**1. Introduction**

The stability of metal complex generally means that it exists under favorable conditions without undergoing decomposition and has a considerable shelf life period [1]. The term stability of metal complex cannot be generalized since the complex may be stable to one reagent/condition and may decompose in presence of another reagent/ condition. The stability of metal complexes can be explained with the help of two different aspects, namely, thermodynamic stability and kinetic stability [2]. Nevertheless, a metal complex is said to be stable if it does not react with water, which would lead to a decrease in the free energy of the system, i.e., thermodynamic stability. On the other hand, the complex is said to possess kinetic stability if it reacts with water to form a stable product and there is a known mechanism through which the reaction can proceed. For example, the system may not have sufficient energy available to break a strong bond, although once the existing bond is broken it could be replaced by new bond which is stronger than the older one [1]. Stability of complex compound is assigned to be its existence in aqueous solution with respect to its bond dissociation energy, Gibbs free energy, standard electrode potential, pH of the solution, and rate constant or activation energy for substitution reactions.

## **1.1 Thermodynamic stability**

Thermodynamic stability of a complex refers to its tendency to exist under equilibrium conditions. It determines the extent to which the complex will be formed or be converted into another complex at the point of equilibrium. In other words, thermodynamic stability of complexes is the measure of tendency of a metal ion to selectively form a specific metal complex and is directly related to the metal-ligand bond energies. The thermodynamic stability of complexes is

represented by formation constant. The formation constant is also known as stability constant, which is the equilibrium constant obtained for the formation metal complex [1, 2].

In general, the metal complexes are not prepared from their corresponding starting materials in gaseous phase but are prepared in aqueous solution. In aqueous solution, a metal cation gets hydrated to give aqua complex of the type [M(H2O)x] n+. When a ligand replaces water molecule from aqua complex ion, a new metal complex is formed and equilibrium is established as shown:

$$\begin{array}{rcl} \text{[M(H}\_{2}\text{O)}\_{x}\text{]}^{\text{n}} & + & \text{[K}\_{f} \\ \end{array} \\ \begin{array}{rcl} \text{K}\_{f} \\ \text{[M(H}\_{2}\text{O)}\_{x}\text{]}\_{x}\text{]}\_{x} & + & \text{H}\_{2}\text{O} \\ \end{array} \tag{1}$$

where x is the number of water molecules, n is the oxidation number of the metal cation, and L is the neutral and monodentate ligand. For simplicity, the above reaction can be written in generalized form as given:

$$\mathbf{^M}\mathbf{^L}\mathbf{<^L}\mathbf{<^L}\mathbf{^M}\mathbf{^L}\tag{2}$$

ii. Electrostatic factor

*DOI: http://dx.doi.org/10.5772/intechopen.90894*

*Stability of Metal Complexes*

the formation of [CdBr4]

octahedral [Cd(H2O)3Br3]

**25**

complex [Cd(H2O)6]

iii. Steric hindrance with increase in number of ligands

iv. Statistical factors (number of replaceable positions)

dral. The reaction sequence for the formation of [CdBr4]

However, in some cases, it is found that Kn+1 > Kn because of unusual structural changes and changes in electronic configuration of the metal ion. The change in electronic structure of the metal ion causes the variation in the crystal field stabilization energy (CFSE). The complex with higher CFSE value will be stable, and the equilibrium constant for that complex formation will be high. One such example is

wise formation constants K1, K2, K3, and K4. The order of stepwise formation constants is observed as follows, K1 > K2 > K3 < K4, which is not in agreement with the common trend of K1 > K2 > K3 > K4. Aqua complex of most of the M2+ ions including Cd2+ are octahedral, whereas the halo complexes of Cd2+ ion are tetrahe-

In the final step, there is an unusual structural change from six coordinated

complex in addition to change in the electronic configuration which lead to K4 > K3. The formation constant (K*f*) is related to the standard Gibbs free energy change

Since ΔG° is a thermodynamic property, the formation constant is the measure of thermodynamic stability. From Eqs. (4) to (6), it can be interpreted that the thermodynamic stability of a complex can be measured in terms of formation constant, Gibbs free energy change, and standard electrode potential. A high negative value of ΔG° indicates that the position of equilibrium favors the product

The formation constant describes the formation of a complex from metal cation

(complex); hence the complex formed will be more stable.

**1.2 Stepwise formation of complex and stepwise formation constants**

and ligands. Bjerrum (1941) defined that the formation of a metal complex in aqueous solution takes place by replacing the water molecule by another ligand (L)

(ΔG°) and standard electrode potential (E°) according to following equations:

2� complex in aqueous solution. The reaction of aqua

2+ with Br� ligand exhibits four stepwise equilibrium or step-

� complex to four coordinated tetrahedral [CdBr4]

ΔG° ¼ �RTlnK*f* (4)

ΔG° ¼ �n*F*E° (5)

hence RTlnK*f* ¼ n*F*E° (6)

2� is given as follows:

2�

The equilibrium constant K*f* of the reaction is given by:

$$\mathbf{K}\_{\circ} - \frac{[\mathbf{ML}]}{[\mathbf{M}][\mathbf{L}]} \tag{3}$$

In the above equation, the concentration of water is not included. Since the solution is dilute, the water molecules which enter the bulk solution do not have much influence on the equilibrium constant. It is observed from Eq. (3) that the higher the value of K*f*, the greater will be the stability of the complex formed. A high value of the equilibrium constant (K*f* > 1.0) also indicates that at equilibrium the activity of complex ML is larger than the product of activities of M and L. Thus, large value of K*f* indicates that the ligand L binds to the metal ion more strongly than H2O and hence L is a stronger ligand than H2O. If K*f* is less than 1.0, then ligand L is weaker than H2O. Thus stability constant is used as a measure of thermodynamic stability of the complex. With a few exceptions, the value of successive stability constants decreases regularly from K1 to Kn, that is, K1 > K2 > K3 > … > Kn�1 > Kn. This trend is illustrated by taking formation of [Cd(NH3)4] 2+ as an example [3, 4]:

$$\begin{aligned} \text{Cd}^{2+} + \text{NH}\_3 &\xleftarrow{\text{Cd(NH}\_3\text{)}^{2+}} ; \text{ K}\_1 = 10^{2.65} \\\\ [\text{Cd(NH}\_3\text{)}]^{2+} + \text{NH}\_3 &\xleftarrow{\text{Cd(NH}\_3\text{)}\_2\text{)}^{2+}} ; \text{ K}\_2 = 10^{2.10} \\\\ [\text{Cd(NH}\_3\text{)}\_2\text{)}^{2+} + \text{NH}\_3 &\xleftarrow{\text{Cd(NH}\_3\text{)}\_3\text{)}^{2+}} [\text{Cd(NH}\_3\text{)}\_3]^{2+} ; \text{ K}\_3 = 10^{1.44} \\\\ [\text{Cd(NH}\_3\text{)}\_3]^{2-} + \text{NH}\_3 &\xleftarrow{\text{Cd(NH}\_3\text{)}\_4\text{)}^{2-}} [\text{Cd(NH}\_3\text{)}\_4]^{2-} ; \text{ K}\_4 = 10^{0.93} \end{aligned}$$

The steady decrease in the value of stepwise formation constants from K1 to Kn is due to:

i. Increase in the number of ligands in coordination sphere that causes to decrease the number of H2O molecules to be replaced and thus the probability of replacement of water molecules decreased

ii. Electrostatic factor

represented by formation constant. The formation constant is also known as stability constant, which is the equilibrium constant obtained for the formation metal

In general, the metal complexes are not prepared from their corresponding starting materials in gaseous phase but are prepared in aqueous solution. In aqueous solution, a metal cation gets hydrated to give aqua complex of the type [M(H2O)x]

When a ligand replaces water molecule from aqua complex ion, a new metal complex

where x is the number of water molecules, n is the oxidation number of the metal cation, and L is the neutral and monodentate ligand. For simplicity, the above

In the above equation, the concentration of water is not included. Since the solution is dilute, the water molecules which enter the bulk solution do not have much influence on the equilibrium constant. It is observed from Eq. (3) that the higher the value of K*f*, the greater will be the stability of the complex formed. A high value of the equilibrium constant (K*f* > 1.0) also indicates that at equilibrium the activity of complex ML is larger than the product of activities of M and L. Thus, large value of K*f* indicates that the ligand L binds to the metal ion more strongly than H2O and hence L is a stronger ligand than H2O. If K*f* is less than 1.0, then ligand L is weaker than H2O. Thus stability constant is used as a measure of thermodynamic stability of the complex. With a few exceptions, the value of successive stability constants decreases regularly from K1 to Kn, that is, K1 > K2 > K3 >

… > Kn�1 > Kn. This trend is illustrated by taking formation of [Cd(NH3)4]

The steady decrease in the value of stepwise formation constants from K1 to Kn is

decrease the number of H2O molecules to be replaced and thus the probability

i. Increase in the number of ligands in coordination sphere that causes to

of replacement of water molecules decreased

is formed and equilibrium is established as shown:

*Stability and Applications of Coordination Compounds*

reaction can be written in generalized form as given:

The equilibrium constant K*f* of the reaction is given by:

n+.

ð1Þ

ð2Þ

ð3Þ

2+ as an

complex [1, 2].

example [3, 4]:

due to:

**24**

However, in some cases, it is found that Kn+1 > Kn because of unusual structural changes and changes in electronic configuration of the metal ion. The change in electronic structure of the metal ion causes the variation in the crystal field stabilization energy (CFSE). The complex with higher CFSE value will be stable, and the equilibrium constant for that complex formation will be high. One such example is the formation of [CdBr4] 2� complex in aqueous solution. The reaction of aqua complex [Cd(H2O)6] 2+ with Br� ligand exhibits four stepwise equilibrium or stepwise formation constants K1, K2, K3, and K4. The order of stepwise formation constants is observed as follows, K1 > K2 > K3 < K4, which is not in agreement with the common trend of K1 > K2 > K3 > K4. Aqua complex of most of the M2+ ions including Cd2+ are octahedral, whereas the halo complexes of Cd2+ ion are tetrahedral. The reaction sequence for the formation of [CdBr4] 2� is given as follows:

$$\begin{aligned} \begin{aligned} \text{[\$\mathsf{Cd}(\mathsf{H}\_{2}\mathsf{O})\_{5}]\$^{2+}\$} + \text{Br}^{\cdot} &\xrightarrow{\mathsf{K}\_{1}} \\ \text{[\$\mathsf{Cd}(\mathsf{H}\_{2}\mathsf{O})\_{5}\$Br]\$^{+}\$} + \text{Br}^{\cdot} &\xrightarrow{\mathsf{K}\_{2}} \\ \text{[\$\mathsf{Cd}(\mathsf{H}\_{2}\mathsf{O})\_{4}\$Br\$]^{2}\$} + \text{Br}^{\cdot} &\xrightarrow{\mathsf{K}\_{3}} \\ \text{[\$\mathsf{Cd}(\mathsf{H}\_{2}\mathsf{O})\_{4}\$Br\$]^{2}\$} + \text{Br}^{\cdot} &\xrightarrow{\mathsf{K}\_{4}} \\ \text{[\$\mathsf{Cd}(\mathsf{H}\_{2}\mathsf{O})\_{3}\$Br\$]^{+}\$} + \text{Br}^{\cdot} &\xrightarrow{\mathsf{K}\_{4}} \end{aligned} \\ \begin{aligned} \text{[\$\mathsf{Cd}(\mathsf{H}\_{2}\mathsf{O})\_{3}\$Br\$]^{2}\$} + \text{Br}^{\cdot} &\xrightarrow{\mathsf{K}\_{1}} \end{aligned} \end{aligned}$$

In the final step, there is an unusual structural change from six coordinated octahedral [Cd(H2O)3Br3] � complex to four coordinated tetrahedral [CdBr4] 2� complex in addition to change in the electronic configuration which lead to K4 > K3.

The formation constant (K*f*) is related to the standard Gibbs free energy change (ΔG°) and standard electrode potential (E°) according to following equations:

$$
\Delta \mathbf{G}^{\circ} = -\mathbf{R} \mathbf{T} \ln \mathbf{K}\_{\circ} \tag{4}
$$

$$
\Delta \mathbf{G}^{\circ} = -\mathbf{n} F \mathbf{E}^{\circ} \tag{5}
$$

$$\text{hence RTInK}\_f = \text{nFE}^\circ \tag{6}$$

Since ΔG° is a thermodynamic property, the formation constant is the measure of thermodynamic stability. From Eqs. (4) to (6), it can be interpreted that the thermodynamic stability of a complex can be measured in terms of formation constant, Gibbs free energy change, and standard electrode potential. A high negative value of ΔG° indicates that the position of equilibrium favors the product (complex); hence the complex formed will be more stable.

#### **1.2 Stepwise formation of complex and stepwise formation constants**

The formation constant describes the formation of a complex from metal cation and ligands. Bjerrum (1941) defined that the formation of a metal complex in aqueous solution takes place by replacing the water molecule by another ligand (L) [5, 6]. It is assumed that this reaction does not occur in a single step but occurs in several steps, and each step is characterized by its individual equilibrium constant called as stepwise formation constant (K). For example, consider the formation of a complex [MLn] formed by the following reactions:

$$\begin{array}{c} \text{ML} + \text{L} \xrightarrow{\text{K}^{\text{I}}} \text{ML} \end{array}$$

Above equation indicates that the overall formation constant (β) is equal to the

Kinetic stability is related to the reactivity of the metal complexes in solution and deals with the rate of the reaction, its activation energy, etc. Kinetic stability is also related to how fast a compound reacts rather than how stable it is. It aids in determining the rate at which the reaction occurs to establish the equilibrium [7]. The term kinetic stability of complexes is classified into labile and inert by Taube on the basis of rate of the reactions. When the rate of substitution of ligands is high, the complex is said to be labile. For example, the copper complex of the formula

when concentrated hydrochloric acid is added to this solution, the solution turns

reaction takes place at room temperature when conc. HCl was added to the aqueous solution. However, only one NH3 ligand was found to be substituted by Cl ligand, when the aqueous solution of the complex was heated with 6M hydrochloric acid.

For metal complexes, the stability and reactivity are described in thermodynamic and kinetic terms, respectively. In particular, the terms stable and unstable are related to thermodynamic aspects, whereas labile and inert terms are related to kinetic aspects. As a rule of thumb, a metal complex is said to be labile if it reacts within 1 min at 25°C, and if it takes longer time, it is considered to be inert.

Thermodynamic stability refers to the energy change that occurs while starting materials are converted to products, that is, ΔG, for the reaction. The change in free energy is given by the equation ΔG = ΔHTΔS = RTlnK, where ΔS is the entropy, ΔH is the enthalpy, and K is the equilibrium constant for the reaction. Kinetic stability refers to reactivity or the ability of the metal complex to undergo ligand substitution reactions. Complexes which undergo extremely rapid ligand substitution reaction are referred to as labile complexes, and complexes that undergo extremely slow ligand substitution reaction are referred to as inert complexes. Sometimes the thermodynamic and kinetic stabilities of complexes are parallel to one another, but often they do not. One of the suitable examples for thermody-

3+ is thermodynamically unstable but kinetically inert. The complex

3+ is thermodynamically unstable since the complex was observed to

decompose very rapidly with rate in the order of 1025 in acidic solution. However, no ligand substitution reaction is found when the complex is kept in acidic solution for several days; hence the complex is kinetically inert. From the above two examples, it can be interpreted that the stability of a complex mainly depends upon the

rate of ligand exchange is very slow, and the ligands are very exchanged with

**2. Relation between thermodynamic and kinetic stabilities**

namically stable and kinetically inert complex is [Ni(CN)4]

substitution reaction very rapidly. On the other hand, the cobalt complex

2+ is labile. In aqueous solution the complex is blue in color, and

2+. On the other hand, in inert complexes the

3+ reacts slowly, and no

2 as it undergoes ligand

product of the stepwise formation constant K1, K2, K3, … , Kn.

**1.3 Kinetic stability**

*Stability of Metal Complexes*

*DOI: http://dx.doi.org/10.5772/intechopen.90894*

[Cu(NH3)4(H2O)2]

[Co(NH3)6]

[Co(NH3)6]

**27**

green giving rise to complex [CuCl4]

difficulty. For example, the cobalt complex [Co(NH3)6]

By assuming the value of activity coefficients as unity, the equilibrium constant K1 for the complex (ML) having one ligand (L) will be given as

$$\mathbf{K}\_{\parallel} = \frac{[\mathbf{M}\mathbf{L}]}{[\mathbf{M}][\mathbf{L}]}$$

When the metal complex ML reacts with one more ligand L,

$$\begin{array}{cccc} \text{ML} & + \text{L} & \xleftarrow{\text{K}\_{2}} \text{ML}\_{2} \end{array}$$

and the equilibrium constant K2 will be

$$\mathbf{K\_2} = \frac{[\mathbf{ML}\_2]}{[\mathbf{ML}][\mathbf{L}]},$$

Similarly, for the formation of the complex MLn from MLn1 and L, the equilibrium constant is represented as follows,

$$\mathbf{K}\_{\mathfrak{n}} = \frac{[\mathbf{M}\mathbf{L}\_{\mathfrak{n}}]}{[\mathbf{M}\mathbf{L}\_{\mathfrak{n}-1}][\mathbf{L}]}$$

The equilibrium constants K1, K2, … , Kn are known as stepwise formation constants. On the other hand, the equilibrium constant for the overall reaction may be considered as

$$\begin{aligned} \text{M} &+ \text{ L} \xrightarrow{\overline{\text{B}\_{1}}} \text{ML}, & \quad \text{B}\_{1} - \frac{\text{[ML]}}{[\text{M}][\text{L}\_{1}]} \\ \text{M} &+ 2\text{L} \xrightarrow{\overline{\text{B}\_{2}}} \text{ML}\_{2}, & \quad \text{B}\_{2} = \frac{\text{[ML}\_{2}]}{[\text{M}][\text{L}\_{2}]^{2}} \\ \text{M} + 3\text{L} \xrightarrow{\overline{\text{B}\_{3}}} \text{ML}\_{3}, & \quad \text{B}\_{3} = \frac{[\text{ML}\_{3}]}{[\text{M}][\text{L}\_{1}]^{3}} \\ \text{M} + \text{nL} &\xrightarrow{\overline{\text{B}\_{n}}} \text{ML}\_{n}, & \quad \text{B}\_{n} = \frac{[\text{ML}\_{n}]}{[\text{M}][\text{L}\_{1}]^{n}} \end{aligned}$$

where β1, β2, β3, … , βn are the equilibrium constants called as overall formation constants and K1, K2, K3, … , Kn are stepwise stability or formation constants. The products of stepwise constants are Ks and βs are related one another. For example, consider the product of stepwise formation constants K1, K2, K3, … , Kn.

*Stability of Metal Complexes DOI: http://dx.doi.org/10.5772/intechopen.90894*

$$\mathsf{K}\_{1}\mathsf{x}\ \mathsf{K}\_{2}\ \mathsf{x}\ \mathsf{K}\_{3}\ \mathsf{x}\ \mathsf{x}\ \dots \mathsf{K}\_{n} \ = \frac{[\mathsf{M}\mathsf{L}\mathsf{L}]}{[\mathsf{M}\mathsf{L}][\mathsf{L}\mathsf{L}]}\ \mathsf{x}\ \frac{[\mathsf{M}\mathsf{L}\mathsf{L}\_{\mathsf{T}}]}{[\mathsf{M}\mathsf{L}][\mathsf{L}\mathsf{L}]}\ \mathsf{x}\ \frac{[\mathsf{M}\mathsf{L}\_{\mathsf{T}}]}{[\mathsf{M}\mathsf{L}\_{\mathsf{T}}][\mathsf{L}\mathsf{L}]}\mathsf{x}\ \cdots \frac{[\mathsf{M}\mathsf{L}\mathsf{n}]}{[\mathsf{M}\mathsf{L}\_{\mathsf{T}\mathsf{n}}][\mathsf{L}\mathsf{L}]}\ \mathsf{x}\ \mathsf{x}\ \cdots$$

$$=\frac{[\mathsf{M}\mathsf{L}\_{\mathsf{T}}]}{[\mathsf{M}\mathsf{M}][\mathsf{L}]}\mathsf{x}\ \mathsf{x}$$

Above equation indicates that the overall formation constant (β) is equal to the product of the stepwise formation constant K1, K2, K3, … , Kn.

#### **1.3 Kinetic stability**

[5, 6]. It is assumed that this reaction does not occur in a single step but occurs in several steps, and each step is characterized by its individual equilibrium constant called as stepwise formation constant (K). For example, consider the formation of a

By assuming the value of activity coefficients as unity, the equilibrium constant

Similarly, for the formation of the complex MLn from MLn1 and L, the equilib-

The equilibrium constants K1, K2, … , Kn are known as stepwise formation constants. On the other hand, the equilibrium constant for the overall reaction may

where β1, β2, β3, … , βn are the equilibrium constants called as overall formation constants and K1, K2, K3, … , Kn are stepwise stability or formation constants. The products of stepwise constants are Ks and βs are related one another. For example, consider the product of stepwise formation constants

complex [MLn] formed by the following reactions:

*Stability and Applications of Coordination Compounds*

and the equilibrium constant K2 will be

rium constant is represented as follows,

be considered as

K1, K2, K3, … , Kn.

**26**

K1 for the complex (ML) having one ligand (L) will be given as

When the metal complex ML reacts with one more ligand L,

Kinetic stability is related to the reactivity of the metal complexes in solution and deals with the rate of the reaction, its activation energy, etc. Kinetic stability is also related to how fast a compound reacts rather than how stable it is. It aids in determining the rate at which the reaction occurs to establish the equilibrium [7].

The term kinetic stability of complexes is classified into labile and inert by Taube on the basis of rate of the reactions. When the rate of substitution of ligands is high, the complex is said to be labile. For example, the copper complex of the formula [Cu(NH3)4(H2O)2] 2+ is labile. In aqueous solution the complex is blue in color, and when concentrated hydrochloric acid is added to this solution, the solution turns green giving rise to complex [CuCl4] 2+. On the other hand, in inert complexes the rate of ligand exchange is very slow, and the ligands are very exchanged with difficulty. For example, the cobalt complex [Co(NH3)6] 3+ reacts slowly, and no reaction takes place at room temperature when conc. HCl was added to the aqueous solution. However, only one NH3 ligand was found to be substituted by Cl ligand, when the aqueous solution of the complex was heated with 6M hydrochloric acid.

#### **2. Relation between thermodynamic and kinetic stabilities**

For metal complexes, the stability and reactivity are described in thermodynamic and kinetic terms, respectively. In particular, the terms stable and unstable are related to thermodynamic aspects, whereas labile and inert terms are related to kinetic aspects. As a rule of thumb, a metal complex is said to be labile if it reacts within 1 min at 25°C, and if it takes longer time, it is considered to be inert.

Thermodynamic stability refers to the energy change that occurs while starting materials are converted to products, that is, ΔG, for the reaction. The change in free energy is given by the equation ΔG = ΔHTΔS = RTlnK, where ΔS is the entropy, ΔH is the enthalpy, and K is the equilibrium constant for the reaction. Kinetic stability refers to reactivity or the ability of the metal complex to undergo ligand substitution reactions. Complexes which undergo extremely rapid ligand substitution reaction are referred to as labile complexes, and complexes that undergo extremely slow ligand substitution reaction are referred to as inert complexes. Sometimes the thermodynamic and kinetic stabilities of complexes are parallel to one another, but often they do not. One of the suitable examples for thermodynamically stable and kinetically inert complex is [Ni(CN)4] 2 as it undergoes ligand substitution reaction very rapidly. On the other hand, the cobalt complex [Co(NH3)6] 3+ is thermodynamically unstable but kinetically inert. The complex [Co(NH3)6] 3+ is thermodynamically unstable since the complex was observed to decompose very rapidly with rate in the order of 1025 in acidic solution. However, no ligand substitution reaction is found when the complex is kept in acidic solution for several days; hence the complex is kinetically inert. From the above two examples, it can be interpreted that the stability of a complex mainly depends upon the

conditions, and it is always recommended to specify the conditions such as pH, temperature, etc. while mentioning the stability of the complex. In brief, it is not necessary for a stable complex to be inert and an unstable complex to be labile.

*3.1.2 Size of central metal cation*

*DOI: http://dx.doi.org/10.5772/intechopen.90894*

*Stability of Metal Complexes*

The order of size of dipositive ions is

**3.2 Nature of ligands**

with NH3, H2O, and F� is:

in the following order:

**3.3 The chelate effect**

chloride, cyanide, and water.

ligand 2,20

**29**

CN�, alkene, phenanthroline, etc.

The stability of metal complex increases with decrease in size of the metal

Ba2þ < Sr2þ <Ca2þ < Mg2þ < Mn2þ < Fe2þ < Co2þ < Ni2þ <Cu2þ >Zn2þ

This order of stability is also in good agreement with the charge to radius ratio concept because the radii decrease from Ba2+ to Cu2+ and then increased to Zn2+.

Ba2þ > Sr2þ >Ca2þ > Mg2þ > Mn2þ > Fe2þ > Co2þ > Ni2þ >Cu2þ <Zn2þ

Basic character of ligands: The greater is the basic character of ligand, the more easily it can donate its lone pair of electrons to the central metal ion and hence greater is the complex stability. In 3D-series metal ion, order of stability of complex

NH3 > H2O >F�

The nature of metal-ligand bond also affects the stability of metal complexes. The higher the covalent character, the greater will be the complex stability. For example, the stabilities of silver complexes have different halide ligands which are

� > AgCl2

Ligands having vacant p- or d-orbital tend to form π bond and hence form stable complexes with metals. Ligands that are capable of forming such π bond are CO,

The chelate effect is that the complexes resulting from coordination of metal ions with the chelating ligand are thermodynamically much more stable than the complexes with non-chelating ligands [10, 11]. Chelating ligands are molecules which can bind to single metal ion through several bonds and are also called as multidentate ligands. Simple (and common) examples include ethylenediamine and oxalate. Non-chelating ligands are ligands that bond to just one site, such as

The chelate effect can be understood by comparing the reaction of a metal ion,

Another such comparison can be made between coordination behavior of chelating 1,2-diaminoethane (ethylenediamine = en) and monodentate ammonia. Such

respectively, with a chelating ligand and with a monodentate ligand having similar/comparable donating groups. During the comparison study, the number of coordination should be maintained equal in both the cases, for example, the value obtained while adding a bidentate ligand is compared with the value obtained for two monodentate ligands. For example, coordination of metal ion with chelating

� > AgF2

�

cations. For M2+ ions, the general trend in stability for complexes is

This trend in stability is known as Irving-Williams series.

AgI2

� > AgBr2

Consider the three complexes [Ni(CN)4] 2, [Mn(CN)6] 3, and [Cr(CN)6] 3. All the complexes are thermodynamically stable, but kinetically they behave in a different manner. The rate of exchange can be measured when carbon-14-labelled cyanide ions are reacted with metal complexes in solution. It indicates that [Ni(CN)4] 2 is labile, [Mn(CN)6] 3 is less labile, and [Cr(CN)6] 3 is inert and proves that not all stable complexes are inert and vice versa.

$$\begin{array}{ccccc} \text{ $ [\mathsf{Nil}(\mathsf{CN})\_4\]\_2$ ^{2-} + 4} & \text{ $ 4}^{\mathsf{T4}}\mathsf{CN}^- & \xrightarrow{\mathsf{V8}\mathsf{N}\mathsf{V}} & \text{[$ \mathsf{Nil}(\mathsf{"}\mathsf{CN})\_4\]\_2^{2-} + 4} & \text{[ $\mathsf{Nil}(\mathsf{"}\mathsf{CN})\_4\}\_2^{2-} \\\\ & & & \text{t}\_{1\mathsf{N2}} = \mathsf{30}\mathsf{sec} \\\\ \text{[$ \mathsf{M}(\mathsf{CN})\_6\}\_2^{3-} + 6\ \mathsf{T}\mathsf{N}\mathsf{N} & \xrightarrow{\mathsf{s}\mathsf{I}\mathsf{s}\mathsf{C}\mathsf{N}\mathsf{N} \\\\ & & \text{t}\_{1\mathsf{N2}} = \mathsf{T}\mathsf{h}\mathsf{r} \end{array}$$

$$\begin{array}{ccccc} \text{[Cl(CN)\$^{3}\$]}^{3-} + & \text{[} & \text{44\$^{2}\$CN}\$^{-} & \text{[} & \text{\$\text{\$Cl\$^{(4}\$CN)\$^{(8}\$)}\$} \\\\ & & & \text{t\$\_{12}\$=24\$days} \end{array}$$

## **3. Factors affecting the stability of metal complexes**

There are several factors that can affect the stability of the metal complexes [2, 5, 8, 9], which include:

#### **3.1 Nature of central metal ion**

#### *3.1.1 Charge on metal cation*

In metal cations, higher oxidation state forms more stable complex than lower oxidation states with ligands such as NH3, H2O, etc. Even few exceptions are there like CO, PMe3, o-phenanthroline, bipyridyl, CN, which form more stable complex with lower oxidation state metals.

#### *3.1.2 Size of central metal cation*

conditions, and it is always recommended to specify the conditions such as pH, temperature, etc. while mentioning the stability of the complex. In brief, it is not necessary for a stable complex to be inert and an unstable complex to be labile.

All the complexes are thermodynamically stable, but kinetically they behave in a different manner. The rate of exchange can be measured when carbon-14-labelled

cyanide ions are reacted with metal complexes in solution. It indicates that

proves that not all stable complexes are inert and vice versa.

**3. Factors affecting the stability of metal complexes**

[2, 5, 8, 9], which include:

2.Nature of the ligand

3.Chelating effect

4.Macrocyclic effect

5.Resonance effect

1.Nature of the central metal ion

6. Steric effect or steric hindrance

**3.1 Nature of central metal ion**

with lower oxidation state metals.

*3.1.1 Charge on metal cation*

**28**

There are several factors that can affect the stability of the metal complexes

In metal cations, higher oxidation state forms more stable complex than lower oxidation states with ligands such as NH3, H2O, etc. Even few exceptions are there like CO, PMe3, o-phenanthroline, bipyridyl, CN, which form more stable complex

2, [Mn(CN)6]

3 is less labile, and [Cr(CN)6]

3, and [Cr(CN)6]

3 is inert and

3.

Consider the three complexes [Ni(CN)4]

*Stability and Applications of Coordination Compounds*

2 is labile, [Mn(CN)6]

[Ni(CN)4]

The stability of metal complex increases with decrease in size of the metal cations. For M2+ ions, the general trend in stability for complexes is

$$\text{Ca}^{2+} < \text{Sr}^{2+} < \text{Ca}^{2+} < \text{Mg}^{2+} < \text{Mn}^{2+} < \text{Fe}^{2+} < \text{Co}^{2+} < \text{Ni}^{2+} < \text{Cu}^{2+} > \text{Zn}^{2+} $$

This trend in stability is known as Irving-Williams series.

This order of stability is also in good agreement with the charge to radius ratio concept because the radii decrease from Ba2+ to Cu2+ and then increased to Zn2+. The order of size of dipositive ions is

$$\text{Ca}^{2+} > \text{Sr}^{2+} > \text{Ca}^{2+} > \text{Mg}^{2+} > \text{Mn}^{2+} > \text{Fe}^{2+} > \text{Co}^{2+} > \text{Ni}^{2+} > \text{Cu}^{2+} < \text{Zn}^{2+} $$

#### **3.2 Nature of ligands**

Basic character of ligands: The greater is the basic character of ligand, the more easily it can donate its lone pair of electrons to the central metal ion and hence greater is the complex stability. In 3D-series metal ion, order of stability of complex with NH3, H2O, and F� is:

$$\text{NH}\_3 > \text{H}\_2\text{O} > \text{F}^-$$

The nature of metal-ligand bond also affects the stability of metal complexes. The higher the covalent character, the greater will be the complex stability. For example, the stabilities of silver complexes have different halide ligands which are in the following order:

$$\text{AgI}\_2^- > \text{AgBr}\_2^- > \text{AgCl}\_2^- > \text{AgF}\_2^-$$

Ligands having vacant p- or d-orbital tend to form π bond and hence form stable complexes with metals. Ligands that are capable of forming such π bond are CO, CN�, alkene, phenanthroline, etc.

#### **3.3 The chelate effect**

The chelate effect is that the complexes resulting from coordination of metal ions with the chelating ligand are thermodynamically much more stable than the complexes with non-chelating ligands [10, 11]. Chelating ligands are molecules which can bind to single metal ion through several bonds and are also called as multidentate ligands. Simple (and common) examples include ethylenediamine and oxalate. Non-chelating ligands are ligands that bond to just one site, such as chloride, cyanide, and water.

The chelate effect can be understood by comparing the reaction of a metal ion, respectively, with a chelating ligand and with a monodentate ligand having similar/comparable donating groups. During the comparison study, the number of coordination should be maintained equal in both the cases, for example, the value obtained while adding a bidentate ligand is compared with the value obtained for two monodentate ligands. For example, coordination of metal ion with chelating ligand 2,20 -bipyridine can be compared with that of monodentate pyridine ligand. Another such comparison can be made between coordination behavior of chelating 1,2-diaminoethane (ethylenediamine = en) and monodentate ammonia. Such

comparison studies revealed that the metal complex formed from chelating ligands are thermodynamically more stable than the complex formed from monodentate ligand. For example, formation of complexes from hydrated cadmium ion, [Cd(H2O)4] 2+ with methylamine (CH3NH2), ethylenediamine (en) and triethylenetetramine (trien), and their stability is in the following order:

**3.6 Steric effect**

*Stability of Metal Complexes*

*DOI: http://dx.doi.org/10.5772/intechopen.90894*

shown in **Figure 3**.

stability of the complex.

**Figure 3.**

**3.7 Crystal field stabilization energy (CFSE)**

*Chelating complexes of Ni(II) ion showing steric effect.*

**4. Determination of stability constants**

**4.1 Spectroscopic methods**

**31**

The presence of bulky substituents in the ligands can affect the stability of the metal complex, and this type of destabilization of metal complex due to bulkiness of the substituent is called as steric effect [13]. For example, consider the ligand 8-hydroxy quinoline and its methyl substituted derivative 2-methyl-8-hydroxy quinolone. Both are bidentate ligands and form chelated complexes with Ni2+ ion as

The complex (II) is less stable than complex (I) because of bulky group attached to an atom adjacent to donor atom which cause a steric hindrance and lower the

The crystal field stabilization energy (CFSE) is one of the most important factors that decides the stability of the metal complexes. CFSE is the stability that arises when a metal ion coordinates to a set of ligands, which is due to the generation of a crystal field by the ligands. Thus, a higher value of CFSE means that the complex is thermodynamically stable and kinetically inert. Some of the notable examples of complexes that have high CFSE are low spin 5d6 complexes of Pt4+ and Ir3+ and square planar 5d8 complexes of Pt2+. All these complexes are thermodynamically stable and kinetically

The determination of metal complexes involves several methods including spectroscopic and potentiometric methods. The determination of stability constant is very significant to understand the role and behavior of ligand(s) in stabilizing the metal complexes and found applications in the fields of biology, environmental study, metallurgy, food chemistry, and many other industrial processes. Some of the methods that are used for the determination of stability constants are given as follows.

UV-Vis spectroscopic technique has been used to determine the stability constant and composition of a complex [14]. The formation of metal complex is indicated by the change in absorbance in the UV-Vis spectroscopy. The relationship

A ¼ ԑ*:*c*:*l*:*

between absorbance (A) and concentration is given by Beer's law as shown.

inert, which undergo ligand substitution reactions extremely slowly [3, 4].

$$\left[\text{Cd}(\text{CH}\_3\text{NH}\_2)\_4\right]^{2+} < \left[\text{Cd}(\text{en})\right]^{2+} < \left[\text{Cd}(\text{trien})\right]^{2+} $$

### **3.4 Macrocyclic effect**

A macrocyclic ligand is a cyclic molecule that contains nine or more atoms in the cyclic structure and has three or more potential donor atoms which can coordinate to the metal ion. It has been observed that the stability of metal complexes in the presence of macrocyclic ligand of appropriate size is higher than the stability of complexes coordinated to open-ended multidentate chelating ligands. Some notable examples of macrocyclic ligands include cyclic crown polyether, heme, etc. [12].

#### **3.5 Resonance effect**

Resonance increases the stability of the complexes. For example, acetylacetonate anion ligand shows resonance, and as a result it forms stable complexes upon reacting with metal ion (**Figure 1**). The ligand-metal π bonding increases the delocalization of electrons compared to free enolate as shown below and leads to increased stability (**Figure 2**).

**Figure 1.** *Resonance structure of acetonylacetonate ligand.*

**Figure 2.** *Acetonylacetonate-metal complex.*


Author details

Mohamed Aboualalaa\* and Hala Elsadek Electronics Research Institute, Cairo, Egypt

\*Address all correspondence to<EMAIL_ADDRESS>
© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Rectenna Systems for RF Energy Harvesting and Wireless Power Transfer DOI: http://dx.doi.org/10.5772/intechopen.89674


**5. Conclusions**

Given the fundamental role played by water networks in daily life and business activities, the present research focuses on suitably operating, managing, and maintaining these assets. In this regard, the problem of optimal sensor placement has been faced with the aim of improving the operations of monitoring and the control of the networks.

Most used methods calculate the sensitivity matrix for a specific simulation time, usually the highest consumption time. The fuzzy DEMATEL handles extended period simulations, suitably transformed into fuzzy numbers. The approach enables us to have information for many horizon simulations, making sensor placement more robust. Other possible applications of fuzzy DEMATEL are the simulations of several leakage scenarios with different emitter coefficients. In that case, the sensitivity matrix could be built considering from small to large leaks.

The use of the sensitivity matrix to generate a conditional entropy helps guarantee the spread of sensors in the network. A clear improvement is found, as observed from the comparisons between results from global sensitivity and global entropy of the sensor network, as shown in the case study.

The use of fuzzy DEMATEL for optimal sensor placement helps water companies identify the most suitable monitoring points. Using conditional entropy, the spread of sensors is guaranteed by using the last positions of the DEMATEL ranking. One important positive point of this approach is the absence of optimisation, which usually requires prior knowledge of the number of sensors to be installed. With the presented fuzzy DEMATEL approach, the sensors' network can be implemented in steps, without requiring new simulations.

The fuzzy DEMATEL approach presented in this paper produces similar results to the ones obtained with the optimisation algorithm in [7]. Both methodologies use sensitivity and entropy to place sensors in the network. The main advantage of fuzzy DEMATEL hinges on the final rank obtained: this rank enables placing new sensors without performing new simulations. In optimisation-based approaches, adding new sensors requires new simulations. Incidentally, the approach of WaterIng© finds a solution with better results for both sensitivity and entropy.

Possible future developments of the presented research may regard further investigations about how to choose other quantitative parameters to collect input data. For example, the proposed modified version of the fuzzy DEMATEL may be integrated with other MCDM methodologies to identify a suitable set of parameters, all related to relationships of influence among the considered factors. The selection of the number of sensors should also be further investigated, so as to provide the utilities with a Pareto-like solution enabling them to select the most appropriate number, an aspect not treated in this paper. Such a joint process made of (multi-objective) optimisation plus MCDM methods can be a way of identifying the optimal number of sensors, using the ranking provided for the fuzzy DEMATEL methodology herein developed.

**Author Contributions:** Conceptualisation, S.C. and J.F.-C.; methodology, B.M.B. and S.C.; software, B.M.B. and I.M.; validation, S.C. and J.F.-C.; formal analysis, J.I. and I.M.; writing—original draft preparation, J.F.-C., B.M.B., and S.C.; writing—review and editing, J.I.; supervision, J.I. and I.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research has been partially supported by the CNPq grant with number 156213/2018-4.

**Conflicts of Interest:** The authors declare no conflict of interest.


**5.1 Humble dome anomaly, Houston, USA**

Gravity map was acquired over the Humble Dome, Houston, Texas. At the earth's surface, the measurements of this salt dome structure reveal a negative circular contoured Bouguer anomaly ([41], Figures 8–16). A Bouguer gravity profile is taken across the center of the Humble salt dome gravity map in Houston ([41], Figures 8–16). The Bouguer gravity profile was subject to a suitable separation method to remove the regional anomaly and obtain the residual gravity anomaly. The residual gravity anomaly profile of about 26 km long was digitized at an interval of 0.26 km (**Figure 10a**).

The R-parameter method procedures were applied to the residual gravity anomaly profile for the available shape parameters (**Table 6**). **Figure 10b–d** express the horizontal and vertical derivative anomalies, the amplitude analytic signal, and the R-parameter 2-D mosaic. It is found that the R-max value is 0.99 corresponds to a

#### **Figure 10.**

*The Humble dome anomaly, USA. (a) Gravity anomaly profile (red dotted lines) and the optimum-fitting model (solid black line), (b) Horizontal and vertical gradients of (a), (c) Analytic signal anomaly using the data of (b), and (d) 2-D mosaic of the R-parameter and the R-max value.*

**Table 6.**

*The Humble dome gravity anomaly, USA. The R-parameter calculated from different shape factors.*

## **Table 7.**

*The Humble dome gravity anomaly, USA. The Estimated parameters.*

spherical shape (*q* = 1.5). The best estimated model parameters are: *q* = 1.5, *z*o = 4.90 m, *x*o = 0 m, and *A* = 269.39 mGal m2 .

The humble dome anomaly has been interpreted by several authors assuming a spherical source to decide the depth of the salt body. The obtained results agree well with those depths to the center that obtained by the published literatures of [36, 41, 47, 54–56] (**Table 7**).

By using a density contrast of 0.13 gm/cm3 of [41], then the depth to the top of the spherical body of the humble dome obtained from the proposed technique is 315 m, which in excellent covenant with the true depth (305 m) confirmed by drilling and seismic information [41]. **Table 8** shows that several other researchers

#### **Table 8.**

*Depth to the top of the spherical body of the Humble dome anomaly, obtained by various approaches using an assumed density contrast (Δ*ρ*) of 0.13 gm/cm3 [41].*

*Gravity Anomaly Interpretation Using the R-Parameter Imaging Technique over a Salt Dome DOI: http://dx.doi.org/10.5772/intechopen.105092*

utilizing the same density contrast found some differences in the depths to the top of this spherical source. The use of simple geometrically bodies in the constrained class of spheres, horizontal cylinders, and vertical cylinders is thus suggested as a way to accurately apply the current methodology to extract depth information. As a result, if exact density contrasts are used, the related radii can be correctly computed as well.


*2.4. Vascular Resistance*

Arterial vascular Resistance (*aVR*) was calculated as millimeters of mercury per milliliter per minute (mmHg/mL/min) based on a previously reported method in adherence to the Poiseuille's Law, using the following formula: [28,29]

$$R = \Delta P/Q$$

*R* = *aVR* = arterial vascular resistance, ∆*P* = blood pressure gradient = mean arterial blood pressure (*MAP*)–mean venous blood pressure (MVP). The mean venous blood pressure (MVP) is estimated to be close to 0 and, as a result, disregarded in the calculation of vascular resistances. This results in the following formula: [28–31]

$$aVR = MAP/aBF$$

#### *2.5. Data Analysis and Synthesis*

Descriptive analysis was performed for patient demographics. Data are shown as mean ± standard deviation. Changes in blood flow and vascular resistance between the different time points within one group were calculated using the paired Student's *t*-test. Blood flow and vascular resistance between DIEP and ms-TRAM flaps at different time points was analyzed using an unpaired Student's *t*-test. Nonparametric data were analyzed with the Wilcoxon matched-pairs rank test within one group, whereas the Mann–Whitney U test was used for analyses of nonparametric data between DIEP and ms-TRAM flaps. The correlation of data assuming Gaussian distribution was calculated using the Pearson correlation coefficient. The Spearman's rank correlation coefficient was used for data not passing a test for normality. The significance level was set at *p* < 0.05. Three outliers (one arterial and two venous blood flow values at the recipient site (Measurement *R*) before anastomosis) were identified using the ROUT method (*Q* = 1%) and appropriately excluded from statistical analysis. Statistical analyses and graphic illustrations were performed using GraphPad Prism (GraphPad Software, Inc., San Diego, CA, USA).

### **3. Results**

A total of 20 female patients receiving 24 DIEP or ms-TRAM flaps for breast reconstruction were included in this prospective study. Patients' average age was 52 years, ranging from 39 to 68 years. Fourteen flaps were harvested as DIEP (57%), and 10 as ms-TRAM (43%). Seven ms-TRAM flaps were classified as ms1-TRAM flap, and three as ms2-TRAM flap, according to the classification by Nahabedian et al. (Table 1) [32]. The median flap weight was 435 g, ranging from 299 to 1169 g. The median weight of DIEP flaps (390 g) was not significantly different from that of ms-TRAM flaps (491 g). The average flap ischemia time was 46 min. The venous coupler size ranged from 2.5 to 3.5 mm.

#### *3.1. Blood Flow Volume (mL/min)*

The average blood flow of the flap artery isolated as pedicle prior to free tissue transfer (F) was 9 ± 4 mL/min (mean ± SD). Its venous outflow was lower (7.5 ± 3.5 mL/min), resulting in an artery-to-vein (A/V) flow ratio of 1.4 ± 0.7. The mean blood flow of the recipient internal mammary artery and vein prior to flap anastomosis (R) was 16.9 ± 6.3 and 9.4 ± 8 mL/min, respectively. After anastomosis (AA), the arterial and venous blood flow volume was 11.3 ± 5.3 and 7.4 ± 4.1 mL/min, respectively, with an A/V flow ratio of 1.8 ± 1.3. The arterial blood flow of the intact recipient artery (R) significantly decreased after anastomosis with the flap artery (AA) (*p* = 0.002). However, the arterial and venous blood flow of the included flaps did not significantly change after flap transfer. (Figure 3) The blood flow of the intact recipient artery (R) did not alter the blood flow of the flaps after anastomosis. There was a significant positive correlation between the arterial inflow and the venous outflow both before (F) and after anastomosis (AA) (*p* < 0.05). The arterial and venous blood flow rates before and after anastomosis in DIEP flaps were lower than in ms-TRAM flaps (Table 2). There was no correlation between the arterial blood flow volume and the flap weight. The flap ischemia time did not change the blood flow rates of the examined flaps.

#### *3.2. Vascular Resistance (mmHg/mL/min)*

The mean arterial vascular resistance (aVR) of the included flaps prior to tissue transfer (10 ± 4.2 mmHg/mL/min) did not significantly change after anastomosis (9.2 ± 5.2 mmHg/mL/min). The vascular resistance of the recipient artery, however, significantly increased from 5.4 ± 2.6 to 9.2 ± 5.2 mmHg/mL/min after anastomosis to the flap (*p* < 0.001). The average arterial vascular resistance (aVR) of DIEP flaps prior to (F) and after flap transfer (AA) was 12 ± 3.8 and 11.2 ± 5.8 mmHg/mL/min, respectively. By contrast, ms-TRAM flaps had significantly lower arterial vascular resistance values prior to (7.2 ± 3 mmHg/mL/min; *p* = 0.004) and after flap reperfusion (6.5 ± 2.3 mmHg/mL/min; *p* = 0.02) (Figure 4 and Table 3). There was no correlation between the arterial vascular resistance and the weight of the included flaps before or after flap transfer.

**Table 1.** Characteristics of the included patients. Abbreviations: DIEP: deep inferior epigastric perforator; ms-TRAM: muscle-sparing transverse rectus abdominis musculocutaneous.

**Figure 3.** Arterial and venous blood flows (mL/min) at three predefined time points (F, R, AA). The bars represent means ± standard error (\* indicates significant differences).

Bold numbers indicate significant differences.

**Figure 4.** Arterial Vascular Resistance (aVR) at three predefined time points (F, R, AA). The bars represent means ± standard error (\* indicates significant differences).

**Table 3.** Comparison of Arterial Vascular Resistances (mmHg/mL/min) of the flap pedicle in situ (F), of the Recipient Artery (R) and After Anastomosis (AA).

The bold numbers indicate significant differences.


*4.2. Reflection on Research Questions*

The first research question referred to the common use-cases of energy communities, which are described in Section 3.1. While a majority of ECs are renewable energy communities, there is an abundance of ways actors can cooperate on energy-related matters. There are also obvious synergies among use-cases for hybrid, or multi-purpose energy communities to be developed. Some ECs already diversify their services, such as acquiring storage after saving up from energy sales revenues [14,89,90]. On the one hand, this trend points to a potential for existing ECs to pilot new unique or hybrid use-cases, leapfrogging some of the initiation-exclusive progression factors and accelerating EC uptake. On the other hand, more research into the development, drivers and barriers of novel use-cases are needed. Especially when it comes to hybrid use-cases and multi-purpose ECs, both the progression factors influencing the projects and the impacts will be a result of multiple interacting core activities. It has been noted in previous reviews that such assessment is a research gap [2,6], and this study has found only one article discussing co-impacts [55].

The second research question referred to the various progression factors of ECs, collected and compiled in Section 3.3. A full classification of progression factors is presented in Appendix A. Due to limitations mentioned above, only one essential classification can be considered conclusive: by lifecycle phase. While the case studies and reviews identified four distinct phases (see Section 3.2), the analysis of progression factors revealed a clear distinction between operation and all other phases. This is reasonable, considering operation refers to the continuity of some form of status-quo, while initiation, design, early implementation, and various further developments are changes in the status quo. Most progression factors refer to initiation either exclusively or together with other phases. In reflection to the practical objective of supporting EC planners and policymakers, the EC progression factors by lifecycle phase are summarized on a project lifecycle wheel, reflecting the weight of each phase (Figure 22).

The third research question referred to the utility of UBEM tools in the various lifecycle phases of ECs, which is described in Section 3.4. It was shown that free, web-based hybrid or reduced order bottom-up models with over-hourly output resolution and heterogeneous output types and energy service modelling are most suitable for social upscaling; while bottom-up co-simulation model with an econometric model, sub-hourly output and diverse range of energy services modelling on district scale and the aforementioned tool are equally the best suited for initiation. There is only one existing tool for the former CityBES [116], and several for the latter HUES [117], UMEM [113], MESCOS [114]. In general, most UBEM capabilities deliver affordances for initiation and design stages, where most progression factors are. This also feeds into the main research question, whether UBEM is a technological trigger. The potential of UBEM, and UBEM-based simulation pipelines lie in the fact that they offer flexible decision-support in the earlier stages of projects, and whenever they are further developed. While decision-support for the operation of energy communities would require short term dynamic predictions on high resolutions to optimize the operation of energy communities, UBEM is a far more cost-efficient, early-stage alternative, requiring less input data and returning easy-to-understand outputs. To provide a quick tool for EC planners, the UBEM capabilities to look for based on progression factors, is summarized on a bipartite graph (Figure 23).

Reflecting on the second practical objective, recommending a development direction for UBEM, the trends in EC use-cases (see discussion above, based on section) make a good argument to invest in UBEM tool agility. The most impactful modelling capabilities were output resolution, output diversity, modularity and web deployment. Resolution on sub-hourly levels is necessary to forecast interactions on P2P energy markets, as trading usually occurs with 15-min frequency [27]. Output diversity and modularity becomes important with the diversification of energy community use-cases, and the growing prevalence of multi-purpose communities, such as green neighbourhoods. The value of UBEM tools is likely going to be determined by how many intertwined inputs and impacts do they handle, whom can be convinced with the evidence simulations provide. In other words, UBEM needs to respond well to in- and output diversification. This is why all affordances are met by USEM tools, whereas only two out of five are met by UBEM-only tools. Tools that either integrate UBEM with other models, such as City Energy Analyst [118], LakeSIM [119], CitySIM [120] and UrbanFootprint [109] with in-built transportation models, or tools that are modular and technically scalable, such as SEMANCO [111], UMEM [113], will be better suited to deliver diverse outputs reflecting EC use-case diversification. However, scalability to diverse, often uncertain and low-quality input data, which necessitates robust modules for data ingestion and pre-processing, is still something UBEM pipelines struggle with [121]. Finally, apart from architecture and functionalities, accessibility to users is also crucial, as seen by the performance of web-based tools versus desktop tools. While this was not explored as modelling tools are designed for engineers, user friendliness could be a pivotal improvement in the EC context. Given that laypeople gain formal powers and responsibilities in the EC model, tools in the future could support simple functionalities for users outside a niche of experts.

**Figure 22.** Energy community lifecycle wheel: distribution of progression factors by lifecycle phase.

Finally, reflecting on the research of energy communities, affordances have been a seamless addition to the conceptual frameworks of transition theory, multi-level perspective (MLP) and strategic niche management, as a missing link between the capabilities of enabling technologies, and the challenges posed by socio-technical transitions. We argue that technological affordances deserve an equal footing with institutional design and behaviour change, among factors that enrich any niche concept, be it a fundamentally technical, or a fundamentally social niche. Furthermore, the concept of MLP substantiates the influence of energy communities and UBEM tools on the user behaviour and preferences, which can gradually change the extraneous forces of the landscape, such as climate change. More articles need to be written on the role of technological affordances in fostering sustainable socio-technical transitions, with a special attention to disruptive technologies.


**Author details**

Farwa Munir1 , Nida Islam2 , Muhammad Hassan Nasir1 , Zainab Anis2 , Shahar Bano2 , Shahzaib Naeem3,4, Atif Amin Baig1 \* and Zaineb Sohail3,4

1 Universiti Sultan Zainal Abidin, Malaysia

2 School of Food and Agriculture sciences, University of Management and Technology, Lahore, Pakistan

3 Surriya Azeem Teaching Hospital, Pakistan

4 Department of Life Sciences, University of Management and Technology, Lahore, Pakistan

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Impact of Hypoxia on Astrocyte Induced Pathogenesis DOI: http://dx.doi.org/10.5772/intechopen.106263*


**9. Advocate for best practices in the postpartum period**

Changing behavior to promote a positive attitude in low- and middle-income countries is an element that should be practiced at the base of primary healthcare settings and referred obstetric hospitals. The duty of the healthcare services is to provide adequate care for women during the postpartum period. Designing effective interventions based on practically sound activities related to the postpartum period, accepted by the local communities and adopted to sustain the well-being of women and their families is a crucial step to maximize engagement and outcomes in these communities.

Such required activities and practices focus on behavioral change and address factors related to effective knowledge, attitudes, and norms as part of the interventions. The World Health Organization guidelines addressing postpartum care are welldefined and able to apply and accommodate such communities with low resources [41]. These interventions often complement and enhance the role played by services such as health promotion and education for health care services like family planning, antenatal care, delivery in a skilled birth attendant, and postnatal care [25, 42]. Social and behavior change interventions are critical to ensure that populations that are most in need can access available services and products. This is often achievable through a well-planned and systematically implemented social and behavior change intervention that is based on formative research. In addition, a good, strategic plan that is based on identifying the barriers, mode of communication to the population, and tailored messages to address specific behaviors to enhance the proper practices of women, family, and healthcare services toward improving the impact of postnatal *Perspective Chapter: Contemporary Challenges in Postnatal Care in Low- and Middle-Income… DOI: http://dx.doi.org/10.5772/intechopen.111446*

practices in low- and middle-income countries is crucial [41]. However, implementing best-practice for postnatal activities may require a better understanding of the situation by the health authorities and relevant stockholders working in the area of health services and care. In addition, it is wise to design a focused strategy, developing interventions and materials, and implementing, monitoring, evaluating, and adjusting the planned strategies [43]. Various activities could be included in this planning strategy such as raising awareness, reducing misinformation, and addressing barriers to various lifesaving and health-promoting interventions among individuals, families, and communities.


**Author details**

Shaopeng Zhong Dalian University of Technology, Dalian, China

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.