Experimental and Modelling Studies on the Reactions of the Sulfate Ion Radical

DE TTK 1949 Expe imen al and Modelling S udies on he Reac ions o he Sul a e Ion Radical Ph.D. hesis Dóka É a Supe iso : D . Gábo Len e UNIVERSITY OF DEBRECEN Chemis y G adua e School Deb ecen, 2016 DE TTK 1949 Expe imen al and Modelling S udies on he Reac ions o he Sul a e Ion Radical Ph.D. hesis Dóka É a Supe iso : D . Gábo Len e UNIVERSITY OF DEBRECEN Chemis y G adua e School Deb ecen, 2016 II III Ezen é ekezés a Deb eceni Egye em Te mésze udományi Dok o i Tanács Kémiai Dok o i Iskola K/2 Koo dinációs és Anali ikai Kémia p og amja ke e ében készí e em a Deb eceni Egye em e mésze udományi dok o i (Ph.D.) okoza ának elnye ése céljából. Deb ecen, 2016. május 27. Dóka É a Tanúsí om, hogy Dóka É a dok o jelöl 2012 - 2015 közö a en megne eze Dok o i Iskola K/2 Koo dinációs és Anali ikai Kémia p og amjának ke e ében i ányí ásommal égez e munkájá . Az é ekezésben oglal e edményekhez és az ezekből szüle e publikációkhoz a jelöl önálló alko ó e ékenységé el megha á ozóan hozzájá ul . Az é ekezés el ogadásá ja asolom. Deb ecen, 2016. május 27. D . Len e Gábo IV V EXPERIMENTAL AND MODELLING STUDIES ON THE REACTIONS OF THE SULFATE ION RADICAL É ekezés a dok o i (Ph.D.) okoza megsze zése é dekében a Kémia udományágban Í a: Dóka É a okle eles egyész és alapokle eles ma ema ikus Készül a Deb eceni Egye em Kémiai Dok o i Iskolája (Koo dinációs és anali ikai kémiai p og amja) ke e ében Téma eze ő: D . Len e Gábo egye emi aná A dok o i szigo la i bizo ság: elnök: D . Kö é Ka alin egye emi aná (DE) agok: D . Tó h Ágo a egye emi aná (SZTE) D . Só ágó Im e p o esso eme i us (DE) A dok o i szigo la időpon ja: 2016. má cius 8. Az é ekezés bí álói: D . ........................................... D . ........................................... D . ........................................... A bí álóbizo ság: elnök: D . ........................................... agok: D . ........................................... D . ........................................... D . ........................................... D . ........................................... Az é ekezés édésének időpon ja: 2016. .............................................. VI VII "In he end, e e y hing will be OK. I i 's no OK, i 's no ye he end." /Fe nando Sabino/ XIV É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 1 1. In oduc ion Sul u (S) is a nonme allic elemen in he 16 h g oup o he pe iodic able, a membe o he oxygen amily o chalcogens. The la e name is a hyb id o he G eek wo d  (khalkos, meaning o e) and he La inized su ix ‘-gen’, meaning bo n o p oduced. This name implies ha he i s wo elemen s o he g oup, oxygen and sul u a e highly equen componen s o o es and mine als, oxygen being he mos abundan elemen in he Ea h’s c us .1 The chalcophile g oup wi hin he Goldschmid classi ica ion comp ises he elemen s which a e likely o o m compounds wi h sul u , mainly p and d block me als o so cha ac e .2,3 Sul u is ubiqui ous in Na u e, i occu s mos ly in he ollowing o ms:  elemen al sul u in he cap ocks o sal domes o in olcanic e up ions  H2S in na u al gas and sul u o ganic subs ances in pe oleum  sul ide o es o me als (PbS, FeS2, CuS, ZnS, HgS e c.).1 Owing o he high abundance o he elemen , sul u has been known since he ancien imes. I is men ioned se e al imes in he Bible as ‘ i e and b ims one’, * in he con ex o hell i e and e e nal mise y. Maybe i is he malodo ous smell and oxic na u e o many sul u compounds ha ea ned he elemen such a nega i e epu a ion (al hough pu e sul u does no smell a all). Fi e and b ims one also appea s in he G eek classics Iliad and Odyssey, al hough Home migh ha e mis akenly e e o he smell o sul u ins ead o he unpleasan odo o ligh ning-gene a ed ozone.4,5 The odo o skunk sp ay is also due o low molecula weigh hiol compounds o me cap ans. The o igin o he name sul u is obscu e, he ea lies appea ances da e back o ea ly La in cul u e o he i s cen u ies BC. I is known no o be a G eek loan wo d, since G eek au ho s called he elemen θεῖον ( heion, ances o o he p e ix hio- o sul u con aining compounds). Concei ably, he wo d de eloped om sulpu o sulphu and inally o sul u . The spelling ‘sulphu ’ pe sis ed, especially in B i ish linguis ic en i onmen , e en hough IUPAC s anda dized he ‘ ’ spelling a ew decades ago, wi hou espec o geog aphical di e ences.6,7 Owing o i s alence elec on composi ion and ca ena ion p ope y, sul u ea u es e sa ile edox beha io wi h signi ican en i onmen al aspec s, biological ele ance as well as indus ial applica ions. * The Lo d es s he igh eous and he wicked, And he one who lo es iolence His soul ha es. Upon he wicked He will ain sna es; Fi e and b ims one and bu ning wind will be he po ion o hei cup. /Psalms 11:5-6/ É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 2 Sul u dioxide (SO2) is one o he so-called c i e ia ai pollu an s. De imen al e ec s o SO2 gas necessi a ed he admission o uppe limi s o daily exposu e, se by EPA (U. S. En i onmen al P o ec ion Agency), o a oid po en ial human heal h and p ope y damage.8 SO2 is a gaseous compound ha accumula es in he a mosphe e by olcanic ac i i y and om an h opogenic sou ces such as combus ion o ossil ene gy ca ie s (due o sul u con amina ions in coal, pe oleum and na u al gas) and me allu gy. Upon di ec exposu e, highe le els o sul u dioxide cause espi a o y i i a ion, induce b onchocons ic ion9 (sho ness o b ea h due o he cons ic ion o pulmona y ai ways) and inc ease he symp oms o as hma ic pa ien s.10 A slow- eleasing SO2 dono molecule, benzo hiazole-sul ina e has ecen ly been disco e ed, which acili a es he examina ion o he biological e ec o inhaled and endogenously gene a ed SO2.11 On a global le el, he majo consequence o a mosphe ic SO2 is he o ma ion o acid ain o acid deposi ion.12-17 Acid ain is ainwa e wi h a pH below he na u al alue o 5.6, which is a esul o he dissolu ion o a mosphe ic CO2. Acidi ica ion o ain all is a ela i ely mode n phenomenon, he consequence o hea y indus ializa ion o he las wo cen u ies. G eenland ice laye s om he 1800s ha e nea ly neu al pH alues. The pH dec ease is agg a a ed by he o ma ion o sul u ic acid om SO2 acco ding o eq. (1), he au oxida ion o hyd a ed SO2. Au oxida ion is a gene ic e m o he eac ions whe e he educ an is oxidized by elemen a y oxygen om ai . The p e ix ‘au o’ e e s o he ac ha he oxidan is seldom added delibe a ely in hese p ocesses bu is simply aken up om he en i onmen . 2 H2O·SO2 + O2 = 2 HSO4− + 2 H+ (1) The lowes pH alue measu ed in ainwa e was 1.5, de ec ed in Wheeling, Wes Vi ginia, in 1979.18 Hea y acid ains lead o ex ended de o es a ion, des uc ion o limes one moun ains and man-made objec s and buildings, such as he Taj Mahal in India, buil en i ely om ma ble. A e y in e es ing and scien i ically challenging aspec o he s epwise o ma ion o H2SO4 om sul u and oxygen is he es o a ion o he Swedish wa ship Vasa, which sank on he maiden jou ney in 1628 and was conse ed unde wa e un il 1961, when he w eckage was sal aged om S ockholm ha bo . Today he emains o he ship a e exhibi ed in he Vasa Musee in S ockholm. The wa e which Vasa sank in was ich in sul a e educing bac e ia. Elemen a y sul u , as well as sul u compounds o in e media e oxida ion s a es accumula ed in he oak beams o he ship du ing he 333 yea s she spen subme ged. E e since he Vasa was b ough o he su ace, scien is s s uggle wi h he massi e acidi ica ion o he skele on because he i on in he bol s ca alyzes he o e all oxida ion o sul u o sul u ic acid.19 É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 3 An ini ia i e eme ged in he ield o geoenginee ing o coun e ac global wa ming based on he global dimming e ec o s a osphe ic sul a e ae osols by he e lec ion o sola adia ion. The concep would endo se he applica ion o missiles and ai c a o deli e sul u dioxide and o he sul u gases in he s a osphe e, o ac as sul a e p ecu so s and hus inc ease he albedo ( e lec i i y) o he plane . Howe e , he ecep ion o such echnological measu es has been con o e sial because hey do no eplace consis en poli ical and social engagemen o he educ ion o o al g eenhouse gas emission. In addi ion, he long- e m ha m ul consequences o he ex a sul u bu den a e unp edic able.20-22 A mosphe ic au oxida ion o SO2 d ew conside able a en ion om ino ganic chemis s, and de ailed mechanis ic s udies e ealed ha he in e media es o he au oxida ion p ocess a e o adical na u e (mainly SO3, SO4, SO5). In gene al, sul a e ion adical (SO4) is one o he mos b oadly s udied ee adical in he li e a u e, along wi h hyd oxyl adical (OH).23-25 SO4 is a highly eac i e ansien species wi h s ong oxidizing powe Eº(SO4/SO42V Recen ly, he ole o sul a e ion adical in a mosphe ic aqueous phase chemis y has been in es iga ed by He mann and co-wo ke s.23,26-29 SO4 is conside ed as an oxidan in so-called ad anced oxida ion p ocesses (AOPs) in wa e and was ewa e ea men , in o de o elimina e o ganic and ino ganic con aminan s.30-35 Simul aneously, ad anced educ ion p ocesses (ARPs) in ol e UV o ul asound p oduced sul i e ion adical (SO3) o he educ i e deg ada ion o ha m ul oxidized pollu an s.36 Sul a e ion adical de i ed oxida ion also has biochemical applica ions. An e icien , unable oo p in ing me hod was de eloped o moni o ing global p o ein oxida ion s a us. O iginal FPOP (Fas Pho ochemical Oxida ion o P o eins) u ilized OH as oxidan . The in oduc ion o SO4 as a oo p in ing agen is an imp o emen due o he sligh ly lowe eac i i y and highe a ge speci ici y compa ed o hyd oxyl adical.37 The p esen hesis is dedica ed o shed u he ligh on he ole o sul a e ion adical in he ansi ion me al ca alyzed and he iodide ion ca alyzed, pho oini ia ed au oxida ion o hyd a ed SO2, and mo e gene ally, he au oxida ion o S(IV). T adi ional me hods o aqueous solu ion kine ics a e employed, as well as lase lash pho olysis o he di ec obse a ion o SO4. Compu a ional simula ions a e ca ied ou o s udy he po en ial e ec o di usion and spa ial inhomogenei ies du ing lase lash pho olysis expe imen s. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 4 2. Li e a u e o e iew 2.1. Redox chemis y o sul u Sul u has a alence elec on con igu a ion o 3s23p4. The e o e, i can occu in compounds in (2)  (+6) oxida ion s a es (e en numbe s a e p e e ed). Due o he wide ange o a ailable oxida ion numbe s, sul u exhibi s e sa ile edox chemis y. This sec ion will ocus on he edox cha ac e is ics o sul u oxyacids and anions along wi h he de i ed sul u oxy adicals. Table 1. Sul u oxyacids, conjuga e oxyanions and he ela ed ee adicals. Fo mula Name o oxyacid Oxida ion s a e(s) Conjuga e anion Rela ed adical H2SO4 sul u ic acid VI sul a e, SO42 hyd ogen sul a e, HSO4 sul a e ion adical,a SO4 H2S2O7 disul u ic acid VI disul a e, S2O72 H2SO5 pe oxomono- sul u ic acid VI pe oxomono- sul a e, SO52 pe oxomono- sul a e ion adical, SO5 H2S2O8 pe oxodi- sul u ic acid VI pe oxodisul- a e, S2O82 H2S2O6 di hionic acid V di hiona e, S2O62 H2Sn+2O6 poly hionic acid V, 0 poly hiona e, Sn+2O62 H2S2O3 hiosul u ic acid IV, 0, (o II, II) hiosul a e, S2O32 (H2SO3) H2O∙SO2 (sul u ous acid) hyd a ed sul u -dioxide IV sul i e, SO32 hyd ogen- sul i e, HSO3 sul i e ion adical, SO3 H2S2O5 disul u ous acid o py osul u ous acid V, III Disul i e; commonly known as me abisul i e o py osul i e, S2O52 H2S2O4 di hionous acid III di hioni e, S2O42 aal e na i e names: sul a e adical anion, sul a e adical É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 5 Table 1 gi es a b ie summa y o hese kinds o species in he o de o dec easing oxida ion numbe .1 The s abili ies o hese acids and sal s a y on a b oad scale, e.g. ee acid o ms o di hionic, ‘sul u ous’ and di hionous acids a e i ually nonexis en , hey a e mos ly ound in solu ions and in sal s as he conjuga e oxyanions. H2O∙SO2 and SO4 a e o u mos impo ance in he p esen hesis, hei spec al and chemical ea u es will be discussed in u he de ail in Sec ions 2.2 and 2.3. Py osul a e sal s will be p esen ed he ein as a sou ce o S(IV) species and o he sul u oxy adicals (SO3, SO5) as congene s o sul a e ion adical. The sul u oxy species p esen ed in Table 1 pa icipa e in a ious edox equilib ia. S anda d elec ode po en ials o a ew edox pai s a e collec ed in Table 2. Table 2. S anda d elec ode po en ials o sul u oxy ions and adicals Redox couplea E° (V) Redox coupleb,c E° (V) S/S2 -0.476 SO2/SO2 -0.17 S/H2Saq 0.142 -0.262 S2O62/S2O3 0.564 -0.288 S2O82/SO42 2.010 -0.31 S2O82/HSO4 2.123 SO3/SO32 0.63 S4O62/S2O32 0.080 0.72 H2SO3/HS2O4 -0.056 0.76 H2SO3/S 0.449 0.89 SO32/S2O42 -1.120 0.73±0.01b SO32/S2O32 -0.571 SO3/HSO3 0.84 SO42H2SO3 0.172 SO4/SO42 2.43 SO42/S2O62 -0.220 2.52-3.08 SO42SO32 -0.930 2.6 SO5/HSO5 1.1 SO5/SO52 0.81±0.02b S2O62/SO3SO32 -0.49 S2O82/SO4SO42 1.39 S4O63/2S2O32 1.07±0.03b a: e .38; b: e .39 ; c: e .40 and e e ences he ein É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 6 SO42 and HSO4 a e he mos equen sul u oxyanions in Na u e. These a e bo h e y s able species, hey a e o med as oxida ion p oduc s o sul u compounds and du ing he decomposi ion o pe oxodisul a e ions. Sul a e sal s ake pa in he composi ion o pa icula e ma e in he a mosphe e. Howe e , sul u ic acid, especially in i s concen a ed o m, is a highly eac i e, s ong oxidizing agen , which is able o dissol e elec oposi i e me als. Disul u ic o py osul u ic acid is ound in uming sul u ic acid (also known as oleum, oil o i iol, o spi i o i iol), i is o med by he dissolu ion o SO3 in H2SO4. Anhyd ous pe oxomonosul a e ion (H2SO5) is also called Ca o’s acid, i is one o he s onges oxidan s known (E°(HSO5/HSO4) = 1.84 V)40. I s conjuga e anion, SO52 is a ailable as he composi e sal Oxone® ( egis e ed adema k o DuPon ), which has been ecognized as a ‘g een’ oxidizing agen as i s educ ion p oduc is sul a e ion and wi h he possible by-p oduc elemen a y oxygen.41,42 Pe oxodisul a e ion (S2O82) is gene ally used in he o m o i s wa e -soluble ammonium o po assium sal s. Pe oxodisul a e sal s a e u ilized as oxidizing and bleaching agen s and o ini ia e adical polyme iza ion p ocesses. Ammonium pe sul a e (APS) is he mos common ini ia o in polyac ylamide gel elec opho esis. S2O82 has e y high elec ode po en ials (see Table 2), hus i is expec ed o be a s ong oxidizing agen , bu i s edox eac ions a e qui e sluggish due o a kine ic ba ie . Sil e (I) ion has been p o ed o be a powe ul ca alys o hese eac ions. They usually ake place as chain eac ions and hei a e de e mining s ep is eq. (2), which is a one-elec on ans e ha p oduces highly eac i e sul a e ion adical.43-45 Ag+ + S2O82 = Ag2+ + SO42 + SO4 (2) Di hiona e ion (S2O62) exhibi s qui e poo edox chemis y, i is highly ine unde common ci cums ances. I canno be p o ona ed in he usual pH ange, and i eac s e en wi h s ong oxidizing agen s only a ele a ed empe a u es. I i pa icipa es in a edox eac ion, he i s s ep is disp opo iona ion in mos cases, whe e sul u (VI) and sul u (IV) a e he di ec p oduc s and he la e can be oxidized apidly by he oxidizing agen .46 Poly hiona es (O3S-(S)n-SO32 o Sn+2O62) a e ela i ely s able sul u oxyanions, con aining a chain o ze o- alen sul u a oms as a linke be ween wo SO3 g oups. Poly hiona es a e equen ly ound in c a e lakes, and hey we e sugges ed o se e as e icien ma ke s o o hcoming olcanic e up ions.47 É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 7 Thiosul u ic acid has no been isola ed so a , i is only known o exis in hiosul a e sal s. S2O32ion is a medium s ong educing agen . I is ex ensi ely used in iodome ic measu emen s in he labo a o y p ac ice and as dechlo ina ing agen in he ex ile indus y.48 Di hionous acid is uns able bo h in i s pu e o m and in aqueous solu ion, di hioni es (S2O42) can be isola ed as anhyd ous sal s. In he p esence o wa e , hey disp opo iona e in o sul i e and hiosul a e anions (especially in acidic medium). Sodium di hioni e is used as a educing agen in indus ial dyeing p ocedu es and o labo a o y pu poses as well.49,50 2.2. Au oxida ion s udies o sul u (IV) Table 1 and Table 2 in he p e ious sec ion show ha +4 is an in e media e oxida ion s a e o sul u . SO2 is gene ally conside ed o be a mode a e educing agen , al hough depending on he eac ion pa ne , i can be an oxidizing agen as well. A well-known example o he la e is he eac ion be ween SO2 and hyd ogen sul ide, which is an impo an s ep o he Claus p ocess (pa en ed in 1883), used simul aneously o he desul u iza ion o c ude oils and he p oduc ion o elemen a y sul u .51 The majo occu ences o S(IV) a oms a e sul u dioxide (SO2), hyd a ed sul u dioxide, H2O∙SO2 and i s dep o ona ed o ms: HSO3 and SO32 ions. S(IV) is also ound in sul u o ganic molecules, such as sul onic acids, sul ona es and sul i e es e s.52,53 The o mula H2OSO2 is gene ally used o deno e dissol ed sul u dioxide because he e is no expe imen al e idence o he exis ence o he ully p o ona ed H2SO3 molecule. The acid dissocia ion cons an alues o he subsequen dep o ona ion s eps o H2O∙SO2 a e pKa,1 = 1.86 and pKa,2 = 6.34. The dime iza ion o sul i e ions in o py osul i e o me abisul i e ions (S2O52) a highe concen a ions is a well-known phenomenon.54 In aqueous medium, he dime ic anion is in equilib ium wi h he hyd ogen sul i e ion, he S2O52 o m only occu s in concen a ed solu ions ( 0.1 M). The e o e, i is con enien o p epa e solu ions o sul i e ions by dissol ing py osul i e sal s, e.g. Na2S2O5.55 In he subsequen sec ions o he hesis, he di e en dep o ona ed o ms o H2O∙SO2 will be collec i ely e e ed o as ‘sul i e ion’ o simply S(IV). The a mosphe ic au oxida ion o S(IV), depic ed in eac ion (1) is he majo sou ce o acid ain o ma ion. SO2 can easily accumula e in ain d ople s, as i s wa e solubili y is much highe compa ed o o he a mosphe ic gases (Table 3).38 Mole ac ions a e compa ed ins ead o he co esponding Hen y’s cons an s because he concen a ion o SO2 passes h ough he limi o alidi y o Hen y’s law.56 The solubili y o sul u dioxide is lowe in acidic medium, which p o ides he basis o he iden i ica ion o sul i e ions wi hin he F esenius sys em.57 É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 8 Table 3. Mole ac ions (X) o a mosphe ic gases in aqueous solu ions. p = 1 a m, T = 25 °C38 X SO2 2.9102 CO2 7.1104 O2 2.5105 N2 1.3105 The kine ics and mechanism o he p ocess ep esen ed by he o e all equa ion shown in eq. (1) d ew conside able a en ion om ino ganic chemis s, a signi ican amoun o expe imen al indings ha e been published on his subjec . Ca aly ic aspec s, pho ochemical phenomena o he ole o ee adicals in he sys em ha e been discussed. 2.2.1. T ansi ion me al ion ca alysis in he au oxida ion o sul u (IV) Nume ous s udies ha e e ealed he ole o ansi ion me al ion ca alysis in he oxida ion o sul u (IV) species. K a and an Eldik in es iga ed he i on(III) ca alyzed au oxida ion o sul u (IV) oxides and conside ed he possible ole o me al-sul i o complexes in he mechanism.58-61 A de ailed kine ic and mechanis ic analysis o he Fe(III)S(IV)O2 sys em was published la e on and p o ed he ca aly ic e ec o i on(III).62 B and and an Eldik examined he in luence o pH, he medium and aging in independen expe imen s.63 These au ho s also p esen ed a comp ehensi e o e iew o he subjec , ocusing on a mosphe ic- ele an p ocesses and mechanisms.40 Acco ding o his summa y, he majo i y o he published eac ion mechanisms o he homogeneous ansi ion me al ca alyzed au oxida ion o sul u (IV) oxides sugges adical mechanisms ha in ol e s eps om he scheme gi en by Bäcks öm, who was he i s o publish mechanis ic obse a ions on eac ion (1).55 He p oposed a adical chain mechanism in ol ing sul oxy adical in e media es, which was suppo ed by he ac ha common adical sca enge s inhibi he eac ion. Fábián and Cso dás e iewed he ole o me al ions in au oxida ion p ocesses om kine ic and mechanis ic poin s o iew.64 Elding and co-wo ke s examined he ca aly ic e ec o manganese, ch omium and anadium ions, and hey obse ed he eme gence o i on-manganese syne gism. They e en conside ed gold(III) as a ca alys in S(IV) au oxida ion based on a educ ion s udy o Au(III) complexes by sul i e and hyd ogen sul i e ions.65-68 Alexande e al. epo ed ha 9-17% o o al sul a e p oduc ion on Ea h can be assigned o oxida ion o S(IV) by O2 ca alyzed by Fe(III) and Mn(II).69 É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 9 Coiche and co-wo ke s s udied he adical in e media es ha a e gene a ed in he au oxida ion p ocess ca alyzed by Co(II) and Cu(II) complexes, and hei po en ial de imen al e ec s on DNA chains.70,71 The ca aly ic e ec o Cu(III) e aglycine complexes on he au oxida ion was ound and s udied by Anas and Ma ge um.72 DNA damage examina ions we e also ca ied ou by Bu ows’s eam wi h Ni(II) and Mn(II) complexes.73-75 Pionee ing wo k on ee adical induced DNA damage was p esen ed by Clemens on Sonn ag.76 2.2.2. Pho ochemical phenomena in he au oxida ion o sul u (IV) Pho oini ia ed au oxida ion in he p esence o i on(II) The au oxida ion p ocesses o sul u (IV) in acidic aqueous solu ion ha e been ex ensi ely s udied by Ke ezsi e al.55,77-79 They obse ed ha he unca alyzed o da k eac ion is e y slow. In he p esence o Fe(II), he a e o he eac ion inc eases, bu i ac s as an auxilia y educing agen a he han a ca alys . The expe imen s ha e been ca ied ou in a diode a ay spec opho ome e , which is a con enien ool o he simul aneous ini ia ion and de ec ion o he eac ion. Acco ding o hei esul s, he unca alyzed au oxida ion akes place h ough exci ed H2OSO2 and HSO5 in e media es and ollows he s oichiome y indica ed in eq. (1).78 The eac ion a e is independen o he concen a ion o dissol ed oxygen in he pH- ange 0.0  1.67, bu shows a well-de ined dependence on ligh in ensi y and sul u (IV) concen a ion. In he p esence o i on(II), he o ma ion o i on(III) ions was de ec ed, which may be in e p e ed by he simul aneous p esence o wo addi ional pa hways. Bo h pa hways con ain he oxida ion o i on(II) in o i on(III) by one o he eac ion in e media es. Figu e 2.1 p esen s he sugges ed scheme o he eac ion. Figu e 2.1. Pho oini ia ed au oxida ion o sul u (IV) in he absence and p esence o i on(II) ions in acidic aqueous phase. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 16 A de ailed kine ic and spec oscopic analysis o sul i e anion adical and i s decay mechanisms was gi en by Waygood and McEl oy.135 Lase lash pho olysis o sodium di hiona e (S2O62)solu ions a 193 nm led o he o ma ion o SO3 and SO32. They epo ed ha he decay o sul i e ion adical is second o de wi h a limi a e cons an o (4.0 ± 0.3)  l08 M1 s1 and akes place by he simul aneous ecombina ion in o di hiona e ion and sel - eac ion in o sul i e ion and SO3. The ela i e a e cons an o eac ion () compa ed o (7) was ound o be 0.8 ± 0.2. SO3 + SO3S2O62  SO3 + SO3SO32 + SO3 (7) Wa neck and colleagues s udied he s eady s a e pho olysis o SO32and HSO3a 254 nm and analyzed he possible ee adical eac ions, a e cons an s and p oduc dis ibu ion in he p esence and absence o dissol ed oxygen.136,137 The li e a u e o pe oxomonosul a e adical (SO5) is limi ed compa ed o he p e iously discussed congene s, al hough due o apid in e con e sion eac ions, he sepa a e in es iga ion o hese adicals is ba ely easible. P ac ically all ee adical s udies connec ed o S(IV) au oxida ion men ioned ea lie deal wi h he pa allel occu ence o SO3, SO4 and SO5 adicals, some o hem wi h SO2 as well. The adical is mos likely gene a ed by he oxygen addi ion o sul i e ion adical and decays by se e al adical- adical and adical-s able species eac ions. A pape om T. N. Das ocuses mainly on SO5 adical, e-e alua ing i s ole in sul i e au oxida ion chains in liquid hyd ome eo s.138 SO5 adical shows a weak abso p ion band be ween 260-265 nm wi h a mola abso p ion coe icien o 1065 ± 80 M1 cm1. 2.4. E ec o inhomogenei ies in as eac ion kine ics As men ioned in he p e ious sec ion o his hesis, he inhomogeneous dis ibu ion o he ansien abso bing species in he sample is a ypical cha ac e is ic o lase lash pho olysis expe imen s. This ac should be aken in o accoun du ing he acquisi ion and p ocessing o ansien abso p ion da a. Sample inhomogenei ies can lead o dis o ed conclusions, especially when he kine ic ace de ec ed is no an exponen ial cu e. Whene e possible, se ing pseudo- i s o de condi ions is desi able in o de o a oid he usage o ac ual ansien concen a ions. Only a hand ul o pape s deal wi h he expe imen al and/o ma hema ical ea men o po en ial inhomogenei y issues and he esul ing e o s in kine ic conclusions. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 17 A he dawn o he lash pho olysis echnique, J. W. Boag analyzed he e ec o non-uni o m dis ibu ion o ini ial ansien concen a ion along and ac oss he analyzing ligh beam.139 He conside ed i s and second o de eac ions and made an e o o gi e analy ical exp essions o he di e ence be ween he ac ual and he expe imen ally de e mined a e cons an s. He assumed ce ain shapes o he ini ial dis ibu ion (see Figu e 2.4) and used p ac ically concei able pa ame e s, such as o al abso bance be ween 0 and 2 ( ypically 0.4-0.6), h > 0.5, expe imen al ime leng h a leas 4-5 hal -li e o he obse ed species. He concluded ha i s o de eac ions a e less in luenced by ini ial dis ibu ions, and wi h he abo e pa ame e alues, he di e ence be ween 𝑘  (as he assigned he obse ed a e cons an ) and k ( he ac ual alue) is less han 1%. I is wo h no ing ha he used he linea ized e sions o he in eg a ed a e laws (which is a sou ce a s a is ical dis o ions i sel ) in his deduc ions and igno ed di usi e mo ion o he pa icles wi hin he expe imen al ime. A) B) Figu e 2.4. Ini ial dis ibu ion o ansien concen a ion along he analyzing ligh beam in lash pho olysis expe imen s. A) Ex eme cases. a = (sine)2, b = iangula , c = sine dis ibu ion; I0 = inciden ligh in ensi y; I( ) = exi ligh in ensi y a ime . B) Expec ed p ac ical dis ibu ions. (a) iangula cap; (b) sine cap; (c) pa abolic cap. The pa ame e h is he a io be ween he minimum and maximum o ini ial concen a ion (0  h  1). Figu es adap ed om Boag, T ans. Fa aday Soc. 1968, Figs. 1 and 4.139 Bazin and Ebbesen s udied he e o o igina ing om a poo o e lap be ween he lase beam and he analyzing (o p obe) beam in gi en expe imen al a angemen s o lase lash pho olysis. They in oduced wo kinds o co ec ion ac o s o such bad o e laps in he lase and p obe di ec ions, and p o ided echnical ad ice on how o de ec hem.140 Ins ead o conside ing ac ual kine ic measu emen s, hey ocused on he de ia ion o he measu ed abso bance (ODexp) om he eal alue (OD ue). Figu e 2.5 shows he possible sou ces o insu icien o e lap be ween he wo ligh beams. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 18 Figu e 2.5. Examples o bad o e lap si ua ions in lase lash pho olysis expe imen s. The solid line ep esen s he analyzed space, he dashed line delinea es he lase beam. The ha ched a ea shows he o e lap. (a) and (b): pe pendicula , (c) pseudo on ace, (d) collinea a angemen . ( he eade migh no ice ha he panels a e labelled clockwise ins ead o ow-con inuously). Figu e adap ed om Bazin and Ebbesen Pho ochem. Pho obiol. 1983, Fig. 1.140 The au ho s assigned x and y o he ac ions no co e ed by he complemen a y beams o cases (a) and (b) in Figu e 2.5. Wi h he no a ions o he igu e, l 'll y  and s 'ss x  ; 0  x, y < 1, and he ela ion be ween OD ue and ODexp is gi en in eq. (8). OD ue = ODexp  SF(x,y)  DF(x) (8) SF alues a e he scale ac o s 1/(1  x) and 1/(1  y), he p opo ionali y ac o s o bad o e lap ac oss and along he analyzing di ec ion, espec i ely. An impo an ou come o hei calcula ions is ha he a io OD ue/ODexp inc eases wi h ODexp, and hey de ined a dis o ion ac o (DF) as he a io o he ela i e e o s a high and low expe imen al alue. DF = ( exp ue OD OD )/( exp ue OD OD )ODexp  0 (9) DF is only a unc ion o x and no y, in he case o bad o e lap along he ligh pa h, OD ue is always linea ly dependen on ODexp. They sugges ha DF ends o cause mo e ouble in da a p ocessing, which con i ms ha i is p e e able o wo k wi h low abso bance alues, as long as he signal- o-noise a io is accep able. Cassidy and Long c ea ed a ma hema ical model o es he alidi y o expe imen al a e cons an s de e mined unde pu a i e pseudo- i s o de condi ions.141 The unde lying chemical É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 19 sys ems we e lase lash pho olysis s udies o CO pho odissocia ion eac ions om ansi ion me al ca bonyl complexes and he subsequen coupling o he ML6 and ML5 o ms. CO(CO)M(CO)M 56 hν (10) 11256 (CO)M(CO)M(CO)M  hν (11) Thei model implies ha M(CO)5 is gene a ed by a lase beam o ci cula c oss sec ion and moni o ed by a second beam in collinea a angemen , in a cylind ical olume. M(CO)5 concen a ion decays eaching ze o a he a ace o he cu e e, and he abso bance can be calcula ed om Bee ’s law. They also conside ed he di usion o M(CO)5 molecules ou side o he moni o ed olume in he case whe e eac ion (11) is su icien ly slow. Ma hema ically, his sys em could be desc ibed by wo-dimensional di usion equa ions coupled o a second o de eac ion. All di usion coe icien s we e supposed o be equal. I was assumed ha M(CO)6 is in high excess compa ed o M(CO)5 and he second o de a e cons an o eq. (11) was calcula ed by he adi ional pseudo- i s o de me hod (plo ing kobs as a unc ion o [M(CO)6], he ob ained slope is k). The pe cen age di e ences we e gi en be ween log(kcalc) and log(kinpu ) alues, whe e k we e used as an inpu pa ame e in he model. Upon conside ing di e en kinds o concen a ion inhomogenei ies and pa ame e se s, he ollowing conclusions we e d awn om hei esul s: i. when he ela i e concen a ion o M(CO)5 was high ( iola ing pseudo- i s o de condi ions), he di usion ou side he cylinde s a ed o in e e e below kinpu = 107 M1 s1, causing up o 14% dec ease ii. inhomogeneous dis ibu ion along he ligh pa h (due o Bee ’s law) did no cause any dis o ion, as long as he high excess o M(CO)6 was main ained iii. when a Gaussian beam p o ile was used o he exci a ion pulse, di usion caused e o s below 107 M1s1, a low ela i e concen a ion o M(CO)6; i . as an in e es ing complemen a y in o ma ion, he pseudo- i s o de plo o he de e mina ion o kcalc was always pe ec ly linea , e en i high e o s we e ound be ween log(kcalc) and log(kinpu ). The e o e, he co ela ion coe icien in his case was no a good indica o o es ing pseudo- i s o de beha io . The esul s o he abo e desc ibed model calcula ions we e no compa ed o expe imen al da a because LFP measu emen s we e ca ied ou wi h pe pendicula a angemen . Sample inhomogenei y issues can be assessed by expe imen al app oaches as well. Bonneau and co-wo ke s published a de ailed manual o he collec ion and analysis o ansien É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 20 abso p ion da a and emphasized he impo ance o co ec ins umen geome y and inhomogeneous ansien dis ibu ions. They sugges ed ha a mi o should be placed a he side o he sample opposi e o he lase exci a ion spo in o de o e lec he pumping ligh back and hus inc ease he abso bed ac ion o ligh and o se inhomogenei ies a he same ime.142 Goez e al. ealized he idea abo e, al hough hey used a solid co ne - ube e o e lec o ins ead o a mi o , in o de o educe Bee inhomogenei y (caused by abso p ion along he ligh pa h o he lase ).143 Re o e lec o s a e less sensi i e o alignmen impe ec ions han mi o s and make i possible o ca y ou measu emen s a di e en wa eleng hs wi hou changing he mi o . The inciden and he e lec ed beams we e mixed wi h he aid o he e o e lec o which had double bene icial e ec : he o al abso bed in ensi y inc eased and he Bee inhomogenei y dec eased ( he o me by a ac o o 1.45-1.65, he la e 2.6-4.8- old). They ound a e y simple ela ion be ween hese wo e ec s. Acco ding o hei calcula ions and measu emen s, in he p esence o he e o e lec o , he abso bed in ensi y inc eased by a ac o o 𝜃, hen he o al dec ease o inhomogenei y equals 2/𝜃-1. Dis o ions a ising om he Gaussian beam p o ile also imp o ed a li le by his me hod, bu he au ho s poin ed ou ha beam shape s o easie expe imen al se ings could co ec o he non-uni o mi y o he beam. Solu ion inhomogenei ies end o cause dis o ions in s opped low (SF) measu emen s as well, al hough he sou ce i he non-uni o m dis ibu ion o concen a ions is concep ually di e en han he ones connec ed o lash pho olysis expe imen s. In he case o he s opped low echnique, he inhomogenei y a ises om he ac ha he mix u e o he eac ing componen s needs a ce ain ime o ill he obse a ion cell ( illing ime). Fo e y apid eac ions, whose hal -li e is compa able o he illing ime o he ins umen , a signi ican di e ence can be o med be ween he on and he a ace o he obse a ion cell (see Figu e 2.6). Ro abache and colleagues de eloped ma hema ical models o esol e second o de a e cons an s o such apid eac ions, aking in o accoun he concen a ion g adien unde app op ia e condi ions. Fi s , hey ea ed i e e sible second o de eac ions, choosing an a bi a y ‘ze o ime’ o he measu emen s. They managed o de e mine a a e cons an o 7  106 M1 s1 his way.144 Thei model was la e imp o ed o emo e he e e sibili y and s a ing ime es ic ions and he a e cons an limi shi ed up by an o de o magni ude.145 Finally, hey comple ed hei esul s by ano he g adien -co ec ed app oach, whe e hey used he s eady s a e abso bance o ming in he low cell be o e he cessa ion o he low.146 The esol ed a e cons an s o bo h me hods, as well as a non-co ec ed second o de ea men o he sake o compa ison, we e ca e ully analyzed using as eac ions o ansi ion me al complexes as an expe imen al model. The a e cons an s o he la e we e p edic ed om he Ma cus heo y.147 É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 21 As a conclusion, second o de a e cons an s o magni ude up o 108 M1 s1 became a ailable om s opped low measu emen s o eac ions whose hal -li es a e less han one hal o he ins umen dead ime ( he ime equi ed o he solu ion o a el he dis ance x + l in Figu e 2.6). Figu e 2.6. Scheme o sample concen a ion g adien in a s opped low expe imen . Figu e adap ed om Dunn e al. J. Phys. Chem. 1996, Fig. 1.146 Conside ing he sub-nanosecond o millisecond ime esolu ion o he lase lash pho olysis echnique, i has impo an o e lap wi h he s opped low me hod om he poin o iew o he o de o magni ude o he accessible a e cons an s. Howe e , he majo di e ences be ween hese echniques s ill hold, i.e. s opped low deals wi h g ound s a e species (e en i e y sho li ed), whe eas LFP ope a es wi h ansien species gene a ed by he high ene gy lase pulse. The lase gene a ion me hod elimina es he need o manual o ins umen al mixing. On he o he hand, he ‘ba ch’ cha ac e is ic o LFP measu emen s is a echnical limi a ion. The poin is ha all g ound s a e molecules a e loca ed in he cu e e a he momen o he lase pulse. The e o e, he e ec o he lase on all componen s has o be es ed indi idually be o e obse ing a adical eac ion and some imes i is impossible o isola e a ce ain componen o abso b he o al amoun o lase ene gy. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 22 3. Resea ch objec i es The p esen hesis is dedica ed o shed u he ligh on he ole o sul a e ion adical in he ansi ion me al ca alyzed au oxida ion o hyd a ed SO2, mo e gene ally, au oxida ion o S(IV). The ca aly ic e ec o sil e (I) ions in he p esence o pe oxodisul a e (S2O82) ions is in es iga ed. T adi ional me hods o aqueous solu ion kine ics a e employed, as well as lase lash pho olysis echnique o he di ec obse a ion o SO4. Compu a ional simula ions a e ca ied ou o s udy he po en ial e ec o di usion and spa ial inhomogenei ies du ing lase lash pho olysis expe imen s. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 23 4. Expe imen al me hods 4.1. Ma e ials All chemicals used in his s udy we e o analy ical eagen g ade and we e pu chased om comme cial sou ces. Sodium sul i e s ock solu ions we e p epa ed eshly om Na2S2O5 (Reanal) e e y day. Whene e necessa y, py osul i e solu ions we e deae a ed by bubbling A (pu i y > 99.95%) o a leas 15 min in o de o inc ease he ep oducibili y o measu emen s unde anae obic condi ions. Po assium pe oxodisul a e s ock solu ions we e p epa ed om K2S2O8 (Reanal). This solu ion was oxygena ed du ing he O2-dependen expe imen s. Sil e (I) ca alys solu ions we e p epa ed by dissol ing a weighed amoun o AgNO3 (Reanal) o a known inal olume. Doubly deionized and ul a il e ed wa e om a Millipo e Q sys em was used in he en i e wo k. Mos o he expe imen s we e ca ied ou a high and cons an acid concen a ion (0.10 o 0.33 M sul u ic acid). The e o e, addi ional sal was no used o adjus he ionic s eng h. 4.2. Ins umen a ion and so wa es 4.2.1. UV- is spec opho ome ic expe imen s ela ed o S(IV) au oxida ion UV- is spec a we e eco ded on a Pe kin Elme Lambda 2S o a Pe kin Elme Lambda 25 scanning spec opho ome e . Kine ic expe imen s we e ca ied ou in s anda d qua z cu e es (op ical pa h leng h = 1.000 cm). The o e all sample olume was 3.00 cm3 in each case. Cons an empe a u e (25.0  0.1 C) was main ained wi h an ex e nal he mos a and ci cula ing he mal ba h. Samples we e p epa ed by he ollowing me hod. Requi ed aliquo s o py osul i e, pe oxodisul a e and sul u ic acid solu ions we e mixed wi h wa e and he mos a ed o 3-4 min. The p ocess was s a ed by adding he ca alys immedia ely p io o commencing he de ec ion in he spec opho ome e . Reac ion a es we e de e mined by linea i ing o da a cu es. One can calcula e he ac ual a e om he slopes o abso bance e sus ime unc ions by using he mola abso p ion coe icien o sul u (IV), known om independen expe imen s. F om a ma hema ical poin o iew, he a e de e mina ion equi es nume ical di e en ia ion. Unde he usual condi ions, he accu acy o eac ion a es a e 10%, indica ed by he e o ba s in Figu e 5.3-Figu e 5.7Figu e 5.9. In he sil e (I) ca alysis s udy, ano he me hod was applied o compu e he eac ion a es (which we e ai ly cons an wi hin a single expe imen ) and compa e hem wi h he esul s o nume ical de i a ion. The slopes o he sec ions p eceding he b eak poin we e calcula ed (see É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 24 Figu e 5.2) The abso bance change can be ans e ed in o concen a ion change by di iding i wi h he (appa en ) mola abso p ion coe icien alid a he pH o he eac ion sys em. The main ad an age o he la e me hod is ha i a oids he possible p oblems a ising om impe ec he mos a ing, which may occu a he beginning o expe imen s. Reac ion a es de e mined wi h he wo di e en me hods we e in e y good ag eemen , and we used he esul s o he me hod o ini ial a es in he inal calcula ions. 4.2.2. Lase lash pho olysis measu emen s Lase lash pho olysis (he ea e e e ed o as LFP) expe imen s ha e been ca ied ou in an LKS.60 nanosecond ansien abso p ion spec ome e , shown in Figu e 4.1. Figu e 4.1. Applied Pho ophysics LKS.60 nanosecond lase lash pho olysis ins umen The ins umen is equipped wi h a Quan el B illian Nd:YAG lase along wi h i s second, hi d, ou h and i h ha monic gene a o s ( e e ed as SHG, THG, FoHG, FiHG). Nd:YAG (Neodymium doped y ium aluminum ga ne ) is a common solid-s a e lase ype, whe e he lasing medium is a Y3Al5O12 c ys al doped wi h 0.1-1% Nd3+. The p ima y wa eleng h o an Nd:YAG lase ligh is 1064 nm, i s ha monics emi a 532 (2nd), 355 (3 d), 266 (4 h) and 213 nm (5 h). Ha monics a e gene a ed by speci ic c ys als ha exhibi non-linea op ical e ec s. Common non-linea c ys als a e KDP, DKDP, LaTiO3, BaTiO3 e c. Table 4. Speci ica ion o he ou h ha monic o Quan el B illan Nd:YAG lase Wa eleng h 266 nm Pulse leng h ( ull wid h a hal maximum) 6 ns Repe i ion a e 10 Hz Ene gy pe pulse (max.) 40 mJ Beam diame e 6 mm Q-swi ch ON É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 25 In he p esen hesis, he ou h ha monic o he Nd:YAG lase was used o gene a e sul a e ion adicals and o he ansien species. Table 4 con ains he cha ac e is ic ea u es o he lase beam. Un o una ely, he i h ha monic gene a o educed he ene gy o he lase pulse oo much and i could no be employed o any p ac ical pu poses in his s udy. Q-swi ching is a equen echnique applied o inc ease lase powe by sho ening he lase pulse. O iginally, he Q- ac o (o quali y ac o ) is a e m o elec onics, i desc ibes he goodness o an RLC ci cui . Q-swi ching is ealized by a Pockels-cell in he LKS.60 ins umen . The analyzing ligh sou ce was a 150 W ozone ee xenon a c lamp (OSRAM 150W/CR OFR) and i s ligh beam en e ed a 1.00  1.00 cm luo escence qua z cu e e. We ha e implied c oss-beam exci a ion, he p obe beam and he lase beam we e in oduced in o he sample in a pe pendicula a angemen . The cu e e was placed in an adjus able sample holde , which was posi ioned ho izon ally so ha he analyzing ligh beam hi close o he on ace o he cu e e whe e lase beam en e ed. This is an impo an se ing as he concen a ion o ansien species gene a ed by he lase exci a ion ypically dec eases apidly wi h he dis ance om he on window (see also Sec ion 5.3.7.). A p og ammable /3.4 g a ing monoch oma o wi h a symme ical Cze ny-Tu ne op ical con igu a ion was combined wi h a R928 pho omul iplie o he ansien signal de ec ion a di e en wa eleng hs. Da a poin s we e collec ed by an Agilen In iniium digi al s o age oscilloscope (model numbe DSO8064A, maximum sampling speed 4 GSa/s (0.25 ns be ween da a poin s), bandwid h 600 MHz, ou pu impedance 50 Ω). The exci a ion o is(bipy idine) u henium(II) chlo ide (Ru(bpy)3Cl2) by he hi d ha monic o he lase (355 nm) was used as a es eac ion (Figu e 4.2).148 Figu e 4.2. A) T ansien abso p ion spec a o is(bipy idine) u henium(II) chlo ide a e 355 nm lase pulse. The signals we e eco ded a he indica ed ime poin s a e he lase pulse. B) Fi s o de decay o iple Ru(bpy)32+. The solid line ep esen s he non-linea leas squa e i o he obse ed da a poin s. [Ru(bpy)32+] = 31 μM,  ex = 355 nm É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 32 Figu e 5.6. Reac ion a es as a unc ion o he pe oxodisul a e ion concen a ion in he au oxida ion o sul u (IV). The solid line ep esen s he bes i o he p oposed mechanism shown in Scheme 1. [S(IV)] = 3.0 mM; [H2SO4] = 0.103 M; [Ag+] = 0.167 mM; pa h leng h = 1.000 cm; [O2] = 0.130 mM; V = 3.00 cm3; T = 25.0 C. Dependence o he eac ion a e on pH Finally, he e ec o pH on he a e o he ze o h o de p ocess is shown in Figu e 5.7. The pH was calcula ed om he concen a ion o added sul u ic acid conside ing he ac ha hyd ogen sul a e ion is no a s ong acid (pKa2 = 1.06 a 25 °C) Figu e 5.7. Reac ion a es as a unc ion o he pH in he au oxida ion o sul u (IV). [S(IV)] = 3.0 mM; [S2O82] = 0.0284 M; [Ag+] = 0.167 mM; [O2] = 0.130 mM; pa h leng h = 1.000 cm; V = 3.00 cm3; T = 25.0 C. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 33 5.1.3. Sugges ed mechanism Ou kine ic obse a ions, in acco dance wi h ea lie esul s o in es iga ions77,79 abou he au oxida ion o S(IV), con i m ha a chain eac ion akes place in he s udied sys em. The ini ia ion s ep is e y likely o be he well-known eac ion be ween sil e (I) and pe oxodisul a e ions (2), which p oduces wo eac i e chain ca ie s, sil e (II) and sul a e ion adicals. Ano he ini ia ion s ep will be men ioned la e , as he e e se di ec ion o a chain e mina ion s ep.     2 44 2 18 2 82 SOSOAgOSAg k (18) Among he p opaga ion s eps, he eac ion o Ag(I) and SO4 p oducing sil e (II) and HSO4 ce ainly occu s (19).     2 4 2 19 4SOAgSOAg k (19) P e ious s udies e ealed ha he possible di ec eac ion be ween sul a e ion adical and sul u (IV) does no play a ole in he au oxida ion p ocess.62,77,79 The e o e, i is easonable o assume ha sil e (II) eac s wi h sul u (IV) in he chain eac ion. Ag(II) is a s ong oxidizing species, which can easily be educed by S(IV) in a one-elec on s ep (20).    3 20 2SOAg(IV)SAg k (20) I is also known om he li e a u e ha sul i e ion adical eac s e y quickly wi h dissol ed oxygen124 and i is likely ha he p oduc o his eac ion, pe oxomonosul a e ion adical (SO5), oxidizes sul u (IV) (21, 22).   5 21 23 SOOSO k (21)   4 2 4 22 5SOSO(IV)SSO k (22) A his poin , one can see ha s eps (19 – 22) compose a chain in which one cycle leads o he o ma ion o wo sul a e ions by he eac ion o one oxygen and wo sul u (IV). Wi h ega d o chain e mina ion, one can conside he disp opo ion o sil e (II) in o sil e (I) and sil e (III) which is also a p e iously published assump ion.43,45 (III)AgAgAg223 2  k (23) É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 34   2 24 Ag2(III)AgAg k (24) Eqs. (23) and (24) desc ibe a e e sible p ocess in which he e e se s ep ac s as ini ia ion, as i p oduces a chain ca ie . This should be aken in o accoun in he de i a ion o he a e law. Sil e (III) is a e y eac i e species and i eac wi h sul u (IV) in a wo-elec on p ocess (25), whe e sil e (I) is ep oduced, eady o join he ca aly ic cycle again.   2 4 52 SOAg(IV)S(III)Ag k (25) Sil e (III) is supposed o occu as he AgO+ oxoca ion in aqueous solu ion, which means ha eac ion (25) possibly occu s as oxygen a om ans e .45 The ecombina ion o sul a e ion adicals o pe oxodisul a e ion (26) has always appea ed in he chain mechanisms o he au oxida ion p ocesses o sul u (IV) examined be o e.77,79 Fo his eason, i seems app op ia e o conside i in he scheme as a possible e mina ion s ep.    2 82 26 4OSSO2k (26) Scheme 1. The sugges ed mechanism o he au oxida ion o sul u (IV) in he p esence o sil e (I) and pe oxodisul a e ions.     2 44 2 18 2 82 SOSOAgOSAg k 1=k18[Ag+][S2O82−] (R1)     2 4 2 19 4SOAgSOAg k 2=k19[Ag+][SO4•−] (R2)     3 obs 20 2SOAg(IV)SAg k 3= 𝑘20 obs[Ag2+][S(IV)] (R3)   5 21 23 SOOSO k 4=k21[SO3•−][O2] (R4)    4 2 4 obs 22 5SOSO(IV)SSO k 5= 𝑘22 obs[SO3•−][S(IV)] (R5) (III)AgAgAg223 2  k 6=k23[Ag2+]2 (R6)   2 24 Ag2(III)AgAg k 7=k24[Ag+][Ag(III)] (R7)    2 4 obs 25 SOAg(IV)S(III)Ag k 8= 𝑘25 obs[Ag(III)][S(IV)] (R8)    2 82 26 4OSSO2k 9=k26[SO4•−]2 (R9) É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 35 Figu e 5.8. The sugges ed mechanism o he au oxida ion o sul u (IV) in he p esence o sil e (I) and pe oxodisul a e ions. 5.1.4. De i a ion o he a e law The egula ma hema ical ea men o chain eac ions is he long-chain app oach.91 Essen ially, i is buil on wo main pilla s:  he s eady-s a e app oxima ion can be applied o e e y eac i e in e media es (Ag(II), Ag(III), SO3, SO4, SO5 in he p esen s udy)  he a e o chain ini ia ion o e mina ion is lowe han hose o he p opaga ion s eps. Two gene ally applied conclusions can be d awn om he assump ions abo e: i. Each p opaga ion s ep has he same a e as he a e o he ne eac ion. ii. The a e o ini ia ion and e mina ion s eps a e equal. I mo e han one ini ia ion o p opaga ion s eps occu , hen equali y e e s o he sum o he a es o a ce ain ype:   kkT, jjI, He e j is he numbe o ini ia ion s eps (I), k is he numbe o e mina ion s eps (T). The a e o eac ion (1) may be desc ibed by eq. (27).     d Od d SOOHd 2 1222    (27) É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 36 The a e is equal o he a e o any p opaga ion s eps, so i can be de i ed om eqs. (19)- (22). I is con enien o use eq. (20) o his pu pose, in o de o simpli y subsequen calcula ions. = 3 = 𝑘20 obs[Ag2+]ss[S(IV)] (28) he e subsc ip ss indica e s eady-s a e concen a ions All eac ions discussed a e supposed o be second o de , and hese a e elemen a y s eps excep o eac ions (20), (22) and (25). In he la e cases, he dep o ona ion o H2OSO2 should be aken in o accoun in he pH- ange o he s udy. H2OSO2 and HSO3 o ms a e ela ed by a as p e-equilib ium. Consequen ly, he a e o s ep (20) is gi en in eq. (29) = [Ag2+]ss(k20[H2O∙SO2] + k20′[HSO3]) (29) Conside ing he equilib ium o he wo S(IV) o ms, he o mula akes he ollowing o m: )][H( ][H [S(IV)]][Ag a2020 a ss 2K'kk K      (30) Implying he long-chain assump ion (ii), one can ob ain eq. (31): 2 ss426 2 ss 2 23ss24 2 8218 ][SO][Ag][Ag(III)][Ag]O][S[Ag     kkkk (31) The s eady-s a e concen a ion o sil e (III) can be exp essed om eq. (32) as ollows: 2 ss 2 23ss24 a a2525 ss ][Ag][Ag[Ag(III)] ][H ][H [S(IV)][Ag(III)]      kk K K'kk (32) ][Ag ][H ][H [S(IV)] ][Ag [Ag(III)] 24 a a2525 2 ss 2 23 ss         k K K'kk k (33) The s eady-s a e concen a ion o sul a e ion adicals can be gi en om he ac ha he a es o p opaga ion s eps a e equal ( 2 = 3): a a2020 ss 2 ss419 ][H ][H [S(IV)]][Ag][Ag][SO K K'kk k      (34) )]([H ][H ][Ag [S(IV)]][Ag ][SO a19 a2020ss 2 ss4Kk K'kk         (35) Subs i u ing he s eady-s a e concen a ions in eqs. (33) and (35) in o eq. (31) yields: É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 37 2 a19 a2020 2 2 2 ss 2 26 2 ss 2 23 24 a a2525 2 ss 2 23 24 2 8218 )]([H ][H ][Ag [S(IV)]][Ag ][Ag ][Ag ][H ][H [S(IV)] ][Ag ][Ag]O][S[Ag                             Kk K'kk kk k K K'kk k kk (36) F om eq. (36), he s eady-s a e concen a ion o sil e (II) can be exp essed:   ][Ag ][H ][H S(IV) ][Ag )]([H ][H ][Ag [S(IV)] 1 ]O][S[Ag ][Ag 24 a a2525 24 2 a19 a2020 2 2 23 26 2 82 23 18 2 ss 2                           k K K'kk k Kk K'kk k k k k (37) The combina ion o eqs. (30) and (37) leads o he inal a e law:   ][Ag ][H ][H S(IV) ][Ag )]([H ][H ][Ag [S(IV)] 1 ]O][S[Ag ][H )][H[S(IV)]( 24 a a2525 24 2 a19 a2020 2 2 23 26 2 82 23 18 a a2020                                k K K'kk k Kk K'kk k k k k K K'kk (38) É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 38 The sugges ed model i s he obse ed kine ic da a e y well. Solid lines in Figu e 5.3- Figu e 5.6 ep esen he bes i o he p oposed mechanism. Figu e 5.9 shows he co ela ion be ween all eac ion a es measu ed a one gi en pH ([H2SO4] = 0.103 M). The ho izon al axis con ains he measu ed a es, while da a on he e ical axis a e he a es calcula ed wi h he pa ame e s om he bes i . The co ela ion plo also con i ms ha he model p o ides excellen quan i a i e in e p e a ion o he kine ic esul s. Figu e 5.9. Co ela ion be ween measu ed and calcula ed a es. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 39 5.2. Lase lash pho olysis s udies on he eac ions o sul a e ion adical 5.2.1. Gene a ion and ecombina ion o he sul a e ion adical (SO4) P e iously published gene a ion me hods and cha ac e iza ion o he sul a e ion adical, SO4, a e ex ensi ely discussed in Sec ion 2.3. In ou expe imen s, SO4 was gene a ed by he pho olysis o an aqueous solu ion o K2S2O8 (3). The adicals a e he p oduc o he homoly ic scission o he pe oxy bond in S2O82– ion.   4 2 82 SOOS hν (39) Whene e equi ed o he calcula ions,  (SO4)450 nm = 1600 dm3 mol–1 cm–1 was used, based on he s udies o McEl oy.118 Following he pho olysis o a 0.0967 M K2S2O8 solu ion a 266 nm, kine ic aces simila o he one in Figu e 5.10 we e de ec ed. The eco ded kine ic aces in he absence o any o he eac an s we e i ed wi h second o de cu es, and hey all ga e a e y good i . The e o e, i is easonable o assume ha he ecombina ion o sul a e ion adicals in o he p ecu so pe oxodisul a e ions akes place unde hese condi ions (40), which is he same p ocess as he las chain e mina ion s ep in Scheme 1. (R9).    2 82 40 4OSSO2k (40) Figu e 5.10. T ansien abso p ion signal o he sul a e ion adical. [K2S2O8] = 0.0967 M, T = 25 °C, V = 3.00 cm3. The solid line ep esen s he i ed second o de cu e (k = 3.91  108 M1 s1). É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 40 The second o de a e cons an o he eac ion, deno ed he e by k40, was de e mined om he i ed pa ame e s conside ing he mola abso p ion coe icien men ioned abo e. The alue o he calcula ed second o de a e cons an was (4.1  0.2)  108 M–1s–1. The ecombina ion p ocess occu s on he millisecond imescale, which equi es special ea men , as he basic se ings o he ins umen a e con igu ed o nanosecond measu emen s. In o de o measu e on longe imescales, he impedance o he oscilloscope has o be inc eased om 50 Ω in o he kΩ ange, up o 1 MΩ, by he ins alla ion o a a iable esis ance box be ween he signal cable om he pho omul iplie ube and p ope oscilloscope channel. Fu he mo e, a longe imescales, he Xe a c lamp has o be ope a ed in con inuous mode ins ead o pulsed mode, o he wise he lamp lashes would be oo sho o he de ec ion o he ansien species. Theo e ically, he LKS.60 ins umen wi h i s ac ual equipmen is able o ollow chemical eac ions on he imescales be ween 1 ns o a ew seconds wi h he con enien ins umen se ings and da a e alua ion me hods implied. In o de o e eal a possible pH-dependence o he a e cons an , k40 was measu ed o e he acidic ange. Figu e 5.11 shows ha he a e cons an o he ecombina ion p ocess is independen o pH in he implied ange. Figu e 5.11. The e ec o pH on he ecombina ion a e o sul a e ion adicals. [K2S2O8] = 0.0967 M, T = 25 °C, V = 3.00 cm3. 5.2.2. Reac ion o sul a e ion adical and sil e (I)-ion In he subsequen s age o ou kine ic in es iga ion, he main ocus was he ole o sul a e ion adical in he au oxida ion p ocess o sul u (IV). One can see om Scheme 1 ha SO4 is a chain ca ie in e media e, i is p oduced in he ini ial s ep (2) and in a p opaga ion s ep by he educ ion o pe oxomonosul a e ion adical. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 41 Figu e 5.12. Abso p ion a 450 nm ollowing he pho olysis o K2S2O8 (0.100 M) solu ion, con aining AgNO3 (6.12 mM). The solid line ep esen s he i ed single exponen ial cu e (kobs = 3.8  107 s1). The eac ion be ween sul a e ion adical and sil e (I) ion is o high impo ance in chain p opaga ion, because i is he p ocess h ough which he ca alys en e s he cycle. The e o e, we in ended o de e mine he a e cons an o eac ion (19) by means o lase lash pho olysis. An aqueous solu ion o AgNO3 was pho olyzed a 266 nm as a blank expe imen in o de o measu e i s con ibu ion o he o e all abso p ion in he eac ion. I was ound ha sil e ni a e does no show any ansien abso p ion a 450 nm, hus he abso p ion can be a ibu ed solely o sul a e ion adical. Figu e 5.12 shows a ep esen a i e ansien abso p ion cu e. The eac ion akes place on he nanosecond imescale, and can be i ed wi h a single exponen ial cu e, hus e e ing o a i s o de p ocess. Concen a ions o he eac an we e se in a way ha pseudo- i s o de condi ions would be ul illed o Ag+ ions o e sul a e ion adicals. A su p ising obse a ion was made ollowing he pho olysis o K2S2O8–AgNO3 aqueous solu ion. A e a ew lase sho s (3-10 depending on he concen a ion a io), da k g ey cloudy p ecipi a ion was seen in he cu e e, i s a he spo o lase exci a ion. Ag2O o ma ion was excluded upon he ac s ha he colo o he p ecipi a e is di e en om b ownish Ag2O, i does no dissol e in sul u ic acid and i appea s e en a e y low pH. The da k g ey p ecipi a ion is hus assumed o be elemen a y sil e , he sou ce o which is unknown so a . I was hough o be p oduced in he pho odecomposi ion o AgNO3, bu in he absence o K2S2O8, he p ecipi a ion did no occu . É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 48 Figu e 5.21. Ra io o second o de a e cons an o he decomposi ion and he mola abso p ion coe icien o chlo ine molecule anion. [K2S2O8] = 0.100 M, () [H2SO4] = 0 M, (▼) [H2SO4] = 0.0049 M, T = 25 °C, V = 3.00 cm3. On he longe ime scale, he second o de decomposi ion o chlo ine molecule anion was de ec ed (see Figu e 5.21). The second o de a e cons an o he decay o Cl2 is (1.4 ± 0.04)  105 s1 cm   (Cl2−) a ei he pH = 2.03 o in unbu e ed aqueous solu ion. 5.2.6. Reac ion o sul a e ion adical wi h b omide ion In he eac ion o sul a e ion adical wi h b omide ion, b omide molecule anion is p oduced in eac ions (47) and (48). Kine ic da a we e collec ed a 360 nm (see spec a in Figu e 5.22).157 B  + SO4 = B + SO42 (47) B  + B ⇌ B 2 (48) Figu e 5.22. Time esol ed ansien abso p ion spec a o he b omine molecule anion. [K2S2O8] = 0.100 M, [KB ] = 0.010 M, V = 3.00 cm3, T = 25 °C, pH = 7 (unbu e ed). Spec a we e eco ded a he indica ed ime poin s a e he lase pulse. Nega i e ime on panel A (-0.1 μs) e e s o he p e-pulse sec ion o he cu es (panel B, < 0). É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 49 Figu e 5.23. Pseudo- i s o de a e cons an s as a unc ion o b omide ion concen a ion in he eac ion o sul a e ion adical and b omide ion. [K2S2O8] = 0.100 M, () [H2SO4] = 0 M, (▼) [H2SO4] = 0.0049 M, T = 25 °C, V = 3.00 cm3. The eac ion was ollowed on sho e and longe imescales, unde pseudo- i s o de condi ions. The second o de a e cons an was ound o be (1.51 ± 0.02)  109 M1 s1 in unbu e ed aqueous solu ion and (1.59 ± 0.03)  109 M1 s1 a pH 2.03 (Figu e 5.23). On he longe ime scale, he second o de decomposi ion o b omine molecule anion was de ec ed, which was ound o be independen om he b omide ion concen a ion (see Figu e 5.24). The second o de a e cons an o he decay o B 2 is (1.8 ± 0.1)  105 s1 cm   (B 2−) in unbu e ed aqueous solu ion and a pH = 2.03. Figu e 5.24. Ra io o second o de a e cons an and mola abso p ion coe icien o he decomposi ion o b omine molecule anion. [K2S2O8] = 0.100 M, [H2SO4] = 0.0049 M, V = 3.00 cm3, T = 25 °C. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 50 5.2.7. Reac ion o sul a e ion adical wi h yp ophan The kine ics and mechanism o he oxida ion o yp ophan (T p) and i s de i a i es by pe oxomonosul a e ions ha e been ecen ly s udied in ou labo a o y.158 Since yp ophan is an a oma ic amino acid wi h nume ous po en ial oxida ion si es (Figu e 5.25), he de ailed cha ac e iza ion o i s oxida ion eac ions is a a he challenging ask ha needs o be app oached by a combina ion o expe imen al echniques. The lase lash pho olysis me hod p o ides an e icien ool o s udy he one elec on oxida ion eac ions o T p ha in ol e sho li ed eac i e in e media es. The one elec on oxida ion o a oma ic amino acids such as yp ophan and y osine plays an impo an ole in he o ma ion o p o ein adicals,159-163 hus pa icipa ing in elec on anspo and edox egula ion. Figu e 5.25. S uc u e o L- yp ophan and L- yp ophanamide. The pho olysis o yp ophan a 266 nm on a mic osecond ime scale led o kine ic cu es con aining a posi i e and a nega i e peak (see ep esen a i e cu e in Figu e 5.26). The posi i e peak could be assigned o he ansien abso p ion o he in e media e p oduc o he pho olysis o T p, whe eas he nega i e peak p esumably co esponds o he lase induced luo escence o T p. Nega i e peaks a e comple ely in e p e able in he con ex o lash pho olysis cu es, since he measu ed alue is in ac he di e ence be ween he abso bance o he g ound s a e species and he exci ed species. Figu e 5.26A shows ha he in ensi y o he nega i e peak exceeds ha o he posi i e one. The a io o hese alues (in a o o he abso p ion peak) could be op imized by he al e a ion o he wa eleng h o he analyzing beam (Figu e 5.26B). The emission- o-abso p ion a io was ound o be op imal a 580 nm, u he kine ic expe imen s we e ca ied ou a his wa eleng h. The 580 nm peak in he ansien spec um o exci ed yp ophan was p e iously assigned o be he pho oioniza ion p oduc o T p, a adical ca ion (T p+).164 É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 51 Figu e 5.26. A) Rep esen a i e kine ic cu e o he 266 nm pho olysis o aqueous solu ion o yp ophan. B) In ensi y o ligh abso p ion and emission in he 266 nm pho olysis o aqueous solu ion o yp ophan, based on kine ic cu es as in panel A. The peak in ensi y co esponds o he absolu e alue o he maxima o he posi i e and nega i e peaks, in abso bance uni s. Condi ions o bo h panels: [T p] = 0.5 mM, unbu e ed, V = 3.00 cm3, T = 25 °C, l = 1.000 cm. The plo s ep esen A) he a e age B) he a e age and s anda d de ia ion o 5 pa allel measu emen s, whe e esh sample was applied o each lase sho . Figu e 5.27 shows he linea dependence o he obse ed pseudo- i s o de a e cons an s on he concen a ion o yp ophan. 580 nm was no sui able o ollow he eac ion a pH 7.21 due o poo signal o noise a io. 520 nm was ound o be op imal wi h ega ds o emission o abso p ion a io. 520 nm is he epo ed abso p ion maximum o T pN adical.162,165-167 Figu e 5.27. Pseudo- i s o de a e cons an s in he eac ion o sul a e ion adical and yp ophan. The da a poin s and e o ba s ep esen he a e age and s anda d de ia ion o 5 pa allel measu emen s, whe e esh sample was applied o each lase sho . The measu ed second o de a e cons an s we e (7.4 ± 0.1) × 109 M1 s1 in unbu e ed solu ion and (8.7 ± 0.4) 109 M1 s1 close o physiological pH (7.21). [K2S2O8] = 0.100 M, unbu e ed (■), pH = 7.21 (20 mM phospha e bu e , ▼), V = 3.00 cm3, T = 25 °C, l = 1.000 cm. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 52 Figu e 5.28. Pseudo- i s o de a e cons an s in he eac ion o sul a e ion adical and L- yp ophanamide. The da a poin s and e o ba s ep esen he a e age and s anda d de ia ion o 5 pa allel measu emen s, whe e a esh sample was applied o each lase sho . The solid line ep esen s he linea leas squa e i o he measu ed poin s. The slope o he line is (8.8 ± 0.2) 109 M1 s1 and he in e cep is (0.8 ± 0.2) 106 s1. [K2S2O8] = 0.100 M, pH = 7.21 (phospha e bu e ), V = 3.00 cm3, T = 25°C, l = 1.000 cm,  = 520 nm. L-T yp ophanamide (T pA) was es ed in expe imen s simila o hose wi h T p, he aqueous solu ion o T pA and K2S2O8 was pho olyzed a 266 nm and he abso bance was ollowed a 520 nm. The obse ed a e cons an depends linea ly on he concen a ion o T pA, wi h a posi i e in e cep on he e ical axis (Figu e 5.28). E ec o dissol ed oxygen concen a ion in he eac ion o sul a e ion adical and yp ophan We al e ed he concen a ion o oxygen in he sul a e ion adical– yp ophan adical sys em in o de o e eal any po en ial in luence o dissol ed oxygen on he obse ed a e cons an s. When a gon o ni ogen was igo ously bubbled in o he eagen solu ions o 15-20 minu es be o e he exci a ion, i had no obse able e ec on he pho olysis o yp ophan solu ion. On he o he hand, upon he applica ion o a lase sho on he de-ae a ed samples, a p e iously unobse ed yellow p oduc appea ed in he solu ions. The cha ac e iza ion o he na u e o his p oduc would equi e de ailed spec oscopic and kine ic s udies. F om a kine ic poin o iew, he inc ease o dec ease o oxygen concen a ion in he solu ions caused only sligh di e ences in he measu ed a e cons an s. The measu ed second o de a e cons an s we e (9.4 ± 0.5) × 109 M1 s1 in ai sa u a ed solu ion and (9.0 ± 0.3) 109 M1 s1 in de-ae a ed samples. Da a poin s ob ained upon oxygena ion o he solu ions s ill show linea dependence, al hough he unc ion has a posi i e in e cep on he e ical axis. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 53 Figu e 5.29. A) Rep esen a i e kine ic cu es in he eac ion o sul a e ion adical wi h L- yp ophan wi h di e en oxygen concen a ions. Oxygen was emo ed by igo ously bubbling a gon in he eagen solu ions o 20 min, whe eas oxygena ion was achie ed by in oducing ex a oxygen in he samples om a gas bo le o 15-20 min. B) Pseudo- i s o de a e cons an s in he eac ion o sul a e ion adical wi h L- yp ophan om kine ic cu es as shown in A). The da a poin s and e o ba s ep esen he a e age and s anda d de ia ion o 5 pa allel measu emen s, whe e esh sample was applied o each lase sho . The solid line ep esen s he linea leas squa e i o he measu ed poin s. The slope o he blue line is (8.4 ± 0.8) 109 M1 s1 and he in e cep is (1.4 ± 0.4) 106 s1. [K2S2O8] = 0.100 M, pH = 7.21 (phospha e bu e ), V = 3.00 cm3, T = 25 °C, l = 1.000 cm,  = 520 nm. Figu e 5.29A shows h ee ep esen a i e kine ic cu es eco ded a 520 nm in ai sa u a ed, de-ae a ed and oxygena ed solu ions, espec i ely. Figu e 5.29B shows he obse ed pseudo- i s o de a e cons an s as a unc ion o he applied yp ophan concen a ion wi h di e en oxygen sa u a ion in he samples. The measu ed second o de a e cons an s we e (9.4 ± 0.5) × 109 M1 s1 in ai sa u a ed solu ion and (9.0 ± 0.3) 109 M1 s1 in de-ae a ed samples. Da a poin s ob ained upon oxygena ion o he solu ions s ill show linea dependence, al hough he unc ion has a posi i e in e cep on he e ical axis. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 54 Al e na i e gene a ion o yp ophanyl adical The li e a u e claims ha yp ophanyl adical can be gene a ed by he oxida ion o aqueous yp ophan by b omine molecule anion (B 2).165,168 The expe imen al cons ain is ha we we e no able o de ec B 2di ec ly upon he pho olysis o b omide solu ion, bu only by he oxida ion o b omide wi h sul a e ion adical (see Figu e 5.23). I is s ill easible o oxidize T p by b omine molecule anion in he p esence o K2S2O8. Howe e , one should ake he oxida ion o T p by sul a e ion adical in o accoun as well acco ding o he abo e men ioned a es. The e o e, in he SO4–T p–b omide sys em, we should conside eq. (47) as well. The in oduc ion o T p inc eases he obse ed a e cons an o he eac ion in such a mix u e (Figu e 5.30). The eac ion was ollowed a 360 nm, he abso p ion maximum o b omine molecule anion, on a mic osecond ime scale. The decay cu es did no i nicely o a single exponen ial cu e. A second o de i was much be e cu es in ag eemen wi h he second o de decay o B 2. Figu e 5.30. Second o de decay o b omine molecule anion in he absence and p esence o L- yp ophan. [K2S2O8] = 0.100 M, unbu e ed solu ion, V = 3.00 cm3, T = 25 °C, l = 1.000 cm. The in oduc ion o 0.3 mM T p led o a 3- old inc ease in he obse ed a e cons an . É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 55 5.2.8. Reac ion o sul a e ion adical wi h y osine Simila ly o he s udy ca ied ou wi h yp ophan, ano he a oma ic amino acid, y osine (Ty ) was also eac ed wi h sul a e ion adical, in o de o measu e he second o de a e cons an o eac ion (49). Ty + SO4  Ty  + SO42 (49) The eac ion was ollowed a 450 nm, because in he applied concen a ion ange, he concen a ion o Ty adical ha is gene a ed is insu icien o p oduce decen abso p ion signal. Unde pseudo- i s o de condi ions, he obse ed a e cons an s showed linea dependence on he concen a ion o y osine, as indica ed in Figu e 5.31. The da a poin s measu ed in acidic solu ions i e y well o linea unc ions going h ough he o igin. The ob ained second o de a e cons an s we e (6.1 ± 0.1)  109 M1 s1 in acidic medium (black line – he pH is no cons an in his case, concen a ion o added sul u ic acid is inc easing) and (5.1 ± 0.1)  109 M1 s1 a pH 2.72. Close o neu al pH, he dependence emains linea , al hough he linea unc ion has a small posi i e in e cep . The second o de ecombina ion o he y osyl adical leads o he o ma ion o di y osine, which is known o ha e an emission peak a 405 nm and o ms he basis o se e al luo escen assays in he biochemical labo a o y p ac ice.169,170 Figu e 5.31. Obse ed a e cons an s in he eac ion o sul a e ion adical and y osine as a unc ion o y osine concen a ions a di e en pH alues. [K2S2O8] = 0.100 M, ■: changing pH ([H2SO4] om 1.5 o 15 mM), ●: pH = 2.72 (measu ed); ▲: pH = 7.14 (0.1 M phospha e bu e ), V = 3.00 cm3, T = 25 °C,  = 450 nm. Solid lines ep esen he linea i o he measu ed da a poin s. The blue line has a slope o (1.4 ± 0.1)  109 M1 s1 and an in e cep o (0.4 ± 0.3)  106 s1. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 56 5.2.9. Reac ion o sul a e ion adical wi h S(IV) In he nex phase o ou s udies, we in ended o examine he eac ion o sul a e ion adical wi h sul u oxy anions (SxOyz-), p e e ably wi h he ones con aining sul u in he oxida ion s a e o +4. Du ing he au oxida ion cycles o S(IV) (see Figu e 5.8), SO3 and SO5 a e p oduced as chain ca ie s along wi h he sul a e ion adical. We sough independen me hods o s udy he eac ions o hese species. We pos ula ed he exis ence o eac ion (): SO4 + SO32SO42 + SO3  To check his possible p ocess, we eac ed sul a e ion adical wi h sul i e solu ions. The echnique was simila o he one applied p e iously: sul a e ion adical was gene a ed by he pho olysis o po assium pe sul a e. Sul u (IV) has an abso p ion peak a 275 nm (see Figu e 5.1) in acidic medium. The e o e, K2S2O8 has o be in high excess in o de o abso b he majo i y o ligh om he inciden (lase ) pulse. In ou sys ems, K2S2O8 is usually p esen in 0.1 M concen a ion in he samples, whe eas he eac an species a e applied in he millimola concen a ion ange, K2S2O8 is in 10-100- old excess. On he o he hand, he eac an species has o be in excess o e he gene a ed sul a e ion adical, because pseudo- i s o de app oach is applied in he da a p ocessing. The pseudo- i s o de condi ions a e a o able in ee adical eac ions because he ac ual concen a ions o he ansien species a e no equi ed. The hi d equi emen is ha he eac an has o be applied in an app op ia e amoun in o de o each decen signal- o-noise a io in he obse ed kine ic cu es. Some imes o he ac o s a e o be conside ed as well, such as he solubili y o he compound, possible ligh sensi i i y, he mal eac ion wi h K2S2O8, e c. Because o he abo e men ioned ac o s, he op imal concen a ion ange should be he subjec o ca e ul conside a ion. Sodium py osul i e o me abisul i e (Na2S2O5) was used as a sou ce o sul i e ions, simila ly o he au oxida ion s udies o S(IV) p esen ed in he Sec ion 5.1. The e ec o pH along wi h dissol ed oxygen concen a ion was examined on he a e cons an o () and he eac ion was ollowed a 450 nm. Signi ican di e ence was obse ed when he medium was changed om neu al o s ongly acidic (Figu e 5.32). É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 57 Figu e 5.32. Pseudo- i s o de a e cons an s as a unc ion o S(IV) concen a ion in he eac ion o sul a e ion adical and S(IV). [K2S2O8] = 0.100 M, pH = 6.98 (0.1 M phospha e bu e , ■) o 1.16 (0.045 M H2SO4, ●), V = 3.00 cm3, T = 25 °C,  = 450 nm. The solid lines ep esen he linea i o he measu ed da a poin s. The black line has a slope o (1.3 ± 0.01)  109 M1s1 and i s in e cep wi h he e ical axis is a (0.8 ± 0.1) s1whe eas he slope o he ed line, hus he espec ing second o de a e cons an is (0.4 ± 0.01)  109 M1s1. The nega i e in e cep a neu al pH shown in Figu e 5.32 implies ha he dissol ed oxygen p esen in he samples migh oxidize a po ion o he S(IV), hus he indica ed alues a e o e es ima ions o he ac ual concen a ions ha pa icipa e in eac ion (). The e o e, he e ec o dissol ed oxygen was es ed by bubbling a gon in he solu ions and epea ing he expe imen s wi h de-ae a ed samples, in neu al and acidic medium as well (Figu e 5.33 and Figu e 5.34). The nega i e in e cep becomes insigni ican when a gon is in oduced, con i ming he con ibu ion o dissol ed oxygen o he oxida ion p ocess. Figu e 5.34 would also sugges ha he concen a ion o dissol ed oxygen ac ually has an in luence on he a e cons an unde acidic condi ions, i only he ed and he blue da a se ies we e aken in o accoun (since he pH alues a e e y close). Howe e , conside ing he black poin s as well, measu ed in ai sa u a ed solu ions such as he ed one, he mo e p obable explana ion is ha he a e cons an is highly sensi i e o pH, and dissol ed oxygen has li le e ec compa ed o he acidi y o he medium. The pH dependence can be obse ed in de-ae a ed samples, oo (Figu e 5.35). É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 64 abso p ion coe icien s a e mo e di icul o de e mine, which leads o a high le el o unce ain y in he  alues106 (see Sec ion 2.3). S ill, we can make a ough es ima ion o [SO4]0, whe e = 0 ep esen s he ime poin o he lase exci a ion (no e ha he exci a ion also pulse has a non-ze o leng h in ime, ~20 ns bu o ou pu poses i can be handled as a poin ). A second o de i o he ecombina ion cu es gi es an idea o he ini ial concen a ion, using  = 1600 M1 cm1 published by McEl oy118 and l = 0.5 cm as an op ical pa h leng h. Fi ing o pu e second o de ecombina ion cu es o sul a e ion adical ga e a alue o 2 104 M, which is compa able o he applied concen a ion o iodide ion. This ac aised some ques ions: why a e he de ec ed cu es exponen ial and why does he dependence on he concen a ion o iodide ion gi e a easonably good s aigh line? Re u ning o he abo e men ioned conside a ions (i-i ), he concen a ion o SO4 is a local alue, i applies o he loca ion o he de ec ion ha is limi ed o a ac ional olume in he cu e e. The o al olume is 3.00 cm3, so i he a e age concen a ion o SO4 is calcula ed o e he o al olume, a much lowe alue is ob ained. Addi ionally, while SO4 goes h ough a apid decay, iodide ion can be pe manen ly eplenished by di usion om ou side o he eac ion space, hus main aining he high excess o iodide o e sul a e ion adical. In he ollowing pa ag aphs, an a emp will be made o analyze he e ec o di usion in he sul a e ion adical–iodide ion sys em and o explo e he e ec o spa ial inhomogenei y on he obse ed a e cons an s. 5.3.2. Reac ion-di usion equa ion using cylind ical coo dina es A gene al eac ion-di usion (he eina e e e ed o as: RD) equa ion has a closed o m shown in (51): )( cRcD c   (51) He e, c is he ec o o concen a ions, D is he ma ix o he di usion coe icien s,  is he Laplace ope a o o Laplacian and R is a complex ope a o embedding all o he ongoing eac ions in he sys em. Dc is called he di usion e m, R(c) o ms he eac ion e m. Inspi ed by he seminal wo k o Alan Tu ing on mo phogenesis (shape o ma ion in biological sys ems),182 eac ion-di usion sys ems s and in he main ocus o esea ch on chemical and biological pa e n o ma ion183-185 as well as o he nonlinea dynamic phenomena such as oscilla ion, chaos o sel -o ganizing sys ems.186,187 É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 65 Eq. (51) is a second o de , semilinea , pa abolic pa ial di e en ial equa ion (PDE) sys em, in which each chemical en i ies is ep esen ed by a ime-dependen a iable.149,188 The solu ion o eq. (51) is a ec o o c( ) unc ions, whe e each concen a ion is explici ly exp essed as a unc ion o ime. The Laplacian () is a di e en ial ope a o wi h a scala alue ha gi es he di e gence o he g adien o a eal alued unc ion. Fo an (x,y,z) unc ion in he h ee-dimensional Euclidean space, 2 2 2 2 2 2 2 zyx          (52) whe e  is he g adien o ,                z , y , x (53) Eq. (52) desc ibes he Laplacian in Ca esian coo dina es, bu i is a o able o ou pu poses o ans o m he p oblem in o a cylind ical coo dina e sys em, since he eac ion space is a ci cula cylinde (see Sec ion 5.3.4). Figu e 5.38 shows he ans o ma ion om Ca esian o cylind ical coo dina es, and eq. (54) is he o m o Laplacian in he new coo dina e sys em. 2 2 22 2 2 211             x (54) The angula ( ou h) e m in eq. (54) can be neglec ed in ou model because o he cylind ical symme y. Thus, applying eq. (54) in eq. (51) yields: )( 1 2 2 2 2cR ccc D c                    x (55) Figu e 5.38. T ans o ma ion om Ca esian o cylind ical coo dina es. x = x, y = ∙ cos(  ) and z = ∙ sin(  ). É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 66 In he p esen case, wo concen a ion unc ions a e o be calcula ed, )( 4 SO x, , c  and )( Ix, , c  , he objec i e is o ga he an insigh o he spa ial dis ibu ion o he eac an s a each pa icula ime poin . 5.3.3. App oxima ion o he pa ial de i a i es In ini esimal quan i ies canno be handled compu a ionally, pa ial de i a i es in ol ed in eq. (55) need o be app oxima ed. T adi ionally, de i a i es a e app oxima ed by ini e di e ences, ha is, he slope o he angen a a ce ain poin on he g aph is close o he slope o a secan lying on wo nea by g aph poin s (Figu e 5.39).189,190 Figu e 5.39. Geome ic in e p e a ion o he ini e di e ences app oxima ion. Gi en wi h o mulae:   Δx ΔxxuΔxxu Δx Δxxuxu Δx xuΔxxu xu' iiiiii i2 )()()()()()(       (56) The le side is he de i a i e o he u(x) unc ion a poin xi,  x is a small a bi a y dis ance on he x axis and he e ms a e called o wa d, backwa d and cen al di e ences, espec i ely (i is easy o see ha he cen al di e ence is he a e age o he o wa d and he backwa d ones). I is e y common in nume ical p oblems (e.g. in eg a ion o unc ions o sea ching o oo s o polynomials) ha an app op ia e g id (also called mesh) is de ined on he domain o he unc ion, alues o he unc ion a e known a he g id poin s and u he alues a e calcula ed using hese p e iously known alues. Equidis an g ids (whe e  x is cons an ) a e use ul and p ac ical o many cases, bu he g id poin s ha e o be chosen cau iously a o he imes o minimize he e o o he app oxima ion ( he di e ence be ween he eal and he calcula ed É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 67 alues). Using such a me hod, complica ed di e en ial and in eg al issues can be disc e ized and ende ed compu a ionally sol able. Highe o de de i a i es can be simila ly es ima ed by ini e di e ences, e.g. second o de cen al di e ence is gi en in eq. (57):   2 )()(2)( Δx ΔxxuxuΔxxu xu" iii i   (57) I is con enien o ew i e eqs. (56) and (57) in o a closed o m using ma ix mul iplica ion. Assuming an equidis an one-dimensional g id wi h an in e al leng h o h, he cen al di e ence in eq. (56) akes he ollowing o m:                  1 1 101 2 1 xi xi xi i u u u h xu' (58) He e, uxi deno es he alue o u a g id poin xi, and xi+1 = xi + h, xi1 = xi  h. The second o de di e ence can be simila ly ep esen ed wi h ma ix mul iplica ion, by                  1 1 121 1 xi xi xi i u u u h xu" (59) Eqs. (58) and (59) a e easily applicable o mul i a ia e unc ions. Ou model equi es a wo dimensional g id o esol e he x and ex en s o he eac ion space. Acco ding o eq. (55), 2 2c x  ,  c and 2 2c   need o be app oxima ed. Applying eqs. (56) and (57) in eq. (55) gi es: 2 11 11 2 11 2 2 2 2 )()(2)( )()( 1 )()(2)( 1 Δ , xc, xc, xc Δ , xc, xc Δx , xc, xc, xc c c x c jijiji jijijijiji i,j                          (60) He e i and j a e he indices o he g id ep esen ing x and , axes and c can ei he be c(SO4) o c(I). The sum o eqs. (61)-(63) yields eq. (60) i eqs. (58) and (59) a e used in a wo- dimensional a angemen . É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 68 2 1 1 2 21 )( )( )( 2100 1 121 1 0012 x , xc , xc , xc x c ji ji ji i j,i                                                             (61) , xc, xc, xc c i jijiji j,i 11 010 11 0 11 010 )()()( 111                                                          (62) 2 11 2 21 210 11 2 11 012 )()()( , xc, xc, xc ci jijiji j,i                                                           (63) The limi a ion o his me hod (i.e. he p oduc ion o he di e ences by ma ix mul iplica ion using coe icien ma ices) a ises om he = 0 case (eq. (62) con ains in he denomina o ), which is one o he bounda y condi ions o sol ing eq. (55). Physically, = 0 is a he cen al axis o he cylinde , no di usion occu s along his axis as a consequence o he cylind ical symme y. This condi ion canno be handled in he ame o he o mula ion abo e, an al e na i e ea men o he di usion e m is gi en in he ollowing sec ions. 5.3.4. Model o he eac ion space Ou desc ip ion o he eac ion space is a modi ied e sion o a model p o ided by Cassidy and Long (see Sec ion 2.4).141 These au ho s published a wo-dimensional model o measu ing pseudo- i s o de a e cons an s in lase lash pho olysis expe imen s in collinea a angemen , whe e he lase beam and he analyzing beam a e pa allel o each o he . In ou calcula ions, we assumed c ossed o pe pendicula a angemen in acco dance based on he expe imen al se up. Figu e 5.40 shows he geome ic model applied o ep esen he physical eac ion space. j  j  j  É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 69 Figu e 5.40. Model geome y o modelling he ole o di usion in lase lash pho olysis expe imen s. See explana ion o he labels in he ex below. The a ow labelled ‘hν’ ep esen s he lase beam and he blue a ow is he analyzing beam ha is used o ollow he concen a ion o he ansien species. Adap ing he common no a ions o Bee ’s law, I0 is he in ensi y o he en e ing ligh beam and I is he in ensi y o he lea ing beam. x and a e he labels o he spa ial axes, L is he pa h leng h o he cu e e in he di ec ion o he lase beam. The c oss sec ion o he lase beam is conside ed o be ci cula wi h 0 adius, and he o igin is ixed o he cen e o his ci cle a he en e ing poin o he lase . The shading e e s o he dec easing concen a ion o he ansien species along he lase beam. Sul a e ion adical is gene a ed by he lase pulse along he x axis, adially om he o igin wi hin 0, hus o ming a cylinde -shaped olume. An ex e nal adius is de ined ( ex, Figu e 5.41) a ound his objec , di usion o bo h sul a e ion adical and iodide ions is allowed om his ou e shell o he in e nal cylinde and ice e sa. Figu e 5.41. C oss sec ion o he eac ion space, app oxima ed by he uni y o an inne ( 0) and ou e ( ex) cylinde . É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 70 5.3.5. Disc e e andom walk model o di usion Acco ding o Sec ion 5.3.4., he eac ion o sul a e ion adical and iodide ion akes place in a cylind ical space, su ounded by an ex e nal ube which is accessible o he di usi e mo ion o he pa icles. In o de o calcula e he spa ial dis ibu ion o each eac an , he eac ion space (including he ou e shell) is di ided in o small olume uni s ha a e shaped like cylinde ings (Figu e 5.42.). Figu e 5.42. Shape o he olume uni s. This kind o esolu ion in o elemen a y olumes o cells eplaces he in e p e a ion in 5.3.3, whe e a wo dimensional g id was in oduced on he x and axes. This model is concep ually di e en , in a sense ha ins ead o app oxima ing each pa ial de i a i es in eq. (55) indi idually, di usion in each olume uni is ea ed as a ma e exchange wi h he neighbo ing cells. The numbe o pa icles in a ce ain cell in a gi en ime in e al changes ia wo ways: species can a i e om he nea by cells and o he s can lea e he uni o en e hose adjacen cells. The e o e, he change o concen a ion in he cell will be he esul an o he ou low and he in low ia di usion. I is impo an o no e ha only he di usion e m is conside ed a his poin , he eac ion e m is in oduced a a la e s age. An a bi a y olume uni is in jux aposi ion wi h ou o he ones, wo in axial, wo in adial di ec ions. In he x di ec ion, hey o m a shape like a longe ube, whe eas in he adial dimension, he smalle ones a e embedded in o he bigge ones. The nea by olume uni s ha e common ‘walls’, h ough which di usion akes place. In acco dance wi h Fick’s 1s law, he low a e o he componen s be ween wo chosen uni s is p opo ional o he common su ace and he concen a ion g adien .56 Reac an s a e only allowed o mo e un il hey each he bo de s o he eac ion space (0   ex and 0  x  L), he e is no lux o ma e on he bounda ies. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 71 Le ’s ake a cylinde ing wi h an inne adius o , an ou e adius o + d and a heigh o dx. Fo he sake o simplici y, we can assume ha d = dx = 1. The su ace o such an objec consis s o ou pa s (see Table 7), wo ci cle ings o annulus o equal a ea, an ou e side and an inne side, bo h o which ha e he shape o a cu ed ec angula . Table 7. Su ace a ea o he pa s o a cylinde ing wi h a g id size o d = dx =1 ou e adius = Su ace a ea F ac ion o he o al a ea Uppe annulus     π π π 121 2 2 4 1 48 12    Lowe annulus     π π π 121 2 2 4 1 48 12    Ou e su ace π2 48 2  Inne su ace π )12(  48 22   To al π )48(  1 Clea ly, he inne su ace o his uni is he ou e su ace o he one inside i and e e sely, i s ou e su ace is equal o he inne su ace o he nex one wi h inc eased adius. The olume o he desc ibed objec is: V = 2   ( 1)2  = (2 1)  (64) The olumes o i s neighbo ing cells a e (2 1)  (uppe and lowe ; x±1, ), (2 +1)  (ou side; x, +1) and (2 3)  (inside; x, 1). As s a ed be o e, he di usion e m can be decomposed in o ou low and in low om and in o each pa icula ly olume uni . The ou low e m is qui e s aigh o wa d o demons a e. I is assumed ha all pa icles lea e he cell, a each su ace pa acco ding o i s a io o he o al su ace (Table 7, column 3). In a gene al olume uni , whe e he ac ual concen a ion is c(x, ), he scheme o he di usion is shown in Figu e 5.43. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 72 Figu e 5.43. Exchange o ma e in a olume uni o gene al posi ion. The uni shown has an inne adius o  1 and an ou e adius o , ha ing an index o n in he adial di ec ion ( = 0 is he i s one, whe e n = 1). The a ios gi en in he igu e ha e o be mul iplied by he di usion coe icien . Blue a ows ep esen he ou low om he cell, igh a ows co espond o he in low om he neighbo ing uni s. Figu e 5.43 e e s o a cell in gene al posi ion, i.e. i is loca ed inside he eac ion space, i does no each any o he bounda ies (  0;  ex; x  0; x  L). When he cell has one o wo bo de su aces, hen i is assumed ha he ac ion o he pa icles co esponding o ha su ace a ea do no lea e he cell. The in low pa is u he di ided in o he in low om he x and neighbo s. In he x di ec ion, cells ha e he same olume (since is cons an ). The e o e, he numbe o esiding pa icles has he same a io as hei concen a ions. Eq. (65) gi es he x in low in o he c(x, ) uni .                    ,x ,x ,x c c c , xc, xc 1 1 4 1 0 4 1 )1( 4 1 )1( 4 1 (65) In he case o he adial in low, no only he common su ace, bu he a io o he olumes is conside ed in he ollowing mul iplica ion: adial in low = n n n, o n,ou n n n, o n,in V V A A x, c V V A A x, c 1 1 1 1 1 1)1()1(       (66) Subs i u ing he known olumes and su aces in o eq. (66) gi es: 12 32 128 22 )1( 12 12 48 2 )1(         n n n n x, c n n n n x, c (67) É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 73 Upon simpli ica ion, he ollowing equa ion is ob ained:                   )( 0 )( 48 22 )1( 48 2 )1( 11 u ccc n n x, c n n x, c ,x ,x ,x (68) He e ( ) and u( ) a e he coe icien s desc ibing he in low om he inne and he ou e cells, espec i ely. Sepa a e ma ices we e de ined o coe icien s con aining he x in low (DX), he in low (DR) and he ou low as well (DE). Using hese ma ices, he igh hand side o eq. (55), s ill wi hou he eac ion e m, can be econs i u ed as eq. (69) D∙(DXc + cDR + DE.c) (69) He e, ∙ is he egula mul iplica ion sign,  is he ma ix mul iplica ion and . is he elemen - wise mul iplica ion o ma ices. Ma ix mul iplica ion is sensi i e o he o de o he ac o s, and he ma ix dimensions ha e o ma ch o a alid ope a ion. 5.3.6. Nume ical in eg a ion Acco ding o he New on-Leibniz o mula, one o he undamen al heo ems o calculus, he de ini e in eg al o an u(x) uni a ia e unc ion be ween xi and xi+1 poin is gi en as   1 1)()()( i i ii x xdssu'xuxu (70) Eq. (70) is in he backg ound in he nume ical solu ions o kine ic di e en ial equa ions, whe e he independen a iable is ime and he dependen a iables a e concen a ions. Ou p e ious e o s we e a ge ed o gi e a easonable app oxima ion o he igh hand side o (55), i.e. he de i a i e o concen a ions wi h espec o ime. The nex s ep is o de ine how o ob ain he c( + h) concen a ions in he possession o he c( ) alues. De ini e in eg a ion is ano he ope a ion ha compu e s canno handle di ec ly (al hough symbolic so wa es such as Ma hema ica con ain nume ous p imi i e unc ions). A ple ho a o algo i hms exis o nume ical in eg a ion, he app oxima ion o de ini e in eg als be ween wo ime poin s (o wha e e is he independen a iable).191 The mos widely used algo i hm in chemical kine ics is he ou h-o de Runge-Ku a me hod (RK4),91 because i is ela i ely easy o code and i has high accu acy, gi en ha ime s ep leng h (h) is chosen co ec ly. Adap i e ime s epping is p ac ical in mos cases, whe e he s ep size g adually changes as he i e a ion p oceeds. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 80 o he apid na u e o he eac ion o sil e (I) and sul a e ion adical became a ailable by he applica ion o he lase lash pho olysis echnique. A newly acqui ed Applied Pho ophysics lase lash pho olysis (LFP) ins umen o nanosecond ime esolu ion allowed us o s udy he eac ions o he sul a e ion adical in a di ec manne . SO4 was gene a ed by he pho olysis o K2S2O8 by a 266 nm pulse and ollowed by i s abso p ion a 450 nm. The second o de a e cons an o i s eac ion wi h sil e (I) ion was de e mined unde pseudo- i s o de condi ions, he measu ed alue is (7.7 ± 0.5)  109 M1 s1 in s ongly acidic medium. This alue app oaches he di usion con olled limi , a i ming he ole o eac ion (19) in chain p opaga ion. Simila ly o he case o sil e (I), he second o de eac ions o sul a e ion adical wi h p e iously ecognized ca alys s o he au oxida ion o S(IV) we e s udied. Ra e cons an s o Ce(III) and iodide ions we e de e mined, as well as u he a e cons an s wi h halide ions, a ew biomolecules and S(IV). In he sul a e ion adicaliodide ion sys em, in e es ing kine ic beha io was obse ed. The eco ded kine ic cu es i ed o double exponen ial kine ics, and bo h i ed pa ame e s showed linea dependence on he concen a ion o iodide ion. One o he wo dependence unc ions wen h ough he o igin. The e o e, he espec i e a e cons an was assigned o eac ion (42). The o he line had a signi ican in e cep wi h he e ical axis, i was hus concluded o belong o he e e sible eac ion o iodide ion and iodine a om, p oducing iodide molecule anion (I2). This was sugges ed as a no el me hod o gene a ion iodine a oms and he equilib ium cons an o (43) was de e mined. Pseudo- i s o de beha io was obse ed in he sul a e ion adicaliodide ion sys em, e en hough he p e equisi e o pseudo- i s o de kine ics, he high excess o iodide ions, was no eached locally a he si e o obse a ion. The po en ial eplenishmen o iodide ions by di usion om ou side he eac ion space was examined by a nume ical model. The eac ion space was di ided in o uni olumes and an ou e adius was de ined inside which di usion o pa icles was allowed. The andom walk model o di usion was applied o simpli y he solu ion o he ope a i e pa ial di e en ial equa ion (PDE) sys em. Using a chemically concei able pa ame e se , i was shown ha o a a e cons an in he 109 M1 s1 o de o magni ude, di usion does no in luence he de e mina ion o he a e cons an wi hin he ime ame o he eac ion. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 81 7. Össze oglalás Ez az é ekezés köz e len oly a ása és kiegészí ése a ku a ócsopo unkban ko ábban lezajlo izsgála oknak a kén(IV) au ooxidációjának kine ikájá al és mechanizmusá al kapcsola osan. Ezek a ko ábbi munkák el á ák a Ce(III) és I ionok ka ali ikus sze epé alamin a Fe(II) ionok lehe séges ész é elé a o oiniciál au ooxidációs mechanizmusban. A kísé le ek so án diódaso os spek o o omé e alkalmaz ak a eakciók indí ásá a és kö e ésé e egya án .54,75-77 Az au ooxidációs olyama ok mechanizmusa gyökös lánc eakció, amelyben szul i -, szul á - és pe oxomonoszul á -iongyökök ( end e SO3, SO4 és SO5 a közös lánc i ők. Az e edmények az mu a ják, hogy a szul á iongyök (SO4) kiemel sze epe öl be a ka alízisben, ké éle okból. A szul á iongyök eakciója a ka alizá o al on os lánc i ő lépés alamin a pe oxodiszul á ionoka e melő másod endű ekombinációja öbbnyi e az egye len jelen ős lánclezá ó lépés. Az au ooxidáció mechanizmusának mélyebb megé ése é dekében célul űz ük ki a mechanizmus elépí ő ész endsze ek ügge len izsgála á . Egy ilyen ész endsze a S(IV) eakciója a lánczá ó lépésben képződő pe oxodiszul á -ionnal, amely élhe ően szinp opo ciós olyama ban szul á iongyökö e mel. Ko ábbi e edmények alapján az emlí e eakció sa as közegben, ka alizá o á ollé ében endkí ül lassú. Az S2O82 ionok edoxi eakciói kine ikai gá lás mia öbbnyi e igen lassúak a nagy edoxipo enciál ellené e is. Az ezüs ionok a pe oxodiszul á ion oxidációs eakcióinak jól isme ka alizá o ai, mi el az iniciáló lépés e mékei a szul á ion melle igen eak í észecskék, Ag(II) és szul á iongyök.43-45 Vizsgála aink so án ezé ezüs -ni á o ad unk a S(IV)–oxigén–pe oxodiszul á eakcióelegyekhez, e ősen sa as közegben. Előkísé le ek alapján a S(IV) au ooxidációja ily módon ha ékonyan iniciálha ó. A o okémiai mellék eakció kizá ása é dekében a diódaso os spek o o omé e alkalmazásá kísé le eink so án kizá uk, no mál spek o o omé e segí ségé el kö e ük a eakció . Ez a dolgoza észle esen isme e i a S(IV) ezüs ionok ál al ka alizál au ooxidációjának kine ikai izsgála á , pe oxodiszul á -ion, min ko-ka alizá o jelenlé ében. A kísé le ekből le on mechanisz ikus kö e kez e ések ugyancsak a dolgoza á gyá képezik. Kilenc lépésből álló mechanizmus ja asol unk (Scheme 1), alamin egy némileg össze e , ugyanakko kine ikailag megalapozo sebességi egyenle e eze ünk le (38) a kine ikai ada ok é elmezésé e. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 82 A szul á iongyök és az ezüs ionok közö i másod endű eakció (Scheme 1; R2) az ezüs ionok ál al ka alizál au ooxidáció ál alunk ja asol mechanizmusának egyik lánc i ő lépése. A sebességi egyenle le eze ése so án a hosszú lánco el é elező megközelí és alkalmaz uk, amely el é elezi, hogy a lánc i ő lépések sebessége nagyobb, min a láncindí ó és a lánclezá ó lépéseké (mi el másképp a lánc eakció nem udna lezajlani), ille e az is, hogy a lánc i ő lépések sebessége megegyezik. Annak igazolásá , hogy a szul á iongyök (SO4) és az Ag+ ionok közö igen gyo s eakció já szódik le, léze es illanó ény- o olízis módsze alkalmazása e e lehe ő é. A anszékünkön nem égiben meg ásá ol Applied Pho ophysics nanoszekundum idő elbon ású illanó ény- o olízis készülék segí ségé el köz e lenül ud uk anulmányozni a szul á iongyök eakcióinak kine ikájá . Az SO4 gyököke K2S2O8 olda o olízisé el állí o uk elő 266 nm hullámhosszúságú léze impulzus segí ségé el. A eakcióka 450 nm-en, a szul á iongyök elnyelési maximumán kö e ük. Az ezüs ionnal aló eakció pszeudo-első endű kö ülmények közö izsgál uk, és a másod endű sebességi állandó mé é éke (7.7 ± 0.5)  109 M1s1 ol , e ősen sa as kö ülmények közö . Ez az é ék megközelí i a di úzió kon ollál eakciók sebességi állandójának maximális é éké , mege ősí e a (19) eakció lánc i ő lépéskén aló ész é elé a mechanizmusban. Az ezüs ionokhoz hasonlóan anulmányoz uk a szul á iongyök másod endű eakciói az au ooxidáció ko ábban megisme ka alizá o ai al is. Megha á oz uk a másod endű sebességi állandók é ékei Ce(III) ionokkal és I ionokkal, alamin egyéb halogenidionokkal, néhány biomolekulá al és S(IV) a almú észecskékkel. A szul á iongyök–jodidion endsze ben é dekes kine ikai iselkedés igyelhe ünk meg. A eakció 340 nm-en, a jód molekulaion (I2) elnyelési maximumán kö e ük és a el e kine ikai gö béke ké exponenciális gö be összegé el illesz e ük. Mindké illesz e sebességi állandó ípusú pa amé e lineá is üggés mu a o a jodidionok koncen ációjá ól. Az egyik lineá is ügg ény á men az o igón, így ez az állandó hozzá endel ük a (42) eakcióhoz. A másik ügg énynek jelen ős üggőleges engelyme sze e ol , így ebből a ügg ényből megha á oz uk a (43) eakció oda- és isszai ányú sebességi állandójá , alamin a olyama o jellemző egyensúlyi állandó . Ezzel új módsze alál unk a jóda omok előállí ásá a. A szul á iongyök–jodidion endsze ben pszeudo-első endű iselkedés apasz al unk, noha ennek el é ele, a jodidionok nagy eleslege lokálisan nem eljesül a eakcióelegyben, mi el a szul á iongyök egy kis é oga észben képződik a léze sugá haladási i ánya ál al megha á ozo módon. Ma ema ikai modell eze ünk be annak izsgála á a, hogy an-e mód É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 83 a jodidionok di úzió ál ali pó lásá a a eakció é en kí üli é észből és ezál al a pszeudo- első endű kine ikához szükséges koncen ációa ány isszaállí ásá a. A henge alakú eakció e e kis é oga elemek e bon o uk és megha á oz unk egy külső suga a , amelyen belül ől megengede a észecskék di úziója a eakció é be és onnan ki elé. A di úzió éle len bolyongás modelljé alkalmaz uk a endsze leí ó pa ciális di e enciál egyenle endsze megoldásának egysze űsí ésé e. Egy kémiailag eális pa amé e készle használa á al az alál uk, hogy 109 M1 s1 nagyság endű másod endű sebességi állandó ese én a di úzió nem be olyásolja a pszeudo-első endű sebességi állandó megha á ozásá , a eakció időskáláján nincs megha á ozó sze epe. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 84 8. Re e ences 1. G eenwood, N. N.; Ea nshaw, A. Chemis y o he Elemen s, 2nd ed.; Bu e wo h- Heinemann: Ox o d, U.K., 1997. 2. Wikipedia - Goldschmid classi ica ion; h ps://en.wikipedia.o g/wiki/Goldschmid _classi ica ion; accessed: 29 Dec 2015 3. Goldschmid , V. M., J. Chem. Soc. 1937, 655-673. 4. The In e ne Classics A chi e - The Odyssey by Home ; h p://classics.mi .edu/Home /odyssey.12.xii.h ml; accessed: 8 Dec 2015 5. Len e, G., Egye emi Me eo ológiai Füze ek 2014, 25, 57-62. 6. Michie, C. A.; Langslow, D. R., B . Med. J. 1988, 297, 1697-1699. 7. Edi o ial, Na . Chem. 2009, 1, 333. 8. Six Common Ai Pollu an s; h p://www3.epa.go /ai quali y/u banai /; accessed: 30 Dec 2015 9. Bannenbe g, G.; A zo i, L.; Xue, J.; Aube son, S.; Kimland, M.; Ry eld , A.; Lundbe g, J. M.; Moldeus, P., Respi a ion; in e na ional e iew o ho acic diseases 1994, 61, 130- 137. 10. Sunye , J.; A kinson, R.; Balles e , F.; Le Te e, A.; Ay es, J. G.; Fo as ie e, F.; Fo sbe g, B.; Vonk, J. M.; Bisan i, L.; Ande son, R. H.; Schwa z, J.; Ka souyanni, K.; s udy, A., Occup. En i on. Med. 2003, 60, e2. 11. Day, J. J.; Yang, Z.; Chen, W.; Pacheco, A.; Xian, M., ACS Chem. Biol. 2016. 12. Huie, R. E.; Ne a, P., A mos. En i on. 1987, 21, 1743-1747. 13. G aedel, T. E.; C u zen, P. J., Sci. Am. 1989, 58-68. 14. Schwa z, S. E., Science 1989, 243, 753-763. 15. Rose, J., En i on. Sci. Technol. 1993, 27, 2627. 16. Lynch, J. A.; Bowe sox, V. C.; G imm, J. W., En i on. Sci. Technol. 2000, 34, 940-949. 17. Penke , S. A.; Jones, B.; B ice, K.; Eggle on, A. E., A mos. En i on. 2007, 41, 154-168. 18. Hewi , C. N.; Jackson, A. V. A mosphe ic science o en i onmen al scien is s; John Wiley & Sons, 2009. 19. Sands öm, M.; Jalileh and, F.; Pe sson, I.; Gelius, U.; F ank, P.; Hall-Ro h, I., Na u e 2002, 415, 893-897. 20. Cha lson, R. J.; Vale o, F. P. J.; Sein eld, J. H., Science 2005, 308, 806-807. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 85 21. C u zen, P. J., Clim. Change 2006, 77, 211-220. 22. Pie ce, J. R.; Weisens ein, D. K.; Heckendo n, P.; Pe e , T.; Kei h, D. W., Geophys. Res. Le . 2010, 37. 23. He mann, H., Phys. Chem. Chem. Phys. 2007, 9, 3935-3964. 24. An oniou, M. G.; A mah, A.; Dionysiou, D. D., Applied Ca alysis B: En i onmen al 2010, 96, 290-298. 25. Gligo o ski, S.; S ekowski, R.; Ba ba i, S.; Vione, D., Chem. Re . 2015, 115, 13051- 13092. 26. He mann, H.; Reese, A.; Zelh e , R., J. Mol. S uc . 1995, 348, 183-186. 27. He mann, H., Chem. Re . 2003, 103, 4691-4716. 28. G gić, I.; Podk ajšek, B.; Ba zaghi, P.; He mann, H., A mos. En i on. 2007, 41, 9187- 9194. 29. He mann, H.; Ho mann, D.; Schae e , T.; B äue , P.; Tilgne , A., ChemPhysChem 2010, 11, 3796-3822. 30. Deng, Y.; Ezyske, C. M., Wa e Res. 2011, 45, 6189-6194. 31. He, X.; A mah, A.; O'Shea, K. E.; Dionysiou, D. D., Wa e Res. 2014, 63, 168-178. 32. Lu ze, H. V.; Bi che , S.; Rapp, I.; Ke lin, N.; Bakkou , R.; Geisle , M.; on Sonn ag, C.; Schmid , T. C., En i on. Sci. Technol. 2015, 49, 1673-1680. 33. Lu ze, H. V.; Ke lin, N.; Schmid , T. C., Wa e Res. 2015, 72, 349-360. 34. Wu, Y.; Bianco, A.; B igan e, M.; Dong, W.; De Sain e-Clai e, P.; Hanna, K.; Mailho , G., En i on. Sci. Technol. 2015. 35. Zhou, D.; Zhang, H.; Chen, L., J. Chem. Technol. Bio echnol. 2015, 90, 775-779. 36. Vellanki, B. P.; Ba chelo , B.; Abdel-Wahab, A., En i on. Eng. Sci. 2013, 30, 264-271. 37. Gau, B. C.; Chen, H.; Zhang, Y.; G oss, M. L., Anal. Chem. 2010, 82, 7821-7827. 38. Handbook o Chemis y and Physics; 93 d ed.; Haynes, W. M.; CRC P ess, 2012-2013. 39. Das, T. N.; Huie, R. E.; Ne a, P., J. Phys. Chem. A 1999, 103, 3581-3588. 40. B and , C.; an Eldik, R., Chem. Re . 1995, 95, 119-190. 41. Bellé , G.; Bá ki, G.; Len e, G.; Fábián, I., J. Coo d. Chem. 2010, 63, 2586-2597. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 86 42. Bellé , G.; Len e, G.; Fábián, I., Ino g. Chem. 2010, 49, 3968-3970. 43. House, D. A., Chem. Re . 1962, 62, 185-203. 44. Kalb, A. J.; Allen, T. L., J. Am. Chem. Soc. 1964, 86, 5107-5112. 45. Kimu a, M.; Kawaji i, T.; Tanida, M., J. Chem. Soc., Dal on T ans. 1980, 726-730. 46. Len e, G.; Fábián, I., Ino g. Chem. 2004, 43, 4019-4025. 47. Takano, B., Science 1987, 235, 1633-1635. 48. Oh, S. R.; Kim, J. K.; Lee, M. J.; Choi, K., En i on. Toxicol. 2008, 23, 211-217. 49. C eu z, C.; Su in, N., P oc. Na l. Acad. Sci. U. S. A. 1973, 70, 1701-1703. 50. Lambe h, D. O.; Palme , G., J. Biol. Chem. 1973, 248, 6095-6103. 51. ChemEnginee ing; h ps://chemenginee ing.wikispaces.com/Claus+p ocess; accessed: 4 Sep 2015 52. Nagy, P.; Win e bou n, C. C. In Ad ances in Molecula Toxicology; Else ie : Ne he lands, 2010; Vol. 4, p 183-222. 53. an Woe den, H. F., Chem. Re . 1963, 63, 557-571. 54. Connick, R. E.; Tam, T. M.; Von Deus e , E., Ino g. Chem. 1982, 21, 103-107. 55. Ke ezsi, I., Fo okémiai jelenségek a szul i ion edoxi eakcióiban, PhD Thesis, Uni e si y o Deb ecen, Deb ecen, Hunga y, 2006. and e e ences he ein 56. A kins, P. W. Physical Chemis y; 6 h ed.; Ox o d Uni e si y P ess: Ox o d, U.K., 1998. 57. Ba cza, L.; Bu á i, A. A minőségi kémiai analízis alapjai; Medicina Kiadó: Budapes , Hunga y, 1997. 58. K a , J.; an Eldik, R., J. Chem. Soc., Chem. Comm. 1989, 790-792. 59. K a , J.; an Eldik, R., Ino g. Chem. 1989, 28, 2306-2312. 60. K a , J.; an Eldik, R., Ino g. Chem. 1989, 28, 2297-2305. 61. K a , J.; an Eldik, R., A mos. En i on. 1989, 23, 2709-2713. 62. B and , C.; Fábián, I.; an Eldik, R., Ino g. Chem. 1994, 33, 687-701. 63. B and , C.; an Eldik, R., T ansi . Me al Chem. 1998, 23, 667-675. 64. Fábián, I.; Cso dás, V., Ad . Ino g. Chem. 2003, 54, 395-461. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 87 65. Be glund, J.; Elding, L. I., A mos. En i on. 1995, 29, 1379-1391. 66. Be glund, J.; Elding, L. I., Ino g. Chem. 1995, 34, 513-519. 67. B and , C.; Elding, L. I., A mos. En i on. 1998, 32, 797-800. 68. F onaeus, S.; Be glund, J.; Elding, L. I., Ino g. Chem. 1998, 37, 4939-4944. 69. Alexande , B.; Pa k, R. J.; Jacob, D. J.; Gong, S., J. Geophys. Res.: A mos. 2009, 114, D02309. 70. Alipazaga, M. V.; Mo eno, R. G.; Lina es, E.; Medei os, M. H.; Coiche , N., Dal on T ans. 2008, 5636-5644. 71. Mo eno, R. G.; Alipazaga, M. V.; Medei os, M. H.; Coiche , N., Dal on T ans. 2005, 1101-1107. 72. Anas , J. M.; Ma ge um, D. W., Ino g. Chem. 1981, 20, 2319-2326. 73. Lepen sio is, V.; Domagala, J.; G gic, I.; an Eldik, R.; Mulle , J. G.; Bu ows, C. J., Ino g. Chem. 1999, 38, 3500-3505. 74. Mulle , J. G.; Hicke son, R. P.; Pe ez, R. J.; Bu ows, C. J., J. Am. Chem. Soc. 1997, 119, 1501-1506. 75. Wie ze bin, K.; Mulle , J. G.; Jame on, R. A.; P a iel, G.; Be nadou, J.; Meunie , B.; Bu ows, C. J., Ino g. Chem. 1999, 38, 4123-4127. 76. on Sonn ag, C. F ee- adical-induced DNA damage and i s epai ; Sp inge , 2006. 77. Ke ezsi, I.; Len e, G.; Fábián, I., J. Am. Chem. Soc. 2005, 127, 4785-4793. 78. Ke ezsi, I.; Len e, G.; Fábián, I., Dal on T ans 2006, 955-960. 79. Ke ezsi, I.; Len e, G.; Fábián, I., Ino g. Chem. 2007, 46, 4230-4238. 80. Bäcks öm, H. L., J. Am. Chem. Soc. 1927, 49, 1460-1472. 81. Bäcks öm, H. L., T ans. Fa aday Soc. 1928, 24, 601-605. 82. Alyea, H. N.; Bäcks öm, H. L., J. Am. Chem. Soc. 1929, 51, 90-109. 83. Hayon, E.; T einin, A.; Wil , J., J. Am. Chem. Soc. 1972, 94, 47-57. 84. Huie, R. E. In Fossil Fuels U iliza ion - En i onmen al conce ns; ACS: ACS Symposium Se ies, 1986; Vol. 319, p 284-292. 85. Bux on, G.; McGowan, S.; Salmon, G.; Williams, J.; Wood, N., A mos. En i on. 1996, 30, 2483-2493. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 88 86. Bensasson, R.; Land, E.; T usco , T. Flash pho olysis and pulse adiolysis: con ibu ions o he chemis y o biology and medicine; Else ie , 2013. 87. The Nobel P ize in Chemis y 1967. Nobelp ize.o g. Nobel Media AB 2014.; h p://www.nobelp ize.o g/nobel_p izes/chemis y/lau ea es/1967/; accessed: 5 Sep 2015 88. The Pho ochemis y Po al; h ps://pho ochemis y.wo dp ess.com/2009/09/21/o igins- o - lash-pho olysis-geo ge-po e /; accessed: 6 Dec 2015 89. No ish, R. G. W.; Po e , G., Na u e 1949, 164, 658. 90. S ehlow, H. Rapid eac ions in solu ion; VCH Weinheim, 1992. 91. Espenson, J. H. Chemical kine ics and eac ion mechanisms, 2nd Ed.; McG aw-Hill: New Yo k, 1995. 92. Pilling, M. J.; Seakins, P. W. Reac ion Kine ics; Ox o d Uni e si y P ess: Ox o d, U.K., 1995. 93. Ho á h, A. Sze e len o okémia; Veszp émi Egye emi Kiadó: Veszp ém, Hunga y, 1998. 94. Tu o, N. J.; Ramamu hy, V.; Scaiano, J. C. P inciples o molecula pho ochemis y: an in oduc ion; Uni e si y science books, 2009. 95. Bakac, A. Physical Ino ganic Chemis y: P inciples, Me hods, and Models; John Wiley & Sons, 2010. 96. K oó, N.; Csillag, L. A léze ek i kai; Mó a Fe enc Köny kiadó: Budapes , Hunga y, 1987. 97. The Nobel P ize in Chemis y 1999. Nobelp ize.o g. Nobel Media AB 2014.; h p://www.nobelp ize.o g/nobel_p izes/chemis y/lau ea es/1999/; accessed: 5 Sep 2015 98. Hug, G. L., (U.S.), N. B. S., Na l. S and. Re . Da a Se . (U. S., Na l. Bu . S and.), NSRDS-NBS 69 1981. 99. Ne a, P.; Huie, R. E.; Ross, A. B., J. Phys. Chem. Re . Da a 1988, 17, 1027-1284. 100. Doglio i, L.; Hayon, E., J. Phys. Chem. 1967, 71, 2511-2516. 101. Doglio i, L.; Hayon, E., J. Phys. Chem. 1967, 71, 3802-3808. 102. Lesigne, B.; Fe adini, C.; Pucheaul , J., J. Phys. Chem. 1973, 77, 2156-2158. 103. Tang, Y.; Tho n, R. P.; Mauldin, R. L.; Wine, P. H., J. Pho ochem. Pho obiol., A 1988, 44, 243-258. É a Dóka: PhD Thesis – Reac ions o he sul a e ion adical 89 104. Huie, R. E.; Cli on, C. L.; Al s ein, N., Radia . Phys. Chem. 1989, 33, 361-370. 105. McEl oy, W. J.; Waygood, S. J., J. Chem. Soc., Fa aday T ans. 1990, 86, 2557-2564. 106. Bonneau, R.; Ca michael, I.; Hug, G. L., Pu e Appl. Chem. 1991, 63, 290-299. 107. Adams, G. E.; Boag, J. W.; Michael, B. D., P oc. Roy. Soc. (London) A 1965, 289, 321- 341. 108. Adams, G. E.; Boag, J. W.; Michael, B. D., T ans. Fa aday Soc. 1965, 61, 1674-1680. 109. Adams, G. E.; Boag, J. W.; Michael, B. D., T ans. Fa aday Soc. 1965, 61, 1417-1424. 110. Hayon, E.; McGa ey, J. J., J. Phys. Chem. 1967, 71, 1472-1477. 111. Weeks, J. L.; Rabani, J., J. Phys. Chem. 1966, 70, 2100-2106. 112. E iksen, T. E.; Lind, J.; Me enyi, G., Radia . Phys. Chem. 1985, 26, 197-199. 113. Huie, R. E.; Cli on, C. L., J. Phys. Chem. 1990, 94, 8561-8567. 114. Roebke, W.; Renz, M.; Henglein, A., In . J. Radia . Phys. Chem. 1969, 1, 39-44. 115. Sha ma, B. Nuclea and adia ion chemis y; K ishna P akashan Media, 1995. 116. Jiang, P.-Y.; Nagaishi, R.; Yo suyanagi, T.; Ka sumu a, Y.; Ishigu e, K., J. Chem. Soc., Fa aday T ans. 1994, 90, 93-95. 117. Loe le , M.; Hudson, R.; Moo e, M.; Ca lson, R., Ica us 2011, 215, 370-380. 118. McEl oy, W. J., J. Phys. Chem. 1990, 94, 2435-2441. 119. Doglio i, L.; Hayon, E., Na u e 1968, 218, 949-950. 120. Doglio i, L.; Hayon, E., J. Phys. Chem. 1968, 72, 1800-1807. 121. Sada -Sha ai, T.; Pucheaul , J.; Fe adini, C., Radia . Phys. Chem. 1981, 17, 283-288. 122. Feng, C.; Tollin, G.; Enema k, J. H., Biochim. Biophys. Ac a 2007, 1774, 527-539. 123. Kiss, T.; Gajda, T.; Gyu csik, B. Be eze és a biosze e len kémiába; Nemze i Tanköny kiadó, 2007. 124. Ne a, P.; Huie, R. E., En i on. Heal h Pe spec . 1985, 64, 209. 125. E ben-Russ, M.; Bo s, W.; Win e , R.; Sa an, M., Radia . Phys. Chem. 1986, 27, 419- 424. 126. E ben-Russ, M.; Michel, C.; Bo s, W.; Sa an, M., F ee Radical Res. 1987, 2, 285-288.