Electrolysis with flowing solution on porous and wire electrodes

ElecaochimisaActa,1970,Vol.lS,pp.783to 793. PergamoaPma. Printedin Northcmfrehnd

ELECTROLYSIS WITH FLOWING SOLUTION POROUS AND WIRE ELECTRODES*

ON

R. E. SIODA Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa 42, ul. Kasprzaka 44, Poland Abstract-The mechanism of electrolysis with a flowing solution on a porous electrode is discussed, and a theory is constructed based on several simplifying assumptions. Equations for the distribution of reactant concentration and of a local limiting cd in the porous electrode have been derived. By integration of the 1ocaI cds an equation for the gross limiting current of electrolysis is obtained. The derived equation compares favourably with the experimental data in a limited range of flow velocities. Electrolysis on the platinum-grid porous electrode, the platinum wire, and the platinumgrid in a cell with flowing solution have been investigated utilizing the process of electroreduction of K,Fe(CN), in 1 M KC1 in water. For the platinum wire and grid electrodes the measured dependence of the limiting current on flow velocity has the form 1 cc on, with n ranging between O-32 and O-42. R&m&-Discussion du m&anisme de I’&ctrolyse d’une solution fluante sur &&rode poreuse, et proposition d’une thborie bask sur des hypothkses simplificatrices. Les Equations de distribution de Ia concentration du reactif et de la densit6 locale de courant limite dans l’&ctrode poreuse sont dbduites. On obtient, par integration des densitds de courant locales, une equation pour le courant limite global de l’&c.trolyse. L’&quation obtenue est en bon accord avec les donn6es exp&-imentales dans un domaine restreint de vitesses d’6couleMent. Des 6lectrolyses sur &&rode poreuse & griIle de platine, sur fil de platine et sur griIle de platine, dans une cellule contenant une solution fluante ont &6 Btudi&s au moyen du processus d’Uectror6duction de I&Fe(CN)@ en solution aqueuse de KC1 1 M. Pour les 6lectrodes a fil de platine et a grille de platine, le courant limite d&pendant de la vitesse d%coulement, suit la forrne I, cc u”, avec n compris entre 0,32 et 0,42. Zvsammenfassung-Der Mechanismus der Elektrolyse an einer porijsen Elektrode mit striimendem Elektrolyten wird diskutiert, auf der Basis mehrerer vereinfachender Annahmen wird eine Theorie aufgestellt. Gleichungen fiir die Konzentrationsverteilung der reagierenden Teilchen und fiir eine lokale Stromdichte in der porSsen Elektrode wurden abgeleitet. Durch Integration der lokalen Stromdichten erhglt man eine Gleichung der globalen Stromdichte der Elektrotyse. In-einem begmzten Bereich der Striimungsgeschwindigkeit stimmt die abgeleitete Gleichung recht gut mit den experimentellen Ergebnissen iiberein. Die Reduktion von K,Fe(CN), in 1 M KC1 wurde an einer porijsen Platinnetz-, an einer Platindraht- und an einer Platingitterelektrode untersucht. Die dabei gemessene Abhlingigkeit des Grenzstromes von der Striimungsgeschwindigkeit hat die Form I, cc z)~, mit n = 0,32-0,42. INTRODUCTION with a flowing solution is an interesting field of electrochemistry. Besides other applications it offers the possibility of a construction of continuous cells for preparative electrolysis in solution. The application of electrolysis in industrial organic synthesis has been so far limited, among other reasons, because of the lack of efficient continuous electrolytic cel1s.l Perskaya and ZaidenmanZ apparently were the first to describe an electrolytic cell with a porous electrode and a flowing solution. The electrode was prepared of platinum powder by a metallo-ceramic method. A few papers have been published describing constructions of flow electrolytic cells used for analysis, separation of metallic ions and purification of water from traces of heavy metals.s4 The cells were built as columns tiled with porous metallic or graphite electrodes through which Two new celIs, one with a pIatinum grid porous flowed the electrolysed solutions, electrode and the other with a graphite-granule electrode have been described recently.‘** ELECTROLYSIS

+ Manuscript received 7 February 1%9. 783

R. E. SODA

784

The voltammetric curves of electrochemical processes have been measured on the electrodes and the dependence of limiting current on flow velocity has been studied. Budeka, Gurevich and Bagotzkys have described a cell with porous Raney nickel electrode which served for the electro-oxidation of ethanol. The mechanism of electrolysis on the porous electrode with flowing solution has been treated theoretically by several investigators. s~*-~~ Complex differential equations, in general not solvable in analytical form, were obtained. Due to the complexity of the existing theories, their application for numerical analysis of experimental results requires computers. In the present paper a theory of flow electrolysis with a limiting current on the The theory is confirmed by the experimental results porous electrode is developed. obtained for the platinum-grid porous electrode. The platinum-wire and -grid electrodes placed in a flowing solution are also described as models for the porous grid electrode. EXPERIMENTAL

TECHNIQUE

Apparatus

The electrolytic apparatus was composed of three main glass parts connected by polyethylene tube as earlier described. ‘** The exchangeable middle part of the apparatus contained a platinum electrode, and attached to the side of the flow tube, the The reference electrodes were separated from the working and reference electrodes. flow system by means of filter-paper plugs. Three different middle parts of the apparatus were used (Fig. l), each containing different platinum electrode. The platinum

FIO. I. Middle parts of the electrolyticcell. 1, platinum-wire electrode; 2, platinum-grid electrode; 3, platinum-grid porous electrode. The side tubes lead to the working, El, and reference, ES, electrodes.

electrodes employed were (1) single wire of O-2-mm diameter and 5-mm length fused along the diameter of the flow tube (2) single 80-mesh grid (wire diameter 0.095 mm) covering the cross-section of the flow tube of 5-mm diameter (3) rolled-together 80-mesh grid forming a porous electrode of 5-mm height and 6-mm diameter.’ The electrolyses were conducted with a working calomel eIectrode, placed above the The potential of the platinum-wire and -grid electrodes was platinum electrode.

Electrolysis with flowing solution on porous and wire electrodes

785

measured against the reference electrode; with the platinum-grid porous electrode two reference electrodes were employed. The upper one measured the potential of the upper surface of the porous electrode by means of a capillary introduced into the flow tube near the surface of the porous electrode. The second measured the potential of the low surface of the porous electrode. The electrolyses on the platinum-grid porous electrode were conducted in such a manner that both the upper and the lower surfaces of the electrode had potential corresponding to the limiting-cd potential plateau, ranging approximately from 0 to -1 V(sce). At more negative potential curves on the than -1 V, hydrogen evolution took place. The voltammetric platinum-wire electrode were registered with Radiometer PO-4 Polariter. The volume velocity of the gravitational flow of the solution was determined by measuring the drop time of the effluent from the cell or by collecting the effluent at time intervals_ The cell was operated with flow velocities ranging from O-006 to I-6 ml/s. The experiments were conducted at room temperature of 25°C. Prior to the experiments the solution was de-aerated by bubbling nitrogen. Chemicals The solutions

were prepared

with KC1 and

K,Fe(CN),

of analytical purity.

RESULTS

of Fe(CN),3- to Fe(CN),4- in 1 N KC1 in waterl* was carried out to test the operation of the electrodes in the flowing solution. Well developed limiting currents were obtained for all the three electrodes. Figure 2 represents the voltammetric curves of the reduction of Fe(oe3on the single wire electrode for two different flow velocities of the solution. The analysis of the wave One-electron

reduction

IO-

0

0.4

0

04

0

04

0

Potential. V kce) FIG. 2. Cyclic voltammetric curves 1 M KC1 in water A, solution-flow velocity O-018 ml/s, Bow velocity 0.072 ml/s, potential-scan

of the reduction of 1.0 x lo-s M K,Fe(CN& in on the platinum-wire electrode. potential-scan rate 0.4 V/min; B, C, D, soIutionrate: B, 0.4 V/min; C, 02 VImin; D, @8 V/min.

R. E. SIODA

786

form of the reduction

is presented

in Fig. 3.

The slope of the line, equal O-061, is

-0.15 f

g 2 -025

-

-03-

-I

1 I

0

FIG. 3. Logarithmic analysis of the reduction wave of K,Fe(CN), wire electrode. Flow velocity O-046 mIls.

on the platinum-

characteristic for reversible, one-electron diffusion-controlled process. During the reversal of the direction of the potential scan a small oxidation current of the formed The magnitude of the oxidation current decreased with Fe(CN),4was observed. increasing flow velocity and decreasing scan velocity (Fig. 2). Figure 4 represents the logarithmic dependence of the magnitude of the limiting

-1.0

-

-1.6

-

__

-2

-_)

0

log’ *

FIG.

4.

Dependence of the limiting reduction current of 4 x lo-* M K,Fe(CN), volume-flow velocity for the platinum-wire electrode.

on

Ekctrolysiswithfiowingsolutionon porousand wireelectrodes

787

current of the reduction on the volume-flow velocity of the solution. The dependence can be described by I1 oc uO*XJ for smaller flow velocities (u < 0.3 ml/s) and I1 cc voarafor higher flow velocities. There is direct proportionality between the magnitude of the limiting reduction current and the concentration of K,Fe(CN),, as seen in Fig. 5, representing the plot in logarithmic co-ordinates of I1 tr-l/s us concentration, c, of K*Fe(CN),. The slope of the line is 1. The limiting currents have been measured for flow velocities ranging from 0.04 and O-07 ml/s and multiplied by u--1/3 to obtain products independent of flow velocity. The voltammetric curves of the reduction of K,Fe(CN), have been also obtained for the single platinum-grid electrode with flowing solution. The logarithmic dependence of the limiting reduction current on flow velocity is presented in Fig. 6. As in the case of the platinum wire electrode, for small flow velocities the dependence is of the form I1 cc ooSS and for higher flow velocities the power for t, increases to o-39. Figure 7 represents the logarithmic dependence of the limiting reduction current K,Fe(CN), on volume flow velocity of the solution for the porous grid electrode. The voltammetric curves of the reduction have been presented before.’ The flow velocities range between 0.006 and O-8 ml/s. In the previous paper a special coefficient was introduced as an indicator of the completeness of the electrolysis with flowing solutiorx7 The coefficient, R, is defined as the ratio of the concentration of the substance undergoing electrolysis trs its initial concentration. It can be calculated according to R =

-&- ,

(1)

0

0 --

I

-4

I

-3

_ -2 h

FIG.

5. Dependenceof

the

ratio I, V-W on

I

-1

c

molar concentration of platinum-wire electrode.

K,Fe(CN),

for the

788

K. E. SIODA

I

1

-20

-1-O log

f

0

c

”

FIG. 6. Dependence of the limiting reduction current of 5 x 1O-a M K,Fe(ClV& voIume-flow velocity for the platinum-grid electrode.

on

where J, is the eIectroIytic current in A, n the number of electrons transferred per molecule of substrate, F the Faraday, tr the volume-flow velocity in I/s, and c,, the initial concentration of the reactant in mol/l. For several points of the curve in Fig. 7 the calculated coefficients R are shown: they decline with increasing flow velocity from 0.90 for u = O-006 ml/s to 0.23 for u = O-8 ml/s. Correspondingly for the respective flow velocity range the calculated concentration of the formed Fe(CN),-a in the out-flowing solution declines from 90% to 23% of the initial concentration of K,Fe(CN),. DISCUSSION

The theoretical groundwork of electrolysis with flowing solution was laid down by Levich.1s,20 He found that the diffusion-controlled limiting current of electrolysis depends on a characteristic flow velocity, U, 18 cc u”,

(2)

where the index n depends on the shape of the electrode and the type of flow. With laminar flow, n is 4 or Q for different electrode shapes. In turbulent flow, n increases significantly to O-8-1. The theoretical predictions of Levich had been confirmed by the experimental work with electrodes of different shapes, as conical,21 tubular,22-aa disk25*aa and wire electrodes .27*28 No mention has been found in the literature of a grid electrode with flowing solution.

Electrolysis withflowingsolutionon porousand wireelectrodce

789

FIG. 7. Dependence of the limitingreductioncurrentof the reductionof 2 x IV M on vohm~flow velocityfor theplatinum-grid porottselectrode.The numhersin the plot repreSent thevaluesof thecoeBkientR.

&Fe(CN),

The above presented arrangement of the wire electrode with flowing solution differs from those described in the literature. Mtiller described a “by-pass” electrode in form of a platinum wire sealed into the wall of a constricted glass tube, through which flowed the solution. He obtained limiting currents on the electrode, but the dependence of the limiting current on flow velocity was not conclusively investigated.*s Laitinen and KolthofPO devised an electrode in form of a platinum wire protruding from the wall of a glass tube rotated at a constant speed. Depending on the range of the rotation speeds, the limiting currents on an electrode of this type increased with $ or g power of the number of revolutions per minute.as Jordan described a platinumwire electrode attached to a plastic fork and placed into a rotated electrolytic solution at a stationary distance from the center of rotation. 87 In accordance with a theoretical prediction the limiting current on the electrode increased with u112in the flow-velocities range l-5 to 150 cm/s. The lack in the literature of a description of anything analogous to the present electrolytic arrangement does not allow one to make comparisons with the present data for the wire and grid electrodes. However, Figs. 4 and 6 show that both the wire and grid electrodes satisfy the Levich equation (2) in the limited range of volume-flow velocities investigated, since between 0 = O-006 and Oe3ml/s the experimental points in Figs. 4 and 6 are described by Iict rV_ This range of flow velocities corresponds to laminar flow. The working of the porous electrode with a flowing solution is a complex process. Inside the porous electrode there are gradients of potential, of concentration of the reactant and of the product of electrolysis, and of the cd. Several investigators have tried to construct one-dimensional models for the porous electrode and to calculate the potential gradient, the cd variation and the concentration gradients.a*‘0-17 The calculations include different kinetic expressions to account for the relation between 10

790

R. E.

SIODA

the local pd at the electrode and the local cd. However, due to the mathematical complexity of the models, analytical solutions of the equations are possible only for special limiting cases.--lb More general solutions can be obtained in numerical form by application of computers.lsJ7 The potential gradient in the porous electrode is formed primarily because of the ohmic resistance of the solution in the pores. For metallic electrodes, eg platinum grid electrode, the pd in the material of the electrode is very low and usually can be ignored. The electrolytic process depends on the local difference between the potential of the material of the electrode and the potential of the adjacent solution,

where the potential of the electrode, qE, is treated as constant for metallic electrodes.31 The potential in the solution, p, is governed by de Y -= dx=

s &,

i ,

(4)

where R,, is the effective specific ohmic resistance of the solution in the pores, s the specific surface of unit volume of the electrode, and i the local cd.~J3-16 The local cd at an element of a porous electrode depends on the local pd between the electrode and the solution, and on the local concentration of the electro-active species. The cd is related to the pd and concentrations of the electro-active species by kinetic equations. At higher potentials, the limiting cd is achieved; its magnitude depends on the solution-flow velocity. The mean solution-flow velocity may not be uniform in the volume of the electrode. It depends on the construction of the electrolytic cell and on the laminar or turbulent type of flow. The new model of the porous electrode presented here is based on several simplifying conditions. It is assumed that cds and the effective ohmic resistance of the solution are low, so that the ohmic potential drop in the volume of the electrode is small, and does not exceed the range of the potential plateau of the limiting cd of the electrolytic process. One can operate the whole electrode at the potential plateau, and the elecelectrode. The condition of limiting cd trode resembles a “pseudo-equipotential” corresponds to a maximum utilization of the electrode. The kinetic equa$ions, significantly complicating the previous theoretical models, do not have to be included in the model of the electrode working with limiting cd. In the present model, by analogy with the theory of LevichLg~m one can express the local, limiting cd at an element of the area of the porous electrode as

* =jnFcqa, lz

(9

wherej is a proportionality constant, n number of electrons transfered per molecule, F the Faraday, c the local concentration of the electro-active species, and Q the specific volume-flow velocity, ie the vohme-flow velocity flowing through a unit of the crosssection area of the electrode. The exponent oc can be obtained experimentally or calculated according to convective-diffusion theory. It seems that in the region of laminar flow a for the platinum-grid porous electrode may adopt values of 0.32-0.42, as measured for the single platinum-grid and the wire electrodes (Figs. 4 and 6).

Electrolysis with flowingsolution on porous and wire electrodes

791

For simplification, one can also assume that the solution passing through the porous electrode has constant linear flow velocity independent of the co-ordinates of an element of the electrode. This allows one to treat the model of the electrode as one-dimensional problem. The solution contains a surplus of a supporting electrolyte, so that migration currents do not have to be taken into account. Imagine a porous electrode with a cross-section area a, and length L along the x-axis. In a steady state, the change of concentration of the substrate -dc caused by an element of the volume of the electrode adx is equal the ratio of the amount dm of the substrate consumed in unit time, and the volume v of the solution flowing through the electrode in unit time, -_dc=df,

(6)

v and dm are v =qa,

dm =

(7)

sia dx

(8)

n17’

where F, n, s, i and q have been already defined. Substituting (7) and (8) into (6) we obtain --

si dc dx = zq ’

(9)

Equation (9) is identical with the one derived by previous authors for a first-order electrode reaction on a porous electrode.13-l7 Substituting for i in (9), the limiting current density from (5), we obtain -- dc = bq (G-1)dx, c

(10)

where b = js. Integration of (lo), and adoption of the initial condition that c = c, for x = 0, yield the equation for the distribution of a steady state reactant concentration in the electrode (working at limiting cd), c = c, exp (-bqcoil) x).

(11)

Substituting (11) for c in (5), we obtain il = jnFc,,qoCexp (- bqta-l) x).

(12)

The gross limiting current of electrolysis, I,, on a porous electrode of length L and cross-section a can be obtained by integration of (12) over the volume of the electrode,

v*, II = Integration leads to

i,s dVe = as

s VI3

II = nFc,v [l -

exp (-

L s0

i, dx.

ba(l”)v(“l)

(13) I,)],

(14)

R. E. SIODA

792

where the specific volume-flow according to (7). By comparison

velocity

q is substituted

by volume-flow

velocity

v,

of (1) and (14) one obtains R=l

-

exp (-&z(~-%(“~~

L).

(15)

From (15) it 3s seen that R increases with the increasing length and cross-section area of the electrode and decreases with the increasing volume-flow rate of the solution. This diminishing of R with increasing flow rate is confirmed by the experimental data of Fig. 7. Re-arranging (14) leads to

nFc,v nFq,v By taking the double logarithim log log

nFc,,v

II

L)

(16)

of (16) one obtains

= (a -

nFc,,v - II

= exp (ba (l-+p-l)

1) log v + log ba(l”)L

-

log 2.303.

07)

Equation (17) can be checked experimentally by plotting of log iog [nFc,u/(nFcOu- IJ ] vs log v for the measured gross limiting currents and flow velocities for the porous electrode. Such a plot, calculated for some of the experimental points of Fig. 7, is presented in Fig. 8. For flow velocities from 0.05-0.98 ml/s the plot is a line of slope

FIG. 8. Dependence of Iog log [n&v/(nFc,o - Q)] OII logarithm of flow velocity for the platinum-grid porous electrode.

of -0.59.

a calculated from the slope is O-41, similar to the measured a for the wire and grid electrodes (Figs. 4 and 6). For smalIer flow velocities (u < 0.05 ml/s) agreement of the experimental data with (17) is not apparent.

Electrolysis with flowing solution on porous and wire electrodes

793

The observed agreement of the theory and experiment in a limited range of flow velocities is worth noting. This agreement exists despite the fact that the present, simplified theory assumes constant flow velocity in the porous electrode . According to hydrodynamics, in the laminar range of flow, one would expect a parabolic distribution of flow velocities in the flow tube containing the porous electrode.32 By application of (4) and (12) one can derive an expression for the potential distribution in the solution inside the porous electrode working at limiting cd. This will be accomplished in a following communication. Acknowle&e~ent-The author is very grateful to Prof. Dr. W. Kemula Baranowski for many very fruitful discussions.

and to Prof. Dr. B.

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