Electrosorption of Ions from Aqueous Solutions by Nanostructured Carbon Aerogel

Journal of Colloid and Interface Science 250, 18–27 (2002) doi:10.1006/jcis.2002.8314, available online at http://www.idealibrary.com on

Electrosorption of Ions from Aqueous Solutions by Nanostructured Carbon Aerogel Tung-Yu Ying,∗ Kun-Lin Yang,∗ Sotira Yiacoumi,∗,1 and Costas Tsouris†,1 ∗ Georgia Institute of Technology, School of Civil and Environmental Engineering, 200 Bobby Dodd Way, Atlanta, Georgia 30332-0512; and †Oak Ridge National Laboratory, Separations and Materials Research Group, P.O. Box 2008, Oak Ridge, Tennessee 37831-6181 E-mail: [email protected], [email protected] Received October 12, 2001; accepted February 21, 2002; published online April 29, 2002

The basic concept of electrosorption is to force charged ions moving toward oppositely charged electrodes by imposing an electric field. When such a field is introduced, electrodes of high conductivity and high surface area form strong electrical double layers near their surfaces. Charged ions are held in the double layer, and once the electric field is removed, the ions are quickly released back to the bulk solution. Because of this reversibility, electrosorption offers several advantages over other conventional technologies. Unlike ion exchange, no acids, bases, or salt solutions are required for regeneration of the surface, thereby substantially reducing the amount of secondary waste. Compared with thermal processes, such as evaporation, electrosorption consumes less energy to achieve similar results. Electrosorption also has operational advantages over electrodialysis and reverse osmosis because no membranes are required. In the earlier studies of electrosorption (1, 6, 7), researchers have shown good removal efficiency of metal ions by activated carbon beds. However, several practical problems are encountered with activated carbon electrodes. For example, significant fractions of the activated carbon surface may be occluded in electrodes that use polymeric binders (1). Such electrodes have characteristically high electrical and mass-transfer resistance. In addition, polymer binders are susceptible to both chemical attack and radiation-induced degradation. Recent efforts have focused on novel electrode materials. Among the new materials that have been developed, carbon aerogel—a monolithic, high-surface-area, and high-electrical-conductivity material— has been shown to have excellent properties for electrosorption (8). According to characterization studies (9–11), carbon aerogel is highly porous and has high surface area (∼400–1000 m2 g−1 ), low electrical resistivity (≤40 m cm), and controllable pore size distribution (≤50 nm). Farmer et al. (12–14) have shown that electrosorption by carbon aerogel electrodes can effectively remove ions such as sodium, chloride, chromium, ammonium, and perchlorate from aqueous solutions. Two primary mechanisms have been suggested for the electrosorption process by porous electrodes: electrical double-layer

Electrosorption is generally defined as potential-induced adsorption on the surface of charged electrodes. After polarization of the electrodes, ions are removed from the electrolyte solution by the imposed electric field and adsorbed onto the surface of the electrodes. Experimental and modeling studies were conducted using two types of carbon aerogel composites of different surface areas to provide a better understanding on the mechanisms of electrosorption. The experimental results revealed that no significant specific adsorption of F− ions occurred, while strong specific adsorption 2+ ions. In addition, although the was observed for NO− 3 and Cu two types of carbon aerogel electrodes had different surface areas, their capacities were found to be very similar because of the electrical double-layer overlapping effect in micropores. An electrical double-layer model developed in our previous work (16), in which the electrical double-layer overlapping correction is included, is expanded in the present work by considering the effect of the specific adsorption on the electrosorption process. Modeling results were compared with experimental data obtained under various conditions. When the overlapping effect and specific adsorption were considered, the model provided results that were in good agreement with experimental data. C 2002 Elsevier Science (USA) Key Words: electrosorption; carbon aerogel; electrical double layer; nanostructured material.

INTRODUCTION

The removal of dissolved inorganic contaminants such as radionuclides, metal ions, and anions from aqueous solutions is of great importance in environmental processes. In addition, effective technologies are needed for the removal of anions, such as nitrates and iodide. Electrosorption has been shown to be a promising technology for such applications involving solutions of low-to-moderate ionic strength. Electrosorption has been investigated for the removal of heavy metal ions and desalination of dilute solutions (1–6).

1

To whom correspondence may be addressed.

0021-9797/02 $35.00

 C 2002 Elsevier Science (USA)

All rights reserved.

18

ELECTROSORPTION OF IONS FROM AQUEOUS SOLUTIONS

formation and chemical reactions occurring at the surface of the electrodes. For simplification, earlier modeling studies considered only the electrical double-layer formation. Johnson and Newman (2) developed a comprehensive theoretical model for ion adsorption by porous carbon electrodes. Their analysis simulates the electrosorption process using a macroscopic model and shows good agreement with experimental data. Farmer et al. (12) attempted to use the Gouy–Chapman theory, developed for simple planar electrodes, to explain their experimental results with carbon aerogel electrodes. Their modeling results, however, show that the surface charge density failed to meet a square-root dependence on electrolyte concentration, which may be due to the self-shielding effect experienced by the porous carbon electrodes. The experimental results of Lin et al. (15) also showed that the self-shielding or double-layer overlapping effect prevents ions from entering the micropores. Since carbon aerogel composites have a high fraction of micropores, the electrical double-layer overlapping effect inside porous electrodes becomes significant and needs to be considered for the simulation of electrosorption processes from a microscopic view. In our previous work (16), we developed an electrical double-layer model by including the double-layer overlapping correction. With this correction, the modeling results were found to be in good agreement with experimental data for NaF at various values of applied voltage and solution concentration. However, when the overlapping effect was not considered, the model overestimated the experimental results. In addition to the double-layer effect—because most of the carbon electrodes are cation responsive—functional groups such as carbonyl and phenolic groups are able to effectively react with cations and hold them with chemical bonds (1). Several researchers have found (17–19) that when specific adsorption occurs, the surface potential of the electrodes is changed because of the adsorbed ions. The experimental results of Farmer et al. (14) show that specific adsorption becomes important for the removal of heavy metals (e.g., chromium) by carbon aerogel electrodes and needs to be taken into consideration in model development. They suggested that although double-layer charging is the major mechanism, specific adsorption also plays a significant role for certain ions. In the present work, the effects of overlapping and specific adsorption on electrosorption of various electrolytes such as those of NaF, NaI, NaNO3 , and Cu(NO3 )2 by carbon aerogel are experimentally and theoretically investigated. Equilibrium experiments were conducted using carbon aerogel electrodes of different surface areas for different ionic species under various operating conditions of applied voltage and solution concentration. In addition, the electrical double-layer model developed in our previous work (16) is expanded here by including the effect of specific adsorption to describe the electrosorption capacity of ions from aqueous solutions by carbon aerogel electrodes. The modeling results are compared with experimental data under various conditions of applied voltage and ion concentration.

19

MATERIALS AND METHODS

Materials and Characterization Two types of carbon aerogels of different surface areas, referred to here as type A and type B, were obtained from Marketech (Port Townsend, WA). Experimental characterization of carbon aerogels includes measurements of surface charge density, electrical capillary maximum (φecm ), specific surface area, and pore size distribution. Of these, pore size distribution and electrical capacitance are the two most important properties to characterize. The pore size distribution determines the available surface area for electrosorption, while the electrical capacitance determines the electrosorption capacity per unit surface area of carbon aerogel. The surface charge density of carbon aerogel material was measured by using a potentiometric titration method with a model 716 DMS automatic titration system (Metrohm, Herisau, Switzerland). The solution was prepared by adding ground carbon aerogel to deionized water, and the desired ionic strength was adjusted by using NaNO3 . During the titration, the pH was adjusted by using 0.1 M HNO3 or 0.1 M NaOH. The electrical capillary maximum (φecm ) of carbon aerogel, which is a measure of how the material responds in the electric field, was determined. The applied electrical driving force must exceed the value of φecm in order to effect electrosorption (18). Measurements of φecm were obtained by increasing the applied voltage at a constant rate (0.33 mV s−1 ) and then recording the change in current. The region in which the current did not change with the voltage corresponds to the φecm of carbon aerogel. These experiments were conducted with solution concentrations of NaF ranging from 25 to 600 ppm. Fluoride ions do not react with the carbon aerogel surface; therefore, the simulation system is simplified when NaF is used because ions can be treated as point charges. The experimental measurements of the pore size distribution and specific surface area of the carbon aerogel type A were described previously (16). In the present work, the pore size distribution and specific surface area of carbon aerogel type B were measured using a similar procedure based on physical adsorption. The physical adsorption measurements were obtained with a Micromeritics ASAP 2010 (Norcross, GA) by using N2 gas at 77 K. The pore size distribution of the carbon aerogel was then deduced from these experimental data. Equilibrium Experiments of Electrosorption Batch experiments were conducted by using a pair of carbon aerogel electrodes. The electrosorption cell consisted of a pair of electrodes formed by attaching thin sheets of carbon aerogel composites to titanium plates as shown in Fig. 1. A separation distance of 0.6 cm between the two electrodes was maintained by using a central hollow piece of Plexiglas. The titanium plates were connected to a direct-current (dc) power supply, model

20

YING ET AL.

MODEL DEVELOPMENT

An electrical double-layer model was developed in our previous work, in which the double-layer overlapping effect is considered, and the effect of specific adsorption is assumed insignificant and can be neglected (16). In the present work, the intention is to expand this model for a more realistic system by including the effect of specific adsorption of ions by carbon aerogel electrodes. The basic equations for surface potential distribution and surface charge density in a symmetric electrolyte solution between two plates of distance w, representing the walls of a single pore of the material, are the same as those employed in our previous work and are described by (16)   d 2 ψ 2zeN0 zeψ = sinh dx2 ε kT FIG. 1. Schematic of the setup for equilibrium experiments of electrosorption; one-half of the electrosorption cell is schematically shown in the circle: (1) Plexiglas cover, (2) Viton gasket, (3) titanium plate, (4) carbon aerogel, (5) Viton gasket with hole, and (6) central Plexiglas.

[1]

and σ0 =

√





zeψd 4ε RT I cosh kT





zeψm − cosh kT

1/2 [2]

with the boundary conditions 3632A (Hewlett Packard, Loveland, CO) with a voltage range of 0 to 15 V and a current range of 0 to 7 A. To measure the total capacity of carbon aerogel, equilibrium experiments were conducted in a continuously recycling system (Fig. 1), in which a total solution volume of 120 mL was maintained. In each experiment, the solution was continuously pumped from a recycling reservoir into the cell and the effluent returned to the reservoir using a Teflon-coated pump (model 7090-62, Cole-Parmer, Barrington, IL). In all the experiments, the solution temperature was kept at 298 K and a slow flow rate around 10 mL min−1 was applied. The solution conductivity was continuously monitored at the outlet of the reactor by using a flow-through conductivity meter, model 3200 (YSI, Yellow Springs, OH). The total capacity of electrosorption was then obtained by converting the change in conductivity to its corresponding concentration using a calibration table made prior to the experiments. The solution pH, temperature, and current were also continuously monitored. Various electrolyte species including those of NaF, NaCl, NaBr, NaI, NaNO3 , and Cu(NO3 )2 were used in this study. During each experiment, the solution was pumped through the cell without an applied voltage until the system reached equilibrium. A desired voltage difference was then applied between the electrodes until a new equilibrium was reached. Regeneration was accomplished by discharging the cells at 0 V or by reversing the polarization of the electrodes. Reverse polarization can increase the regeneration effectiveness and/or reactivate the carbon aerogel electrodes. The reproducibility of these findings was confirmed by repeating several electrosorption experiments under identical conditions. The average deviation in the total capacity was approximately 10%, and the maximum deviation was below 20%.

dψ =0 dx

and

ψ = ψm

ψ = ψd

at x = ±

at x = 0

[3a]

and w , 2

[3b]

where x represents the distance variable, ψ is the electrical potential, σ0 is the surface charge density, e is the charge of the electron, N0 is the total number of the ions in the bulk solution, ε is the dielectric constant of the medium, z is the valence of the ions, k is the Boltzmann constant, T is the absolute temperature, R is the gas constant, and I is the ionic strength. If the thickness of the inner layer of the electrical double layer is small compared with the pore width w, it is reasonable to assume that the diffuse layer boundaries are located at x = w/2 and x = −w/2, respectively. Therefore, ψd and ψm represent the diffuse-layer potential and the midplane potential, respectively. By solving Eqs. [1] and [2] along with their boundary conditions, one can thus obtain the surface charge density inside a pore. The individual capacity for each pore is then calculated by multiplying σ0 by the surface area of the pore and the Faraday constant. The total capacity is obtained by integrating the capacity of an individual pore over the whole range of the pore size distribution. The diffuse-layer potential ψd near the anode, where an external voltage V is applied, is expressed as follows in our previous study in which specific adsorption is not considered (16), ψd =

V σ0 − φecm − , 2 C1

[4]

ELECTROSORPTION OF IONS FROM AQUEOUS SOLUTIONS

where φecm denotes the potential at the electrical capillary maximum and can be obtained from the experiments discussed under Materials and Methods. The parameter C1 in Eq. [4] represents the inner-layer capacitance, which can be assumed to remain constant over a low-voltage range (20). It should also be noted here that only the outer Helmholtz plane is considered in the model. The difference between V /2 and ψd (= φecm + σ0 /C1 ) in Eq. [4] can be viewed as the potential difference across the electrical double layer and is the driving force to adsorb ions. In the case that no specific adsorption occurs on the surface of electrodes, the value of φecm is unaffected by the salt concentration (18). In our previous work, a pair of constant values of φecm and C1 was employed in the electrical double-layer model and good agreement with the experimental data of electrosorption of NaF was obtained, in which specific adsorption is insignificant (16). When specific adsorption occurs on the surface of an electrode, the surface charge density changes as well as the surface potential, which implies the driving force—the potential difference between the electrode surface and diffuse layer—changes. Grahame and Parsons (21) suggested that the potential difference across an electrical double layer can be separated into two parts: a chemical part and an electrical part. Because the charge on the electrode may affect the strength of the chemical bond between electrode surface and adsorbed ions, the chemical part is assumed to depend on the surface charge density of the electrode and the solution concentration (21). Grahame and Parsons established a relationship between the surface concentration of specific adsorbed ions (n), the ionic concentration in bulk solution (c), and the potential difference across the double layer (ψ), 

 −zeψ n = K c exp , kT

21

analogous to that shown in Eq. [5], K1 = exp(K 2 φecm ), c

[6]

where K 1 and K 2 are constants that can be obtained from experimental data. The carbon aerogel used in this study is cationresponsive, and the total capacity is, thus, determined by its anion capacity (1). Therefore, constants K 1 and K 2 in Eq. [6] are unique for each anion. RESULTS AND DISCUSSION

Characterization of Carbon Aerogel Surface area measurements. Two types of carbon aerogel with different surface areas were examined. The differential surface area of each (type A and type B) is shown in Fig. 2 as a function of the pore size. The BET surface area was determined to be 412 m2 g−1 for carbon aerogel type A and 602 m2 g−1 for carbon aerogel type B. For both types, the results in Fig. 2 ❛ demonstrate that most of the pores ❛ are smaller than 200 A , and there are no pores larger than 1000 A. Meanwhile, a large portion ❛ of the pore size is below 10 A, where strong electrical doublelayer overlapping is expected. It is interesting to note that for carbon aerogel of surface area 412 m2 g−1 (type A), 77% of the surface area is attributed to micropores (<2 nm) and only 23% to mesopores (2–50 nm). On the other hand, 85% of the surface area is attributed to micropores and only 15% to mesopores for carbon aerogel type B. These results indicate that the difference in surface area between these two types of carbon aerogels is due mainly to the micropores, as also illustrated in Fig. 2. Therefore, the carbon aerogel with

[5]

where K is a constant for a given system. In Eq. [5], the solution concentration and the exponential of the potential difference show a linear relationship. The potential difference used in this work is represented by the sum of φecm and σ0 /C1 , as shown in Eq. [4]. The value of φecm is also affected by the salt concentration and cannot be assumed constant when specific adsorption occurs (18). This behavior is because when an anion is specifically adsorbed, the presence of anions near the surface will tend to drive electrons back into the electrode, and in order to restore the electroneutrality it is necessary to give the electrode a more negative polarization. As the activity of that ion in the aqueous solution is increased, the tendency to adsorb is increased and further negative polarization is required. In order to include the effect of specific adsorption in the model, it is necessary to determine the value of φecm as a function of solution concentration. Because φecm is part of the potential difference, an assumption is, therefore, made that the relationship between the solution concentration (c) and φecm is

FIG. 2. Pore size distribution of carbon aerogel types A and B (specific surface areas of 412 and 602 m2 g−1 , respectively).

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YING ET AL.

higher surface area may not result in higher electrosorption capacity due to the effect of electrical double-layer overlapping in the region of micropores. Based on the characterization experiments, no macropores were found in the carbon aerogel material. The detailed pore size distribution for carbon aerogel obtained from the characterization studies is used in the electrical doublelayer model developed in this work to estimate the total capacity of electrosorption. Measurements of surface potential and electrical capillary maximum. Surface charge density measurements were obtained from potentiometric titrations. The point of zero charge (pzc) is at pH 9.2, and the surface charge increases with decreasing pH. The surface charge density found for the carbon aerogel surface is very small and is comparable to that for activated carbon material (22, 23). This result indicates that the electrostatic force is insignificant when no external potential is applied. Experiments for measuring φecm were conducted at NaF concentrations ranging from 25 to 600 ppm. The value of φecm was determined to be in the range of 0.1 to 0.2 V with respect to one electrode.

FIG. 4. pH 4.9.

Electrosorption experiment using 50-ppm Cu(NO3 )2 solution:

Equilibrium Experiments of Electrosorption The effects on electrosorption of important experimental parameters such as chemical species, solution concentration, and applied voltage were investigated. The effects of specific adsorption and different types of carbon aerogel on electrosorption capacity were examined. Figure 3 shows a typical result of electrosorption of Na+ and F− ions. The conductivity did not drop significantly before the external electric field was applied, which indicates that specific adsorption of Na+ and F− was insignificant. Once the electric field was applied, the solution conduc-

FIG. 3. Typical equilibrium electrosorption experiment using 100-ppm NaF solution: pH 6.9.

tivity decreased rapidly because ions were attracted by oppositely charged electrodes. Also, the current rose sharply right after electric field was applied, indicating transport of charged ions through the solution. After a short period of time, the current was again zero, meaning that the system had reached a new equilibrium state. Furthermore, after the electric field was removed, the conductivity returned to its initial value, demonstrating that electrosorption is a reversible process (i.e., that ions are released back into the solution by the electrodes). As shown in Fig. 3, the solution pH increased very quickly from about 7 to 10 when voltage was applied and then returned to its initial value. This behavior implies that when voltage is applied, OH− ions are released from the electrode surface. Experiments with one-sided carbon aerogel were conducted, with one of the electrodes (anode or cathode) constructed of carbon aerogel and the other of platinum. The solution pH dropped from 7.5 to 6.5 when the carbon aerogel electrode served as cathode, while the solution pH increased from 6 to 9.5 when this electrode served as anode. This result indicates that the change in pH in the electrosorption experiments is controlled by electrode reactions: cathode reactions tend to lower the pH, while anode reactions tend to increase the pH. Effect of specific adsorption. Figure 4 illustrates typical results for electrosorption experiments using Cu(NO3 )2 in which strong specific adsorption was observed. The conductivity decreased significantly before application of the electric field, which indicates that Cu(NO3 )2 ions have strong affinity with carbon aerogel material. Once the electric field was applied, some of the adsorbed ions were released back into solution due to repelling electrostatic forces and then removed by the oppositely charged electrode. After the electric field was removed, the solution conductivity returned to a value corresponding to

23

ELECTROSORPTION OF IONS FROM AQUEOUS SOLUTIONS

Specific Adsorption Capacity Total Capacity at 1.2 V

60

Total Capacity at 1 V

Capacity (µmol/g)

the equilibrium state of specific adsorption. The electrosorption phenomena can be also described by the current change history in Fig. 4. The current change history in this case is different from the result shown in Fig. 3. As shown in Fig. 4, when the electric field was applied, the current rose rapidly and then returned to 0 at a slower rate than the current change shown in Fig. 3. The explanation for this behavior is that significant amounts of specifically adsorbed ions were released from the electrodes when an electric field was applied, which resulted in a longer transport time for the charged ions to move to the oppositely charged electrodes. The same behavior was observed in several experiments with solutions of varying concentrations of Cu(NO3 )2 . From these experiments, it can be concluded that two primary mechanisms of ion removal in electrosorption processes by carbon aerogel electrodes exist: specific adsorption and electrosorption. Additionally, because of the specific adsorption of charged ions on the surface of carbon aerogel, the surface charge density or surface potential of the carbon aerogel material changes. Therefore, the electrical capillary maximum of carbon aerogel cannot be assumed to be a constant. Various chemical species were used in the study of specific adsorption by carbon aerogel electrodes, including NaF, NaCl, NaBr, NaI, and NaNO3 solutions. Table 1 shows experimental results of these ion species at similar initial solution concentrations and under the same operating conditions. The specific adsorption capacity is defined as the quantity of ions removed without an applied voltage (in micromoles per gram of carbon aerogel), and the total capacity is defined as the total quantity of ions removed by the electrosorption process. In all cases, the specific adsorption capacity increased as the solution concentration increased. For F− , Cl− , Br− , and I− , the amount of specific adsorption is relatively small compared to their total capacity. Also, the total capacity of anion removal increases in the order of Cl− , Br− , and I− —probably because the iodide ions have a partial charge-transfer coefficient higher than that of the bromide and chloride ions. The partial charge-transfer coefficient is an indicator of how many electrons can be released from the adsorbate to an adsorbent. In the case of NO− 3 ions, the specific adsorption becomes significant. Because all the solutions have only Na+ ions as cations, it can be concluded that the specific adsorption depends on the affinity of anion species with the carbon aerogel surface. The NO− 3 ions apparently have higher affinity than the other anions used in this study.

40

20

0 50 100 Concentration (ppm)

0

FIG. 5.

150

Effect of specific adsorption on electrosorption of NaNO3 solutions.

Figure 5 shows the experimental results for specific adsorption capacity and total capacity of NaNO3 solutions at various solution concentrations and two values of applied voltages. All capacities (total and specific adsorption) increased linearly with the solution concentration in the range of applied voltage 0– 1.2 V. The specific adsorption in Fig. 5 shows a strong capacity for ion removal (comparable to the total capacity of electrosorption at 1-V applied voltage), which implies that specific adsorption is competitive with electrostatic force. However, at higher values of applied voltage, the total capacity is largely enhanced, which implies that electrosorption becomes the dominant mechanism over specific adsorption. Effect of electrical double-layer overlapping. All the experimental results discussed so far were obtained by using carbon aerogel of surface area 412 m2 g−1 (type A). Type B carbon aerogel has a higher surface area of 602 m2 g−1 . As shown in Fig. 2, the difference in surface areas between these two types of composites is mainly in the micropore region. Figure 6 compares results for electrosorption experiments using NaF solutions for types A and B electrodes at various solution concentrations and at an applied voltage of 1.2 V. Both measured total capacities are increased with solution concentration. Although the surface areas were different, the total capacities were found to be very

TABLE 1 Comparison of Specific Adsorption Capacity and Total Capacity for Different Anions Chemical species

F−

Cl−

Br−

I−

NO− 3

Solution concentration (M) Specific adsorption capacity (µmol/g) Total capacity at 1.2 V (µmol/g)

1.0 × 10−3 3.76 65.63

1.0 × 10−3 3.57 23.75

1.0 × 10−3 3.01 58.79

1.0 × 10−3 3.45 62.62

9.5 × 10−4 9.5 39.8

Solution concentration (M) Specific adorption capacity (µmol/g) Total capacity at 1.2 V (µmol/g)

2.4 × 10−3 5.76 116.2

2.4 × 10−3 15.74 77.14

2.4 × 10−3 10.14 108.1

2.4 × 10−3 24.39 153.8

1.8 × 10−3 25.2 58.6

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YING ET AL.

TABLE 2 Cutoff Pore Width and Available Surface Area for Different Types of Carbon Aerogels and Various Conditionsa (Calculated from the Electrical Double-Layer Model)

160 Type A Type B

80

40

0 0

100 200 Concentration (ppm)

Cutoff❛ width (A)

Available surface area (m2 /g)

Type A carbon aerogel (ppm NaF) 100

7.3

205.1

Type B carbon aerogel (ppm NaF) 64 100 134 258

8.0 7.3 6.8 6.4

165.9 175.6 192.0 216.4

a

300

400

FIG. 6. Comparison of the total capacity of NaF solutions for type A (412 m2 g−1 ) and type B (602 m2 g−1 ) carbon aerogel electrodes at 1.2 V.

close at various concentrations. This behavior is attributed to the electrical double-layer overlapping effect in the micropore region. Because a large portion of the pore ❛size of 602 m2 g−1 (type B) carbon aerogel is located below 10 A , a strong electrical double-layer overlapping is expected. The effect of electrical double-layer overlapping can be also described by Eq. [2]. In this equation, the square root of the bracketed expression is not always positive. Due to overlapping of the electrical double layers, the surface charge density falls quickly with a decrease of pore width w. A specific width wm exists at which the bracketed value on the right-hand side of Eq. [2] approaches zero, which means that the surface charge density becomes zero as well. It was concluded that it is impossible to allow counterions to move in a pore of width less than wm (i.e., the electrical double layer exists only for pore widths width is quite significant since larger than wm ). This cutoff pore ❛ its size may vary from 5 to 50 A , depending on the diffuse-layer potential and the Debye–H¨uckel constant κ. The results shown in Fig. 6 are therefore reasonable because these micropores do not contribute to electrosorption. The electrical double-layer model has been successfully used to describe electrosorption of NaF solutions by carbon aerogel of surface area 412 m2 g−1 (type A) without specific adsorption (16). In this case, the two model parameters, the inner-layer capacitance C1 and the electrical capillary maximum φecm , were assumed to be constants and have the values of 20 µF cm−2 and 0.13 V, respectively. As shown in Fig. 6, the effect of electrical double-layer overlapping on the total capacity can be further illustrated by examining the cutoff pore width calculated from the model. By definition, the largest pore size having zero capacity is the cutoff pore width. The physical importance of this parameter is that—because of the strong overlapping effect—any pore of smaller width does not contribute to the effective surface area

Applied voltage = 1.2 V, C1 = 20 µF/cm2 , and φecm = 0.13 V.

available for electrosorption. To demonstrate the overlapping effect, Table 2 lists the cutoff pore width and available surface areas of the two types of carbon aerogel at various solution concentrations. The cutoff pore width and available surface area are shown to be similar for the two types of carbon aerogel, and for this reason, they have similar total capacity. Also, for a given applied voltage, the cutoff width decreased as the concentration increased. This phenomenon was attributed to the compression of the electrical double layer under higher ionic strength, which leads to a higher total capacity. Comparison between Modeling Results and Experimental Data Electrosorption without specific adsorption. Modeling results and experimental data for NaF at various applied voltages for type A carbon aerogel (412 m2 g−1 ) are compared in Fig. 7. The model that includes overlapping correction describes well 250 Experimental Data

200 Total Capacity (µmol/g)

Total Capacity (µmol/g)

120

Modeling Results

150

100

50

0 0

0.5 Voltage (V)

1

1.5

FIG. 7. Total capacity as a function of applied voltage for 400-ppm NaF solution: C1 = 20 µF/cm2 ; φecm = 0.13 V.

ELECTROSORPTION OF IONS FROM AQUEOUS SOLUTIONS

25

of the electrode surface, while the increase of total capacity becomes larger as the value of applied voltage is increased. Electrosorption with specific adsorption. In the preceding discussion, the electrical capillary maximum is assumed to be constant for the case of insignificant specific adsorption. This assumption, however, is not valid when specific adsorption becomes significant as, for example, in the case of electrosorption of NaNO3 and Cu(NO3 )2 . As discussed above, once charged ions are adsorbed by the electrode surface, the surface charge density, as well as the value of φecm , is changed. A relationship between φecm and solution concentration is established in Eq. [6], where the constants, K 1 and K 2 , can be determined from experimental data. Experimental results of electrosorption of NaNO3 by using carbon aerogel of surface area 412 m2 g−1 were used in combination with modeling results to find the values of φecm that best describe the data at an applied voltage of 1.2 V and varied solution concentrations. The relationship between φecm and solution concentration is then obtained for NO− 3, φecm = −0.087 ln(c) + 0.5647,

[7]

FIG. 8. Comparison of modeling results and experimental data for type B carbon aerogel (surface area = 602 m2 g−1 ) using NaF solution at various concentrations and different values of applied voltage: C1 = 20 µF/cm2 ; φecm = 0.13 V.

where φecm is measured in V and c in parts per million. Equation [7] was used in the electrical double-layer model to predict the electrosorption data for NaNO3 solutions at various values of applied voltage and solution concentration. As shown in Fig. 9, the measured and calculated total capacities both show

the experimental data obtained up to a maximum voltage of 1.4 V, indicating that this model captures the basic phenomena during electrosorption by porous electrodes. If the overlapping effect is not taken into account, all pores will contribute to the total capacity of electrosorption and the model will overestimate the total capacity. Both experimental and modeling results shown in Fig. 7 indicate that the electrosorption capacity did not increase significantly at low applied voltage (<0.6 V) and that it then increased rapidly when the applied voltage was increased from 0.6 to 1.4 V. The finding that the electrosorption capacity does not increase with voltage in the lower range is attributed to the electrical capillary maximum (φecm ) of the carbon aerogel composite. From the φecm measurements, the value of φecm was determined to be between 0.1 and 0.2 V with respect to one electrode, or between 0.2 and 0.4 V with respect to the applied voltage. The electrostatic driving force is used to balance the φecm voltage until the applied voltage increases beyond 0.4 V. Bubbles were also produced as the applied voltage was increased above 1.4 V. For the carbon aerogel of 602 m2 g−1 surface area, the same model parameters, C1 = 20 µF cm−2 and φecm = 0.13 V, were used to verify the electrical double-layer model at various concentrations and applied voltages. A comparison of modeling results and experimental data for NaF concentrations ranging from 25 to 250 ppm and for applied voltages from 0.6 to 1.2 V is shown in Fig. 8. A logarithmic relationship between total capacity and solution concentration is observed. The total capacity of carbon aerogel was found to increase with an increase in the solution concentration or applied voltage. The rate of increase is slower at higher solution concentration due to the saturation

FIG. 9. Comparison of experimental data and modeling results for electrosorption of NaNO3 at various concentrations and different values of applied voltage. For modeling results in which specific adsorption is considered, φecm is treated as a function of solution concentration (see Eq. [7]). For the results in which specific adsorption is not considered, φecm remains constant (0.13 V) and C1 = 20 µF/cm2 .

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YING ET AL.

40 Experimental Data Modeling Results

Total Capacity (µmol/g)

30

20

10

0 0

20 40 Concentration (ppm)

60

80

FIG. 10. Comparison of experimental data and modeling results for electrosorption of Cu(NO3 )2 at various concentrations and at applied voltage of 1.2 V: φecm is a function of solution concentration (see Eq. [7]); C1 = 20 µF/cm2 .

a linear increase with solution concentration. The modeling results that included the effect of specific adsorption are also in good agreement with experimental data under various conditions. In addition, this figure indicates that when the effect of specific adsorption (dotted line) is not considered (i.e., φecm remains constant at 0.13 V), the model overestimates the total capacity. Figure 10 compares modeling predictions that considered specific adsorption with electrosorption experimental data for Cu(NO3 )2 . As observed before, the total capacity increased with solution concentration. Also, by using the same relationship between φecm and solution concentration as shown in Eq. [7], the modeling results agree well with the experimental data. The comparisons of experimental data and modeling results with and without specific adsorption indicate that the model can be used to describe the total capacity of the electrosorption processes by carbon aerogel for a given set of operating conditions. CONCLUSIONS

This article investigates electrosorption of ions from aqueous solutions by carbon aerogel. Carbon aerogel has been shown to be an ideal material for an electrode because of its low electrical resistivity and large surface area. Electrosorption by carbon aerogel has several advantages over existing techniques (e.g., ion exchange, evaporation, and reverse osmosis), including ease of regeneration, reduced secondary waste, and energy savings. Experimental and modeling studies were conducted using two types of carbon aerogel, varying solution concentrations, different chemical species, and various values of applied voltage to provide a better understanding of the electrosorption mecha-

nisms by porous materials. In all cases, the adsorption capacity of the carbon aerogel electrodes increases with increasing solution concentration, applied voltage, and available surface area of the electrodes for adsorption. Experimental results indicated no significant specific adsorption of F− ions by carbon aerogel, while strong specific adsorption was observed for NO− 3 and Cu2+ ions. When specific adsorption occurs, it becomes competitive with electrosorption and affects the surface potential of the electrodes. An electrical double-layer model that includes the effect of electrical double-layer overlapping and specific adsorption was developed to predict electrosorption. Unlike the traditional approach, which considers the total surface area of the material available for electrosorption, the present study considers the pore size distribution of the electrode material. Since carbon aerogel consists mainly of micropores and mesopores, the effect of the electrical double-layer overlapping becomes significant and must be considered. The modeling results indicated that when the pore size is smaller than the cutoff pore width, the electrical double layers disappear because of the overlapping effect. Therefore, these pores do not contribute to electrosorption. The experimental results demonstrated that the total capacities for two types of carbon aerogel electrodes that have different surface areas are very similar because of the electrical double-layer overlapping effect in micropores. A strong specific adsorption of cupric and nitrate ions by carbon aerogel was observed. The surface potential is changed significantly when specific adsorption occurs, and its value depends on the solution concentration. The effect of specific adsorption is therefore included in the electrical double-layer model by employing a relationship between surface potential and solution concentration. Modeling results were compared with experimental data for electrosorption obtained under various conditions. When the overlapping effect and specific adsorption were considered, a good agreement between modeling results and experimental data was obtained. ACKNOWLEDGMENTS Support for this research was provided by the National Science Foundation through a Career Award (BES-9702356 to S.Y.), and by the Environmental Management Science Program, Office of Environmental Management, and the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC. The authors acknowledge partial support of this project by the Georgia Institute of Technology Molecular Design Institute, under Prime Contract N00014-951-1116 from the Office of Naval Research. The authors are also thankful to Dr. E. Steven Vittoratos for conducting specific surface area and pore size distribution measurements of the carbon aerogel material and to Dr. Marsha K. Savage for editing the manuscript.

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