Cyklická voltametrie s rotující diskovou elektrodou (RDE)
Cílem úlohy je zjištění plochy elektrody a difúzního koeficientu kombinací CV se stacionární elektrodou a RDE experimentem. Cyklická voltametrie (cyclic voltammetry, CV) je jednou z mnoha metod odvozených od polarografie, při které prochází zkoumanou soustavou elektrický proud. Při CV je zkoumaný roztok podroben potenciálu vloženému na elektrody následujícím způsobem: potenciál je lineárně zvyšován od počátečního (initial) k „zlomovému“ (vertex) potenciálu, což je tzv. dopředný (forward) scan a poté je snižován ke konečnému (final) potenciálu (zpětný - reverse scan); počáteční potenciál je zpravidla shodný s konečným potenciálem, dopředný a zpětný scan pak tvoří jeden cyklus. Podle potřeby se provádí jeden nebo více cyklů, pokud je technika omezena jen na polovinu cyklu, hovoříme o LSV technice (linear sweep voltammetry). Rychlost, s jakou je potenciál měněn (scan rate) určuje časové okno experimentu. Výsledkem CV experimentu je závislost proudu protékajícího soustavou na vloženém napětí, tj. voltamogram. Moderní přístroje pro měření voltamogramů (potenciostaty) používají tříelektrodové zapojení. Proto je pro provedení experimentu zapotřebí tří elektrod: •
pracovní (working – např. skelný uhlík, uhlíková pasta, uhlíkové vlákno, Pt, Au, Hg, (Hg film) apod.)
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referentní (reference – kalomelová nebo argentochloridová elektroda)
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pomocné (auxiliary – zpravidla Pt drátek či plíšek)
• Potenciostat nutí procházet mezi pracovní a pomocnou elektrodou takový proud, aby mezi pracovní a referentní elektrodou byl dodržen požadovaný potenciálový program. Roztok vhodný pro voltametrické studium musí obsahovat kromě zkoumané látky ještě nadbytek pomocného (indiferentního) elektrolytu, při měření ve vodném prostředí se zpravidla přidává vhodná sůl (KCl, KNO3, pufr). Koncentrace pomocného elektrolytu by měla být taková, aby iontová síla zkoumané látky tvořila maximálně 3 % z celkové iontové síly roztoku. Při práci
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s pevnými elektrodami je zapotřebí materiál elektrody před každým scanem vyleštit pomocí aluminy (skelný uhlík), nebo diamantovou pastou (kovové elektrody). V určitých případech postačuje na elektrodu vložit dostatečně vysoký potenciál, který způsobí desorpci nečistot z povrchu elektrody a oxidaci / redukci povrchové vrstvy (tzv. elektrochemické čištění elektrody). Kromě CV existuje mnoho dalších voltametrických technik. Navzájem se liší ve způsobech, jakými se během experimentu mění potenciál pracovní elektrody. Při některých technikách je aplikován postupně se zvyšující či snižující potenciál, při jiných jde o náhlou změnu potenciálu nebo složité sekvence pulzů. Dále se rozlišuje, jestli je roztok během analýzy v klidu, nebo se pohybuje vzhledem k pracovní elektrodě. Ve většině případů se roztok nepohybuje, existuje ale i řada hydrodynamických metod, při kterých se roztok pohybuje definovaným způsobem. Rotující disková elektroda je příkladem hydrodynamické metody. Pracovní elektroda rotuje poměrně vysokou rychlostí. Rotační pohyb zajistí definovaný tok roztoku k disku elektrody, podobný víru unášejícímu roztok se zkoumanou látkou k elektrodě (obr. 1).
Výsledný voltamogram má podobu sigmoidní vlny, jejíž výška poskytuje analytický signál. Pro pochopení dějů probíhajících při RDE experimentu je důležitá vrstvička roztoku těsně
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přiléhající k elektrodě, která se pohybuje zároveň s ní. V této z hlediska elektrody nepohybující se vrstvě (stagnant layer) probíhá transport zkoumané látky difúzí. Na tuto vrstvu navazuje Prandtlova (hraniční) hydrodynamická vrstva, ve které se každá další vrstva molekul pohybuje pomaleji než vrstvy předchozí, od určité vzdálenosti od elektrody je roztok v klidu. Zvyšováním otáček elektrody lze kontrolovat – snižovat – tloušťku difúzní vrstvy. Analyzovaná látka, jak je patrno z obrázku, je k elektrodě unášena dvěma typy transportu. Nejprve jsou molekuly analyzované látky vírem kolmým k elektrodě unášeny k vnějšímu okraji difúzní vrstvy. Poté molekuly difundují k povrchu elektrody (toto je klíčové pro pochopení RDE - pohyb konvekcí unáší molekulu depolarizátoru nejprve kolmo k elektrodě, poté ji rotace elektrody "odhodí na stranu". Pokud by zároveň neprobíhala difúze, molekula by se k povrchu elektrody nikdy nedostala). Čím užší je difúzní vrstva, tím rychleji molekula dosáhne povrchu elektrody. Proto jsou při vyšších otáčkách RDE zaznamenávány vyšší hodnoty proudu. Na rozdíl od CV se stacionární elektrodou lze u CV s RDE dosáhnout od určitého potenciálu limitního proudu, tj. proudu, který je určen pouze rychlostí transportu studované látky k elektrodě (obr. 1).
Velikost limitního proudu IL je pro RDE určena jak příspěvkem difúze, tak i příspěvkem konvekce (tj. pohybem roztoku vůči elektrodě), matematický rozbor problému vede k tzv. Levičově rovnici: IL = (0,620)·n·F·A·D2/3·ω1/2·ν–1/6·c, kde ω je úhlová rychlost rotace elektrody (rad·s-1), ν je kinematická viskozita roztoku (cm2·s-1), c je koncentrace elektroaktivní látky (mol·cm-3), D její difúzní koeficient (cm2·s-1). Kinematická viskozita je poměr viskozity roztoku k jeho hustotě. Pro čistou vodu je její hodnota ν = 0,0100 cm2·s-1, pro 1.0 mol·dm-3 KNO3 je ν = 0,00916 cm2·s-1 (hodnoty platí pro teplotu 20°C). 3
Postup práce: 1. Seznamte se s ovládáním potenciostatu, jeho kalibrací, způsoby čištění elektrod atd. 2. Proměřte CV K3[Fe(CN)6] na RDE elektrodě v klidu, tj. bez otáčení, v rozsahu 500 až -100 mV vs. SCE, 10 mV.s-1. Z Randles – Ševčíkovy rovnice (návod viz úloha "Cyklická voltametrie") spočítejte součin A·D1/2. 3. Poté proveďte CV scany při deseti různých nastavení otáček v rozsahu přístroje. Před započetím CV scanu nechte minimálně deset sekund ustálit hydrodynamické poměry v elektrodové nádobce. 4. Proměřte limitní proudy jednotlivých voltamogramů, vyhodnoťte závislost IL na ω (převed’te rychlost v otáčkách za minutu na rychlost vyjádřenou v radiánech za sekundu). 5. Pomocí nelineární regrese této závislosti získejte součin A·D2/3. 6. Z hodnot A·D1/2 a A·D2/3 (dvě rovnice o dvou neznámých) získejte plochu elektrody a difúzní koeficient Fe(CN)63-.
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Otáčky rotační elektrody údaj na měřidle
otáčky za sekundu
dle regrese
50 100 150 200 250 max
14 28 42 55 75 120
13 27,9 42,8 57,7 72,6
80 70
y = 0,298x - 1,9 R2 = 0,9934
otáčky za sekundu
60 50 40 30 20 10 0 0
50
100
150
200
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údaj na m ěřidle
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Veniamin Grigorievich (Benjamin) Levich b. March 30, 1917, Kharkov, Russia d. January 19, 1987, in Englewood, New Jersey, USA
Veniamin Grigorievich (Benjamin) Levich was a leading scientist in the field of electrochemical hydrodynamics, which he was the first to establish as a separate scientific discipline. His research activities also included gas-phase collision reactions, the quantum mechanics of electron transfer. He is the best known for the development of a rotating-disk electrode as a tool for electrochemical research. The famous Levich equation describing a current at a rotating disk electrode is named after him. Veniamin Levich was the most highly placed Jewish "refusnik" scientist to be allowed to emigrate from the Soviet Union. Veniamin Grigorievich (Benjamin) Levich was born on March 30, 1917 in Kharkov. Levich studied physics and graduated at the University of Kharkov in 1937 at the age of twenty. He was very lucky to meet Prof. L.D. Landau in the University. Later Prof. Landau became his scientific advisor and Levich was the most successful pupil of Prof. Landau. Levich performed his Ph.D. study in the Moscow Pedagogical University where he studied interfacial phenomena together with Prof. Landau. During the WWII Levich was involved in studies practically important for defense. However, Levich has never interrupted his work related to fundamental theoretical problems of physical chemistry. The first Levich's paper giving theoretical consideration of electrical current passing through electrolyte solutions was published in the beginning of 40s when Levich was 26 years old.
Levich worked at the Institute of Physical Chemistry of the USSR Academy of Sciences (19401958) and later at the Institute of Electrochemistry of the USSR Academy of Sciences in Moscov (headed by A.N. Frumkin), the world's lagest institute of physical electrochemistry. Levich was head of the theoretical department in the Institute of Electrochemistry from 1958 until 1972 and was also a full professor and department head, first of theoretical physics at the Moscow Institute of Physics and Engineering (1954-1964). Later he received the post of Professor of Chemical Mechanics at Moscow State University (the chair was created especially for him). He was a man who had the good fortune to create a subfield in science and to dominate it during his lifetime.
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The field concerned is hydrodynamics applied to the relative movemen of the solution near an electrode. Levich can be regarded as a pioneer for hydrodynamic electrochemistry. Levich's scientific results on the theory of convective diffusion were very important contribution to electrochemical kinetics. Veniamin Levich was a researcher of extraordinary originality and productivity who during his lifetime, authored more than three hundred scientific papers ranging from electrochemistry to turbulence, flows with chemical reactions, and flows dominated by variations in surface tension. He was, for example, the first to show conclusively that the seemingly paradoxical observation that the rise velocity of small air bubbles in viscous liquids equals that of solid spheres having the same density is due to the accumulation of trace amounts of surface-active agents on the gasliquid interface. This fact has important implications in a large variety of mass transfer operations. He also showed, against all prior expectations, that certain viscosity-dominated flow phenomena, such as the attenuation of capillary waves or the steady rise velocity of moderatesized bubbles in low viscosity liquids, can be computed simply through knowledge of the corresponding motion of fluids having zero viscosity. Other papers dealt with theories of gasphase collision reactions, the photoemission of electrons from electrodes into solutions, and the quantum mechanics of electron transfer between ions in solution and between an ion and an electrode. In addition, Veniamin Levich authored a four-volume treatise on Theoretical Physics, which rivals in scope the famous series by Landau and Lifshitz. His fundamental contributions to theoretical physics and physical chemistry have only been worldwide recognized after the publication of the English translation of his monograph "Physicochemical Hydrodynamics" in 1962 (V.G. Levich, Physicochemical Hydrodynamics, Prentice-Hall: Englewood Cliffs, NJ, 1962; first Russian edition was published in 1952). Textbooks on electrochemistry refer to him in the field of rotating disk electrodes where the Levich equation describes the mass-transferlimited condition for the current response. A new field of research was thereby born at the interface between physics and chemistry, which clears with the effects of fluid motion on chemical and physicochemical transformations and conversely with the influence of the latter on the motion of fluids. This book was widely acclaimed as a masterful synthesis of different branches of science that had, until then, developed separately. Indeed, Levich showed how to create a scientific unity out of seemingly highly diverse phenomena by lucidly expounding the relatively few underlying patterns and basic laws of science. This was achieved by using mathematical analysis to explain experimental observations and by citing the results of measurements with sufficient frequency to illustrate principles without, however, overburdening the reader with detail. Even though out of print, this book still brims with a wealth of useful information and, as befits a classic, it is very much a pleasure to read. Later, he was persuaded by Frumkin to apply his talents to the quantum theory of charge transfer, where he led a research group of some twenty-five members. It should be noted that Levich always tried to bring the scientific results originated from electrochemistry to other scientific areas, to make the results more general and useful for physical chemistry and chemical technology. Veniamin Levich was elected a corresponding member of the USSR Academy of Sciences in 1958, and his meteoric rise within the academic establishment of the Soviet Union as well as his research productivity would have continued unabated had he not in 1972 applied to emigrate. 7
After consultations with his wife Tanya and his sons Alexander and Evgenii, he decided to apply for emigration to Israel. When Levich announced his plans to emigrate to Israel, it was still Soviet times and his announcement attracted intense scrutiny by the KGB, who wanted to prevent his leaving the USSR. Immediately his teaching post was abolished, he was demoted to the rank of a 'scientific worker' without supervisory responsibilities. (In fact, during this period and prior to his emigration, Levich's primary source of income was his stipend as a corresponding member of the USSR Academy of Sciences.) Shortly afterwords his younger son Evgenii was illegally transported to a military camp in the Soviet Arctic. Levich was informed that he would never be allowed to emigrate, because of his knowledge of state secrets. His former colleagues and collaborators, almost without exception, found reasons to distance themselves from him; Soviet journal editors declined to publish his articles. Official Soviet point of view on Levich's emigration is outlined in memoirs of Russian academician L.S. Pontryagin. Unfortunately, his anti-Semitic memoirs about Levich are written in Russian, so western readers cannot understand the horror of that time. Actually, his memoirs were published in 1998, so the time didn't change the approach! A campaign for the Levich family was organized by Dr. Brian Spalding of Imperial College London. This campaign attracted considerable attention, particularly when it became known that western publications including Nature, distributed in photostat form in the Soviet Union, had all references to Levich deleted from them. But the campaign was suddenly halted with the news that Levich had reached a gentleman's agreement with the emigration authorities: if the public outcry ceased, his sons Alexander and Evgenii would be allowed to emigrate at once together with their wives, and Veniamin Levich and his wife Tanya would follow a year later. But when the time came for the senior members of the Levich family to emigrate, the Soviet authorities denied any knowledge of such an agreement. In 1977, a conference on physicochemical hydrodynamics was held in Oxford, in honour of Levich's 60th birthday. Such an honour is virtually a matter of routine for scientists of his rank in the Soviet Union, but in his circumstances, no Soviet honours could be expected. The conference was so succesful scientifically that it was decided to launch a regular series of Levich conferences. The second was held in Washington, DC in 1978. After a six-year struggle and with help from the international scientific community, as well as a visit to the Soviet Union by Senator Edward M. Kennedy, Professor Levich and his wife Tanya were finally allowed to emigrate from the Soviet Union to Israel in 1978. They settled first in Israel, where the University of Tel Aviv had, for several years, been keeping a chair ready for the most distinguished Soviet scientist ever to settle in his ethnic home. Upon his arrival in Israel, Professor Levich also received offers of employment from several universities in the United Kingdom, the USA as well as many other countries. However, in March, 1979, he finally accepted the invitation to become the Albert Einstein Professor of Science at City College of New York, where he established the Institute of Applied Chemical Physics. The official charter for the Institute was approved by the City University of New York Board of Trustees on August 6, 1979. Shortly after he took up this post, however, his wife Tanya had to have massive heart surgery, from which she never fully recovered. She died in 1984. Professor Levich also continued his scientific duties at Tel Aviv University, Israel, and strong links between Tel Aviv University and the NY City College were established.
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Professor Levich, who served as the first director of the Institute, originally coined the term physico-chemical hydrodynamics, which refers to phenomena governed by the interaction of fluid mechanics, heat and mass transfer, and chemical reactions. The broad aim of the Institute has been to investigate key problems in this area from a fundamental and multifaceted perspective. In his later years, his research dealt with aspects of theoretical turbulence, but it is a measure of his universality that he felt equally at home among physicists, chemists, chemical engineers, fluid mechanicists, applied mathematicians, and biologists. Professor Levich received many honours during his life, including the Palladium Medal of the American Electrochemical Society in 1973. He was elected a foreign member of the Norwegian Academy of Sciences in 1977 and a foreign associate of the U.S. National Academy of Engineering in 1982. He was also a member of numerous scientific organizations, although on leaving the USSR in 1978 he had to relinquish his Soviet citizenship and, therefore, was expelled from the USSR Academy of Sciences. Veniamin Grigorievich (Benjamin) Levich died on January 19, 1987, in Englewood, New Jersey, USA. He was a unique scientist who left a permanent imprint and legacy in this world. It was after Professor Levich's untimely death that the Institute was renamed, in his honor, as the Benjamin Levich Institute for Physico-Chemical Hydrodynamics.
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