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Mass transfer to a carbon or graphite felt electrode
0013-4686/!40 $3.00 + 0.00 0 1990. PcrgamonPresspk.
&/ectrochimica Acta, Vol. 35, No. 9. pp. 1369-1376, 1990. Printedin Great Britain.
MASS TRANSFER TO A CARBON GRAPHITE FELT ELECTRODE B.
DELANGHE, S. TELLIER*
OR
and M. ASTRUC
Laboratoire de Chimie Analytique, CURS-Universite de Pau et des Pays de l’Adour, Avenue de Wniversite, 64000 PAU, France (Received 27 July 1989; in revbed form 21 November 1989)
Abstract-Mass transfer correlations to a carbon or graphite felt flow-through electrode have been established using two electrochemical reactions: [Fe(CN),13- /[Fe(CN)J- and Hti+/Hg’. The correlations a*k, vs v obtained with hexacyanoferrate were reproducible and independent of electrode thickness. Correlations established for mercury demonstrated that mass transfer to the felt was lower and varied with felt thickness. Variation of actual specific electrode area with the electrochemical reaction concerned and the nature of felt surface may explain these phenomena. It is proposed that mass transfer studies to flow-through electrodes should be backed by a study of the specific electrode area in the same electrochemical conditions. * Key words: mass transfer, flow-through, carbon felt, hexacyanoferrate.
allows the achievement of very high chemical conversion yields. The forced circulation of the electrolyte and the high specific area of the electrode are the reasons why an improved mass transfer is obtained, so that their efficiency is larger than that of conventional electrodes. Several forms of flow-through porous electrodes have heen studied: granular electrodes[ l-41, stacks of metallic grids[5-101, metallic foams[l 11, metal
NOMENCLATURE
t?=j%t* A a* b CO CL 4
D Edovnslreall E upstream I k, L m, 4 CO-CL R=-.---
correlation parameter in equation (4) geometric surface area (definition in the text), cm-’ specific surface area, cm-’ exponent in mass transfer correlations effluent concentration, mol cm-) influent concentration, mol cm-’ particulate dimension; fiber diameter for the felts, cm diffusion coefficient, cm* s-’ downstream cathode potential, V upstream cathode potential, V intensity, A mass transfer coefficient, cm s-’ electrode thickness, cm parameters in dimensionless correlation (equation (1)) conversion yield
CO
Re =d,F
”
Reynolds’ number
SC =;
Schmidt’s number
Sh =k,$
Sherwood’s number
c
electrolyte flow rate, cm s-’
Greek symbols
B
(mD ’ -qdi- yy_ ,,) correlation equation (2)
P
specific mass of the felt (g cm-“) kinematic viscosity, cm* s-’
Y
mercury.
parameter in
or carbon felts[12-171 and reticulated vitreous carbon[l8]. Amongst them, carbon or graphite (in fact graphitized carbon) felts are the materials characterized by the smallest dimension with a fiber diameter of 9 or 10 micrometers. This property has for consequence the largest electrode area per volume unit. These electrodes are therefore the most efficient of all. Very high chemical efficiencies are obtained even by using very thin flow-through electrodes and that in turn allows the design of electrochemical reactors where fluxes are parallel. When designing such electrochemical reactors, it is necessary to know the mass transfer rate towards the electrode surface in given hydrodynamic conditions (to thus correlate the mass transfer coefficient to the flow rate of solution through the electrode). A survey of the literature evidenced more than serious disagreement between authors. Therefore a new evaluation of the mass transfer towards carbon felt electrodes was undertaken by using, with the same reactor, either a reference soluble redox system (hexacyanoferrate III/II) or a metal deposition (Hg(II)/HgO).
1. INTRODUCTION Introduction of three dimensional electrochemical reactors working *Author to whom correspondence
in
electrodes in steady-state
should be addressed.
2. THEORY The mass transfer towards a three dimensional electrode, operated under forced-flow and diffusional control conditions, may be evaluated from the I369
B. DELANOHEet al.
1370
dimensionless relation between Sherwood, Reynolds and Schmidt numbers: Sh = mRebScq,
(1)
where m, b, q are real numbers. Expressing the dimensionless numbers of particular experimental conditions (supporting electrolyte, electrochemical reaction, electrode) equation (1) may give an expression of the mean mass transfer coefficient, /c, : k, = flu”,
(2)
where v is the fluid flow rate in the reactor, and /I is a real number. Several relations of this form have been proposed for diverse electrode materials. The carbon and graphite felts rank high considering both mass transfer and specific surface area. The values of /I and b vary with the type of electrode material and even when considering only graphite felts large differences may be noted[ 13, 141(Table 1). The results of Schmal et a/.[151 obtained with individual fibers seem to validate the correlation established by Bek and Zamyatin[l3] but the values established by Oren and Soffer[l6] and the correlation obtained by Kinoshita and Leach[l4] are in disagreement. The experimental determination of the mass transfer coefficient must be made out of reaction control of the overall transfer. This may be realised by using a cell design schematised in Fig. 1 with an electrode thickness L and a constant ascending flow of solution (flow rate v). If plug flow conditions and negligible axial dispersion are assumed, the mass balance may be expressed through the expression of the conversion yield, R: (3)
1 -exp[-a*k,,,il,
R = 1 -$=
L
”
J
where C, and C, stand for respectively the effluent and influent concentrations of the reacting species; a* is the specific surface area of the electrode material. Therefore the expression (2) may be modified into: a*k, = avb,
(4)
with a =/3a*. Equation (4) may be used for predicting conversion yields or designing reactors for definite experimental conditions as a and b are measurable parameters.
3. EXPERIMENTAL
SECTION
3.1. Electrode materials Carbon and graphite felts used in this study are produced by Carbone-Lorraine. Their characteristics are gathered in Table 2. The geometric surface areas in Tables 1 and 2 are obtained from the calculation of the total surface area per volume unit of the felt, when considering fibers as perfect non-porous cylinders. For the values in Table 2, the specific mass of the felts given by the supplier, and a carbon material density of 1.7 gcrnm3 are considered. It should be taken into account that the specific area might be different from the geometric surface area: it may be
Mass transfer to a carbon or graphite felt electrode
elecl.rode feed
Fig. 1. Schematised running of the felt electrode,
higher because of a roughness effect, or lower because of a possible partial blocking of the fiber electrode surface. It is only a rough approximation of the area involved in electrochemical reactions. These materials are hydrophobic and their utilisation in aqueous solutions needs a preliminary moistening treatment. We noticed that these industrial products may sometimes present heterogeneities in specific mass, thickness etc. Carbon felt contains more impurities than graphite felt. 3.2. Electrochemical reactor The electrochemical cell is presented in Fig. 2. It is a methacrylate cylinder with an ascending flow of electrolytic solution. A plastic foam is located upstream to the felt and acts as a calming section. The counter electrode (ruthenium on a titanium grid) is situated downstream of the working felt to prevent gas bubbles produced by anodic oxidation of the solvent from accumulating on the felt. The current feeder to the felt is a titanium grid. The active section of the carbon felt is 1.54 cm* for the lower thicknesses and 2.01 cm* for the other felts. An see fitted with a capillary agar-KNO, junction is placed immediately downstream of the working felt electrode. The electrical circuit comprises a Tacussel PRT 40-5X potentiostat and AOIP MNS 1 E 1 multimeters. The electrolytic solution is stocked in a 25 I tank maintained at 291 + 1 K and is forced through the cell by an Ismatec MVCA peristaltic pump. The flow rate v was varied from 0.3 to 6 cm s-‘. The feed solutions are sparged with nitrogen to remove oxygen that might be reduced. The solution circuit is open and effluents can be sampled at the exit of the electrochemical cell. 3.3. Solutions Two types of electrolytic solutions have been used as influents. Equimolar solutions (10m3M) of potassium hexacyanoferrate (II) and (III) in 0.5 M sodium hydroxide. The choice of equimolar ratios of these chemicals
1371
is due to the results of several authors[l9-211 who demonstrated that the highest values of the heterogeneous rate constant were obtained in these conditions. The diffusion coefficient of Fe(CN):- is 7.4 x 10e6 cm* s-‘[22]. The kinematic viscosity of the solution is 1.OOx lo-* cm* s-‘. Mercuric chloride, in 3 M sodium chloride, has been chosen because of the high heterogeneous rate constant of mercury deposition and of its actual industrial significance. The solutions were 2 x 10e5 M or 5 x 10e6 M Hg(I1). In these solutions, equilibrium calculations indicate that mercury(I1) is mainly (97%) present as Hg[Cl,]*-. The diffusion coefficient of Hg(I1) is 10e5 cm* s-I[181 and the kinematic viscosity of the solution 0.96 x lo-* cm* s-‘. 3.4. Analysis of solutions Effluents are sampled in steady state (after 5 min of electrolysis). The determinations of hexacyanoferrate (II) and (III) are made by voltammetry on a rotating platinum disk electrode (Tacussel ED1 65120, PRT 500 LC potentiostat, EPL 1 recorder). Mercury is determined by cold vapor atomic absorption spectrometry (IL 151) after reduction by NaBH,. 3.5. Electrolysis potential The evaluation of the mass transfer parameters of carbon felts needs electrolysis experiments in situations where the reaction rate has no influence. It was therefore necessary to assign convenient conditions by determining intensity-potential and conversion yield-potential curves. Hexacyanoferrate (III). The curves presented in Fig. 3 have been obtained with a 1.2 mm thick graphite felt. The residual current, Ia, becomes nonnegligible only for E < -0.2 V; it may be due to the reduction of residual oxygen and to that of reducible surface groups. Some of these groups (particularly quinonic ones) may play an important role as mediators of oxygen reduction[23]. The reproducibility of I, is low, due both to the difficulty of outgassing the 25 1 of solution used in one experiment and to the heterogeneity of the electrode material. Moreover, when using thicker felts, well defined diffusion plateaux can be obtained on R-E curves (curves with 0 and 0, Fig. 5) whereas the corresponding I-E curves do not present a horizontal plateau (Fig. 4). This fact means that the hexacyanoferrate reduction is made under diffusion control whereas the intensity is affected by secondary reactions such as reduction of residual oxygen, adsorbed impurities, or electroactive surface groups. Therefore, a part of the intensity is lost for the hexacyanoferrate reduction. In this way, the determination of the mass transfer coefficient from measurements of the limiting diffusion current-a procedure very often chosen in the
Table 2. Main characteristics of electrode material Felt
Graphite
Carbon
Fiber diameter/m Mean thickness/cm Mass per unit area/gm-’
0.12 150
9 x 10-b 0.35 250
0.13
10 x 10-h 0.4
1
0.125 325 RVG 1000
0.07 1 185 RVG 2000
170 0.131 310 RVC 1000
260 0.065 150 RVC 2000
1000 0.100 235 RVC 4000
Specific mass/g cm-’ Geometric area/cm-’ Commercial denomination
0.9 950 0.105 275 RVG 4000
B. DELANGHEer nl.
1372
ct 10
2 ,3 ,4 5 6 .7 .B .9
1M
I 5!a
Fig. 2. Electrolytic cell: (1) capillary agar-KNO, junction; (2) fixative ring; (3) ruthenied titanium grid; (4) circular platinum wires; (5) current feed grid (titanium grid); (6) felt; (7) fixative ring; (8) capillary agar-KNO, junction; (9) calming section (plastic foam); (10) current feed. literature[ l-l 5]-seems
difficult in the case of carbon
felt electrodes. For these electrodes, the determination of the product a*k,,, must be made from the measurements of conversion yields, as suggested by Bek and Zamyatin[l3]. It is the reason why all following quantitative data have been obtained from the analysis of cell effluents. Electrolysis potential was always chosen as anodic as possible on the diffusion plateau to avoid any intervention of solvent reduction processes. The effect of electrode thickness (Figs 4 and 5) creates a shift of the diffusion plateau towards cathodic potentials, as a consequence of the ohmic drop AE = (Eupstream - Edownstmm) in the solution through the electrode. The potential drop AE increases with the electrode thickness, L, and the flow rate, u[24]. The occurrence of non-unity conversion yields with thick felts necessitates high values of the flow rate. In these conditions, we have measured
0
-200
-400
40
-SW
E~-~&.CE.
I
-1ooo
-1ml
L
m
Fig. 4. I-E curves.: (0) 0.13 cm thick carbon felt, v = 2.91 ems-I; (0) 0.4cm thick carbon felt, v = 1.57cm s-t; (0) 0.35 cm thick graphite felt, v = 1.97cm s-t; K,Fe(CN), = lo-) M; NaOH = 0.5 M.
values of AE up to 400 mV instead of less than 50 mV for thin electrodes (RVG or RVC 1000). As the diffusion plateau is obtained only when the whole electrode works in diffusion-limited conditions, the shift of the plateau may be explained by the intervention of the ohmic potential drop AE. From these preliminary experiments, convenient electrolysis potentials have been defined as between - 0.3 and - 0.4 V, and as - 1.OV/see for respectively 0.12 and 0.35 cm thick graphite felts; for 0.13 and 0.4 cm thick carbon felts electrolysis potentials have been chosen at -0.8 and -0.9V/sce, respectively. Mercury (ZZ). Experiments with mercury have been limited to graphitized electrode materials (Fig. 6). Low concentrations of mercury (II) have been used (50 times lower than hexacyanoferrate concentrations), reducing both electrolysis current and ohmic drop. Then the relative importance of the residual current due to secondary reaction is all the greater. There is no serious distortion of the R-E
t _S---75
75
5Q:
8
.!a
75
Y-o----O--
;I 250 D:
a: -~----~-O-~25
25
25
al
0
E
Fig. 3. I-E and R-E curves: 0.12 cm thick graphite felt; v = 1.06cm s-r; lo-’ M K,Fe(CN),; 0.5 M NaOH.
-“AUK*
/““mv-a%
-1600-rim
dmstm
Fig. 5. R-E curves: (0) 0.13 cm thick carbon felt, v = 2.91 ems-‘; (0) 0.4cm thick carbon felt, v = 1.57cm s-l; (0) 0.35cm thick graphite felt, v = 1.97cms-‘. lo-” M K,Fe(CN),; 0.5 M NaOH.
1373
Mass transfer to a carbon or graphite felt electrode
Fig. 6. I-E curves: 0.12 cm (0) and 0.9 cm (a) thick graphite felt with 2.95 cm s-’ and 1.01 cm s-’ flow rates, respectively. 4 ppm Hg (2 x lo-‘M); 3 M NaCl.
curves in Fig. 6 even with thick electrodes and high solution velocity. In these conditions intensitypotential curves may not be used at all due to the relatively higher importance of the irreproducible residual current; only conversion yield-potential curves were used in the calculations. We have verified that there is no deposition of insoluble salts (such as mercurous chloride) in these experimental conditions and that the solubility of metallic mercury is negligible. Electrolysis potentials for the evaluation of mass transfer coefficients have been chosen as -0.5, -0.6 and -0.9 V/see for respectively 0.12, 0.35 and 0.9 cm thick graphite felts.
Four different experiments have been made using 0.12 cm thick graphite felt and a -0.3 V/see potential applied to the working felt except for curve 2 (- 0.4 V/see). The similarity between the regression slopes which have been obtained demonstrates that in both situations, the electrode is working under diffusion control. The corresponding values of a and b are presented in Table 3. The mean values have been obtained by a nonlinear regression applied to the whole set of results of the four experiments. Relation (4) for a 0.12 cm thick graphite felt then becomes specifically:
3.6. Cyclic voltammetry on graphite fibers Cyclic voltammetry experiments have been performed with individual fibers extracted from 0.12 cm thick graphite felt; voltammograms are obtained by using Tacussel PRT lo-O.5 potentiostat and G.S.T.P. 3 signal generator, and are recorded with a Bryans XY recorder 29 A.3.
The reproducibility is better for b than for a (up to 15%). These variations may, at least for a part, be explained by the heterogeneity of commercial carbon or graphite felts: the specific mass of felt samples may vary by up to 10%. Another possible major reason of dispersion of a values is the presence of chemical heterogeneities either in commercial product or generated during fiber pretreatment. The various felts under study have specific mass which differs from each other. Their mass transfer parameters calculated from Fig. 8 may be compared only after a normalisation: a*k, ,a& P P The correlation parameters are then in very good agreement (Table 4). It is thus possible to conclude that the mass transfer towards carbon or graphite felt electrodes may be defined by the same correlation:
4. RESULTS
AND DISCUSSION
4.1. Hexacyanoferrate (N/U) The correlation of a*k, with v for the reduction of hexacyanoferrate (III) is presented in Fig. 7.
a*k m = 7.1 v’.‘~.
(5)
a* k, = 57 v”36, P Table 3. Correlation parameters (conditions in the text) a
b
1 2 3 4
8.0 7.1 6.7 6.3
0.34 0.39 0.38 0.37
Mean
7.1
0.36
Experiment I -
-62
-0.3 log(V)
0.0 I
_(
0.1
0.
c
cm4
Fig. 7. Graphical correlations between a*/~, and the flow rate v for 0.12cm thick graphite felt. 10-l M K,Fe(CN),; 0.5 M NaOH.
1374
B. DELANGHE et al.
1.5
-10
’
b
0.
. IqM
d2 I
.
0.4
.
0.6
t
ms-
Fig. 8. Graphical mass transfer correlations obtained with: (0) 0.35 cm thick graphite electrode; (0) 0.13 cm thick carbon electrode; (0) 0.4 cm thick carbon electrode. 10e3 M K,(CN),; 0.5 M NaOH. The line (-.-.-) is obtained from the 0.12 cm graphite felt.
independently of felt thickness and flow rate. This is in contradiction with the conclusions of Kinoshita and Leach[ 141 who obtained different correlations with 0.175 and 0.25 cm thick electrodes. Correlation (5) is in quite good agreement with that proposed by Bek and Zamyatin[ 131but concerns a four times more extended range of v values. It is also in agreement with the correlation of Schmal et a[,[15]. It must be noted, however, that all these relations have been obtained with the same electrochemical reactants [Fe(CN)&/[Fe(CN)J-. Other authors, working with other reactants (Br,/Br-) obtained differing results. The difference can neither be explained by the differing feed solution (particularly the kinematic viscosity and the diffusion coefficient) nor by the fiber diameter. Actually, the introduction of dimensionless parameters into equation (6) yields to a more general expression: $ Sh = 1.6 x 104Re0.36, whereas the results of Kinoshita into the same form are: $Sh
(7)
and Leach[l4] put
= 9.8 x 102Re0.72
solution through the felt electrode much lower. The experimental mass transfer relations obtained are presented in Fig. 9 where they are also compared with results obtained with hexacyanoferrate (III). The slopes of the lines for mercury deposition in Fig. 9 are similar to those obtained for [Fe(CN),]‘-, but their intercepts on the axis are significantly lower. Two independent experiments have been performed with 0.12 cm thick felts submitted to slightly different pretreatments; the slope seems to be higher for the more oxidizing pretreatment. The mass transfer correlations extracted from Fig. 9 are presented in Table 5. In the case of mercury deposition, significantly distinct correlations are established for the various electrode thicknesses. It appears from these data that a correlation established with one felt with the deposition of mercury (II) may not be extrapolated to electrodes of different thicknesses, or having received a differing pretreatment nor to hexacyanoferrate (III) reduction. These conclusions cannot be easily compared with those of the literature. Oren and Soffer[l6] did not propose any mass transfer correlation but they obtained two values of the product a*k,, which were 0.65 and 1.48 S-I for two flow rates, respectively 0.39 and 0.83 cm s-l. The electrode material used for their study was RVG 2000. For this felt, the results given in this paper for the product a*k,,, would be respectively 2.12 and 2.8 s-’ for the corresponding flow rates. These values are clearly higher than those of Oren and Soffer[l6]. However, it should be noticed that these authors used a flow-by electrode set up and very thick carbon felt (9.5 cm). Therefore, the fibers were situated lengthways relative to the flow and perhaps an anisotropy effect might explain-at least partially-the differing results. Actually Schmal et a1.[15], for the same arrangement (flow-by electrodes), obtained lower results than those of Bek and Zamyatin[l3]. The nature of the felt treatment could also explain the differences because it seems that such a parameter can influence the conversion yields. 4.3. Cyclic voltammetry and discussion Cyclic voltammetric studies on single graphite fibers extracted from the felts have been real&d 4 4.1.
for a 0.175 cm thick felt and: SSh
4.0.
= 7.5 x 102Re0,6’
3.9 *
for a 0.25 cm thick felt. Equation from these expressions.
(7) clearly differs
4.2. Mercury As the reactant concentration is very small the electrolysis current is very low and the ohmic drop in Table 4. The correlation parameters (conditions in the text) Felt
L/cm
Graphite
b
0.12 0.35
a/P 57 53
0.36 0.38
0.13 0.40
53 51
0.38 0.34
_
3.6.
-1.5
-1.3
-1.1
-0.9
-0.7
-0.5
e
b3m=L)
Fig. 9. Graphical mass transfer correlations obtained from the mercury (II) redox system and from 0.12 cm (0 and 0); 0.35 cm (A) and 0.9cm (0) graphite felts. 1 ppm Hg (5 x 10m6M); 3 M NaCI. The line (-.-.--) presents the mass transfer correlation obtained from the hexacyanoferrate (III/II) redox-system.
Mass transfer to a carbon or graphite felt electrode
1375
Table 5. Mass transfer correlations at graphite felt electrodes Correlation Electrolytic solution Electrode thickness/cm
0.12 0.127 0.35 0.9
Hg2+ 4 2 U0,39 3’1 U0.43 3: 1 vO,W 3.7 v0,42
FW%I’7.1 oO.36 4.1 vO.36 6.0 vO.)~
8.5 x 103Reo-42
Yin this experiment a more oxidising pretreatment
in an attempt to elucidate these difficulties. The voltammograms obtained with hexacyanoferrate (III) (Fig. 10B) are typical of a reversible reaction on a cylindrical microelectrode such as those described by Aoki[25] and Amatore[26]. The curves registered with mercury, in similar experimental conditions (Fig. IOA), present two well defined peaks corresponding to superficial processes already described such as adsorption or cation exchange with surface groups or superficial graphite oxides[27, 281. The predominant mercury species in solution being (HgCl,)2- the mercury cation exchange necessitates a very high lability of the complex that seems possible considering mercury reactivity. The nucleation step of deposited mercury on these electrodes does not seem limiting as the conversion yield-potential curves presented in Fig. 6 have a well defined diffusion plateau. In these results there is no evidence that the number of nucleation sites increases with negative electrode potential as suggested by Golas[29]. To explain the efficiency differences it thus seems necessary to call upon variations of the active specific
(A)
fl@
E / S.CE.
PP%
Hd’ 7.6 x 103Re0.39 6.1 x 103Reo”) 10.1 x 103Reo.Q
(mV)
I3-
16 4 x 103Reo.36
’
has been applied to the 0.12 cm felt electrode.
area of the fibers with the pretreatment applied and the type of electrochemical reaction involved. The reduced efficiency observed for mercury deposition could be explained by lower densities of active sites. This hypothesis is in agreement with the fact that hexacyanoferrate (III) data are self coherent[l3, 15, this work] but those obtained with other electrochemical systems (bromine[ 141, mercury[ 161) are different.
5. CONCLUSION The mass transfer correlation towards carbon or graphite felt electrodes established from the reduction of hexacyanoferrate (III) is in good agreement with the expression proposed by Bek and Zamyatin[l3]. The present paper extends the validity of this correlation (0.36 cm s-r flow rate: 0.12-0.4 cm thickness). The correlation established by Schmal et a/.[ 151is also approximately in agreement, the differing experimental conditions explaining slight discrepancies. However, in identical experimental conditions, the mass transfer correlations established from the reduction of mercury (II) are different and vary with electrode thickness. Similar observations were made by Kinoshita and Leach[l4] using another electrochemical reaction. It seems therefore that the electrochemical reactivity of graphite felts varies with the reaction mechanism involved, or in practical terms that the active specific surface area a* is not equal to the geometric area and may vary with the nature of the electrolytic solution. Another paper will be devoted to the study of the variations of the active specific surface area with solution composition.
REFERENCES 1. F. Coeuret, Elecfrochim. Acra 21, 185 (1976). 2. H. Olive and G. Lacoste, Elecfrochim. Acfa 24, 1109
E 1 S.CE.
(mV)
Fig. 10. Cyclic voltammograms obtained from anodically pretreated graphite fiber and the solutions containing: (A) 5 x 10m4M Hg; 3 M NaCl; (B) lo-’ M K,Fe(CN),; 0.5 M NaOH. Potential sweep rate: 50 mV s-l.
(1979). 3. M. A. Enriquez-Granados, D. Hutin and A. Storck, Electrochim. Acra 27, 303 (1982). 4. G. H. Sedahmed, J. appl. Electrochem. 17, 746 (1987). 5. R. E. Sioda, J. electroanal. Chem. 70, 49 (1976). 6. R. E. Sioda, Electrochim. Acta 22, 439 (1977). 7. A. Storck, P. M. Robertson and N. Ibl, Electrochim. Acra 24, 373 (1979). 8. F. Leroux and F. Coeuret, Electrochim. Acta 28, 1857 (1983). 9. M. M. Letord-Quemere, F. Coeuret and J. Legrand, Electrochim. Acra 33, 881 (1988).
1376
B. DELANGHEet al.
10. S. Piovano and U. Bohm, J. appl. Elecrrochem. 17, 123 (1987). 11. S. Langlois and F. Coeuret, J. appl. Elecfrochem. 19,Sl (1989). 12. J. M. Maracino, F. Coeuret and S. Langlois, Electrochim. Acra 32, 1303 (1987). 13. R. Yu Bek and A. P. Zamyatin, Sov. Elecrrochem. 14, 1034 (1978). 14. K. Kinoshita and S. C. Leach, J. electrochem. Sot. 129, 1993 (1982). 15. D. Schmal, J. Van Erkel and P. J. Van Duin, J. appl. Elecrrochem. 16, 422 (1986). 16. Y. Oren and A. Soffer, Elecrrochim. Acta 28, 1649 (1983). 17. M. Abda, Y. Oren and A. Soffer, Elecrrochim. Acta 32, 1113 (1987. 18. M. Matlosz and J. Newman, J. elecrrochem. Sot. 133, 1850 (1986). 19. R. Sohr and L. Muller, Electrochim. Acta 20, 451 (1975).
20. M. Noel and P. N. Anantharaman. Analyst 110, 1095 (1985). 21. W. J. Blaedel and G. W. Sehieffer, J. electroanal. Chem. 80, 259 (1977). 22. J. C. Bazan and A. J. At-via, Electrochim. Acta 10, 1025 (1965). 23. T. Nagaoka, T. Sakai, K. Ogura and T. Yoshino, Anal. Chem. 58, 1953 (1986). 24. H. Olive and G. Laeoste., Electrochim. Acfa 2!!, 1303 (1980). 25. K. Aoki, K. Honda, K. Tokuda and H. Matsuda, J. electroanal. Gem. 182, 267 (1985). 26. C. A. Amatore, M. R. Deakin and R. M. Wightman, J. elecrroanal. C&m. 206, 23 (1986). 27. P. M. Korach, M. R. Deakin and R. M. Wightman, J. phys. Chem. 90,4612 (1986). 28. T. E. Bdmonds, J. R. Dean and S. I.&if, Anal. Chim. Acta 212, 23 (1988). 29. J. Golas and J. Osteryoung, Anal. Chim. Acta 181,211 (1986).
&/ectrochimica Acta, Vol. 35, No. 9. pp. 1369-1376, 1990. Printedin Great Britain.
MASS TRANSFER TO A CARBON GRAPHITE FELT ELECTRODE B.
DELANGHE, S. TELLIER*
OR
and M. ASTRUC
Laboratoire de Chimie Analytique, CURS-Universite de Pau et des Pays de l’Adour, Avenue de Wniversite, 64000 PAU, France (Received 27 July 1989; in revbed form 21 November 1989)
Abstract-Mass transfer correlations to a carbon or graphite felt flow-through electrode have been established using two electrochemical reactions: [Fe(CN),13- /[Fe(CN)J- and Hti+/Hg’. The correlations a*k, vs v obtained with hexacyanoferrate were reproducible and independent of electrode thickness. Correlations established for mercury demonstrated that mass transfer to the felt was lower and varied with felt thickness. Variation of actual specific electrode area with the electrochemical reaction concerned and the nature of felt surface may explain these phenomena. It is proposed that mass transfer studies to flow-through electrodes should be backed by a study of the specific electrode area in the same electrochemical conditions. * Key words: mass transfer, flow-through, carbon felt, hexacyanoferrate.
allows the achievement of very high chemical conversion yields. The forced circulation of the electrolyte and the high specific area of the electrode are the reasons why an improved mass transfer is obtained, so that their efficiency is larger than that of conventional electrodes. Several forms of flow-through porous electrodes have heen studied: granular electrodes[ l-41, stacks of metallic grids[5-101, metallic foams[l 11, metal
NOMENCLATURE
t?=j%t* A a* b CO CL 4
D Edovnslreall E upstream I k, L m, 4 CO-CL R=-.---
correlation parameter in equation (4) geometric surface area (definition in the text), cm-’ specific surface area, cm-’ exponent in mass transfer correlations effluent concentration, mol cm-) influent concentration, mol cm-’ particulate dimension; fiber diameter for the felts, cm diffusion coefficient, cm* s-’ downstream cathode potential, V upstream cathode potential, V intensity, A mass transfer coefficient, cm s-’ electrode thickness, cm parameters in dimensionless correlation (equation (1)) conversion yield
CO
Re =d,F
”
Reynolds’ number
SC =;
Schmidt’s number
Sh =k,$
Sherwood’s number
c
electrolyte flow rate, cm s-’
Greek symbols
B
(mD ’ -qdi- yy_ ,,) correlation equation (2)
P
specific mass of the felt (g cm-“) kinematic viscosity, cm* s-’
Y
mercury.
parameter in
or carbon felts[12-171 and reticulated vitreous carbon[l8]. Amongst them, carbon or graphite (in fact graphitized carbon) felts are the materials characterized by the smallest dimension with a fiber diameter of 9 or 10 micrometers. This property has for consequence the largest electrode area per volume unit. These electrodes are therefore the most efficient of all. Very high chemical efficiencies are obtained even by using very thin flow-through electrodes and that in turn allows the design of electrochemical reactors where fluxes are parallel. When designing such electrochemical reactors, it is necessary to know the mass transfer rate towards the electrode surface in given hydrodynamic conditions (to thus correlate the mass transfer coefficient to the flow rate of solution through the electrode). A survey of the literature evidenced more than serious disagreement between authors. Therefore a new evaluation of the mass transfer towards carbon felt electrodes was undertaken by using, with the same reactor, either a reference soluble redox system (hexacyanoferrate III/II) or a metal deposition (Hg(II)/HgO).
1. INTRODUCTION Introduction of three dimensional electrochemical reactors working *Author to whom correspondence
in
electrodes in steady-state
should be addressed.
2. THEORY The mass transfer towards a three dimensional electrode, operated under forced-flow and diffusional control conditions, may be evaluated from the I369
B. DELANOHEet al.
1370
dimensionless relation between Sherwood, Reynolds and Schmidt numbers: Sh = mRebScq,
(1)
where m, b, q are real numbers. Expressing the dimensionless numbers of particular experimental conditions (supporting electrolyte, electrochemical reaction, electrode) equation (1) may give an expression of the mean mass transfer coefficient, /c, : k, = flu”,
(2)
where v is the fluid flow rate in the reactor, and /I is a real number. Several relations of this form have been proposed for diverse electrode materials. The carbon and graphite felts rank high considering both mass transfer and specific surface area. The values of /I and b vary with the type of electrode material and even when considering only graphite felts large differences may be noted[ 13, 141(Table 1). The results of Schmal et a/.[151 obtained with individual fibers seem to validate the correlation established by Bek and Zamyatin[l3] but the values established by Oren and Soffer[l6] and the correlation obtained by Kinoshita and Leach[l4] are in disagreement. The experimental determination of the mass transfer coefficient must be made out of reaction control of the overall transfer. This may be realised by using a cell design schematised in Fig. 1 with an electrode thickness L and a constant ascending flow of solution (flow rate v). If plug flow conditions and negligible axial dispersion are assumed, the mass balance may be expressed through the expression of the conversion yield, R: (3)
1 -exp[-a*k,,,il,
R = 1 -$=
L
”
J
where C, and C, stand for respectively the effluent and influent concentrations of the reacting species; a* is the specific surface area of the electrode material. Therefore the expression (2) may be modified into: a*k, = avb,
(4)
with a =/3a*. Equation (4) may be used for predicting conversion yields or designing reactors for definite experimental conditions as a and b are measurable parameters.
3. EXPERIMENTAL
SECTION
3.1. Electrode materials Carbon and graphite felts used in this study are produced by Carbone-Lorraine. Their characteristics are gathered in Table 2. The geometric surface areas in Tables 1 and 2 are obtained from the calculation of the total surface area per volume unit of the felt, when considering fibers as perfect non-porous cylinders. For the values in Table 2, the specific mass of the felts given by the supplier, and a carbon material density of 1.7 gcrnm3 are considered. It should be taken into account that the specific area might be different from the geometric surface area: it may be
Mass transfer to a carbon or graphite felt electrode
elecl.rode feed
Fig. 1. Schematised running of the felt electrode,
higher because of a roughness effect, or lower because of a possible partial blocking of the fiber electrode surface. It is only a rough approximation of the area involved in electrochemical reactions. These materials are hydrophobic and their utilisation in aqueous solutions needs a preliminary moistening treatment. We noticed that these industrial products may sometimes present heterogeneities in specific mass, thickness etc. Carbon felt contains more impurities than graphite felt. 3.2. Electrochemical reactor The electrochemical cell is presented in Fig. 2. It is a methacrylate cylinder with an ascending flow of electrolytic solution. A plastic foam is located upstream to the felt and acts as a calming section. The counter electrode (ruthenium on a titanium grid) is situated downstream of the working felt to prevent gas bubbles produced by anodic oxidation of the solvent from accumulating on the felt. The current feeder to the felt is a titanium grid. The active section of the carbon felt is 1.54 cm* for the lower thicknesses and 2.01 cm* for the other felts. An see fitted with a capillary agar-KNO, junction is placed immediately downstream of the working felt electrode. The electrical circuit comprises a Tacussel PRT 40-5X potentiostat and AOIP MNS 1 E 1 multimeters. The electrolytic solution is stocked in a 25 I tank maintained at 291 + 1 K and is forced through the cell by an Ismatec MVCA peristaltic pump. The flow rate v was varied from 0.3 to 6 cm s-‘. The feed solutions are sparged with nitrogen to remove oxygen that might be reduced. The solution circuit is open and effluents can be sampled at the exit of the electrochemical cell. 3.3. Solutions Two types of electrolytic solutions have been used as influents. Equimolar solutions (10m3M) of potassium hexacyanoferrate (II) and (III) in 0.5 M sodium hydroxide. The choice of equimolar ratios of these chemicals
1371
is due to the results of several authors[l9-211 who demonstrated that the highest values of the heterogeneous rate constant were obtained in these conditions. The diffusion coefficient of Fe(CN):- is 7.4 x 10e6 cm* s-‘[22]. The kinematic viscosity of the solution is 1.OOx lo-* cm* s-‘. Mercuric chloride, in 3 M sodium chloride, has been chosen because of the high heterogeneous rate constant of mercury deposition and of its actual industrial significance. The solutions were 2 x 10e5 M or 5 x 10e6 M Hg(I1). In these solutions, equilibrium calculations indicate that mercury(I1) is mainly (97%) present as Hg[Cl,]*-. The diffusion coefficient of Hg(I1) is 10e5 cm* s-I[181 and the kinematic viscosity of the solution 0.96 x lo-* cm* s-‘. 3.4. Analysis of solutions Effluents are sampled in steady state (after 5 min of electrolysis). The determinations of hexacyanoferrate (II) and (III) are made by voltammetry on a rotating platinum disk electrode (Tacussel ED1 65120, PRT 500 LC potentiostat, EPL 1 recorder). Mercury is determined by cold vapor atomic absorption spectrometry (IL 151) after reduction by NaBH,. 3.5. Electrolysis potential The evaluation of the mass transfer parameters of carbon felts needs electrolysis experiments in situations where the reaction rate has no influence. It was therefore necessary to assign convenient conditions by determining intensity-potential and conversion yield-potential curves. Hexacyanoferrate (III). The curves presented in Fig. 3 have been obtained with a 1.2 mm thick graphite felt. The residual current, Ia, becomes nonnegligible only for E < -0.2 V; it may be due to the reduction of residual oxygen and to that of reducible surface groups. Some of these groups (particularly quinonic ones) may play an important role as mediators of oxygen reduction[23]. The reproducibility of I, is low, due both to the difficulty of outgassing the 25 1 of solution used in one experiment and to the heterogeneity of the electrode material. Moreover, when using thicker felts, well defined diffusion plateaux can be obtained on R-E curves (curves with 0 and 0, Fig. 5) whereas the corresponding I-E curves do not present a horizontal plateau (Fig. 4). This fact means that the hexacyanoferrate reduction is made under diffusion control whereas the intensity is affected by secondary reactions such as reduction of residual oxygen, adsorbed impurities, or electroactive surface groups. Therefore, a part of the intensity is lost for the hexacyanoferrate reduction. In this way, the determination of the mass transfer coefficient from measurements of the limiting diffusion current-a procedure very often chosen in the
Table 2. Main characteristics of electrode material Felt
Graphite
Carbon
Fiber diameter/m Mean thickness/cm Mass per unit area/gm-’
0.12 150
9 x 10-b 0.35 250
0.13
10 x 10-h 0.4
1
0.125 325 RVG 1000
0.07 1 185 RVG 2000
170 0.131 310 RVC 1000
260 0.065 150 RVC 2000
1000 0.100 235 RVC 4000
Specific mass/g cm-’ Geometric area/cm-’ Commercial denomination
0.9 950 0.105 275 RVG 4000
B. DELANGHEer nl.
1372
ct 10
2 ,3 ,4 5 6 .7 .B .9
1M
I 5!a
Fig. 2. Electrolytic cell: (1) capillary agar-KNO, junction; (2) fixative ring; (3) ruthenied titanium grid; (4) circular platinum wires; (5) current feed grid (titanium grid); (6) felt; (7) fixative ring; (8) capillary agar-KNO, junction; (9) calming section (plastic foam); (10) current feed. literature[ l-l 5]-seems
difficult in the case of carbon
felt electrodes. For these electrodes, the determination of the product a*k,,, must be made from the measurements of conversion yields, as suggested by Bek and Zamyatin[l3]. It is the reason why all following quantitative data have been obtained from the analysis of cell effluents. Electrolysis potential was always chosen as anodic as possible on the diffusion plateau to avoid any intervention of solvent reduction processes. The effect of electrode thickness (Figs 4 and 5) creates a shift of the diffusion plateau towards cathodic potentials, as a consequence of the ohmic drop AE = (Eupstream - Edownstmm) in the solution through the electrode. The potential drop AE increases with the electrode thickness, L, and the flow rate, u[24]. The occurrence of non-unity conversion yields with thick felts necessitates high values of the flow rate. In these conditions, we have measured
0
-200
-400
40
-SW
E~-~&.CE.
I
-1ooo
-1ml
L
m
Fig. 4. I-E curves.: (0) 0.13 cm thick carbon felt, v = 2.91 ems-I; (0) 0.4cm thick carbon felt, v = 1.57cm s-t; (0) 0.35 cm thick graphite felt, v = 1.97cm s-t; K,Fe(CN), = lo-) M; NaOH = 0.5 M.
values of AE up to 400 mV instead of less than 50 mV for thin electrodes (RVG or RVC 1000). As the diffusion plateau is obtained only when the whole electrode works in diffusion-limited conditions, the shift of the plateau may be explained by the intervention of the ohmic potential drop AE. From these preliminary experiments, convenient electrolysis potentials have been defined as between - 0.3 and - 0.4 V, and as - 1.OV/see for respectively 0.12 and 0.35 cm thick graphite felts; for 0.13 and 0.4 cm thick carbon felts electrolysis potentials have been chosen at -0.8 and -0.9V/sce, respectively. Mercury (ZZ). Experiments with mercury have been limited to graphitized electrode materials (Fig. 6). Low concentrations of mercury (II) have been used (50 times lower than hexacyanoferrate concentrations), reducing both electrolysis current and ohmic drop. Then the relative importance of the residual current due to secondary reaction is all the greater. There is no serious distortion of the R-E
t _S---75
75
5Q:
8
.!a
75
Y-o----O--
;I 250 D:
a: -~----~-O-~25
25
25
al
0
E
Fig. 3. I-E and R-E curves: 0.12 cm thick graphite felt; v = 1.06cm s-r; lo-’ M K,Fe(CN),; 0.5 M NaOH.
-“AUK*
/““mv-a%
-1600-rim
dmstm
Fig. 5. R-E curves: (0) 0.13 cm thick carbon felt, v = 2.91 ems-‘; (0) 0.4cm thick carbon felt, v = 1.57cm s-l; (0) 0.35cm thick graphite felt, v = 1.97cms-‘. lo-” M K,Fe(CN),; 0.5 M NaOH.
1373
Mass transfer to a carbon or graphite felt electrode
Fig. 6. I-E curves: 0.12 cm (0) and 0.9 cm (a) thick graphite felt with 2.95 cm s-’ and 1.01 cm s-’ flow rates, respectively. 4 ppm Hg (2 x lo-‘M); 3 M NaCl.
curves in Fig. 6 even with thick electrodes and high solution velocity. In these conditions intensitypotential curves may not be used at all due to the relatively higher importance of the irreproducible residual current; only conversion yield-potential curves were used in the calculations. We have verified that there is no deposition of insoluble salts (such as mercurous chloride) in these experimental conditions and that the solubility of metallic mercury is negligible. Electrolysis potentials for the evaluation of mass transfer coefficients have been chosen as -0.5, -0.6 and -0.9 V/see for respectively 0.12, 0.35 and 0.9 cm thick graphite felts.
Four different experiments have been made using 0.12 cm thick graphite felt and a -0.3 V/see potential applied to the working felt except for curve 2 (- 0.4 V/see). The similarity between the regression slopes which have been obtained demonstrates that in both situations, the electrode is working under diffusion control. The corresponding values of a and b are presented in Table 3. The mean values have been obtained by a nonlinear regression applied to the whole set of results of the four experiments. Relation (4) for a 0.12 cm thick graphite felt then becomes specifically:
3.6. Cyclic voltammetry on graphite fibers Cyclic voltammetry experiments have been performed with individual fibers extracted from 0.12 cm thick graphite felt; voltammograms are obtained by using Tacussel PRT lo-O.5 potentiostat and G.S.T.P. 3 signal generator, and are recorded with a Bryans XY recorder 29 A.3.
The reproducibility is better for b than for a (up to 15%). These variations may, at least for a part, be explained by the heterogeneity of commercial carbon or graphite felts: the specific mass of felt samples may vary by up to 10%. Another possible major reason of dispersion of a values is the presence of chemical heterogeneities either in commercial product or generated during fiber pretreatment. The various felts under study have specific mass which differs from each other. Their mass transfer parameters calculated from Fig. 8 may be compared only after a normalisation: a*k, ,a& P P The correlation parameters are then in very good agreement (Table 4). It is thus possible to conclude that the mass transfer towards carbon or graphite felt electrodes may be defined by the same correlation:
4. RESULTS
AND DISCUSSION
4.1. Hexacyanoferrate (N/U) The correlation of a*k, with v for the reduction of hexacyanoferrate (III) is presented in Fig. 7.
a*k m = 7.1 v’.‘~.
(5)
a* k, = 57 v”36, P Table 3. Correlation parameters (conditions in the text) a
b
1 2 3 4
8.0 7.1 6.7 6.3
0.34 0.39 0.38 0.37
Mean
7.1
0.36
Experiment I -
-62
-0.3 log(V)
0.0 I
_(
0.1
0.
c
cm4
Fig. 7. Graphical correlations between a*/~, and the flow rate v for 0.12cm thick graphite felt. 10-l M K,Fe(CN),; 0.5 M NaOH.
1374
B. DELANGHE et al.
1.5
-10
’
b
0.
. IqM
d2 I
.
0.4
.
0.6
t
ms-
Fig. 8. Graphical mass transfer correlations obtained with: (0) 0.35 cm thick graphite electrode; (0) 0.13 cm thick carbon electrode; (0) 0.4 cm thick carbon electrode. 10e3 M K,(CN),; 0.5 M NaOH. The line (-.-.-) is obtained from the 0.12 cm graphite felt.
independently of felt thickness and flow rate. This is in contradiction with the conclusions of Kinoshita and Leach[ 141 who obtained different correlations with 0.175 and 0.25 cm thick electrodes. Correlation (5) is in quite good agreement with that proposed by Bek and Zamyatin[ 131but concerns a four times more extended range of v values. It is also in agreement with the correlation of Schmal et a[,[15]. It must be noted, however, that all these relations have been obtained with the same electrochemical reactants [Fe(CN)&/[Fe(CN)J-. Other authors, working with other reactants (Br,/Br-) obtained differing results. The difference can neither be explained by the differing feed solution (particularly the kinematic viscosity and the diffusion coefficient) nor by the fiber diameter. Actually, the introduction of dimensionless parameters into equation (6) yields to a more general expression: $ Sh = 1.6 x 104Re0.36, whereas the results of Kinoshita into the same form are: $Sh
(7)
and Leach[l4] put
= 9.8 x 102Re0.72
solution through the felt electrode much lower. The experimental mass transfer relations obtained are presented in Fig. 9 where they are also compared with results obtained with hexacyanoferrate (III). The slopes of the lines for mercury deposition in Fig. 9 are similar to those obtained for [Fe(CN),]‘-, but their intercepts on the axis are significantly lower. Two independent experiments have been performed with 0.12 cm thick felts submitted to slightly different pretreatments; the slope seems to be higher for the more oxidizing pretreatment. The mass transfer correlations extracted from Fig. 9 are presented in Table 5. In the case of mercury deposition, significantly distinct correlations are established for the various electrode thicknesses. It appears from these data that a correlation established with one felt with the deposition of mercury (II) may not be extrapolated to electrodes of different thicknesses, or having received a differing pretreatment nor to hexacyanoferrate (III) reduction. These conclusions cannot be easily compared with those of the literature. Oren and Soffer[l6] did not propose any mass transfer correlation but they obtained two values of the product a*k,, which were 0.65 and 1.48 S-I for two flow rates, respectively 0.39 and 0.83 cm s-l. The electrode material used for their study was RVG 2000. For this felt, the results given in this paper for the product a*k,,, would be respectively 2.12 and 2.8 s-’ for the corresponding flow rates. These values are clearly higher than those of Oren and Soffer[l6]. However, it should be noticed that these authors used a flow-by electrode set up and very thick carbon felt (9.5 cm). Therefore, the fibers were situated lengthways relative to the flow and perhaps an anisotropy effect might explain-at least partially-the differing results. Actually Schmal et a1.[15], for the same arrangement (flow-by electrodes), obtained lower results than those of Bek and Zamyatin[l3]. The nature of the felt treatment could also explain the differences because it seems that such a parameter can influence the conversion yields. 4.3. Cyclic voltammetry and discussion Cyclic voltammetric studies on single graphite fibers extracted from the felts have been real&d 4 4.1.
for a 0.175 cm thick felt and: SSh
4.0.
= 7.5 x 102Re0,6’
3.9 *
for a 0.25 cm thick felt. Equation from these expressions.
(7) clearly differs
4.2. Mercury As the reactant concentration is very small the electrolysis current is very low and the ohmic drop in Table 4. The correlation parameters (conditions in the text) Felt
L/cm
Graphite
b
0.12 0.35
a/P 57 53
0.36 0.38
0.13 0.40
53 51
0.38 0.34
_
3.6.
-1.5
-1.3
-1.1
-0.9
-0.7
-0.5
e
b3m=L)
Fig. 9. Graphical mass transfer correlations obtained from the mercury (II) redox system and from 0.12 cm (0 and 0); 0.35 cm (A) and 0.9cm (0) graphite felts. 1 ppm Hg (5 x 10m6M); 3 M NaCI. The line (-.-.--) presents the mass transfer correlation obtained from the hexacyanoferrate (III/II) redox-system.
Mass transfer to a carbon or graphite felt electrode
1375
Table 5. Mass transfer correlations at graphite felt electrodes Correlation Electrolytic solution Electrode thickness/cm
0.12 0.127 0.35 0.9
Hg2+ 4 2 U0,39 3’1 U0.43 3: 1 vO,W 3.7 v0,42
FW%I’7.1 oO.36 4.1 vO.36 6.0 vO.)~
8.5 x 103Reo-42
Yin this experiment a more oxidising pretreatment
in an attempt to elucidate these difficulties. The voltammograms obtained with hexacyanoferrate (III) (Fig. 10B) are typical of a reversible reaction on a cylindrical microelectrode such as those described by Aoki[25] and Amatore[26]. The curves registered with mercury, in similar experimental conditions (Fig. IOA), present two well defined peaks corresponding to superficial processes already described such as adsorption or cation exchange with surface groups or superficial graphite oxides[27, 281. The predominant mercury species in solution being (HgCl,)2- the mercury cation exchange necessitates a very high lability of the complex that seems possible considering mercury reactivity. The nucleation step of deposited mercury on these electrodes does not seem limiting as the conversion yield-potential curves presented in Fig. 6 have a well defined diffusion plateau. In these results there is no evidence that the number of nucleation sites increases with negative electrode potential as suggested by Golas[29]. To explain the efficiency differences it thus seems necessary to call upon variations of the active specific
(A)
fl@
E / S.CE.
PP%
Hd’ 7.6 x 103Re0.39 6.1 x 103Reo”) 10.1 x 103Reo.Q
(mV)
I3-
16 4 x 103Reo.36
’
has been applied to the 0.12 cm felt electrode.
area of the fibers with the pretreatment applied and the type of electrochemical reaction involved. The reduced efficiency observed for mercury deposition could be explained by lower densities of active sites. This hypothesis is in agreement with the fact that hexacyanoferrate (III) data are self coherent[l3, 15, this work] but those obtained with other electrochemical systems (bromine[ 141, mercury[ 161) are different.
5. CONCLUSION The mass transfer correlation towards carbon or graphite felt electrodes established from the reduction of hexacyanoferrate (III) is in good agreement with the expression proposed by Bek and Zamyatin[l3]. The present paper extends the validity of this correlation (0.36 cm s-r flow rate: 0.12-0.4 cm thickness). The correlation established by Schmal et a/.[ 151is also approximately in agreement, the differing experimental conditions explaining slight discrepancies. However, in identical experimental conditions, the mass transfer correlations established from the reduction of mercury (II) are different and vary with electrode thickness. Similar observations were made by Kinoshita and Leach[l4] using another electrochemical reaction. It seems therefore that the electrochemical reactivity of graphite felts varies with the reaction mechanism involved, or in practical terms that the active specific surface area a* is not equal to the geometric area and may vary with the nature of the electrolytic solution. Another paper will be devoted to the study of the variations of the active specific surface area with solution composition.
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E 1 S.CE.
(mV)
Fig. 10. Cyclic voltammograms obtained from anodically pretreated graphite fiber and the solutions containing: (A) 5 x 10m4M Hg; 3 M NaCl; (B) lo-’ M K,Fe(CN),; 0.5 M NaOH. Potential sweep rate: 50 mV s-l.
(1979). 3. M. A. Enriquez-Granados, D. Hutin and A. Storck, Electrochim. Acra 27, 303 (1982). 4. G. H. Sedahmed, J. appl. Electrochem. 17, 746 (1987). 5. R. E. Sioda, J. electroanal. Chem. 70, 49 (1976). 6. R. E. Sioda, Electrochim. Acta 22, 439 (1977). 7. A. Storck, P. M. Robertson and N. Ibl, Electrochim. Acra 24, 373 (1979). 8. F. Leroux and F. Coeuret, Electrochim. Acta 28, 1857 (1983). 9. M. M. Letord-Quemere, F. Coeuret and J. Legrand, Electrochim. Acra 33, 881 (1988).
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10. S. Piovano and U. Bohm, J. appl. Elecrrochem. 17, 123 (1987). 11. S. Langlois and F. Coeuret, J. appl. Elecfrochem. 19,Sl (1989). 12. J. M. Maracino, F. Coeuret and S. Langlois, Electrochim. Acra 32, 1303 (1987). 13. R. Yu Bek and A. P. Zamyatin, Sov. Elecrrochem. 14, 1034 (1978). 14. K. Kinoshita and S. C. Leach, J. electrochem. Sot. 129, 1993 (1982). 15. D. Schmal, J. Van Erkel and P. J. Van Duin, J. appl. Elecrrochem. 16, 422 (1986). 16. Y. Oren and A. Soffer, Elecrrochim. Acta 28, 1649 (1983). 17. M. Abda, Y. Oren and A. Soffer, Elecrrochim. Acta 32, 1113 (1987. 18. M. Matlosz and J. Newman, J. elecrrochem. Sot. 133, 1850 (1986). 19. R. Sohr and L. Muller, Electrochim. Acta 20, 451 (1975).
20. M. Noel and P. N. Anantharaman. Analyst 110, 1095 (1985). 21. W. J. Blaedel and G. W. Sehieffer, J. electroanal. Chem. 80, 259 (1977). 22. J. C. Bazan and A. J. At-via, Electrochim. Acta 10, 1025 (1965). 23. T. Nagaoka, T. Sakai, K. Ogura and T. Yoshino, Anal. Chem. 58, 1953 (1986). 24. H. Olive and G. Laeoste., Electrochim. Acfa 2!!, 1303 (1980). 25. K. Aoki, K. Honda, K. Tokuda and H. Matsuda, J. electroanal. Gem. 182, 267 (1985). 26. C. A. Amatore, M. R. Deakin and R. M. Wightman, J. elecrroanal. C&m. 206, 23 (1986). 27. P. M. Korach, M. R. Deakin and R. M. Wightman, J. phys. Chem. 90,4612 (1986). 28. T. E. Bdmonds, J. R. Dean and S. I.&if, Anal. Chim. Acta 212, 23 (1988). 29. J. Golas and J. Osteryoung, Anal. Chim. Acta 181,211 (1986).