Metal ion vs. log βMY values.
\r\n\tThe aim of this book will be to describe the most common forms of dermatitis putting emphasis on the pathophysiology, clinical appearance and diagnostic of each disease. We also will aim to describe the therapeutic management and new therapeutic approaches of each condition that are currently being studied and are supposed to be used in the near future.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"278931ae110500350d8b64805c70f193",bookSignature:"Dr. Eleni Papakonstantinou",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/7934.jpg",keywords:"Atopic eczema, Interleukin, Topical corticosteroids, Hand eczema, Blisters, Pruritus, Irritant contact dermatitis, Allergic contact dermatitis, Discoid eczema, Sebaceous glands, Inflammatory dermatitis, Facial rash",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"February 5th 2019",dateEndSecondStepPublish:"March 19th 2019",dateEndThirdStepPublish:"May 18th 2019",dateEndFourthStepPublish:"August 6th 2019",dateEndFifthStepPublish:"October 5th 2019",remainingDaysToSecondStep:"2 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"203520",title:"Dr.",name:"Eleni",middleName:null,surname:"Papakonstantinou",slug:"eleni-papakonstantinou",fullName:"Eleni Papakonstantinou",profilePictureURL:"https://mts.intechopen.com/storage/users/203520/images/system/203520.jpg",biography:"Dr. med. Eleni Papakonstantinou is a Doctor of Medicine graduate and board certified Dermatologist-Venereologist. She studied medicine at the Aristotle University of Thessaloniki, in Greece and she continued with her dermatology specialty in Germany (2012-2017) at the University of Magdeburg and Hannover Medical School, where she completed her dissertation in 2016 with research work on atopic dermatitis in children. During this time she gained wide experience in the whole dermatological field with special focus on the diagnosis and treatment of chronic inflammatory skin diseases and also the prevention and treatment of melanocytic and non-melanocytic skin tumors. Her research interests were beside atopic dermatitis and pruritus also the pathophysiology of blistering dermatoses. In addition to lectures at german and international congresses, she has published several articles in german and international journals and her work has been awarded with various prizes (poster prize of the German Dermatological Society for the project: 'Bullous pemphigoid and comorbidities' (DDG Leipzig 2016), 'Michael Hornstein Memorial Scholarship' (EADV Athens 2016), travel grant (EAACI Vienna 2016). Since 2017, she works as a specialist dermatologist in private practice in Dortmund, in Germany. Parallel she co-administrates an international dermatologic network, Wikiderm International and she writes a dermatology public guide for patients, as she is convinced that evidence-based knowledge has to be shared not only with colleagues but also with patients.",institutionString:"Private Practice, Dermatology and Venereology",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"16",title:"Medicine",slug:"medicine"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"270941",firstName:"Sandra",lastName:"Maljavac",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/270941/images/7824_n.jpg",email:"sandra.m@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"6550",title:"Cohort Studies in Health Sciences",subtitle:null,isOpenForSubmission:!1,hash:"01df5aba4fff1a84b37a2fdafa809660",slug:"cohort-studies-in-health-sciences",bookSignature:"R. Mauricio Barría",coverURL:"https://cdn.intechopen.com/books/images_new/6550.jpg",editedByType:"Edited by",editors:[{id:"88861",title:"Dr.",name:"R. Mauricio",surname:"Barría",slug:"r.-mauricio-barria",fullName:"R. 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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"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"8424",title:"Laser-Driven Proton Acceleration Research and Development",doi:"10.5772/7967",slug:"laser-driven-proton-acceleration-research-and-development",body:'\n\t\tUp to now the acceleration of charged particles in most cases is based on the radio-frequency based technology. Another approach is to employ ultrahigh collective fields of plasmas produced by high-power lasers. Using various schemes, these plasma fields can be used to accelerate electrons, protons, and heavier ions. Laser-driven ion beams exhibit unique properties, among which are short duration, small source size, large number of particles, low emittance, etc. The laser-driven acceleration is inherently a very compact process, because the acceleration typically takes place within a micrometer spatial and picosecond time scales; the acceleration field can exceed TV/m, which allows achieving multi-MeV/nucleon ion energies. For the detailed reviews, see (Borghesi et al. 2006; Mourou et al. 2006) and references therein. The peculiar properties of the laser-driven proton beam, namely short duration, low emittance, and large particle number have been used in the proton imaging, which allows measurement of transient field distribution in plasma experiments (Borghesi et al. 2001); the broad proton energy spectrum allows multi-frame time-resolved studies in single shot. A compact laser-based laboratory setup has been used for the proof-of-principle radiological experiment (Yogo et al. 2009), which can be applicable in the biological, medical, and space research (Murakami et al. 2009). There are many other attractive potential applications of the laser-driven ion beams, among which the hadron therapy (Bulanov et al. 2002; Bulanov & Khoroshkov 2002), fast ignition (Roth et al. 2001), injectors into conventional accelerators (Krushelnick et al. 2000; Cowan et al. 2004), material processing, isotope production (Nemoto et al. 2001; Fritzler et al. 2003), pion production (Bychenkov et al. 2001), pump-probe experiments using simultaneous production of proton beam and THz radiation (Sagisaka et al. 2008), x-rays (Orimo et al. 2007), electrons (Li et al. 2006), and so on.
\n\t\t\tFor many applications, the parameters of the presently available laser-driven ion beams need to be improved. In particular, it is necessary to increase the maximum ion energy, simultaneously achieving high conversion efficiency. At present, this is an active area of research. Up to now a substantial part of results has been obtained with relatively large-scale, single-shot picosecond and sub-picosecond laser systems (Hatchett et al. 2000; Snavely et al. 2000; Fuchs et al. 2006; Robson et al. 2007; Henig et al. 2009). However, for many applications a compact, repetitive ion source is necessary. For such applications, it is attractive to use high-power femtosecond lasers, which have smaller pulse energies at the same power levels, and therefore can provide higher repetition rates. In this Chapter we present the results of proton acceleration and plasma diagnostic experiments (Pirozhkov et al. 2009c) conducted with a repetitive femtosecond J-KAREN laser at the Advanced Photon Research Center, Japan Atomic Energy Agency. In Sections 2 and 3 we describe the laser parameters and the results of the experiments and discuss the influence of several parameters on the maximum proton energy; we show the strong influence of the laser contrast on the proton acceleration process. In Section 4 we analyze the results of the on-target laser contrast measurement, which has been performed at full laser power using the properties of radiation reflected from the target. In Section 5 we describe the laser-driven proton beam manipulation using permanent magnet quadrupoles. In Section 6 we describe the radioactivation experiments using multi-MeV laser-driven proton source.
\n\t\tUp to now, the highest proton energies, the largest proton numbers and conversion efficiencies have been obtained using high-energy ps and sub-ps lasers. The proton energies close to 60 MeV (Hatchett et al. 2000; Snavely et al. 2000; Robson et al. 2007) have been achieved using petawatt lasers based on the Chirped Pulse Amplification (CPA) technology (Strickland & Mourou 1985). In these experiments, thin foil targets were irradiated by the focused laser pulses with intensities exceeding 1020 W/cm2; regardless of the target material, the accelerated ions were predominantly protons originating from the water or hydrocarbon surface contamination. If the contamination was removed e.g. by joule or laser heating, heavier ions had been accelerated (Hegelich et al. 2002; McKenna et al. 2004). The acceleration has been attributed to the process known as Target Normal Sheath Acceleration (TNSA) (Hatchett et al. 2000; Mora 2003).
\n\t\t\t\tThe experiments in which multi-10 MeV/nucleon protons and ions were accelerated within very short acceleration distances have caused great interest to the field of laser-driven ion acceleration. One of the attractive directions of research is miniaturization of the accelerator employing compact, relatively high-repetition rate CPA lasers with even shorter (femtosecond) pulse durations; the compactness and higher repetition rate can be achieved in this case because of the smaller pulse energy required to provide similar peak power and intensity. However, at present the achievable proton energies in this case are lower. Despite this, a number of application and proof-of-principle experiments have been performed with the ion and proton beams driven by compact femtosecond lasers. Ion energies up to 10-20 MeV/nucleon (Fukuda et al. 2009) and the laser-to-proton beam conversion efficiencies up to 3% (proton energy > 0.8 MeV) (Nishiuchi et al. 2008) have been demonstrated.
\n\t\t\tThe experiments described in this Chapter (Pirozhkov et al. 2009c) have been conducted using hybrid OPCPA/Ti:Sapphire J-KAREN laser (Kiriyama et al. 2008; Kiriyama et al. 2009); here OPCPA stands for the Optical Parametric Chirped Pulse Amplification. The laser consists of a CPA oscillator with high pulse energy, which facilitates achieving higher contrast, saturable absorber, stretcher, two- or three-stage OPCPA based on type I BBO crystals, two 4-pass Ti:Sapphire amplifiers, and vacuum compressor. The cryogenic cooling of the final amplifier (down to 100 K) removes thermal lensing, which allows 10 Hz operation with high laser beam quality. The saturable absorber efficiently reduces the Amplified Spontaneous Emission (ASE) after the CPA oscillator, which is crucial for the solid target irradiation experiments, including the ion acceleration (see Sections 3 and 4). The laser provides ~30 fs, ~ 1 J pulses at the wavelength of ≈ 820 nm with the nanosecond contrast higher than 1010. Employing an f/3 Off-Axis Parabola (OAP) mirror, the pulses are focused down to a 3-4 μm spot (Full Width at Half Maximum, FWHM). The short pulse duration and small focal spot allow achieving the peak irradiance of up to 1020 W/cm2.
\n\t\t\t\tThe temporal pulse shape on the femtosecond time scale (Figure 1) was measured with the home-built Transient Grating Frequency-Resolved Optical Gating (TG FROG) system (Pirozhkov et al. 2008). The measured FWHM and effective widths of the pulses are τFWHM\n\t\t\t\t\t = 28 fs, τeff\n\t\t\t\t\t = 35 fs without and τFWHM\n\t\t\t\t\t = 35 fs, τeff\n\t\t\t\t\t = 47 fs with the saturable absorber. (The effective width is the ratio of the pulse energy to the peak power.) The pulse duration with the saturable absorber is somewhat larger, because the saturable absorber introduces some high-order dispersion into the spectral phase, which cannot be compensated by the compressor. The power shown in Figure 1 is calculated from the FROG data using the measured on-target pulse energies. The on-target energies without/with the saturable absorber are EL\n\t\t\t\t\t = 880±20 mJ and 720±20 mJ, respectively, which corresponds to the peak powers of P\n\t\t\t\t\t0 = EL\n\t\t\t\t\t/τeff\n\t\t\t\t\t = 25 TW and 15 TW.
\n\t\t\t\tFemtosecond pulse shape of J-KAREN laser measured with the Transient Grating Frequency-Resolved Optical Gating (TG FROG), the dispersion of the window and air has been subtracted. The red line corresponds to the case without the saturable absorber, the FWHM pulse duration τFWHM\n\t\t\t\t\t\t\t = 28 fs, effective pulse duration τeff\n\t\t\t\t\t\t\t = 35 fs (FROG error = 0.008, N = 128), on-target energy EL\n\t\t\t\t\t\t\t = 880 mJ, peak power P\n\t\t\t\t\t\t\t0 = 25 TW. The blue line corresponds to the case with the saturable absorber, τFWHM\n\t\t\t\t\t\t\t = 35 fs, τeff\n\t\t\t\t\t\t\t = 47 fs (FROG error = 0.002, N = 256), EL\n\t\t\t\t\t\t\t = 720 mJ, P\n\t\t\t\t\t\t\t0 = 15 TW. Inset, the same data in the log scale.
The intensity distribution of the laser pulses focused by the f/3 OAP was measured by a microscope objective at full laser power operation; the pulses were attenuated using reflection from wedges and with neutral-density filters. Without the saturable absorber, the focal spot has an elliptical shape with side lobes [Figure 2 (a)]. The major and minor axes of the ellipse have the FWHM sizes of 5.7±0.7 μm and 2.28±0.11 μm, with the effective radius of reff\n\t\t\t\t\t = 2.82±0.10 μm (the errors are standard deviations of shot-to-shot fluctuations). With the saturable absorber, the shape of the focal spot is nearly circular [Figure 2 (b)], with the FWHM of 3.3±0.3 μm and reff\n\t\t\t\t\t = 2.73±0.12 μm. The derived peak intensity is I\n\t\t\t\t\t0 = P\n\t\t\t\t\t0/(πreff\n\t\t\t\t\t\n\t\t\t\t\t2) = 1.0×1020 W/cm2 without and 0.7×1020 W/cm2 with the saturable absorber.
\n\t\t\t\tFocal spot of J-KAREN laser focused with the f/3 off-axis parabola. The spot is measured with a microscope objective at full power mode, the laser beam is attenuated by wedges and filters. (a) The case without the saturable absorber, the spot size FWHM = 5.7 μm × 2.3 μm (major and minor axes of the fitted ellipse), effective radius reff\n\t\t\t\t\t\t\t = 2.8 μm, derived peak irradiance I\n\t\t\t\t\t\t\t0 = 1.0×1020 W/cm2. (b) The case with the saturable absorber, FWHM = 3.3 μm (nearly circular), reff\n\t\t\t\t\t\t\t = 2.7 μm, I\n\t\t\t\t\t\t\t0 = 0.7×1020 W/cm2.
Sub-nanosecond and picosecond contrast of J-KAREN laser in the three operation modes measured with the 3rd order cross-correlator: the thin red line is for the case of CPA oscillator, 3-stage OPCPA, and two multi-pass amplifiers (no saturable absorber). The blue dashed line is for the similar case but with the saturable absorber installed after the CPA oscillator. The thick green line is the same as the blue dashed line, but 2-stage (nonsaturated) OPCPA is used. The actual nanosecond contrast is ~ 2-3 times higher than shown in the figure due to the insufficient temporal resolution of the cross-correlator (~ 120 fs); the estimated actual contrasts for the three cases are ~ 5×106, ~ 5×108, and ~ 5×1010. The inset shows the same data in more details within the time range of ± 60 ps.
The contrast in different operation modes has been measured with the high-dynamic range 3-rd order cross-correlator (Figure 3). The saturable absorber improves the contrast by a factor of ~100. A similar improvement has been achieved by non-saturated OPCPA operation (two OPCPA stages instead of three) (Kiriyama et al. 2008).
\n\t\t\tA typical schematic layout of the experiments is shown in Figure 4. The OAP focused p-polarized laser pulses onto a tape or ribbon targets at the incidence angle of 45 . The tape target (Nayuki et al. 2003) supplied fresh surface for each shot, which allowed taking advantage of the high-repetition rate laser operation. The tapes were made from polyimide with the thicknesses of 7.5 μm and 12.5 μm. The ribbon targets were made from metal (Al, Au, Pt, Pd, etc.) with the thicknesses down to 200 nm.
\n\t\t\t\tExperimental setup. The p-polarized multi-10 TW laser pulses are focused by the f/3 off-axis parabola (OAP) to the irradiances up to 1020 W/cm2, the incidence angle on the target is 45 . The target can be a polyimide tape with the thickness of 7.5 μm or 12.5 μm as well as Al, Au, Pd, or Pt ribbon with the thickness from few μm down to 200 nm. The constantly moving tape targets allow the repetitive proton acceleration at 1 Hz. The protons originating from the surface contamination are accelerated at the rear side of the target, predominantly perpendicular to the target surface. The protons are detected with several instruments, including the absolutely calibrated Time-of-Flight (ToF) spectrometers at 0 and ±22.5 from the target normal (proton energy spectrum), CR-39 nuclear track detectors with the range filters (proton beam foot-print), and Thomson parabola with CR-39 detector (energy spectra of protons and other ions) (not shown). The laser-plasma interaction is studied with the interferometry and measurements of reflectivity and transmission. (a) A schematic layout. (b) A photo of the target chamber from the top with the superposed laser beams, mirrors, calorimeters, proton beam direction, and directions of observation with the Time-of-Flight spectrometers.
The protons were detected by the Time-of-Flight (ToF) spectrometers, CR-39 nuclear track detectors, and Thomson parabola. The ToF spectrometers (Nakamura et al. 2006; Yogo et al. 2007) were installed at the target normal direction and ±22.5 from it. In order to select the proton signal and reduce noise, the ToF spectrometers contained sweeping magnets removing all but the most energetic electrons, Al filters blocking laser and other light, and relatively thin plastic scintillator and the bent light guide that prevented the transmitted x-rays to enter the photomultiplier tube. The ToF spectrometers were absolutely calibrated with the conventional accelerator. The ToF spectrometers provide the proton spectrum immediately after the shot. This together with the constantly moving tape target allowed 1 Hz shooting, which has been used for quick optimization of the proton acceleration conditions. The CR-39 detectors with the range filters were used for the angular distribution and emittance measurements. Thomson parabola ion analyzer was used to check the contribution of other ion species.
\n\t\t\t\tTo understand the laser-plasma interaction details, we used several plasma diagnostics. The probe beam split by a pellicle from the main pulse was used for shadowgraphy at 820 nm and interferometry at 820 and 410 nm (2ω) (Sagisaka et al. 2004; Sagisaka et al. 2006). To measure the laser energy reflected from and transmitted through the target, we used in-vacuum calorimeters. The calorimeter measuring the transmitted energy was used to measure the on-target laser pulse energy, when the target situated on a motorized 3-axis stage was moved out of the beam. Simultaneously, the third calorimeter measured leakage through one of the dielectric mirrors. After such cross-calibration, the on-target energy in each shot was derived from the dielectric mirror leakage, which allowed obtaining specular reflectivity and transmission.
\n\t\t\tWe used a broad range of laser and target parameters to study the laser-driven acceleration properties and dependences on parameters. In order to achieve the maximum proton energies, a repetitive operation was employed to optimize the laser contrast, target position, pulse duration, etc.
\n\t\t\t\tThe dependence of the maximum proton energy on the effective pulse duration is shown in Figure 5. The pulse duration was varied by moving a grating in the compressor. The laser pulse shape was measured using the TG FROG (Figure 1) (Pirozhkov et al. 2008). The spectrum and spectral phase measured with the TG FROG at some grating position allow calculating the shape of the laser pulse at any other grating position with high accuracy, as it was checked by direct comparison of the measured and calculated pulses. The effective pulse duration in Figure 5 is therefore calculated from the TG FROG data obtained with the shortest pulse. The dependence of the maximum proton energy on the pulse duration is rather smooth, with the maximum at somewhat elongated pulse. This can be understood using the model of electrostatic acceleration of protons at the rear side of the target (Mora 2003; Fuchs et al. 2006) with the additional limit that the acceleration distance equals the sheath diameter (Robson et al. 2007). The dependence of the proton energy on the pulse duration obtained from this model (the dashed curve in Figure 5) agrees well with the measurements.
\n\t\t\t\tThe femtosecond pulses typically have a complicated structure in time. In particular, they have several kinds of preceding light, such as the ASE, prepulses, and picosecond pedestal. The preceding light can damage the target and create the preformed plasma well before the main pulse. To understand the influence of the preformed plasma on the proton acceleration, we employed the time-resolved interferometry using the femtosecond probe pulse (Sagisaka et al. 2004; Sagisaka et al. 2006). Figure 6 shows the results of interferometry taken at 50 ps before the main pulse arrival. The ion spectra at the target normal direction recorded simultaneously with the interferograms shown in Figure 6 are shown in Figure 7. In the case of a relatively low contrast (~5×106), the preplasma with the size of few hundred μm was formed [Figure 6 (a)], and the proton energy was 2.3 MeV. On the other hand, when the high contrast mode was used (~ 5×1010), the preplasma was not detectable [Figure 6 (c)], which means it was smaller than ~20-30 μm. The maximum proton energy in this case was 3.5 MeV. The smaller proton energy in the case of lower contrast can be explained by the rear surface disruption and/or bending (Mackinnon et al. 2001; Lindau et al. 2005). Interestingly, when we adjusted the duration of the ASE in the lower-contrast case (no saturable absorber, contrast ~5×106) by shifting the gating time of the Pockels Cell (PC) by 300 ps, the proton energy increased up to 4.1 MeV in some shots; the preplasma size was in this case intermediate [Figure 6 (b)]. The proton energy higher than in the case with the saturable absorber can be understood by larger laser power and intensity, which were achieved without the saturable absorber, by increased absorption in the preformed plasma (Gibbon & Bell 1992; Borghesi et al. 1999; Ping et al. 2008; Pirozhkov et al. 2009a), and by the laser pulse self-focusing in the preplasma with the optimum scale length (Bychenkov et al. 2001; McKenna et al. 2008).
\n\t\t\t\tMaximum proton energy at 0 (along the target normal) vs. the effective pulse duration τeff\n\t\t\t\t\t\t\t. The target is 7.5 μm polyimide tape, the saturable absorber is not used. The individual shots are shown with the squares, the several-shot average with the stars and the error bars (the standard deviation of shot-to-shot fluctuations). The dashed line shows the calculated dependence; the model used for the calculation is described in (Fuchs et al. 2006) with the additional limitation of the acceleration length equals the sheath diameter (Robson et al. 2007).
Taking advantage of the repetitive operation, we studied the stability of the proton acceleration (Figure 8). Although the case with the optimum preplasma allowed achieving higher proton energies in some shots, the proton acceleration was less stable than in the case of high laser contrast. We measured the maximum proton energies at the target normal direction (0 ) and at 22.5 from normal in 13 (40) consecutive shots without (with) the saturable absorber. In the case of higher contrast, the average proton energy was higher and fluctuations were smaller, which is important for many applications requiring stable ion beam. Further, in the high-contrast case the maximum proton energy at 0 was always larger than at 22.5 . In the case of lower contrast, the shot-to-shot fluctuations were large, and the maximum proton energies at these two angles were nearly same. Instability of the proton acceleration in the lower contrast case can be explained by the unstable nature of the preplasma itself, as well as relativistic self-focusing, which is also a kind of instability (Litvak 1970). Angular distributions of proton beam at different contrast conditions are described in details in (Yogo et al. 2008).
\n\t\t\t\tPreplasma diagnostic using the interferometry with 820 nm femtosecond probe pulses 50 ps before the main laser pulse. The target is 7.5 μm thick polyimide tape. The three different laser operation modes with different contrasts are used: (a) without the saturable absorber, 3-stage OPCPA, (thin red line in Figure 3), Pockels Cell (PC) voltage on at -1 ns; (b) same as (a), but the PC voltage on @-0.7 ns (corresponds to the ASE duration shorter by 0.3 ns); (c) with the saturable absorber and 2-stage non-saturated OPCPA (thick green line in Figure 3), PC off (corresponds to the ASE duration of ~ 3 ns).
Proton energy spectra at several modes of laser operation with different contrasts: The thin red line corresponds to the mode with the CPA oscillator, no saturable absorber, and 3-stage OPCPA (thin red line in Figure 3). The thin black line corresponds to same case but with the shorter by 0.3 ns ASE duration (also thin red line in Figure 3, because the contrast is not affected significantly by the Pockels Cell within the measurement range of -0.5 … +0.1 ns). The thick green line corresponds to the mode with the saturable absorber and 2-stage (nonsaturated) OPCPA (thick green line in Figure 3). The dotted lines show the characteristic noise levels in the corresponding ToF spectra. The interferograms taken in the same shots [Figure 6(a) – (c)] are shown near the spectra.
Maximum proton energy in the consecutive shots with the same shooting parameters, the repetitive proton acceleration at 1 Hz employing the 7.5 μm thick polyimide tape target. (a) Maximum proton energy vs. shot number; solid symbols correspond to observation at 0 (along the target normal direction), open symbols at 22.5 off the normal in the same shots. Blue circles (red squares) correspond to the case with (without) the saturable absorber (in both cases, 3-stage OPCPA is used). (b) The histograms of maximum proton energy distributions at 0 (along the target normal) corresponding to the frame (a).
It has been shown in simulations (Esirkepov et al. 2006) and experiments (Neely et al. 2006; Antici et al. 2007; Ceccotti et al. 2007) that very thin (sub-micrometer to nanometer-scale) targets can provide higher proton energy and larger conversion efficiency, provided that the laser contrast is sufficiently high so that the target is not damaged by the preceding light. We compared the proton acceleration from ribbon targets with the thickness from 1 μm to 200 nm. The proton energies from 1 μm thick Au targets were larger than from thinner targets (Figure 9). Although the nanosecond contrast was sufficiently high, the target was probably disturbed by the picosecond pedestal or prepulses at few tens of picoseconds before the main pulse (Figure 3).
\n\t\t\t\tProton energy spectra at the target normal direction in several shots with different targets. The saturable absorber is used, 2-stage not-saturated OPCPA, Pockels Cell voltage off (3 ns ASE). The thick blue lines correspond to the 1 μm thick Au targets; the thin red lines correspond to the 200 nm thick Pd, Pt, and Au targets.
The laser contrast strongly affects ion acceleration. In particular, in the TNSA regime higher ion energy is expected from thinner target in the ideal case, but in real experiments the rear surface of very thin targets is perturbed due to the preplasma formation, so there is an optimum target thickness (Kaluza et al. 2004). The ASE can even turn the originally solid-density target into a near-critical density plasma cloud (Matsukado et al. 2003; Yogo et al. 2008), so the acceleration mechanism changes, and the ions are accelerated by a long-living charge separation electric field, sustained by a quasistatic magnetic field of dipole vortex (Bulanov et al. 2005; Bulanov & Esirkepov 2007; Fukuda et al. 2009).
\n\t\t\tIn order to understand the influence of the laser contrast in the described experiments, we performed the laser contrast diagnostics based on the target reflectivity measurement. The reflectivity was measured using calibrated calorimeters at full power operation in the real shooting conditions. The detailed description of this technique and experiments performed at three different laser systems can be found in (Pirozhkov et al. 2009a; Pirozhkov et al. 2009b). The data obtained with J-KAREN laser are shown in Figure 10.
\n\t\t\tOn-target contrast diagnostic using the reflectivity of solid target at full laser power. The specular reflectivity R is measured with the in-vacuum calibrated calorimeter (Figure 4). The spot size is varied by moving the target by distance T from best focus, the distance is measured along the laser beam, T< 0 corresponds to the target shifted toward the Off-Axis Parabola (OAP). (a) Specular reflectivity R vs. target position T. The error bars include the calibration errors and measured noise. (b) R vs. derived average intensity (bottom axis) and fluence (top axis) (the average over the FWHM spot area, accounting for the 45 incidence angle). The red open circles are the single-shot data, the black filled circles are the average values; the horizontal error bars are due to the target zero position uncertainty; the vertical error bars include shot-to-shot fluctuations, calibration errors, and measured noise.
The data were taken with the saturable absorber present and 3-stage OPCPA, the contrast was ~ 5×108 with the ASE duration of 3 ns. The dependence of the reflectivity on the target position [Figure 10 (a)] exhibits a dip at best focus position T = 0. Such dip corresponds to the insufficient laser contrast. The specular reflectivity decreases due to both the increased absorption in the preplasma and the beam break-up. The dependence of the reflectivity on the average intensity and fluence [Figure 10 (b)] shows that the reflectivity was still high at the average intensity of ~ 2×1017 W/cm2, which is ~ 100 times smaller than the intensity at best focus. Therefore, a ~ 100-fold improvement of the contrast was necessary to avoid the preplasma formation by the ASE. This factor had been achieved by using non-saturated (2-stage) OPCPA operation, which was used to shoot sub-μm targets (Figure 9). However, in the latter case the picosecond pedestal or prepulses might be able to produce the preplasma, which led to the decreased proton energies observed in the case of 200 nm targets.
\n\t\tThe perspective mechanisms of laser-driven ion acceleration promise to provide quasi-monoenergetic, low-divergence ion beams (Kuznetsov et al. 2001; Esirkepov et al. 2004; Esirkepov et al. 2006). However, in the present experiments the typical ion beam divergence is ~10 , and the energy spectrum is wide (energy spread ~100%) (Borghesi et al. 2006). This is disadvantageous for many applications of the laser-driven ion beams, which are possible at present. Here we can point out the radiobiological studies (Yogo et al. 2009), ion beam injector to the postaccelerator (Krushelnick et al. 2000; Cowan et al. 2004), etc. Therefore, it would be desirable to modify the ion beam divergence and spectrum. There were several proposals and demonstrations of various techniques, including the use of a curved target (Bulanov et al. 2000; Sentoku et al. 2000; Ruhl et al. 2001; Patel et al. 2003) (focusing or collimation of the proton beam), laser-driven plasma microlens (Toncian et al. 2006) (proton beam focusing and energy selection), phase rotation using a radio-frequency electric field (Nakamura et al. 2007; Ikegami et al. 2009; Wakita et al. 2009) (modification of the proton energy spectrum and beam divergence), and use of permanent magnet quadrupoles (PMQs) (Schollmeier et al. 2008; Ter-Avetisyan et al. 2008; Nishiuchi et al. 2009) (focusing or collimation of the ion beam, energy band selection). In this Section, we describe the experiment in which the efficient proton beam manipulation with the PMQs was demonstrated (Nishiuchi et al. 2009). The feature of this experiment is the 1 Hz repetition rate and the large acceptance angle of the PMQs, which allowed achieving high proton flux.
\n\t\t\tThe experiment was performed with J-KAREN laser with the on-target pulse energy of 0.7 J, pulse duration of 30 fs, peak irradiance of ~1020 W/cm2, and the ASE contrast and duration of 107 and 1 ns, respectively. The setup was similar to the one shown in Figure 4. However, the pair of PMQs was installed at the target rear side, as shown in Figure 11.
\n\t\t\tOriginally, the proton beam with the energy band from 1.9 to 2.8 MeV had a typical divergence of 10 (half angle), as it is demonstrated in the frame (a). The acceptance angle of the first PMQ was also ~10 (half angle). Thus, nearly all protons were accepted at this stage. The first PMQ focused the protons in the vertical and defocused in the horizontal planes. Due to the defocusing, some of the protons were not collected with the second PMQ. Those protons which were collected were further focused in the horizontal and defocused in the vertical planes with the second PMQ. As a result, the focus point was formed at the distance of 650 mm from the target. The proton beam profiles recorded with the CR-39 nuclear track detectors at the best focus as well as several other positions are shown in the frames (b) – (g) of Figure 11 (the proton energy range is 2.2 to 3.1 MeV). At the best focus, the CR-39 image has the dimensions of ~3 mm × 8 mm. However, due to the etch pit overlapping (detector saturation), this visible spot size is overestimated, and the real spot was smaller.
\n\t\t\tApart from the proton beam profile, we also measured the proton energy spectra with the ToF spectrometer situated at 1.93 m from the target. The original spectrum (without the PMQs) is shown in Figure 12 (a) by the line 2. With the PMQs, the spectrum becomes quasi-monoenergetic due to the strong chromatic aberrations of the PMQs (namely, most of the
\n\t\t\tFocusing of the laser-driven proton beam with two permanent magnet quadrupoles (PMQs). Schematic layout of the setup is shown in the vertical (side view) and the horizontal (top view) planes. The first PMQ has the field gradient of 55 T/m, thickness of 50 mm, and open diameter of 35 mm; the acceptance half-angle is ~10 , which is similar to the proton beam divergence. The second PMQ parameters are the field gradient of 60 T/m, thickness of 20 mm, and diameter of 23 mm. The octagonal frames (a) – (g) at the bottom of the figure show the experimental results obtained with 12.5 μm polyimide tape target; the proton beam profiles are recorded with the CR-39 nuclear track detectors covered with the Al range filter, the darker regions correspond to the higher proton density. The left CR-39 picture [frame (a)] is the original beam profile before the PMQs (Al 40 μm filter, 1.9 to 2.8 MeV). The frames (b) – (g) show the proton beam profiles at 450, 550, 650 (best focus), 750, 850, and 927 mm from the target (2.2 to 3.1 MeV). At the best focus [650 mm, frame (d)], the visible beam size is ~3 mm × 8 mm; these dimensions are overestimated due to the CR-39 saturation (etch pit overlapping) at the center of the image. The proton beam profiles in the blue insets on the frames (b) – (g) are obtained using the Monte-Carlo simulations; the spatial scales are the same as in the CR-39 images.
low-energy protons, except those near the axis, are strongly deflected by the first PMQ and do not pass through the aperture of the second PMQ).
\n\t\t\tEach frame (b) – (g) in Figure 11 also contains the inset, which shows the result of the Monte-Carlo simulation of the proton beam profile at the corresponding position. The parameters of the original proton beam (spectrum, divergence) and the beam transport system in the simulation was set in accordance with the experimental conditions. The close similarity of the experimental beam profiles with the simulation suggests that the alignment accuracy was sufficient in the experiment; we found that the accuracy of the magnet positioning should be ~100 μm. Additional evidence of the similarity is shown in Figure 12 (a), where the spectrum measured with the ToF is compared with the simulated one. The similarity of the experimental results and the simulation allows us to derive conclusions about the detailed parameters of the focused proton beam. In particular, we can simulate the proton energy spectrum at the focal plane (this is not same as the spectrum measured with the ToF at the distance of 1.93 m). The simulated spectrum is shown in Figure 12 (b); here the protons passing through the 3 mm diameter aperture are included. The spectrum is quasi-monoenergetic, with the energy of 2.4±0.1 MeV. The transport efficiency of the beamline for the energy range of 2.3 – 2.5 MeV was ~0.3. The loss was due to the second PMQ, as shown in the schematic layout in Figure 11. The efficiency of 0.3 should be compared with the transport efficiency of the divergent beam without the PMQs, which is ~ 1.7×10-4 (1.7×103 times smaller). Simulation also allowed calculating the duration of the proton bunch, which was ~1 ns. This is much shorter than the typical achievable value, which is determined by the strong dispersion of the usual proton beam with a large energy spread.
\n\t\t\tThe passive nature of the magnetic beamline led to the high stability of the spectrum after the PMQ pair. The pointing stability of the proton beam was 0.25±0.1 (standard deviation of shot-to-shot fluctuations). The instability of the proton number within the energy range of 2.4±0.1 MeV was 20%; this value included the fluctuations of the proton number, divergence, and pointing of the proton beam during the acceleration stage, originating from the laser, target, and plasma instabilities.
\n\t\t\tThe demonstrated technique of the ion beam focusing can be useful in many applications of the laser-driven ion beams, including such field as high-energy density physics, radiography, nuclear physics, astrophysics, radiobiological studies, chemistry, material sciences, etc.
\n\t\t\ta) The black line (1) is the spectrum of the proton beam focused with the PMQs; the spectrum is measured with the absolutely-calibrated Time-Of-Flight (ToF) spectrometer at the distance of 1.93 m from the target. The blue line (2) is the original spectrum (without the PMQs) at the same ToF position. The red line (3) is the simulated spectrum at the TOF position. (b) Proton energy spectrum within the 3 mm diameter circular aperture at the focal plane (simulation).
Multi-MeV laser-driven proton beams can induce nuclear reactions (Ledingham et al. 2003; McKenna et al. 2003). In fact, these nuclear reactions were used for the proton beam diagnostic in many experiments (Hatchett et al. 2000; Snavely et al. 2000; McKenna et al. 2004; Clarke et al. 2008). Another possible application of the nuclear reactions induced by laser-driven proton beams is the thin layer activation (TLA) (Racolta et al. 1995), which allows studying the wear of tools, for example cutting tools made from cubic boron nitride (BN) or artificial polycrystalline diamond (DIA) (Conlon 1985; Vasváry et al. 1994). In TLA, the thin layer of tool is activated by selecting the appropriate energy range of the proton beam. Measuring the residual activity, it is possible to determine the loss of the surface material with the high sensitivity. Various isotopes can be activated, including iron, titanium, chromium, etc., which opens wide possibilities for the industrial diagnostic. The typical reaction threshold is from few to 10 MeV, which means that compact laser systems can be used.
\n\t\t\tIn this Section, we describe the results of the proof-of-principle experiment on the BN target activation (Ogura et al. 2009). The experimental setup is shown in Figure 13 (a). The parameters of J-KAREN laser used in this experiment were as follows: the pulse energy of ~1 J, the pulse duration of 30 fs, the peak irradiance of ~1020 W/cm2, the ASE contrast of higher than 1010. The target for the laser was polyimide tape. At the rear side of the tape, the BN sample was installed. The laser-driven proton beam induced the reaction 11B(p,n)11C, which has the threshold of 2.76 MeV. The maximum proton energy in this experiment ranged from 2.8 to 3.5 MeV, larger than the reaction threshold.
\n\t\t\ta) Experimental setup for irradiation of BN sample with the laser-driven proton beam. (b) Radiation spectrum measured using GSO [Gd2SiO5(Ce)] scintillation counter (solid line). The blue dotted line denotes the background. (c) The decay curve of annihilation photons with the fitted half-life time of T\n\t\t\t\t\t\t1/2 = 20.9±0.7 min, which corresponds to the decay of 11C (T\n\t\t\t\t\t\t1/2 = 20.39±0.02 min).
The isotopes 11C produced in the nuclear reaction decay through the positron emission with the half-life time T\n\t\t\t\t1/2 = 20.39±0.02 min (ENSDF, NNDC Online Data Service, ENSDF database [http://www.nndc.bnl.gov/ensdf/]). The positrons annihilate with the emission of two photons with the energy of 0.511 MeV, directed at 180 to each other. The annihilation photon spectrum recorded with the GSO scintillation counter (Leo 1987) is shown in Figure 13 (b). From the decay curve shown in the inset, the half-life time can be deduced: T\n\t\t\t\t1/2 = 20.9±0.7 min, which corresponds to the decay time of 11C. After 60 laser shots, the activity of the sample was measured to be 11.1±0.4 Bq. Using the 10 Hz laser operation during 10 minutes (6000 shots), the activity in the kBq range can be obtained, which is sufficient for the typical TLA diagnostic. Finally, we note that, unlike the situation with many other applications, the large divergence angle and the broad energy spectrum of the laser-induced proton beam can be convenient for the thin layer activation industrial diagnostic.
\n\t\tIn conclusion, the laser-driven ion acceleration is the perspective new technique. The laser-driven ion beams have unique properties, such as ultrashort bunch duration, low emittance, small source size, and large particle number. The laser-driven acceleration is a very compact process, which takes place on the micrometer scale. For many applications, a repetitive ion beam is desirable, which can be achieved employing femtosecond laser systems. We described the performance of laser and properties of proton beam by the example of experiments performed in the Advanced Photon Research Center, Japan Atomic Energy Agency with J-KAREN laser. In particular, we described the dependence of the maximum proton energy on the laser pulse duration and found the optimum of few hundred femtoseconds for the given experimental conditions. We also depicted the influence of laser contrast and demonstrated the method of its diagnostic. We described two application experiments, in which the stable, repetitive (1 Hz) laser-driven proton beam was focused by the permanent magnet quadrupoles, and was used for the BN target activation, which can be applicable in the industrial testing of tools and mechanisms using the thin layer activation technique.
\n\t\tWe are grateful for the expert support of J-KAREN laser team. This work was supported by the Special Coordination Funds for Promoting Science and Technology (SCF) commissioned by the Ministry of Education, Science, Sports and Culture (MEXT) of Japan and partly by Specially Promoted Education and Research by MEXT.
\n\t\tStability 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.
IntechOpen publishes different types of publications
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