Quantitative insight into the effect of ions size and electrodes pores on capacitive deionization performance

Journal Pre-proof Quantitative insight into the effect of ions size and electrodes pores on capacitive deionization performance Pei Shui, Emad Alhseinat PII:

S0013-4686(19)32047-X

DOI:

https://doi.org/10.1016/j.electacta.2019.135176

Reference:

EA 135176

To appear in:

Electrochimica Acta

Received Date: 10 February 2019 Revised Date:

25 June 2019

Accepted Date: 29 October 2019

Please cite this article as: P. Shui, E. Alhseinat, Quantitative insight into the effect of ions size and electrodes pores on capacitive deionization performance, Electrochimica Acta (2019), doi: https:// doi.org/10.1016/j.electacta.2019.135176. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Quantitative insight into the effect of ions size and electrodes pores on capacitive deionization performance Pei Shuia , Emad Alhseinatb,c,∗ a School

of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China of Chemical Engineering, Khalifa University, P.O 127788, Abu Dhabi, United Arab Emirates c Center for Membrane and Advanced Water Technology, Khalifa University, P.O 54224, Abu Dhabi, United Arab Emirates

b Department

Abstract In this work, effect of ions size is combined with the influence of pore size to provide a quantitative simulation method to evaluate CDI desalination performance. The method is capable of simulating the equilibrium and dynamic behaviours of the CDI. The simulation provides instructive observations that are important to enhance the current state of the art in CDI research and facilitate its implantation into industrial scale. For example, the desalination performance of CDI for high salinity water can be enhanced by using electrodes with small pore size (less than 2nm), while electrodes with higher pore size performs better for lower salinity water. From design respective it is therefore recommended to use electrodes with different pore sizes for multi-stage CDI process, as the salinity of water will increase from one stage to another. For electrolyte of a given concentration, the specific desalination capacity increases when the pore size becomes smaller till approach a threshold pore size and then dramatically decreases, particularly this is most severe for high salinity water. Therefore, careful and precise design approach for the electrode pore size is crucial. As ions of smaller volume can accumulate more for the same pore size limit, the analysis inspires us an innovative approach: to enhance the CDI performance through reducing the size of ions by weakening the hydration, which has been ∗ Fax:

+971-(0)2-4472442; Tel: +971-(0)2-4018155 Email address: [email protected] (Emad Alhseinat)

Preprint submitted to Journal of LATEX Templates

November 2, 2019

achieved by employing the electromagnetic wave in our experiments. Keywords: capacitive deionization, electrical double layer, electromagnetic wave, desalination efficiency, ions size, simulation

1. Introduction Water scarcity is one of major problems that limiting social and economic development in the 21st century and universal welfare is being threatened by water shortage. Despite the fact that 71% of the earth’s crust is covered with water, 97% of this water is saline water and only 3% is fresh water. When taking into account that 90% of this 3% fresh water is frozen in glaciers, fresh water can be categorized as an “endangered” commodity and should be considered priceless[1]. Thus, massive effort is being invested in scientific research for developing new desalination technology and enhancing the efficiency of proven ones. The current used desalination technologies i.e. Reverse Osmosis (RO), Electro-Dialysis (ED), Multi-Effect Distillation (MED) and Multi-Stage Flash (MSF) are supporting millions of people surviving everyday. However, these technologies are intense energy consumers and with high carbon foot print[2]. Even though, alternative less energy intensive technologies being developed such as capacitive deionization (CDI)[3, 4] still have several issues related to process efficiency, which have to be resolved before reaching industrial deployment[5]. The CDI was initially introduced as “electrochemical demineralization of water” by Blair and Murphy[6] In late 1960s and the theory behind that was incomprehensively explained by electrochemical reactions, and later it was found the that the primary reason for this electrochemical demineralization is the capacitance of electrodes. The EDL hypothesis was first introduced by Helmholtz[7] and used to explain this capacitive mechanism and later improved by Stern[8] with the widely-accepted “Gouy-Chapman-Stern” (GCS) model: a compact layer of charge close to the solid surface and a diffuse layer of ions of both signs extend toward the bulk solution[9]. The CDI performance depends on the electrode material properties i.e. sur-

2

face area, pore size and distribution, applied electrical potential and the solution characteristics i.e. concentration and composition[10, 11, 12, 13]. The interactions among aforementioned factors need to be considered carefully for proper optimization of CDI process. Attempts to investigate the effect of electrode material pore structure and size on the EDL development still face challenges, particularly there still have no analytical nor general-reliable approximate solutions been obtained for the EDL on rough or porous surfaces. Despite so, the assumption of flat smooth electrode surfaces was studied thoroughly and significant insights have been obtained[14]. Caudle[15] and Farmer[16] firstly took the credit for reporting the significant influence of average electrode pore size on the ion removal performance[12], and later Yang et al.[17] used the cut-off pore size as the smallest width of the EDL to model its overlapping effect. Kant and Singh provided a series of intensive study to provide generic approach for dealing with capacitance of arbitrary shaped surface and pores[18, 19, 20] and rough electrodes[21]. Noked et al.[22] attempted to study the effect of pore/ion size ratio on electrosorption. An important observation of theirs was that the EDL charging is impeded when the pore dimension of electrode material and hydrated radius of ions are within the same scale. They pointed out that higher ionic strength causes smaller hydration shells and this helps ions to enter into smaller pores. Particularly, when the pore size of the porous structure electrode is very small, the insufficient extension of the EDL will lead to a lower ion adsorption amount compared to the classic GCS model prediction. For strongly overlapped EDL (usually happens in < 2nm micro porous structure), it is suitable to adopt the “Donnan” assumption that assumes a constant electrical potential for the electrolyte inside the micro porous structure of the electrode[23, 24]. However, studies[10, 25, 26] also indicated that a weak EDL-overlapping would bring optimum performance for the CDI process and recommended to use porous electrodes with mesopores. Therefore, it is essential to have fine enough porous structure for sufficient acting surface area, while it is also important to make the porous structure not too small so that weak EDL-overlapping dominants. 3

In further attempt to investigate the interaction between pore structure and ion size, Peng et al.[27] studied the performance of 2D hexagonal space groups and 3D symmetry cubic carbon in removing ions of different size, and reported that a better removal performance for small size ions can be achieved by 2D hexagonal space groups, while the removal performance for large size ions can be achieved by 3D symmetry cubic carbon. These findings emphasis that the pore size distribution, the porous structure, the ions size are all key parameters in CDI performance. In this work, we presented a reliable model that is compatible for different pore size distributions (not limited to < 2nm as m-Donnan model requires), counting for three possible EDL regimes: overlapping regime where the pore is small enough that the EDL in the pore can achieve a complete overlapping, here the entire pore volume is within the EDL region; transition regime where the pore is not small enough, part of the pore volume is out of the EDL region and need to be excluded from the overall pore volume to obtain the actual volume of the EDL region; pseudo-plane regime where the pore structure is so large that can be treated equivalent to a plane with same surface area, hence EDL can develop completely. Furthermore, the effect of ions size is combined with the influence of pore size to provide a quantitative method to evaluate electrode material desalination performance. Hence, novel approach to model the performance of CDI in terms of ions removal and process energy consumption is provided. The thickness of the EDL is calculated with different pore size and match the approximation from the literature[28]. The model is capable of simulating the equilibrium and dynamic behaviours of the CDI and its accuracy was validated through comparison with analytical solutions (once possible), literature data and experimental results. In particular, this model was successfully validated by the cyclic voltammetry(CV) experiments that we used to measure the capacitance of the electrode material. Being able to think and analyse out of the box, electromagnetic treatment was introduced as an effective way to enhance CDI performance. Magnetic treatment of water for preventing or reducing crystallization fouling (scale) build-up 4

has been successfully applied for more than one century [29]. It is believed that electromagnetic wave affects the hydrations shells strength and thus reduce the effective size of the dissolved ions [30]. Our preliminary experiments showed interesting enhancement in the ions removal once electromagnetic wave was introduced to the CDI process. We simulated the CDI enhancement by adopting the size of dehydrated ions with our model, and the result matched with the experimental observation once the magnetic wave was applied. Detail discussion was included in Section 4.3. It has been reported that altering ion hydration shall is possible using an external electromagnetic field. For example, Murad[30] showed that a magnetic field could weaken interactions between water and hydrated ion clusters. Holysz et al.[31] suggested that magnetic field treatment causes changes in the hydrating water structure around ion. It is known that ionic mobility can be enhanced in strong magnetic fields[32]. The effect of magnetic fields on the physicochemical properties of tap water has been investigated recently by Wang et al.[33], who observed a change in evaporation rate and a decrease of specific heat and boiling point after magnetization. Magnetic field has also been shown to affect gas separation behaviour as proved by Karanikolos et. al[34]. However, the mechanism through which magnetic fields influence solvent structures and solvent-solute interactions and gas separation is not yet fully understood so that it can be exploited. Our preliminary studies show that applying a magnetic field can give a promising degree of enhancement of capacitive deionization as presented in this paper. A full compressive study on the effect of electromagnetic radiation on hydration and CDI performance is beyond the scope of this paper and will be published in separate paper.

5

2. Methodology 2.1. CDI process model The transport of ions in low-ionic strength electrolyte under the action of electric field can be described by the Nernst-Planck equation: ∂ci = ~u · ∇ci = ∇ · (Di ∇ci + µi ci Di ∇V ) (1) ∂t Where Di is diffusion coefficient of the ion species and µi is the electrical mobility given by Einstein-Smoluchowski relation[35]: µi =

zi e kB T

. The micro scale process

governed by Nernst-Planck equation is considered to be instantaneous[36], and the velocity ~u in the boundary region is minimal due to the no-slip boundary, hence Eq 1 is simplified to Eq 2: zi e ci Di ∇V = 0 (2) kB T whose solution[37] can be simplified to Poisson-Boltzmann equation which deDi ∇ci +

scribes the equilibrium structure of the diffuse layer in EDL: zi V zi Vbulk + η = ln ci,bulk + + ηbulk (3) Vref Vref where η is the general excess term defining the ions size effect, chemical potential ln ci +

and other effects. For a particular ion species i, ci is the concentration, zi is the charge number. V is the local electrical potential, Vref (= kB T /e) is the thermal reference potential defined by Boltzmann constant kB , operating temperature T , and electron charge e. The footnote bulk represents the variable in the bulk flow region which obeys electroneutral condition. This work mainly focuses on the ions size effect, hence η concludes the “Boublik-Mansoori-Carnahan-Starling-Lelan” (BMCSL) equation of state[38, 39, 40, 41]:   2ξ 3 d3 3ξ 2 d3 3ξ2 di + 3ξ1 d2i + ξ0 d3i η = − 1 + 23 i − 22 i ln (1 − ξ3 ) + ξ3 ξ3 1 − ξ3   2 3ξ2 d2i ξ2 ξ − 5ξ + 2 3 + + ξ1 di − ξ23 d3i 32 2 3 ξ3 (1 − ξ3 ) ξ3 (1 + ξ3 ) 6

(4)

where di is the diameter of ion species i and:

ξj =

X πdj ci i

i

(5)

6

Throughout the CDI process, the Poisson equation should always be satisfied:

∇ · (ε∇V ) = −

X

ezi ci

(6)

V |xdif f = Vbulk

(7)

i

with the boundary condition of EDL:

ε

dV | = −σe = −CSt VSt , dx xSt

Here σ is the surface charge density on electrode with dimension of #/m2 (number of electron charges per unit surface area), ε is the permittivity of the solution. The footnote xSt represents the location of Stern layer (also known as outer Helmholtz plane) where the diffuse layer of EDL starts, and footnote xdif f represents where the diffuse layer of EDL ends. As a practice experience, usually xdif f F = 3xDeb [42] is considered to be distant enough to accommodate the fully developed EDL so that the potential would have almost achieved the electroneutrality condition. xdif f F is a preset limit for the nature extent of the EDL. In this study, the empirical estimation xdif f = xdif f F is adopted when no further restriction (discussed in Section 2.2) applied. xDeb is the Debye length, a natural length scale defined by the ionic strength (I) of the solution[43, 36]: r xDeb =

εkB T , 2I

I=

1X 2 (zi e) ci,bulk 2 i

(8)

Taking anode as example, usually the value of electrical potential in EDL would be dropping while the location becomes farther away from the electrode surface. However, if the pore size is too small (< 2nm), the EDLs would be strongly overlapping. Under such condition, a location can be farther away from one side of the pore surface yet meanwhile closer to the other side. Therefore, it is feasible to assume that the potential in these micropores becomes constant 7

(the m-Donnan model[24]) and the capacitance characteristic in this regime was measured and reported by Largeot, et al.[44] However, aside from strong EDL overlapping, weak overlapping can be triggered if the pore size of the electrode material is not small enough. In such scenario, internal distribution of potential and concentration still exists inside the EDL. Suggested by literature[45], for a micro pore structure simplified as parallel plane, when weak EDL overlapping happens, the xdif f can be estimated as half of the plane distance. One important work in this paper is providing a quantitative method to evaluate the influence of pore size to the electrode material desalination performance. The no overlapping and weak overlapping approximation of EDL can be summarised in the following general definition:

xdif f =

V oldif f ap

(a) EDL overlapping occurred

(9)

(b) EDL fully extended

Figure 1: Evaluating the extent of EDL. The blue area represents the region covered by EDL and the green area represents the bulk region of the solution.

In Eq 9, ap is the surface area of a single pore of the porous electrode and V oldif f is the volume covered by the EDL in each pore. A location is defined to be inside V oldif f when its distance to the closest electrode surface is smaller than the natural EDL extent xdif f F (= 3xDeb ). Figure 1 shows how xdif f is calculated with different pore size.

8

Then, an overall potential balance restriction closures the model:

Vapp = VSt,+ + Vdif f,+ + VSt,− + Vdif f,− + Vmtl

(10)

where Vapp is the operating electrical potential between anode and cathode, VSt is potential drop through the Stern layer and Vdif f is the potential drop through the diffuse layer, both can be obtained with a given σ by aforementioned equations. The potential drop on the anode should be equal to the that on the cathode for 1:1 salt without ion effect due to symmetry, and this symmetry will be broken when size effect of different ions are considered[46]. Vmtl is the potential drop through the bulk region of the solution, which can be analogously described in the form of Ohm’s law and eventually achieves 0 at the steady state of the CDI process:

Vmtl = Vbulk,+ − Vbulk,− =

  0,

steady

 J · (Rbulk + Rele,+ + Rele,− ) ,

processing

(11)

where J is the surface current density, Rbulk is the resistance of the bulk solution region and Rele is the resistance of electrode region (including the EDL in the pore structure and the electrode itself). Define ni as the ion numbers in the molecular formula. For example, for CaCl2 , nCa = 1 and nCl = 2. The ion removal amount per unit surface area (Γi ) can be obtained by integrating the ion concentration difference through the entire domain, and each ion removal amount divides its ni should equal to the removal amount of the corresponding salt molecule per unit surface area (Γ ). By nature, for a salt molecule, no matter Γ is calculated by its anion or cation component, the value is same: 1 Γ = Γi = ni

Z

cathode

(ci − ci,bulk ) dx

(12)

anode

In CDI process, part of the transported electron charge is contributed by the counter-ion adsorption from solution to the EDL, and the other part is

9

contributed by the co-ion expulsion back to solution. Therefore, charge transfer can never 100% contribute to the salt removal. The ratio between Γ and σ is used to describe the efficiency of utilizing the charge to desalinate. For a steady system, this ratio is defined as integral charge efficiency Λ[47], describing the overall charge utilization efficiency. For a processing system, this ratio is defined as differential charge efficiency λ[48], describing the transient charge utilization efficiency at time point t:

Λ=

Γ , σ

λ (t) ≈

λ (t) =

Γ (t + δt) − Γ (t) σ (t + δt) − σ (t)

Γ [σ (t) + δσ] − Γ [σ (t)] δσ

(13)

(14)

Both Λ and λ can be seen as evaluation index for energy efficiency of CDI process. In practice, it may cause huge numerical error when calculating λ by the difference of Γ and σ between neighbouring time steps (especially when the time step is large), hence an artificial perturbation to σ is introduced instead to obtain λ approximately, as shown in Eq 14. By definition, the current in the circuit brings change to the charges:

αaele ·

dσ = Aele · J dt

(15)

In Eq 15, the right hand side is the current travelling through the projection area of electrode Aele , and the left hand side is the overall charges changing rate on acting electrode surface area αaele . It is difficult to directly measure the precise surface area of a porous medium with mesoscale porous structure, therefore BET surface area is used instead[49]. α is the surface acting ratio, defined as the ratio of surface area being actually utilized in the CDI process over the entire BET surface area. Since J would eventually approach to 0 when CDI process becomes steady, the resistance in Eq 11 would not affect the final salt removal amount, but only affect the time and the energy needed to achieve the steady status. As shown in Figure 6, Rbulk , Rele,+ , Rele,− are all related to the device and solution property. Rbulk can be calculated through the device 10

geometry and solution conductivity data, and in this work Rele is assumed to follow the similarity and their resistance is modelled by a ratio β to the Rbulk :

Rele,+ + Rele,− = βRbulk (SOLU T ION, DEV ICE)

(16)

The salt concentration in the device and external container can then be calculated:

V oldev ·

dcbulk = ψf low · (cctn − cbulk ) − Aele · J · λ dt

(17)

dcctn = ψf low · (cbulk − cctn ) dt

(18)

V olctn ·

Here, cctn is the salt concentration in the external container, V oldev is the solution volume of CDI device and V olctn is the volume of the external container. ψf low is the flow rate come out from the external container to the device and Aele · J · λ is the CDI salt removal rate. 2.2. Pore size effect model The specific capacitance of an EDL system cannot proportionally increase with the specific surface area of the electrode material, partially due to the ions size effect. This phenomenon was observed in both CDI and super capacitor researches[50, 49, 51]. Experiment works reported that pore size of 2 ∼ 50nm might be the optimum choice for the EDL capacitance[52, 53], as well as for desalination with CDI[54]. On the other hand, a EDL system with low specific capacitance may still be considered as a good design due to its low charge efficiency[55, 56, 57]. The optimum range of pore size suggested by literature (2 ∼ 50nm) is anyhow too wide. In order to provide quantitative evaluation method for the influence of pore size on material desalination performance, it is essential to first find the relation between the surface area and pore size. The general description is:

aele =

 X V olpore ωpore dpore pore 11

(19)

Here ω is the geometry factor links the volume and area for a pore. Each type of porous material has its own pore size distribution, and abundant research can be found in the porous material research community. When the pore size of the electrode material changes, usually both the surface area per unit mass and the pore volume per unit mass would change. Hence the representative porous material description in this paper is: the overall pore volume V olall is fixed as a constant, and the porous structure is unified with an average pore size dave (which means relation between volume and surface area for each pore is definable). By this definition, it is possible to obtain a direct relation between aele and dave :

aele

V olall =ω , dave

   ω=2    ω=4     ω = 6

parallel cylinder

(20)

sphere

(a) SEM image of micro structure

(b) cylindrical structure example: same overall pore

of ACB material in this work

volume with different pore size and area

Figure 2: Cylindrical structure dominated porous electrode material (ACB) used in this study.

In this work, we have used activated carbon (ACB) material whose micro structure is cylinder dominated as shown in Figure 2a. Therefore ω ≈ 4 is expected in this study. In practice, our experiment measurement shows that the ACB material has about 3.8nm average pore size, 0.68cm3 /g specific volume and 1265m2 /g specific area which consists of 831m2 /g internal and 434m2 /g surface

12

16

7

14

500ppm 1000ppm 5000ppm 6 10000ppm 20000ppm 5 30000ppm

2nm 5nm 10nm 20nm 30nm 50nm

12 xdiff (nm)

xdiff (nm)

8

4 3

10 8 6

2

4

1

2

0

0 5

10

15

20

25

30

0

5000

Effective pore size (nm)

10000

15000

20000

25000

30000

Concentration (ppm)

(a) diffuse layer length vs. effective pore size

(b) diffuse layer length vs. solution concen-

for solution concentration 500 ∼ 30000ppm

tration for effective pore size 2 ∼ 50nm

Figure 3: Diffuse layer length in different situation. The development of xdif f is limited due to the pore size, as shown by the coincident curve in (a) and horizontal bar in (b).

area. Eq 20 is defined for internal structure and ω calculated with 831m2 /g is 4.64, which is very close to the expected value 4. Figure 2b shows how different dp lead to different aele under this relation and the xdif f described by Eq 9 can then obtain a piecewise function:

dp = υdave ,

xdif f

 dp     ω h = xdif f F · 1 −     x dif f F

xdif f F dp

i

dp 2

≤ xdif f F

dp 2

≥ xdif f F

dp 2

 xdif f F

(21)

In Eq 21, the second line of the right hand side is for cylinder structure and each structure should formulate its own transition equation based on Eq 9. According to Eq 21, the xdif f defined by dp refers to three EDL regimes: • Overlapping regime: The pore is small enough, thus the EDL of the pore can achieve a complete overlapping. In this regime, the entire pore volume is within the EDL region, V oldif f = V olp ; • Transition regime: The pore is not small enough, part of the pore volume is out of the EDL region and need to be excluded from the overall pore volume to obtain the actual volume of the EDL region; 13

1

1 xDeb (nm)

10

xDeb (nm)

10

0.1

0.01

500ppm 1000ppm 5000ppm 10000ppm 20000ppm 30000ppm 0

0.2

0.1

0.4

0.6

0.8

1

1.2

1.4

0.01

1.6

500ppm 1000ppm 5000ppm 10000ppm 20000ppm 30000ppm 0

0.2

0.4

Vapp (V)

0.6

0.8

1

1.2

1.4

1.6

Vapp (V)

(a) CSt = 0.2/F 2

(b) CSt = 2.0/F 2

Figure 4: Debye length xDeb vs. allied potential Vapp . The dash lines for Debye length and the solid lines for effective Debye length.

• Pseudo-plane regime: The pore structure is so large that can be treated as equivalent to a plane with same surface area, EDL can develop completely. Considering that internal and external area are both part of the porous structure, apparently the actual effective pore diameter dp should be larger than the measured dave . Hence for ACB material, dp needs another subsidy related to the internal/external area ratio (υ = 1265/831). The final effective pore size for ACB is 5.78nm(= υdave ) for the EDL calculation in this paper. However, this approximation is considering the pore external surface area as part of the cylindrical pore area and has certain shortcomings, especially when the pore size is significant smaller than the Debye length of the system. Hence it is important to first evaluate the potential influence of this approximation by V

f )) [58, 59] to the pore comparing the effective Debye length (= xDeb / cosh( 2Vdif ref

size. Figure 4 demonstrates the xDeb and effective xDeb under different solution concentration and applied potential Vapp . The xDeb itself is Vapp independent while the effective xDeb decrease significantly with increasing Vapp . According to the figure, for the most cases in this paper whose Vapp = 1.2V , the effective xDeb is far less than the pore size of ACB (5.78nm), which makes is acceptable to include external area into internal pore area in terms of effective pore size. 14

Some literatures[21, 20] have provided theory and model work about the effect of surface roughness of the electrode material in CDI process, which can probably strengthen the fidelity of the effect pore size concept further. For cylindrical porous structure material assumed in this study, Figure 3a shows how xdif f varies with different material pore size for given electrolyte concentration, and Figure 3b shows how xdif f varies with different cbulk for given pore size. The result in the figure indicates that: in overlapping regime, xdif f is solely dependent on the pore size and independent of cbulk , and the relation between xdif f and dp in this regime is proportional; in pseudo-plane regime, the EDL extends sufficiently and approach to the preset limit xdif f F , which is independent of pore size, but dependent on electrolyte cbulk ; in transition regime, xdif f gradually switches its developing pattern with enlarging pore size from proportional relation to constant. This transition of xdif f between different regimes summarized by Eq 21 plays a key role in the design practice. Once the relation between dp and xdif f is established, it is possible to predict the desalination performance of different porous structure design. It is important to notice that the target of this paper is not to find a new material description, but to provide a tool to utilize the existing material description. There have been many in-depth studies on the shape and size effect of the porous electrode. Huang suggested a simplified model which assumed all the pores are cylindrical and summarized the effect of the pore size of electrodes to three different pore size regimes by absolute pore size[60]. Kant and Singh proposed a comprehensive approach to implement the general shape and size effect of the electrode by using mean and Gaussian curvatures and theirs fluctuation functions[18, 61]. And those studies are well validated with the experimental work by Simon and Gogostsi[62]. The geometry description of this paper is close to Huang’s assumption with several improvements: first, this paper uses simplified geometric arguments to characterize the shape different pore structures (Eq.20); second, it is obvious that the characteristic od the EDL is better scaled by the Debye length of the system rather than the absolute pore size, hence this paper the three regimes of the CDI process is categorized by 15

Eq.21. 200

500ppm 1000ppm 5000ppm 10000ppm 20000ppm 30000ppm Specific CSt

Cele,m (F/cm3)

150

100

50

0

0

2

4

6

8

10

12

14

16

18

20

Effective pore size (nm)

(a) Relation beween volumetirc capaci-

(b) Volumetirc capacitance vs.

effective

tance and pore size (2r) considering the

pore size by simulation with approximate

morphological comlexity[18]

condition in Kant and Singh’s work[18]

Figure 5: The relation between volumetric capacitance and pore size predicted by (a) Kant and Singh’s model (b) This paper.

Though the approach in this paper over-simplified the shape and size effect of the electrode pore structure, it is still capable of capturing the dominant feature of the relation between the capacitance (both salt and electron) and the pore size, and obtain certain similarity to more comprehensive model. Figure 5a comes from Kant and Singh’s work[18], which predicts the relation between the volumetric capacitance of the electrode material and the pore size. Figure 5b is a simulation work with method in this paper, and the configuration is modified to approximate Figure 5a (CSt = xSt /εSt ≈ 0.15625F/m2 , the relative permittivity of solution is 38, details in the literature[18]). Despite the model difference, both figures demonstrate similar curves in pore size range 2nm ∼ 20nm. This pattern for capacitance curve with pore size was confirmed by multiple researches[19, 62, 63]. This capacitance determined by the pore size is a major contributor of the salt removal capacity for a CDI system, but not the sole factor. The charge efficiency[47], on the other hand, determines how many percentages of the electrical capacitance can be utilized in the salt removal, the detail is discussed in Section 4 of this paper.

16

The simplicity and compatibility of the model in this work makes it possible to study the synergies of the electrode pore structure and ion-size effect. However, an in-depth work employing more sophisticated models with detailed and generic description to the pore structures can definitely reveal further insights in the future, especially for the combination effect of the electrode structure and ion size in electrode with bimodal porosity[20]. 2.3. Experiment setup

(a) circuit of a typical CDI process

(b) our laboratory CDI experiment setup

Figure 6: The CDI system based on EDL theory in this study.

Figure 6 shows the circuit of a typical CDI process and our laboratory CDI experiment setup, which consists of CDI unit cell, power supply and conductivity monitor. The CDI cell consists of two parallel electrodes that are assembled with a 3mm gap between the electrodes. The CDI experiments were configured in batch mode and were carried out at 25 ± 1◦ C, by maintaining the total volume (100mL) of the aqueous feed (600mg/L NaCl) constant throughout the desalination-regeneration cycles. The desalination efficiency of the CDI setup was studied at optimum DC cell potential of 1.2V and flow rate of 10mL/min. In the batch mode configuration, the aqueous NaCl solution was continuously circulating in a closed loop, while the conductivity of the solution was constantly monitored (by SevenCompact, Mettler Toledo), until the saturation condition was reached.

17

3. Model Validation 3.1. Verification with theory For ideal monovalent salt solution without ions size effect, analytical solution exists[48]:

σ = 4cbulk · xDeb · sinh

CSt (0.5Vapp − Vdif f ) Vdif f = 2Vref e

Γ = 8cbulk · xDeb · sinh2

Vdif f , 4Vref

Λ = tanh

Vdif f 4Vref

(22)

(23)

Therefore, it is possible to verify the simulation method with this ideal problem[64]. Models with and without ions size effect are compared with the analytical solution, in order to check if and when the ions size effect would be significant. In the following figures (Figure 7, 8), the symbol plots are analytical solutions (solved by simple iterations) and line plots are obtained by solving discretized equations of Eq 6 in the one-dimensional control domain (xSt → xdif f ). The dash lines represent simulation results without ions size effect and the solid lines represent simulation results with ions size effect (with same diameter 0.7nm for both anion and cation). In all the figures the dash lines agree very well with the point plots. Figure 7 shows how surface charge density σ and integral charge efficiency Λ develop with increasing operating electrical potential Vapp . The CSt used is 0.2F/m2 in Figure 7a and 2.0F/m2 in Figure 7b. In both case the cbulk is 10mM and remains constant (means infinite supply from the external container). The result in Figure 7b also agrees well with the GCSCS model[65] result in the literature[37] (The GCSCS model is a simplified version of BMCSL model used in this paper: it considers all the ions in the solution are of the same size). It is obvious that the ion concentration in the EDL will increase when CSt or Vapp increases, together with an increasing ions size effect as a counter effect for the ions accumulation. This increasing ions size effect is confirmed by the larger deviation between different simulation models in the figures. An important

18

1

0.8

0.8

0.6

0.6

0.4

0.4

Λ

σ (#/nm2)

1

0.2

0.2

σ Λ

0 0

0.2 0.4 0.6 0.8

1

0

1.2 1.4 1.6

Vapp (V) (a) CSt = 0.2/F 2

7

1

6

0.8

4

0.6

3

0.4

Λ

σ (#/nm2)

5

2 1

0.2

σ Λ

0 0

0.2

0.4

0.6

0.8

1

1.2

0 1.4

1.6

Vapp (V) (b) CSt = 2.0/F 2 Figure 7: Verification between theory and simulation with varying applied potential Vapp and fixed cbulk = 10mM . Blue plots: surface charge density σ. Red plots: integral charge efficiency Λ. Symbol: Theoretical prediction (no ions size effect); dash line: simulation prediction (no ions size effect); solid line: simulation prediction (with ions size effect).

19

1.2

0.6 0.55

1

0.5 Γ (#/nm2)

Cdl (F/m2)

0.8 0.6 0.4

0.45 0.4 0.35 0.3

Theory (no ion size) Simulation (no ion size) Theory (ion size)

0.2 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Theory (ion size) Simulation (no ion size) Simulation (ion size)

0.25 1.8

0.2

2

0

50

CSt (F/m2)

100

150

200

cbulk (mM)

(a) Relation between Cdl and CSt , Vapp = (b) Relation between Γ and cbulk , Vapp = 1.2V , CSt = 0.2/F 2 .

1.2V , cbulk = 10mM .

Figure 8: Relation among Cdl , CSt , Γ with the ions size effect ions. Symbol: theoretical prediction (no ions size effect); dash line: simulation prediction (no ions size effect); solid line: simulation prediction (with ions size effect).

suggestion extracted from Figure 8a is: at Vapp = 1.2V and cbulk = 10mM , when CSt drops from 2.0F/m2 to 0.2F/m2 , the overall ions size effect decreases from almost 50% to around 5%, and is expected to be even less significant when CSt drops further. On the other hand, as shown in Figure 7, once CSt is settled, the red plots would not differ too much to each other, means that Λ would not intensively been affected by the ions size effect, and tends to solely dependent on Vapp . The deviance of Λ between with or without ions size effect is no more than 5% for both 0.2F/m2 and 2.0F/m2 cases. The results also suggest that higher CSt and Vapp can provide better energy efficiency. It is important to notice that the model input parameter is the Stern layer capacitance CSt , while the capacitance measured by experiment or provided by manufacture is the overall EDL capacitance Cdl of the material :

Cdl =

CSt VSt VSt + Vdif f

(24)

Therefore, it is essential to estimate CSt from the given Cdl before the simulation. Usually CSt is just slightly larger than Cdl . Using CSt as an initial estimation, a series of bisection calculations would approach Eq 24. Figure 8a

20

shows the relation between CSt and Cdl at Vapp = 1.2V and Cbulk = 10mM . This figure presents the increasing influence of the ions size effect with increasing CSt . It suggests when dealing with relatively large CSt (> 0.4F/m2 ), neglecting the ions size effect may cause significant error. Figure 8b shows how Γ changes with increasing cbulk with fixed Vapp = 1.2V and CSt = 0.2F/m2 . The result suggests when the electrolyte becomes denser, the desalination performance degrades. If the ions size effect is neglected, the degradation is not very obvious (Γ decreases less than 10% when cbulk increases from 10mM to 200mM ). If the ions size effect is included, the degradation is strengthened to almost 40%. Considering the result suggested by Figure 8a, an even stronger degradation can be expected if CSt increases further. 3.2. Validation with experiment Experiment Setup

Electrode type

CAG

Electrode dimension

115 × 55mm2

Electrode mass

2 × 0.7g

Gap between electrodes

3mm

Specific capacitance

30F/g

Electrolyte solute

NaCl

Specific surface area

600m2 /g

Electrolyte concentration

600ppm

Electrode type

ACB

Electrolyte flow rate

10mL/min

Electrode mass

2 × 0.3g

External container volume

46.47mL

Specific capacitance

251.3F/g

Electrical potential

1.2V

Specific surface area

1265m2 /g

Table 1: Experiment information sheet

In this section the simulation procedure was validated by experiments with the setup shown in Figure 6b. The electrode material (Figure 9) of one experiment was commercial carbon aerogel (CAG) , which was used in many studies[17, 66, 67], the other one was our lab-made activated carbon from leaf base of date palm (ACB) [68, 69]. The experiment configuration and electrode information are listed in Table 1. The CSt was 0.058F/m2 for CAG and 0.234F/m2 for ACB, which was calculated by the specific capacitance in Table

21

1 and Eq 24. The hydrated diameter of ions is 0.716nm for Na+ and is 0.664nm for Cl – [70].

(a) CAG electrode

(b) ACB elcetrode

Figure 9: Photos of electrodes used in this study.

In the experiment, the salt concentration was obtained by measuring the conductivity of the electrolyte in the external container. The specified desalination capacity Γm was defined as the salt mass adsorbed by the CDI device over the electrode mass (sum of anode and cathode). The salt adsorption amount was calculated based on the concentration change. For CAG electrode, the Γm reported by experiment was 3.42mg/g. If processed without any fitting (assuming 100% utilisation of surface area), the simulated Γm would be 3.59mg/g without ions size effect and 3.53mg/g with ions size effect. This suggested that the surface acting ratio α in Eq 15 for the CAG electrode was about (3.42/3.59 ≈)95.1% without ions size effect and (3.42/3.53 ≈)96.9% with ions size effect. The specific capacitance of CAG provided by manufacture was small, means the ions amount was also few, hence the difference caused by ions size effect should not be significant, as reported in Figure 7. The resistance ratio β can be determined by the time to achieve steady status, which ws about 30 for CAG electrode. By implementing the model parameters α and β the comparison between experiment and simulation matches almost perfectly, as shown in Figure 10a. For ACB electrode, as shown in Table 2, the Γm reported by experiment was 9.89mg/g. The simulation analysis suggested model parameters of α ≈ 73.9% without ions size effect and α ≈ 94.5% with ions size effect and β ≈ 2. The

22

600

4 3.5

580

cbulk (ppm)

560 Salt concentration Exp Salt concentration Sim Salt removal Exp Salt removal Sim

540 520

2.5 2 1.5

Γm (mg/g)

3

1 500

0.5

480 0

0 20 40 60 80 100 120 140 160 180 Time (min) (a) CAG electrode

600

12

580

10

560 Salt concentration Exp Salt concentration Sim Salt removal Exp Salt removal Sim

520 500

6

Γm (mg/g)

cbulk (ppm)

8 540

4

480

2

460 0

20

40

60

0 80 100 120 140 160 180 Time (min)

(b) ACB elcetrode Figure 10: Validation between experiment and simulation by comparing the desalination process with time. Blue plots: specific salt removal capacity(mg salt per g electrode mass). Red plots: electrolyte concentration in ppm. Symbol: experiment measurement. Solid line: simulation prediction. The raw data measured in the experiment is the conductivity of the solution and then converted to the NaCl concentration.

23

CAG

ACB

Γm (mg/g)

3.42

9.89

α (no size effect)

95.1%

73.9%

α (size effect)

96.9%

94.5%

β

30

2

removal time (min)

∼ 160

∼ 40

Table 2: Validation result of CAG and ACB

specific capacitance of ACB reported by experiment was much larger than CAG, hence the ions size effect should be relatively significant, which was confirmed by the much larger α difference. The smaller β suggested a less resistance of ACB electrode than CAG electrode, which was also a fact. The ACB case also achieved good agreement between experiment and simulation. However, the desalination performance of the ACB electrode was obviously worse than its measured parameters indicate: the specific capacitance of ACB was (251.3/30 ≈ )8.38 times larger than CAG, yet the Γm was only (9.89/3.42 ≈)2.89 times larger. This obviously could be explained by the pore and ions size effect of the different cases. The length of fully developed EDL (xdif f F ) was about 8.93nm for this validation case. For CAG electrode, the average pore size provided by manufacturer was about 80nm( 8.93nm), and for ACB electrode the effective pore size was only 5.78nm(< 8.93nm). The pore size of ACB leads to a severe EDL overlapping and consequently weaken its desalination performance. 3.3. Validation of dynamic process In this section the model’s compatibility to dynamic charging/discharging cycles of the CDI process was tested. Two different working mode were tested to evaluate the simulation method comprehensively. For the CDI process shown in Figure 11a,the adsorption-desorption behaviour of CDI cells was studied for more than 3 cycles using a constant-voltage charging method[71]. In this case, the conductivity reading of the external electrolyte container was monitored in real time. Due to the desalination, the conductivity reading continuously 24

decreased. The power supply would be switched off when the conductivity reading dropped to 330µS/cm and let the salt concentration recover, then the power supply would be switched on again once conductivity reading climbed to 380µS/cm and then a new cycle of desalination started. This periodic process was carried on for several cycle and its time developing result was compared to the simulation output with same configuration. The green cycle point in Figure 11a was from experiment data and the red line was from simulation. In the comparison, a different pattern happened for the initial cycle due to establishment of the EDL, therefore the comparison should start at the end of first half cycle (t ≈ 25s in Figure 11a) instead of beginning. In Figure 11b, the cyclic voltammetry (CV) process used to measure the capacitance of the ACB material was reproduced by simulation. CV is a widely accepted electro analytical method to study electrochemical properties of an analyte in solution. We used a three electrode system in CV experiments. The working electrode was covered by ACB, the reference electrode was Ag/AgCl. At the beginning of a CV experiment, the potential (measured between the working electrode and the reference electrode) grew linearly versus time till a preset value, and then the potential reduced linearly to the initial value. Hence the voltage input was a triangular wave with scan rate of constant magnitude, the maximum potential change was called potential window (0.8V in this study), and the current was measured between the working electrode and the counter electrode. In the simulation, the anode and the cathode worked as a symmetric pair, hence half of the simulation domain are adopted to compare with the experiment measurement. We plot the Current density the ACB electrode against the potential for both simulation (solid lines) and experiment (dash lines) in Figure 11b. The scan rate of the voltage varies from 10mV /s to 500mV /s. If the system was a pure capacitor, a rectangular graph would be presented in the plot; if the system was a pure resistor, the plotting would decline to the diagonal. Once the model constants were calibrated by one set of the experiment data, e.g., scan rate 10mV /s in this study, the simulation can successfully capture all those 25

180 Experiment Simulation Volume Effect 175

Concentration (ppm)

170 165 160 155 150 145 0

20

40

60

80

100

120

140

160

180

Time (min)

(a) Charging/discharging process with CAG electrode. Symbol: experiment measurement of the salt concentration; line: simulation prediction. The simulation was given the same solution and potential conditions as the experiment. 120 90

Current density (A/g)

60 30 0 -30

10 mv/s 50 mv/s 100 mv/s 200 mv/s 300 mv/s 400 mv/s 500 mv/s

-60 -90 -120 -0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

Potential (V vs. Ag/AgCl)

(b) CV process with ACB electrode of different scan rate. The simulation is plotted in solid line and the experiment is plotted in the dash line, same colour represents same scan rate.

26

Figure 11: Validation of dynamic charging/discharging process.

capacitive and resistive features as well as experiments for all the rest sets (scan rate 50mV /s ∼ 500mV /s) without changing model constants any more, which offered a strong evidence for the validity of the model.

4. Result and discussion 4.1. CDI performance of different pore size without ions size effect 40

30 25

0.4 0.35 0.3 ν (mg/J)

35

Γm (mg/g)

0.45

500ppm 1000ppm 5000ppm 10000ppm 20000ppm 30000ppm

20 15

0.25 0.2

500ppm 1000ppm 5000ppm 10000ppm 20000ppm 30000ppm

0.15

10

0.1

5

0.05

0

0 5

10

15

20

25

30

5

Effective pore size (nm)

10

15

20

25

30

Effective pore size (nm)

(a) specific desalination capacitance Γm vs.

(b) energy efficiency ν vs. effective pore size

effective pore size at given cbulk

at given cbulk

40

25

2nm 5nm 10nm 20nm 30nm 50nm

0.45 0.4 0.35 ν (mg/J)

30 Γm (mg/g)

0.5

2nm 5nm 10nm 20nm 30nm 50nm

35

20 15

0.3 0.25 0.2 0.15

10

0.1

5

0.05

0

0 0

5000

10000

15000

20000

25000

30000

0

5000

10000

Concentration (ppm)

15000

20000

25000

30000

Concentration (ppm)

(c) specific desalination capacitance Γm vs.

(d) energy efficiency ν vs. cbulk at given

cbulk at given effective pore size

effective pore size

Figure 12: Desalination performance of ACB electrode, neglecting ions size effect.

In this section, the desalination performance was studied without considering the ions size effect. The amount of desalination can be evaluated through the specific desalination capacity Γm , which is determined by Cdl and integral charge

27

efficiency Λ, both affected by dp . Therefore it is possible to build relation curves between Γm and dp , as shown in Figure 12a. Here dp is 5.78nm for the ACB made in our lab, and can be extended to other possible value by by Eq 20 and Eq 21 with aele and xdif f changed simultaneously. In this work the effect of different electrolyte concentration was studied in detail, from very dilute one (500ppm), to sea water level (∼ 30000ppm). Several important pattern can be found from the Γm curves. When the pore size was relatively large, Γm was smaller for higher cbulk , this meant the CDI process would have worse performance when dealing with higher salinized water. The reason behind this phenomenon was: the system was working in the pseudo-plane regime where the EDL develops completely. The length of a completely developed EDL (xdif f F ) is reciprocal to the ionic strength I, which is a representative for the cbulk (Eq 8). Therefore a higher cbulk would cause a narrower EDL and lead to a poorer desalination ability. When the pore size was very small, Γm was larger for higher cbulk . As mentioned before, the xdif f F is reciprocal to the cbulk . When the pore size was small, it may be still large enough to accommodate the fully developed EDL of a highly salinized water, but cannot provide enough space for a wider EDL of less salinized water. Therefore in case of small pore size material, the higher salinity, the less suffering from the EDL overlapping, and the better desalination ability. On the other hand, for electrolyte of a particular concentration, when the pore size became smaller, the specific desalination capacity increased till approach to a threshold pore size, and then decreased. This relation was due to the synthetical effect of the surface area and EDL development. The peak value of the Γm , and the pore size to obtain this peak, were both determined by cbulk : a higher cbulk solution gave higher limit for Γm , but in order to achieve that, a smaller pore size was required. The gradient of Γm close to the peak was sharp, especially for higher cbulk solution, therefore careful and precise design approach is crucial. The energy cost of the CDI process can be evaluated by the energy efficiency ν, which is defined as the salt adsorption per unit energy. The energy efficiency 28

is an expression of the integral charge efficiency Λ, thus is dominated by the EDL development, and becomes also a function of pore size and cbulk . ν increased when the EDL overlapped less and maximizes when EDL was fully developed, as shown in Figure 12b. Each particular cbulk determined a corresponding fully extended EDL length xdif f F , higher cbulk solution lead to narrower xdif f F and less requirement for pore size to accommodate it. Therefore higher cbulk solution can achieve its maximum ν at a smaller pore size and be superior at a small range of pore size. However this advantage was limited, as the smaller pore size came with much larger desalination resistance (poor energy efficiency performance), its maximum ν was smaller than that of dilute one. In Figure 12c and Figure 12d the performances of certain pore size (2 ∼ 50nm) were studied with developing cbulk (pore size< 2nm part could be handled by m-Donnan model, it is not the focus of this paper). For pore size= 2nm, as the size was so small that it cannot provide enough space to accommodate the fully developed EDL at even very high concentration, therefore a monotone increasing relation can be observed between Γm and cbulk , as well as ν. For other cases, it was always possible to find a peak in the curve of each pore size, due to the sectioned relation between EDL length and pore size in Eq 21. Taking the green curve (5nm pore size) and cyan curve (10nm pore size) as examples, an important fact can be extracted from the Figure 12c and Figure 12d: a poorer desalination capacity oriented design (10nm worse than 5nm) may come with a higher energy efficiency performance (10nm better than 5nm). 4.2. CDI performance of different pore size with ions size effect The conclusion of last section applied approximately to CDI process with very low capacitance, or the ions size was negligible. The actual situation happens in current desalination practice is CDI process with considerable capacitance and hydrated ions of relatively large size. In such case, the ions size effect cannot be neglected. For NaCl solution in this study, the diameter of hydrated ions was same as the validation. By employing the ions size effect calculated by Eq 5, the new relation for desalination and energy efficiency performance were 29

20

14 12

0.4 0.35 0.3 ν (mg/J)

16

Γm (mg/g)

0.45

500ppm 1000ppm 5000ppm 10000ppm 20000ppm 30000ppm

18

10 8

0.25 0.2

500ppm 1000ppm 5000ppm 10000ppm 20000ppm 30000ppm

0.15

6 4

0.1

2

0.05

0

0 5

10

15

20

25

30

5

Effective pore size (nm)

10

15

20

25

30

Effective pore size (nm)

(a) specific desalination capacitance Γm vs.

(b) energy efficiency ν vs. effective pore size

effective pore size at given cbulk

at given cbulk

18

12 10

2nm 5nm 10nm 20nm 30nm 50nm

0.45 0.4 0.35 ν (mg/J)

14 Γm (mg/g)

0.5

2nm 5nm 10nm 20nm 30nm 50nm

16

8 6

0.3 0.25 0.2 0.15

4

0.1

2

0.05

0

0 0

5000

10000

15000

20000

25000

30000

0

5000

10000

Concentration (ppm)

15000

20000

25000

30000

Concentration (ppm)

(c) specific desalination capacitance Γm vs.

(d) energy efficiency ν vs. cbulk at given

cbulk at given effective pore size

effective pore size

Figure 13: Desalination performance of ACB electrode, considering ions size effect.

(a) desalination capacity design contour

(b) energy efficiency design contour

Figure 14: Design contour of ACB electrode for NaCl of different working concentration and effective electrode pore size. The ions size effect s considered.

30

demonstrated in Figure 13. In the last section, the peak of Γm kept growing while the cbulk increasing when the ions size effect was neglected (Figure 12a). In Figure 13a, when the ions size effect was considered, if the cbulk was not too large (< 10000ppm), the peak of Γm also increased, but the increase amount became less and less when the cbulk increased. When cbulk became too large (20000ppm and 30000ppm), the peak of Γm decreased with the increasing cbulk . The dp to obtain the peak of Γm decreased with the increasing cbulk , which followed similar pattern of the Section 4.1. The profiles in Figure 13 showed several limitations to choose very small pore structure. When the ions size effect was negligible, a very small pore structure can provide significantly higher Γm (Figure 12c) for high concentration electrolyte. However, this advantage would be hugely weakened when the ions size effect need to be considered (Figure 13c). Figure 13d demonstrated another limitation to choose very small pore structure in energy efficiency aspect. When cbulk increased, due to the ions size effect, the energy efficiency of all cases drops significantly comparing to Figure 12d. A very small pore structure can make the energy expense too high for the desalination process. For the ACB electrode based CDI process in this work, considering the ions size effect, a medium size pore structure (5nm), which would not suffer too much from neither pore surface area nor ions size effect, can provide a favourable desalination capacity while also maintaining a reasonable energy efficiency. Figure 14 presented two design contours for the ACB electrode. The colour in the figure represented the result at certain effective pore size (x axis) and electrolyte concentration (y axis). Each curve in Figure 13a can be taken as a y contour in Figure 14a and each curve in Figure 13c can be taken as a x contour. The red zone in each figure was the region with the favoured value. Based on both design contours, it is possible to provide a pore design poor at desalination capacity aspect but good at energy efficiency aspect, or vice versa. The aforementioned discussion demonstrated clearly that an optimised pore design may become very ineffective due to a small design error, or due to the change of cbulk . Therefore it is necessary to examine the design quantitatively 31

and comprehensively in case by case basis. 4.3. CDI enhancement by interfering ions size effect The CDI performance in Section 4.1 was generally better than that in Section 4.2 due to the absence of the ions size effect. This suggested the possibility to improve the CDI process by possible means to decrease the effective ions size. One way we have tried is to use electromagnetic wave to break the hydration of the ions. The CDI experiment setup shown in Figure 6b was equipped with an electromagnetic device which produced an altering frequency magnetic field of a maximum 25mT intensity orthogonal to the water flow. The electromagnetic device was installed in the feed line immediately before the CDI cell. Same experiment procedure discussed in Section 3.2 was followed while electromagnetic waves were generated and interfering with the feed solution. The results presented in Figure 15 showed that applying electromagnetic field in the feed stream enhanced the adsorption capacity of the ACB electrode by 25% compared to the original one. It is believed that the electromagnetic field affects the hydrogen bonding between the water molecules and thus affect ions size and its mobility towards the electrodes[30]. To confirm, the effect of electromagnetic field, different electrode materials were tested. It was found that magnetic field feed stream enhanced the adsorption capacity for all tested electrodes material but with different percentages. The dehydrated diameter of ions[70] used in this study was 0.190nm for +

Na and 0.362nm for Cl – . Interestingly, the enhancement of the magnetic field, found experimentally, agreed perfectly with our model prediction for dehydrated ions as can be seen in Figure 15. This confirmed that ions size along with the electrodes pores size have major role in CDI performance. The design contours for this dehydrated case were presented in Figure 16, which showed the enhancement of Γm and ν under such condition. The peak value was higher and the favoured region was broader than Figure 14. Further work is being carried out in our laboratory to investigate the effect of electromagnetic waves in solute-solvent interaction and its effect in enhancing CDI performance. 32

14

600

12

580 560 Γm: exp normal Γm: exp magnet Γm: sim hydrated Γm: sim dehydrated cbulk: exp normal cbulk: exp magnet cbulk: sim hydrated cbulk: sim hydrated

8 6 4

540 520

cbulk (ppm)

Γm (mg/g)

10

500 480

2

460

0 0

20

40

60

80

100

120

140

160

440 180

Time (min)

Figure 15: Electromagnetic enhanced CDI process: experiment and simulation. Green plots: CDI process under normal condition. Blue plots: CDI process with electromagnetic treatment (experiment) or dehydrated ions condition (simulation). Symbol: experiment measurements. Solid line: specific salt capacity from simulation prediction. Dash line: electrolyte concentration from simulation prediction.

(a) desalination capacity design contour

(b) energy efficiency design contour

Figure 16: Design contour of ACB electrode for NaCl, after electromagnetic treatment. The contours are presented with same legends of Figure 14, the red (preferred) region is much larger, due to much smaller ion size effect.

33

Also, there was non-negligible disparity between experiment and simulation for both cases. Several possible explanations are proposed for this phenomenon. First, our current modelling work is based on the modified Poisson-Boltzmann equation (Eq.3), which assumes that the transition of ion over infinitely small distance takes place instantly, while the real situation can be more complicated that a flow-wise concentration distribution may exist, and will cause lag to the desalination process comparing to the current model. Second, the desalination progress of the CDI experiment was monitored by measuring the conductivity of the solution in the container, and the dilution in the container also needs time, which may cause certain system error.

5. Conclusion This work provided a quantitative method to evaluate the influence of pore size on electrodes material desalination performance, and make it possible to predict the desalination performance of different pore structure design. The model was examined by several complicated charging/discharging CDI process to ensure its validity. The analyses suggested: when the pore size is relatively large, the CDI process will have worse performance when dealing with higher salinized water; when the pore size is very small, the higher salinity, the less suffering from the EDL overlapping, and the better desalination performance. The results suggested that a best desalination capacity optimized electrode design may not always provide the best energy efficiency, but more usually leads to the opposite, as a very small pore structure can make the energy expense too high for the desalination process. Clearly, the current CDI process can be improved by having multi stage processes, and within each stage the bulk concentration varies little so that a certain optimized porous size for this stage can be selected based on the design contour introduced in this paper. Finally, the enhancement of the electrode capacity and overall salts removal due to applying magnetic field was proven by the experiment, and can be well explained by the combining influence of the electrode pores structure and ions size effect. Further study

34

of the detail mechanism of this enhancement can bring notable benefit in both science and application.

Acknowledgement The authors gratefully acknowledge the financial support from Khalifa University for KUIRF L2 project, award No. 8431000012.

Appendix For steady status simulation, the numerical scheme is: • Calculation level I: When Vapp is given, 1 Provide an initial estimate of σ; 2 Calculate VSt from Eq 7; 3 Calculate Vdif f from Eq 6 (Process Calculation level II ); 4 Examine if VSt and Vdif f satisfy Eq 10, if not, update σ and iterate from step 2. • Calculation level II: In this calculation level, Eq 7 is discretized and solved in the diffusive layer. The length of diffusive layer is set to xdif f and the grid numbers is 300 (Figure 17) .The discretization leads to Eq 25 and Eq 26, which can be solved with the boundary condition Eq 27: 0

0

Vn+1 − Vn d2 V dV 0 1X = ≈ = − ezi ci d x2 dx xn+1 − xn ε i V0 =

dV Vn+1 − Vn ≈ dx xn+1 − xn

0 1 Vstart = − σe, ε

Vend = Vbulk

1 Obtain boundary condition Eq 27 from σ; 2 Provide an initial estimate of Vstart at xSt ; 35

(25)

(26)

(27)

Figure 17: Discretized calculation domain for diffuse layer region. The profile is the electrical potential solved discretely, as well as the local concentration of each ion species.

3 Calculate Eq 25 and Eq 26 to obtain Vend (Process Calculation level III ); 4 Examine if Vend = Vbulk , if not, update Vstart and iterate from step 3. • Calculation level III: This calculation level aims to solve the local concentration of ion species i under the effect of general excess term η. In this work, η is used for ions size effect defined by Eq 4. Consider an electrolyte containing i different types of ion, its concentration matrix is:

h c = c1

···

ci

iT

(28)

And it needs to be solved through:

   F (c) =  

f1 .. . fi





ln c1 +

    =   ln ci +

z1 V Vref

zi V Vref

+ η − ln c1,bulk − .. .

z1 Vbulk Vref

+ η − ln ci,bulk −

zi Vbulk Vref

− ηbulk

− ηbulk





    =  

0 .. .

0 (29)

Eq 29 can be solved by Newton’s method:

cnew = cold − Jac−1 [F (cold )] · F (cold )

(30)

Where Jac is the Jacobian matrix of F(c). Iterate Eq 30 until it converges. 36

    

• Dynamic process modification: Here are modifications for simulating the transient problems. 1 In Calculation level I, the σ is given by initial condition; 2 Process Calculation level I with given σ and obtain VSt and Vdif f ; 3 Obtain Vmtl from Eq 10 to Eq 11 by given Vapp and calculated VSt , Vdif f ; 4 Calculate dynamic response through Eq 14 to Eq 18. We notice there were some research also calling Debye length xDeb as the diffuse layer length, which may cause ambiguity. In fact, since the end of diffuse layer is where the solution achieves electroneutrality (the bulk solution), there is no clear boundary for diffuse layer. By experience, xdif f F = 3xDeb is broad enough to accommodate the diffuse layer and is used in this paper. The following figure is the independence test of this xdif f F setting: 0.17

1 0.9

0.16

0.8 0.7 0.6

0.14 Λ

Cdl (F/m2)

0.15

0.13

Analytical 1 xDeb 2 xDeb 3 xDeb 4 xDeb 5 xDeb 6 xDeb

0.12 0.11 0.1

0

0.2

0.4

0.6

0.8

1

1.2

0.5 Analytical 1 xDeb 2 xDeb 3 xDeb 4 xDeb 5 xDeb 6 xDeb

0.4 0.3 0.2 0.1 1.4

0

1.6

0

Vapp (V)

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Vapp (V)

(a) Overall Capacitance Cdl vs. Vapp

(b) Charge efficiencty Λ vs. Vapp

Figure 18: Independency test of xdif f F . xdif f F varies from 3xDeb to 6xDeb . GCS model without ion size effect, CSt = 0.2F/m2 , cbulk = 10mM , no porous structure.

In Figure 18, it is clear that xdif f F = xDeb is problematic and 3xDeb or even larger diffuse layer length provides acceptable results. The Independency of the grid number (= 300) has been examined as well.

37

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