**2. Capacitive deionization**

#### **2.1. Historical background**

In 1960s, the concept of capacitive deionization (CDI) was introduced at the University of Oklahoma by G.W. Murphy as an alternative water treatment method and was called "electrochemical demineralization of water." Activated carbon powder (charged electrode sheets) and flow-through electrode architecture were selected for the first designed CDI system to treat saline water. Carbon electrodes were capable of capturing salt ions as a result of the static electrical force and the physical adsorption [9–11]. Murphy and Caudle combined mass balance and transport equations to obtain a model which described the salt concentration as function of time [12]. It was believed that ion removal is attributed to specific chemical groups present on the surface which are reduced or oxidized (faradaic reactions) and create ionic bond with salts [13].

Evans studied the mechanism of "electrochemical demineralization," which is the CDI process, and carried out the mass balance analysis to explain the fundamental idea behind ion removal. Evans' explanation analysis was similar to Murphy's findings and it was added that the concentration of surface groups determines the salt removal efficiency [14].

However, Murphy's and Evans's classical views on water desalination by porous electrodes are no longer valid and have been replaced by the common electric double layer theory (EDL) which describes the capacitive storage of ions in electrode pores [9, 10].

In 1968, a commercialization study on CDI, a demineralization unit, was initiated by Reid et al. to sustain the CDI process for long-term operation and without losing electrode adsorption capacity over time. Furthermore, it was demonstrated that the CDI unit is effective for the removal of other ions besides sodium and chloride which include calcium, magnesium, sulfate, nitrate and phosphate ions [13].

In 1970s, Johnson et al. [15] proposed a reversible electrosorption model for electrode regeneration by removing the applied electric potential to release the captured ions back to a concentrate flow. Salt adsorption mechanism was investigated to be a result of the EDL theory which was known as "potential-modulated ion sorption." A porous electrode model and electrode charge voltage dependence were developed to conclude that electrode capacity depends on the EDL electrical capacity, the available surface area and the applied cell voltage. Johnson and Newman indicated that CDI is economically feasible only if stable electrodes can be produced [9, 10, 15, 16].

produced from industrial wastes. Hence, improving water purification technologies is impor-

Today, there are numerous water and wastewater treatment technologies that are commercially selected and utilized based on both water feed characteristics and required water product quality. For example, high saline water (seawater) is usually treated in advanced reverse osmosis (RO) membrane desalination plants; a membrane consists of a porous layer of polymeric or metal material that allows the passage of fluid with restrictions to salt particles. Pressure-driven membrane technology has no side pollution effects and requires a small footprint for installation. However, membrane processes require applying low/high pressures to pump water for filtration and thereby increasing energy consumption and water production cost [4–6]. In contrast, low saline water (e.g., groundwater, surface water and brackish water) is better treated with industrial emerging technologies, which are different from membranes to reduce energy costs, such as electrodialysis (ED) and capacitive deion-

In 1960s, the concept of capacitive deionization (CDI) was introduced at the University of Oklahoma by G.W. Murphy as an alternative water treatment method and was called "electrochemical demineralization of water." Activated carbon powder (charged electrode sheets) and flow-through electrode architecture were selected for the first designed CDI system to treat saline water. Carbon electrodes were capable of capturing salt ions as a result of the static electrical force and the physical adsorption [9–11]. Murphy and Caudle combined mass balance and transport equations to obtain a model which described the salt concentration as function of time [12]. It was believed that ion removal is attributed to specific chemical groups present on the surface which are reduced or oxidized (faradaic reactions) and create ionic bond with

Evans studied the mechanism of "electrochemical demineralization," which is the CDI process, and carried out the mass balance analysis to explain the fundamental idea behind ion removal. Evans' explanation analysis was similar to Murphy's findings and it was added that

However, Murphy's and Evans's classical views on water desalination by porous electrodes are no longer valid and have been replaced by the common electric double layer theory (EDL)

In 1968, a commercialization study on CDI, a demineralization unit, was initiated by Reid et al. to sustain the CDI process for long-term operation and without losing electrode adsorption capacity over time. Furthermore, it was demonstrated that the CDI unit is effective for the removal of other ions besides sodium and chloride which include calcium, magnesium,

the concentration of surface groups determines the salt removal efficiency [14].

which describes the capacitive storage of ions in electrode pores [9, 10].

sulfate, nitrate and phosphate ions [13].

tant to secure fresh water for the coming generations [3–6].

ization (CDI) [7, 8].

18 Desalination and Water Treatment

salts [13].

**2. Capacitive deionization**

**2.1. Historical background**

In 1990s, CDI technology captured the attention of scientific scholars and many released publications were about developing an effective carbon electrode with large internal surface area and good conductivity for better water deionization. The summarized timeline of CDI development is shown in **Figure 1** [13].

**Figure 1.** Timeline of scientific developments of CDI, indicating milestones since the inception of CDI in 1960 [13].

#### **2.2. Fundamental concept**

The fundamental concept of CDI technology is simply associated with electrosorption of ions at the surface of a pair of electrically charged electrodes (high porous carbon materials) [17]. The electrosorption phenomenon can be understood by the classical EDL theory which explains the charge-voltage and salt-voltage characteristics of the cell that strongly depends on electrodes properties. Basically, it is approximated that charge transfer along the cell is only attributed to electronic charge (in the carbon electrode) and ionic charge (in the aqueous phase), while surface charge from chemical adsorption/carbon redox chemistry is neglected [18]. In other words, there will be no voltage drop across the EDL if the material is not charged since the two components of charge sum up to zero, and only local voltage differences relative to a reference electrode play a role and not absolute potentials [13, 17, 18].

The concept of the EDL dates back to Helmholtz, in the nineteenth century, who assumed that there should be a condensed layer of counterions that directly compensates the surface charge, meaning that all surface charges are directly charge compensated by countercharges adsorbed to the surface [19]. If this holds, ion/charge transport in CDI would be ideally described by Helmholtz-model which states that one full salt molecule (one cation at the cathode and one anion at the anode) would be removed for every electron transferred from one electrode to the other giving us unity charge efficiency.

Unfortunately, porous CDI electrodes do not condense ions right next to their surface; instead, ions remain diffusively distributed in a layer close to the surface. Hence, Gouy-Chapman (GC) described that there must be a diffuse layer combined by an inner stern (or compact) layer in between the electrodes (the carbon matrix) and the diffuse layer. Structure of the EDL according to the Gouy-Chapman-Stern (GCS) theory for a single planar EDL is shown in **Figure 2** [20–22].

**2.3. Advantages**

planar EDL [13].

ronmentally friendly [29].

Effective water desalination at lower costs is considered as one of the grand technological challenges of the twenty-first century. Common commercial technologies such as reverse osmosis, electrodialysis, thermal distillation and multistage flash distillation have been developed to achieve efficient desalination. However, the latter technologies consume a lot of energy and may not be a cost-effective manner for water desalination. Recently, CDI has gained much attention as a desalination technology alternative for brackish water (which has low or moderate salt content) due to its simple design, low energy consumption, economical feasibility,

**Figure 2.** Structure of the electrical double layer (EDL) according to the Gouy-chapman-stern (GCS) theory for a single

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CDI does not involve membranes and therefore it is a low-pressure process of deionization which does not require energy for pumping water or any other means (except for a fairly low applied voltage). Moreover, CDI stores applied potential as a capacitive energy and one may recover this energy again to further reduce power consumption and operating expenses [27, 28]. In other words, electrode discharge step (regeneration) can be recovered and utilized to charge a neighboring cell (electrosorption) for ion rejection [13]. Possibility of electrode fouling during the desalination-regeneration cycles is relatively low, hence, making this technology more attractive for desalting water. CDI does not have additional contaminants (e.g., chemicals) released from the process which makes CDI technology envi-

From previous discussed advantages, CDI becomes very suitable in providing fresh water and agricultural water with low cost and without pollution [26, 30]. Despite that CDI may not

high efficiency, safety and environmental friendliness [23–27].

Diffuse layer observations show that ion concentrations progressively decay with increasing distance from the surface. The characteristic distance for the counterion concentration and potential to decay by a factor of *e* (~2.7) is known as the Debye length (*λD*). It was estimated that the diffuse layer starts to fade away after 2 or 3 times the Debye length. The Debye length of a sodium chloride (NaCl) solution of 10 mM ionic strength is approximately 3.1 nm at 20°C. GCS theory assumes that there is no overlapping of the diffuse layer extending from one surface with a nearby surface. However, micropores (<2 nm) in activated carbon particles are generally less than the Debye length, thus the EDL overlap situation occurs [13].

Based on the EDL concept, CDI desalination occurs when putting a charged carbon electrode in contact with ionic solution, and then counterions will occupy the electrode-electrolyte interface in the pores inside the carbon particles due to the presence of the Coulomb force which forms the EDL. It should be noted that ions are not only removed by the electrical adsorption, but there will be a contribution from the physical adsorption effect. However, the regeneration step takes place when there is reduction in the applied potential (charge) and/ or reversed polarity which results in the removal of Coulomb force and/or reversing the force effect (i.e., there will be a repulsion force between held ions and charge) and therefore releasing the held ions back to the concentrate solution. Desalination/regeneration steps form one complete CDI treatment cycle [9].

Activated Carbon Cloth for Desalination of Brackish Water Using Capacitive Deionization http://dx.doi.org/10.5772/intechopen.76838 21

**Figure 2.** Structure of the electrical double layer (EDL) according to the Gouy-chapman-stern (GCS) theory for a single planar EDL [13].

#### **2.3. Advantages**

**2.2. Fundamental concept**

20 Desalination and Water Treatment

The fundamental concept of CDI technology is simply associated with electrosorption of ions at the surface of a pair of electrically charged electrodes (high porous carbon materials) [17]. The electrosorption phenomenon can be understood by the classical EDL theory which explains the charge-voltage and salt-voltage characteristics of the cell that strongly depends on electrodes properties. Basically, it is approximated that charge transfer along the cell is only attributed to electronic charge (in the carbon electrode) and ionic charge (in the aqueous phase), while surface charge from chemical adsorption/carbon redox chemistry is neglected [18]. In other words, there will be no voltage drop across the EDL if the material is not charged since the two components of charge sum up to zero, and only local voltage differences relative

The concept of the EDL dates back to Helmholtz, in the nineteenth century, who assumed that there should be a condensed layer of counterions that directly compensates the surface charge, meaning that all surface charges are directly charge compensated by countercharges adsorbed to the surface [19]. If this holds, ion/charge transport in CDI would be ideally described by Helmholtz-model which states that one full salt molecule (one cation at the cathode and one anion at the anode) would be removed for every electron transferred from one

Unfortunately, porous CDI electrodes do not condense ions right next to their surface; instead, ions remain diffusively distributed in a layer close to the surface. Hence, Gouy-Chapman (GC) described that there must be a diffuse layer combined by an inner stern (or compact) layer in between the electrodes (the carbon matrix) and the diffuse layer. Structure of the EDL according to the Gouy-Chapman-Stern (GCS) theory for a single planar EDL is shown in **Figure 2** [20–22]. Diffuse layer observations show that ion concentrations progressively decay with increasing distance from the surface. The characteristic distance for the counterion concentration and potential to decay by a factor of *e* (~2.7) is known as the Debye length (*λD*). It was estimated that the diffuse layer starts to fade away after 2 or 3 times the Debye length. The Debye length of a sodium chloride (NaCl) solution of 10 mM ionic strength is approximately 3.1 nm at 20°C. GCS theory assumes that there is no overlapping of the diffuse layer extending from one surface with a nearby surface. However, micropores (<2 nm) in activated carbon particles are

generally less than the Debye length, thus the EDL overlap situation occurs [13].

Based on the EDL concept, CDI desalination occurs when putting a charged carbon electrode in contact with ionic solution, and then counterions will occupy the electrode-electrolyte interface in the pores inside the carbon particles due to the presence of the Coulomb force which forms the EDL. It should be noted that ions are not only removed by the electrical adsorption, but there will be a contribution from the physical adsorption effect. However, the regeneration step takes place when there is reduction in the applied potential (charge) and/ or reversed polarity which results in the removal of Coulomb force and/or reversing the force effect (i.e., there will be a repulsion force between held ions and charge) and therefore releasing the held ions back to the concentrate solution. Desalination/regeneration steps form one

to a reference electrode play a role and not absolute potentials [13, 17, 18].

electrode to the other giving us unity charge efficiency.

complete CDI treatment cycle [9].

Effective water desalination at lower costs is considered as one of the grand technological challenges of the twenty-first century. Common commercial technologies such as reverse osmosis, electrodialysis, thermal distillation and multistage flash distillation have been developed to achieve efficient desalination. However, the latter technologies consume a lot of energy and may not be a cost-effective manner for water desalination. Recently, CDI has gained much attention as a desalination technology alternative for brackish water (which has low or moderate salt content) due to its simple design, low energy consumption, economical feasibility, high efficiency, safety and environmental friendliness [23–27].

CDI does not involve membranes and therefore it is a low-pressure process of deionization which does not require energy for pumping water or any other means (except for a fairly low applied voltage). Moreover, CDI stores applied potential as a capacitive energy and one may recover this energy again to further reduce power consumption and operating expenses [27, 28]. In other words, electrode discharge step (regeneration) can be recovered and utilized to charge a neighboring cell (electrosorption) for ion rejection [13]. Possibility of electrode fouling during the desalination-regeneration cycles is relatively low, hence, making this technology more attractive for desalting water. CDI does not have additional contaminants (e.g., chemicals) released from the process which makes CDI technology environmentally friendly [29].

From previous discussed advantages, CDI becomes very suitable in providing fresh water and agricultural water with low cost and without pollution [26, 30]. Despite that CDI may not be capable of treating sea water (high saline water); it is still efficient to remove salt concentrations up to 10 g/L. Accordingly, water shortage problems in arid areas and contaminated brackish water-rich regions can be overcome with the advantageous CDI technology [13].

from the abovementioned equation and multiplying the result by (−1) to have a positive number

It is defined as the ratio of adsorbed salt over charge and calculated from Eq. (2) by multiplying the total adsorbed salts on the electrodes (mol/g) by Faraday's constant (C/mol) and then divided by the total amount of charge density transferred for adsorption cycle (C/g). Charge efficiency is used to analyze static electrode CDI cycles as an integral property and it must be less than unity (or approaching one for the ideal case). Charge efficiency is a function of the applied potential during charging/discharging and initial salt concentration. Increasing charging and discharging voltages and decreasing feed concentrations will result in higher charge efficiency. Higher values of charge efficiency lead to lower energy

*Σ* = (*SAC*/*M*) × Ϝ \_\_\_\_\_\_\_\_\_\_

where Γ is the deionization capacity upon applying a cell voltage (mol/g), Ϝ is the Faraday's constant (96485.33 C/mol), Σ is the total charge transferred (C/g) and is calculated through integrating the current over time per electrode mass to give an estimate on the total amount of charge delivered in Coulombs per gram of electrode during the adsorption cycle, *SAC* is the salt adsorption capacity (see Section 2.5.3) and is calculated from Eq. (3) with the unit (mg/g), *M* is the molar mass of NaCl (58.4 g/mol), *I* is the measured current density (A/g, where A = Amperes = C/s), *t* is the charging time (s) and ∫*I dt* =C/g, where C = Coulomb. Current is generally higher in magnitude during charging when compared to discharging. The above equation is valid for any CDI system, symmetric or asymmetric cells with/without redox reactions as long as the current and salt rejection are measured from experiment [17, 24, 25].

Salt adsorption capacity (SAC) is defined as the amount of ions in milligram electroadsorbed per gram of electrodes; see Eq. (3). This is also known as "specific salt adsorption capacity" and gives information on the electrosorption capacity of both electrodes of a cell's charge–discharge cycle. One may calculate the maximum salt adsorption capacity (mSAC), which is also known as equilibrium salt adsorption capacity (eqSAC), when the measured conductivity of

*SAC* (*mg*/*g*) = (*C*0 − *Cf*)*V* \_\_\_\_\_\_\_ *m* (3)

(mg/L), *m* refers to the total mass of the two carbon electrodes when dry (g) and *V* represents the volume of NaCl solution (L). However, if the effluent was discharged, the amount of ion adsorption per unit mass of carbon electrodes can be calculated from Eq. (4) [17, 23, 27];

are the initial and final (or equilibrium) concentrations of NaCl solution

(due to flushing/cleaning the system with DI water) [29, 32].

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Activated Carbon Cloth for Desalination of Brackish Water Using Capacitive Deionization

∫*I dt* (2)

since *C f*

*2.5.2. Charge efficiency*

consumption [17, 24, 25].

*2.5.3. Salt adsorption capacity*

where *C*0

and *Cf*

the cell effluent no longer changes over time [17].

will be much higher than *C* 0

*Λ* = *Γ* × Ϝ \_\_\_\_

CDI technology does not require expensive designed parts/materials for the construction phase. Materials required to build a CDI cell are commercially available and cheap which include, but not limited to, a pair of porous electrodes (e.g., carbon), a porous separator between the two electrodes, a conductive rod material (e.g., graphite) to be attached to both electrodes and connected to a potentiostat (to transfer a typical applied potential of 1–1.4 V) and a designed acrylic support/reservoir with an inlet and outlet [17].

#### **2.4. Operating conditions**

Since this chapter is related to using activated carbon cloth (ACC) as an electrode in the CDI cell, the reported operating conditions in this section are for ACC-CDI systems. Laxman et al. and Myint et al. have investigated the use of ACC (Zorflex FM-100) for CDI brackish water desalination. Zorflex ACC thickness was about 1.0 mm, electrode area was 8.4 cm2 and specific surface area was approximately 1100 m2 /g. The ACC was grafted/coated with zinc oxide (ZnO) micro/nanomaterials (nanoparticles, nanorods, microsheets and microspheres) by a simple and low-temperature hydrothermal method to enhance salt removal from the improved electrode conductivity [29, 31, 32].

Based on the literature data for ACC-CDI systems, studied feed water, NaCl solution concentration should be between 100 and 1000 ppm (typically a salt concentration between 5 and 50 mM and/or 0.5 and 5 mS/cm) and applied potential must be in the range 0.6–1.6 V DC (typically 1.2 V to avoid water hydrolysis at 1.23 V). The system should be operated under room temperature and normal atmospheric pressure with a flowrate of 2 mL/min (and may reach up to 1–4 L/min). Flowrate values could be changed/increased and might not have much effect on salt adsorption. Desalination/regeneration time should be approximately 25 min (typically 10 min for desalination and 10 min for regeneration, or charge–discharge cycle can have any duration/time, from very short ~4 min, with little adsorption, to very long >90 min, depending on when equilibrium concentration becomes steady with time). Salt rejections could reach up to 25 and 35% for plain ACC and ACC deposited with ZnO nanorods, respectively, and electrode electrosorptive capacity could reach up to 8.1 mg/g [17, 31, 32].

#### **2.5. Performance metrics and equations**

#### *2.5.1. Desalination (salt removal) efficiency*

It is defined as how much salt ions can be removed from brackish water in a CDI cell; see Eq. (1).

$$R \text{ (\%)} = \frac{C\_0 - C\_f}{C\_0} \times 100 \tag{1}$$

where *C* 0 and *C f* are the initial and final (or equilibrium) concentration in ppm "mg/L" (or conductivity in μS/cm) of saline (NaCl) solution. Regeneration efficiency can also be calculated from the abovementioned equation and multiplying the result by (−1) to have a positive number since *C f* will be much higher than *C* 0 (due to flushing/cleaning the system with DI water) [29, 32].

#### *2.5.2. Charge efficiency*

be capable of treating sea water (high saline water); it is still efficient to remove salt concentrations up to 10 g/L. Accordingly, water shortage problems in arid areas and contaminated brackish water-rich regions can be overcome with the advantageous CDI technology [13].

CDI technology does not require expensive designed parts/materials for the construction phase. Materials required to build a CDI cell are commercially available and cheap which include, but not limited to, a pair of porous electrodes (e.g., carbon), a porous separator between the two electrodes, a conductive rod material (e.g., graphite) to be attached to both electrodes and connected to a potentiostat (to transfer a typical applied potential of 1–1.4 V)

Since this chapter is related to using activated carbon cloth (ACC) as an electrode in the CDI cell, the reported operating conditions in this section are for ACC-CDI systems. Laxman et al. and Myint et al. have investigated the use of ACC (Zorflex FM-100) for CDI brackish water desalination. Zorflex ACC thickness was about 1.0 mm, electrode area was 8.4 cm2

oxide (ZnO) micro/nanomaterials (nanoparticles, nanorods, microsheets and microspheres) by a simple and low-temperature hydrothermal method to enhance salt removal from the

Based on the literature data for ACC-CDI systems, studied feed water, NaCl solution concentration should be between 100 and 1000 ppm (typically a salt concentration between 5 and 50 mM and/or 0.5 and 5 mS/cm) and applied potential must be in the range 0.6–1.6 V DC (typically 1.2 V to avoid water hydrolysis at 1.23 V). The system should be operated under room temperature and normal atmospheric pressure with a flowrate of 2 mL/min (and may reach up to 1–4 L/min). Flowrate values could be changed/increased and might not have much effect on salt adsorption. Desalination/regeneration time should be approximately 25 min (typically 10 min for desalination and 10 min for regeneration, or charge–discharge cycle can have any duration/time, from very short ~4 min, with little adsorption, to very long >90 min, depending on when equilibrium concentration becomes steady with time). Salt rejections could reach up to 25 and 35% for plain ACC and ACC deposited with ZnO nanorods, respectively, and

It is defined as how much salt ions can be removed from brackish water in a CDI cell; see Eq. (1).

*C*0

ductivity in μS/cm) of saline (NaCl) solution. Regeneration efficiency can also be calculated

are the initial and final (or equilibrium) concentration in ppm "mg/L" (or con-

and

/g. The ACC was grafted/coated with zinc

× 100 (1)

and a designed acrylic support/reservoir with an inlet and outlet [17].

electrode electrosorptive capacity could reach up to 8.1 mg/g [17, 31, 32].

specific surface area was approximately 1100 m2

improved electrode conductivity [29, 31, 32].

**2.5. Performance metrics and equations**

*2.5.1. Desalination (salt removal) efficiency*

where *C* 0

and *C f*

*R* (%) = *C*0 − *C* \_\_\_\_\_*f*

**2.4. Operating conditions**

22 Desalination and Water Treatment

It is defined as the ratio of adsorbed salt over charge and calculated from Eq. (2) by multiplying the total adsorbed salts on the electrodes (mol/g) by Faraday's constant (C/mol) and then divided by the total amount of charge density transferred for adsorption cycle (C/g). Charge efficiency is used to analyze static electrode CDI cycles as an integral property and it must be less than unity (or approaching one for the ideal case). Charge efficiency is a function of the applied potential during charging/discharging and initial salt concentration. Increasing charging and discharging voltages and decreasing feed concentrations will result in higher charge efficiency. Higher values of charge efficiency lead to lower energy consumption [17, 24, 25].

$$
\Lambda = \frac{\Gamma \times \text{F}}{\Sigma} = \frac{(\text{SAC/M}) \times \text{F}}{\int \text{I} \, dt} \tag{2}
$$

where Γ is the deionization capacity upon applying a cell voltage (mol/g), Ϝ is the Faraday's constant (96485.33 C/mol), Σ is the total charge transferred (C/g) and is calculated through integrating the current over time per electrode mass to give an estimate on the total amount of charge delivered in Coulombs per gram of electrode during the adsorption cycle, *SAC* is the salt adsorption capacity (see Section 2.5.3) and is calculated from Eq. (3) with the unit (mg/g), *M* is the molar mass of NaCl (58.4 g/mol), *I* is the measured current density (A/g, where A = Amperes = C/s), *t* is the charging time (s) and ∫*I dt* =C/g, where C = Coulomb. Current is generally higher in magnitude during charging when compared to discharging. The above equation is valid for any CDI system, symmetric or asymmetric cells with/without redox reactions as long as the current and salt rejection are measured from experiment [17, 24, 25].

#### *2.5.3. Salt adsorption capacity*

Salt adsorption capacity (SAC) is defined as the amount of ions in milligram electroadsorbed per gram of electrodes; see Eq. (3). This is also known as "specific salt adsorption capacity" and gives information on the electrosorption capacity of both electrodes of a cell's charge–discharge cycle. One may calculate the maximum salt adsorption capacity (mSAC), which is also known as equilibrium salt adsorption capacity (eqSAC), when the measured conductivity of the cell effluent no longer changes over time [17].

$$\text{SAC (mg/g)} = \frac{(\text{C}\_{\text{o}} - \text{C}\_{\text{f}})V}{m} \tag{3}$$

where *C*0 and *Cf* are the initial and final (or equilibrium) concentrations of NaCl solution (mg/L), *m* refers to the total mass of the two carbon electrodes when dry (g) and *V* represents the volume of NaCl solution (L). However, if the effluent was discharged, the amount of ion adsorption per unit mass of carbon electrodes can be calculated from Eq. (4) [17, 23, 27];

$$\text{SAC (mg/g)} = \frac{C\_f Qt}{m} \tag{4}$$

where *Cf* represents the final ion concentration of NaCl solution (mg/L), *Q* is the flow rate of the solution (L/min), *t* is the electrosorption time (min) and *m* is the mass of the two carbon electrodes (g) [17, 23, 27, 31, 33, 34].

#### *2.5.4. Average salt adsorption rate*

This metric gives information on the rate of salt sorption, and is usually in the units (mg/g/ min) with the (min) referring to the charging time, (mg) referring to the mass of salt removed, (g) referring to the mass of the two electrodes together and average salt adsorption rate (ASAR) is calculated from Eq. (5).

$$ASAR = \frac{SAC}{t} \tag{5}$$

*Cs* = *i*(*E*) \_\_\_

*C*\_\_*e*

**3. Carbon electrode materials for CDI**

*i*(*E*) is the instantaneous current and power delivered during the scan (A).

**Figure 3.** Kim-Yoon plot for (ASAR) in a flow by CDI cell vs. (SAC) as a function of charging voltage.

simulated by the Langmuir isotherm (1918) as in Eq. (8), by plotting *Ce*

is the equilibrium concentration of salt ions (mg/L), *qe*

*qe*

(L/mg) is the Langmuir constant related to the adsorption energy [33].

where *E*1

where *Ce*

and *KL*

& *E*2

*2.5.6. Langmuir isotherm*

*mv* (7)

/*qe* vs. *Ce* .

represents the amount of elec-

(8)

are the potential ranges (V), *m* is the electrode mass (g), *v* is the scan rate (mV/s),

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Adsorption data of the electrolyte with respect to carbon electrode in CDI systems can be

= \_\_\_\_\_ 1 *qm KL* + *C*\_\_\_*e qm*

troadsorbed ions at equilibrium per unit weight of carbon electrode (mg/g), *qm* is the maximum adsorption capacity (mg/g) with respect to the complete surface monolayer coverage

Carbon is a large chemical family and represents a wide range of materials that are mainly composed by the carbon element. Among them, graphite and diamond are the two with crystal

where *t* stands for the deionization time (min) and *SAC* refers to the salt adsorption capacity (mg/g). Zhao et al. reported the highest value of ASAR which is 2.3 mg/g/min for a membrane CDI cell architecture (see Section 4.3) with sub-equilibrium charging times and 300-mm-thick electrodes [17, 27, 35, 36].

Kim-Yoon proposed KY diagrams which combine two CDI metrics, salt adsorption capacity (SAC) and salt adsorption rate (ASAR), in a single plot. KY diagram can be used in optimization studies for CDI cells. For example, KY was plotted for a flow by CDI cell with static film electrodes (Kuraray YP50F-activated carbon powder) as a function of the charging voltage as shown in **Figure 3**, and the discharge voltage was set to zero for all experiments. Calculations were carried out at varied half-cycle time (HCT; the charging and discharging steps were of the same duration) and the charging voltage was set between 0.9 and 1.3 V. Dividing SAC by ASAR is equal to twice the half-cycle time (HCT) and optimum operational values are shown by black circles [17, 27, 35, 36].

#### *2.5.5. Specific capacitance*

It is defined as the cell or electrode charge storage capacity, expressed in Farads per gram (F/g), and is estimated from capacitive charge and the applied cell voltage as in Eq. (6) and/or Eq. (7). The specific capacitance is often referred to a single electrode capacitance. Capacitance and desalination (salt removal) are not equivalent but are linked by the charge efficiency (see Section 2.5.2). Cyclic voltammetry measurements should be performed on the working electrode using a potentiostat with a specific scan rate (mV/s) and a potential widow (e.g., −0.4 V to +0.4 V), to obtain voltammogram diagrams and then calculate the specific electrode capacitance from obtained data and given Equations [17, 27, 29, 31].

$$C\_s = \int\_{t\_i}^{E\_t} \frac{i\triangle dE}{[2(E\_2 - E\_t)mv]} \tag{6}$$

Activated Carbon Cloth for Desalination of Brackish Water Using Capacitive Deionization http://dx.doi.org/10.5772/intechopen.76838 25

**Figure 3.** Kim-Yoon plot for (ASAR) in a flow by CDI cell vs. (SAC) as a function of charging voltage.

$$\mathbf{C}\_s = \frac{i(E)}{mv} \tag{7}$$

where *E*1 & *E*2 are the potential ranges (V), *m* is the electrode mass (g), *v* is the scan rate (mV/s), *i*(*E*) is the instantaneous current and power delivered during the scan (A).

#### *2.5.6. Langmuir isotherm*

*SAC* (*mg*/*g*) = *Cf Qt* \_\_\_\_

*ASAR* = \_\_\_\_

electrodes (g) [17, 23, 27, 31, 33, 34].

*2.5.4. Average salt adsorption rate*

24 Desalination and Water Treatment

(ASAR) is calculated from Eq. (5).

electrodes [17, 27, 35, 36].

by black circles [17, 27, 35, 36].

*2.5.5. Specific capacitance*

where *Cf*

*m* (4)

*t* (5)

represents the final ion concentration of NaCl solution (mg/L), *Q* is the flow rate of

*SAC*

the solution (L/min), *t* is the electrosorption time (min) and *m* is the mass of the two carbon

This metric gives information on the rate of salt sorption, and is usually in the units (mg/g/ min) with the (min) referring to the charging time, (mg) referring to the mass of salt removed, (g) referring to the mass of the two electrodes together and average salt adsorption rate

where *t* stands for the deionization time (min) and *SAC* refers to the salt adsorption capacity (mg/g). Zhao et al. reported the highest value of ASAR which is 2.3 mg/g/min for a membrane CDI cell architecture (see Section 4.3) with sub-equilibrium charging times and 300-mm-thick

Kim-Yoon proposed KY diagrams which combine two CDI metrics, salt adsorption capacity (SAC) and salt adsorption rate (ASAR), in a single plot. KY diagram can be used in optimization studies for CDI cells. For example, KY was plotted for a flow by CDI cell with static film electrodes (Kuraray YP50F-activated carbon powder) as a function of the charging voltage as shown in **Figure 3**, and the discharge voltage was set to zero for all experiments. Calculations were carried out at varied half-cycle time (HCT; the charging and discharging steps were of the same duration) and the charging voltage was set between 0.9 and 1.3 V. Dividing SAC by ASAR is equal to twice the half-cycle time (HCT) and optimum operational values are shown

It is defined as the cell or electrode charge storage capacity, expressed in Farads per gram (F/g), and is estimated from capacitive charge and the applied cell voltage as in Eq. (6) and/or Eq. (7). The specific capacitance is often referred to a single electrode capacitance. Capacitance and desalination (salt removal) are not equivalent but are linked by the charge efficiency (see Section 2.5.2). Cyclic voltammetry measurements should be performed on the working electrode using a potentiostat with a specific scan rate (mV/s) and a potential widow (e.g., −0.4 V to +0.4 V), to obtain voltammogram diagrams and then calculate the specific electrode

> *E*1 *E*2

\_\_\_\_\_\_\_\_\_\_ *i*(*E*)*dE*

[2(*E*2 − *E*1)*mv*] (6)

capacitance from obtained data and given Equations [17, 27, 29, 31].

*Cs* = ∫

Adsorption data of the electrolyte with respect to carbon electrode in CDI systems can be simulated by the Langmuir isotherm (1918) as in Eq. (8), by plotting *Ce* /*qe* vs. *Ce* .

$$\frac{C\_\epsilon}{q\_\epsilon} = \frac{1}{q\_m K\_\epsilon} + \frac{C\_\epsilon}{q\_m} \tag{8}$$

where *Ce* is the equilibrium concentration of salt ions (mg/L), *qe* represents the amount of electroadsorbed ions at equilibrium per unit weight of carbon electrode (mg/g), *qm* is the maximum adsorption capacity (mg/g) with respect to the complete surface monolayer coverage and *KL* (L/mg) is the Langmuir constant related to the adsorption energy [33].

#### **3. Carbon electrode materials for CDI**

Carbon is a large chemical family and represents a wide range of materials that are mainly composed by the carbon element. Among them, graphite and diamond are the two with crystal structures and are not property adsorption materials because of the lack of surface area. Others are normally referred to as amorphous carbon. Earlier studies in the last few decades showed that carbon electrodes are promising in CDI cells because of their very high specific surface area, and thereby resulting in better electrosorption and higher salt rejections. Common carbon electrodes, which are utilized for CDI, are activated carbon, activated carbon powder, activated carbon cloth, carbon aerogel, carbon nanotubes, carbon nanofibers, ordered mesoporous carbon and graphene [9, 13].

#### **3.1. Selected parameters for an ideal electrode**

**3.2. Specific surface area of various electrodes**

several previous studies reported by Jia et al. [9].

 Cell architectures and CDI designs**

**4.1. Flow between electrodes**

reduce fouling issues [17, 38–42].

**4.2. Flow-through electrodes**

As discussed earlier, higher specific surface area is the most important parameter in selecting an ideal carbon electrode for the CDI cell to ensure the maximum adsorption. Hence, **Table 1** shows the specific area of various carbon non-composites and composite electrodes [9].

\*ACC: Activated Carbon Cloth; AC: Activated Carbon; CNT: Carbon Nanotubes; OMC: Ordered Mesoporous Carbon.

**Table 1.** Specific surface area of various carbon non-composite and composite electrodes, as measured and reported from

**Electrode Specific surface area**

Activated Carbon Cloth for Desalination of Brackish Water Using Capacitive Deionization

**(m2 /g)**

http://dx.doi.org/10.5772/intechopen.76838

27

In this architecture, CDI contains a pair of porous carbon electrodes parted by a spacer where feed water flows (feed water flows perpendicular to the applied electric field direction (see **Figure 4A**)). Flow between electrodes, which is also known as flow by electrodes, is the oldest and most used CDI architecture and was widely employed in various experiment works, including, but not limited to, removing salt from numerous feed waters, inspecting novel electrode materials performance and performing fundamental studies of salt sorption on porous electrodes. Traditional CDI design has advantages over newer designs due to its simplicity (no membranes or flow electrodes), which can potentially lower the system cost and

This architecture is defined as a CDI cell, with a pair of porous carbon electrodes parted by a thinner spacer, in which the feed goes directly through the electrodes and parallel to the applied electric field direction (**Figure 4B**). Flow-through electrodes system is used in a threeelectrode cell to study fundamental performance parameters such as charge efficiency. Flowthrough electrodes allow faster cell charging relative to flow-between systems. The primary

**Table 1.** Specific surface area of various carbon non-composite and composite electrodes, as measured and reported from several previous studies reported by Jia et al. [9].

#### **3.2. Specific surface area of various electrodes**

As discussed earlier, higher specific surface area is the most important parameter in selecting an ideal carbon electrode for the CDI cell to ensure the maximum adsorption. Hence, **Table 1** shows the specific area of various carbon non-composites and composite electrodes [9].


*2.2. Synthesis of Wood-Based Cationic CNCs*

The initiator modified CNC materials (CNC-BriB) were first synthesized according to our previously reported procedure with slight modifications [23]. Pristine spray-dried CNCs were reacted with 2-bromoisobutyryl bromide (BriB bromide) at two different ratios with respect to anhydroglucose units (AGU) in CNCs ([Br]/[AGU]), 5:3 for CNC-BriB-1 and 5:12 for CNC-BriB-2 (for a detailed experimental procedure of CNC-BriB, refer to SI & Supplementary Figure S1). CNC-BriB was then grafted with either poly (METAC) or poly (AEM) via SI-SET-LRP at different ratios of monomer to AGU such as [METAC/AGU] = 50:3 or 60:3 and [AEM/AGU] = 50:3 (Table 1). A general procedure for the preparation of cationic CNCs is as follows: CNC-BriB (350 mg) was dispersed in a MeOH:H2O solvent mixture (100 mL, 1:1 v/v) in a 250 mL Schlenk flask. The reaction mixture was degassed under N2 gas for 45 min prior to the addition of the monomer METAC or AEM (50 and/or 60 mmol) and copper (I) bromide (0.5 mmol). The suspension was degassed again before addition of bpy or PMDETA (1 mmol) and the reaction mixture was vigorously stirred at room temperature for 24 h. The resulting crude cationic CNC was then centrifuged (3 × 12,000 rpm at 10 ◦C for 30 min) with a 1:3 ratio of H2O:MeOH. The residual solid was resuspended in water and extensively dialyzed (MWCO 3500 Da) against deionized water for 1 week with daily constant change of water. The suspension was then freeze-dried to afford purified CNCs as white flaky material. The syntheses of other cationic CNCs are described in detail in the supporting information and Supplementary Table S1.

**Table 1.** Different molar ratios of [Br]/[AGU] and [monomer]/[AGU] for the fabrication of cationic CNCs.


**6. Methodology**

Potatoes (*Solanum tuberosum L)* and yeast (*Saccharomyces cereviceae)* contain more than 60% of protein, this consumption by the post- larva is consistent with the protein requirement, and also this source contains immune system stimulant compounds such as β-glucan, nucleic acids like manna oligosaccharides that increase the immune response (Champagne et al., 2009). When yeast gets attached to the intestine of the larvae, on their 27th day after birth, it produces a higher secretion of amylase and this stimulates the enzymes located on the membrane cells in the brush border shape (Austin & Brunt, 2009, as cited in Montet & Ray, 2009).

Potatoes (*Solanum tuberosum L*) have been used as a nutrient because they play an energetic roll due to their high levels of starch (60% – 80%), of the dry matter is starch.  It is also a good source of vitamins B1, B3, B6, folate, pantothenic acid, riboflavin and minerals, such as potassium, phosphorus and magnesium, Potatoes also contain dietary antioxidants, which may play a part in preventing diseases related to ageing (Murniece et al., 2011; FAO, 2008a).

The enrichment with flour provides protein (50%) and high level of lecithin to the living food. Few authors have shown the incidence in growth and intestine morphology improvement including soy oatmeal (Murray et al., 2010). Despite its limitations, the incidence of scoliosis and mouth twisting in the larvae is reduced with the addition of lecithin Salze et al., 2010). Gutiérrez-Espinoza and Vásquez-Torres (2008), confirm that soy in different presentations has a high digestibility index in White Cachama juveniles (*Piaractus brachypomus*) and can be used without restrictions on this specie (Guillaume et al., 2004; Sealey et al., 2009).

The mutual action of these three nutrients over the productive and reproductive parameters of Daphnia magna can be demonstrated with this research, thorough its exposition to eight diets. These diets include yeast, potato and soy oatmeal, with 15 and 30 ppm concentrations of nutrient and enrichment compound, determining productive and reproductive parameters, creation of life history and comparing populations under stress conditions.

Daphnia magna was used, with two populations: one with adults and the other with young breeders (32 specimens / population). *Daphnia magna* was seeded individually (1 Daphnia/tank) in multicells with 24 tanks, each one with 3 mL capacity, covered with parafilm. The compartments were fully filled with the culture medium according to the treatment. The daily exchange for a culture medium was 50%. Concentrations of 30 mg/L and 15 mg/L were prepared for the culture medium for each of the nutrient with discolored water. The treatments used were the following:

Treatment 1: 15 ppm *S. cereviceae*, 15 ppm potato, 15 ppm soy oatmeal flour.

Treatment 2: 15 ppm *S. cereviceae*, 15 ppm potato, 30 ppm soy oatmeal flour.

Treatment 3: 15 ppm *S. cereviceae*, 30 ppm potato, 15 ppm soy oatmeal flour.

Treatment 4: 15 ppm *S. cereviceae*, 30 ppm potato, 30 ppm soy oatmeal flour.

Treatment 5: 30 ppm *S. cereviceae*, 15 ppm potato, 15 ppm soy oatmeal flour.

Treatment 6: 30 ppm *S. cereviceae*, 15 ppm potato, 30 ppm soy oatmeal flour.

Treatment 7: 30 ppm *S. cereviceae*, 30 ppm potato, 15 ppm soy oatmeal flour.

Treatment 8: 30 ppm *S. cereviceae*, 30 ppm potato, 30 ppm soy oatmeal flour.

The whole production was preserved in a laboratory with the following environmental conditions: 1.200 masl (meters above the sea level), 22 ± 3 °C room temperature, 12 light hours, 12 dark hours, 7.0 ± 0.6 pH water, during 20 days. Eight treatments were used with four replica/treatment.

These are the productive and reproductive parameters of Daphnia magna:

#### **6.1 Growth and corporal weight: Productive variables**

Maximum density (Dmax):

$$\text{Dmáx} = \frac{\text{Final population}}{\text{Volume}} \equiv \left[ \frac{\text{Individulas}}{\text{Volume}} \right] \tag{1}$$

Daily average density (Dmd):

$$\text{Dmd} = \frac{\text{Final population}}{\text{T}} \equiv \left[ \frac{\text{Individulas}}{\text{Time}} \right] \tag{2}$$

Doubling Time (Td):

250 Aquaculture

in different presentations has a high digestibility index in White Cachama juveniles (*Piaractus brachypomus*) and can be used without restrictions on this specie (Guillaume et al.,

The mutual action of these three nutrients over the productive and reproductive parameters of Daphnia magna can be demonstrated with this research, thorough its exposition to eight diets. These diets include yeast, potato and soy oatmeal, with 15 and 30 ppm concentrations of nutrient and enrichment compound, determining productive and reproductive parameters, creation of life history and comparing populations under stress conditions.

Daphnia magna was used, with two populations: one with adults and the other with young breeders (32 specimens / population). *Daphnia magna* was seeded individually (1 Daphnia/tank) in multicells with 24 tanks, each one with 3 mL capacity, covered with parafilm. The compartments were fully filled with the culture medium according to the treatment. The daily exchange for a culture medium was 50%. Concentrations of 30 mg/L and 15 mg/L were prepared for the culture medium for each of the nutrient with discolored

The whole production was preserved in a laboratory with the following environmental conditions: 1.200 masl (meters above the sea level), 22 ± 3 °C room temperature, 12 light hours, 12 dark hours, 7.0 ± 0.6 pH water, during 20 days. Eight treatments were used with

≡

≡

Individuals

Individuals

Volume ൨ (1)

Time ൨ (2)

Treatment 1: 15 ppm *S. cereviceae*, 15 ppm potato, 15 ppm soy oatmeal flour. Treatment 2: 15 ppm *S. cereviceae*, 15 ppm potato, 30 ppm soy oatmeal flour. Treatment 3: 15 ppm *S. cereviceae*, 30 ppm potato, 15 ppm soy oatmeal flour. Treatment 4: 15 ppm *S. cereviceae*, 30 ppm potato, 30 ppm soy oatmeal flour. Treatment 5: 30 ppm *S. cereviceae*, 15 ppm potato, 15 ppm soy oatmeal flour. Treatment 6: 30 ppm *S. cereviceae*, 15 ppm potato, 30 ppm soy oatmeal flour. Treatment 7: 30 ppm *S. cereviceae*, 30 ppm potato, 15 ppm soy oatmeal flour. Treatment 8: 30 ppm *S. cereviceae*, 30 ppm potato, 30 ppm soy oatmeal flour.

These are the productive and reproductive parameters of Daphnia magna:

Dmáx= Final population Volume

Dmd= Final population T

**6.1 Growth and corporal weight: Productive variables**

2004; Sealey et al., 2009).

four replica/treatment.

Maximum density (Dmax):

Daily average density (Dmd):

water. The treatments used were the following:

$$\text{Td} = \frac{0.693}{\text{k}} \equiv \text{[días]} \tag{3}$$

Specific growth rate (k):

$$\mathbf{k} = \frac{\text{Ln(final population)} \cdot \text{Ln(PobblInitial population inicial)}}{\text{TiempoTime}} \equiv \left[ \frac{1}{\text{day}} \right] \tag{4}$$

Performance (r):

$$\mathbf{r} = \frac{\text{(Final population)} \cdot \text{(Initial population)}}{\text{Time}} \equiv \left[ \text{individuals}^\* \frac{1}{\text{Time}} \right] \tag{5}$$

Numeric growth (PN):

$$P\_{\mathcal{N}} = \mathsf{b}^\* \overline{\mathsf{N}} \equiv \left[ \# \text{ individuals} \ast \frac{1}{\text{Time}} \right] \tag{6}$$

N̅= individual media number

b= birth rate population, in a period of time.

Birth rate (b) (Edmodson equation):

$$\mathbf{b} = \ln(\mathbf{E}/\mathbf{D} + 1) \equiv [\# \text{ neurons}] \tag{7}$$

E= egg number /female D= egg development time (days).

Another way to calculate the birth rate is:

$$\mathbf{k} = \mathbf{b} + \mathbf{d} \tag{8}$$

therefore:

$$\mathbf{b} = \mathbf{k} \cdot \mathbf{d} \tag{9}$$

Individuals average number (N�):

$$\bar{\mathbf{N}} = \frac{(\text{No} + \text{N}\_t)}{2} \tag{10}$$

No=individuals initial number Nt=individual number after a period of time t

Biomass productivity (Pw):

$$\mathbf{P}\_{\mathcal{W}} = \mathbf{b}^\* \overline{\mathbf{N}}^\* \overline{\mathbf{W}} \equiv \left[ \frac{\text{Biomass}}{\text{Volume}} \ast \frac{1}{\text{Time}} \right] \tag{11}$$

W̅=Final weight at the end of the period. N̅= Individuals media number b= birth rate population, in a period of time.

Mortality rate (d):

$$\text{Ind} = \frac{\text{Ln(Final pop. of encounters)} \cdot \text{Ln(Initial pop. of encounters)}}{\text{T}} \equiv \left[\frac{\text{1}}{\text{day}}\right] \tag{12}$$

Biomass (B):

$$\text{B} = \frac{\text{(Average number)\*(Final weight)}}{\text{T}} \equiv \left[\frac{\text{Biomass}}{\text{Volume}}\right] \tag{13}$$

Production rate (I de P):

$$\text{I de P=} \frac{\text{P}}{\text{B}}\tag{14}$$

Final weight (pf) was determined as dry weight. Every Daphnia was dried up with tissue paper (analytical scale, 0.0001g. precision), expressed in mg/L.

#### **6.2 Reproductive variables**

Egg number/female (HPP). The egg number/female was determined in the microscope (10x and 40x).

Neonate number/female (NPP). This count was made directly.

The measurement of the rest of the variables was taken directly from the data base, such as:

Egg development time (tm), number of days passed between the appearance of the egg in the incubation chamber and the presence of the neonate.

Offspring number (NC)

First reproduction age (EPR), in days.

Production frecuency (FR), in hours.

The born individuals were moved to another tank with the same treatment. Neonate mortality was evaluated here.

#### **6.3 Life history parameters**

Daily measurements were made in 32 young breeders and in 32 adults, keeping a follow up during the 21 days (duration of the research). The frequency of the observation was 12 hours to differentiate seeded population and produced population.

The reproduction net rate (Ro) and the generation time (Tc), were calculated according to the Lotta equation (1913).

$$\sum\_{\mathbf{x}=0}^{n} \mathbf{l}\_{\mathbf{x}} \mathbf{m}\_{\mathbf{x}} \text{(exp}^{\text{-}\text{rx}}) = \mathbf{1} \tag{15}$$

lx= survival in a specific time starting in the birth period. mx= fertility in a specific period x=period (from 0 to 21 days) r= intrinsic grow rate

Net reproduction rate (Ro):

252 Aquaculture

Ln�Final pop. of neonates)-Ln�Initial pop. of neonates)

I de P= P B

Final weight (pf) was determined as dry weight. Every Daphnia was dried up with tissue

Egg number/female (HPP). The egg number/female was determined in the microscope (10x

The measurement of the rest of the variables was taken directly from the data base, such as: Egg development time (tm), number of days passed between the appearance of the egg in

The born individuals were moved to another tank with the same treatment. Neonate

Daily measurements were made in 32 young breeders and in 32 adults, keeping a follow up during the 21 days (duration of the research). The frequency of the observation was 12 hours

The reproduction net rate (Ro) and the generation time (Tc), were calculated according to

B= �Average number)\*�Final weigth)

paper (analytical scale, 0.0001g. precision), expressed in mg/L.

Neonate number/female (NPP). This count was made directly.

the incubation chamber and the presence of the neonate.

to differentiate seeded population and produced population.

T � � 1

T � �Biomass

day� (12)

(14)

Volume � (13)

W̅=Final weight at the end of the period.

b= birth rate population, in a period of time.

N̅= Individuals media number

d=

Production rate (I de P):

**6.2 Reproductive variables**

Offspring number (NC)

mortality was evaluated here.

**6.3 Life history parameters**

the Lotta equation (1913).

First reproduction age (EPR), in days. Production frecuency (FR), in hours.

Mortality rate (d):

Biomass (B):

and 40x).

$$\mathbf{R\_o = \sum\_{\chi=0}^{n} 1\_{\chi} \mathbf{m\_{\chi}}} \tag{16}$$

Generation time (Tc):

$$\mathbf{T} = \mathbf{1} \Big/\_{\mathbf{R}\_o} \sum\_{\mathbf{x}=\mathbf{0}}^{\mathbf{n}} \mathbf{1}\_{\mathbf{x}} \mathbf{m}\_{\mathbf{x}} \mathbf{x} \tag{17}$$

Where Ro= net reproductive rate and Tc= generation time.

#### **6.4 Statistical methodology**

An experimental classification design was used, fully randomized, fixed effect, symmetric, balanced, 23 factorial arrangement, with 4 replicas, n=32 to each population. The results were compared through ANOVA and Tukey test with α=0.05. An exploratory descriptive analysis, one-dimensional for each condition type, was established. Data transformation to the square root function was used on egg number/female and neonates number variables. For survival and mortality percentages, arcsine transformation was applied. SAS version 9.1 Statistical package was used.

$$\mathbf{T} = \mathbf{1}\_{\parallel} \Big|\_{\mathbf{R}\_{\odot}} \sum\_{\mathbf{x}=\mathbf{0}}^{n} \mathbf{1}\_{\times} \mathbf{m}\_{\times} \,\mathrm{X}$$

$$Y\_{ij:k} = \mu + L\_i + P\_j + E\_s + LP\_{ij} + LE\_{is} + PE\_{js} + LPE\_{ijs} + \mathcal{E}\_{k\{js\}} \tag{18}$$

Where*Yijsk* : represented de number variable of *Daphnia magna.*

: Experiment average effect

*Li* : Yeast effect

*Pj* : Potato dosage effect

*Es* : Enrichment effect

*k ijs* ( ) : Experimental error Additionally, a comparison test with adult population and young breeders was made. To do this, the Mann Whitney test was applied, for the productive variables: daily average density (Dmd), doubling time (Td), specific growth rate (k), performance (r) and biomass productivity (Pw) and for reproductive parameters: egg number/female (HPP), neonates number/female (NPP), litter number (NC), net reproduction rate (Ro) and generation time (Tc). A correlation analysis was completed between the variables. For reproduction net rate and generation time, one way analysis of the variance and the Tukey test took place, in order to compare the life history parameters between the different diets.


*Genetic Targets May Be a Promising Future for Osteoporosis DOI: http://dx.doi.org/10.5772/intechopen.110336*

association which it is caused by this SNP. The genotypes of the LRP5rs121908669 were distributed according to three groups (GG, CC, and GC).

Several statistical applications (binary logistic regression test, Related-Samples McNemar Change Test, chi-square test) were used to study the relationship between mild osteogenesis imperfecta and postmenopausal osteoporosis and osteopenia. Chisquare test was used to study the association between carrier of (mild osteogenesis imperfecta—postmenopausal osteoporosis, osteopenia) and clinical data (height, age of onset of bone complaint). Statistical applications (Related-Samples McNemar Change Test, chi-square Test, Odd Ratio test) were used to study the relationship of genotypes of LRP5rs121908669 with femur T-score and the relationship of genotypes of LRP5rs121908669 with lumbar T-score. Chi-square test, Odd Ratio test, and likelihood ratio test were used to study the relationship of genotypes of LRP5rs121908669 with clinical data (body mass index).