Optimization of electroless Ni Zn P deposition process: experimental study and mathematical modeling

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1 Electrochimica Acta 49 (2004) Optimization of electroless Ni Zn P deposition process: experimental study and mathematical modeling Basker Veeraraghavan, Hansung Kim, Branko Popov Department of Chemical Engineering, Center for Electrochemical Engineering, University of South Carolina, Columbia, SC 29208, USA Received 8 October 2003; received in revised form 21 January 2004; accepted 26 January 2004 Available online 12 April 2004 Abstract A mathematical model based on mixed potential theory was developed which was used to optimize a non-anomalous Ni Zn P electroless deposition process developed by us at USC. The model was developed by assuming an adsorption step in addition to the electrochemical steps. The concentrations of the Zn and Ni complex were estimated by solving the material balances in addition to the electroneutrality condition and the equilibrium relations. The composition of the coating was estimated from the partial current densities of all charge transfer reactions, which occur at the electrode electrolyte interface. The model results showed that the adsorption plays a significant role in the alloy deposition process. From the model results, it was seen that the addition of Zn ions to the bath inhibits the deposition rate by changing the surface coverage of the adsorbed electroactive species on the electrode surface. The model indicated that an increase of ph of the bath increases the alloy deposition rate Elsevier Ltd. All rights reserved. Keywords: Electroless Ni Zn P deposition; Mixed potential theory; Adsorption; Mathematical model 1. Introduction Zn Ni alloys are considered as possible replacement for Cd coatings for corrosion protection of steel substrates. The current technology available for Zn Ni plating includes both alkaline and acid plating [1 6]. Deposit characteristics of Zn Ni as compared to the conventional zinc include benefits of extended corrosion resistance and significantly harder deposits. Also, the presence of nickel imparts a good barrier resistance to the coating. However, the electrodeposition of such alloys is anomalous in nature, with the co-deposition resulting in a higher amount of Zn in the final deposit [7,8]. Due to the high zinc content in the deposit, these alloys are more electronegative than cadmium and hence dissolve rapidly in any corrosive environments. Typical nickel composition in the Zn Ni alloy is 10 15%, Submitted as a technical paper to Dr. E.J. Cairns, Editor, Electrochimica Acta, Environmental Energy Technologies Division, Building 90, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, USA. Corresponding author. Tel.: ; fax: address: popov@engr.sc.edu (B. Popov). and any further increase in nickel composition is based on using a higher-than-predicted Ni/Zn ratio in the bath [9 12]. Attempts were made to decrease the anomaly in case of Zn Ni alloys by either introducing inert species in the bath or by developing a ternary alloy [10,11]. Zhou and Keefe [12] have studied the effect of tin additions on the anomalous deposition of Zn Ni alloy. The nickel ratio increased from 6 to 8% with the addition of small amounts of tin. However, the observed small increase of Ni content in the alloy did not improve the Zn Ni barrier properties. A novel technique for deposition of non-anomalous Ni Zn P coatings with high nickel content (74 wt.% as compared to wt.% in the conventional plating method) was developed recently [13]. Our corrosion studies indicated that these coatings can be used as a replacement for Cd in sacrificial protecting steel [14]. Ni Zn P coatings were deposited using an electroless method. In this paper, a theoretical kinetic model based on mixed potential theory was developed in order to optimize our electroless Ni Zn P deposition process from alkaline electrolytes [13]. Mixed potential theory has been used to explain electroless deposition processes, initially by Paunovic [15] and then by Donohue [16]. According to the mixed potential theory, the /$ see front matter 2004 Elsevier Ltd. All rights reserved. doi: /j.electacta

2 3144 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) electroless plating process occurs due to a combination of the oxidation and reduction reactions, the rates of which are equal and opposite at any given time of deposition. Also, mixed potential theory has been used in the literature to explain various electroless deposition processes such as copper deposition from formaldehyde bath and nickel deposition from hypophosphite bath [17 21]. The model presented in this paper simulates the surface coverage of Zn, Ni, and P species under various bath conditions. The model simulations were also compared to the experimental data obtained using RDE experiments. 2. Experimental 2.1. Electrolyte preparation and deposition Rotating disc electrode (RDE) studies and surface characterization techniques were used to understand the Ni Zn P electroless process and to determine how the alloy composition varies with the electrolysis conditions. Ni Zn P composites were prepared from a bath containing 35 g/l nickel sulfate (NiSO 4 6H 2 O), 85 g/l sodium citrate (C 6 H 8 O 7 Na 3 2H 2 O), and 50 g/l ammonium chloride (NH 4 Cl). Sodium hypophosphite (NaH 2 PO 2 ) was used as a reducing agent for the autocatalytic process. Ni Zn P coatings with different amounts of Zn were obtained by varying the amount of zinc sulfate (ZnSO 4 7H 2 O) in the bath. The temperature of deposition was maintained at 85±1 C using a double-jacketed vessel with a temperature controller. The time of deposition was kept constant at 1 h. The bath ph was maintained at 10.5 during the deposition process by adding sodium hydroxide (NaOH). All solutions were prepared with analytical grade reagents (obtained from Sigma Aldrich) and distilled water. The experimental conditions are given in Table Characterization studies Energy dispersive analysis using X-rays (EDAX) was used to analyze the Ni Zn P ratio of the deposits. The elec- Table 1 Experimental conditions used in the study Composition of electrolyte (g/l) NiSO 4 6H 2 O 35 ZnSO 4 7H 2 O 5 20 Sodium citrate 85 NH 4 Cl 50 Sodium hypophosphite 20 Experimental conditions Angular velocity: ω, (rpm) 400 Radius of the disk electrode: r (cm) 0.25 Kinematic viscosity: υ (cm 2 /s) ph 10.5 Temperature ( C) 85 trochemical characterization was done using an EG & G PAR model 273A potentiostat/galvanostat interfaced with a computer and a three-electrode setup. The rotating disk electrode with the coating was used as the working electrode and a platinum wire was used as the counter electrode. A standard calomel electrode (SCE) was used as the reference electrode. In the model, appropriate corrections were made for the potential of the SCE with respect to the temperature of the deposition process (E SCE at 85 C = V versus NHE). The mixed potential for the deposition was then measured using a SCE. Linear polarization studies during the deposition process were obtained by scanning the potential 10 mv above and below the deposition potential after initiating the deposition process. 3. Electroless model development The following reactions were considered in the model: Oxidation of hypophosphite [21,22] H 2 PO 2 + H 2 O Catalyticsurface H 2 PO 3 + 2H + + 2e (1) Reduction reaction for P [21,22] 2H 2 PO 2 + H + + e P + HPO H 2 O + H 2 (2) Reduction reaction for Ni [22] Ni(NH 3 ) e Ni + 6NH 3 (3) Reduction reaction for Zn [22] Zn(NH 3 ) e Zn + 4NH 3 (4) H 2 evolution reaction [21,22] 2H + + 2e H 2 (5) 3.1. Concentration profile in diffusion layer The concentration profiles for each of the reacting species are described by the steady-state convective diffusion equation for a rotating disk electrode [23]: D j 2 C j x 2 = v C j x x The boundary conditions are given by: C N j D j x = s ji i j at x = 0 (7) n j F i=1 where n is the number of reactions occurring at the electrode surface. The stoichiometric co-efficient s ji for each species j of reaction i is found out by writing the reaction in the form s ji M i n j e (8) i where M i are the species involved in each of the reactions C j = C b,j at x = δ (9) (6)

3 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) where C b,j is the concentration of the species at the bulk of the electrolyte. Under laminar flow conditions, the fluid velocity v x can be expressed as [23] v x = ax 2 ω 3/2 υ 1/2 (10) where a = , is the angular velocity of the rotating disk electrode and υ the kinematic viscosity of the electrolyte. Also, for a rotating disk electrode under steady-state conditions, the diffusion layer thickness δ j for each of the species is defined by the relation [23] δ j = 1.61D 1/3 j ω 1/2 υ 1/6 (11) where D j is the diffusion coefficient of the species Adsorption of species at the electrode surface At the electrode surface, the electroactive species are adsorbed on the surface according to the following reactions: H 2 PO 2,s H 2 PO 2,ad (12) Zn(NH 3 ) 4,s Zn(NH 3 ) 4,ad 2+ Ni(NH 3 ) 6,s Ni(NH 3 ) 4,ad 2+ H s + H ad + (13) (14) (15) The surface coverage for each species follows an equilibrium isotherm of the form θ j = b jc s,j (16) 1 + b j C s,j where b j is the concentration dependant adsorption co-efficient for each of the reacting species. The empirical relations for the dependence of b j on the concentration of all electroactive species on the surface were obtained by fitting the experimental alloy compositions to the model results. An example for dependence of b H2 PO 2 on the surface concentration of hypophosphite ions (C s,h2 PO 2 ) is presented in Fig. 1. A similar approach for the adsorption phenomenon has been used to explain the inhibition of nitric acid reduction by chloride ions [24]. The total surface coverage was defined as: θj = 1 (17) It is assumed that desorption of any product from the electrode surface is fast enough that at any given time during the deposition process, the electrode surface is covered only by the reacting species Application of mixed potential theory According to the mixed potential theory, the electroless process occurs at the potential (mixed potential) where the net current is zero. Thus, at this potential the current density due to the anodic reaction (oxidation of hypophosphite) is equal to the sum of the cathodic current densities (reduction of Ni, Zn, P, and H 2 ). The following condition accounts for various partial current densities i 1 = i 2 + i 3 + i 4 + i 5 (18) where i 1 is the current density due to oxidation of hypophosphite, i 2 represents the partial current density of P reduction, i 3 is the partial current density of Ni reduction, i 4 corresponds to the partial current density for Zn reduction and i 5 is the partial current density due to hydrogen evolution reaction. In order to ensure the validity that the partial current densities are equal to the current densities, the composition of the alloy was checked at several points of the electrode surface using EDAX analysis. The alloy surface composition varied in the range of ±0.5 wt.% indicating that a uniform film has been deposited on the surface. Fig. 1. Dependence of adsorption co-efficient b j on the surface concentration C s,j for hypophosphite ions.

4 3146 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) Table 2 Kinetic parameters used in the model Kinetic parameters H 2 PO 2 H 2 PO 2 Ni(NH 3 ) 2+ 6 Zn(NH 3 ) 2+ 4 H + (anodic) a (cathodic) a (cathodic) a (cathodic) a (cathodic) a Diffusion co-efficient: D (cm 2 /s) Exchange current density: i 0 (A/cm 2 ) b b Symmetry factor: β Number of electrons: n Stability constant: K j ( 10 7 mol 2 /l 2 ) 0.17 a 2.1 a a Data obtained from [21,22,26,27]. b Parameter assumed in this model. Assuming Tafel approximations, the current density for the anodic reaction is given by: [ ] (1 i 1 = i 0,1 (θ H2 PO 2 ) 0.5 β1 )n 1 F (θ H ) exp η 1 (19) RT while the cathodic current densities are: ( i 2 =i 0,2 (θ H2 PO 2 )(θ H ) 0.5 exp β ) 2n 2 F RT η 2 (20) ( i 3 =i 0,3 (θ Ni ) 0.8 exp β 3n 3 F RT η 3 ( i 4 =i 0,4 (θ Zn ) 0.5 exp β 4n 4 F RT η 4 ( i 5 =i 0,5 (θ H ) 0.6 exp β 5n 5 F RT η 5 ) ) ) (21) (22) (23) where j is the overpotential and β j is the symmetry factor for the respective reactions. In each of the current potential relationship, the exponent terms to which the surface coverages of the participating species are raised can be estimated from the expression [25]: γ j = q j + βs j (24) where j is the exponent to which the surface coverage of the respective species is raised, q j is the reaction order for the cathodic reactants, s j is the stoichiometric coefficient of species j in the electrode reaction and β is the symmetry factor for the reaction. The q j is related to s j according to the following equation [25]: q j p j = s j (25) where p j is the reaction order for anodic reactants. The overpotential for each reaction is given by the relation η j = E m E eq,j (26) where E m is the mixed potential of the deposition process and E eq,j is the equilibrium potential for the respective reaction as determined by the concentration of the species involved in the reaction. The equilibrium potential for each reaction is given by E eq,j = E 0,j RT n j F log Πc oxi Πc red (27) where E 0 is the standard potential for each reaction. For simplicity, the activity of H 2 PO 3 and HPO 3 2 is assumed to be unity for determining the equilibrium potentials of reactions (1) and (2). Since Zn and Ni are present in the complexed form, the equilibrium potentials was estimated using the following relation: E eq,j = E 0,j RT n j F log K j RT n j F log Πc oxi Πc red (28) where K j is the stability constant of the complexed species. The above equations are solved simultaneously to obtain the unknown quantities such as: the partial current densities along with the mixed potential for the deposition process. Once the partial current densities are obtained, the weight of each element (Ni, Zn, and P) in the deposit were obtained by using the Faraday s law: m j = M ji j t (29) n j F The data obtained from the model were compared with the experimental results. The kinetic parameters used in the model for the different reactions to fit the experimental results are presented in Table 2 [21,22,26,27]. The kinetic parameters that were not available in the literature were assumed in this study. 4. Results and discussion The ph of the bath plays a very important role in determining the composition of the Ni Zn P deposits. A complete analysis of the equilibrium reactions between various species was performed to analyze the effect of ph on the concentration of the electroactive species in the bath. According to the Pourbaix [28] ph potential diagrams of zinc and nickel, both metals precipitate to form their respective hydroxides with an increase of ph above 7.0. The presence of a complexing agent such as ammonia prevents the precipitation. In the presence of ammonia, the following complexes are formed: Zn(OH) 2 + 4NH 3 Zn(NH 3 ) OH (30) Ni(OH) 2 + 6NH 3 Ni(NH 3 ) OH (31)

5 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) Fig. 2. Variation in equilibrium concentrations of complexed Zn and Ni species as a function of bath ph. Material balances coupled with various equilibrium relations and electroneutrality conditions were used to plot the ph concentration diagram. The governing equations and the computational details are summarized in the appendix. Fig. 2 shows the equilibrium concentration of different electroactive species as a function of bath ph. The concentration of the zinc and nickel complexes varies with increase of ph above 9.0. The nickel to zinc complex concentration ratio increases with increase in ph. This variation in the concentration of nickel and zinc complexes is expected to favor the nickel deposition from alkaline electrolytes. Our initial studies indicated that zinc cannot be deposited auto-catalytically in the absence of nickel ions. The mixed deposition potentials estimated in the electrolyte containing 35 g/l NiSO 4 and 50 g/l NH 4 Cl in the presence of complexing agents were found to depend on zinc ion concentration and were in the range between V versus SCE for 5 g/l ZnSO 4, and V versus SCE for 20 g/l ZnSO 4. Zn Ni alloys with similar composition ratio can be electrodeposited at V versus SCE from the same bath without hypophosphite ions, indicating that nickel ions catalyzes the zinc deposition at this potential. Since the cathodic and anodic reactions of any of the autocatalytic processes are independent when they occur simultaneously [18], it is possible to study the anodic polarization of hypophosphite in the presence and absence of ions on different catalytic surfaces. The results would represent the true anodic current that would occur in the complete bath. Thus, to determine why zinc deposits in the presence of nickel ions, the hypophosphite oxidation was studied on Fig. 3. Polarization studies of hypophosphite oxidation on different substrates.

6 3148 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) Fig. 4. Dimensionless concentration profiles for the various reactants as a function of distance from the electrode surface. nickel and iron substrates in the presence of only complexing agents. The hypophosphite oxidation curves obtained on nickel and iron are shown in Fig. 3. The results indicated the nickel surface catalyzes the hypophosphate oxidation reaction. This behavior has also been observed by Ohno et al., [18] in which they studied the effect of different catalytic surfaces on the oxidation of hypophosphite. Thus, in case of electroless deposition of Ni Zn alloys, the reaction is initiated by a spontaneous displacement reaction between iron substrate and the nickel ions present at the interface. As a result, iron dissolves while nickel deposits on the surface. The formed thin nickel film causes the oxidation of hypophosphate to occur at approximately 1.1 V versus SCE, which enables zinc reduction and formation of Ni Zn P alloy. Fig. 4 shows the model predictions of dimensionless concentration profiles for each of the reacting species near the electrode surface. The concentration of the hydrogen ions at the electrode surface drops to zero, suggesting that the diffusion process controls the hydrogen evolution reaction. This can be expected due to a very low concentration of the H + ions in the electrolyte at ph The other reactions are controlled by the charge transfer reactions at the electrode/electrolyte interface. Fig. 5 shows the Evans diagram for the processes occurring at the electrode-electrolyte interface during the Ni Zn P autocatalytic deposition. The system was simulated for a ZnSO 4 concentration of 5 g/l. The intercepts for the different reactions were calculated based on the effective exchange current density, given by the product of the equilibrium exchange current density and the surface coverages of the species involved in the reaction as given by Eqs. (19) (23). As shown in Fig. 5, the partial current densities for Ni deposition are higher than those observed for Zn and P deposition. The potential at which the oxidation line and the overall reduction line crosses is the mixed Fig. 5. Evans diagram showing the various reactions happening during the electroless deposition process for a ZnSO 4 concentration of 5 g/l.

7 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) Fig. 6. Comparison of mixed potential E m and plating current density i pl obtained from the model and the experiments as a function of ZnSO 4 concentration in the bath. potential of the deposition process. The current density at the intersection corresponds to the electroless plating current density. Fig. 6 compares the predicted and experimental mixed potential values and plating current densities as a function of ZnSO 4 concentration in the bath. As shown in Fig. 6, the mixed potential becomes more positive by increasing the ZnSO 4 concentration in the electrolyte. This result is consistent with the experimental observation. The experimental current densities were obtained by calculating the current required for the deposition of different elements using Faraday s law. As shown in Fig. 6, the plating current densities predicted by the model are marginally higher than the experimental values. This can be expected since the experimental values do not include the current due to hydrogen evolution reaction. It can also be seen that the plating current density decreases as a function of ZnSO 4 concentration. This result suggests that the addition of Zn ions inhibits the deposition process. This result is also consistent with the findings by Leukonis et.al. [29] who observed that Zn 2+ ions (apart from Ag + and Cd 2+ ions) act as an inhibitor for the electroless Ni P process. Further, the inhibition effect of zinc ions on the Ni Zn P deposition process has been reported previously [7,10,13]. Ohno et al., [18] used linear polarization to predict the plating rate of an electroless process. According to this study, the plating current density is equivalent to the reciprocal of the polarization resistance. The relationship between Fig. 7. Linear polarization studies performed during the deposition process as a function of ZnSO 4 concentration in the bath.

8 3150 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) Fig. 8. Variation in surface coverages of the different reacting species as a function of ZnSO 4 concentration in the bath. the plating current density and the polarization resistance is given by the equation: i pl K = 1 (32) R p where K is a constant related to the deposition process being studied. Eq. (32) is similar to the Stern Geary relation for predicting the corrosion rates of a metal, although the implication in the case of electroless deposition is different. Ohno et al. [18] used this method to predict the plating rate of electroless copper deposition process. Using this technique, the polarization resistances were estimated as a function of the Zn ions in the bath. The potential was scanned 10 mv above and below the mixed potential after initiating the deposition process. The results are shown in Fig. 7. As shown in Fig. 7, the addition of Zn ions in the bath increases the polarization resistance, thereby suggesting that the zinc ions inhibit the deposition process. Fig. 8 shows the model predictions of the surface coverage for all electroactive species participating in the deposition process as a function of ZnSO 4 concentration in the bath. By increasing the Zn ion concentration in the bath, the surface coverage of Ni ions decreases while the Zn ion surface coverage increases. Thus, it can be expected that the Ni content in the deposit would decrease as a function of ZnSO 4 concentration in the bath. Also, in Fig. 8, the surface coverage of hypophosphite ions increases with increase of zinc ion concentration in the bath which does not agree with the observed decrease of overall plating current density, i pl presented in Fig. 6. In fact, one should expect opposite to occur, an increase in the overall current density with an increase in hypophosphite ion surface coverage. The results Fig. 9. Variation in Ni content as a function of ZnSO 4 concentration in the bath.

9 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) Fig. 10. Variation in Zn and P content as a function of ZnSO 4 concentration in the bath. Fig. 11. (a) Comparison of mixed potential E m and plating current density i pl obtained from the model and the experiments as a function of ph of the bath. (b) Variation in surface coverages of the reacting species as a function of bath ph.

10 3152 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) Fig. 12. Comparison of Ni, Zn, and P contents of the coating obtained from the model and the experiments as a function of ph of the bath. can be explained by taking into account that the effective exchange current density for hypophosphite oxidation also controlled by the hydrogen ion surface coverage as seen in Eq. (19). It can be seen from Fig. 8 that hydrogen ion surface coverage decreases as a function of zinc ion concentration in the bath, thereby reducing the effective exchange current density for hypophosphite oxidation. The effective exchange current density for hypophosphite decreases from to A/cm 2 when the Zn ion concentration is increased from 5 to 20 g/l. This results in reducing the current for hypophosphite oxidation, thereby reducing the overall plating current density. A decrease of the rate of reaction (2) due to a decrease in hydrogen ion surface coverage with increasing the Zn concentration, may be another possible explanation for the observed increase in hypophosphite ion surface coverage. Fig. 9 compares the model and experimentally estimated alloy compositions as a function of ZnSO 4 concentration in the electrolyte. The results are in agreement with the observations discussed in Figs. 7 and 8. Fig. 10 shows the variation in the Zn and P content in the deposit as a function of ZnSO 4 concentration in the bath. The Zn content in the deposit increases as a function of Zn ion concentration, in agreement with observations presented in Fig. 8. The predicted P content decreases with increasing the ZnSO 4 concentration in the bath. As discussed above, the observed decrease in the hydrogen ion surface coverage decreases the rate of reaction (2), resulting in a decrease in the P content in the alloy. Another important parameter that affects the deposition process is the ph of the bath. As seen from Eq. (27), increasing the ph of the bath results in shifting the hypophosphite oxidation potential to more negative values. This shift in the hypophosphite oxidation potential causes the plating mixed potential to become more negative thus increasing the plating current density, as shown in Fig. 11a and b shows the surface coverage of the reacting species as a function of the bath ph. The zinc surface coverage decreases with an increase of the ph which results in an increase of the alloy deposition rate. Fig. 12 compares the model and experimental results for variation of the Ni, Zn and P contents in the deposit as a function of the ph of the bath. It can be seen that the model results fits well with the experimental data, validating the assumptions made in the model. 5. Conclusions A theoretical kinetic model based on mixed potential theory was developed to explain the processes occurring during the electroless deposition of the Ni Zn P alloy from alkaline electrolytes. The model simulates the surface coverage of Zn, Ni, and P under various bath conditions. The model simulations were compared to the experimental data obtained using RDE experiments. The composition of the coating was estimated from the partial current densities of all electroactive species participating in the deposition process. The model results showed that the adsorption plays a significant role in the alloy deposition. Addition of Zn ions to the bath inhibits the deposition rate by changing the surface coverage of the adsorbed electroactive species on the electrode surface. The zinc surface coverage decreases while the alloy deposition rate increases with an increase of the ph of the bath. The model results fit well with the experimental data thus validating the assumptions made in the model. Acknowledgements Financial Support by Dr. John Sedriks and Dr. Vinod Agarvala, The Office of Naval Research under grant No: N and AESF Research Contract, Project 107 are gratefully acknowledged. This work was

11 B. Veeraraghavan et al. / Electrochimica Acta 49 (2004) also supported by Sandia National Laboratories. Sandia is a multiprogram laboratory operated by Sandia Corporation, A Lockheed Martin Company, for the United States Department of Energy under contract DE-AC AL Appendix A. Nomenclature List of symbols a a constant, b j concentration dependant adsorption co-efficient for species j, (cm 3 /mol) C s,j surface concentration of species j, (mol/cm 3 ) C b,j bulk concentration of species j, (mol/cm 3 ) D j diffusion coefficient for species j, (cm 2 /s) E 0,j standard-state potential for reaction j, (V) E eq,j equilibrium potential for reaction j, (V) E m mixed potential for the electroless deposition process, (V) F Faraday s constant, C/(g.eq) i j current density for reaction j involved in the deposition process, (A/cm 2 ) i 0,j equilibrium exchange current density for reaction j, (A/cm 2 ) i pl plating current density for the deposition process,(a/cm 2 ) K j stability constant for the complexed species j, dimensionless M j molecular weight of species j, (g/mol) m j mass of component j in the deposit, (g) n j number of electrons for species j involved in the electrode reaction q j reaction order for the cathodic reactants, dimensionless p j reaction order for the anodic reactants, dimensionless R gas constant, J/(gmol/K) R p polarization resistance measured during the electroless deposition process, ( cm 2 ) s ji stoichiometric co-efficient for species j involved in reaction i, dimensionless t time of deposition process, (s) T absolute temperature, (K) v x velocity component in axial direction, (cm/s) x normal distance from the electrode, (cm) Greek symbols β j symmetry factor for reaction j δ j thickness of Nernst stagnant diffusion layer, (cm) γ j exponents in surface coverage dependence of the exchange current density for species j, dimensionless η j surface voverpotential for reaction j, (V) υ kinematic viscosity of the electrolyte, (cm 2 /s) θ j ω Appendix B surface coverage for species j involved in the electrode reaction, dimensionless rotation speed for the disk electrode, (rad/s) The electroless bath used for deposition consists of 35 g/l NiSO 4 6H 2 O, 15 g/l ZnSO 4 7H 2 O, 85 g/l Sodium citrate and 50 g/l ammonium chloride. The variables to be determined are as follows: [Zn 2+ ], [Ni 2+ ], [Zn(OH) + ], [Ni(OH) + ], [Zn(OH) 2 ], [Ni(OH) 2 ], [Zn(NH 3 ) 4 2+ ], [Ni(NH 3 ) 6 2+ ], [Zn 2 (OH) 3+ ], [OH ], [SO 4 2 ], and [HSO 4 2 ]. The concentration of [H + ] depends on the specified ph. The equations used for the determination of the equilibrium concentrations are Material balance on zinc: [ZnSO 4 ] ad = [Zn 2+ ] + [Zn(OH) + ] + 2[Zn 2 (OH) 3+ ] + [Zn(OH) 2 ] + [Zn(NH 3 ) 2+ 4 ] Material balance on nickel: [NiSO 4 ] ad = [Ni 2+ ] + [Ni(OH) + ] + [Ni(OH) 2 ] + [Ni(NH 3 ) 2+ 6 ] Electroneutrality conditions: [H + ] + 2[Zn 2+ ] + 2[Ni 2+ ] + [Zn(OH) + ] + [Ni(OH) + ] + 3[Zn 2 (OH) 3+ ] + 2[Zn(NH 3 ) 2+ 4 ] + 2[Ni(NH 3 ) 2+ 6 ] = [HSO 4 ] + 2[SO 2 4 ] + [OH ] The equilibrium conditions: [H + ][SO 4 2 ] k 1 [HSO 4 ] = 0 [Zn 2+ ][OH ] k 2 [Zn(OH) + ] = 0 [Ni 2+ ][OH ] k 3 [Ni(OH) + ] = 0 [H + ][OH ] k 4 = 0 [Zn 2+ ] 2 [OH ] k 5 [Zn 2 (OH) 3+ ] = 0 [Zn(OH) + ][OH ] k 6 = 0 [Ni(OH) + ][OH ] k 7 = 0 [Zn(OH) 2 ][NH 3 ] ad 4 k 8 [Zn(NH 3 ) 4 2+ ][OH ] 2 = 0 [Ni(OH) 2 ][NH 3 ] ad 6 k 9 [Ni(NH 3 ) 2+ 6 ][OH ] 2 = 0 The above equations were solved simultaneously by using Maple. The various rate constants used in the equations are as follows [22]: k 1 = , k 2 = , and k 3 = mol/l, k 4 = , k 5 = , k 6 = , k 7 = , k 8 = , and k 9 = mol 2 /l 2.

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