Metal ion vs. log βMY values.
\r\n\t
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From the Ferrari F1 Team to Automobili Lamborghini, he has worked on Electrical/Electronics systems, he has expertise in Research & Design, Supply Quality and Product Development. Currently, he is System Responsible for Passive Safety & ADAS of Maserati vehicles at Maserati S.p.A.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"112023",title:"Dr.",name:"Luigi",middleName:null,surname:"Cocco",slug:"luigi-cocco",fullName:"Luigi Cocco",profilePictureURL:"https://mts.intechopen.com/storage/users/112023/images/system/112023.jpg",biography:'Dr. Luigi Cocco has received his master\'s degree in Telecommunication Engineering and his Ph.D. in Information Engineering before to join the automotive industry. Since 2005, From the Ferrari F1 Team to Automobili Lamborghini, he has worked on Electrical/Electronics systems; he has expertise in Research & Design, Supply Quality and Product Development. 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His research interests include electronic measurements and digital signal processing, he has published several papers and three books with InTech: "Modern Metrology Concerns” (2012), "New Trends and Developments in Metrology” (2016) and "Standards, methods, and solutions of Metrology” (2018).',institutionString:"Maserati S.p.A.",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"3",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"11",title:"Engineering",slug:"engineering"}],chapters:[{id:"74236",title:"New Robust Control Design of Brake-by-Wire Actuators",slug:"new-robust-control-design-of-brake-by-wire-actuators",totalDownloads:46,totalCrossrefCites:0,authors:[null]},{id:"74309",title:"Role of Bearings in New Generation Automotive Vehicles: Powertrain",slug:"role-of-bearings-in-new-generation-automotive-vehicles-powertrain",totalDownloads:72,totalCrossrefCites:0,authors:[null]},{id:"74420",title:"Hydrogen Fuel Cell Implementation for the Transportation Sector",slug:"hydrogen-fuel-cell-implementation-for-the-transportation-sector",totalDownloads:120,totalCrossrefCites:0,authors:[null]},{id:"73891",title:"Quantum Calculations to Estimate the Heat of Hydrogenation Theoretically",slug:"quantum-calculations-to-estimate-the-heat-of-hydrogenation-theoretically",totalDownloads:60,totalCrossrefCites:0,authors:[null]},{id:"73339",title:"Generation and Relaxation of Residual Stresses in Automotive Cylinder Blocks",slug:"generation-and-relaxation-of-residual-stresses-in-automotive-cylinder-blocks",totalDownloads:69,totalCrossrefCites:0,authors:[null]},{id:"74124",title:"Quality and Trends of Automotive Fuels",slug:"quality-and-trends-of-automotive-fuels",totalDownloads:25,totalCrossrefCites:0,authors:[null]},{id:"74097",title:"Hydrogen Storage: Materials, Kinetics and Thermodynamics",slug:"hydrogen-storage-materials-kinetics-and-thermodynamics",totalDownloads:49,totalCrossrefCites:0,authors:[null]},{id:"73923",title:"Hybrid Steering Systems for Automotive Applications",slug:"hybrid-steering-systems-for-automotive-applications",totalDownloads:53,totalCrossrefCites:0,authors:[null]}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"280415",firstName:"Josip",lastName:"Knapic",middleName:null,title:"Mr.",imageUrl:"https://mts.intechopen.com/storage/users/280415/images/8050_n.jpg",email:"josip@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"45278",title:"Brain Mapping of Language Processing Using Functional MRI Connectivity and Diffusion Tensor Imaging",doi:"10.5772/56501",slug:"brain-mapping-of-language-processing-using-functional-mri-connectivity-and-diffusion-tensor-imaging",body:'Because the brain’s language systems have no end organs for interacting directly with the external world, language systems work with sensory (ears or eyes) and motor (mouth and hands) systems, which are the only brain systems with direct links to external environment. Liberman contributed to understanding of how the language by ear (listening) and language by mouth (reading) systems work together at the behavioral level and also become integrated to support acquisition of language by eye (reading) [1]. Berninger and colleagues extended the work of Liberman and colleagues at the Haskins Laboratory to language by hand (writing), which is not just a motor skill as many assume [2]. This University of Washington research team also showed that Language by Ear, Language by Mouth, Language by Eye, and Language by Hand are separate, but interacting functional language systems, which draw on common as well as unique processes at the behavioral [3] and brain levels of analysis [4]. Moreover, each of the functional language systems has different levels of organization, ranging from subword, to word, to syntax, to text, and has connections with other brain systems such as working memory, attention and executive functions, and cognitive.
The emerging work on the complex functional language systems that connect with other brain systems illustrates the need for brain imaging methods that not only assess localized brain areas or functions but also their structural and functional connections. First, we discuss how the modern imaging techniques have confirmed knowledge of localized structures and functions first acquired in autopsy studies with patients. Second, we discuss how advances in imaging techniques are adding knowledge about the structural and functional connections among specific functional language systems.
In early work in neurolinguistics researchers studied people with brain lesions and discovered relationships between the patient’s specific language deficit and the location of the lesion. In this way, they discovered that two areas in the brain are involved in language processing: Wernicke\'s area located in the posterior section of the superior temporal gyrus in the dominant cerebral hemisphere. People with a lesion in this area of the brain develop receptive aphasia, a condition in which there is a major language comprehension impairment, but the capability for speech production remains intact. The other area is Broca\'s area located in the posterior inferior frontal gyrus of the dominant hemisphere. Patients with a lesion to this area develop expressive aphasia and are unable to produce speech even though they are able to understand other’s that they hear [4].
Neurolinguist researchers have adopted non-invasive brain imaging techniques such as functional magnetic resonance imaging and electrophysiology to study language processing in individuals without impairments [5]. For example, in the study of phonological processing, the receptive processing of phonemes in heard words has been localized to Wernicke\'s area (posterior Brodmann\'s Area [BA] 22) and BA 40 [6] [7-11], and expressive production of phonemes during speech has been localized to the posterior Broca\'s area (BAs 44 and 6) [11-15]. Thus, research using these newly developed brain imaging techniques has confirmed what was was classically thought based on patient studies for right-handed individuals: The two major language areas are Broca’s area for production of language by mouth [16] and Wernicke’s area for comprehension of language by ear [17], which receives input from the ear through the auditory cortex. The arcuate fasciculus, a fiber pathway that originates in the temporal lobe and curves in an anterior/posterior direction to project to the frontal lobe [18], was thought to connect these 2 areas.
Figure 1 that follows shows these important language processing areas of the brain superimposed on a side/surface view of the brain based on more recent non-invasive brain imaging methods. These areas may also play a role in production of language by hand (writing) and comprehension of language by eye (reading), via related processing in angular gyrus and supramarginal gyrus [4].
Brain regions important for language. Broca’s area (blue), auditory cortex (pink), Wernicke’s area (green), Supramarginal gyrus (yellow), angular gyus (orange). (Figure from the wikipedia website http://en.wikipedia.org/wiki/File:Brain_Surface_Gyri.SVG).
In 2010 the US National Institute of Health (NIH) announced the Human Connectome Project:
“Knowledge of human brain connectivity will transform human neuroscience by providing not only a qualitatively novel class of data, but also by providing the basic framework necessary to synthesize diverse data and, ultimately, elucidate how our brains work in health, illness, youth, and old age.” Included in this connectome is the study of language-related neural connections which enable the brain to perform written and oral language.
Mullen [19] has on online manual that defines several important terms used in research about structural and functional networks.
The study of human brain connectivity generally falls under one or more of three categories: structural, functional, and effective [20].
Structural connectivity denotes networks of anatomical (e.g., axonal) links) for which the primary goal is to understand what brain structures are capable of influencing each other via direct or indirect axonal connections. Structural connectivity might be studied in vivo using invasive axonal labeling techniques or noninvasive MRI-based diffusion weighted imaging (DWI/DTI) methods. These methods cannot measure individual axons but can measure the water diffusion signal from a group of axons that have parallel geometric properties within a fiber bundle. DTI connectivity is influenced by the number of axons and the amount of myelination within the fiber bundle.
Diffusion Tensor Imaging (DTI) tractography is a neuroimaging technique that allows for the virtual dissection of fiber tracts in the living brain based on the directionally biased diffusion of water in white matter [21]. DTI analysis provides several parameters that quantify the properties of the fiber bundle: fractional anisotropy ( a measure of the amount of anisotropy of water diffusion between the primary fiber direction and the perpendicular to the primary fiber direction); axial water diffusion diffusivity ( the amount of water diffusion along the primary direction of the fiber bundle); radial diffusivity ( the amount the water diffusion perpendicular to the primary direction of the fiber bundle); mean diffusivity (characterizes the overall mean-squared displacement of water molecules); relative anisotropy; and volume ratio. These parameters can be calculated on a voxel by voxel basis within the DTI image The exact equations used to calculate these DTI parameters have been published by LeBihan et al [22]. Other important parameters that characterize the fiber bundle are the tractography analysis which is a procedure to demonstrate the neural tracts[23]. These neural tracts have properties such as mean fiber length, fiber volume, and mean FA within the fiber tract. This tractography analysis can be used to measure connectivity between specific regions of the brain such as between Broca’s area and Wernicke’s area or other language-related brain regions. The figures that follow (Figures 2 A, 2B, and 2C) show an example of fibers tract4s connected to Broca’s area in the left hemisphere.
DTI fiber tracts connected to Broca’s area. Sagittal view (part A), axial view (part B), and coronal view (part C) showing fibers in the frontal and temporal lobe. The color coding of the fibers is related to the amplitude of the fractional anisotropy within the fiber. A color scale bar is shown at the bottom.
DTI [24-27] has been used to study language connections. For example, DTI studies have identified association between variation in white matter microstructure and differences in reading skill [28] [29] [30]. Klingberg et al [30] found that white matter diffusion anisotropy in the temporo-parietal region of the left hemisphere was significantly correlated with reading scores within the reading-impaired adults and within the control group. Nioqi et al [28] found strong correlation between fractional anisotropy (FA) values in a left temporo-parietal white matter region and standardized reading scores of typically developing children. Deutsch et al [29] found that white matter structure (as measured by fractional anisotropy) and coherence index (CI) significantly correlated with behavioral measurements of reading, spelling, and rapid naming performance in children. Glasser et al used Diffusion Tensor Imaging (DTI) tractography to detect leftward asymmetries in the arcuate fasciculus [31]. The arcuate fasciclus is a pathway that links temporal and inferior frontal language cortices and is divided into 2 segments with different hypothesized functions, one terminating in the posterior superior temporal gyrus (STG) and another terminating in the middle temporal gyrus (MTG). STG terminations were strongly left lateralized and overlapped with phonological activations in the left but not the right hemisphere, suggesting that only the left hemisphere phonological cortex is directly connected with the frontal lobe via the arcuate fasciculus. MTG terminations were also strongly left lateralized, overlapping with left lateralized lexical--semantic activations. Smaller right hemisphere MTG terminations overlapped with right lateralized prosodic activations. They used a recent model of brain language processing to explain 6 aphasia syndromes [31].These studies demonstrate the potential for using DTI to measure white matter structural changes in dyslexia.
Functional connectivity denotes symmetrical correlations in activity between brain regions during information processing. Here the primary goal is to understand which regions are functionally related through correlations in their activity, as measured by some imaging technique. Functional connectivity is a powerful noninvasive technique used to investigate the distribution of neural networks in healthy participants and affected subjects, which can be characterized by low-frequency fluctuations in the BOLD signal when the subject is performing a task [32, 33]. The BOLD response of a continuous task leads to coherent signal changes in anatomically different, but functionally connected, brain structures and thus implies the existence of neuronal connections between these regions. Coherent signal changes in anatomically different brain structures imply the existence of neuronal connections between these regions. Exploratory data analysis methods have the attractive feature of being model free and thus allowing unbiased studies of brain signal responses.
Examples in fMRI/PET include principal component analysis (PCA), independent component analysis (ICA), and cluster analysis. There are also model-free analyses of interregional connectivity [34-41]. A popular form of functional connectivity analysis using functional magnetic resonance imaging (fMRI) has been to compute the pairwise correlation (or partial correlation) in BOLD activity for a large number of voxels or regions of interest within the brain volume. The figure 3 below shows an example pair of BOLD signals that have a high degree of correlation. For example functional MRI connectivity can be used to study the functional signal correlations between Broca’s area and Wernicke’s area.
Example of the time course of fMRI signals from two different brain regions which are functionally connected. Notice that the two signals (black and red lines) are closely correlated but not exactly the same.
In contrast to the symmetric nature of functional connectivity, effective connectivity denotes asymmetric or causal dependencies between brain regions. Here the primary goal is to identify which brain structures in a functional network are causally influencing other elements of the network during some stage or form of information processing. Often the term “information flow” is used to indicate directionally specific (although not necessarily causal) effective connectivity between neuronal structures. Popular effective connectivity methods, applied to fMRI and/or electrophysiological (EEG, iEEG, MEG) imaging data, include dynamic causal modeling, structural equation modeling, transfer entropy, and Granger-causal methods. An example of fMRI connectivity using Broca’s area as a seed region is shown below in Figure 4.
FMRI connectivity analysis related to left-sided Broca’s area using FSL’s Independent Component Analysis software Melodic combined with UW software. The red plot shows the time course of this ICA component and the plot in blue shows the frequency spectrum. Notice that there are several anatomical regions of the brain that are involved in this component including the left frontal lobe (which includes Broca’s area), left and right parietal lobe, left and right temporal lobe.
Currently, imaging research studies of dyslexia are moving away from simply localizing task-related activation to regions of interest (ROI) to analyzing functional connectivity among different brain regions in specific task environments [42] or resting states [43]. Previous functional connectivity studies of dyslexia were mostly focused on the angular gyrus. Asynchrony of regional cerebral blood flow changes in the angular gyrus and extrastriate occipital/temporal lobe regions suggested functional disconnection during single word reading [44]. Pugh et al [45] showed functional disconnections between the angular gyrus and temporal and occipital areas (namely, lateral extrastriate, medial extrastriate, and primary visual cortex) in the left hemisphere specific to the phonological processing. Shaywitz et al. [46] found functional connections between the occipitotemporal region and inferior frontal gyrus in the left hemisphere in normal readers under a real-word reading condition. Poor readers, in contrast, exhibited more functional connections between the left occipitotemporal region and right middle and inferior frontal gyri [46].
Shaywitz et al documented that the important difference between compensated young adults with a history of dyslexia and young adults who are good readers without a history of dyslexia lies in connectivity among regions rather than in regions of activation per se [46]. Milne et al. [47] reported that an individual with developmental dyslexia showed increased activation, as the phonological processing demands increased, in the left inferior frontal gyrus, right parietal cortex, right occipital cortex, and cerebellum. Both the Shaywitz et al. [46] and Milne et al. [47] studies had shown the importance of connectivity between posterior and anterior language systems in supporting the reading process. Betan et al, [48] have recently used fMRI connectivity to examine task-specific modulations of effective connectivity within a left-hemisphere language network during spelling and rhyming judgments on visually presented words. They used dynamic causal modeling to show that each task preferentially strengthened modulatory influences converging on its task-specific site (LTC for rhyming, IPS for spelling). Their findings also showed that switching tasks led to changes in the target area influenced by the IFG, suggesting that the IFG may play a pivotal role in setting the cognitive context for each task [48].
Our first DTI Study [49] identified differences between adults with and without dyslexia (which is also a writing disorder, [50]) in the right inferior gyrus (See Figure 5). This is one of the same regions where structural differences were found between dyslexics and good readers in an MRI structural study (Eckert et al., 2003) [51] and the same region where functional differences were found in an fMRI orthographic task contrast before but not after orthographic treatment (Richards et al., 2006a) [52]. Trends towards less activation in right inferior frontal gyrus were associated with improved phonological decoding following treatment (Richards et al., 2006b) [53].
Group differences for controls > dyslexics in analysis of fractional anisotropy with FSL-based TBSS software. Crosshair on a significant cluster near R inf. frontal gyrus.
Trends towards less activation in right inferior frontal gyrus were associated with improved phonological decoding following treatment [53]. These findings suggest that right inferior frontal gyrus plays a role in orthographic coding, a process which our behavioral studies for nearly two decades have shown contributes uniquely to handwriting, spelling, and composition[54]. Thus, we predict that in studies in progress children with handwriting disabilities will differ from good writers in the right inferior frontal gyrus.
Differences in functional connectivity were also found between children with and without dyslexia before but not after treatment on a phonological spelling task (phoneme mapping—deciding whether letter(s) in pair of pronounceable nonwords could stand for the same sound[55]. These data were analyzed with a seed point correlational method for functional connectivity from four seed points based on prior studies: inferior frontal gyrus, middle frontal gyrus, the occipital region, and cerebellum. Before treatment, there was a significant difference in fMRI connectivity between children with dyslexia and normal reading controls in the degree of connectivity between left inferior frontal gyrus and the following regions: right and left middle frontal gyrus, right and left supplemental motor area, left precentral gyrus, and right superior frontal gyrus. There were no significant differences when seed regions were placed in the middle frontal gyrus, occipital gyrus or cerebellum. Children with dyslexia had greater functional connectivity from the left inferior frontal gyrus seed point to the right inferior frontal gyrus than did the children without dyslexia as shown in Figure 6.
Group difference map for dyslexics greater than controls. The individual maps used in this analysis were correlation maps created when the seed ROI in the left inferior frontal gyrus was compared to the rest of the brain voxels.
The children with dyslexia then participated in a 3-week instructional program that provided explicit instruction in linguistic awareness, alphabetic principle (taught in a way to maximize temporal contiguity of grapheme–phoneme associations and to train both phonological and orthographic loops), decoding and spelling. At Time2, the treated children with did not differ from the children without dyslexia in any of the clusters in the group. The main result was that children with dyslexia had greater functional connectivity from the left inferior frontal gyrus seed point to the right inferior frontal gyrus than did the children without dyslexia before but not after treatment [55]. Thus, the structural and functional connectivity studies provided converging evidence for abnormalities related to inferior frontal gyrus (on right or left) in children with dyslexia.
Stanberry et al [35] developed a model of fMRI connectivity based on earlier results that predicts that for normal readers there will be functional connectivity among 5 major reading-related brain regions: (a) frontal lobe (including the inferior frontal gyrus and middle frontal gyrus); (b) parietal lobe (including the angular gyrus); (c) visual processing areas (including occipitotemporal region); (d) fusiform/lingual word form region; and (e) the cerebellum. This model is generally consistent with that reported by other research groups for normal reading [46]; it is also consistent with phonological loop in verbal working memory as a deficit in dyslexia [56, 57]. We predicted that individual dyslexics may have impaired connectivity in any one or a combination of these major circuits. In our first fMRI connectivity study, we investigated differences in cortical networks used by adult controls compared to adult dyslexics during the previously described Phoneme Mapping. By definition, functional connectivity refers to a correlation or synchronization between the time courses of activation of two brain regions. We hypothesized that two brain regions that work together have similar temporal response profiles [58]. A model-independent method was used to analyze the time-synchronized activations induced by the phoneme mapping paradigm (adapted from [59]) presented during a continuous task presentation. A standard fMRI acquisition and analysis of the on-off block design was also performed using Phoneme Mapping. Native English speakers ranging in age from 30 to 45 years participated in the connectivity study: 10 healthy right-handed control males (fathers from the family genetics study who did not meet research criteria for dyslexia on tests and also did not have a history of reading problems) and 13 right-handed, otherwise healthy, adult males who did meet the research criteria for dyslexia and had a history of reading and writing problems. The two groups did not differ significantly in mean Verbal IQ [dyslexics, M=113.8 (SD = 10.3); controls, M=107.7 (SD=11.1), but the dyslexics were significantly lower than the control fathers on each of the reading, spelling, and RAN measures.
Structural and functional MR images were collected in accordance with institutional regulations (IRB approval) on a commercial 1.5T MR scanner (General Electric, Waukesha, WI) equipped with echo-speed gradients and a standard birdcage head coil. Functional images were acquired using an echo-planar sequence with imaging parameters set as follows:
“On-Off” task: 20 axial slices, FOV 24cm x 24cm, BW +/- 62.5 kHz, TR 2000ms, TE 40ms, Flip 82 deg, slice thickness 6mm, gap 1mm, resolution 64x64, 162 time points; Continuous task: 20 axial slices, FOV 24cm x 24cm, BW +/- 62.5 kHz, TR 2000ms, TE 40 ms, Flip 82 deg, slice thickness 6mm, gap 1mm, resolution 64x64, 483 time points.Cardiac and respiratory rates were digitally recorded with a pulse oximeter and a flexible belt, respectively, using a sampling frequency of 100Hz. Three different seed regions were used for connectivity analysis – right and left inferior frontal gyrus and cerebellum.
For the standard block fMRI acquisition and analysis of controls, fMRI brain activation was detected in the following brain regions: for the right side - inferior frontal gyrus, middle frontal gyrus, cerebellum crus I, cerebellum crus II, occipital gyrus, superior parietal gyrus, inferior parietal gyrus, angular gyrus, lingual gyrus, and fusiform gyrus; for the left side – superior parietal gyrus, angular, occipital gyrus, cerebellum crus I, cerebellum crus II, lingual.
For the fMRI connectivity analysis of the continuous phoneme mapping paradigm, we narrowed the five region model above to a focus on three regions based on structural MRI differences in dyslexics from a family genetics study [51]. Results showed that (a) when the right IFG was chosen as the seed region, significant differences (p<.05) were found between dyslexics and controls in right inferior frontal triangularis, bilateral fusiform, bilateral middle and inferior occipital gyri, right angular gyrus, bilateral ITG and cerebellum; (b) when the left IFG was chosen as the seed region, significant differences (p<.05) were found between dyslexics and controls in the following brain regions: right inferior frontal triangularis, right middle occipital gyrus, right inferior occipital gyrus, and right cerebellum (VI); and (c) when the cerebellum was chosen as the seed region, significant differences (p<.05) were found between dyslexics and controls in the following brain regions: bilateral superior frontal gyrus, left middle frontal gyrus, right angular gyrus, and right middle occipital gyrus. Adult dyslexics, when compared to controls, had impaired cortical connections in brain regions important for phonological processing. The abnormality in functional connectivity from cerebellum in dyslexics may be related to Klingberg et al.’s [30] finding, based on DTI, that white matter diffusion anisotropy in the temporo-parietal region of the left hemisphere is significantly correlated with reading in normal and dyslexic readers. Insufficient myelination of the axonal pathways is one possible explanation for the low anisotropy index values observed in poor readers [60]. Structural abnormalities in white matter pathways could interfere with neuronal transmission, which will directly affect the synchrony of the BOLD signal. Of most importance, functional disconnections were also observed when seed regions were set in bilateral IFG. Bilateral IFG and right cerebellum were found to be abnormal in child dyslexics compared to normal controls ascertained using the same research criteria in our structural MRI studies [51]. Also see Berninger, Raskind, Richards et al. [50].
One of the great potential techniques in this area of language connectivity analysis is the integration of both functional and structural connectivity as shown by Morgan et al [61]. They measured connections between Wernicke\'s (WA), Broca\'s (BA) and supplementary motor area (SMA). Along the path between BA and SMA, they showed that fibers tracked measured from DTI generally formed a single bundle and the mean radius of the bundle was positively correlated with functional connectivity. They concluded that the insights gained from this work offers a useful guidance for non-invasive means to evaluate brain network integrity in vivo for use in diagnosing and determining disease progression and recovery [61]. The concept of integrating information across brain imaging modalities will allow the study of human language network as a systems approach. Another futuristic concept has been described by Rota et al [62] where they discuss the mechanisms of cortical reorganization underlying the enhancement of speech. They were able to measure changes in functional and effective connectivity induced in subjects who learned to deliberately increase activation in the right inferior frontal gyrus [62]. Also, see [63] for a model of the four multi-leveled functional language systems, which provides the conceptual framework for testing a model that differentiates among typical oral and written language learners (OWLs), dysgraphia, dyslexia, and OWL LD at the behavioral (phenotype and response to instruction) and brain levels of analysis.
The language connectivity findings discussed in this chapter suggest that structural and functional connectivity are adding and will continue to add to our understanding of language and language learning. There are specific language pathways and connections that are crucial for language acquisition and function. The integrity of these connections can be tested using structural DTI and functional MRI connectivity imaging. Individuals with learning and language disabilities have been reported to have different fMRI and DTI measurable connections than those with normal language functions. Once the techniques have been fully tested and developed, the application of language connectivity techniques to the individual assessment, treatment design, and response to treatment would also have enormous practical applications in the clinic and schools.
This project received support from the NIH/NICHD Grant 1P50HD071764 (overall PI Virginia Berninger, PI of project 3 Todd Richards).
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,
Using the stability constant method, these ternary complexes were found out, and using the parameters such as Δ log K and log X, these ternary complex data were compared with binary complex. The potentiometric technique at room temperature (25°C) was used in the investigation of some binary complex formations by Abdelatty Mohamed Radalla. These binary complexes are formed with 3D transition metal ions like Cu2+, Ni2+, Co2+, and Zn2+ and gallic acid’s importance as a ligand and 0.10 mol dm−3 of NaNO3. Such types of aliphatic dicarboxylic acids are very important biologically. Many acid-base characters and the nature of using metal complexes have been investigated and discussed time to time by researchers [7].
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 K, percentage of relative stabilization (% R. S.), and log X were evaluated and discussed. Now it provides the outline about the various complex species for the formation of different solvents, and using the concentration distribution, these complexes were evaluated and discussed. The conductivity measurements have ascertained for the mode of ternary chelating complexes.
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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