Modeling and simulation of electrodeposition: Effect of electrolyte current density and conductivity on electroplating thickness

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1 Advanced Materals Scence esearch Artcle ISSN: Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness Anl Mahapatr 1,2 * and Santsh Kumar Suggu 2 1 Department Bmedcal Engneerng, Wchta State Unversty, USA 2 Department Industral and Manuacturng Engneerng, Wchta State Unversty, USA Abstract Electrplatng r electrdepstn s a prcess carred ut n an electrchemcal cell where a current s used t rm a catng n a metal surace. Develpng and ptmzng cndtns r electrplatng s tme cnsumng and mdelng and smulatn culd be used t ptmze the electrdepstn prcess. Electrlyte current densty and cnductvty are mprtant parameters r an electrdepstn system as they dctate the verall ecency lw ns n the electrlyte system and thus ptmzatn these parameters s necessary. In ths manuscrpt we reprt the develpment a mathematcal mdel t predct the electrdepstn cpper n cbalt chrme ally n an electrchemcal cell wth cpper and cbalt chrme ally as the electrdes and cpper sulate as the electrlyte. The develped mdel was valdated usng experments. The catng thckness the samples was characterzed usng scannng electrn mcrscpe () and a thckness gage. At 3 mn the mdel predcted the cpper thckness t be 11.7 µm whle expermentally the catng thckness was und t be /-1.79 (mean +/- SD) usng and /-1.36 (mean +/- SD) usng thckness gauge. When predctng eect current densty the mdel accurately predcts general trends hwever the mdel seems t vary rm expermental values n regns where there s sgncant eect the electrchemcal duble layer that the mdel des nt accunt r. The mdel accurately predcts the trend eect electrlyte cnductvty n catng rmatn. The mdel can thus be used as a startng pnt t predct eect prcess parameters n electrdepstn thckness Intrductn Smulatn usng mathematcal mdelng s a tl that s used t predct, evaluate r ptmze the perrmance a prpsed / current system under study ver tme [1,2]. Smulatn s perrmed under specc nput cndtns and utput the mdel s cmpared wth that the actual system [3]. Physcal prcesses culd be mdeled t mnmze expermental trals necessary r ptmzatn the physcal prcess [4]. Smulatn mdelng helps desgners and engneers t understand the ways and cndtns, n whch a part culd al, the lads t can wthstand and helps t avd recurrng usage physcal prttypes t analyze desgns r new and exstng parts [5]. There are varus types smulatn mdelng such as stchastc [6], dynamc [7] and Multphyscs mdellng [8]. A stchastc mdel s perrmed rm a surce randmness as t s based n certan assumptns the system under study [9]. Statstcal mdelng s a stchastc mdel [1]. Examples ths type mdelng are lnear regressn [11], multple regressn [12], etc. Mnte-Carl methd s a type stchastc mdellng [13]. Dynamc mdellng [14] represents tme aspect a system. Smulatn mdelng used r ptmzng materal handlng n a plant wuld be an example under ths categry [15]. Multphyscs mdelng ncrprates prncple physcs, chemstry blgy and engneerng n a mathematcal statement that descrbes the phenmena r system under cnsderatn [16]. Electrplatng r electrdepstn s a prcess carred ut n an electrchemcal cell where a current s used t rm a catng n a metal [17]. In the electrchemcal cell the metal t be cated s the cathde and the ande can be ne the tw: sacrcal ande (dsslvable ande) r permanent ande (nert ande) [18]. Electrlyte n the electrchemcal cell acts as a medum r the mvement electrns and rms the electrc crcut between the electrdes [19]. Oxdatn ccurs at the ande whle reductn reactn ccurs at the cathde resultng n electrdepstn [2]. Electrplatng s used r varus applcatns ncludng crrsn prtectn [2]. Fr example, electrplatng Palladum s used t manuacture catalytc cnverters because t has the ablty t absrb excess hydrgen. Fasteners are electr-plated t have a better crrsve resstance [21]. Majrty the electrcal parts and cmpnents are used ater electrdepstn prcess. Slver electrplatng has been used n cpper r brass t enhance ts cnductvty and als used n slcn slar cells t ncrease ts peratng ecency by.4% [22]. Nckel platng, tn platng and varus allys are used r crrsn prtectn n nuts, blts, husngs, brackets, ther metal parts and cmpnents [23]. Thugh expensve, gld electrplatng prvdes nt nly crrsn, but als tarnsh prtectn [24]. Develpng and ptmzng cndtns r electrplatng s tme cnsumng and mdelng and smulatn culd be used t ptmze the electrdepstn prcess. Varus examples exst n the lterature *Crrespndence t: Anl Mahapatr, Department Bmedcal Engneerng, Wchta State Unversty, 1845 Farmunt Street, Wchta, KS 6726, USA, Tel: ; E-mal: anl.mahapatr@wchta.edu Key wrds: multphyscs mdelng, electrdepstn, electrplatng, C-Cr ally eceved: August 1, 218; Accepted: August 2, 218; Publshed: August 23, 218 Adv Mater Sc, 218 d: /AMS.1143 Vlume 3(2): 1-9

2 Mahapatr A (218) Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness that demnstrates the benets mdelng electrdepstn t predct platng utcmes [25-27]. Fr example Obad et al., mdeled the electrplatng hexavalent chrmum t ptmze the electrde spacng and ande heght t btan unrm thckness the catng [28]. Lss catng unrmty was bserved when the electrde spacng decreased whle greater electrde dstance ncreased the unrmty the rmed catng [28]. The smulatn results prved that an deal electrde separatn dstance was necessary t btan a unrm catng. It was als prved that, larger sze ande as cmpared t cathde resulted n a nn-unrm catng [28]. Hughes et al., demnstrated that the electrde knetcs played an mprtant rle n the electrdepstn prcess [29]. Electrde knetcs dened the depstn prcess usng the rate determnng step and current dstrbutns. Ther smulatn results prved that varables lke surace electrde ptental and the n cncentratn n the electrlyte als nluenced the knetcs asscated wth the depstn prcess [29]. Optmzatn electrdepstn new systems wuld requre ptmzatn prcess cndtns relevant t that system. Ths wuld requre sgncant changes t a mdel r develpng a new mdel specc t that system. Electrlyte current densty and cnductvty are mprtant parameters r an electrdepstn system as they dctate the verall ecency lw ns n the electrlyte system and thus ptmzatn these parameters s necessary. In ths manuscrpt we reprt the develpment a mathematcal mdel t predct the electr depstn cpper n cbalt chrme ally n an electrchemcal cell wth cpper and cbalt chrme ally as the electrdes and cpper sulate as the electrlyte. Theretcal descrptn and mdel develpment Gvernng equatns A mathematcal mdel was develped t predct the electrdepstn cpper n cbalt chrme ally and t evaluate the eect electrlyte current densty and cnductvty n electrplatng thckness. Electrplatng ccurs due t mass transprt n the slutn as a result mgratn n electrc eld, dusn n cncentratn gradent and cnvectn n a lw eld [3]. The transprt equatn whch was appled n the dusn layer was based n the lux equatn the nc speces n the slutn. The general mass balance equatn s gven belw N = z u Fc φ D c + V c (1) Where N - mlar lux, Z - charge number, U - mblty, F Faradays cnstant, C - cncentratn, D Dusvty, - ptental n the electrlyte, V - velcty The lux equatns explanng the behavr electrchemcal systems are related t the Secnd Law Thermdynamcs [31]. Cnsder tw neghbrng vlume elements V' and V'' a slutn that have same temperature and pressure but derent electrchemcal ptentals ther cnsttuents. The derence between the electrchemcal ptental speces, µ and µ, n these vlume elements mples that ths speces tends t mve rm ne vlume element t the ther as there s n dstrbutn equlbrum. Ths mtn speces rm ne vlume element t ts neghbr s genercally called transprt speces. As the transprt the derent speces n slutn takes place under thermal and mechancal equlbrum, the change n nternal energy U these tw vlume elements s du = TdS + µ dn (2) du = TdS + µ dn (3) Where T s the thermdynamc temperature, S s the entrpy and n the number mles speces. Cnsderng the exchange matter between V' and V'', whch takes place wthut energy exchange wth ther surrundngs, t s satsed that T ( ds + ds ) = ( µ µ ) dn (4) Each ndvdual term the sum s pstve when the transprt speces s nt cupled t transprt ther speces. In ths case, dn s determned nly by ( µ µ ) and speces mves twards the regn n whch ts electrchemcal ptental s lwer, that s, dn < when µ < µ and vce versa. Fr example, ths takes place n the case nc speces n dluted slutns. When the transprt derent speces s cupled, ne r mre terms n the sum culd be negatve, but the sum s always pstve. The transprt the speces s descrbed n terms ether ts velcty V r ts lux densty J = cv. I the area the surace between the tw vlume elements s da and ts rentatn s gven by the unt vectr ˆn (rm V t V ), the number mles speces crssng the surace n a tme dt s dn = J nˆ dadt. When the derence between µ and µ s nt very large, t can be assumed that the rate change the amunt speces, ( dn ) dt, s prprtnal t the derence µ - µ r t the gradent ths ptental nrmal t the surace, µ / ˆ n µ n. The velcty speces n lnear apprxmatn s expressed as V = u µ (5) Where u s ts mblty Flux densty takes the rm Dc J = cv = uc µ = µ (6) T Where s the unversal gas cnstant and the Ensten relatn between mblty and dusn cecent, D =u T, has been used. At cnstant temperature and pressure, the gradent µ s caused by the changes n cmpstn and electrcal ptental ø s that µ = T ln c + z F φ (7) Where F s the Faraday cnstant and z the charge number speces. Substtutng Equatn (7) n Equatn (6), the Nernst-Planck lux equatn N = D( c + zc φ ) (8) l s btaned, where dentes the rat F/T. The terms n the rghthand sde ths equatn represent the transprt mechansms dusn and mgratn, respectvely. Dusn s a cnsequence the randm thermal mtn the partcles whch makes the cncentratn all speces unrm. Mgratn causes the nluence the electrc eld, E = φ l, n the randm mtn the charged partcles, and Equatn (8) shws that the partcles a cmpnent ther velcty alng the drectn the electrc eld as a result ths nluence. Flux speces due t bulk lw n a mvng lud n X-drectn, ( F ) = uc (9) x Therere, the lux expressn r each speces can be wrtten as N = z u Fc φ D c + V C (1) l Where the nc mblty u, s assumed t be related t the dusn cecent D by the Nernst-Ensten equatn [32] Adv Mater Sc, 218 d: /AMS.1143 Vlume 3(2): 2-9

3 Mahapatr A (218) Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness The materal balance equatn r each nc speces at every pnt wthn the dusn layer s as llws c =. N + t (11) Where s the prductn rate speces due t hmgeneus chemcal reactns. Under the assumptn, varatns n cmpstn are neglgble n the electrlyte and mgratn ns gves the net cntrbutn t current n the electrlyte equatn. The cncentratn gradents n the abve equatns are neglected n the Secndary Current depstn nterace and the current densty s btaned rm Ohm s law d = σl φl (12) Where σ l dentes the electrlyte cnductvty. Snce the electrlyte cmpstn s assumed t be cnstant, the materal balances are unslved r the Secndary current dstrbutn, The electrneutralty cndtn s gven by the llwng expressn: = (13) n = zc Electrde knetcs Electrdepstn s a cmbnatn xdatn and reductn reactns ccurrng at the electrdes makng the electrde knetcs very sgncant r the mdelng electrdepstn. Cnsder the reactn gven belw: A B (14) K and K b are the rate cnstants the rward and backward reactns respectvely. eactn rates: The reactn rate, als knwn as rate reactn r speed reactn, r a reactant r prduct n a partcular reactn s dened as hw ast r slw a reactn ccurs. The rate rward reactn can be calculated by: = kc A (15) The rate backward reactn can be calculated by: b = kc b B (16) The net rate reactn can be calculated by: net = (17) b Substtutng equatns (15) and (16) n (17), we get net = kc A kc (18) b B Equlbrum: Equlbrum s pnt at whch the net reactn rate s zer. Frm the abve equatns, we can btan the equlbrum cncentratn rat as llws k CB = K = (19) k C b A Where K s the equlbrum cnstant (K) ate cnstant vares wth temperature, generally t ncreases wth T. The rate cnstant (K) and temperature are related by: K Ae ( Ea / T ) = (2) Where, E a =actvatn energy, =gas cnstant and A=pre expnental actr Actvatn energy: Actvatn energy [33] s the barrer that has t be vercme by the reactants bere they are cnverted t prduct. Mre energy s requred by the reactants when there s a larger barrer r the actvatn energy. K Ae ( Ea / T ) = (21) Expnent term ( E a / T e ) s a prbablstc eature the energy barrer cmpnent whch has t crssed. Pre expnental actr A, als knwn as requency actr, gves a number tmes the attempt was made t vercme the energy barrer cnsder the electrde reactn: + ne = (22) Where k and k b are the rward and backward reactn rate cnstants respectvely. Ths s a general redx reactn, where O represents xdzed state and represents reduced state. Fr ths reactn, the equlbrum state s gverned by the Nernst equatn, whch relates the equlbrum ptental the electrde (E eq ) t the cncentratn the reactants and prducts (O and ) η = E E (23) eq Overvltage: A gven current wll requre a penalty that shuld be pad n terms electrde ptental-penalty called vervltage [34] due t rreversblty. C = / ( ) Eeq E T nf ln C (24) E_eq s the expected electrde ptental and E s the electrde ptental η = a + blg (25) Where a and b are cnstants and I s the current densty. Ths s the Tael equatn. Knetcs electrde reactns ates rward and backward reactn + ne = (26) Fr the abve reactn, the rate the rward reactn s gven by: = k C (, t) = / nf (27) c Where C (,t) s the surace cncentratn O. ate the backward reactn s gven by: = K C (, t) = / nf (28) b b a eactn rate and current are crrelated. eductn ccurs at the cathde and xdatn at the ande. Net reactn rate: The net reactn rate r net current s gven by c a net = b = = = [ k C (, t) kc b (, t)] (29) nf nf Ptental dependence k and k b Bth k and k b are ptental dependent unctns The rward reactn, whch s a reductn, s an electrn acceptng prcess. The rate reactn ncreases when the electrde ptental reaches hgher negatve because the electrde lses electrns mre easly. The ppste happens n the backward reactn,.e., xdatn reactn. Adv Mater Sc, 218 d: /AMS.1143 Vlume 3(2): 3-9

4 Mahapatr A (218) Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness At equlbrum: The electrde ptental and xdatn and reductn cncentratns make net reactn rate zer. Thus: = ; (3) c a b It can als be wrtten as: kc(, t) = kc (, t) (31) b C (, t) ln( kb) ln( k ) = ln[ ] (32) C (, t ) Therere, callng n the Nernst equatn: C (, t) ln( k ) b ln( k ) = ln[ ] F / T ( E E ) C (, t) = (33) Upn derentatng the abve equatn wth respect t E, we get: [ ln( k )] [ (1 / )] / [ b ln k T F + [ ] = 1 E E (34) 1 α + α = 1 (35) The terms n the let hand sde the reactn sum up t 1 and called symmetry actrs (r ne electrn transer n the reactn). eductve and xdatve symmetry actrs The reductve symmetry actr s asscated wth the rward reactn whch s represented by α [ ln(1 / k )] T / F[ ] = α E The xdatve symmetry actr therere becmes (1-α) (36) { ln( k )} T / F[ b ] = 1 α (37) E The term α s the measure the symmetry energy barrer. I the change n the ptental s same n bth sdes the barrer, then α=.5=1- α. Any asymmetry n the change causes ractnal values α. Standard rate cnstants: 1 ln( ) = α FE / T + c (38) k I, k = k, then E=Eº k = k e Smlarly: k b [] α F [ ( )( E E )] T (39-a) = k e (39-b) b k and k b are termed as standard rate cnstants I the cncentratns xdatn and reductns are same, and the ptental s mantaned at Eº t cause any current lw: Frm abve equatn, k = k b The larger the value Kº, the aster s the equlbrum. eactns wth small standard rate cnstants are slw. The standard rate cnstant s large r smple redx cuples The Butler-Vlmer thery αnf (1 α) nf { {[ ]( E E )} { {[ ]( E E )} T T = nfk[ C(, te ) C(, te ) ] (4) Where n s the number electrns transerred. Ths s the Butler Vlmer [35] rmulatn electrde knetcs. There are tw cmpnents, current.e., andc and cathdc, and t s expnentally dependent n ptental. The net reactn rate s gven by: = / nf = [ k C (, t) k C (, t)] (41) net b = nf[ k C (, t) k C (, t)] (42) b Substtutng the values r k and k b αnf (1 α) nf { {[ ]( E E )} { {[ ]( E E )} T T = nfk[ C(, te ) C(, te ) ] (43) Ths rmulatn s called the Butler Vlmer rmulatn electrde knetcs At Equlbrum: nf {[ ]( nf E E )} {[ ]( E E )} T T C(, t) C(, te ) = [ k][ e ] (44) nf At equlbrum, = Thckness depstn The depstn prcess s assumed t take place thrugh the llwng smpled mechansm: 2+ + Cu e Cu + = (45) + Cu + e = Cu (46) The rst step s rate determnng step (DS), and the secnd step s assumed t be at equlbrum, whch gves the llwng relatn r the lcal current densty as a unctn ptental and cpper cncentratn: c ct = c 2 +, re Fn Cu Fn [exp exp ] T Cu T where n dentes the ver ptental dened as S, 1 eq (47) n = φ φ φ (48) where (s,) dentes the electrnc ptental the respectve electrde. Equatn at the cathde s gven by: 1.5 F( φ φ φ ) 1.5 F( φ φ φ ) 2F T Cu T. C 2+ S, cat 1 eq Cu - exp C 2 +, re exp S, cat 1 eq ] Cu2+ N n= (49) where n dentes the nrmal vectr t the bundary. Equatn at the ande s 1.5 F( φ φ φ ) Cu 1.5 F( φ φ φ ) 2F T Cu T C 2+ S, an 1 eq S, an 1 eq Cu2+. - exp C 2 +, re exp ] N n= (5) The amunt depstn s understd by the Faraday s laws electrlyss [36] whch states that the amunt a materal depsted n an electrde s prprtnal t the amunt electrcty used. Fr reductn ne mle a gven metal n (charge n + ), n mles electrns are used r reductn. The ttal cathdc charge r the catng, Q(C), s the prduct the number gram mles the metal cated, m, and the number electrns requred r the reductn reactn, n, Avgadr s number, N a (number atms n a mlecule), and the electrcal charge per electrn, Qe(C). Thus, charge requred t reduce m mles metal s gven by Q = mnn Qe (51) a Adv Mater Sc, 218 d: /AMS.1143 Vlume 3(2): 4-9

5 Mahapatr A (218) Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness The prduct Avgadr s number, N a (the number atms n a mle), and the electrcal charge per electrn, Qe(C) gves the Faraday cnstant, F. The number mles the metal reduced by charge Q s: m = Q / nf (52) The ttal charge used n the depstn can be calculated by the prduct the current, I (A), and the tme depstn, t (sec), where the depstn current s cnstant. When current vares wth tme durng the depstn prcess, Q can be calculated by, Q = I dt (53) The weght the depst, W(g), can be calculated by prduct the number mles metal reduced and atmc weght, Mw, the depsted metal s gven by: Mw W = I dt nf (54) The thckness the depstn, d (cm), can be slved by: W Mw d = I dt ρa = nfρa (55) Where s the densty the metal (g = cm 3 ) and A s the area depstn (cm 2 ). Bundary cndtns All bundares (B1 and B4) were nsulatng: N. n Cu 2 + = (56) Intal cndtns The ntal cndtns the electrlyte were: C 2 Cu + = C (57) Cmputer mplementatn and smulatn Fgure 1 shws the schematc representatn electrdpstn and the crrespndng mdel gemetry r smutaltn the electrdepstn prcess. Fnte element methds were used t dscretze the multphyscs gvernng equatns. A nte element slver stware COMSOL was used t smulate and predct platng thckness under vared prcess cndtns. The mdel was set as a tw demnsnal (2D) tme dependent mdel (Fgure 1). The depstn at cathde and the dsslvng the ande was set t take place at 1% current yeld. Durng the electrplatng prcess, changes n the electrlytc densty the electrchemcal cell ccurs whch wuld result n the change n the densty at ande and cathde. These changes culd nduced ree cnvectn n the cell, hwever based n ur assumptn that the varatn n cmpstn s small, the ree cnvectn cmpnent was neglected. The prcess was assumed t be tme dependent as the bundary the cathde was mvng as the depstn the metal was takng place. The mdel s gverned by mass cnservatn r the cpper ns Cu 2+ and sulphate SO 4-2 and the electrneutralty cndtn. The upper bundary represented ande, and cathde was placed at the bttm. The vertcal walls were assumed t be nsulated (Fgure 1). Expermental methds The develped mathematcal mdel was valdated expermentally. The electrplatng Cpper n Cbalt-Chrme was cnducted n a electrlytc cell. The electrlytc slutn was prepared wth 1 gms. CuSO 4 n 1 ml dstlled water and 7 ml 1N H 2 SO 4. The Fgure 1. Schematc Depctn Electrdepstn (tp) and Crrespndng Mdel Gemetry r Smulatn the Electrdepstn Prcess (bttm) slutn was kept n the strrer t mx hmgenusly. A cbalt chrme strp 14 cm 14 cm was taken and an mmersn area 1.4 cm 1.4 cm cm was used and cpper strp 14 cm 14 cm was taken and an mmersn area 1cm 1cm was used. The cpper strp was cnnected t the ande and the cbalt chrme was cnnected t the cathde were mmersed n the electrlyte and then current was passed. Electrplatng was cnducted under varyng electrlyte cnductvtes such as; 4.23 S/ m 2,1.9 S/m 2,.93 S/m 2 and.54 S/m 2 and varyng current denstes such as; (A/m 2 ), (A/m 2 ) and (A/m 2 ). Pst depstn the samples were ar dred and characterzed r catng thckness. The samples were characterzed wth Scannng electrn mcrscpe () and a thckness gauge. Fr thckness analyss usng acrss sectnal vew the cated sample was taken and the thckness the catng determned. Fur replcates were carred ut and the catng thckness values were reprted as mean +/- standard devatn (SD). An analyss varance, ANNOVA (tw way/ne way) was used t determne statstcal sgncant derences at the 95% cndence level. esults and Dscussn Fgure 2 shws the thckness change the electrdepsted cpper n cbalt chrme ally versus tme as predcted by the develped mathematcal mdel. Frm the smulated results (Fgure 2) we see that Adv Mater Sc, 218 d: /AMS.1143 Vlume 3(2): 5-9

6 Mahapatr A (218) Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness Eect current densty n catng thckness T evaluate the eect current densty n catng thckness the mdel was used t smulate and predct the electrplatng thckness at three derent current denstes. Ths experment was cnducted wth derent current denstes at an electrlyte cnductvty 4.23 S/m 2 n 1.4 cm 1.4 cm area cntact. The derent current denstes used were (A/m 2 ), (A/m 2 ) and (A/m 2 ). The expermental and predcted values are shwn n gure 5 r duratn 46 mnutes. Fgure 2. Electrdepsted cpper catng thckness change n cathde as a unctn tme r the rst 5 sec the catng hasn t started, as the tme ges by we see a steady catng Cu n C-Cr. At the end 3 sec we see the predcted catng thckness n C-Cr t be.19 mm. T valdate the mdel an electrdepstn experment was carred ut wth same parameters as the mdel predctn r duratn 3mn (18 secs). Electrlyte test parameters r ths experments ncluded an electrlyte cnductvty 4.23 S/m 2, current densty (A/m 2 ) and a 1.4 cm 1.4 cm area cntact. Fur replcates were carred ut t evaluate the varance test results. The samples were characterzed wth Scannng electrn mcrscpe () and a thckness gauge t measure the thckness the catngs rmed. Fgure 3 shws a representatve mage used r calculatn the catng thckness whle the thckness gauge was drectly used n the sample t measure the thckness. Fr each sample measurement readngs were taken at ur derent pnts and the average reprted. Fgure 4 shws the cmparsn mdeled (smulated) thckness and expermentally btaned thckness values. Frm gure 4 and table 1, t can be seen that at 3 mn the mdel predcted the cpper thckness t be 11.7 µm (.117 mm) whle expermentally the average catng thckness was und t be / (mean +/- SD) usng and /-1.36 (mean +/- SD) usng thckness gauge. Fgure 4 shws that there was lt varatn thckness values when usng as cmpared t the thckness gauge. It can be seen (Fgure 4) that the thckness gauge measurement values ( /-1.36) were und t be clser t the predcted values (11.7) as cmpared t that thckness values (9.445+/-1.79). Ths varatn culd be attrbuted t the challenges asscated wth usng the r measurng catng thckness. In a precse crss sectnal vew was requred t measure the thckness accurately. Devatn rm an accurate crss sectnal vew (9O) culd result n varatn thckness values. Als the layer was nt unrm t culd cause varatn n the thckness values measured. Thckness gauge measurements were relatvely cnsstent n ts measurements. Hwever the relatve accuracy the predcted and expermental values valdates ur mdel. Ths demnstrates the prelmnary applcablty the mdel n predctng electr depstn cpper n cbalt chrme substrate. Frm gure 5 and table 2 we can see that the mdel predcted a catng thckness 17.3, 17.6 and 18 mcrmeters at current densty (A/m 2 ), (A/m 2 ) and (A/m 2 ) respectvely. The mdel thus predcts neglgble derences wth changes n current densty. The expermental value the catng thckness cnducted under same cndtns shwed sgncant derences when cmpared t the smulated values. Fgure 5 shwed expermental values t be lwer than smulated cndtns at lwer current denstes (A/m 2 ) and (A/m 2 ) whle expermental values were hgher than smulated values at hgher current densty (A/m 2 ). Ths can be explaned by the rmatn an electrchemcal duble layer surrundng the electrdes whch plays a crtcal rle n the dusn ns rm and twards the electrdes. The phenmenn electrchemcal duble layer and ts eect n dusn ns has been well dcumented n the lterature [37-39]. At lwer current densty there wll be a hgher resstance rm the duble layer resultng n ewer ns gng thrugh the duble layer resultng n lwer catng values. Whle at hgher current densty the ns vercme the resstance the duble layer whch results n hgher catng thckness. The develped smulated mdel currently des nt accunt r the duble layer Table 1. Expermental valdatn mathematcal mdel Current Thckness (mcrmeter) at 3 mn (18 secs) Smulatn Sample 1.7 A / /-.29 Sample 2.7 A / /-.48 Sample 3.7 A / /-1.85 Sample 4.7 A / /-.85 Average / /-1.36 Table 2. Eect current densty n catng thckness Thckness (mcrmeter) Current Densty E+2 (A/m 2 ) Tme (mn) Smulatn /-.9 5+/ / / / / / /-.73 Current Densty E+2 (A/m 2 ) Tme (mn) Smulatn / /-.37 Current Densty E+2 (A/m 2 ) Tme (mn) Smulatn / / / / / / / /-1.25 Adv Mater Sc, 218 d: /AMS.1143 Vlume 3(2): 6-9

7 Mahapatr A (218) Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness r shrter perd tme (25 mns) whle r lnger perd the mdel predcted lwer values as cmpared expermental values btaned. Fr current densty (A/m 2 ) the smulated mdel verpredcted the catng thckness r all tme duratns. These behavrs can agan be explaned by the electrchemcal duble layer. At scenars where the resstance the duble layer s prmnent the mdel under predcts the expermental values and at lnger perds tme the mdel als ver predcts the expermental value. Fgure 3. epresentatve mages that were used r evaluatng elecrdepsted cpper catng thckness Catng thckness (mcrmeters) Smula n Sample 1 Sample 2 Sample 3 Sample 4 Fgure 4. Cmparsn mdeled and expermentally determned electrdepsted cpper catng thckness values Eect electrlyte cnductvty n catng thckness Ths expermental test was cnducted wth derent electrcal cnductvtes the electrlyte keepng the ther parameters cnstant (duratn 46 mns and current densty (A/m 2 ). The electrlyte cnductvty evaluated were 4.23 S/m 2, 1.9 S/m 2,.93 S/m 2 and.54 S/m 2 n a 1.4 cm 1.4 cm area cntact. The results rm the experment are tabulated n Table 3. Table 3 shws a decreasng trend n the smulated thckness catngs wth decrease n the electrcal cnductvty the electrlyte. Expermental determnatn the catng under smlar cndtns resulted n a catng under ne cndtn (4.23 S/m 2 ), whle the catng ether was nt unrmly rmed r nt rmed at all under ther cndtns (1.9,.93 and.54 S/m 2 ). Thus althugh the mdel accurately predcted the general trends, expermental bservatns ndcated dcultes n rmng a unrm catng at thse electrlyte cnductvtes (1.9,.93 and.54 S/m 2 ). Thus bth the mdel and experments ndcates the requrement apprprate electrlyte cnductvty r the electrdepstn t ccur. Lack apprprate cnductvty wuld hnder lw ns wthn the electrlyte slutn leadng t dcultes n rmatn a unrm catng. Summary and Cnclusns In summary we have develped a mathematcal mdel t smulate the electrdepstn cpper n cbalt-chrme ally. At 3 mn the Table 3. Electrdepstn catng at varyng electrlyte cnductvtes Thckness (mcrmeter) Cnductvty (S/m 2 ) Smulatn ±.37 2 NA NA ±.47 NA NA NA NA: catng nt unrmty rmed Fgure 5. Smulated and expermental catng thckness at varyng current denstes at 46 mnutes rmatn and ts eect n catng thckness. Ths s smethng that wll be needed t be ncrprated t smulate mre accurate predctns ver a wde range n current denstes. Cmparng and gauge thckness values we see smlar hgher derence wth larger catng thckness as cmpared t lwer thckness due t larger varances measurements as dscussed prevusly. Fgure 6 and gure 7 shws the catng thckness vs tme r current densty (a/m 2 ) and (a/m 2 ) respectvely. bth gures 6 and 7 shws a general trend ncreasng catng thckness wth ncrease tme perd depstn. Fr current densty (A/m 2 ) the smulated mdel clsely predcted the catng thckness Fgure 6. Smulated and expermental electrplatng thckness vs. tme at current densty A/m 2 Adv Mater Sc, 218 d: /AMS.1143 Vlume 3(2): 7-9

8 Mahapatr A (218) Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness 8. Odette G, Wrth BD, Bacn DJ, Ghnem NM (21) Multscale-Multphyscs Mdelng adatn-damaged Materals: Embrttlement Pressure-Vessel Steels. MS Bull 26: Altug Y, Wagner AB (212) Surce and Channel Smulatn Usng Arbtrary andmness. IEEE Trans In Thery 58: Evstgneev IV, Schürger K (1994) A lmt therem r randm matrces wth a multparameter and ts applcatn t a stchastc mdel a large ecnmy. Stch Prcess Ther Appl 52: Tanaka H, Watada J (1988) Pssblstc lnear systems and ther applcatn t the lnear regressn mdel. Fuzzy Sets and Systems 27: Albrecht P (1983) Parametrc multple regressn rsk mdels: Thery and statstcal analyss. Insurance: Mathematcs and Ecnmcs 2: La Y (29) Adaptve Mnte Carl methds r matrx equatns wth applcatns. J Cmput Appl Math 231: Fgure 7. Smulated and expermental electrplatng thckness vs. tme at current densty A/m 2 mdel predcted the cpper thckness t be 11.7 µm whle expermentally the catng thckness was und t be /-1.79 (mean +/- SD) usng and /-1.36 (mean +/- SD) usng thckness gauge. The relatve accuracy the predcted and expermental values valdates ur mdel. Ths demnstrates the prelmnary applcablty the mdel n predctng electr depstn cpper n cbalt chrme substrate. When predctng eect current densty the mdel accurately predcts general trends hwever the mdel seems t vary rm expermental values n regns where there s sgncant eect the electrchemcal duble layer that the mdel des nt accunt r. The mdel accurately predcts the trend eect electrlyte cnductvty n catng rmatn. The mdel can thus be used as a startng pnt t predct eect prcess parameters n electrdepstn thckness hwever mdcatns are needed t ncrprate expermental realtes nt accunted r n the mdel. 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9 Mahapatr A (218) Mdelng and smulatn electrdepstn: Eect electrlyte current densty and cnductvty n electrplatng thckness 32. Lu X (1997) Applcatn the Nernst-Ensten equatn t cncrete. Cem Cncr es 27: Ca J, Jn C, Yang S, Chen Y (211) Lgstc dstrbuted actvatn energy mdel Part 1: Dervatn and numercal parametrc study. Bresur Technl 12: Seyed H, Abam Z and Glab S (212) Cmprehensve Analyss the Impacts Derent Parameters n Transmssn Lne Swtchng Overvltages. Internatnal evew n Mdellng and Smulatns 5: Nren DA, Hman MA (25) Claryng the Butler Vlmer equatn and related apprxmatns r calculatng actvatn lsses n sld xde uel cell mdels. J Pwer Surces 152: Kamata M, Paku M (27) Explrng Faraday's Law Electrlyss Usng Znc Ar Batteres wth Current egulatve Ddes. J Chem Educ 84: Marchev VA (1991) A new pssblty applcatn electrn tunnelng eects n electrchemcal duble layer structure nvestgatns. Surace Scence 25: Su YZ, Fu YC, We YM, Yan JW, Ma BW (21) The Electrde/Inc Lqud Interace: Electrc Duble Layer and Metal Electrdepstn. Chem Phys Chem 11: Sh H (1996) Actvated carbns and duble layer capactance. Electrchmca Acta 41: Cpyrght: 218 Mahapatr A. Ths s an pen-access artcle dstrbuted under the terms the Creatve Cmmns Attrbutn Lcense, whch permts unrestrcted use, dstrbutn, and reprductn n any medum, prvded the rgnal authr and surce are credted. Adv Mater Sc, 218 d: /AMS.1143 Vlume 3(2): 9-9