SiC-CDC
HIPE SiC-CDC
0.52
1.98
1.14
1309
2720
2351
1376
2260
2120
0.67
4.00
1.24
3704 | Energy Environ. Sci., 2013, 6, 3700–3712
Fig. 4 Cumulative pore size distributions calculated from QSDFT models of the
three tested CDC-materials, as well as the suggested correlation function for the
ion adsorption capacity, z(s). PSD curves shifted up by 0.4 mL g 1 for HIPE SiC-CDC
and 1.0 mL g 1 for OM SiC-CDC.
in Raman spectroscopy (see ESI†). TiC-CDC (Fig. 3A) powders
are composed of anisometric particles with a size distribution
ranging from approximately 1 to 10 mm and an average size of
5 mm. Compared to that, the structures of OM SiC-CDC and
HIPE SiC-CDC differ in many aspects. HIPE SiC-CDC has a
cellular pore structure as can be seen from Fig. 3C. Owing to the
HIPE synthesis route, the material exhibits 2 to 4 mm sized cages
that are interconnected by 300 to 500 nm sized windows. The
walls are highly porous, but yet in the nanometer range. Thus,
this material exhibits a hierarchical pore structure consisting of
macro-, meso-, and micropores. For the other materials used in
this study, macropores are only present in the form of large
pores between carbon particles, but not within the porous
particles themselves. OM SiC-CDC was synthesized as a powder
of strand-like particles (Fig. 3B) having an average strand
diameter of approximately 1 mm. These strands are built from
nanorods which are arranged in a hexagonal ordered fashion
and have very narrowly distributed mesopores located in
between (Fig. 3B). The narrow distribution in the mesopore size
is due to the method of nanocasting which employs ordered
mesoporous silica templates as conformally corresponding exotemplates for the resulting CDC.64,67–71 Besides the ordered
mesopores, micropores are also present in OM SiC-CDC. As a
consequence, this material has a hierarchy of micro- and mesopores but no internal macropores.68
The data for cumulative pore volume, see Fig. 4, show a
hierarchical pore size distribution (PSD) with contributions from
micro- and mesopores for HIPE and OM SiC-CDC, while TiCCDC is predominantly microporous: more than 90 vol% of the
pores is smaller than 2 nm (see Table S1 in the ESI†). HIPE SiCCDC shows a total percentage of 37 vol% of mesopores and for
OM SiC-CDC the majority of the total pore volume is associated
with mesopores (75 vol%). In that regard, HIPE SiC-CDC has
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the largest total micropore volume (0.72 mL g 1) of the CDCmaterials. The hierarchic porosity of OM SiC-CDC is exemplied
by its two narrow distribution maxima at approximately 1 nm
and 4 nm. HIPE SiC-CDC does not show such a strongly
pronounced bimodality, but it still exhibits two pore size
distribution maxima at around 1 nm and another one at 2.4 nm.
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4.2
Equilibrium desalination performance
Equilibrium data for salt adsorption and charge are presented
in Fig. 5, based on underlying data for the desalination cycle for
which examples given in Fig. S5 and S6 of the ESI,† using a
symmetric CDI cell. Fig. 5A and B present data for salt adsorption and charge per gram of both electrodes, as functions of cell
voltage. In Fig. 5B and C, the salt adsorption is presented relative to that at zero cell voltage in a two-electrode CDI cell. Fig. 5D
presents the calculated total ion concentration in the pores
(relative to an uncharged electrode), per mL intraparticle pore
volume (for all pores below a size of 30 nm), as a function of the
charge, also expressed per mL of intraparticle pores. The data
for pore volume are given in Table 1 and Fig. 4. Fig. 5A and B
show that the material with the highest capacitance (22.3 F g 1
at 5 mM NaCl, low-voltage limit), OM SiC-CDC, also has the
highest salt adsorption capacity, 12.8 mg g 1 at a cell voltage of
Vcell ¼ 1.2 V. Per gram of carbon (not total electrode) the
adsorption is 15.1 mg g 1 at 1.2 V.
Energy & Environmental Science
Figs. 5A and B clearly show how with increasing cell voltage
both charge and salt adsorption increase non-linearly. This is
different from typical results for EDL capacitors where the charge
increases linearly with voltage (see ref. 15). Fig. 5C plots salt
adsorption vs. charge (both expressed in mol g 1; for salt by
dividing the data of Fig. 5B by Mw,NaCl and for charge by dividing
the results of Fig. 5A by Faraday's number), which is a novel
representation, which shows how all three datasets overlap.
Fig. 5C also shows that the total ion adsorption is always somewhat less than the charge, i.e., the charge efficiency (L ¼ salt
adsorption/charge) is below unity.73 The high suitability of the
materials tested for CDI can be deduced from the fact how close
the measured charge efficiency is to unity, with measured values
of L generally beyond 0.85. Indeed, Fig. 5C shows how close the
data points are to the “100% charge efficiency line”, the ideal
limit where for each electron transferred one full salt molecule is
removed. Interestingly, beyond the rst data points (charge
density 0.1 mmol g 1) the data run parallel to the “100% charge
efficiency line” which demonstrate that in this range, for each
additional electron transferred, a full salt molecule is adsorbed,
i.e., the differential salt efficiency is unity.15,74 Fig. 5C clearly
makes the point that a strong correlation exists between the
capacitance of a material (how much charge can be stored for a
given cell voltage, typically evaluated under conditions of use for
EDL capacitors) and desalination performance in CDI.47
Fig. 5 Equilibrium salt adsorption and charge in porous carbon electrodes prepared from OM SiC-CDC (squares), HIPE SiC-CDC (circles), and TiC-CDC (triangles). (A)
Equilibrium charge SF and (B) equilibrium salt electrosorption Gsalt as functions of cell voltage, both per gram of both electrodes. (C) Charge and salt adsorption
recalculated to mol g 1, and plotted one versus the other. (D) Total pore ion concentration vs. charge per unit intraparticle volume (<30 nm). Salt concentration cN 5
mM NaCl. Lines represent fits using the modified Donnan model with in (D), matt,ref as the single fitting parameter. (*) Data relative to adsorption at Vcell ¼ 0.
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Evaluating the data in Fig. 5B per unit pore volume (all pores
<30 nm), one can calculate a salt adsorption of 0.39 M for TiCCDC, 0.20 M for HIPE SiC-CDC, and 0.13 M for OM SiC-CDC, at
a cell voltage of 1.2 V. This salt adsorption, SA, having dimension M, just as the z-function that will be discussed shortly, see
Fig. 4, is equal to half the total ion concentration in the intraparticle pores (<30 nm) as given in Fig. 5D (relative to salt
adsorption at zero voltage), evaluated for a symmetric twoelectrode cell. Clearly, per unit pore volume the performance is
decreasing in this order, which is opposite to the order when the
more common metric of mg g 1 is used (as plotted in Fig. 5B).
Careful assessment of the inuence of pore size increments on
desalination performance is required, and care must be taken
in dening what is the “best” material, which may relate to
electrode mass or volume, dependent on the nal application.
Next, we dene the performance ratio of a material, or PR. As
we will take HIPE SiC-CDC as the reference, for HIPE this value is
unity, PR ¼ 1. For TiC-CDC, which has twice the desalination per
unit pore volume compared to HIPE at the reference conditions,
PR ¼ 2. Likewise for OM SiC-CDC the value is PR ¼ 0.66.
In a later section we will discuss how well the value of PR
correlates with known data of the material's total pore volume,
BET SSA, and full pore size distribution. If here a correlation can
be found, this would allow one to estimate the PR of a new
material when only the PSD is known, without having data of
CDI experiments available. From the PR-value, desalination
performance at the reference conditions of a symmetric CDI cell
operating at Vcell ¼ 1.2 V and for a salinity level of 5 mM NaCl
can then be calculated. But in addition, knowing PR it will also
be possible to calculate desalination at any other condition
(different salinity, voltage, cell design), with the aid of the mDmodel, which requires knowledge of the three parameters matt,
CSt,vol,0 and a that are used in the mD-model. Thus, we rst
address, when the value of PR is known, how we can calculate
appropriate values to be used in the mD-model, which then
predicts desalination, not only under the reference conditions
as dened above, but also at other voltages (see Fig. 5B), other
salinities, and very different CDI cell designs. The procedure
that we propose is that relative to the reference material (HIPE
SiC-CDC), for which the three parameters in the mD-model,
being matt, CSt,vol,0 and a, are determined as explained below, for
materials with a different PR, the following rescalings are used:
to matt is added a term ln(PR), CSt,vol,0 is multiplied by PR, and a
is divided by PR. This procedure is based on the nding that
rescaling the total pore volume by PR gave a perfect match to the
data. However, to avoid introducing the concept of a theoretical
volume different from the actual one, for which there is no
physical basis, the above procedure is proposed. In this way,
once the value of PR of a new material is calculated (from the
PSD data and using the z(s)-curve), then by correlating to the
known performance of HIPE SiC-CDC, its CDI performance can
be directly predicted.
The values for matt, CSt,vol,0, and a for HIPE SiC-CDC are
calculated as follows. The novel representation in Fig. 5D is the
starting point to derive by a structured method the parameters
in the mD-model. Moreover the data in Fig. 5D can be tted only
by adjusting the value of matt, without any inuence of Stern
3706 | Energy Environ. Sci., 2013, 6, 3700–3712
Paper
layer properties on this t, see eqn (S3) and (S4) in the ESI.† For
HIPE an optimum value of matt ¼ 2.0 kT is found, in line with
values used in previous work.29,30 Next, for HIPE the full data of
Fig. 5A and B must be tted by optimizing CSt,vol,0 and a,
for which only one combination ts the curves well (namely,
CSt,vol,0 ¼ 72 MF m 3 and a ¼ 50 F m3 mol 2). Having established all of these values, the curves for the other two materials
in Fig. 5A, B, and D automatically follow, and a very satisfactory
t is obtained. Using a constant Stern layer capacity does not t
the data well, see Fig. S5 in the ESI† for a comparison with a
calculation with a ¼ 0.
4.3 Direct prediction of the desalination performance based
on porosity analysis
We aim to nd a method to correlate desalination performance
in CDI to the porosity analysis of the carbon material. This is a
hotly debated topic and the claim is oen made that for CDI
pores must be mesoporous (i.e., above 2 nm),43,44 or even beyond
20 nm (ref. 45) to avoid overlap of electrical double layers in the
pores, an effect that is claimed to be deleterious for CDI.
However, electrodes made of microporous AC and CDC powders
showed very high performance in CDI, higher than electrodes
based on mesoporous carbon aerogels.15,47,75 Also for the materials tested in this work, the predominantly microporous
carbons (TiC-CDC, and HIPE SiC-CDC) show a general trend of
higher salt adsorption per unit pore volume than the predominantly mesoporous OM SiC-CDC.
One question remains: what porosity metrics are most suitable to predict CDI performance? In agreement with ref. 47, we
nd that desalination is positively correlated, even proportional, with the volume of pores smaller than 1 nm (see Fig. S3A
and Table S1 in the ESI†), but only for materials that are mainly
microporous. However, when including in the correlation
materials with a signicant portion of mesopores, such as HIPE
SiC-CDC and even more so for OM SiC-CDC, for these materials
a signicant deviation from this proportionality (between salt
adsorption and pore volume in pores <1 nm) is observed, with a
much higher salt electrosorption than predicted based on this
correlation, which can be explained by the contribution of
mesopores to the ion immobilization. This contribution is not
as high, per unit volume, as for micropores, but mesopores
nevertheless also contribute to the ion electrosorption capacity.
Thus, this measure of pore volume <1 nm cannot be the input
parameter for a reliable predictive method. This situation is
quite different from that in ref. 47 where it was demonstrated
that for microporous carbons (AC and TiC-CDC), a positive
correlation between the volume of pores smaller than 1 nm and
the CDI performance could be established with a negative
correlation of salt adsorption with BET SSA and with the total
pore volume.
An appropriate metric based on PSD is not just correlated
with salt adsorption, but ideally is proportional with desalination. Proportionality implies that the metric is a true measure of
desalination, with an increase in this metric by a factor 2,
resulting also in a two-times increased desalination. Such a
metric is more likely to have a chemical–physical basis than a
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metric that is merely correlated with desalination. In Fig. S3 of
ESI† we show four metrics based on the PSD and their proportionality with the salt adsorption performance: micropore
volume <1 nm, <2 nm, total pore volume, and BET SSA.
However, a satisfying t is not observed in either case. Thus, we
cannot establish a clear and unambiguous proportionality
between the salt electrosorption capacity and either of these
metrics (see Fig. S3 in the ESI†).
Still, porosity measurements present a very facile method to
characterize porous carbons and it remains very attractive to
base a predictive CDI performance method on porosity data. We,
thus, propose a new approach to predict the CDI performance,
based on considering the relevance to salt adsorption of each
pore size increment, which we call “salt adsorption capacity
analysis” (or, z-analysis), which determines the relevance of each
size increment to the measured desalination under one reference condition (Vcell ¼ 1.2 V, cN ¼ 5 mM NaCl, symmetric cell).
The function z is a property with dimension M and describes for
the reference condition the contribution to desalination by a
CDI cell of a certain pore size, s, per unit pore volume (within the
carbon in one electrode). Deriving the z(s)-function is done by
the simultaneous t of the experimentally available PSD of a set
of materials to their desalination performance. This analysis
quanties the fact that salt electrosorption depends not only on
the total pore volume, but also on the pore size distribution: the
volume associated with some pores contributes more to the total
sorption capacity than other pores.
Mathematically, the aim of the analysis is to nd the
z(s)-function, see Fig. 4, by which the salt adsorptions (SAs) of a
set of materials (at the reference condition) predicted by eqn (1),
t as closely as possible the measured values of SA. Note that the
ratio of this SA to the SA of our reference sample (HIPE
SiC-CDC) is the performance ratio, PR. In the z(s)-analysis, the
total salt adsorption in mg g 1 of a symmetric two-electrode cell
is given by eqn (1)
Energy & Environmental Science
SA mg g
1
¼ Mw;NaCl
ðV
zðsÞdV
ð0smax
dV
¼ Mw;NaCl
fzðsÞf gds; f ¼
ds
0
(1)
where Mw,NaCl is the molar mass of NaCl (58.44 g mol 1) and V
is the pore volume (we will consider in all cases the pore size
distribution up to a size of 30 nm) in mL g 1, see Table 1. In
the z(s)-analysis it is assumed that each material will have a
different PSD, see Fig. 4, but that only one common function
for z(s) is allowed. Note that eqn (1) describes the salt
adsorption not per gram of electrode material, but per gram
of carbon, which in all of our experiments is 85% of the electrode mass.
To nd the optimum z(s)-function we have used various
methods, using e.g. predened functions, but in the end we
decided to use a “function-free” approach in which the value of
z is adjusted separately for each increment in size s, with the
only imposed constraint that z must be decreasing with size s.
Assuming, instead, as a rst approximation z to be invariant
with pore size s, we obtain the parity plot of Fig. 6A, where for
the three CDC-materials, and also for twelve other materials
(listed in Table 2) we show the correlation between the predicted value of SA and the measured value. As can be observed
in Fig. 6A, there is a large deviation between the measured and
predicted salt adsorption when assuming z to be constant at z ¼
0.21 M and not varying with pore size.
Next we discuss our results of using a modied z(s)-function.
The optimized z(s)-function is found by a least-square tting
procedure of the difference of predicted (see eqn (1) above) and
measured desalination. Several a priori constraints are
imposed:
(1) The full PSD curve is divided in short size ranges of
0.1 nm, for each of which the value of z can be adjusted by the
optimization routine, independently of the others.
Fig. 6 Parity plots for salt adsorption (cN ¼ 5 mM, Vcell ¼ 1.2 V) for three carbide-derived carbons (grey diamonds) and twelve other materials (red triangles) per gram
of carbon in both electrodes combined. (A) Salt adsorption capacity z assumed independent of pore size s. (B) Optimized z(s)-function, see Fig. 4.
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Table 2 Salt electrosorption performance reported for different electrode
materials applied for CDI (equilibrium adsorption of NaCl as a function of total
mass of both electrodes combined). Gsalt: equilibrium salt electrosorption; CNT–
RGO: carbon nanotubes and reduced graphene composite; MWCNTs: multiwalled carbon nanotubes; RGO: reduced graphite oxide; AC: activated carbon;
CDC: carbide-derived carbon. Entries sorted by ascending salt electrosorption
capacity
Salt
Cell
concentration
voltage (V) (mg L 1)
CNT–RGO
1.2
1.6
MWCNTs
1.2
RGO
2.0
Carbon xerogel 1.2
Carbon xerogel 1.2
Carbon onions 1.2
CWZ-22 (AC)
1.2
Carbon aerogel 1.3
1.2
Mast carbon
S-TE3 (AC)
1.2
Norit DLC
Super50 (AC)
Mast carbon
1.2
S-TE11 (AC)
Kuraray
1.2
YP50-F (AC)
Microporous
1.25
carbon aerogel
monoliths
TiC-CDC
1.2
TiC-CDC
1.2
HIPE SiC-CDC 1.2
TiC-CDC
OM SiC-CDC
MSP-20 (AC)
1.2
1.2
1.2
Gsalt
(mg g 1)
Ref.
50
50
3000
65
260
260
290
290
2000
290
0.7
0.9
1.7
1.8
3.1
3.3
3.9
5.3
7.1
7.6
78
79
80
80
This work
This work
75
This work
290
7.7
This work
290
8.5
This work
290
9.1
This work
2900
9.6
13
290
290
290
290
290
290
290
10.1
10.4
11.1
13.6
12.4
12.8
14.3
77
This work
47
This work
47
This work
This work, 81
(2) With increasing size s, z is not allowed to increase, but
only to stay constant or decrease. Thus, we impose the rather
stringent condition that the z(s)-curve must monotonically
decrease and the smallest pore size will have the highest z.
(3) We assume that beyond a certain size, when EDL overlapping starts to become minor, and desalination must be
proportional with area, that desalination per unit volume must
be inversely proportional with pore size. We impose this
condition from a rather arbitrarily chosen point of a size of s ¼
6 nm.
We apply this analysis method to the three CDC-materials
discussed before, and we arrive at the z(s)-curve as sketched in
Fig. 4, where for a size s from 1.1 to 6.0 nm a constant z is
predicted of z ¼ 0.11 M, from a size s 0.7–1.1 nm we have z ¼
0.28 M and below s ¼ 0.7 nm z ¼ 0.51 M. (Note that the
computer routine predicts tiny variations within each “block”,
and we removed these slight changes manually giving the z(s)curve plotted in Fig. 4, which was used as input in Fig. 6B). Next
the optimized z(s)-correlation function is validated by applying
it to twelve different materials, see Fig. 6B. As can be observed,
for the three CDC-materials the t is now perfect, while also for
the other materials, the t between predicted desalination
3708 | Energy Environ. Sci., 2013, 6, 3700–3712
(x-axis) and actual desalination (y-axis) has improved
substantially.
This analysis demonstrates that pores smaller than 1.1 nm
contribute more substantially to desalination than larger pores.
The nding of a very high value of the electrosorption capacity
associated with these micropores is in good agreement with our
previous study on a comparison of CDC and AC materials47 and
is also in line with the data presented in Table 1 and Fig. S3A
(see ESI).† It is closely related to the reported phenomenon of
the anomalous increase in capacitance in EDL-capacitors in
subnanometer-sized pores.49,76
In conclusion, the z(s)-analysis gives the possibility to predict
the CDI performance for both common and specialized carbons,
purely based on easy-to-access cumulative PSD data. In contrast
to this accuracy, our results (Fig. 6A and S3†) also underline that
a convoluted, single value of pore analysis such as average pore
size, total specic surface area, or total pore volume is not suited
for direct prediction of the salt electrosorption capacity. Clearly,
the complexity of carbon porosity must be appreciated and PSD
data must be combined with consideration of the desalination
efficiency of each pore size increment.
A spreadsheet le for the z-analysis based on arbitrary PSDdata is provided as ESI.†
4.4
Kinetics of salt electrosorption and charge transfer
Besides equilibrium electrosorption, the dynamics of ion
sorption is of great importance for the practical application of
CDI devices, and for a comprehensive understanding of differences between different porous carbon materials. In this section
we apply for the rst time a rigorous procedure based on a twodimensional porous electrode theory that predicts the dynamical CDI behavior of a porous carbon electrode, see the ESI,†
based on ion electrodiffusion through the interparticle pores in
the electrodes, and ion electrosorption in the intraparticle
pores. Electrosorption is described by the modied Donnan
(mD) model for which appropriate parameter values for matt,
CSt,vol,0, and a were derived in Section 4.2 (see Fig. 5). The mD
model not only predicts desalination at the reference condition
of Vcell ¼ 1.2 V and for cN ¼ 5 mM NaCl, but also for other
conditions, and in addition, also describes electrosorption in a
dynamic calculation during which the salt concentration in the
interparticle pores becomes signicantly different from cN, to
drop for a short period during desalination, while increasing
sharply, again only for a short period, during ion release.31 The
only dynamic tting parameter is the ion diffusion coefficient.
As depicted in Fig. 7, the porous electrode theory describes
the rate of salt electrosorption and charge accumulation in CDI
electrodes very well for the materials with a fair amount of
mesopores (HIPE SiC-CDC, and OM SiC-CDC). The only difference in the input values for these calculations is the electrode
thickness and inter- and intraparticle porosity, all calculated
from geometrical measurements (see also Tables 2 and S6 in the
ESI†), and the parameters for the mD model obtained from the
equilibrium analysis of Section 4.2. The dynamics are described
by the ion diffusion coefficient, for which a value of D ¼
1.34 10 9 m2 s 1 is used for all materials (see ESI†).
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Fig. 7 (A) Kinetics of charge transfer during the adsorption step and (B) salt electrosorption in CDI, as a function of time for OM SiC-CDC (squares), HIPE SiC-CDC
(circles) and TiC-CDC (triangles). Lines are fits using two-dimensional porous electrode theory.
While hierarchic porous carbons, that is, OM SiC-CDC and
HIPE SiC-CDC, yield an excellent agreement between the
measured and calculated dynamic behavior, for TiC-CDC which
has practically no mesopores, and is much denser (Table S5 in
ESI†), we do obtain a good t of the salt electrosorption rate, but
at the same time the charge accumulation rate (current) is
underestimated initially. This possibly relates to a transport
resistance from the interparticle space to the intraparticle
space, see Section 5.3 in the ESI.†
4.5 Effect of electrode thickness on salt electrosorption and
charge transfer
As we have seen, ion transport is strongly inuenced by the
structure of the pore network, with a very good description of
the dynamics of desalination performance for the hierarchical
materials, as shown in Fig. 7. To further validate the twodimensional porous electrode theory for these hierarchical
materials, electrodes characterized by the same mass density
Fig. 8 (A) Salt electrosorption and (B) charge transfer during the electrosorption step in CDI, as a function of time and electrode thickness, L, for electrodes made of
OM SiC-CDC. Lines are predictions using two-dimensional porous electrode theory. (C and D) Calculation results as a function of electrode packing density.
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but different thicknesses were prepared from OM SiC-CDC. The
choice of this material was motivated by the excellent correlation between data and model shown in Fig. 7. As shown in
Fig. 8A and B, there is a very strong inuence of the electrode
thickness on both the salt electrosorption and the charge
transfer rate. By increasing the thickness of the electrodes, the
rate by which the maximum desalination is reached in the CDI
process slows down, while as expected the nal equilibrium
values (dened per gram of material) remain exactly the same.
We see that this applies for both the charge accumulation rate
and the salt electrosorption rate. Fig. 8C and D analyze theoretically the effect of higher (or lower) electrode packing density
(the overall electrode mass density, as presented in column 2 of
Table S5†), by reducing the interparticle volume while keeping
the mass and total intraparticle volume the same. Fig. 8D shows
the interesting effect that a reduction of the interparticle
volume is at rst advantageous, with the time to reach 50% of
the maximum desalination rst decreasing (reaching a
minimum value in the range of porosities between 30 and 60%),
with this time increasing again for even lower porosities. The
positive effect of a higher packing density of the electrode is that
the length of the pathways for ions to traverse across the electrode goes down (the deepest regions of the electrode are more
quickly reached), while the opposite effect at low porosity is
because the transport pathways are being squeezed out of the
electrode, with the apparent resistance for ion transport
increasing (i.e., simply no transport pathways remain).
These observations have a number of important implications, because optimized kinetics are very important for actual
CDI application. As Fig. 8 demonstrates, faster ion electrosorption (per unit mass of electrode) can be achieved by
decreasing the electrode thickness and by optimizing the electrode porosity. Thus, our study demonstrates that it is not only
important to appreciate the micro- and mesopores present
inside a carbon particle, but also to understand the porous
carbon electrode in its entirety. The latter also entails the pores
in between the carbon particles, and the total thickness of an
electrode.
5
Conclusions
We have studied capacitive deionization of water using three
carbide-derived porous carbon materials with strongly varying
contributions to the total pore volume originating from microand mesopores, and compared performance with various
reference materials. We have demonstrated that there is no
direct relationship between salt electrosorption capacity and
typical pore metrics such as BET SSA and the total volume of
pores. However, we have demonstrated that the salt electrosorption capacity can be predicted by analysis of the pore size
distribution and the pore volume correlated with incremental
pore size ranges, considering that differently sized pores exhibit
a different electrosorption capacity for the removal of salt ions.
This analysis has been validated by comparison to literature
data and other carbon materials and we were able to quite
reliably predict the CDI performance of a range of carbons used
for CDI.
3710 | Energy Environ. Sci., 2013, 6, 3700–3712
Paper
Modeling is an important part of CDI performance analysis,
not only to access information on the equilibrium salt removal
capacity but also to gain understanding of the ion electrosorption process. Using the diffusion coefficient as the only
dynamic t parameter, two-dimensional porous electrode
theory is capable of predicting the dynamics of charge accumulation and the resulting process of salt electrosorption for
the CDC-materials with sufficient amounts of mesopores. For
materials without pores in this size range, the theory underestimates the initial current. Although CDI is a complex process
depending on various parameters, such as pore volume, pore
size distribution and process parameters, our work demonstrates that prediction of the CDI dynamic equilibrium salt
adsorption capacity and the kinetics for ow-by electrodes is
feasible. These results will facilitate the rational development of
carbon electrode designs for CDI. An important next step will be
to adapt our model to more advanced CDI techniques, such as
ow-through CDI,13,82 CDI using wires,30 or CDI using owing
electrodes.19
Acknowledgements
Part of this work was performed in the TTIW-cooperation
framework of Wetsus, Centre of Excellence for Sustainable
Water Technology. Wetsus is funded by the Dutch Ministry of
Economic Affairs, the European Union Regional Development
Fund, the Province of Friesland, the City of Leeuwarden, and
the EZ/Kompas program of the “Samenwerkingsverband NoordNederland”. We thank the participants of the themes “Capacitive Deionization” and “Advanced Waste Water Treatment” for
their involvement in this research. The authors also thank
Matthew Suss (Stanford University, USA) and James London
(University of Kentucky, USA) for providing pore size distribution data, and Taeyoung Kim for providing activated carbon
sample called MSP-20. Dr Mesut Aslan and Dr Emilie Perre
(both at INM) are thanked for their help with the gas sorption
analysis. Rudolf Karos (INM) is thanked for his help with XRD
analysis. VP acknowledges funding received from the Bayer
Early Excellence in Science Award and Prof. Eduard Arzt (INM)
is thanked for his continuing support.
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