Electrolytic Composite Ni-PTFE Coatings- An Incorporation of Guglielmi's Model for the Phenomena of...

Surface and Coatings Technology 157 (2002) 282289

0257-8972/02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved.PII: S0257-897202.00180-9

Electrolytic composite NiPTFE coatings: an adaptation of Guglielmismodel for the phenomena of incorporation

P. Bercot *, E. Pena-Munoz , J. Pagettia, b a Laboratoire de Chimie des Materiaux et interfaces, Pole Corrosion, Traitements de Surface et Systemes Electrochimiques,a `

16 route de Gray 25000 Besancon, FranceUniversidad de Monterry, Morones Priesto 4500 Pte., Garza Garcia, NL, Mexicob

Received 20 February 2002; accepted in revised form 18 April 2002

Abstract

Co-deposition of inert particles in a metallic matrix enables the production of a large range of composite materials with uniqueproperties. Previous work on examination of the effects of the variation of experimental conditions has produced someunderstanding of the mechanism. When stirring is carried out using a rotating disk electrode, the hydrodynamic conditions arewell defined and can be taken into account. In this paper the model proposed by Guglielmi, which does not take into accountagitation of the bath, has been used and modified to explain results for NiPTFE deposition incorporating a correction based onthe speed of magnetic rotation. 2002 Elsevier Science B.V. All rights reserved.

Keywords: Plating; Nickel; Polytetrafluoroethene (PTFE); Composite

1. Introduction

The possibility of incorporating particles finely dis-persed in a metallic matrix by plating has led to a newgeneration of composites that present interesting chem-ical and physical properties w149x. These propertiesdepend on several variables, such as the shape and sizeof the particles in the plating bath and their distributioninside the composite, which is influenced by the coatingstructure and morphology.First of all, mathematical modelling of nickelpoly-

tetrafluoroethene (PTFE) co-deposition is complexbecause the PTFE particles do not take part in anyreduction reaction during the electrochemical process.The PTFE particles are non-conducting. Moreover, thereis a need to introduce a dispersion of PTFE particles toavoid the problems related to difficult wettability. In thiscase, the magnetic stirring bar must keep the dispersionstable for the success of the operation. In order to studythe co-deposition process, a magnetic stirring bar hasoften been used for others kind of particles w112x.

*Corresponding author. Tel.: q33-303-81-66-20-30; fax: q33-303-81-66-20-33.

E-mail address: [email protected] (P. Bercot).

Other factors also influence the composite properties,such as the nature of the bath, the type of particle w1316x, the particle size w17x and concentration in the bathw2,7,10,14,15,18,19x, the surface charge of the particlesw7,2022x, the current density w2,8,1315,23,24x, thetemperature w25,26x, the pH w25,27,28x, and mainly thedegree of stirring, which has to be analysed w7,20,25,2931x. Contrary to inorganic particles, such as alumina,zircon oxide, silicon carbide and barium sulfate, PTFEparticles cannot have a small negative or positive chargein an electrolytic bath w29,3139x.Among all the existing models, Guglielmis model

w40x was adopted because it has been checked withdifferent co-deposition systems (e.g. NiSiC and NiTiO w40x, NiAl O w41x, CuAl O w42,43x, Cu2 2 3 2 3TiO w43x, AgAl O w44x, CrC w45x, CuSiC w46x,2 2 3CuP w47x, ZnNi particles w35x, CoSiC w48x, NiSiC w23x and NiMoS w49x).2In order to develop the mathematical model, experi-

ments were performed in solutions containing PTFEparticles at different concentrations. The validation ofthis model for nickelPTFE coatings was carried out indirect current using mechanical stirring solutions.

283P. Bercot et al. / Surface and Coatings Technology 157 (2002) 282289

Fig. 1. Electrochemical device.

Fig. 2. Co-deposition of NiPTFE at various cathodic current densityvalues J with vs500 rev. min .y1c

Hydrodynamic conditions depend on the stirring barspeed v, which leads to results not validated by thepredicting Guglielmi model.Taking into account the influence of hydrodynamic

conditions, a correction factor was added to the Gug-lielmi model to adapt the mathematical model in orderto predict the incorporation of PTFE particles in nickeldeposits under magnetic stirring.

2. Experimental

Electrolytic coatings were performed in a classicalnickel sulfamate bath without brightener w50x:

Ni(NH SO )2 3 2 300 g ly1

NiCl2 10 g ly1H BO3 3 30 g ly1PTFE 550 g ly1

Operating conditions:

pH 45J 17 A dmy2T 55"1 8Cv 4001000 rev. miny1

A suspension of PTFE particles was added to theelectrolytic bath. The particles had an average sizesmaller than 0.5 mm. Dispersion was stabilised using anon-ionic wetting agent. In order to make a comparativestudy, nickel deposits were also realised under the sameoperating conditions.The experimental set-up used to make up the electro-

lytic coatings included a cell (Fig. 1) into which twoelectrodes were placed: the anode was made up of nickelrounds and the cathode was formed by a 12-cm2copper sheet.A stirring bar placed at the bottom of the cell was

used for varying the hydrodynamic conditions. To deter-

mine the PTFE incorporation rate under different hydro-dynamic conditions, the rotating speed v of the stirringbar was varied from 400 to 1000 rev. min .y1First, the copper cathode was degreased in a classical

alkaline bath at 55 8C, then rinsed in deionized waterand finally etched in a classical acidic bath. It was thencovered with a 10-mm layer of nickel using the bathpreviously described.

3. Results and discussion

3.1. Description of Guglielmis model

The model of Guglielmi w40x has two major objectivesthat aim to:

Establish the influence of particle concentration inthe bath over the incorporation rate in nickel electro-deposits; and

Quantify the rate of particle incorporation as a func-tion of current density.The knowledge of the curves a vs. C, in which a is

the volume fraction of particles in the deposit and C theconcentration of particles in the bath, has experimentaland theoretical importance. The hypothesis of a Lang-muir adsorption isotherm was put forward from the avs. C curve shapes, for which a particle saturation effectis noted when the concentration increases w51x.Guglielmi based his model on the similarity between

the experimental co-deposition and Langmuir isothermcurves. We reproduced this result in experiments withnickelPTFE (Fig. 2).Guglielmi deduced a connection between a and the

concentration C of particles in the bath w40x:B EC MJ 1o .. C Fs exp h AyB qC (1)

a nFdV kD Go

where:a: volume % of particles in suspension in the

deposit (vol.%)

284 P. Bercot et al. / Surface and Coatings Technology 157 (2002) 282289

Fig. 3. Ratio Cya according to the PTFE concentration in the bath at various current density values.

h: overpotential (V)A: constant in Tafel equation for metal deposition

(V )y1B: constant in Tafel equation for particle

deposition (V )y1C: volume % of particles in suspension in the

bath (g l or vol.%)y1d: density of the electrodeposited metal (g dm )y3F: Faradays constant (Fs96500 C) (C mol )y1J :o exchange current density (A dm )y2k: coefficient of adsorption (l g or vol.% )y1 y1M: molecular weight of the electrodeposited metal

(g mol )y1n: valence of the electrodeposited metalV :o constant for particle deposition (dm s )y1

For coatings carried out with various current densityvalues, the plot of Cya against C gives a series ofstraight lines, which converge towards the same pointon the C-axis.According to Eq. (1), when Cyas0, this point

represents the value y1yk, which makes it possible toobtain the adsorption coefficient value k.Fig. 3 shows the lines obtained for our nickelPTFE

system. Current density was in the range of 17 Adm with mechanical stirring at a rotating speed v ofy2the stirring bar of 500 rev. min . C and a are expressedy1as a volume percentage (for C, 1%s30 g l ).y1From extrapolation of the experimental linear curves,

it is then possible to calculate the value of the y1ykpoint of intersection with the C-axis. In our case y1yksy0.53 and ks1.9, which is of the same order ofmagnitude obtained by Guglielmi w40x for NiTiO .2

3.2. Calculation of constants B and Vo

If we agree with the assumption according to whichthe particles are fixed at the cathode by electrochemicaldischarge of the adsorbed cations, the electrochemicalparameters B and V can be related to the PTFE particles.oThen an approximation of the current densityJ fJ e can be made, and the ratio ByA is calculatedAhc ousing the following substitution:

AyB h 1yByA Ah ByA 1yByA( ) ( ) ( ) ( )J e sJ e sJ J (2)o o o cSubstituting the last expression into Eq. (1), we obtain:

nFdV Co ByAy1( )as J (3)cByAMJ 1ykqC .oand taking logarithms, we obtain a linear relationshipbetween log(a) and log(J ):c

w B EnFdVoC Flogas logx ByAMJD GoyB EzC

.qlog q ByAy1 log J (4) .|C F c1ykqC .D G~

From the experimental results, the curves log(a) vs.log(J ) were plotted and are shown in Fig. 4. Calculationcof the slopes of the linear regression lines enables thededuction of ByA.Since all the curves are parallel, the ratio ByA remains

constant whatever the PTFE concentration in the bath.The value computed for the ratio ByA is 0.66, which

is close to that obtained by Guglielmi w40x for NiTiO , where ByAs0.65.2In our system, the ByA ratio is lower than 1. This

means that the Ni cations adsorbed on the particles arereduced more slowly than the solvated Ni cations. The


Fig. 4. Curves of log (a) vs. log (J ) for the NiPTFE system at various current density values.c

Fig. 5. Theoretical (dotted lines) and experimental curves (full lines) of a vs. C for each current density value, with vs500 rev. min .y1

fact that B is lower than A can be noted and involves adecrease in a when the current density increases wEq.(3)x.For J s1 A dm , the straight regression line of they2c

curves log(a) vs. log(J ) cross the a-axis at the pointcK , which value makes it possible to calculate V .o oThen

w B EnFdVoC FK sloga s logxo wJ s1xc ByAMJD GoyB EzCqlog (5)|C F1ykqC .D G~

and

B EByA 1ykqCMJo KoC FV s 10 (6)o nFd CD GThe value found for V was 0.072 mm s .y1o

3.3. Validation and comments

After we determined all the electrochemical constantsof the various systems, the theoretical curves of co-deposition of a vs. C were plotted using the Guglielmiexpression wEq. (1)x and were compared with the exper-imental results.In accordance with Guglielmis theory, the co-depo-

sition curves have the same shape and a increases with


Fig. 6. Incorporation rate according to the stirring of the solution, at various PTFE concentrations and a current density of J s3 A dm .y2c

the concentration of particles up to 30 g l . Thisy1increase is fast from 0 to 10 g l , slow from 10 to 30y1g l and finally weakly decreases from 30 to 50 gy1l .y1Fig. 5 gives an outline of the results. It clearly appears

that all the curves have the same shape, whatever thecurrent density value.Moreover, the connection between a and J is alsoc

highlighted. The rate of particle incorporation decreaseswhen the current density increases. The Guglielmi pre-diction (dotted lines) remains always higher than theexperimental results (full lines).

3.4. Hydrodynamic effect

To study the influence of the hydrodynamic effect onthe incorporation rate, we carried out tests at variousspeeds of the stirring bar used in the electrolytic bath.The angular velocity of the stirring bar varied from 400to 1000 rev. min and the current density was fixed aty1J s3 A dm (Fig. 6).y2cFrom the shape of these curves several comments can

be made:

There is an optimum incorporation rate, which is afunction of both the particle concentration in the bathand the stirring bar speed.

This optimum incorporation rate increases with bothC and v.

At high rotating speed, which corresponds to strongstirring of the bath, the incorporation rate decreases,whatever the PTFE concentration.

The problems linked with the maintenance of particlesin suspension seem to be at the origin of this behaviour.Indeed, the most significant incorporation rate for aPTFE concentration of 10 g l is obtained with vsy1500 rev. min , whereas for a concentration of 30 gy1

l , the optimum is obtained with vs700 rev. min .y1 y1Thus, we can distinguish different hydrodynamic flowsin connection with the stirring bar speed.For a fixed particle concentration C in the bath, when

the angular velocity v is slow (for instance 400 rev.min ), the incorporation rate remains low. This corre-y1sponds to a laminar flow. When v increases to valuesfrom 500 to 800 rev. min , the optimum of the avy1curve is reached. This indicates a maximum incorpora-tion rate (marked with a vertical arrow), which corre-sponds to a transient laminarturbulent flow. Finally,when v reaches values higher than 800 rev. min , thisy1corresponds to a pure turbulent flow and the incorpora-tion rate decreases.These results are in accordance with the analysis by

Fransaer et al. w29x concerning the influence of fluidflow velocity, particle concentration and current densityon the particle deposition rate.

3.5. Discussion

Comparing experimental and theoretical curves (Fig.5), Guglielmis model has predicted higher values thanthose obtained experimentally. Since the differences arealways of the same nature, this means that the theoreticalresults depend on other parameters that are not takeninto account in the model.In particular, significant parameters, such as the

hydrodynamic conditions, pre-treatment of PTFE parti-cles and components included in the sulfamate bath, arenot included in Guglielmis model.Celis and Roos w42x and Buelens w52x, in their model

based on a statistical approach, included the effects ofseveral parameters of the process that Guglielmi neglect-ed, such as the adsorption of ionic species on the particlesurface, the particle nature, the ions to be reduced, thebath components and the hydrodynamic conditions.


Fig. 7. Curve used for the calculation of parameters h and m. Resultsobtained with vs500 rev. min and J s3 A dm .y1 y2c

Fig. 9. Comparison between theoretical, experimental and correctedcurves for NiPTFE deposits carried out with J s3 A dm and vsy2c500 rev. min .y1

Fig. 8. Comparisons between the experimental (full lines) and thecorrected model (dotted lines); J s3 A dm .y2c

They proposed a model suitable for many experimentalsystems that include solid particles and fine metalparticles. Their model has the advantage of being vali-dated with particles of 0.05-mm diameter, which corre-sponds to the average size of the PTFE particles in oursystem. However, they used a rotating disk electrode tocontrol the hydrodynamic conditions in order to set uptheir model. In our case, which is a practical case, thismodel is not available since magnetic stirring does notperfectly control the hydrodynamic flow.Fransaer et al. w29x have advanced a new approach to

the fundamental study of the influence of hydrodynamicconditions. Their study was based on the calculation ofthe forces that act on the particle and which are at theorigin of their migration towards the cathode. Knowl-edge of the particle trajectories inside the solution makesit possible to determine the fluid velocity in the vicinityof the cathode. The fluid velocity field allows theestablishment of a more complete statistical analysis,which leads to an estimate of the probability of particlecapture in the coating.As our work is related to the influence of mechanical

stirring, we can analyse the hydrodynamic conditions

by varying the angular velocity v in order to insert acorrective factor into the expression for a.

3.6. Corrective factor applicable to the Guglielmi model

To try to evaluate the corrective factor, we havesimultaneously analysed a vs. C (Fig. 2) and a vs. v(Fig. 6) curves, as the other parameters previouslyquoted from Celis and Roos w42x and Buelens w52x areconstant.Then Eq. (3) can be written this way:

nFdV Co ByAy1( ) .as J hf v,C (7)cByAMJ 1ykqC .owhere f (v,C) is a function that can be determined fromexperimental curves and h is a constant that is availablein the range of transient laminarturbulent flow.To determine f (v,C), software (MATLAB) was used

for an approximation of the differences between theo-retical and experimental a values to obtain a model thatreproduces satisfactory experimental results.This procedure leads to a polynomial, which describes

the system correctly. This polynomial has the followinggeneral form:

3 2 .f v sav qbv qcvqd (8)

where a, b, c and d are constants computed by thesoftware:

as5.87=10y9bsy1.31=10y5cs8.76=10y3dsy1.51

Since the function obtained only depends on v in therange from 400 to 1000 rev. min , it is possible toy1separate this function f (v,C) into a product of twoindependent functions, so that f (v,C)sf(v) f (C).


Fig. 10. Comparison between the experimental results (full lines) andthe corrected model (dotted lines) at various current density valueswith vs500 rev. min .y1

Then . .asa hf v f C (9)theo

wherenFdV Co ByAy1( )a s J (3a)theo cByAMJ 1ykqC .o

For calculation of the function f (C), we consider thatit has the form f (C)sC , where m is a parameter tombe determined.The final formulation of a becomes:

m .asha C f v (10)theoAccording to the experimental results, we can plot,

on a logarithmic scale, the ratio aywa f (v)xshC .mtheoThe parameters h and m are directly calculated by thismethod. For a stirring bar speed of 500 rev. min andy1a current density of 3 A dm (Fig. 7), the values fory2h and m are: hs0.8 and ms0.08.Inserting these values in w10x, we finally obtain:

m . .asa 0.8C f v (11)theoThe dotted lines in Fig. 8 show the h f (C) f (v)

corrected curves obtained with this function optimisedfor three different concentrations of PTFE and for acurrent density of 3 A dm .y2When we compare the experimental results (full lines)

and the corrected model results (dotted lines), we notethat they are close. Thus Eq. (11) is valid when vvaries, but this function has to be applied to a vs. C tovalidate it.Results obtained using Eq. (11) with a constant

stirring bar speed of 500 rev. min and a currenty1density of 3 A dm are shown in Fig. 9. Experimentaly2curves, and theoretical curves calculated from Gugliel-mis model and from our corrected mathematical modelare plotted.Once more the experimental and corrected curves are

very close. Therefore, Eq. (11) remains valid when Cvaries.We finally note that the function f (v,C) is valid in

the two systems, namely a vs. v and a vs. C. However,the way in which the given function is determined doesnot make it possible to advance assumptions on itsorigin.Results obtained for other current density values are

shown in Fig. 10. We also note that the model remainsvalid independently of the current density value.Finally, the model corrected with the function f (v,C)

remains valid whatever the operating conditions are,namely stirring (in the range of 500800 rev. min ),y1the PTFE concentration in the bath (up to 30 g l )y1and the current density (varying from 1 to 7 A dm ).y2

4. ConclusionsThe analysis and calculation presented in this paper

indicate that the corrective factor h f (v,C) added to the

Guglielmi model is an adequate basis for studying theincorporation rate of PTFE particles into nickel electro-lytic coatings performed under magnetic stirring.The comparison between experimental results and

theoretical predictions proves the predominance of thefluid flow. Magnetic stirring is not an adequate methodfor carrying out a fundamental study compared to theuse of a rotating disk electrode for electrolytic co-deposition w53x. However, the reproducibility of theexperiments and the good agreement between theoreticaland experimental results indicate that it is possible inthe future to approach industrial problems using amathematical model that takes into account the realhydrodynamic conditions.For instance, such a model could be applicable in the

connector industry, in which products are manufacturedusing a reel-to-reel technique.

5. List of symbols

a: volume of particles in suspension in deposit(vol.%)

a :theo theoretical volume of particles in suspension indeposit (vol.%)

h: overpotential (V)u: fraction of area occupied by particles partially

incorporated in the metal layers: fraction of area occupied by weakly adsorbed

particlesv: angular velocity (rev. min )y1A: constant in Tafel equation for metal deposition

(V )y1B: constant in Tafel equation for particle

deposition (V )y1C: volume of particles in suspension in the bath

(g l or vol.%)y1d: density of the electrodeposited metal (g dm )y3F: Faradays constant (Fs96 500 C mol )y1


h: constantJ :c current density (A dm )y2J :o exchange current density (A dm )y2k: coefficient of adsorption (l g or vol.% )y1 y1K :o constant (vol.%)m: constantM: molecular weight of the electrodeposited metal

(g mol )y1n: valence of the electrodeposited metalS: total area of the electrode (dm )2S :l area occupied by the weakly adsorbed particles

(dm )2S :s area occupied by the particles already fixed in

the deposit (dm )2V: total volume (metalqparticles) deposited

(dm )3V :m volume of metal electrodeposited (dm )3V :o constant for particle deposition (dm s )y1V :p volume of particles strongly adsorbed (dm )3

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