Studies of Nickel Electrocrystallization on Platinum Ultramicroelectrodes

A eletrocristalização de níquel foi estudada sobre ultramicroeletrodo (UME) de platina. O comportamento dos transientes de corrente indicou um processo de nucleação instantânea sob controle cinético. A aplicação do modelo de Abyaneh mostrou que os núcleos crescem com uma geometria do tipo calota esférica, possuindo valores diferentes para as constantes de velocidade no sentido paralelo e per pen dic u lar à superfície. As constantes de velocidade para o crescimento de núcleos no sentido paralelo variaram de 5,97 x 10 a 1,92 x 10 mol cm s, com o aumento do potencial de -0,57 a -0,63 V, enquanto que as correspondentes constantes no sentido per pen dic u lar apresentaram valores em torno de 1,44 x 10 mol cm s. As relações en tre estas forneceram os ângulos de contato, cujos valores aumentaram de 27,5 a 87,6 graus. Finalmente, o número de núcleos formados aumentou com o potencial, de 0,43 x 10 a 379,09 x 10 cm.


In tro duc tion
The ini tial stages in the electrodeposition of sev eral met als onto dif fer ent sub strates fre quently oc cur by the birth and three-dimensional growth of nu clei.Dur ing a short time in ter val af ter a potentiostatic pulse, ap plied to gen er ate the nu clei, they grow free of in ter ac tions with neigh bors.Within a such time do main, if the rate de ter mining step is the dif fu sion of ions to wards the sur face, potentiostatic tran sients should pres ent a lin ear de pendence of the ris ing cur rents on t 1/2 or t 2/3 .The con se quence of such a dif fu sion-controlled pro cess is the for ma tion of a num ber of per fectly spher i cal nu clei on the sur face.2][3][4][5] for ei ther the in stan ta neous (i vs. t 1/2 ) or the pro gres sive (i vs. t 3/2 ) birth of a large num ber of nu clei.7][8][9] in a study of three-dimensional nu cle ation on a fi nite num ber of ac tive sites fol lowed by dif fu sion-controlled growth of nuclei.Those au thors pro posed that the cur rent max ima in tran sients pro vide the in for ma tion re quired to eval u ate the den sity of ac tive sites on the sur face and the rate of nu cleation per ac tive site.In stan ta neous or pro gres sive nu cleations are shown to be spe cial cases of the gen er al ized model.Milchev et al . 10,11stud ied the for mation-dissolution equi lib rium of nu clei at crit i cal sizes.In the very ini tial time do main, the sta bil ity of newly-born nu -clei is highly de pend ent on ex per i men tal con di tions.These au thors have iden ti fied two dis tinct mech a nisms of crit i cal nu cleus for ma tion, namely: (i) by the di rect at tach ment of ions from the elec tro lyte, or (ii) by sur face dif fu sion of ad-atoms on the sub strate.
In the ab sence of dif fu sion lim i ta tions, the char ac ter istics of the nu cle ation pro cess con trolled by charge trans fer are quite dif fer ent.In or der to an a lyze the nu cle ation growth con trolled by elec tron trans fer it is nec es sary to estab lish two dif fer ent growth rates, one in the per pen dic u lar and the other in the par al lel di rec tion in re la tion to the substrate.Ac cord ing to the val ues of these rate con stants, the shape of the nu clei may vary from hemi spher i cal (when both rate con stants pres ent the same value) to spher i cal cap (when the rate con stant par al lel to the sur face is greater than the per pen dic u lar one).A de tailed model tak ing these spe cial char ac ter is tics into ac count was de vel oped by Abyaneh [12][13][14][15][16] in his stud ies of Ni nu cle ation.Fig. 1 pres ents the sche matic model for the nu cle ation of a spher i cal-cap nu cleus form 16 .In this fig ure, v and v' rep re sent speeds of growth par al lel and per pen dic u lar to the sub strate re spectively, S u is the ac tual flat area cut through by a slice dy at a dis tance y away from the sub strate, and θ is the con tact angle which de fines the ec cen tric ity of the spher i cal-cap.The au thor stated that for in stan ta neous nu cle ation: (i) for short pe ri ods the cur rent is pro por tional to the square of time and is given by: where z is the num ber of elec trons, F is the Far a day constant, M is the mo lar mass of the de posit, k and k ' are the rate con stants rel a tive to par al lel and per pen dic u lar growth re spec tively, N o is the num ber of nu clei, ρ is the den sity of the de pos ited spe cies and t is the time.
(ii) the cur rent tran sient pres ents only one max i mum be fore the steady-state is reached; and (iii) the steady-state cur rent value is ob tained when t → ∞, For pro gres sive nu cle ation, items (ii) and (iii) are also valid, but Eq. 1 changes to: with A be ing the nu cle ation rate.The gen eral cur rent-time equa tions in this model are: τ for pro gres sive nu cle ation (5)   with the func tion G( τ), de rived from the sta tis tic of treatment adopted, be ing re spon si ble for the unique max i mum in the cur rent tran sient.The uti li za tion of ultramicroelectrodes (UMEs) in electrocrystallization stud ies brought with it some nov elties.UMEs are elec trodes with at least one of their di mensions on the or der of mi crom e ters.Their small size is com pa ra ble to the thick ness of the dif fu sion layer.Sev eral ad van tages of such elec trodes have al ready been described [17][18][19][20] .Their char ac ter is tics can over come some lim ita tions in nu cle ation stud ies, for ex am ple: (a) all of the inves ti ga tion meth ods used for electrocrystallization, such as chronoamperometry, suf fer from the o ret i cal and ex per imen tal un cer tain ties re lated to the lack of knowl edge about the en ergy dis tri bu tion on the non-ideal equipotential surface and (b) mul ti ple nu cle ation pres ents ques tions re lated to over lap and in ter fer ence.The pro gres sive birth of nu clei im plies a vari a tion in crys tal lite sizes on the sur face.Almost all of these un cer tain ties di min ish when stud ies of mul ti ple nu cle ation are car ried out in elec trodes with small di men sions.More over, UMEs con sti tute an ad e quate tool for the in ves ti ga tion of the birth and growth of a sin gle nucleus.
De spite the ad van tages stated above, the use of UMEs pres ents brings some dif fi cul ties.A disk is the most use ful UME shape, due to the fa cil ity in pol ish ing the sur face af ter each de po si tion.Nev er the less, dif fu sion to wards the electrode sur face is com pli cated be cause the edge of the disk electrolyzes the so lu tion, pre vent ing ions from reach ing the cen ter of the elec trode.As a con se quence, it is nec essary to de velop equa tions which prop erly de scribe the transient be hav ior.One at tempt to do so was re cently per formed in our Lab o ra tory 21 with the aim of de scrib ing dif fu sion con trolled nu cle ation pro cess on a disk-shaped UME.How ever, the kinetically con trolled nu cle ation processes on that kind of UME have not yet re ceived at ten tion.
In this sense, the ob jec tive of this work is to study the mul ti ple electrocrystallization of Ni on a disk-shaped Pt UME (di am e ter of 40 µm) from a mod i fied Watts bath, in or der to ver ify the ap pli ca bil ity of the con ven tional Abyaneh model to this kinetically con trolled pro cess on a very small sub strate.

Ex per i men tal
A two-electrode polarographic Py rex ® cell (with an approx i mate vol ume of 25 mL) was used to per form the exper i ments.This cell had a Tef lon ® cover with ap pro pri ate holes to hold a cal o mel sys tem as the ref er ence elec trode, Fig ure 1.The nu cle ation of spher i cal cap growth forms 16 .
wich also served as the sec ond ary elec trode, the work ing elec trode, and the deaeration fa cil ity.
All po ten tials quoted in this work were re ferred to the hy dro gen ref er ence elec trode (-0.241V vs. sat u rated cal omel elec trode 22 ).
The work ing UME was ob tained by seal ing a Pt wire (φ = 40 µm) in a Py rex ® tube and pol ish ing the tip with a 1500 grid em ery pa per in or der to ex pose the cross sec tion in the shape of a mi cro-disk.The elec trode pre pared follow ing this method pre sented a geo met ric area of 1.3 10 -5 cm 2 .The real area of this elec trode was eval u ated as 4.0 10 -5 cm 2 by cy clic voltammetry in 0.5 M NaOH so lu tions through the in te gra tion of the H-adsorption peaks 23,24 .
The elec tro lytic bath con sisted of a mod i fi ca tion of the con ven tional Watts bath, and con tained 330 g L -1 NiSO 4 .6H 2 O + 45 g L -1 Ni(NO 3 ) 2 .6H 2 O + 37 g L -1 H 3 BO 3 .The con tri bu tions of the hy dro gen evo lu tion re ac tion to the to tal mea sured cur rents were eval u ated from ex per i ments in an equiv a lent bath whose Ni 2+ salts were re placed by Na + ones.All re agents were Merck P.A., and the wa ter was puri fied by a Milli-Q sys tem from Millipore.Be fore each exper i ment the elec tro lyte was deaerated by bub bling N 2 (White Mar tins, SS) for 15 min.
The elec tro chem i cal ex per i ments were per formed with a EG&G PARC model 273 potentiostat-galvanostat linked to a 386 PC mi cro com puter through a GPIB in ter face.The soft ware used to con trol the ex per i ments was the M270 from EG&G PARC.

Re sults and Dis cus sion
The electrocrystallization of Ni on a disk-shaped Pt UME was stud ied by chronoamperometry.In or der to estab lish the range of po ten tials for per form ing the potentiostatic jumps, cy clic voltammetric ex per i ments were ini tially car ried out in the elec tro lytic so lu tion between 1.0 and -1.0 V at 0.1 V s -1 .The voltammetric response pres ents the cross-over of the an odic and cath odic branches, char ac ter is tic of the nu cle ation pro cess, at a poten tial value near -0.5 V.This phe nom e non is a con sequence of sur face area in creas ing due to metal electrodeposition.Also, the voltammogram shows that it is dif fi cult to pro mote the redissolution of the de pos ited Ni layer un der the ex per i men tal con di tions used.There fore, the elec trode sur face had to be pol ished be fore each chronoamperometric ex per i ment.An ex am ple of this voltammogram is shown in Fig. 2. From these pre lim i nary voltammetric ex per i ments a po ten tial range from -0.57 to -0.63 V was es tab lished for use in the Ni electrocrystallization stud ies.Thus, the po ten tial jumps were per formed from 0.94 V to the set of val ues spec i fied in fig. 3.
The cur rent tran sients ob tained from the chronoamperometric ex per i ments are dis played in Fig. 3.
The cur rents of the ris ing part of the tran sient prior to the max i mum, cor rected for the real area of the Pt sub strate, were plot ted against sev eral func tions of t (t 1/2 , t 3/2 , t 2 and t 3 ) as di ag nos tic cri te ria 5,16 .The ex cel lent lin ear re la tionships of I to t 2 are shown in Fig. 4, thus in di cat ing an in stanta neous 3D nu cle ation and growth pro cess un der ki netic con trol.This con clu sion is sup ported by the re sults of Amblard et al. 25 , whose trans mis sion elec tron mi cro graphs for sev eral times dur ing the tran sient showed a con stant num ber of nu clei grow ing un til over lap, thus con firm ing in stan ta neous nu cle ation.More over, the mi cro graphs also re vealed that nu clei do not have per fect hemi sphere shape, but re sem ble a "spher i cal cap" ge om e try.
As al ready dis cussed in the In tro duc tion, a model taking these spe cial char ac ter is tics of Ni electrodeposition into ac count was de vel oped by Abyaneh and Fleischmann [12][13][14] and Abyaneh 15,16 .As such, Eqs. 1, 2 and 4 can be used to de scribe the tran sients ob tained here.This model con sid ers the nu clei to be spher i cal caps with dif ferent val ues for the con tact an gle, as de fined by the dif fer ent k and k' rate con stant val ues.
The val ues of θ, k', k and N0 can be cal cu lated from the ex per i men tal cur rent tran sients dis played in Fig. 3 us ing the fol low ing re la tion ship de rived from Abyaneh's model 16 : where where ε is the ec cen tric ity of the nu cleus.Since Equa tion (6) stands for the max i mum in the current tran sients, us ing the ex per i men tal val ues of t max and ob tain ing τ max from Ta ble 1 of Ref. 16, it is pos si ble to cal cu late P i for each tran sient.τ max is the non-dimensional pa ram e ter for time, de pend ing on the con tact an gle.In this sense, for θ > 50 degrees, τ max = 1.6, while for θ ≤ 50 de grees, τ max = 1.8.So, it is pos si ble to eval u ate P i , as sum ing, τ max = 1.6 at first, and, if θ re sults in less than 50 de grees, chang ing the τmax value to 1.8 and re cal cu lat ing Pi.Such ap prox i ma tions clearly sim plify the task of cal cu lat ing the var i ous pa ram e ters of Abyaneh's model.
Equa tions 1, 2, and 7 im ply that the lin ear re la tion ships of i vs. t 2 shown in Fig. 4 should pres ent slopes given by slope ≅ + + ∞ 2 1 cos cos θ θ i P i (10)   where i ∞ is the lim it ing cur rent den sity, cor rected by the elec tro chem i cal area of the to tally Ni-covered elec trode (1.47 x 10 -4 cm 2 , as cal cu lated by cy clic voltammetric exper i ments in the α-Ni(OH)2 po ten tial re gion 27 ) and by the hy dro gen evo lu tion re ac tion con tri bu tion.There fore, Eq. 10 is use ful for cal cu lat ing the value of θ for each tran sient.
The val ues of i ∞ are eas ily ob tained from the tran sients displayed in Fig. 3.These val ues must be cor rected for the limit ing cur rents due to the hy dro gen evo lu tion re ac tion ob tained from dis tinct tran sients per formed on a to tally cov ered elec trode sur face in a Ni 2+ -free elec tro lyte.The cor rected val ues of i ∞ are shown in Ta ble 1 and used to calcu late θ for each tran sient.Ta ble 1 also shows the step poten tials, slopes, P i , con tact an gles, and ec cen tric i ties (ε) for each curve.The slopes and P i val ues are dic tated by the vari a tion of ei ther the num ber of nu clei (which in creases with po ten tial) or the time for the max i mum (which di minishes with po ten tial) in the tran sients, as de picted by Eqs. 1 and 9.
The vari a tion of θ with the step po ten tial de serves special at ten tion.As θ → 90°, the shape of the nu clei approaches to a hemi sphere (and ε → 1).This sit u a tion is achieved when both growth rates, in the per pen dic u lar and par al lel di rec tions have the same value.At low val ues of step po ten tials, the rate con stant in the par al lel di rec tion should be greater than in the per pen dic u lar one.This dif ference gen er ates spher i cal caps with low val ues of ε and θ.This sug gests that the vari a tion of the rate con stant in the par al lel di rec tion with po ten tial is smaller than that in the per pen dic u lar di rec tion.In this case, the ris ing of the po lariza tion val ues tends to equal ize the ve loc i ties, thus in creasing the con tact an gle.This be hav ior will be fur ther an a lyzed be low.
The val ues for k' were di rectly ob tained from the lim iting cur rent of each tran sient us ing Eq. 2. The in tro duc tion of pa ram e ters k' and θ in Eq. 8 al lows the cal cu la tion of k.Using Eq. 1 the num ber of nu clei was de ter mined from the slope of each straight line shown in Fig. 4. The re sults of the Ta ble 1.The nu cle ation pa ram e ters in volved in the cal cu la tion of θ.
-E V slope x 10 cal cu la tions are pre sented in Ta ble 2 to gether with the step po ten tials and the val ues of I max , t max , and N 0 .The var i ous I max / I ∞ re la tion ships are greater than 1.218, as pos tu lated in Abyaneh's model 16 , which may ac count for the pronounced max ima in the tran sients.An im por tant anal y sis to be made from Ta ble 2 is the de pend ence of the rate con stant on the po ten tial.The rate con stant in the par al lel di rec tion (k) is strongly in hib ited by in creases in the step po ten tial.This highly un ex pected result may be ex plained by the hy dro gen co-evolution on bare Pt sur faces in this cath odic po ten tial range.The oc cupa tion rate of the sur face ac tive sites by ad sorbed H (which in creases with the cath odic po ten tial) may make the growth of nu clei in the par al lel di rec tion dif fi cult.An other pos sibil ity is re lated to the in creas ing num ber of nu clei on such a small elec trode sur face, which will be dis cussed be low.More over, the val ues of k' are in de pend ent of the po ten tial, an ex pected re sult be cause they are ob tained di rectly from the lim it ing diffusional cur rent val ues (Eq.2) which are not de pend ent on the po ten tial.The small vari a tions ob served in the k' val ues with the step po ten tials might be a con sequence of al ter ations in the lim it ing cur rents caused by changes in the sur face area, which can even ex trap o late the bound aries of the sub strate 19 .The de ter mined val ues of k and k' are in close agree ment with the as sump tions made above to ex plain the val ues re ported in Ta ble 1, i.e., the influ ence of the step po ten tials on the ge om e try of the nu clei.
Finally, the num ber of nu clei greatly in creases with the cath odic po ten tial.Al though this is nor mal be hav ior in instan ta neous nu cle ation, it can bring about dra matic con sequences in the par al lel rate con stants.The large num ber of nu clei (40,000 at the most cath odic po ten tial) could promote in hi bi tion zones that di min ish the growth rates in the par al lel di rec tion.

Con clu sions
This work re ports for the first time, to the au thors' knowl edge, ex per i men tal re sults from Ni electrocrystallization on Pt UMEs.This is also one of the few ex am ples of ex per i men tal ap pli ca tions of Abyaneh's model.The val ues ob tained seem to in di cate that Abyaneh's model may be ap plied to such small elec trodes.This con ve nient be hav ior is re lated to the ki netic con trol in Ni nu cle ation and growth, since the tra di tional mod els are in ac cu rate to de scrib ing dif fu sion-controlled pro cesses on UMEs.In this case, proper dif fu sion-controlled equa tions had to be de vel oped 21 .
The cal cu lated con tact an gles showed that nu clei grow in a spher i cal cap ge om e try.This was fully con firmed by the dis tinct val ues of the rate con stants re lated to the growth of the nu clei in the per pen dic u lar and par al lel di rec tions in re la tion to the sur face, as well as their de pend ence on the step po ten tial.The in ter pre ta tion of this phe nom e non is com pletely based on Abyaneh's model.
The co-evolution of hy dro gen, first on Pt and then on Ni sur faces, also plays an im por tant role in the tran sient shapes and de serves spe cial at ten tion.Nev er the less, it is pos si ble to eval u ate its con tri bu tion and sub tract it from the Ni electrocrystallization re sponse.
The cor rect eval u a tion of elec tro chem i cal ac tive ar eas is also very im por tant be cause in the as cen dant branch of the tran sients the sub strate was smooth plat i num, re placed Ta ble 2. The ki netic pa ram e ters for the tran sients.
-E V Imax x 10 6 A tmax s k' x 10 7 mol cm -2 s -1 k x 10 7 mol cm -2 s -1 N0 x 10  by elec tro de pos it ed nickel in the lim it ing cur rents re gion.Both sur faces re quire ap pro pri ate meth ods to eval u ate the elec tro chem i cal ar eas.Finally, the large num ber of nu clei de pos ited on the small elec trode sur face may pro mote an in hib i tory ef fect on the rate con stants for par al lel growth.The for ma tion of such a large num ber of nu clei is re lated to the in ter ac tions be tween plat i num and nickel.

Ac knowl edg ments
The au thors wish to thank CNPq for the stu dent and research grants.

Fig ure 4 .
Fig ure 4. The lin ear de pend ence of I vs. t 2 for the ris ing part of the tran sients for Ni electrocrystallization on a Pt UME.