Parameters of the distribution of the dry event duration in Ichkeul basin
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More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
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\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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\r\n\tIt is well known that noncommunicable diseases are responsible for nearly 40% of premature deaths all over the world. One modifiable risk factor for such mortality rates is people's lifestyles such as unhealthy diets, physical inactivity, tobacco exposure and excess alcohol use. People of all ages are affected by these diseases and premature deaths. The World Health Organization and Governments have become more concerned with these increasing and worrying statistics and have set to reduce premature deaths from noncommunicable diseases by one third by 2030. The aim of this book is to provide the reader with an overview of the current empirical work on the topics concerning health economics and lifestyles from different perspectives including the socioeconomic determinants of lifestyles, the impacts and the costs of noncommunicable diseases due to unhealthy lifestyles, the effects of public programs to promote healthy lifestyles, health insurance coverage, lifestyles and noncommunicable diseases coverage, the socioeconomic inequity associated with unhealthy lifestyles, and a particular focus is placed on the economics of the four main lifestyle diseases: cardiovascular diseases, diabetes, cancer and chronic respiratory diseases.
",isbn:null,printIsbn:null,pdfIsbn:null,doi:null,price:0,priceEur:null,priceUsd:null,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"ef77e9a5ebf778a9feb96f1454554d50",bookSignature:"Ph.D. Aida Isabel Tavares",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/6729.jpg",keywords:"Lifestyle economics, Health economics, Health policy, Lifestyle programs, Public health economics, Markets and regulation, Health demand,Health inequity, Preventive healthcare, Noncommunicable disease burden, Health insurance and lifestyles, Pharmaceutical industry and lifestyles, Socioeconomic determinants and impacts",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"December 1st 2017",dateEndSecondStepPublish:"December 20th 2017",dateEndThirdStepPublish:"February 20th 2018",dateEndFourthStepPublish:"May 11th 2018",dateEndFifthStepPublish:"July 10th 2018",remainingDaysToSecondStep:"3 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"196819",title:"Prof.",name:"Aida Isabel",middleName:null,surname:"Tavares",slug:"aida-isabel-tavares",fullName:"Aida Isabel Tavares",profilePictureURL:"https://mts.intechopen.com/storage/users/196819/images/system/196819.jfif",biography:"Aida Isabel Tavares holds a Ph.D. in Economic Analysis awarded by the Autonoma University of Barcelona in 2008. \r\nShe has been dedicated to research in Applied Health Economics and she published several articles in international peer-reviewed journals. She has also published one book in public economics. Her research areas include health economics and policy, health systems, socioeconomic determinants of health, regulation in health markets and economics evaluation. Dr. Tavares has also been teaching at different universities, specifically several courses related to microeconomics, public economics, and health economics. Currently, she collaborates with the Centre of Studies and Research in Health of the University of Coimbra in Portugal and she an Assistant Professor in Lisbon School of Economics and Management - University of Lisbon.",institutionString:"ISEG - Lisbon School of Economics & Management, University of Lisbon",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"5",totalChapterViews:"0",totalEditedBooks:"1",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"7",title:"Business, Management and Economics",slug:"business-management-and-economics"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"220812",firstName:"Lada",lastName:"Bozic",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/220812/images/6021_n.jpg",email:"lada@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:"7846",title:"Universal Health Coverage",subtitle:null,isOpenForSubmission:!1,hash:"03f74e6a4e925b7368b87e813bc29e1f",slug:"universal-health-coverage",bookSignature:"Aida Isabel Tavares",coverURL:"https://cdn.intechopen.com/books/images_new/7846.jpg",editedByType:"Edited by",editors:[{id:"196819",title:"Prof.",name:"Aida Isabel",surname:"Tavares",slug:"aida-isabel-tavares",fullName:"Aida Isabel Tavares"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. 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:"40837",title:"Characterization of the Events of the Dry Spell in a Basin Northern Tunisia",doi:"10.5772/50824",slug:"characterization-of-the-events-of-the-dry-spell-in-a-basin-northern-tunisia",body:'One form of drought is the interruption of the rainy season by a so called dry spell. Dry spell can be defined as a sequence of dry days including days with less than a threshold value of rainfall. The analysis of the historical occurrence of droughts and its probability of recurrence is important. This information is extremely useful for planning and design applications in agriculture and environment and many other sectors. Drought is perceived as a two-dimensional phenomenon (intensity and duration) witch is integrated on a spatial basis (regional drought). The two basic dimensions (intensity and duration) require that bivariate frequency analysis is required for linking return periods to both dimensions levels. This approach should be considered as an intermediate step towards a more comprehensive approach, which is related to anticipate damages of specific sectors.
One criticism, however, is that the first-order Markov chain has a relatively short memory that may limit the model’s ability to reproduce adequately long dry and/or wet spells, as well as interannual variability [1, 2, 3, 4, 5]. Higher-order Markov chains [6, 7] often improve these inadequacies; however, they require an estimation of more parameters thereby placing stricter demands on the amount of input data. Moreover, the estimation of more parameters results in a higher uncertainty in these parameters and subsequently, the model itself. An alternative to the Markov chain process is to use the wet-dry spell model. This is known as an alternating renewal model, that is, to simulate wet and dry spells separately by fitting their durations to an appropriate probability distribution such as the negative binominal or geometric distribution [2, 6, 8, 9, 10, 11, 12], or empirical distribution [13]. The characteristics of multi-day wet and dry spells is often important for investigating likely scenarios for agricultural water requirements, reservoir operation for analyses of antecedent moisture conditions [8, 14], and runoff generation in a watershed. The main objective of this paper is the event-based analysis of the dry spells based on daily records and the influence of a climatic evolution for identifying dry events under Mediterranean climatic conditions. Previous literature on the statistics of dry spells based on daily records is limited. Studies have primarily dealt with the length of dry and wet spells [10, 15, 16, 17, 18, 19, 20, 21].
In Tunisia, regardless of the origin of disturbances, the situations that give rise to copious rainfall remain dependent of important polar meridian flows, especially at altitude. Yet located on the southern margin of the Mediterranean, Tunisia is, wide inter-annual, that very irregularly affected by these flows. In years when the advections of polar air to the south are deep and frequent correspond to rainy periods in the country. In years when the cold air flows are limited in frequency and extension, constitute on the other hand, periods of low rainfall or drought.
So, given the character of atmospheric circulation, rainfall in Tunisia can only be unevenly distributed across seasonal and highly variable inter-annual scale. These same characters of atmospheric circulation are, with the assistance of geographic factors, in the origin of important regional contrasts rainfall.
The case study used as a base for the approach and the methodology of this research is the downstream basin of the Ichkeul Lake, situated in northern Tunisia (Figure 1). This area has a surface of approximately 1500 square kilometres. The wet season extends from September to April, although the beginning or the end of this wet season can move several weeks. Average seasonal precipitation is 600 mm, varies from 450 to 700 mm following the location and altitude. Mean evaporation (from a free water surface) is around 1490 mm yearly. The average annual temperature is around 17.5°C. The rainfalls are recorded in Ghézala-dam rain gauge, from 1968 to 2010. The mean is 701.3 mm; the coefficient of variation is 0.23. In this 42-year period the wettest year was recorded in 1995-1996, with 1104.3 mm, and the driest year in 1987-1988, with 408.6 mm. For the monthly rainfall, the mean is 56.8 mm; and the coefficient of variation is 0.67. The wettest month during the period from 1968 to 2010 was February 1996, with 341.1 mm, and the driest month, during the rainy season, was October 2001, with 0.5 mm. On average, for this period, the wettest month was December, with 105.5 mm of rainfall, and the driest month was May, with 26.8 mm of rainfall. The wet seasons are separated by dry seasons from almost four months. The rainfall events seem to be grouped over several wet days, separated by dry periods from variable duration. However, rainfall events lasting only one day can be observed. Daily precipitation series, available for a sufficiently long period, of five rain gauges located in this region have been analyzed.
In the wet-dry spell approach, the time-axis is split up into intervals called wet periods and dry periods (Figure 2). A rainfall event is an interval in which it rains continuously (it is an uninterrupted sequence of wet periods). The definition of event is associated with a rainfall threshold value which defines wet. The limit 4 mm day-1 has been selected because it corresponds to the average daily evapotranspiration in the area. This amount of water corresponds approximately to the expected daily evaporation rate, thus marking the lowest physical limit for considering rainfall that may produce utilizable surface water resources during the rainy season which lasts from September to April [8, 11]. In this approach, the process of rainfall occurrences is specified by the probability laws of the length of the wet periods (storm duration), and the length of the dry periods (time between storms or inter-event time).
Location of the study area, Tunisia
Several distributions have been used for the length of the wet and dry periods; the exponential distribution, the discrete negative binomial distribution “see [11]”. For the wet period length, the Weibull distribution has also been used to model short time-increment rainfall occurrences [22]. Other studies used different probability distributions for the length of wet and dry periods [8, 10, 23].
The varying duration of the events requires that the cumulative rainfall amounts corresponding to each event should be conditioned by the duration of the event. The identification and fitting of conditional probability distributions to rainfall amounts may be problem, especially in the case of short records and for events with extreme (long) durations.
Definitions for the event based analysis
A rainfall event m in a given rainy season n will be characterized by its duration Dn,m, symbolizing the number of subsequent rainy days, and by the total accumulated rainfall depth of Hn,m of Dn,m rainy days in mm [8].
Where N is the total number of observed rainy season and Mn the number of events/rainy season n; hj stands for the daily rainfall totals in mm. Note that hj > 0 and that for at least one hj > 4 mm. In order to define the temporal position of an event within the rainy season, a time parameter is needed. In study of [24], this time parameter is usually the interarrival time. In this investigation, the interarrival time is replaced by the interevent time or dry event Zn,m (Figure 2). Dry event represents the number of days without rainfall between two subsequent rainfall events. The beginning of the first rainfall event in autumn, in September, marks the beginning of the rainy season, while the end of the last rainfall event in spring, in April, marks the term of the rainy season. Thus, a wet season, with variable length, must start with a rainfall event and end with a rainfall event. Thus, the dry season lasts approximately four months. The length of the rainy season is defined as the time span between the start of the first and the end of the last event of the given season; while the "annual" climatic cycle is determined as the time lapsed between the onsets of two subsequent rainy seasons (Figure 2). The climatic cycle define the position of the first rainfall event within the rainy season. However, the length of the year is fixed at 365 days, and it is taken as a constant [8].
If the series of successive precipitations do not form independent events, the waiting time follows a gamma distribution with two parameters instead of an exponential distribution [24]. Consequently, if the time is discretized in days, the distribution of time separating two events is represented by the negative binomial distribution [11, 25] which is the equivalent discrete distribution of the gamma distribution:
where n = 0, 1, 2, … and r and p are estimated by:
It is necessary to subtract 1 to n because the negative binomial distribution starts with n = 0 whereas time separating two events lasts, per definition, at least 1 day (n = 1). Consequently f(n=0) is the probability of a dry event lasting 1 day.
As a regression analysis shown, the length of the dry event (time lapsed between rainfall events) or interevent time can be assumed to be independent from all other characteristics of the rainfall event. Thus the distribution of the dry event follows an unconditional probability distribution function. The dry event duration can only assume integer values. As the example Figure 3 reveals, the shortest interruption (one day) is the most frequent one. Almost one fourth of the observed interevent times are only one day long. Nevertheless, the observed range is much longer than that of the rainfall event duration (table 1). Dry periods up to 30 or even days may be recorded (table 2), even though the probability of such extreme length occurring in the middle of the rainy season is small. The very fact that the mean length fluctuates between 7 and 9 days and the high standard deviation are both serious warnings about the unreliability of assuming an evenly distributed precipitation during the rainy season. The univariate negative binomial pdf has been found as best fitted to describe the distribution of the dry event (Figure 3).
Rain gauge | Observation period | No. of data n | Longest observed in duration days | Arithmetic mean (day) | Standard deviation | Coefficient of variation |
Ghézala-dam | 1968/2010 | 895 | 56 | 7.39 | 8.00 | 1.08 |
O. J. Jebel Antra | 1961/2010+ | 984 | 55 | 7.56 | 8.03 | 1.06 |
Sidi Salem | 1959/2010 | 1078 | 64 | 7.58 | 8.22 | 1.08 |
Frétissa | 1982/2010 | 532 | 60 | 8.96 | 9.09 | 1.01 |
Sidi Abd el Basset | 1968/2010++ | 569 | 81 | 9.18 | 9.49 | 1.03 |
Parameters of the distribution of the dry event duration in Ichkeul basin
Distribution of dry event duration, O. J. Jebel Antra rain gauge
Rain gauge | Observation period | No. of data | Maximum no. of seasonal dry events observed | Arithmetic mean of no. of dry event per rainy season | Standard deviation of the no. of dry event per rainy season | Duration of the maximum seasonal dry event (day) | Arithmetic mean of the maximum seasonal dry event (day) | Standard deviation (day) |
Ghézala-dam | 1968/2010 | 895 | 30 | 21.31 | 4.39 | 56 | 30.66 | 9.53 |
O. J. Jebel Antra | 1961/2010+ | 984 | 30 | 21.39 | 4.30 | 55 | 30.45 | 9.73 |
Sidi Salem | 1959/2010 | 1078 | 34 | 21.15 | 4.24 | 64 | 30.82 | 10.80 |
Frétissa | 1982/2010 | 532 | 35 | 20.07 | 4.82 | 60 | 35.37 | 10.83 |
Sidi Abd el Basset | 1968/2010++ | 569 | 31 | 20.32 | 5.13 | 81 | 34.53 | 12.66 |
Comparison of the variability of the number of events/season and that of the maximum seasonal dry event
For planning purposes, the longest dry spells associated with different return periods are of fundamental importance. These values were obtained by modelling this process by GEV (General Extreme Value distributions) distributions which shows the best fit (Figure 4 and 5). Table 3 shows the estimated duration of extreme dry events obtained. From table 3 a few rainy seasons characterized by a favourable distribution of rainfall can hide the statistics fact that for a statistical recurrence period of one year, may it produce at least one of more than 20 days (rain gauges of Frétissa and Sidi Abdel Basset). This can be justified by low altitude and unfavourable exposure to rain for these stations (opposite the prevailing wind north-west) and a low annual rainfall in the two rain gauges. For the median the values obtained are critical, the duration of the extreme dry event is almost or more 30 days for all rain gauges; about 4 decades in the Frétissa rain gauge (35 days). For a hundred-year recurrence period, a longest dry spells up to 71.5 days may be registered at Sidi Abdel Basset rain gauge of low average annual rainfall (450 mm).
Distribution of the longest dry spell at Ghézala-dam rain gauge
Probability of exceedance | Return period | Ghézala-dam | O. J. Jebel Antra | Sidi Salem | Frétissa | Sidi Abd el Basset |
99 | 1.01 | 11.9 | 13.5 | 11.4 | 15.3 | 16.5 |
95 | 1.05 | 16.3 | 16.8 | 15.8 | 20.2 | 20.3 |
90 | 1.11 | 18.8 | 18.9 | 18.3 | 23.1 | 22.7 |
80 | 1.25 | 22.2 | 21.6 | 21.7 | 26.8 | 25.9 |
50 | 2 | 29.4 | 28.1 | 29.2 | 35 | 33.5 |
20 | 5 | 37.9 | 36.8 | 38.1 | 44.8 | 43.7 |
10 | 10 | 42.8 | 42.6 | 43.4 | 50.5 | 50.4 |
4 | 25 | 48.2 | 49.8 | 49.5 | 57.1 | 58.9 |
2 | 50 | 51.9 | 55.1 | 53.6 | 61.5 | 65.2 |
1 | 100 | 55.1 | 60.4 | 57.4 | 65.6 | 71.5 |
0.5 | 200 | 58.1 | 65.6 | 60.8 | 69.3 | 77.8 |
0.1 | 1000 | 63.8 | 77.7 | 67.9 | 76.8 | 92.2 |
Estimates of extreme dry event durations
Distribution of the longest dry spell (middle season) at Ghézala-dam rain gauge
To analyze the severity of extreme dry events, the central part of the rainy season for the period from December to March was chosen. Dry events occurring in the core of the rainy season were identified as those ending within the timespan of December - March. Thus any dry event resulting from a rain of start or end of rainy season is not counted. It is important to examine the occurrence of these longest dry spells, during the central part of the rainy season and the whole season, for different return periods. The exceedance probability Pe (N), that an extreme long dry event would occur at least once within a given statistical recurrence period of T years must be equal to the reciprocal value of the product λT:
where\n\t\t\t\t\t denotes the expected number of dry events/year (season). λT specifies the expected number of trials needed to observe at least once the extreme duration of N days associated with the return period of T years. The length of the extreme dry spell N can then be obtained from the cumulative negative binomial pdf:
Figure 6 shows the negative binomial distribution fitted to the station Ghézala dam. Table 4 shows the estimated duration of dry events N obtained by this method. Significant differences for a small number of observations between the results obtained using the method of event-based analysis and the extreme seasonal value approach are due to the conceptual difference between these methods. It appears that few rainy seasons characterized by a favorable distribution of rainfall can hide the statistics fact that on 21 or 22 dry events it is likely to produce at least one of more than 24 days.
Distribution of the time lapsed between rainfall events (inter-event time), Ghézala Dam rain gauge
By focusing on the dry spell event, the duration of the rainfall event Dn,m will in fact be identified as inter-event time. This change of roles fits the original Poisson model better. Since rainfall events are shorter, their duration follows the geometrical pdf, as theoretically required. The analysis show that approximately, 50 % of the events indeed last at most one day, the persistence of uninterrupted sequences of rainy days sometimes lasting beyond two weeks (the maximum observed duration is 17 days) (table 5). However the frequency of such long-duration events decreases rapidly with increasing duration. The empirical and fitted geometric pdf of event duration at the Ghézala-dam rain gauge are displayed in Figure 7.
Probability of exceedance | Statistical recurrence period | GEV distribution fitted to the seasonal extreme values | Model series of non-extreme values Negative binomial pdf | ||
Maximum number of dry days in the core of the rainy season | Extreme number of dry days in the rainy season | Duration of the seasonal extreme event | Expected value of the sample size to be considered | ||
99 | 1.01 | 6 | 11 | 23 | 21.52 |
95 | 1.05 | 10 | 16 | 24 | 22.37 |
90 | 1.11 | 12 | 18 | 25 | 23.65 |
80 | 1.25 | 16 | 22 | 26 | 26.63 |
50 | 2 | 24 | 29 | 29 | 42.62 |
20 | 5 | 34 | 38 | 36 | 106.55 |
10 | 10 | 40 | 43 | 42 | 213.1 |
4 | 25 | 48 | 48 | 49 | 532.75 |
2 | 50 | 53 | 52 | 55 | 1065.5 |
1 | 100 | 58 | 56 | 56 | 2131 |
0.5 | 200 | 63 | 59 | 58 | 4262 |
0.1 | 1000 | 74 | 65 | 65 | 21310 |
Estimates of extreme dry event durations at Ghézala-dam rain gauge
Rain gauge | Observation period | No. of data n | Longest observed in duration days | Arithmetic mean (day) | Standard deviation | Coefficient of variation |
Ghézala-dam | 1968/2010 | 937 | 13 | 2.89 | 1.98 | 0.68 |
O. J. Jebel Antra | 1961/2010+ | 1029 | 16 | 2.62 | 1.85 | 0.70 |
Sidi Salem | 1959/2010 | 1129 | 17 | 2.53 | 1.83 | 0.72 |
Frétissa | 1982/2010 | 569 | 11 | 2.32 | 1.63 | 0.70 |
Sidi Abd el Basset | 1968/2010++ | 597 | 10 | 1.89 | 1.21 | 0.64 |
Parameters of the distribution of the rainfall event duration in Ichkeul basin
By taking account of the assumption of the sequential independence of the rainfall events, as formulated above, the Poisson density function should adequately describe the distribution of the number of events per season:
Where N described the number of events during a rainy season. The parameter is the average number of events per rainy season.
Distribution of rainfall event duration, Ghézala-dam rain gauge
Figure 8 shows the fitted Poisson probability density function. Table 6 summarizes the parameters of the pdfs for all rain gauges. The arithmetic mean is 22.31 and the standard deviation 4.39 for Ghézala-dam rain gauge. The goodness-of-fit has been assessed by the Kolmogorov-Smirnov test at the 95% significance level. The arithmetic mean appears to provide a stable estimate of the parameter λ of the Poisson pdf, since this statistic is also the maximum likelihood estimator; it is used to estimate λ, in preference to the sample variance, which shows more substantial fluctuations [23].
Distribution of the number of rainfall events per season, Ghézala-dam rain gauge
Rain gauge | Observation period | No. of data n | Maximum no. of seasonal rainfall events observed | Arithmetic mean of no. of rainfall event per rainy season | Standard deviation of the no. of rainfall event per rainy season | Variance of the no. of rainfall event per rainy season |
Ghézala-dam | 1968/2010 | 42 | 31 | 22.31 | 4.39 | 19.34 |
O. J. Jebel Antra | 1961/2010+ | 46 | 31 | 22.39 | 4.30 | 18.51 |
Sidi Salem | 1959/2010 | 51 | 35 | 22.15 | 4.24 | 18.01 |
Frétissa | 1982/2010 | 27 | 36 | 21.07 | 4.82 | 23.30 |
Sidi Abd el Basset | 1968/2010++ | 28 | 32 | 21.32 | 5.13 | 26.37 |
Parameters of the distribution of the number of rainfall event per season in Ichkeul basin
The phenomenon of a rainy season followed by a dry season constitutes an annual cycle. As shown in table 7, the expected value of the cycle confirms the annual characteristic of this phenomenon, and the low coefficient of variation indicates the stability of this expected value. Nevertheless, a negative skewness can be consistently observed. The log Pearson type III pdf provides a good fit to distribution of the length of the climatic cycle. Figure 9 presents an example of empirical versus fitted theoretical pdf.
It is found that a climatic cycle with an above average length is generally followed by a shorter one, thus preventing any long lasting shift of the rainy season.
Rain gauge | No. of data points | Arithmetic mean (day) | Standard deviation | Coefficient of variation | Coefficient of skewness |
Ghézala-dam | 42 | 364.6 | 15.25 | 0.042 | 0.355 |
Oued J. Jebel Antra | 45 | 364.1 | 18.34 | 0.050 | 0.196 |
Sidi Salem | 50 | 365.6 | 22.87 | 0.063 | -0.007 |
Frétissa SM | 26 | 368.2 | 23.49 | 0.064 | -0.375 |
Sidi Abd el Basset | 27 | 364.7 | 17.94 | 0.049 | -0,306 |
Statistical parameters for the length of the climatic cycle in Ichkeul basin
Distribution of the length of the climatic cycle, Sidi Salem rain gauge
In order to carry out a criticism of the influence of a climatic evolution three cases are considered for the Ghézala-dam rain gauge: i) the complete daily precipitation series, ii) series divided into two sub-series, iii) series divided into three sub-series. Table 8 shows the calculated statistics for Ghézala-dam rain gauge.
From the data available at the Ghézala-dam rain gauge, it is possible to bring to the force the non-stationarity of the rainfall time-series for the period from 1968 to 2010. It is possible to isolate the periods of rainfall anomaly (strongly rainy periods or drought). One try to evaluate the behaviour of some statistical methods largely employed in research of climatic variability.
Simulated variability is that of a brutal change of the average. The procedures concerned are the Pettitt and Buishand test [26] (see Figure 10 and 11). Since the p-value calculated (0.374 for the Pettitt test and 0.652 for Buishand test) are greater than the significance level alpha = 0.05, we can not reject the null hypothesis H0 stating that the data are homogeneous. The risk of rejecting the null hypothesis H0 even tough is true is 37.37% for Pettitt test and 65.19% for Buishand test. The results show that the null assumption (absence of rupture) is accepted at 99 % significance level around the p-value. The threshold value 4 mm day-1 was selected. Table 9 summarizes the statistical characteristics of dry events for Ghézala-dam rain gauge in this hypothesis. It indicates that for the second period (89-2010), the maximum number of observed seasonal dry events is identical to the complete time series, whereas that of the first period (68-89), it is slightly inferior. The arithmetic mean of maximum seasonal dry events differs respectively during the two periods. The larger the standard deviation is high; east the dispersion of the observations of a variable. Consequently compared with the complete time series, the time series of the second period (89-2010) is dispersed.
Period of observation | No. of data | Minimum annual precipitation (mm) | Maximum annual precipitation (mm) | Arithmetic mean of annual precipitation (mm) | Standard deviation of annual precipitation | Coefficient of variation of annual precipitation |
1968/2010+ | 42 | 408.6 | 1104.3 | 701.39 | 168.03 | 0.23 |
1968/1989* | 21 | 408.6 | 960.7 | 671.90 | 128.82 | 0.19 |
1989/2010* | 21 | 420.3 | 1104.3 | 730.88 | 198.65 | 0.27 |
1968/1982§ | 14 | 514.4 | 903.6 | 671.31 | 107.68 | 0.16 |
1982/1996§ | 14 | 408.6 | 1104.3 | 720.17 | 218.49 | 0.30 |
1996/2010§ | 14 | 461.9 | 940.8 | 712.70 | 167.99 | 0.23 |
Statistics of the annual precipitation at the Ghézala-dam rain gauge
The maximum dry event (56 days) was occurred during the second period. Similarly, the maximum arithmetic mean value of the longest duration is during this period. However, the coefficient of variation, which represents the dispersion of the observations, is practically identical to the complete time series. The maximum number of observed seasonal dry events is recorded during the second period (82-96) and the third period (96-2010). For the later period, the arithmetic mean is approximately equal to that of the complete time series. A different standard deviation shows dispersion more distinguished during this period (96-2010). The maximum dry event occurred during the period (82-96). The average duration of the longest dry event is more remarkable during the last two periods (82-96) and (96-2010). A standard deviation, during the period (82-96), is much more significant (12.82) explaining a more significant dispersion of this series (C.V. = 0.40 while C.V. = 0.31 for the complete time series).
Period of observation | No. of data | Maximum no. of seasonal dry events observed | Arithmetic mean of no. of dry event per rainy season | Standard deviation of the no. of dry event per rainy season | Duration of the maximum seasonal dry event (day) | Arithmetic mean of the maximum seasonal dry event (day) | Standard deviation (day) |
1968/2010+ | 42 | 30 | 21.31 | 4.39 | 56 | 30.66 | 9.53 |
1968/1989* | 21 | 28 | 22.04 | 4.08 | 46 | 28.04 | 8.34 |
1989/2010* | 21 | 30 | 20.57 | 4.67 | 56 | 33.28 | 10.11 |
1968/1982§ | 14 | 27 | 23.14 | 2.71 | 40 | 28.28 | 5.83 |
1982/1996§ | 14 | 30 | 19.78 | 5.60 | 56 | 31.85 | 12.82 |
1996/2010§ | 14 | 30 | 21.00 | 4.00 | 47 | 31.85 | 8.87 |
Comparison of the variability of the number of events/season and that of the maximum seasonal event, Ghézala-dam rain gauge.
Test of Pettitt for the annual precipitation, Ghézala-dam rain gauge
Test of Buishand for the annual precipitation, Ghézala-dam rain gauge
This case study, using rainfall records of the Ichkeul basin, illustrates the independency between the durations of wet and dry events. It is shown that dry spells occur randomly during the rainy season. In this region dry spells can well be described by the negative binomial pdf. The procedure defines the inter-event time as being the dry event period. For the rainfall event duration, the theoretical requirement of the fitted geometric pdf are satisfied (Figure 7). It has to be pointed out that the event-based definition of the rainy season does not exactly fit the theoretical condition. Rainy seasons have variable lengths, as they are a stochastic function of the events themselves. For planning purposes, the longest dry spells associated with the various statistical recurrence periods are derived on the basis of the fitted GEV distributions. Event-based analysis is also useful to check the spatial properties of dry events. Event-based analysis, even if it is carried out on the basis of few years of observation, can rely on large number of data points (table 2). While the expected number of events/season is still derived from very few data, this estimate is more reliable than the approximate expected length of the longest seasonal dry spell, since this variability of the former is usually less than that of the latter, for the same data sets (table 10).
Rain gauge | No. of data | Coefficient of variation of the number of dry events-season (Cv1) | Coefficient of variation of the longest seasonal dry event (Cv2) | Cv2/Cv1 |
Ghézala-dam | 42 | 0.20 | 0.31 | 1.55 |
Oued J. Jebel Antra | 46 | 0.20 | 0.31 | 1.55 |
Sidi Salem | 51 | 0.20 | 0.35 | 1.75 |
Frétissa | 27 | 0.24 | 0.30 | 1.25 |
Sidi Abd el Basset | 28 | 0.25 | 0.36 | 1.44 |
Coefficient of variation of the number of dry events-season and that of the longest seasonal dry spell.
The procedure adopted allowed us to study the influence of climatic variation and the threshold value of negligible precipitation in identifying dry events. Another application of the event-based analysis is the study of the effects of climate change.
This study, which relied on daily data, describes characteristics of dry spell and their extreme cases. These features are important when estimating the drought risks. Although the region selected for study is not semi arid, data were not always available at the required level of detail. As a result, the detail of the studied events depended on the data collection stations involved. This lack of data is partially compensated by the daily series. In general, this study aimed to define droughts under specific conditions in terms of dry event. We also synthesised information for use in models of climatic risk, infrastructure damage mitigation and environmental management.
During 1987 – 1989 and 1993 – 1995 drought was characterized by two subsequent dry years. The drought management system has been applied. It was based on reactive decisions. The system is based in three phases: (i) Before drought (preparedness and early warning); (ii) Drought management (mitigation when drought is upon) and (iii) Subsequent drought (when drought is over). During each of the three phases different measures are applied. The Drought Management Phase is characterized by the execution of the planning programs of drought mitigation. Depending on the type, intensity and duration of the drought event, different scenarios are adopted [27].
The year is considered dry when the precipitation deficit is beyond 50% of the mean historically established value. The probability to have a dry year is 7 to 23% in the region. From such situation results a substantial shortage in the available water resources, a production falling and range shortage, and some problems related to the domestic water supply appear. Livestock sickness could be observed, because of diet change and unbalanced nutrition regime. In order to attenuate those problems a mitigation program is executed. For livestock safeguard, the identification of the animal nutriments stocks is established and an importation planning, if necessary, is fitted in order to gap the deficiency. Prevision of vaccination campaigning on the livestock against the sickness related to drought. To satisfy the domestic water demand, in urban as well as in rural areas, a program of aquifers uses is adopted, the use of the surface water resources is avoided or minimized. Particular attention is given to water transportation until the rural drought sensitive regions. Establishing reservoirs water management plan regarding the evolution of the climatic conditions. The eventuality of a second dry year is specially taken in account. Intensification of the preparedness operations related to the next year up going (short loans, soil tillage, seeds distribution …). When drought is over, several measures are taken. This is the intensification of the vulgarization program related to the soil tillage and farming practices in order to maximize the valorisation of the precipitation coming during the subsequent drought wet year. Available water resources evaluation (reservoirs and aquifers) is made. Reconstitution of the aquifers water reserves by the artificial recharging is followed. Like other action initiated, evaluation of the mitigation program efficiency and estimation of their cost.
In the following, the hydrological drought in this basin, including the water resources reservoirs management under drought and the water supply conditions, is presented. It is important to underline those water resources reservoirs management involving the application of water supply rationing depends on water storage at end April. Rainfall deficit during the period between the beginning of September and end April is an important index indicating the water resources availability situation. This period is the most determining of the hydrological drought and its impact on the reservoirs storages.
During 1987 – 1989 drought was severe in the whole country. During this period the water catchments in the reservoirs has been less than 50% of dams’ capacity. During 1993 – 1995 drought was similar to the former event described above. Rainfall deficit was ranged between 33 to 56% and was around 35% on the national scale. During this drought, data on the water catchments recorded in dams located in this region that were under exploitation in this date are presented in table 11.
Dams | Use starting date | Minimal water input (Mm3) | Year |
Joumine | 1983 – 1984 | 17.9 | 1993 – 1994 |
Ghézala | 1984 – 1985 | 0.5 | 1993 – 1994 |
Minimal water input recorded in dams under exploitation located in this region
The decision tools used for water management, during 1992 – 1995, were based on the measurement instrumentation spread in the water supply locations, information and data transfer to the Central Direction for decision taking, the filed databases, specialized software and simulation models related to the water management optimization. The drinking water supply (for domestic …) has been ensured without any restriction during the successive years 1992 – 1993, 1993 – 1994 and 1994 - 1995.
The agricultural water demand was satisfied during 1992 – 1993 and 1993 – 1994. A restriction plan was prepared for 1994 – 1995. This plan was applied in March 1995 and adapted in July 1995 regarding the water resources situation. For the irrigated areas, the restriction has been about 50% (with normal year as reference). This restriction ranged from 19.5 to 27.5% referring to a dry conditions year (1993 – 1994). Therefore during this year (1993 – 1994), in spite of the dry conditions all agricultural demand was satisfied. Farmers adopted some “self modifications” in their farming systems to adapt them to drought situation [27].
From all the previous drought management events, actions related to agricultural production (crop systems and livestock care) were well monitored. It is from the practical decisions taken during 1992 – 1995 drought events that tools decisions linked to water reservoir management were tested.
Voltammetry is an electrochemical technique for current-voltage curves, from which electrode reactions at electrode-solution interfaces can be interpreted. Since current-voltage curves, called voltammograms, include sensitive properties of solution compositions and electrode materials, their analysis provides not only chemical structures and reaction mechanisms on a scientific basis but also electrochemical manufacture on an industrial basis. The voltammograms vary largely with measurement time except for steady-state measurements, and so it is important to pay attention to time variables. Voltage is a controlling variable in conventional voltammetry, and the current is a measured one detected as a function of applied voltage at a given time.
\nThe equipment for voltammetry is composed of electrodes, solution, and electric instruments for voltage control. Electrodes and electric instruments are keys of voltammetry. Three kinds of electrodes are desired to be prepared: a working electrode, a counter one, and a reference one. The three will be addressed below.
\nLet us consider a simple experiment in which two electrodes are inserted into a salt-included aqueous solution. When a constant current is applied to the two electrodes, reaction 2H+ + 2e− → H2 may occur at one electrode, and reaction 2OH− → H2O2 + 2e− occurs at the other. The current is the time variation of the electric charge, and hence it is a kind of reaction rate at the electrode. Since the applied current is a sum of the two reaction rates, one being in the positive direction and the other being in the negative, it cannot be attributed to either reaction rate. A technique of attributing the reactions is to use an electrode with such large area that an uninteresting reaction rate may not become a rate-determining step. This electrode is called a counter electrode. The current density at the counter electrode does not specifically represent any reaction rate. In contrast, the current density at the electrode with a small area stands for the interesting reaction rate. This electrode is called a working electrode. It is the potential difference, i.e., voltage, at the working electrode and in the solution that brings about the electrode reaction. However, the potential in the solution cannot be controlled with the working electrode or the counter one. The control can be made by mounting another electrode, called a reference electrode, which keeps the voltage between an electrode and a solution to be constant. However, the constant value cannot be measured because of the difference in phases. A conventionally employed reference electrode is silver-silver chloride (Ag-AgCl) in high concentrated KCl aqueous solution.
\nAn electric instrument of operating the three electrodes is a potentiostat. It has three electric terminals: one being a voltage follower for the reference electrode without current, the second being a current feeder at the counter electrode, and the third being at the working electrode through which the current is converted to a voltage for monitoring. A controlled voltage is applied between the working electrode and the reference one. These functionalities can readily be attained with combinations of operational amplifiers. A drawback of usage of operational amplifiers is a delay of responses, which restricts current responses to the order of milliseconds or 10 kHz frequency.
\nVoltammetry includes various types—linear sweep, cyclic, square wave, stripping, alternating current (AC), pulse, steady-state microelectrode, and hydrodynamic voltammetry—depending on a mode of the potential control. The most frequently used technique is cyclic voltammetry (CV) on a time scale of seconds. In contrast, currently used voltammetry at time as short as milliseconds is AC voltammetry. We describe here the theory and tips for practical use of mainly the two types of voltammetry.
\nThe theory of voltammetry is to obtain expressions for voltammograms on a given time scale or for those at a given voltage. First of all, it is necessary to specify rate-determining steps of voltammograms. There are three types of rate-determining steps under the conventional conditions: diffusion of redox species in solution near an electrode, adsorption on an electrode, and charging processes at the double layer (DL). Electric field-driven mass transport, called electric migration, belongs to rare experimental conditions, and hence it is excluded in this review. When a redox species in solution is consumed or generated at an electrode, it is supplied to or departed from the electrode by diffusion unless solution is stirred. When it is accumulated on the electrode, the change in the accumulated charge by the redox reaction provides the current. Whenever electrode voltage is varied with the time, the charging or discharging of the DL capacitor causes current. Therefore, the three steps are frequently involved in electrochemical measurements.
\nA mass transport problem on voltammetry is briefly described here. The redox species is assumed to be transported by one-directional (x) diffusion owing to heterogeneous electrode reactions. Then, the flux is given by f = −D(∂c/∂x), where c and D are the concentration and the diffusion coefficient of the redox species, respectively. Redox species in solution causes some kinds of chemical reaction through chemical reaction rates, h(c, t). Then the reaction rate is the sum of the diffusional flux and the chemical reaction rate, ∂c/∂t = −∂f/∂x − h(c, t). Here the equation for h = 0 is called an equation of continuum. Eliminating f with the above equation on the assumption of a constant value of D yields ∂c/∂t = D(∂2c/∂x2) − h(c, t). This is an equation for diffusion-chemical kinetics. The expression at h = 0 is the diffusion equation. A boundary condition with electrochemical significance is the control of c at the electrode surface with a given electrode potential. If the redox reaction occurs in equilibrium with the one-electron transfer at the electrode, the Nernst equation for the concentrations of the oxidized species, co, and the reduced one, cr, holds.
\nwhere Eo is the formal potential. If there is no adsorption, the zero-flux condition in the absence of accumulation is valid:
\nThe other conditions are concentrations in the bulk (x → ∝) and the initial conditions.
\nIf the mass transport is controlled only by x-directional diffusion, cr and co are given by the diffusion equations, ∂c/∂t = D(∂2c/∂t2) for c = cr or co. An electrochemically significant quantity is not concentration in any x and t, but a relation between the surface concentrations and the current (the flux at x = 0). On the assumption of Do = Dr = D, of the initial and boundary conditions, (cr)t = 0 = c*, (co)t = 0 = 0, and (cr)x = ∞ = c*, (co)x = ∞ = 0, a solution of the initial-boundary problem is given by [1].
\nwhere j is the current density. The common value of the diffusion coefficients yields co + cr = c* for any x and t. Inserting this relation and Eq. (3) into the Nernst equation, (co)x = 0 = c*/[1 + exp[−F(E − Eo)/RT]], we obtain the integral equation for j as a function of t or E.
\nWhen the voltage is linearly swept with the time at a given voltage scan rate, v, from the initial potential Ein, Eq. (3) through the combination with the Nernst equation becomes
\nThe above Abel’s integral equation can be solved by Laplace transformation. When the time variation is altered to the voltage variation through E = Ein + vt, the current density is expressed as
\nwhere ζ = (E − Eo)F/RT and ζi = (Ein − Eo)F/RT. Evaluation of the integral has to resort to numerical computation. Current at any voltage should be proportional to v1/2, as can be seen in Eq. (5). The voltammogram for v > 0 rises up from Eo, takes a peak, and then deceases gradually with the voltage. The decrease in the current is obviously ascribed to relaxation by diffusion. The peak current density is expressed by
\nat Ep = Eo + 0.029 V at 25°C, where 0.446 comes from the numerical calculation of the integral of Eq. (5).
\nPractical voltage-scan voltammetry is not simply linear sweep but cyclic voltammetry (CV), at which applied voltage is reversed at a given voltage in the opposite direction. The theoretical evaluation of the voltammogram should be at first represented in the integral form with the time variation and then express the time as the voltage. One of the features of the diffusion-controlled cyclic voltammograms is the difference between the anodic peak potential and the cathodic one, ΔEp (in Figure 1), of which value is 59 mV at 25°C.
\nVoltammograms calculated from Eq. (5) for v = (a) 180, (b) 80 and (c) 20 mV s−1.
AC voltammetry can be performed when the time variation of voltage is given by E = Edc + V0eiωt, where ω is the frequency of applied AC voltage, i is the imaginary unit, V0 is its voltage amplitude, and Edc is the DC voltage. A conventional value of V0 is 10 mV. When this voltage form is inserted into Eq. (3) together with the Nernst equation, the AC component of the current density is represented by [2].
\nA voltammogram (j vs. Edc) at a given frequency takes a bell shape, which is expressed by sech2{(Edc − Eo)/RT}. The functional form of sech2 is shown in Figure 2. The peak current appears at Edc = Eo.
\nVoltammogram calculated from Eq. (10).
The AC-impedance technique often deals with the real impedance, Z1, = 1/2Y1 and the imaginary one, Z2 = −1/2Y1, where Y1 is the real admittance given by
\nHere Y2 is the imaginary admittance, equal to Y1. Since Z1 = −Z2, the Nyquist plot, i.e., −Z2 vs. Z1, is a line with the slope of unity. The term 1 + i in Eq. (7) has come from (Dω)1/2, originating from (Diω)1/2. Therefore, it can be attributed to diffusion. In other words, diffusion produces the capacitive component as a delay.
\nWhen the redox species with reaction R = O + e− is adsorbed on the electrode and has no influence from the redox species in the solution, the sum of the surface concentrations of R and O is a constant, Γ*. Then the surface concentration of the oxidized species, Γo, is given by the Nernst equation:
\nThe time derivative of the redox charge corresponds to the current density, j = d(FΓo)/dt. Application of the condition of voltage sweep, E = Ein + vt, to Eq. (9) yields.
\nThe voltammogram takes a bell shape (Figure 2), of which peak is at E = Eo, similar to the AC voltammogram. The current at any voltage is proportional to v. Since the negative-going scan of the voltage provides negative current values, the cyclic voltammogram should be symmetric with respect to the I = 0 axis. The peak current is expressed as jp = F2Γ*v/4RT. The width of the wave at jp/2 is 90 mV at 25°C.
\nSince a phase has its own free energy, contact of two phases provides a step-like gap of the free energy, of which gradient brings about infinite magnitude of force. In order to relax the infinity, local free energy varies from one phase to the other as smoothly as possible at the interface. The large variation of the energy is compensated with spontaneously generated space variations of voltage, i.e., the electric field, which works as an electric capacitor. The capacitance at solution-electrode interface causes orientation of dipoles and nonuniform distribution of ionic concentration, of which layer is called an electric double layer (DL).
\nWhen the time variation of the voltage is applied to the DL capacitance, Cd, the definitions of the capacitance (q = CdV) and the current lead
\nwhere Cd generally depends on the time. This dependence is significant for understanding experimentally observed capacitive currents.
\nThe DL capacitance has exhibited the frequency dispersion expressed by Cd = (Cd) 1Hz f −λ, called the constant phase element [3, 4, 5] or power law [6, 7], where λ is close to 0.1. Inserting this expression and V = V0eiωt into Eq. (11) yields
\nThis is a simple sum of the real part of the current and the imaginary one, indicating that the equivalent circuit should be a parallel combination of a capacitive component and a resistive one, both depending on frequency. Since the ratio, −Z2/Z1, for Eq. (12) is 1/λ, the Nyquist plots have slopes less than 10 rather than infinity.
\nIf the capacitive charge is independent of the time, the capacitive current should be I = d(CV)/dt = C(E − Eo)/v. Therefore, it takes a horizontal positive (v > 0) and a negative line (v < 0), as shown in Figure 3 (dashed lines). When the time dependence of C, i.e., Cd = (Cd)0t−λ, is applied to Eq. (11), for the forward and the backward scans, respectively, we have
\nCapacitive voltammograms by CV at v= 0.5 V s−1 for (dashed lines) the ideal capacitance and for Eq. (13) (solid curves) at λ = 0.2.
The variation of CV computed from Eq. (13) (Figure 3, solid curves) is similar to our conventionally observed capacitive waves.
\nVoltammograms can identify an objective species by comparing a peak potential with a table of redox potentials and furthermore determine its concentration from the peak current. Their results are, however, sometimes inconsistent with data by methods other than electrochemical techniques if one falls in some pitfalls of analytical methods of electrochemistry. For example, a peak potential is influenced by a reference electrode and solution resistance relevant to methods. Peak currents are varied complicatedly with mass transport modes as well as associated chemical reactions. Since the theory on voltammetry covers only some restricted experimental conditions, it can rarely interpret the experimental data successfully. This review is devoted to some voltammetric tips which can lead experimenters to reasonable interpretation.
\nIt is rare to observe a reversible voltammogram in which both oxidation and reduction waves appear in a symmetric form with respect to the potential axis at a similar peak potential, as in Figure 1. Frequently observed voltammograms are irreversible, i.e., either a cathodic or an anodic wave appears; a value of a cathodic peak current is quite different from the anodic one in magnitude; a cathodic peak potential is far from the anodic one. These complications are ascribed to chemical reactions and/or phase transformation after the charge-transfer reaction. A typical example is deposition of metal ions on an electrode. The complications can be interpreted by altering scan rates and reverse potentials.
\nA wave at a backward scan is mostly attributed to electrode reactions generated by experimenters rather than to species latently present in the solution. That is, it is artificial. It is caused either by the reaction of the wave at the forward scan or the reaction of the rising-up current just before the reverse potential. A source of the backward wave can be found by changing the reverse potentials.
\nSome voltammograms have more than two peaks at one-directional scan. The appearance of the two can be interpreted as a two-step sequential charge-transfer reaction. However, multiple waves appear also by combinations of chemical reactions and adsorption. The peak current and the charge for this case are quite different from the predicted ones, as will be described in Section 3.2. Change in scan rates may be helpful for interpreting the multiple waves.
\nIt is possible to predict theoretically a controlling step of voltammograms from their shape (a bell type corresponding to an adsorption wave or a draw-out type corresponding to a diffusion wave). However, the shape strongly depends on chemical complications, adsorption, and surface treatment of the electrodes. When redox species in solution is partially adsorbed on an electrode, the electrode process is far from a prediction because of very high concentration in the adsorbed state. A draw-out-shaped wave can be observed even for the adsorbed control. It is important to estimate which state the reacting species takes on the electrode. Potentials representing of voltammetric features do not express a controlling step in reality although the theory does. One should pay attention to the current. The peak current controlled by diffusion with one-electron transfer is given by Ip = 0.27 cAv1/2 μA (c, bulk concentration mM; A, electrode area mm2; v, potential sweep rate mV s−1). The microelectrode behavior sometimes comes in view at v < 10 mV s−1, A < 0.1 mm2, so the measured current is larger than the estimated value. On the other hand, the peak current controlled by adsorption is given by Ip = 1.6 Av nA when one redox molecule is adsorbed at 1 nm2 on the electrode. The voltammogram by adsorption often differs from the ideal bell shape due to adsorbed molecular interaction and DL capacity. Division of the area of the peak by the scan rate yields the amount of adsorbed electricity. Comparison of this with the anticipated amount of adsorption may be helpful for understanding the electrode process.
\nThe peak potential difference ΔEp between the oxidation wave and the reduction wave (Figure 1) has been used for a prediction of the reaction mechanism. For example, ΔEp = 60 mM suggests the diffusion-controlled current accompanied by one-electron exchange, whereas ΔEp = 30 mM infers a simultaneous reaction with two electrons. Then what would happen for 120 mV which is sometimes found? A half-electron reaction might not be accepted. Potential shift over 60 mV occurs by chemical complications. In contrast, the voltammogram by adsorbed species shows theoretically a bell shape with the width, E1/2 = 90 mV, at the half height of the peak (Figure 2). This value is based on the assumption of the absence of interaction among adsorbed species. However, adsorption necessarily yields such high concentrations as strong interaction.
\nIt is necessary to pay attention to the validity of analyzing ΔEp and E1/2. The peak potential is the first derivative of a voltammogram. Since ΔEp is a difference between the two peaks, it is actually the second-order derivative of the curves in the view of accuracy. In other words, the accuracy of ΔEp is lower than that of peak current. Furthermore, peak potentials as well as E1/2 readily vary with scan rates owing to chemical reactions and solution resistance. One should use the peak current for data analysis instead of the potentials.
\nVoltammograms of a number of redox species have been reported to be diffusion controlled from a relationship between Ip and v1/2. The redox species exhibiting diffusion-controlled current is, however, limited to ferrocenyl derivatives under conventional conditions. Voltammograms even for [Fe(CN)6]3−/4− and [Ru(NH3)6]3+ are deviated from the diffusion control for a long-time measurement. Why have many researchers assigned voltammograms to be the diffusion-controlled step? The proportionality of Ip to v1/2 in Eq. (6) has been confused with the linearity, Ip = av1/2 + b (b ≠ 0). The plot for the adsorption control (Ip = kv) also shows approximately a linear relation for Ip vs. v1/2 plot in a narrow domain of v, as shown in Figure 4B. The opposite is true (Figure 4A). Therefore, it is the intercept that determines a controlling step of either the diffusion or adsorption. Some may say that the intercept can be ascribed to a capacitive current. If so, the peak current should be represented by Ip = av1/2 + bv, which exhibits neither linear relation with v1/2 nor v.
\nPlots of Ip of (A) K3Fe(CN)6 and (B) polyaniline-coated electrode against v1/2 and v. Both plots show approximately linear relations.
There is a simple method of determining a controlling step either by diffusion or adsorption. Current responding to diffusion-controlled potential at a disk electrode in diameter less than 0.1 mm would become under the steady state after a few seconds [8]. Adsorption-limited current should become zero soon after the potential application. Many redox species, however, show gradual decrease in the current because reaction products generate an adsorbed layer which blocks further electrode reactions.
\nIt is well known that currents vary not only with applied voltage but also with the time. It is not popular, however, to discuss quantitatively time dependence of CV voltammograms. Enhancing v generally increases the current and causes the peak potential to shift in the direction of the scan. A reason for the former can be interpreted as generation of large current at a shorter time (see Eqs. (6) and (10)), whereas the latter is ascribed to a delay of reaction responses as well as a voltage loss of the reaction by solution resistance. Then the voltage effective to the reaction is lower than the intended voltage, and so the observed current may be smaller than the predicted one. Although Ip is related strongly with Ep, the relationship has rarely been examined quantitatively.
\nA technique of analyzing the potential shift is to plot Ip against Ep, [9] as shown in Figure 5. If the plots on the oxidation side (Ip > 0) and the reduction side (Ip < 0) fall each on a straight line, the slope may represent conductivity. If values of both slopes are equal, the slope possibly stands for the conductivity of the solution or membrane regardless of the electrode reaction. The potential extrapolated to the zero current on each straight line should be close to the formal potential. Since this plot is simple technically, the analytical result is more reliable than at least discussion of time dependence of Ep.
\nPlots of Ip vs. Ep by CV of the first (circles) and the second (triangles) peak of tetracyanoquinodimethane (TCNQ), and ferrocene (squares) in 0.2 M (CH3)4NPF6 included acetonitrile solution when scan rates were varied, where triangles were displayed by 0.4 V shift.
Most researchers have quoted the Randles-Sevcik equation, jp = 0.446 (nF)3/2c*(Dv/RT)1/2, for the diffusion-controlled peak current without hesitation, where n is the electron transfer number of the reaction. According to Faraday’s law, the electrolytic quantity is proportional to nc*. Why is the peak current proportional to n3/2 instead of n? Let us consider voltammetry of metal nanoparticles (about 25 nm in diameter) composed of 106 metal atoms dispersed in solution. Faraday’s law predicts that the current is 106 times as high as the current by the one metal atom. However, Randles-Sevcik equation predicts the current further (106)1/2 = 1000 times as large, just by the effect of the potential scan. The order 3/2 is specific to CV. The order of n for AC current and pulse voltammetry is 2 [10]. On the other hand, the diffusion-controlled steady-state currents at a microelectrode and a rotating disk electrode are proportional to n. Comparing the differences in the order by methods, we can predict that the time variation of the voltage increases the power of n.
\nLet a potential width from a current-rising potential to Ep be denoted by ΔE. When an n-electron transfer reaction occurs through the Nernst equation at which F in Eq. (1) is replaced by nF, the concentration-potential curve takes the slope n times larger than that at n = 1 (see co/cr ≅ nF(E − Eo)/RT near E = Eo in Eq. (1)). Then we have (ΔE)n = (ΔE)n = 1/n. The period of elapsing for (ΔE)n becomes shorter by 1/n, as if v might be larger by n times. Then v in Eq. (6) should be replaced by (nv)1/2. Combining this result with the flux j/nF, the current becomes n3/2 times larger than that at n = 1. Therefore, the factor n3/2 results from the Nernst equation. This can be understood quantitatively by replacing F in Eq. (3) by nF. There are quite a few reactions for n ≥ 2 both for Nernst equation and in the bulk as stable species. The term n3/2 is valid only for a concomitant charge-transfer reaction, i.e., simultaneous occurrence n-electron transfer rather than a step-by-step transfer. Apparent two-electron transfer reactions in the bulk, for example, Cu, Fe, Zn, and Pb, cause other reactions immediately after the one-electron transfer.
\nAn electrochemical response is observed as a sum of the half reactions at the two electrodes. In order to extract the reaction at the working electrode, a conventional technique is to increase the area of the counter electrode so that the reaction at the counter electrode can be ignored. If the counter electrode area is increased by 20 times the area of the working electrode, the observed current represents the reaction of the working electrode with an error of 5%. Let us consider the experiment in which nanoparticles of metal are coated on a working electrode for obtaining capacitive currents or catalyst currents. Then, the actual area of the working electrode can be regarded as the area of the metal particles measured by the molecular level. Then, the area will be several thousand times the geometric area so that the observed current may represent the reaction at the counter electrode. This kind of research has frequently been found in work on supercapacitors. On the other hand, if the electrode reaction is diffusion controlled, the current is determined by the projected area of the diffusion layer. Then the current is not affected by the huge surface area of nanoparticles.
\nIt is important to examine whether or not a reaction is controlled by at a counter electrode. A simple method is to coat nanoparticles also on the counter electrode. Then the current in the solution may become so high that the potential of the working electrode cannot be controlled. It is better to use a two-electrode system. Products at the counter electrode are possible sources of contaminants through redox cycling.
\nThe Ag-AgCl electrode is most frequently used as a reference electrode in aqueous solution because of the stable voltage at interfaces of Ag-AgCl and AgCl-KCl through fast charge-transfer steps, regardless of the magnitude of current density. The “fast step” means the absence of delay of the reaction or being in a quasi-equilibrium. The stability without delay is supported with high concentration of KCl.
\nWhen an Ag-AgCl electrode is inserted to a voltammetric solution, KCl necessarily diffuses into the solution, associated with oxygen from the reference electrode. Thus, the reference electrode is a source of contamination by salt, dichlorosilver and oxygen. It is interesting to examine how much amount a solution is contaminated by a reference electrode [9]. Time variation of ionic conductivity in the pure water was monitored immediately after a commercially available Ag-AgCl electrode was inserted into the solution. Figure 6 shows rapid increase in the conductivity as if a solid of KCl was added to the solution. Oxygen included in the concentrated KCl may contaminate a test solution. Even the Ag-AgxO electrode, which was formed by oxidizing silver wire, increased also the conductivity, probably because the surface is in the form of silver hydroxide. As a result, no reference electrode can be used for studying salt-free electrode reactions. If neutral redox species such as ferrocene is included in a solution, the potential reference can be taken from redox potential of ferrocene.
\nTime-variation of conductivity of water into which (circles) Ag|AgCl, (triangles) Ag|AgxO, and (squares) AgCl-coated Ag wire were inserted. Conductivity measurement was under N2 environment.
When a constant voltage is applied to the ideal capacitance C, the responding current decays in the form of exp(−t/RC), where R is a resistance in series connected with C. It has been believed that a double-layer capacitance in electrochemical system behaves as an ideal capacitor, where R is regarded as solution resistance. However, any exponential variation cannot reproduce transient currents obtained at the platinum wire electrode in KCl aqueous solution, as shown in Figure 7. The current decays more slowly than by exp(−t/RC), because it is approximately proportional to 1/t. The property of non-ideal capacitance is the result of the constant phase element of the DL capacitance, as described in Section 2.3. The dependence of 1/t can be obtained approximately by the time derivative of q = V0C0t−λ for the voltage step V0.
\nChronoamperometric curves when 0.2 V vs. Ag|AgCl was applied to a Pt wire in 0.5 M KCl aqueous solution. Solid curves are fitted ones by exp(-t/RC) for three values of RC.
The slow decay is related with a loss of the performance of pulse voltammetry, in which diffusion-controlled currents can readily be excluded from capacitive currents. The advantage of pulse voltammetry is based on the assumption of the exponential decay of the capacitive current. Since the diffusion current with 1/t1/2 dependence is close to the 1/t dependence, it cannot readily be separated from the capacitive current in reality. A key of using pulse voltammetry is to take a pulse time to be so long as a textbook recommends.
\nHigh-performance potentiostats are equipped with a circuit for compensation of resistance by a positive feedback. Unfortunately, the circuit is merely useful because voltammograms depend on intensity of compensation resistances of the DL capacitance. It should work well if the DL capacitance is ideal.
\nAC techniques have an advantage of examining time dependence at a given potential, whereas CV has a feature of finding current-voltage curves at a given time. The former shows the dynamic range from 1 Hz to 10 kHz, while the latter does conventionally from 0.01 to 1 Hz. This wide dynamic range of the AC technique is powerful for examining dynamics of electrode reactions. Analytical results by the former are often inconsistent with those by the latter, because of the difference in the time domain. The other scientific advantage of the AC technique is to get two types of independent data set, frequency variations of real components and imaginary ones by the use of a lock-in amplification. The independence allows us to operate mathematically the two data, leading to the data analysis at a level one step higher than CV. An industrial advantage is the rapid measurement, which can be applied to quality control for a number of samples. The analysis of AC impedance necessarily needs equivalent circuits of which components do not have any direction relation with electrochemical variables.
\nData of the electrochemical AC impedance are represented by Nyquist (Cole-Cole) plots, that is, plots of the imaginary component (Z2) of the impedance against the real one (Z1), as shown in Figure 8. The simplest equivalent circuit for electrochemical systems is the DL capacitance Cd in series with the solution resistance RS. The Nyquist plot for this series circuit is theoretically parallel to the vertical axis (Figure 8A-a), but experiments show a slope of 5 or more (Figure 8A-b). This behavior, called constant phase element (CPE) and the power law, has been verified for combinations of various materials and solvents [6, 7, 11, 12]. The equivalent circuit for Eq. (12) is a parallel combination of capacitance and resistance (Figure 8B). Even without an electrode reaction, current always includes a real component.
\n(A) Nyquist plots for a RC-series circuit with ideal capacitor (a) and DL capacitor (b). (B) Equivalent circuit with the power-law of Cd. (C) Randles circuit.
The equivalent circuit with the Randles type is a parallel combination of the ideal DL capacitor Cd with the ideal resistance Rct representing the Butler-Volmer-type charge-transfer resistance. Practically, the Warburg impedance (the inverse of Eq. (8)) due to diffusion of redox species is incorporated in a series into Rct (Figure 8C). Rct cannot be separated from the DL resistance because of the frequency dispersion. Since even the existence of Rct is in question (Section 3.12), it is difficult to determine and interpret Rct. The usage of a software that can analyze any Nyquist plots will provide values of R and C. Even if analyzed values are in high accuracy, researches should give them electrochemical significance.
\nResidual current varies with treatments of electrodes such as polishing of electrode surfaces and voltage applications to an extremely high domain. It can often be suppressed to yield reproducible data when the electrode is replaced by simple platinum wire or carbon rod having the same geometric area. Simple wire electrodes are quite useful especially for measurements of DL capacitance and adsorption. One of the reasons for setting off large residual current is that the insulator of confining the active area is not in close contact with the electrode, so that the solution penetrated into the gap will give rise to capacitive current and floating electrode reactions. Since the coefficient of thermal expansion of the electrode is different from that of the insulator, the residual current tends to get large with the elapse from the fabrication of the electrode. This prediction is based on experience, and there are few quantitative studies on residual currents.
\nUnexpected gap has been a technical problem at dropping mercury electrodes. If solution penetrates the inner wall of the glass capillary containing mercury, observed currents become irreproducible. Water repellency of the capillary tip has been known to improve the irreproducibility in order to reduce the penetration. A similar technique has been used for voltammetry at oil-water interfaces and ionic liquid-water interfaces at present.
\nVoltammograms are said to vary with electrode reaction rates, and the rate constants have been determined from time dependence of voltammograms. The fast reaction of which rate is not rate determining has historically been called “reversible.” In contrast, such a slow reaction that a peak potential varies linearly with log v is called “irreversible.” A reaction between them is called “quasi-reversible.” The distinction among the three has been well known since the theoretical report on the quasi-reversible reaction by Matsuda [1]. This theory is devoted to solving the diffusion equations with boundary conditions of the Butler-Volmer (BV) equation under the potential sweep. As the standard rate constant ks in the BV equation becomes small, the peak shifts in the direction of the potential sweep from the diffusion-controlled peak. Steady-state current-potential curves in a microelectrode [13] and a rotating disk electrode also shift the potential in a similar way. According to the calculated CV voltammograms in Figure 9, we can present some characteristics: (i) if the oxidation wave shifts to the positive potential, the negative potential shift should also be found in the reduction wave. (ii) Both the amounts of the shift should have a linear relationship to log v. (iii) The shift should be found in iterative measurements. (iv) The peak current should be proportional to v1/2.
\nCV voltammograms (solid curves) at a normally sized electrode and steady-state voltammograms (dashed curves) at a microelectrodes in 12 μm in diameter, calculated theoretically for v = 0.5 V s−1, D = 0.73 × 10−5 cm2 s−1, ks = (a) 0.1, (b) 0.01, (c) 0.001, (d) 0.0001 cm s−1. The potential shift of CV is equivalent to the wave-shift at a microelectrode through the relation, v = 0.4RTD/αFa2 (a: radius).
The authors attempted to find a redox species with the above four behaviors. Some redox species can satisfy one of the four requirements, but do not meet the others. Most reaction rate constants have been determined from the potential shift in a narrow time domain. They are probably caused by follow-up chemical reactions, adsorption, or DL capacitance. For example, CV peak potentials of TCNQ and benzoquinone were shifted at high scan rates, whereas their steady-state voltammograms were independent of diameters of microdisk electrodes even on the nanometer scale [14]. The shift at high scan rates should be due to the frequency dispersion of the DL capacitance, especially the parallel resistance in the DL (Figure 8B). Values of the heterogeneous rate constants and transfer coefficients reported so far have depended not only on the electrochemical techniques but also research groups. Furthermore, they have not been applied or extended to next developing work. These facts inspire us to examine the assumptions and validity of the BV formula.
\nLet us revisit the assumptions of the BV equation when an overvoltage, i.e., the difference of the applied potential from the standard electrode potential, causes the electrode reaction. The rate of the oxidation in the BV equation is assumed to have the activation energy of α times the overvoltage, while that of the reduction does that of (1 − α) times. This assumption seems reasonable for the balance of both the oxidation and the reduction. However, the following two points should be considered. (i) Once a charge or an electron is transferred within the redox species, the molecular structure changes more slowly than the charge transfer itself occurs. The structure change causes solvation as well as motion of external ions to keep electric neutrality. These processes should be slower than the structure change. If the overvoltage can control the reaction rate, it should act on to the slowest step, which is not the genuine charge-transfer process. (ii) Since a reaction rate belongs to the probability theory, the reaction rate (dc/dt) at t is determined with the state at t rather than a state in the future. In other words, the rate of the reduction should have no relation with the oxidation state which belongs to the future state. The BV theory assumes that the α times activation energy for the oxidation is related closely with 1-α times one for the reduction. This assumption is equivalent to predicting a state at t + Δt from state at t + 2Δt, like riding on a time machine. This question should be solved from a viewpoint of statistical physics.
\nDevelopment of scanning microscopes such as STM and AFM has allowed us to obtain the molecularly and atomically regulated surface images, which have been used for interpreting electrochemical data. Then the electrochemical data are expected to be discussed on a molecular scale. However, there is an essential problem of applying photographs of regularly arranged atoms on an electrode to electrochemical data, because the former and the latter include, respectively, microscopically local information and macroscopically averaged one. A STM image showing molecular patterns is information of only a part of electrode, at next parts of which no atomic images are often observed but noisy images are found. Electrochemical data should be composed of information both at a part of the electrode showing the molecular patters and at other parts showing noisy, vague images. Noisy photographs are always discarded for interpreting electrochemical data although the surfaces with noisy images also contribute electrochemical data.
\nAn ideal experiment would be made by taking STM images over all the electrodes that provide electrochemical data and by obtaining an averaged image. However, it is not only impossible to take huge amounts of images, but the averaged image might be also noisy. It may be helpful to describe only a possibility of reflecting the STM-imaged atomic structure on the electrochemical data.
\nVoltammograms by adsorbed redox species, called surface waves, are frequently different from a bell shape (Figure 2). Really observed features are the following: (i) the voltammogram does not suddenly decay after the peak, exhibiting a tail-like diffusional wave; (ii) the peak current and the amount of the electricity are proportional to the power less than the unity of v; (iii) the oxidation peak potential is different from the reduction one; (iv) the background current cannot be determined unequivocally; and (v) voltammograms depend on the starting potential. Why are experimental surface waves different from a symmetric, bell shape in Figure 2?
\nA loss of the symmetry with respect to the vertical line passing through a peak can be ascribed to the difference in interactions at the oxidized potential domain and at the reduced one. Since redox species takes extremely high concentration in the adsorbed layer, interaction is highly influenced on voltammetric form. When the left-right asymmetry is ascribed to thermodynamic interaction, it has been interpreted not only with Frumkin’s interaction [15] but also Bragg-Williams-like model for the nearest neighboring interactive redox species [16]. On the other hand, most surface waves are asymmetric with respect to the voltage axis even at extremely slow scan rates. This asymmetry cannot be explained in terms of thermodynamics of intermolecular interaction, but should resort to kinetics or a delay of electrode reactions. There seems to be no delay in the electrode reaction of the monomolecular adsorption layer, different from diffusion species. The delay resembles the phenomenon of constant phase element (CPE) or frequency power law of DL capacitance, in that the redox interaction may occur two-dimensionally so that the most stable state can be attained. This behavior belongs to a cooperative phenomenon [17]. A technique of overcoming these complications is to discuss the amount of charge by evaluating the area of the voltammogram. It also includes ambiguity of eliminating background current and assuming the independence of the redox charge from the DL charge.
\nThe simplest theories for voltammetry are limited to the rate-determining steps of diffusion of redox species and reactions of adsorbed species without interaction. Variation of scan rates as well as a reverse potential is helpful for predicting redox species and reaction mechanisms. Furthermore, the following viewpoints are useful for interpreting mechanisms:
comparison of values of experimental peak currents with theoretical ones, instead of discussing ΔEp and E1/2;
examining the proportionality of Ip vs. v or vs. v1/2, i.e., zero or non-zero values of the intercept of the linearity;
a reference electrode and a counter electrode being a source of contamination in solution;
attention to very slow relaxation of DL capacitive currents;
inclusion of ambiguity in the equivalent circuit with the Randles type.
IntechOpen publishes different types of publications
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\n\nRESEARCH CHAPTER – A research chapter reports the results of original research thus contributing to the body of knowledge in a particular area of study.
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