Electrochemically induced spreading of electrolyte films on metal substrates

J. Elecrroanoi.

C&m,

Elsewer Sequoia S A.

183 (1985)

205-222

Lausanne

- Pnnted

205

in The Netherlands

ELECTROCHEMICALLY INDUCED SPREADING ON METAL SUBSTRATES PART 1. POTENTIAL OF OXYGEN

L.M. BAUGH.

F.L

Ever Ready Lrd,

(Received

TYE

DEPENDENCE,

l

CURRENT DISTRIBUTION

FILMS

AND ROLE

and N C WHITE

Technrcaf Dtvtsron. Tanjrefd Lea, Stanley.

17th February

OF ELECTROLYTE

1984;

in reused

Co

Durham,

form 1Gth September

DH9

9QF (Great Brrrarn)

1984)

ABSTRACT 4 detailed exammatron has been made of the electrochemical variableswhrch deterrnme the rate of spreading of concentrated alkahne electrolyte films on vertical parllally immersed negatweiy polarised metal substrates. viz. NI. Au and Sn. When hydrogen evolution is the major reaction occumng al the metal surface, the spreadmg rate IS directly proportIonal to potentlal and inversely proportional to film length However, when oxygen reduction is the major reachon. the spreztdmg rate IS Independent of poknlid and film length. These observations can be reconciled by assummg that rhe important parameter controllmg the driving force for spreadmg IS aksozated with Ihe ma&tude of current flowmg mto,‘through the region of the mtnnslc memscus front at the base of the spreading film The variables controllmg ihe magmtude of this current are different accor&ng to Ihe nature of the particular faradac process which pertwns. The spreadng characteristics of the elecirolyte film are lherefore a!so different.

INTRODUCTION

In an earlier investigation [l] it was shown that the maJor driving force for the spreading of alkaline electrolyte films on partially immersed negatively polarised metal substrates IS associa:ed-with current flow across the metal/film interface. Two reactions are of importance. In a nitrogen atmosphere hydrogen evolution is the process which must be correlated with the spreading rate. This occurs via the reduction of water 2H20+2e--,2OH-+H2 However,

(1)

in an oxygen atmosphere

oxygen reduction

must also be considered

0,+2H,O+4e--,4OH-

* PreKnl

address:

0022-0728/85/.$03.30

(2)

~ddlesex

Polytechmc,

Bounds Green Road,

Q 1985 Elsevler Sequoia S.A.

London.

Nil

tNQ,

Great

Britain.

206

There are two consequences of these cathodlic reactions. Firstly, alkah metal cations are transported by electrical migration into the film from the bulk electrolyte. Secondly, the alkali concentration within the film is increased relative to that in the bulk solution. These findings are in agreement with those of Hull and James [2] who postulated that electroosmosis was the major driving force responsible for the spreading phenomenon with a minor contribution from vapour phase transportation of water. Baugh et al. [l] suggested that the Marangoni effect could also be considered as a viable explanation since the alkaline concentration gradient would be expected to generate a positive surface tenslo: gradlent between the spreading film and the bulk electrolyte. in a later stud; [3] Baugh et al. attempted to distinguish between the two mecharusms but the results were inconcluslve. Nevertheless, vapour phase transportation of water Into the film, due to the differential alkali concentration, was shown to contribute to the overall water supply in agreement with the findlngs of Hdi and James [2]. Both groups of investigators also agreed that equilibrium electrocapillary phenomena could not account for the observations. In view of the uncertaintles concerning the major drivmg force for spreading, a further expenmental investigation of the problem was colrsidered necessary. In the present paper, an attempt has been made to provide a more quantrtatlve correlation between the spreadmg rate and the electrical variables. This correlation will be extended to include a consideration of the properties of the electrolyte in a second communication. Shortly after completion of the experimental work discussed in these commumcations, Nlentiedt [4] and Nlentiedt and Laig-Horstebrock [5] published their views on the problem. These workers postulate t 1;.:t alkali metal cations, underpotentlal deposlted on the metal surface wIthin t& spreading film, diffuse a short distance along the metal beyond the film front and there react with water vapour to form drops of electrolyte. Coalescence of these electrolyte droplets to produce a contlnuous film is assumed to constitute the mechamsm of spreadmg. EXPERIMENTAL

The apparatus, preparation of electrodes and general procedure have been described previously [l]. In certain experiments a potential ramp was applied to the metal/electrolyte/f~Im system so as to obtam the relatIonshIp between current and potential at constant film length. This was achieved by he use of a Chemical Electromcs Linear Sweep Generator coupled to the potentl>stat which applied the ramp at the rate of 50 mV mu- -. In order to determine the speclflc resisttvity of a spreading film s:le followmg specially constructed electrode assembly was utilised. This consisted of a rectangular block on nylon mto which two rectangular Ni strips and a rectangular Ni plate (2 cm X 0.5 cm) were set so that they were electrically insulated from each other. The three electrodes were placed very close to each other with their maJor axes in parallel which m turn were In parallel w-th the minor axis of the block. The sequence was plate-strip-strip. Electrical cont.z.cts to the three electrodes were made on one side

207

of the block and epoxy resin used to seal the contacts. The other side of the block was polished flat. An electrolyte film was allowed to develop across all three the plate end of the assembly into electrodes by initially partially immersmg electrolytes and applying a negative potential. The resistivity of the resulting film could then be determined between the two strip electrodes using a Wayne Kerr B642 conductivity meter after the assembly had been removed from the electrolyte reservoir. All measurements were carried out in 6.8 mol drne3 (30% w/w) KOH solutions which were prepared free of metal Impurities by pre-electrolysis for one week at a current density of 1 mA cm-’ using a spiral Zn cathode and spiral NI anode of large surface areas. Pre-electrolysis was not used in the earlier studies [1,3]. Experiments were conducted, m either a nitrogen or oxygen atmosphere, in a thermostatically controlled cabinet at a temperature of 30 + O.l”C. Humidity was controlled by placing an open dish of 6.8 moi d;rrm3 KOH in the cabinet The reference electrode used thro,lghout the investigation was Hg/HgO/KOH (6.8 mol dmp3). RESULTS

AND

DISCUSSION

Rate deterrnrrtrng effect of porentral 111a nitrogen atmosphere

Figures la and b show schematically two stages in the development of a spreading film [F] on a negatively polarised vertical metal plate partially immersed in an electrolyte solution [E] showing the dlrection of current lines from the secondary electrode. These lines indicate the direction of nugrating cations and at the metal surface continuity of current is satisfied by reaction (1). At short times the current passes through the bulk solution mto the mtnnslc meniscus which develops instantaneously. These lines are shown as S-A, S-B and S-C in Fig. la. At longer times a spreading film develops and current passes into it as shown by lme S-C in Fig. lb. Although only a few representative current lines are shown m Fig. 1 it is obvious that the current flow can be distributed over the entire length of the metal/electrolyte and metal/‘fllm interfaces. Figure 2 shows plots of film length, I, vs: time, r. over a broad range of apphed potentials, E, from - 500 mV to - 1800 mV on a partially immersed Au electrode. Figure 3 shows these plots in graphically differentiated form which reveals the rate of spreading, di/dt, as a function of C. From Fig. 3 It IS clear that although the rate increases with E, it is inversely related to 1. Figure 4 shows the relationship between the measured current, I, and I for various E values. In all cases, the current falls with time dunng the spreading process m apparent correlation with the fall in spreading rate. Sunilar results were obtamed for 1Vi and Sn substrates. Using the data of Fig. 2 and a curve fitting procedure, the exact relationship between I and I was found to be / = k,c’/’ where, .‘c, is a potential

(3) dependent

constant.

Figure

5 illustrates

this relation&p

and

(a)

(b) t>> 0

t-c

/ __C-

/’

n (F) on the surface of a Fig. 1 Schematic represenlatlon of the ievelopmenl of an electroly!e nrgaurely polarlsed vcr:vzal metal plate (M) parually immersed :n an electrolyte solwon (E) showrig Ihe dlrecuon of current lines from the secondary electrodes (S). (a) at sort limes. (b) al long times (Film thickness exaggerated for clartly)

t/mm Fjg 2 Film length as a funcuon of 1:me durmg the spre3dlng In a nitrogen armosphzre. at various polentlals: (A) - 1800. - 1050. (0) - 900. (e) - 800. (B) - 700. (A) - 500 mv.

of 6.8 mol dm-’ (0) - 1500. (0)

KGH C-I an Au subslrate f) - 1150. (x) - 1350.

209

demonstrates Differentiation of time rate = dl/dt

that It pertains irrespective of of eqn. (3) yields an expression

the nature of the metal substrate. for the spreading rate as a function

= k,t-'/2

(4)

where kz = k/2. Combination

of eqns. (3) and (4) yields the important

result

rate = k,l-'

(5)

where k, = kf/2. Relationship (5) indicates that at constant applied potential, the spreadmg rate is inversely proportional to the film length. Figure 6 illustrates this relationship

for

a range

of

potentials

on

Au.

If

It is assumed

that

the same

mechanism of spreading persists at long times then expressron (5) indicates that only when I + cc will the spreading process cease. Figure 7 shows the relationsLp between spreading rate and applred potential for various film lengths and substrate meta. Is. It is clear that these plots are linear and to a fist approximation the data is independent of the nature of the substrate metal. It is also interesting to note that tbe plots have a common intercept at - 703 mV. The relationship between spreadmg rate and potenttal can therefore be represented rate=

--k,(E+7rJO)

(6)

where k, is a constant

Rg

3. Clpreacmg

substrate -1150.

rate as a function

m a mtrogen (x)

which varies

-1050,

(0)

atmosphere. -900,

(e)

of

with film length and E is the applied

ume dunng

at various -800

mV

the

sprea_Jlng of

potentials:

(A)

-1800,

6.8 (0)

mol

dmm3

-1500.

KOH (0)

potentral

on an Au -1350.

(+)

210

(with sign) in mV. (The negative sign in eqn. (6) is necessary to indicate that the rate more negative.) For values of E which are positive of .- 700 increases as E becomes mV. eqn. (6) predicts negative lates which are physically meaningless. At these potentials. it can be concluded that the driving force for spreading is zero. The Independence of the spreadin g rate upon the nature of the substrate metal demonstrated in Fig. 7 is iI surprising result in view of the fact that the current _leasured during the e:cperiments Laried by over three orders of magnitude. These results strongly suggest that in a deoxygenated atmosphere, the spreading rate is Ilot related to the measwed current. FigmIre 8 provides a more visual confirmation of this conclusion. Thus the correlation which appears to exist between the data for Au in Figs. 2 nd 3, although not considered to be fortuitous, is nevertheless of linuted value in providmg further insight into the spreading mechanism. In order to reconcile the lack of correlatton between the rate and measured current, it is

tlmln F1g_4. Measured current as a function of time at vanous poreritxals during the spreading of 6 8 mol d.Tm3 KOH on an Au substrate m a mtrogen atmosphere, (t ) - 1150, (X ) - 1050. (0) - 900, (e) - 800. (e) -700mV

211

Fig 5 Fllrn length as a funcuon of the square root of time at various potentials for the spreadmg of 6 8 mV on a Sn substrate. (0) -1350 .mV on an Au mol dm -3 KOH m a mtrogen atmosphere. A -1800 substrate, (x) - 1050 mV on a NI substrate

a mtrogen

atmosphere,

at various potentials-

(0)

- 1500. (0)

- 1350.

( + ) - 1150. ( X ) - 1050 mV.

+ NI x Au D Sn

IO

700

900

I300

1000

1100

1$Or;300

1400

1500

1600

1700

181

I

Fig 7 Spreadmg rate as a fL7ction of poteltlai at vx~ous film lengths for 6 8 mol dmm3 KOH nttrogen atmosphen- (+) NI substrate, (A) Sn substrate, (X) Au substrate.

tn a

n U

-1800

4I

+ X

0

-1500 +

n

3t ';._ E "a 2

X

n

2 s :I

fi

--

_@._

1

1

L____-_-_--*--

OlI

JJA

-1150 +

X

-

100 1

-1050

-x_ --_-----__,350

---1050

-f 10 I

-1350

X

11

I

T_15OO +

10

mA

Iroo

Fig 8 Spreading rate as a function of measured current at various potentials for 6 8 mol dmd3 KOH m a nitrogen .atmosphere. (+) NI substrate data, (X) Au substrate data, (a) Sn substrate data. () uuttal rate (/ + 0). (- - -) rate for a 3 mm film.

necessary to assume that only a small fraction of i is involved in providing the driving force for spreading. Thus an understanding of the current distribution within the metal/electrolyte/fiIm system is of importance. Current

distribution

and the importance

of iR effects

in a nitrogen atmosphere

Direct measurements of the resistance of the electrolyte film per unit length produced values in the range 5-10 X lo3 51 cm- ‘. It is presumed that the range of values obtained is caused by variation in film constitution and/or thickness. Assuming the conductivity of KOH within the film to be approximately equal to that in the bulk and usmg.the relation R = l/kwr

(7)

Fig 9. Polansatlon CU~\~S(I vs. E) for the system Au/6.8 developed at various potentiak- (a) - 1800, (0) - 1500,

- 900, (a) - 800. (B) -700.

(A) -500

mV.

mol drnm3 KOH/fii,‘& with 1 cm films - 1350, (+) - 1150. (X) - 1050. (0)

(0)

214

where k IS the specific conductivity of 30% (w/w) KOH, H*is the film widr.h and T is the ftlm thickness; values of T in the range l-2 pm were deduced..Using the mean fdm resistivity value, simple calculations were made to determine the potential drop which would develop within the fdm assuming that only 10% of the measured current actually flowed to the film front. There calculations were made for films of various length in the range 3.1-1.5 cm and growth potentials in the range -700 to - 1800 mV. It was discerned that only at the most positive potentials (E > 1.050 V) could the magmtude of the IR drop be considered small by comparison with the applied potential. Thus, only at these potentials is it feasible for a significant proportion of the current to flow into the film region. In order to prove these p~edictlons. Au/electrolyte/film systems were polarised to yield current-potential curves. The results are shown m Fig. 9. Despite the spread it is clear there IS no s;rstematic trend with either film length or growth potential. At the more positive potenttats the characteristics are consistent with a charge-transfer controlled hydrogen evolution reactlon (E a log I) but at the higher potentials with a resistance controlled reaction (E a I). From the slopes of the plots in Fig. 9 values for the elecrro!yte resistance between th e Au and reference electrodes were determined as i f 0.2 Qt. These values are very small compared with the film reslstivity (S-10 x lo3 Q cm-‘). These results provide further proof that at the more negative potentials current flow is restncted pnmarily to the mtrinslc meniscus, i.e. i J I,. Having estabhshed the asymmetric nature of the current distribution it was necessary to link this quantrtatively with the spreading rate data. In view of the preceeding discusslon and in particular the lack of any correlation between the spreading rate and the total measured current, it can be concluded that the “seat” of

I I mm Rg K3H

10. “Effectwe”

reswance

on a Au substrate

(E/rate)

rn a mtrogen

as a function atmosphere.

of Trim length for the spreadmg

of 6.8 mol dme3

215

the dnving force/pressure resides over a small distance on the metal plate between the meniscus and lower film region. It is postulated that current flow in the vicinity of the “leading edge” of the meniscus at the meniscus front, imr, is the parameter which should be correlated with the spreadin g rate. This is experiientally in accessible. It may be supposed that if current flow into this region were constant then the driving force for spreading would also be constant. It may also be assumed that the other major force involved IS a frictional one between the spreading film and metai plate which acts in opposition to the electrical driving force. The resultant of these two forces ultimately determines the spreading rate. Appendix A outlines a simple theory which accounts qualitatively for the observations m a nitrogen atmosphere. The final equation is = kE’/I “N, (8) or E’/uN,

= kl

Current

d~nribumn

(9) If relationship (9) is correct a plot of E/rate vs. I will be Linear and pass through the or&m. Figure 10 provides proof of the validity of thus simple model which identifies Ohm’s Law together with frictional considerations as central ‘0 an understanding of the empirical relationships (3-6). and spreadmg

characterwms

m an oxygen

atmosphere

A consideratton of the spreading characteristics m an oxygen atmosphere aids an understanding of the spreading mechanism and in particular the current distribu-

121 o-

t lmin

Fig 11. Film length as a function of ume (log I) durmg me spreadlug of 6 8 mol drnm3 KOH on a NI ) and oxyger. (- - -) atmosphere. at various potentials (0) - i350 substrate m a mtrogen (mV. ( X ) - 1050 mV. (0) - 900 mV.

216

tion, since, under the high overpotentia) conditions pertaining, oxygen penetrates directly into the film region where it reacts at the metal surface according to eqn. (2). Further, the current generated is experimentally accessible and facilitates any corre!ation with the spreading rate. Figure ! 1 shows plots of film length vs. time at three potentials on a Ni electrode m both nitrogen and oxygen atmospheres. At - 1350 mV it is clear that oxygen has no effect on the rate of spreading but as the potentiaI is made more positive (- 1050 mV) a small enhancement in the rate is evident. At still more positive potentials (- 900 mV) the effect of oxygen becomes significant with the rate being enhanced over that in nitrogen by a factor of ca. 2. In order to understand why rate enhancement cccurs only at the mere positive potentials, it is necessary to compare the polarisatio,l characteristics for the Ni/eIectrolyte/film system, in an oxygen atmosphere wi;h those in a mtrogen atmosphere. This is shown in Fig. 12. In a

Rg 12. Polansatlon curves (log I VS. E) for the system Ni/6 8 mol dmw3 KOH/film/N, wth a 5 mm film showmg the Tafel hne for hydrogen evolution and hnuting oxygen reduction current, (x) mtrogen atmosphere, (0) oxygen atmosphere (- - -) uncorrected for tR Ixses, () corrected for IR losses.

“17

nitrogen atmosphere the characteristics reduce to a Tafel line for hydrogen evolution (eqn. 1) at all potentials. However, in an oxygen atmosphere, the Tafel line is only evtdent at potentials more negative ihan -1200 mV. At more posttive values a diffusion controlled oxygen’reduction current is clearly evident due to the limited rate of oxygen diffusion through the electrolyte film to the metal surface. Thus oxygen is capable of significantly increasing current flow Gthin the system only at well with the spreading data of Fig. 11 potentials > - 1200 mV. This correlates where rate enhancement also commences in this potential region. These results strongly suggest that the driving force for spreading is inextricably linked with current flow within the film, i,, or current flow through the meniscus front region, lmr, since all current passing to the film must also pass through the meniscus front, i.e. in the case of the oxygen atmosphere, ir = l,,,r. Figure 13 shows a plot of the oxygen reduction current as a function of ftlm length in the range O-4 mm at a potential of - 1050 mV. This plot is a good straight line passing through the ongin. Its linearity demonstrates that :mder the electrochemical conditions employed and over the dista,lces considered. oxygen reduction cxcurs over the entire length of the metal/film interface and that the current density at any point IS constant. In the case of a diffuston limited process the current density

x

2

/

1 < 5

/

.__-_______--_-

-___

---

--

_---______

--_

d 1

/

C

;,

1

2

l/mm

Fig 13 Oxygen reduction current (KOH on a NI substrate. mol dra-’

X -)

,

(

3

4

and current

density (-

-

-)

dunng

the spreading

of 6 8

218

is independent of potential. Thus the ohmic potential loss per unit length of film is also independent of potential. Although the film IS highly resistive and ohmic losses are considerable, the applied overvoltage which compensates for these losses is also considerable. This results in a situation where the overpotential determines the exterri of current penetration into the film [6]. Since 9 is large. current penetration will be stgnificant. This current dtstribution in oxygen is in contrast with that observed in a mtrogen atmosphere where no increase in current is observed as a function of film length. These comparisons predict that the relationship between spreading rate and film length will also be different In the two atmospheres. Ftgure 14 compares and contrasts the relationship between the spreading rate attributed to hydrogen evolution with that attrtbuted to oxygen reduction as a functton of film length at potenttais of - 1050 mV and -900 mV. The rates attrrbuted to oxygen reduction alone were obtained by subtracting the rates in a nitrogen atmosphere from the total rates in an oxygen atmosphere. It is clear that in the case of spreading induced by oxygen reduction, the rate is mdependenr of ftlm iength in contrast with that induced by hydrogen evolutton discussed earlier. The results depicted in Figs. 13 and 14 refer to expenments conducted in an atmosphere of pure oxygen. However, in view of the experimentally accesslbie nature of or values 1t-1the presence of oxygen, it was of interest to attempt a direct correlation between these values with the spreading rate over a wide range. This was achieved using various nuxtures of O2 and N2 in the range O-10058 oxygen. Frgure shows the spreading rate as a functron of current density in the film for films of

/ /

_E

/

/

b_OS-

/’

go42 03-

/

/

/

//

/'

/d Ol00

0

Y

/,

5:' 1 1

’

,/ I

,

,

X

OZ-

0’

*

"

A

,s

o- * 2

31

4,

51

0 L-l,cm6-,

I

I

1

7

8

9

I 10

Fig 14 Spreadmg rate attnbuted to oxygen reducuon () or hydrogen evoluuon (- - -) as a - 900 function of reciprocal film length for 6 8 mol dm -3 KOH on a NI substrate. ( X) - 1050 mV. !o) mV

219

Fig 15. Spreadmg rate as a function of oxygen reduction substrate al - 900 mV

current de*wty

for 6.8 mol dm-’

KOH 01: a NI

constant length (2.5 mm). It can be seen that over a considerable range of oxygen concentrations, the rate is directly proportional to thts current. This is an important result. The above results demonstrate conclusively that u,>der the experimental conditions employed the spreading rate attributed to oxygen reductiou is proportional to the current density at the metal/film interface and indl.pendent of ftlm length. These results can be understood and reconciled with the earlier developed theory for spreading in a nitrogen atmosphere without incurring any changes in the proposed mechanism of spreading (see Appendix B). The fmal r~:s~~ltis

Equation (10) shows that the rate of spreading resulting from oxygen reduction can only be increased by mcreasmg lCdr which for a given film thickness depends solely on the oxygen concentration within the atmosphere in which experiments are conducted. CONCLUSIONS

Table 1 summaries the experimental deductions ftom the present investtgation and provides an expltnatron of probable links between the experimental variables. It is proposed that irrespective of the nature of the elzctrochemica: reactton which occurs, the important factor which controls the driving force for spreading is the

TABLE Summary

1 of expenmental

Nitrogen atmosphere (EG -700mV) 2 H,O+Ze+2OH-

observations

and deducilons

which determine

the rate of spreading

Oxygen atmosphere

(E> -12OOmV) +H,

0,+2H,0+4e-

+4OH-

current flowmg into/through the region of the intrinsic meniscus front, l,.,,t, at the base of the spreading him. Thrs dnving force is assumed to be opposed by viscous drag which increases with film length When hydrogen evolution is the predominant electrochemical process, i,, is controlled by charge transfer and ohmic effects which prohibit current penetration into the film region. Consequently, i,, and therefore the driving force for spreading remains constant. However, the increasing frictional drag results in a fall in spreading rate with film length. When oxygen reduction is the predominant electrochemical process, I,,,~ is controllzd by the rate of oxygen diffusion through the film to the metal/fdm interface, sin,= continurty of current must be maintained, I I = I,,,[. Current penetration into the film region for films < 4 mm in length is not prohibited and the driving force for spreading increases with increase in area of the charge transfer (metal/film) interface. The opposing frictional drag is therefore compensated and the spreading rate remains constant. ACKNOWLEDGEMENT The authors wish to thank the Directors

of Ever Ready

Ltd. for permission

to

publish this work. APPENDIX

A. PROPOSED

MODEL FOR SPREADING

IN A NITROGEN

ATMOSPHERE

If Fd is the net electrical driving force for spreading on a plate of umt width and Ohm’s law applies to the relatronship between current flow into the meniscus front and applied potential,

Fd = k,E’/R,,

= k51,r

(Al)

where E’ is the potential w.r.t. the critical potential f<)r spreading, (viz. -700 rnV2 and R,, is the mean resistance for current flow to the r-reniscus front. The parametewhich drrecrly generates the force/pressure for spreading is the potential E’ which in

221

turn can be equated with an electrical field operatin, (J within the film in the region close to the intrinsic meniscus. This acts upon the ionic components within the electrolyte to produce the currertt I,~_ Continuity of current across the metal/memscus front interface is achieved via the hydrogen evolution reactron. Similarly, if F, IS the net frictional force then it can be shown that F, = k,lv,~

(AZ)

where f is the film length at any instant and v is the mean velocity of the spreading

process.

is the resultant

If F,,,

=

film then (A3)

L, = 6 - F, :.Fne, = k, E’/R,, --‘vN,

force acting on the spreading

- k,lvNz

(A4)

WJ((~,E’/%,)

-4x,

(AsI

>

of (eqn. A5) can be made if it is assumed that Fd = F, 3 left hand term within the brackets ( Fd) is dominant. Hence

Simplification

VNZ

=

Fnrl, i.e. the

k,E’/R,,I

(A61

Some credence can be given to this assumption in view of the very small spreading rates observed in practice. For a given electro!yte, R,, is constant and therefore UN,

=

(~47)

k,E’/i

APPENDIX

B PROPOSED

MODEL

FOR SPREADING

IN AN OXYGEN

The drtving force for spreading in an oxygen atmosphere magnitude of current flow rhruugh the meniscus front region

AThlOSPHERE

IS associated

5 = kyl,r

with the (BI)

This equation is identical m form with eqn. (Al). But since there must be equality of current passmg through the meniscus front and that passing across the metal film interface *rl,r = i, = zcdll

(Bz)

where I,~~ is the current density at the metal/film length per unit width of film. Hence

interface,

i.e. current

& = k,z,,J

(B3)

The frictional reactions

retarding

force will be identtcal

n-respective

of the particular

4 = k&o2 on the spreading

F,,, = Fd - F, = k9kd Vo, _ =

P/W

electrode (B4

The net force acting

:.

per unit

film wil’ therefore

be (B5)

-

(w

wvo, )(

kd,d

-

F,,,

)

(B7)

222

Using the same assumption as simpllfxation of eqn. (B7) yields

in lhe

nitrogen

case

that

Fd = F, x=- F,,,,

then

uo, = k IOId REFERENCES 1 L M Baugh, J A Cook. J A Lee, J Appl Eleclrochem, 8 (1978) 253 2 M N Hull and HJ James. J. Electrochcm Sot , 124 (1977) 332 3 L-M Baugh, J.A Cook and F.L Tye m J Thomson (Ed ). Poser Sources 7. Academic Press. London, 1979. p 519 4 H W. Nlentredr. J Power Sources. 8 (1982) 257 5 H W. Nlermedt and H Larg Horsrebrock. J. Power Sources. 8 (1982) 267 Fuel Cells and Fuel Ba~tenes. Wiley, New York. i968. p 264. G H A Liebhafsky and E-’ Calms,