Deformation of the foundation for the case ’a’.
\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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Unflagging growth of anthropogenic activities has been causing changes in the Earth’s climate. These changes have led to the changes of weather in comparison to the past. Changes in weather frequently have brought increased values of loads (e.g. due to wind, snow and water) which can significantly influence reliability (see, e.g. Tikalsky et al., 2005; Pustka et al., Raizer, 2009; Briaud et al., 2014; Králik and Králik, 2014; Markova et al., 2014; Pustka, 2014; Janas et al., 2015; Pustka, 2015; Koteš et al., 2016) of (civil) engineering structures. To assure required level of reliability of these structures, it is necessary to deal with this issue. Climate’s changes have brought, among others, heavier precipitations which have led to excessive water flows or even to floods. This unexpected flows of water can significantly damage bridge structures crossing these watercourses (see, e.g. Cajka and Manasek, 2005; Link et al., 2008; Pasiok and Stilger-Szydlo, 2010; Burns et al., 2011; Wang et al., 2011; Yu et al., 2011; Khosronejad et al., 2012; Collins et al., 2013; Lin et al., 2014; Afzali, 2015; Ehteram and Meymand, 2015; Klinga and Alipour, 2015; Fael et al., 2016; Mohamed et al., 2016). In association with this growing risk, a study examining effects of scour to a bridge abutment was elaborated.
\nIn the following model, an example of a bridge pier (Strasky et al., 2001; Navratil, 2004; CNI, 2005; Parke and Nigel, 2008; Navratil and Zich, 2013; Sucharda and Brozovsky, 2013) is considered. To analyse interaction between the basement rock and foundation (see, e.g. CNI, 1988; CNI, 2004; Cajka et al., 2011; Cajka, 2013a,b,c; Cajka et al., 2014; Unlu et al., 2013; Hrubesova et al., 2015; Lahuta et al., 2015; Hrubesova et al., 2016; Cajka et al., 2016a,b; Labudkova and Cajka, 2016) a parametric study has been created. In the study, the finite element method on elastic subsoil has been utilised. The floods increase the cross-section of the river bed and change the properties of the foundation soil under the foundation (see, e.g. Ettema et al., 2000). In the first stage, the soil saturates with water. In the second stage fine-grained particles will wash away. In the third stage, parts of the basement rock will be washed off.
For the calculation of interaction between the foundation and basement finite element method has been used (FEM consulting, 2002). The foundation has been modelled in a 2D environment using spatial components. For the basement rock, an element with effects of an elastic foundation has been used. The
The most efficient way for solutions of interaction tasks is a 2D model of the basement rock. Such model represents correctly, through a surface model, deformation properties of the whole mass of the foundation soil. The physical properties are expressed by means of subsoil parameters. The set of the interaction parameters is marked briefly as
As a material for the foundation concrete C16/20 has been considered. Dimensions of the abutment pier are evident from Figure 1. The pier has been loaded by the horizontal load-carrying structure of the bridge (forces
Scheme of the abutment pier with considered loads.
As far as the structure of the abutment pier is concerned, the foundation structure has been used only for the calculation. The loading of the whole upper construction has been re-calculated and simplified. Only the vertical loading and bending moment in the centre of gravity of the stem have been taken into consideration. The basement rock has been modelled using the
The foundation with considered distributions of the basement rock stiffness
The flow of water washes away the basement rock. This reduces the contact surface resulting in increase of the stress in the foundation joint. Because of the non-homogeneous distribution of the tension in the foundation joint, the settlements in points 1 and 2 (see Figure 2) are different. Consequently, the foundation joint rotates. Table 1 shows the settlements of the pier in the points 1 and 2 and the total rotation. Assumed deformation of the foundation is shown in Figure 3. Rotation is calculated according to Eq. (1):
Assumed deformation of the foundation.
Origin (1.9 – | Δ | Rotation of foundation [deg] | Max. stress on foundation surface [MPa] | |||
---|---|---|---|---|---|---|
0.0 | 1.9 | 6.92 | 11.98 | 5.06 | 0.152 | 0.299 |
0.1 | 1.8 | 5.50 | 14.95 | 9.46 | 0.285 | 0.361 |
0.2 | 1.7 | 3.68 | 19.07 | 15.39 | 0.464 | 0.435 |
0.3 | 1.6 | 1.35 | 24.81 | 23.46 | 0.707 | 0.526 |
0.4 | 1.5 | –1.66 | 32.88 | 34.54 | 1.042 | 0.638 |
0.5 | 1.4 | –5.57 | 44.37 | 49.94 | 1.506 | 0.778 |
0.6 | 1.3 | –10.71 | 60.99 | 71.70 | 2.163 | 0.955 |
0.7 | 1.2 | –17.56 | 85.45 | 103.01 | 3.109 | 1.182 |
0.8 | 1.1 | –26.83 | 122.29 | 149.12 | 4.506 | 1.479 |
0.9 | 1.0 | –39.65 | 179.31 | 218.96 | 6.632 | 1.877 |
1.0 | 0.9 | –57.82 | 270.62 | 328.44 | 10.004 | 2.426 |
Deformation of the foundation for the case ’a’.
Figure 2 shows the
Dependency of the rotation of the foundation surface for
In case (b) (see Figure 2), the interaction parameter
Origin (1.9 – | Δ | Rotation of foundation [deg] | Max. stress on foundation surface [MPa] | |||
---|---|---|---|---|---|---|
0.0 | 1.9 | 6.92 | 11.98 | 5.06 | 0.152 | 0.299 |
0.1 | 1.8 | 6.29 | 13.30 | 7.02 | 0.212 | 0.321 |
0.2 | 1.7 | 5.60 | 14.81 | 9.21 | 0.278 | 0.344 |
0.3 | 1.6 | 4.88 | 16.52 | 11.64 | 0.351 | 0.364 |
0.4 | 1.5 | 4.12 | 18.42 | 14.31 | 0.431 | 0.381 |
0.5 | 1.4 | 3.33 | 20.54 | 17.21 | 0.519 | 0.396 |
0.6 | 1.3 | 2.53 | 22.85 | 20.32 | 0.613 | 0.405 |
0.7 | 1.2 | 1.74 | 25.36 | 23.63 | 0.712 | 0.410 |
0.8 | 1.1 | 0.96 | 28.05 | 27.09 | 0.817 | 0.409 |
0.9 | 1.0 | 0.22 | 30.90 | 30.69 | 0.925 | 0.401 |
1.0 | 0.9 | –0.35 | 33.78 | 34.13 | 1.029 | 0.392 |
Deformation of the foundation for the case ’b’.
Combination of both the previous situations represents the case ’c’. Here, the
Origin (1.9 – | Δ | Rotation of foundation [deg] | Max. stress on foundation surface [MPa] | |||
---|---|---|---|---|---|---|
0.0 | 1.9 | –3.57 | 59.18 | 62.75 | 1.893 | 0.38 |
0.1 | 1.8 | –9.10 | 74.74 | 83.84 | 2.530 | 0.427 |
0.2 | 1.7 | –18.68 | 98.10 | 116.78 | 3.526 | 0.49 |
0.3 | 1.6 | –36.13 | 135.23 | 171.35 | 5.181 | 0.574 |
0.4 | 1.5 | –70.31 | 199.51 | 269.82 | 8.192 | 0.691 |
0.5 | 1.4 | –141.30 | 319.79 | 461.09 | 14.184 | 0.861 |
0.6 | 1.3 | –323.69 | 602.49 | 926.18 | 30.374 | 1.182 |
0.7 | 1.2 | –669.93 | 1253.43 | 1923.36 | 91.693 | 2.009 |
Deformation of the foundation for the case ’c’.
Because the soil is saturated with water and fine-grain particles have been washed off, the stiffness will decrease (see Figure 2). In contrast to the calculation with the linear distribution (case ’b’), a step division of
Origin (1.9 – | Δ | Rotation of foundation [deg] | Max. stress on foundation surface [MPa] | |||
0.0 | 1.9 | 6.92 | 11.98 | 5.06 | 0.152 | 0.299 |
0.1 | 1.8 | 6.29 | 13.30 | 7.02 | 0.212 | 0.321 |
0.2 | 1.7 | 5.65 | 14.75 | 9.09 | 0.274 | 0.342 |
0.3 | 1.6 | 5.06 | 16.27 | 11.21 | 0.338 | 0.369 |
0.4 | 1.5 | 4.52 | 17.84 | 13.31 | 0.401 | 0.372 |
0.5 | 1.4 | 4.09 | 19.39 | 15.30 | 0.461 | 0.38 |
0.6 | 1.3 | 3.77 | 20.87 | 17.10 | 0.516 | 0.382 |
0.7 | 1.2 | 3.59 | 22.24 | 18.65 | 0.562 | 0.379 |
0.8 | 1.1 | 3.56 | 23.45 | 19.88 | 0.600 | 0.372 |
0.9 | 1.0 | 3.69 | 24.17 | 20.48 | 0.618 | 0.36 |
1.0 | 0.9 | 3.96 | 25.29 | 21.33 | 0.643 | 0.346 |
Deformation of the foundation for the case ’d’.
Figure 4 summarises the results of the conditions described above. Also, the chart shows the rotation of the foundation surface. Table 1–Table 4 can be used to determine the values for a specific case and to determine the maximum stress that appears in the contact surface. The structure collapses if the basement rock plasticizes and the load-carrying capacity is lost. According to the limiting rotation requirements by CNI (1988), the ratio
The work was supported from sources for conceptual development of research, development and innovations 2016 at the VŠB-Technical University of Ostrava that were granted by the Ministry of Education, Youths and Sports of the Czech Republic. In this undertaking, theoretical results gained in the project GAČR 16-08937S were partially exploited.
\nConflict of interest
\nThe authors declare that there is not conflict of interest.
Stability constant of the formation of metal complexes is used to measure interaction strength of reagents. From this process, metal ion and ligand interaction formed the two types of metal complexes; one is supramolecular complexes known as host-guest complexes [1] and the other is anion-containing complexes. In the solution it provides and calculates the required information about the concentration of metal complexes.
Solubility, light, absorption conductance, partitioning behavior, conductance, and chemical reactivity are the complex characteristics which are different from their components. It is determined by various numerical and graphical methods which calculate the equilibrium constants. This is based on or related to a quantity, and this is called the complex formation function.
During the displacement process at the time of metal complex formation, some ions disappear and form a bonding between metal ions and ligands. It may be considered due to displacement of a proton from a ligand species or ions or molecules causing a drop in the pH values of the solution [2]. Irving and Rossotti developed a technique for the calculation of stability constant, and it is called potentiometric technique.
To determine the stability constant, Bjerrum has used a very simple method, and that is metal salt solubility method. For the studies of a larger different variety of polycarboxylic acid-, oxime-, phenol-containing metal complexes, Martel and Calvin used the potentiometric technique for calculating the stability constant. Those ligands [3, 4] which are uncharged are also examined, and their stability constant calculations are determined by the limitations inherent in the ligand solubility method. The limitations of the metal salt solubility method and the result of solubility methods are compared with this. M-L, MLM, and (M3) L are some types of examples of metal-ligand bonding. One thing is common, and that is these entire types metal complexes all have one ligand.
The solubility method can only usefully be applied to studies of such complexes, and it is best applied for ML; in such types of system, only ML is formed. Jacqueline Gonzalez and his co-worker propose to explore the coordination chemistry of calcium complexes. Jacqueline and et al. followed this technique for evaluate the as partial model of the manganese-calcium cluster and spectrophotometric studies of metal complexes, i.e., they were carried calcium(II)-1,4-butanediamine in acetonitrile and calcium(II)-1,2-ethylendiamine, calcium(II)-1,3-propanediamine by them.
Spectrophotometric programming of HypSpec and received data allows the determination of the formation of solubility constants. The logarithmic values, log β110 = 5.25 for calcium(II)-1,3-propanediamine, log β110 = 4.072 for calcium(II)-1,4-butanediamine, and log β110 = 4.69 for calcium(II)-1,2-ethylendiamine, are obtained for the formation constants [5]. The structure of Cimetidine and histamine H2-receptor is a chelating agent. Syed Ahmad Tirmizi has examined Ni(II) cimetidine complex spectrophotometrically and found an absorption peak maximum of 622 nm with respect to different temperatures.
Syed Ahmad Tirmizi have been used to taken 1:2 ratio of metal and cimetidine compound for the formation of metal complex and this satisfied by molar ratio data. The data, 1.40–2.4 × 108, was calculated using the continuous variation method and stability constant at room temperature, and by using the mole ratio method, this value at 40°C was 1.24–2.4 × 108. In the formation of lead(II) metal complexes with 1-(aminomethyl) cyclohexene, Thanavelan et al. found the formation of their binary and ternary complexes. Glycine, l-proline, l-alanine, l-isoleucine, l-valine, and l-leucine are α-amino acids, and these are important biologically [6]. These α-amino acids are also investigated by potentiometric technique at 32°C. The mixed ligands were also studied using these methods. 50% (v/v) DMSO-water medium used for the determination of acidity constants and their stability constants these type ligands. In a stepwise manner, the ternary complexes were synthesized.
Using the stability constant method, these ternary complexes were found out, and using the parameters such as Δ log
The above acids (gallic and aliphatic dicarboxylic acid) were taken to determine the acidity constants. For the purpose of determining the stability constant, binary and ternary complexes were carried in the aqueous medium using the experimental conditions as stated above. The potentiometric pH-metric titration curves are inferred for the binary complexes and ternary complexes at different ratios, and formation of ternary metal complex formation was in a stepwise manner that provided an easy way to calculate stability constants for the formation of metal complexes.
The values of Δ log
A study by Kathrina and Pekar suggests that pH plays an important role in the formation of metal complexes. When epigallocatechin gallate and gallic acid combine with copper(II) to form metal complexes, the pH changes its speculation. We have been able to determine its pH in frozen and fluid state with the help of multifrequency EPR spectroscopy [8]. With the help of this spectroscopy, it is able to detect that each polyphenol exhibits the formation of three different mononuclear species. If the pH ranges 4–8 for di- or polymeric complex of Cu(II), then it conjectures such metal complexes. It is only at alkaline pH values.
The line width in fluid solutions by molecular motion exhibits an incomplete average of the parameters of anisotropy spin Hamilton. If the complexes are different, then their rotational correlation times for this also vary. The analysis of the LyCEP anisotropy of the fluid solution spectra is performed using the parameters determined by the simulation of the rigid boundary spectra. Its result suggests that pH increases its value by affecting its molecular mass. It is a polyphenol ligand complex with copper, showing the coordination of an increasing number of its molecules or increasing participation of polyphenol dimers used as ligands in the copper coordination region.
The study by Vishenkova and his co-worker [8] provides the investigation of electrochemical properties of triphenylmethane dyes using a voltammetric method with constant-current potential sweep. Malachite green (MG) and basic fuchsin (BF) have been chosen as representatives of the triphenylmethane dyes [9]. The electrochemical behavior of MG and BF on the surface of a mercury film electrode depending on pH, the nature of background electrolyte, and scan rate of potential sweep has been investigated.
Using a voltammetric method with a constant-current potential sweep examines the electrical properties of triphenylmethane dye. In order to find out the solution of MG and BF, certain registration conditions have been prescribed for it, which have proved to be quite useful. The reduction peak for the currents of MG and BF has demonstrated that it increases linearly with respect to their concentration as 9.0 × 10−5–7.0 × 10−3 mol/dm3 for MG and 6.0 × 10−5–8.0 × 10−3 mol/dm3 for BF and correlation coefficients of these values are 0.9987 for MG and 0.9961 for BF [10].
5.0 × 10−5 and 2.0 × 10−5 mol/dm3 are the values used as the detection limit of MG and BF, respectively. Stability constants are a very useful technique whose size is huge. Due to its usefulness, it has acquired an umbrella right in the fields of chemistry, biology, and medicine. No science subject is untouched by this. Stability constants of metal complexes are widely used in the various areas like pharmaceuticals as well as biological processes, separation techniques, analytical processes, etc. In the presented chapter, we have tried to explain this in detail by focusing our attention on the applications and solutions of stability of metal complexes in solution.
Stability or formation or binding constant is the type of equilibrium constant used for the formation of metal complexes in the solution. Acutely, stability constant is applicable to measure the strength of interactions between the ligands and metal ions that are involved in complex formation in the solution [11]. A generally these 1-4 equations are expressed as the following ways:
Thus
K1, K2, K3, … Kn are the equilibrium constants and these are also called stepwise stability constants. The formation of the metal-ligand-n complex may also be expressed as equilibrium constants by the following steps:
The parameters K and β are related together, and these are expressed in the following example:
Now the numerator and denominator are multiplied together with the use of [metal-ligand] [metal-ligand2], and after the rearranging we get the following equation:
Now we expressed it as the following:
From the above relation, it is clear that the overall stability constant βn is equal to the product of the successive (i.e., stepwise) stability constants, K1, K2, K3,…Kn. This in other words means that the value of stability constants for a given complex is actually made up of a number of stepwise stability constants. The term stability is used without qualification to mean that the complex exists under a suitable condition and that it is possible to store the complex for an appreciable amount of time. The term stability is commonly used because coordination compounds are stable in one reagent but dissociate or dissolve in the presence of another regent. It is also possible that the term stability can be referred as an action of heat or light or compound. The stability of complex [13] is expressed qualitatively in terms of thermodynamic stability and kinetic stability.
In a chemical reaction, chemical equilibrium is a state in which the concentration of reactants and products does not change over time. Often this condition occurs when the speed of forward reaction becomes the same as the speed of reverse reaction. It is worth noting that the velocities of the forward and backward reaction are not zero at this stage but are equal.
If hydrogen and iodine are kept together in molecular proportions in a closed process vessel at high temperature (500°C), the following action begins:
In this activity, hydrogen iodide is formed by combining hydrogen and iodine, and the amount of hydrogen iodide increases with time. In contrast to this action, if the pure hydrogen iodide gas is heated to 500°C in the reaction, the compound is dissolved by reverse action, which causes hydrogen iodide to dissolve into hydrogen and iodine, and the ratio of these products increases over time. This is expressed in the following reaction:
For the formation of metal chelates, the thermodynamic technique provides a very significant information. Thermodynamics is a very useful technique in distinguishing between enthalpic effects and entropic effects. The bond strengths are totally effected by enthalpic effect, and this does not make any difference in the whole solution in order/disorder. Based on thermodynamics the chelate effect below can be best explained. The change of standard Gibbs free energy for equilibrium constant is response:
Where:
R = gas constant
T = absolute temperature
At 25°C,
ΔG = (− 5.708 kJ mol−1) · log β.
The enthalpy term creates free energy, i.e.,
For metal complexes, thermodynamic stability and kinetic stability are two interpretations of the stability constant in the solution. If reaction moves from reactants to products, it refers to a change in its energy as shown in the above equation. But for the reactivity, kinetic stability is responsible for this system, and this refers to ligand species [14].
Stable and unstable are thermodynamic terms, while labile and inert are kinetic terms. As a rule of thumb, those complexes which react completely within about 1 minute at 25°C are considered labile, and those complexes which take longer time than this to react are considered inert. [Ni(CN)4]2− is thermodynamically stable but kinetically inert because it rapidly exchanges ligands.
The metal complexes [Co(NH3)6]3+ and such types of other complexes are kinetically inert, but these are thermodynamically unstable. We may expect the complex to decompose in the presence of acid immediately because the complex is thermodynamically unstable. The rate is of the order of 1025 for the decomposition in acidic solution. Hence, it is thermodynamically unstable. However, nothing happens to the complex when it is kept in acidic solution for several days. While considering the stability of a complex, always the condition must be specified. Under what condition, the complex which is stable or unstable must be specified such as acidic and also basic condition, temperature, reactant, etc.
A complex may be stable with respect to a particular condition but with respect to another. In brief, a stable complex need not be inert and similarly, and an unstable complex need not be labile. It is the measure of extent of formation or transformation of complex under a given set of conditions at equilibrium [15].
Thermodynamic stability has an important role in determining the bond strength between metal ligands. Some complexes are stable, but as soon as they are introduced into aqueous solution, it is seen that these complexes have an effect on stability and fall apart. For an example, we take the [Co (SCN)4]2+ complex. The ion bond of this complex is very weak and breaks down quickly to form other compounds. But when [Fe(CN)6]3− is dissolved in water, it does not test Fe3+ by any sensitive reagent, which shows that this complex is more stable in aqueous solution. So it is indicated that thermodynamic stability deals with metal-ligand bond energy, stability constant, and other thermodynamic parameters.
This example also suggests that thermodynamic stability refers to the stability and instability of complexes. The measurement of the extent to which one type of species is converted to another species can be determined by thermodynamic stability until equilibrium is achieved. For example, tetracyanonickelate is a thermodynamically stable and kinetic labile complex. But the example of hexa-amine cobalt(III) cation is just the opposite:
Thermodynamics is used to express the difference between stability and inertia. For the stable complex, large positive free energies have been obtained from ΔG0 reaction. The ΔH0, standard enthalpy change for this reaction, is related to the equilibrium constant, βn, by the well thermodynamic equation:
For similar complexes of various ions of the same charge of a particular transition series and particular ligand, ΔS0 values would not differ substantially, and hence a change in ΔH0 value would be related to change in βn values. So the order of values of ΔH0 is also the order of the βn value.
Kinetic stability is referred to the rate of reaction between the metal ions and ligand proceeds at equilibrium or used for the formation of metal complexes. To take a decision for kinetic stability of any complexes, time is a factor which plays an important role for this. It deals between the rate of reaction and what is the mechanism of this metal complex reaction.
As we discuss above in thermodynamic stability, kinetic stability is referred for the complexes at which complex is inert or labile. The term “inert” was used by Tube for the thermally stable complex and for reactive complexes the term ‘labile’ used [16]. The naturally occurring chlorophyll is the example of polydentate ligand. This complex is extremely inert due to exchange of Mg2+ ion in the aqueous media.
The nature of central atom of metal complexes, dimension, its degree of oxidation, electronic structure of these complexes, and so many other properties of complexes are affected by the stability constant. Some of the following factors described are as follows.
In the coordination chemistry, metal complexes are formed by the interaction between metal ions and ligands. For these type of compounds, metal ions are the coordination center, and the ligand or complexing agents are oriented surrounding it. These metal ions mostly are the transition elements. For the determination of stability constant, some important characteristics of these metal complexes may be as given below.
Ligands are oriented around the central metal ions in the metal complexes. The sizes of these metal ions determine the number of ligand species that will be attached or ordinated (dative covalent) in the bond formation. If the sizes of these metal ions are increased, the stability of coordination compound defiantly decreased. Zn(II) metal ions are the central atoms in their complexes, and due to their lower size (0.74A°) as compared to Cd(II) size (0.97A°), metal ions are formed more stable.
Hence, Al3+ ion has the greatest nuclear charge, but its size is the smallest, and the ion N3− has the smallest nuclear charge, and its size is the largest [17]. Inert atoms like neon do not participate in the formation of the covalent or ionic compound, and these atoms are not included in isoelectronic series; hence, it is not easy to measure the radius of this type of atoms.
The properties of stability depend on the size of the metal ion used in the complexes and the total charge thereon. If the size of these metal ions is small and the total charge is high, then their complexes will be more stable. That is, their ratio will depend on the charge/radius. This can be demonstrated through the following reaction:
An ionic charge is the electric charge of an ion which is formed by the gain (negative charge) or loss (positive charge) of one or more electrons from an atom or group of atoms. If we talk about the stability of the coordination compounds, we find that the total charge of their central metal ions affects their stability, so when we change their charge, their stability in a range of constant can be determined by propagating of error [18]. If the charge of the central metal ion is high and the size is small, the stability of the compound is high:
In general, the most stable coordination bonds can cause smaller and highly charged rations to form more stable coordination compounds.
When an electron pair attracts a central ion toward itself, a strong stability complex is formed, and this is due to electron donation from ligand → metal ion. This donation process is increasing the bond stability of metal complexes exerted the polarizing effect on certain metal ions. Li+, Na+, Mg2+, Ca2+, Al3+, etc. are such type of metal cation which is not able to attract so strongly from a highly electronegative containing stable complexes, and these atoms are O, N, F, Au, Hg, Ag, Pd, Pt, and Pb. Such type of ligands that contains P, S, As, Br and I atom are formed stable complex because these accepts electron from M → π-bonding. Hg2+, Pb2+, Cd2+, and Bi3+ metal ions are also electronegative ions which form insoluble salts of metal sulfide which are insoluble in aqueous medium.
Volatile ligands may be lost at higher temperature. This is exemplified by the loss of water by hydrates and ammonia:
The transformation of certain coordination compounds from one to another is shown as follows:
A ligand is an ion or small molecule that binds to a metal atom (in chemistry) or to a biomolecule (in biochemistry) to form a complex, such as the iron-cyanide coordination complex Prussian blue or the iron-containing blood-protein hemoglobin. The ligands are arranged in spectrochemical series which are based on the order of their field strength. It is not possible to form the entire series by studying complexes with a single metal ion; the series has been developed by overlapping different sequences obtained from spectroscopic studies [19]. The order of common ligands according to their increasing ligand field strength is
The above spectrochemical series help us to for determination of strength of ligands. The left last ligand is as weaker ligand. These weaker ligand cannot forcible binding the 3d electron and resultant outer octahedral complexes formed. It is as-
Increasing the oxidation number the value of Δ increased.
Δ increases from top to bottom.
However, when we consider the metal ion, the following two useful trends are observed:
Δ increases with increasing oxidation number.
Δ increases down a group. For the determination of stability constant, the nature of the ligand plays an important role.
The following factors described the nature of ligands.
The size and charge are two factors that affect the production of metal complexes. The less charges and small sizes of ligands are more favorable for less stable bond formation with metal and ligand. But if this condition just opposite the product of metal and ligand will be a more stable compound. So, less nuclear charge and more size= less stable complex whereas if more nuclear charge and small in size= less stable complex. We take fluoride as an example because due to their smaller size than other halide and their highest electro negativity than the other halides formed more stable complexes. So, fluoride ion complexes are more stable than the other halides:
As compared to S2− ion, O22− ions formed more stable complexes.
It is suggested by Calvin and Wilson that the metal complexes will be more stable if the basic character or strength of ligands is higher. It means that the donating power of ligands to central metal ions is high [20].
It means that the donating power of ligands to central metal ions is high. In the case of complex formation of aliphatic diamines and aromatic diamines, the stable complex is formed by aliphatic diamines, while an unstable coordination complex is formed with aromatic diamines. So, from the above discussion, we find that the stability will be grater if the e-donation power is greater.
Thus it is clear that greater basic power of electron-donating species will form always a stable complex. NH3, CN−, and F− behaved as ligands and formed stable complexes; on the other hand, these are more basic in nature.
We know that if the concentration of coordination group is higher, these coordination compounds will exist in the water as solution. It is noted that greater coordinating tendency show the water molecules than the coordinating group which is originally present. SCN− (thiocynate) ions are present in higher concentration; with the Co2+ metal ion, it formed a blue-colored complex which is stable in state, but on dilution of water medium, a pink color is generated in place of blue, or blue color complex is destroyed by [Co(H2O)6]2+, and now if we added further SCN−, the pink color will not appear:
Now it is clear that H2O and SCN− are in competition for the formation of Co(II) metal-containing complex compound. In the case of tetra-amine cupric sulfate metal complex, ammonia acts as a donor atom or ligand. If the concentration of NH3 is lower in the reaction, copper hydroxide is formed but at higher concentration formed tetra-amine cupric sulfate as in the following reaction:
For a metal ion, chelating ligand is enhanced and affinity it and this is known as chelate effect and compared it with non-chelating and monodentate ligand or the multidentate ligand is acts as chelating agent. Ethylenediamine is a simple chelating agent (Figure 1).
Structure of ethylenediamine.
Due to the bidentate nature of ethylenediamine, it forms two bonds with metal ion or central atom. Water forms a complex with Ni(II) metal ion, but due to its monodentate nature, it is not a chelating ligand (Figures 2 and 3).
Structure of chelating configuration of ethylenediamine ligand.
Structure of chelate with three ethylenediamine ligands.
The dentate cheater of ligand provides bonding strength to the metal ion or central atom, and as the number of dentate increased, the tightness also increased. This phenomenon is known as chelating effect, whereas the formation of metal complexes with these chelating ligands is called chelation:
or
Some factors are of much importance for chelation as follows.
The sizes of the chelating ring are increased as well as the stability of metal complex decreased. According to Schwarzenbach, connecting bridges form the chelating rings. The elongated ring predominates when long bridges connect to the ligand to form a long ring. It is usually observed that an increased a chelate ring size leads to a decrease in complex stability.
He interpreted this statement. The entropy of complex will be change if the size of chelating ring is increased, i.e., second donor atom is allowed by the chelating ring. As the size of chelating ring increased, the stability should be increased with entropy effect. Four-membered ring compounds are unstable, whereas five-membered are more stable. So the chelating ring increased its size and the stability of the formed metal complexes.
The number of chelating rings also decides the stability of complexes. Non-chelating metal compounds are less stable than chelating compounds. These numbers increase the thermodynamic volume, and this is also known as an entropy term. In recent years ligands capable of occupying as many as six coordination positions on a single metal ion have been described. The studies on the formation constants of coordination compounds with these ligands have been reported. The numbers of ligand or chelating agents are affecting the stability of metal complexes so as these numbers go up and down, the stability will also vary with it.
For the Ni(II) complexes with ethylenediamine as chelating agent, its log K1 value is 7.9 and if chelating agents are trine and penten, then the log K1 values are 7.9 and 19.3, respectively. If the metal ion change Zn is used in place of Ni (II), then the values of log K1 for ethylenediamine, trine, and penten are 6.0, 12.1, and 16.2, respectively. The log βMY values of metal ions are given in Table 1.
Metal ion | log βMY (25°C, I = 0.1 M) |
---|---|
Ca2+ | 11.2 |
Cu2+ | 19.8 |
Fe3+ | 24.9 |
Metal ion vs. log βMY values.
Ni(NH3)62+ is an octahedral metal complex, and at 25 °C its log β6 value is 8.3, but Ni(ethylenediamine)32+ complex is also octahedral in geometry, with 18.4 as the value of log β6. The calculated stability value of Ni(ethylenediamine)32+ 1010 times is more stable because three rings are formed as chelating rings by ethylenediamine as compared to no such ring is formed. Ethylenediaminetetraacetate (EDTA) is a hexadentate ligand that usually formed stable metal complexes due to its chelating power.
A special effect in molecules is when the atoms occupy space. This is called steric effect. Energy is needed to bring these atoms closer to each other. These electrons run away from near atoms. There can be many ways of generating it. We know the repulsion between valence electrons as the steric effect which increases the energy of the current system [21]. Favorable or unfavorable any response is created.
For example, if the static effect is greater than that of a product in a metal complex formation process, then the static increase would favor this reaction. But if the case is opposite, the skepticism will be toward retardation.
This effect will mainly depend on the conformational states, and the minimum steric interaction theory can also be considered. The effect of secondary steric is seen on receptor binding produced by an alternative such as:
Reduced access to a critical group.
Stick barrier.
Electronic resonance substitution bond by repulsion.
Population of a conformer changes due to active shielding effect.
The macrocyclic effect is exactly like the image of the chelate effect. It means the principle of both is the same. But the macrocyclic effect suggests cyclic deformation of the ligand. Macrocyclic ligands are more tainted than chelating agents. Rather, their compounds are more stable due to their cyclically constrained constriction. It requires some entropy in the body to react with the metal ion. For example, for a tetradentate cyclic ligand, we can use heme-B which forms a metal complex using Fe+2 ions in biological systems (Figure 4).
Structure of hemoglobin is the biological complex compound which contains Fe(II) metal ion.
The n-dentate chelating agents play an important role for the formation of more stable metal complexes as compared to n-unidentate ligands. But the n-dentate macrocyclic ligand gives more stable environment in the metal complexes as compared to open-chain ligands. This change is very favorable for entropy (ΔS) and enthalpy (ΔH) change.
There are so many parameters to determination of formation constants or stability constant in solution for all types of chelating agents. These numerous parameters or techniques are refractive index, conductance, temperature, distribution coefficients, refractive index, nuclear magnetic resonance volume changes, and optical activity.
Solubility products are helpful and used for the insoluble salt that metal ions formed and complexes which are also formed by metal ions and are more soluble. The formation constant is observed in presence of donor atoms by measuring increased solubility.
To determine the solubility constant, it involves the distribution of the ligands or any complex species; metal ions are present in two immiscible solvents like water and carbon tetrachloride, benzene, etc.
In this method metal ions or ligands are present in solution and on exchanger. A solid polymers containing with positive and negative ions are ion exchange resins. These are insoluble in nature. This technique is helpful to determine the metal ions in resin phase, liquid phase, or even in radioactive metal. This method is also helpful to determine the polarizing effect of metal ions on the stability of ligands like Cu(II) and Zn(II) with amino acid complex formation.
At the equilibrium free metal and ions are present in the solution, and using the different electrometric techniques as described determines its stability constant.
This method is based upon the titration method or follows its principle. A stranded acid-base solution used as titrate and which is titrated, it may be strong base or strong acid follows as potentiometrically. The concentration of solution using 103− M does not decomposed during the reaction process, and this method is useful for protonated and nonprotonated ligands.
This is the graphic method used to determine the stability constant in producing metal complex formation by plotting a polarograph between the absences of substances and the presence of substances. During the complex formation, the presence of metal ions produced a shift in the half-wave potential in the solution.
If a complex is relatively slow to form and also decomposes at measurable rate, it is possible, in favorable situations, to determine the equilibrium constant.
This involves the study of the equilibrium constant of slow complex formation reactions. The use of tracer technique is extremely useful for determining the concentrations of dissociation products of the coordination compound.
This method is based on the study of the effect of an equilibrium concentration of some ions on the function at a definite organ of a living organism. The equilibrium concentration of the ion studied may be determined by the action of this organ in systems with complex formation.
The solution of 25 ml is adopted by preparing at the 1.0 × 10−5 M ligand or 1.0 × 10−5 M concentration and 1.0 × 10−5 M for the metal ion:
The solutions containing the metal ions were considered both at a pH sufficiently high to give almost complete complexation and at a pH value selected in order to obtain an equilibrium system of ligand and complexes.
In order to avoid modification of the spectral behavior of the ligand due to pH variations, it has been verified that the range of pH considered in all cases does not affect absorbance values. Use the collected pH values adopted for the determinations as well as selected wavelengths. The ionic strengths calculated from the composition of solutions allowed activity coefficient corrections. Absorbance values were determined at wavelengths in the range 430–700 nm, every 2 nm.
For a successive metal complex formation, use this method. If ligand is protonate and the produced complex has maximum number of donate atoms of ligands, a selective light is absorbed by this complex, while for determination of stability constant, it is just known about the composition of formed species.
Bjerrum (1941) used the method stepwise addition of the ligands to coordination sphere for the formation of complex. So, complex metal–ligand-n forms as the following steps [22]. The equilibrium constants, K1, K2, K3, … Kn are called stepwise stability constants. The formation of the complex metal-ligandn may also be expressed by the following steps and equilibrium constants.
Where:
M = central metal cation
L = monodentate ligand
N = maximum coordination number for the metal ion M for the ligand
If a complex ion is slow to reach equilibrium, it is often possible to apply the method of isotopic dilution to determine the equilibrium concentration of one or more of the species. Most often radioactive isotopes are used.
This method was extensively used by Werner and others to study metal complexes. In the case of a series of complexes of Co(III) and Pt(IV), Werner assigned the correct formulae on the basis of their molar conductance values measured in freshly prepared dilute solutions. In some cases, the conductance of the solution increased with time due to a chemical change, e.g.,
It is concluded that the information presented is very important to determine the stability constant of the ligand metal complexes. Some methods like spectrophotometric method, Bjerrum’s method, distribution method, ion exchange method, electrometric techniques, and potentiometric method have a huge contribution in quantitative analysis by easily finding the stability constants of metal complexes in aqueous solutions.
All the authors thank the Library of University of Delhi for reference books, journals, etc. which helped us a lot in reviewing the chapter.
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\\n"}]'},components:[{type:"htmlEditorComponent",content:"Our business values are based on those any scientist applies to their research. We have created a culture of respect and collaboration within a relaxed, friendly and progressive atmosphere, while maintaining academic rigour.
\n\nCo-founded by Alex Lazinica and Vedran Kordic: “We are passionate about the advancement of science. As Ph.D. researchers in Vienna, we found it difficult to access the scholarly research we needed. We created IntechOpen with the specific aim of putting the academic needs of the global research community before the business interests of publishers. Our Team is now a global one and includes highly-renowned scientists and publishers, as well as experts in disseminating your research.”
\n\nBut, one thing we have in common is -- we are all scientists at heart!
\n\nSara Uhac, COO
\n\nSara Uhac was appointed Managing Director of IntechOpen at the beginning of 2014. She directs and controls the company’s operations. Sara joined IntechOpen in 2010 as Head of Journal Publishing, a new strategically underdeveloped department at that time. After obtaining a Master's degree in Media Management, she completed her Ph.D. at the University of Lugano, Switzerland. She holds a BA in Financial Market Management from the Bocconi University in Milan, Italy, where she started her career in the American publishing house Condé Nast and further collaborated with the UK-based publishing company Time Out. Sara was awarded a professional degree in Publishing from Yale University (2012). She is a member of the professional branch association of "Publishers, Designers and Graphic Artists" at the Croatian Chamber of Commerce.
\n\nAdrian Assad De Marco
\n\nAdrian Assad De Marco joined the company as a Director in 2017. With his extensive experience in management, acquired while working for regional and global leaders, he took over direction and control of all the company's publishing processes. Adrian holds a degree in Economy and Management from the University of Zagreb, School of Economics, Croatia. A former sportsman, he continually strives to develop his skills through professional courses and specializations such as NLP (Neuro-linguistic programming).
\n\nDr Alex Lazinica
\n\nAlex Lazinica is co-founder and Board member of IntechOpen. After obtaining a Master's degree in Mechanical Engineering, he continued his Ph.D. in Robotics at the Vienna University of Technology. There, he worked as a robotics researcher with the university's Intelligent Manufacturing Systems Group, as well as a guest researcher at various European universities, including the Swiss Federal Institute of Technology Lausanne (EPFL). During this time he published more than 20 scientific papers, gave presentations, served as a reviewer for major robotic journals and conferences and, most importantly, co-founded and built the International Journal of Advanced Robotic Systems, the world's first Open Access journal in the field of robotics. Starting this journal was a pivotal point in his career since it proved to be the pathway to the foundation of IntechOpen with its focus on addressing academic researchers’ needs. Alex personifies many of IntechOpen´s key values, including the commitment to developing mutual trust, openness, and a spirit of entrepreneurialism. Today, his focus is on defining the growth and development strategy for the company.
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