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Mass transport studies at rotating cylinder electrode: Influence of the inter-electrode gap
Electrochimica Acta 55 (2010) 3275–3278
Contents lists available at ScienceDirect
Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta
Mass transport studies at rotating cylinder electrode: Influence of the inter-electrode gap ˜ b Fernando F. Rivera a , José L. Nava b,∗ , Mercedes T. Oropeza c , Alejandro Recéndiz d , Gilberto Carreno a
Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco No. 186, C.P. 09340, México, D.F., Mexico Departamento de Ingeniería Geomática e Hidráulica, Universidad de Guanajuato, Av. Juárez No. 77, C.P. 36000, Guanajuato, Guanajuato, Mexico Instituto Tecnológico de Tijuana, Centro de Graduados e Investigación Blvd. Industrial s/n, C.P. 22500, Tijuana, B.C., Mexico d Servicios Industriales Pe˜ noles S.A. de C.V., Centro de Investigación y Desarrollo Tecnológico, C.P. 27300, Torreón, Coahuila, Mexico b c
a r t i c l e
i n f o
Article history: Received 11 September 2009 Received in revised form 22 December 2009 Accepted 22 December 2009 Available online 11 January 2010 Keywords: Rotating cylinder electrode Mass transport characterization Dimensionless correlation Copper deposition Triiodide reduction
a b s t r a c t This study shows the effect of using two different inter-electrode gaps on the RCE mass transport characterization. The average mass transport coefficient was calculated using the limiting current technique, using the soluble reduction of triiodide (smooth RCE interface) and the copper deposition (roughness RCE interface) in KNO3 and H2 SO4 , respectively. Based on the analysis of the Sh = aReb Sc0.356 correlation, the values of the constant a, associated with shape and cell dimensions, were 0.89 and 3.8, in the soluble system (I3 − /I− ), for the gaps of 2.4 and 3.2 cm, respectively, indicating that this coefficient increases with inter-electrode space. While for copper deposition, these values were 0.00081 and 0.014, for the gaps of 2.4 and 3.2 cm. The constant b, associated with hydrodynamic regime, exhibits values of 0.43 and 0.33 for the gaps of 2.4 and 3.2 cm, respectively, in the system I3 − /I− , indicating that hydrodynamics on the smooth RCE diminishes according to the inter-electrode space. While for the system (Cu(II)/Cu), the values of b were 0.91 and 0.88, for the gaps of 2.4 and 3.2 cm. These values were higher for the copper deposition than for the soluble system, due to microturbulence at the roughened (and often powdery deposits) RCE interface. From the analysis performed in this paper is clear that inter-electrode gap and hydrodynamics on the smooth and roughness RCE interface (given by the nature of reduction reaction) modify the mass transport correlation. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The rotating cylinder electrode electrochemical reactor (RCE) is one of the most common geometries for different types of studies, such as metal ion recovery [1–4], alloy formation [1,3], electrosynthesis [3], corrosion [1,3], effluent treatment [5–9] and Hull cell studies [10,11]. RCEs are particularly well suited for high mass transport studies in the turbulent flow regime [1,12–16]. The mass transport control is imposed by the rotation speed of the inner cylinder and the applied limiting current density. When the fluid flow is generated entirely by an inner RCE, the characteristics of mass transport conditions can be described by a dimensionless group correlation of the following form [1,3,12,16]: Sh = aReb Sc0.356
(1)
where the Sherwood number (Sh = km d/D) describes mass transport by forced convection, the Reynolds number (Re = ud/) is an indication of the fluid flow regime, and the Schmidt number (Sc = /D)
∗ Corresponding author. Tel.: +52 4731020100x2275; fax: +52 4731020100x2209. E-mail addresses: [email protected], [email protected] (J.L. Nava). 0013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2009.12.060
relates the electrolyte transport properties. The average mass transport coefficient is described by km , d is the diameter of the RCE, D is the diffusion coefficient, u is the peripheral velocity, and is the kinematic viscosity. The mass transport correlation is best evaluated through analysis of experimental data [1,3,12,16]. The experimental constant a, is associated with the electrode geometry and shape as well as with the cell dimensions, whereas b is associated with the hydrodynamic regime [1,3,16]. In a previous paper Rivera and Nava [16] discussed the influence of plates and concentric cylinder used as a counter electrode on the RCE mass transport characterization during copper deposition. Based on the correlation described by Eq. (1) Rivera and Nava [16] discussed that both, the shape and area of the counter electrode, influence the values of a. The value of b, depends on the shape of the counter electrode, indicating that plates provoke higher turbulence promoting action than concentric cylinder. Moreover, powdery copper deposits, on the RCE, improve microturbulence at the roughened RCE interface [16]. It is important to mention that, in general, there are no references in the literature that show the effect of the inter-electrode gap on the RCE mass transport characterization. Moreover, the mass transport studies performed in the same RCE showing the effect of
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the reaction mechanism involved is also rather limited. A study in that direction may be important because when designing a RCE reactor, it is necessary to know the accurate mass transport towards the electrode surface in given experimental conditions. The objective of this work is to show, on one hand, the effect of inter-electrode gap, and, on the other hand, the influence of different electrochemical systems, on the RCE mass transport characterization. The I3 − /I− and Cu(II)/Cu in KNO3 and H2 SO4 , respectively, were employed as the model reactions. 2. Experimental The solutions used in this work were prepared of analytic grade reactants and deionised water Milli-QTM . The I3 − ion and Cu(II) concentrations were 5 and 15.7 mM in 0.5 M KNO3 and 1.0 M H2 SO4 , respectively. Each electrolytic solution was deoxygenated with nitrogen for about 10 min before each experiment. 2.1. Equipment A potentiostat–galvanostat EG&G model PAR 273 and M270 software was used for all chronoamperommetric experiments. 2.1.1. RCE experiments Fig. 1 shows the diagram of a device built up for laboratory studies, consisting of a 500-cm3 glass reactor with a temperature bath and 8.5 cm inner diameter. 304-type stainless steel cylinders with 2.1 and 3.8 cm of diameter and a length of 11 cm were used as cathodes. The two diameters of the cylinder provide the two interelectrode gaps. As anodes were used four 13 cm long, 1.8 cm wide and 0.3 cm thick graphite bars were attached to the reactor walls and connected between each other. 115 V and 70 W CaframoTM electric motor of variable velocity was used to rotate the inner cylinder. The potentials were measured vs. saturated mercury: mercurous sulfate electrode (sat. MSE) Radiometer AnalyticalTM model XR200. Table 1 shows RCE reactor parameters and electrolyte transport properties. 2.2. Methodology 2.2.1. Experimental determination of the mass transport coefficients at the RCE electrode A series of potential pulses were applied to the RCE, using the cell described in Section 2.1.1, starting from open circuit potential OCP in the potential range of −1.4 ≤ E ≤ −0.4 V vs. sat. MSE during 5 s,
Table 1 RCE reactor parameters and electrolyte properties. Reaction volume, VR RCE length RCE radius, R1 Reactor radius, R2 Length, width and thick of the plates used as anodes (attached to the reactor walls) RCE area, ARCE (in contact with electrolyte), R1 = 1.9 cm RCE area, ARCE (in contact with electrolyte), R1 = 1.05 cm Diffusion coefficient (Cu2+ ), DCu2+ [16] Diffusion coefficient (I3 − ), DI3 − [17] Kinematic viscosity, [16]
350 cm3 11 cm 1.9 cm 1.05 cm 4.25 cm 13 cm × 1.8 cm × 0.3 cm 80 cm2 42 cm2 5.94 × 10−6 cm2 s−1 1.12 × 10−5 cm2 s−1 0.01 cm2 s−1
and −0.85 ≤ E ≤ −0.5 V vs. sat. MSE, for the electrochemical systems of (I3 − /I− ) and (Cu(II)/Cu), respectively. From these chronoamperograms, sampled current density (at 4.5 s) vs. cathodic potential pulse curves were constructed (j–E). The average mass transport coefficient, km , was calculated experimentally from limiting current density (jL ) obtained from polarization curves according to equation: km =
jL zFC0
(2)
where jL is the value of limiting current density plateau, z is electron number, F is the Faraday constant, and C0 is the electroactive species concentration in the bulk solution. The jL values were measured at potentials of −1.0 and −0.85 V vs. sat. MSE, for (I3 − /I− ) and (Cu(II)/Cu), respectively, assuming that the potential distribution on the RCE interface is homogeneous. The studies were made at Reynolds numbers within 34 × 103 < Re < 322 × 103 interval, in turbulent flow [12,16]. It is important to mention that at such turbulent conditions the convection originating from the rotation of the inner cylinder predominates over the convection induced by the gas (oxygen) generated at the counter electrode, which is quickly removed from the counter electrode and electrolyte. The experiments were carried out for the RCE radiuses (R1 ) of 1.9 and 1.05 cm, which provide two inter-electrode gaps (R2 –R1 ) of 2.4 and 3.2 cm, respectively. It is important to mention that the reactor radius (R2 ) remains constant with a value 4.25 cm. The authors decided to construct the polarization curves using sampled current density vs. cathodic potential instead of linear sweep voltammetry technique, because a voltammetric study always involves the competition between the formation rate of deposits at the interface and the polarization rate of the electrode. This last problem is eliminated in the potential pulse technique [16]. 3. Results and discussion
Fig. 1. (a) Rotating cylinder electrode scheme. (b) Frontal view.
Fig. 2a and b shows the cathodic polarization curves at different Reynolds numbers obtained when the reduction of triiodide is carried out on the RCE with inter-electrode gap of 2.4 and 3.2 cm, respectively. This figure shows that the limiting current region where the iodide reduction becomes completely mass transport controlled lies approximately between −1.2 and −0.8 V vs. sat. MSE and that, as expected, the current densities increase with the Reynolds number. Fig. 3a and b is similar to that presented in Fig. 2a and b, only that such curves were obtained during the reduction of cupric ions. The shape of these curves differs from that obtained in the soluble system, giving greatest current density values due to the copper concentration is three times larger than triiodide. In addition, the
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Fig. 4. Comparison of the mass transport correlations, evaluated from the limiting currents similar to those shown in Figs. 2 and 3. (a) I3 − /I− , gap 2.4 cm; (b) I3 − /I− , gap 3.2 cm; (c) Cu(II)/Cu, gap 2.4 cm and (d) Cu(II)/Cu, gap 3.2 cm.
Fig. 2. Typical sampled current density vs. cathodic potential pulse curves, constructed from typical current transients at sampling time of 4.5 s, at different Reynolds numbers shown in the figure. Electrolyte: 5 mM I3 − in 0.5 M KNO3 , T = 298 K. RCE devices with inter-electrode gap of: (a) 2.4 cm and (b) 3.2 cm.
limiting current plateaus in the curves of Fig. 3 are poorly defined due to early stages of growth of the copper metal on the stainless steel surface, and hence, an increase in the electrode surface roughness. However; there is a slightly change of slope, between −0.85 ≤ E ≤ −0.80 V vs. sat. MSE, that approaches to plateau; this last potential interval is in agreement to that previously reported about copper deposition on stainless steel RCE [2,16], where the process is mass transport controlled. The mass transport coefficients were evaluated by liming current density measurements (Eq. (2)), at holding potential of −1.0 and −0.85 V vs. sat. MSE, for triiodide and cupric reduction processes, respectively. These values were comprised between (4.9 × 10−3 < km < 8.5 × 10−3 ) cm s−1 and (0.23 × 10−3 < km < 1.4 × 10−3 ) cm s−1 , for triiodide and cupric reduction processes, respectively. Subsequently, dimensionless correlations were evaluated using the km values for each Reynolds number and the transport properties are shown in Table 1 (Eq. (1)). Fig. 4 shows the comparison of mass transport characterization obtained for the (I− /I3 − ) and (Cu(II)/Cu) processes on the RCE with inter-electrode gap of 2.4 and 3.2 cm. The analysis of Fig. 4 demonstrates that the mass transport is favored by the soluble process, triiodide reduction (Fig. 4a and b) as compared to the powdery copper deposits, on the RCE (Fig. 4c and d), respectively. The enhanced mass transport by triiodide can be associated with its diffusion coefficient value, which is 1.9 times higher than for cupric ions (Table 1). Table 2 exhibits the experimental values of a, and b from Eq. (1) for the two inter-electrode gaps and electrochemical systems. An analysis of Table 2, system I3 − /I− , shows that the value of a, associated with shape and cell dimensions, were 0.89 and 3.8, for the gaps of 2.4 and 3.2 cm, respectively, indicating that this coefficient increases with inter-electrode space. For the system Table 2 Mass transport correlations (Sh = aReb Sc0.356 ) in RCE reactor.
Fig. 3. Typical sampled current density vs. cathodic potential pulse curves, constructed from typical current transients at sampling time of 4.5 s, at different Reynolds numbers shown in the figure. Electrolyte: 15.7 mM CuSO4 in 1 M H2 SO4 , T = 298 K. RCE devices with inter-electrode gap of: (a) 2.4 cm and (b) 3.2 cm.
Electrolytic solution
Inter-electrode gap (R2 –R1 )
a
b
I3 − /I− I3 − /I− Fe(CN)3− Cu2+ Cu2+ Cu2+ Cu2+
2.4 3.2 – 2.4 3.2 2.4 –
0.89 3.8 1.356 0.00081 0.014 0.012 0.079
0.43 0.33 0.63 0.91 0.88 0.95 0.92
a b
This work This work [14]a This work This work [16]b [1,3]
This correlation was obtained in a RCE covered with expanded metal. This correlation was obtained in RCE (four counter electrodes).
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(Cu(II)/Cu), where occurs the same dependence, the values of a were 0.00081 and 0.014, for the gaps of 2.4 and 3.2 cm. The values of a were higher for triiodide than for cupric ions; this fact can be associated with its diffusion coefficient value, as mentioned above. The constant b, associated with hydrodynamic regime, exhibits values of 0.43 and 0.33 for the gaps of 2.4 and 3.2, respectively, in the system I3 − /I− , indicating that hydrodynamics on the smooth RCE diminishes according to the inter-electrode space, as expected. For the system (Cu(II)/Cu), where occurs the same dependence, the values of b were 0.91 and 0.88, for the gaps of 2.4 and 3.2. The values of the exponent b were higher for the copper deposition than for the soluble system. This last, is associated to microturbulence at the roughened RCE interface [1,3,16]. The values of b >0.8 are frequently found for rough electrodeposits, while for a hydrodynamically smooth surface these values are < 0.7 [1]. The coefficient a and exponent b, obtained in this investigation, were also compared in Table 1 with those reported by Grau and Bisang [14] (reduction of Fe(CN)6 3− on a RCE with expanded metal), Walsh and coworkers [1,3] (copper deposition in a RCE), and Rivera and Nava [16] (copper deposition on RCE). The differences of the mass transport correlation for the soluble system (I3 − /I− ) and that reported during the reduction of ferricyanide in Ref. [14], can be attributed to the RCE covered with expanded metal. Moreover, authors in Refs. [1,3,14] do not specify any ratio between R1 and R2 , or an inter-electrode gap parameters and electrode materials. For the above, we do not consider appropriate to give a more detailed discussion. From the analysis of these correlations and the obtained herein, it is clearly observed that hydrodynamics on the smooth and roughness RCE interface, geometrical parameters and diffusion coefficient of electroactive specie modify the mass transport correlation. The mass transport correlation of RCE is best evaluated through analysis of experimental data, because it depends on the interelectrode gap, hydrodynamics on the smooth and rough RCE interface (given by the nature of reduction reaction), diffusion coefficient, type of fluid flow pattern [12], cell geometry [1,3], anode [16] and cathode arrangements [1,14]. 4. Conclusions Measurements of mass transport on the RCE (both with two different inter-electrode gaps) have been systematically investigated. The average mass transport coefficient was calculated using the limiting current technique, using the soluble reduction of triiodide (smooth RCE interface) and the copper deposition (roughness RCE interface) in KNO3 and H2 SO4 , respectively.
Based on the analysis of the Sh = aReb Sc0.356 correlation, the values of the constant a, associated with shape and cell dimensions, were 0.89 and 3.8, in the soluble system (I3 − /I− ), for the gaps of 2.4 and 3.2 cm, respectively, indicating that this coefficient increases with inter-electrode space. While for copper deposition, these values were 0.00081 and 0.014, for the gaps of 2.4 and 3.2 cm. The values of this constant, a, were higher for the (I3 − /I− ) system (with diffusion coefficient of 1.12 × 10−5 cm2 s−1 ) than for the Cu(II)/Cu process (with diffusion coefficient of 5.94 × 10−6 cm2 s−1 ), suggesting that a is also favored with diffusion coefficient of electroactive specie. The constant b, associated with hydrodynamic regime, exhibits values of 0.43 and 0.33 for the gaps of 2.4 and 3.2 cm, respectively, in the system I3 − /I− , indicating that hydrodynamics on the smooth RCE diminishes according to the inter-electrode space. While for the system (Cu(II)/Cu), the values of b were 0.91 and 0.88, for the gaps of 2.4 and 3.2. These values were higher for the copper deposition than for the soluble system, due to microturbulence at the roughened (and often powdery deposits) RCE interface. For the design purposes of RCE, it is recommendable that the electrochemical engineer should obtain experimentally the corresponding mass transport correlation, because it depends on the inter-electrode gap, hydrodynamics in the smooth and rough RCE interface (given by the electrochemical reaction), transport properties of electrolyte, cell geometry, and anode and cathode arrangements. References [1] J. Low, C. Ponce de León, F.C. Walsh, Aust. J. Chem. 58 (2005) 246. [2] J.L. Nava, E. Sosa, C. Ponce de León, M.T. Oropeza, Chem. Eng. Sci. 56 (2001) 2695. [3] D.R. Gabe, G.D. Wilcox, J. González-Garcia, F.C. Walsh, J. Appl. Electrochem. 28 (1998) 759. [4] F.S. Holland, U.S. Patent 4,028,199 (1977). [5] F.C. Walsh, Pure Appl. Chem. 73 (2001) 1819. [6] J.M. Grau, J.M. Bisang, J. Chem. Technol. Biotechnol. 77 (2002) 465. [7] F.C. Walsh, in: J.D. Genders, N.L. Weinberg (Eds.), Electrochemistry for a Cleaner Environment, Electrosynthesis, New York, NY, 1992. [8] G. Chen, Sep. Purif. Technol. 38 (2004) 11. [9] F. Rivera, I. Gonzalez, J.L. Nava, Environ. Technol. 29 (2008) 817. [10] C. Madore, M. Matlosz, D. Landolt, J. Appl. Electrochem. 22 (1992) 1155. [11] N. Zech, E.J. Podlaha, D. Landolt, J. Appl. Electrochem. 28 (1998) 1251. [12] D.R. Gabe, J. Appl. Electrochem. 4 (1974) 91. [13] D.R. Gabe, F.C. Walsh, J. Appl. Electrochem. 14 (1984) 565. [14] J.M. Grau, J.M. Bisang, J. Appl. Electrochem. 35 (2005) 285. [15] A.H. Nahlé, G.W. Reade, F.C. Walsh, J. Appl. Electrochem. 25 (1995) 450. [16] F.F. Rivera, J.L. Nava, Electrochim. Acta 52 (2007) 5868. [17] I. Rodriguez, Mass transport characterization of a flow channel reactor with parallel plates used as electrodes, M.Sc. thesis, Universidad Autónoma Metropolitana-Iztapalapa, México, D.F., 2006.
Contents lists available at ScienceDirect
Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta
Mass transport studies at rotating cylinder electrode: Influence of the inter-electrode gap ˜ b Fernando F. Rivera a , José L. Nava b,∗ , Mercedes T. Oropeza c , Alejandro Recéndiz d , Gilberto Carreno a
Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco No. 186, C.P. 09340, México, D.F., Mexico Departamento de Ingeniería Geomática e Hidráulica, Universidad de Guanajuato, Av. Juárez No. 77, C.P. 36000, Guanajuato, Guanajuato, Mexico Instituto Tecnológico de Tijuana, Centro de Graduados e Investigación Blvd. Industrial s/n, C.P. 22500, Tijuana, B.C., Mexico d Servicios Industriales Pe˜ noles S.A. de C.V., Centro de Investigación y Desarrollo Tecnológico, C.P. 27300, Torreón, Coahuila, Mexico b c
a r t i c l e
i n f o
Article history: Received 11 September 2009 Received in revised form 22 December 2009 Accepted 22 December 2009 Available online 11 January 2010 Keywords: Rotating cylinder electrode Mass transport characterization Dimensionless correlation Copper deposition Triiodide reduction
a b s t r a c t This study shows the effect of using two different inter-electrode gaps on the RCE mass transport characterization. The average mass transport coefficient was calculated using the limiting current technique, using the soluble reduction of triiodide (smooth RCE interface) and the copper deposition (roughness RCE interface) in KNO3 and H2 SO4 , respectively. Based on the analysis of the Sh = aReb Sc0.356 correlation, the values of the constant a, associated with shape and cell dimensions, were 0.89 and 3.8, in the soluble system (I3 − /I− ), for the gaps of 2.4 and 3.2 cm, respectively, indicating that this coefficient increases with inter-electrode space. While for copper deposition, these values were 0.00081 and 0.014, for the gaps of 2.4 and 3.2 cm. The constant b, associated with hydrodynamic regime, exhibits values of 0.43 and 0.33 for the gaps of 2.4 and 3.2 cm, respectively, in the system I3 − /I− , indicating that hydrodynamics on the smooth RCE diminishes according to the inter-electrode space. While for the system (Cu(II)/Cu), the values of b were 0.91 and 0.88, for the gaps of 2.4 and 3.2 cm. These values were higher for the copper deposition than for the soluble system, due to microturbulence at the roughened (and often powdery deposits) RCE interface. From the analysis performed in this paper is clear that inter-electrode gap and hydrodynamics on the smooth and roughness RCE interface (given by the nature of reduction reaction) modify the mass transport correlation. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The rotating cylinder electrode electrochemical reactor (RCE) is one of the most common geometries for different types of studies, such as metal ion recovery [1–4], alloy formation [1,3], electrosynthesis [3], corrosion [1,3], effluent treatment [5–9] and Hull cell studies [10,11]. RCEs are particularly well suited for high mass transport studies in the turbulent flow regime [1,12–16]. The mass transport control is imposed by the rotation speed of the inner cylinder and the applied limiting current density. When the fluid flow is generated entirely by an inner RCE, the characteristics of mass transport conditions can be described by a dimensionless group correlation of the following form [1,3,12,16]: Sh = aReb Sc0.356
(1)
where the Sherwood number (Sh = km d/D) describes mass transport by forced convection, the Reynolds number (Re = ud/) is an indication of the fluid flow regime, and the Schmidt number (Sc = /D)
∗ Corresponding author. Tel.: +52 4731020100x2275; fax: +52 4731020100x2209. E-mail addresses: [email protected], [email protected] (J.L. Nava). 0013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2009.12.060
relates the electrolyte transport properties. The average mass transport coefficient is described by km , d is the diameter of the RCE, D is the diffusion coefficient, u is the peripheral velocity, and is the kinematic viscosity. The mass transport correlation is best evaluated through analysis of experimental data [1,3,12,16]. The experimental constant a, is associated with the electrode geometry and shape as well as with the cell dimensions, whereas b is associated with the hydrodynamic regime [1,3,16]. In a previous paper Rivera and Nava [16] discussed the influence of plates and concentric cylinder used as a counter electrode on the RCE mass transport characterization during copper deposition. Based on the correlation described by Eq. (1) Rivera and Nava [16] discussed that both, the shape and area of the counter electrode, influence the values of a. The value of b, depends on the shape of the counter electrode, indicating that plates provoke higher turbulence promoting action than concentric cylinder. Moreover, powdery copper deposits, on the RCE, improve microturbulence at the roughened RCE interface [16]. It is important to mention that, in general, there are no references in the literature that show the effect of the inter-electrode gap on the RCE mass transport characterization. Moreover, the mass transport studies performed in the same RCE showing the effect of
3276
F.F. Rivera et al. / Electrochimica Acta 55 (2010) 3275–3278
the reaction mechanism involved is also rather limited. A study in that direction may be important because when designing a RCE reactor, it is necessary to know the accurate mass transport towards the electrode surface in given experimental conditions. The objective of this work is to show, on one hand, the effect of inter-electrode gap, and, on the other hand, the influence of different electrochemical systems, on the RCE mass transport characterization. The I3 − /I− and Cu(II)/Cu in KNO3 and H2 SO4 , respectively, were employed as the model reactions. 2. Experimental The solutions used in this work were prepared of analytic grade reactants and deionised water Milli-QTM . The I3 − ion and Cu(II) concentrations were 5 and 15.7 mM in 0.5 M KNO3 and 1.0 M H2 SO4 , respectively. Each electrolytic solution was deoxygenated with nitrogen for about 10 min before each experiment. 2.1. Equipment A potentiostat–galvanostat EG&G model PAR 273 and M270 software was used for all chronoamperommetric experiments. 2.1.1. RCE experiments Fig. 1 shows the diagram of a device built up for laboratory studies, consisting of a 500-cm3 glass reactor with a temperature bath and 8.5 cm inner diameter. 304-type stainless steel cylinders with 2.1 and 3.8 cm of diameter and a length of 11 cm were used as cathodes. The two diameters of the cylinder provide the two interelectrode gaps. As anodes were used four 13 cm long, 1.8 cm wide and 0.3 cm thick graphite bars were attached to the reactor walls and connected between each other. 115 V and 70 W CaframoTM electric motor of variable velocity was used to rotate the inner cylinder. The potentials were measured vs. saturated mercury: mercurous sulfate electrode (sat. MSE) Radiometer AnalyticalTM model XR200. Table 1 shows RCE reactor parameters and electrolyte transport properties. 2.2. Methodology 2.2.1. Experimental determination of the mass transport coefficients at the RCE electrode A series of potential pulses were applied to the RCE, using the cell described in Section 2.1.1, starting from open circuit potential OCP in the potential range of −1.4 ≤ E ≤ −0.4 V vs. sat. MSE during 5 s,
Table 1 RCE reactor parameters and electrolyte properties. Reaction volume, VR RCE length RCE radius, R1 Reactor radius, R2 Length, width and thick of the plates used as anodes (attached to the reactor walls) RCE area, ARCE (in contact with electrolyte), R1 = 1.9 cm RCE area, ARCE (in contact with electrolyte), R1 = 1.05 cm Diffusion coefficient (Cu2+ ), DCu2+ [16] Diffusion coefficient (I3 − ), DI3 − [17] Kinematic viscosity, [16]
350 cm3 11 cm 1.9 cm 1.05 cm 4.25 cm 13 cm × 1.8 cm × 0.3 cm 80 cm2 42 cm2 5.94 × 10−6 cm2 s−1 1.12 × 10−5 cm2 s−1 0.01 cm2 s−1
and −0.85 ≤ E ≤ −0.5 V vs. sat. MSE, for the electrochemical systems of (I3 − /I− ) and (Cu(II)/Cu), respectively. From these chronoamperograms, sampled current density (at 4.5 s) vs. cathodic potential pulse curves were constructed (j–E). The average mass transport coefficient, km , was calculated experimentally from limiting current density (jL ) obtained from polarization curves according to equation: km =
jL zFC0
(2)
where jL is the value of limiting current density plateau, z is electron number, F is the Faraday constant, and C0 is the electroactive species concentration in the bulk solution. The jL values were measured at potentials of −1.0 and −0.85 V vs. sat. MSE, for (I3 − /I− ) and (Cu(II)/Cu), respectively, assuming that the potential distribution on the RCE interface is homogeneous. The studies were made at Reynolds numbers within 34 × 103 < Re < 322 × 103 interval, in turbulent flow [12,16]. It is important to mention that at such turbulent conditions the convection originating from the rotation of the inner cylinder predominates over the convection induced by the gas (oxygen) generated at the counter electrode, which is quickly removed from the counter electrode and electrolyte. The experiments were carried out for the RCE radiuses (R1 ) of 1.9 and 1.05 cm, which provide two inter-electrode gaps (R2 –R1 ) of 2.4 and 3.2 cm, respectively. It is important to mention that the reactor radius (R2 ) remains constant with a value 4.25 cm. The authors decided to construct the polarization curves using sampled current density vs. cathodic potential instead of linear sweep voltammetry technique, because a voltammetric study always involves the competition between the formation rate of deposits at the interface and the polarization rate of the electrode. This last problem is eliminated in the potential pulse technique [16]. 3. Results and discussion
Fig. 1. (a) Rotating cylinder electrode scheme. (b) Frontal view.
Fig. 2a and b shows the cathodic polarization curves at different Reynolds numbers obtained when the reduction of triiodide is carried out on the RCE with inter-electrode gap of 2.4 and 3.2 cm, respectively. This figure shows that the limiting current region where the iodide reduction becomes completely mass transport controlled lies approximately between −1.2 and −0.8 V vs. sat. MSE and that, as expected, the current densities increase with the Reynolds number. Fig. 3a and b is similar to that presented in Fig. 2a and b, only that such curves were obtained during the reduction of cupric ions. The shape of these curves differs from that obtained in the soluble system, giving greatest current density values due to the copper concentration is three times larger than triiodide. In addition, the
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Fig. 4. Comparison of the mass transport correlations, evaluated from the limiting currents similar to those shown in Figs. 2 and 3. (a) I3 − /I− , gap 2.4 cm; (b) I3 − /I− , gap 3.2 cm; (c) Cu(II)/Cu, gap 2.4 cm and (d) Cu(II)/Cu, gap 3.2 cm.
Fig. 2. Typical sampled current density vs. cathodic potential pulse curves, constructed from typical current transients at sampling time of 4.5 s, at different Reynolds numbers shown in the figure. Electrolyte: 5 mM I3 − in 0.5 M KNO3 , T = 298 K. RCE devices with inter-electrode gap of: (a) 2.4 cm and (b) 3.2 cm.
limiting current plateaus in the curves of Fig. 3 are poorly defined due to early stages of growth of the copper metal on the stainless steel surface, and hence, an increase in the electrode surface roughness. However; there is a slightly change of slope, between −0.85 ≤ E ≤ −0.80 V vs. sat. MSE, that approaches to plateau; this last potential interval is in agreement to that previously reported about copper deposition on stainless steel RCE [2,16], where the process is mass transport controlled. The mass transport coefficients were evaluated by liming current density measurements (Eq. (2)), at holding potential of −1.0 and −0.85 V vs. sat. MSE, for triiodide and cupric reduction processes, respectively. These values were comprised between (4.9 × 10−3 < km < 8.5 × 10−3 ) cm s−1 and (0.23 × 10−3 < km < 1.4 × 10−3 ) cm s−1 , for triiodide and cupric reduction processes, respectively. Subsequently, dimensionless correlations were evaluated using the km values for each Reynolds number and the transport properties are shown in Table 1 (Eq. (1)). Fig. 4 shows the comparison of mass transport characterization obtained for the (I− /I3 − ) and (Cu(II)/Cu) processes on the RCE with inter-electrode gap of 2.4 and 3.2 cm. The analysis of Fig. 4 demonstrates that the mass transport is favored by the soluble process, triiodide reduction (Fig. 4a and b) as compared to the powdery copper deposits, on the RCE (Fig. 4c and d), respectively. The enhanced mass transport by triiodide can be associated with its diffusion coefficient value, which is 1.9 times higher than for cupric ions (Table 1). Table 2 exhibits the experimental values of a, and b from Eq. (1) for the two inter-electrode gaps and electrochemical systems. An analysis of Table 2, system I3 − /I− , shows that the value of a, associated with shape and cell dimensions, were 0.89 and 3.8, for the gaps of 2.4 and 3.2 cm, respectively, indicating that this coefficient increases with inter-electrode space. For the system Table 2 Mass transport correlations (Sh = aReb Sc0.356 ) in RCE reactor.
Fig. 3. Typical sampled current density vs. cathodic potential pulse curves, constructed from typical current transients at sampling time of 4.5 s, at different Reynolds numbers shown in the figure. Electrolyte: 15.7 mM CuSO4 in 1 M H2 SO4 , T = 298 K. RCE devices with inter-electrode gap of: (a) 2.4 cm and (b) 3.2 cm.
Electrolytic solution
Inter-electrode gap (R2 –R1 )
a
b
I3 − /I− I3 − /I− Fe(CN)3− Cu2+ Cu2+ Cu2+ Cu2+
2.4 3.2 – 2.4 3.2 2.4 –
0.89 3.8 1.356 0.00081 0.014 0.012 0.079
0.43 0.33 0.63 0.91 0.88 0.95 0.92
a b
This work This work [14]a This work This work [16]b [1,3]
This correlation was obtained in a RCE covered with expanded metal. This correlation was obtained in RCE (four counter electrodes).
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(Cu(II)/Cu), where occurs the same dependence, the values of a were 0.00081 and 0.014, for the gaps of 2.4 and 3.2 cm. The values of a were higher for triiodide than for cupric ions; this fact can be associated with its diffusion coefficient value, as mentioned above. The constant b, associated with hydrodynamic regime, exhibits values of 0.43 and 0.33 for the gaps of 2.4 and 3.2, respectively, in the system I3 − /I− , indicating that hydrodynamics on the smooth RCE diminishes according to the inter-electrode space, as expected. For the system (Cu(II)/Cu), where occurs the same dependence, the values of b were 0.91 and 0.88, for the gaps of 2.4 and 3.2. The values of the exponent b were higher for the copper deposition than for the soluble system. This last, is associated to microturbulence at the roughened RCE interface [1,3,16]. The values of b >0.8 are frequently found for rough electrodeposits, while for a hydrodynamically smooth surface these values are < 0.7 [1]. The coefficient a and exponent b, obtained in this investigation, were also compared in Table 1 with those reported by Grau and Bisang [14] (reduction of Fe(CN)6 3− on a RCE with expanded metal), Walsh and coworkers [1,3] (copper deposition in a RCE), and Rivera and Nava [16] (copper deposition on RCE). The differences of the mass transport correlation for the soluble system (I3 − /I− ) and that reported during the reduction of ferricyanide in Ref. [14], can be attributed to the RCE covered with expanded metal. Moreover, authors in Refs. [1,3,14] do not specify any ratio between R1 and R2 , or an inter-electrode gap parameters and electrode materials. For the above, we do not consider appropriate to give a more detailed discussion. From the analysis of these correlations and the obtained herein, it is clearly observed that hydrodynamics on the smooth and roughness RCE interface, geometrical parameters and diffusion coefficient of electroactive specie modify the mass transport correlation. The mass transport correlation of RCE is best evaluated through analysis of experimental data, because it depends on the interelectrode gap, hydrodynamics on the smooth and rough RCE interface (given by the nature of reduction reaction), diffusion coefficient, type of fluid flow pattern [12], cell geometry [1,3], anode [16] and cathode arrangements [1,14]. 4. Conclusions Measurements of mass transport on the RCE (both with two different inter-electrode gaps) have been systematically investigated. The average mass transport coefficient was calculated using the limiting current technique, using the soluble reduction of triiodide (smooth RCE interface) and the copper deposition (roughness RCE interface) in KNO3 and H2 SO4 , respectively.
Based on the analysis of the Sh = aReb Sc0.356 correlation, the values of the constant a, associated with shape and cell dimensions, were 0.89 and 3.8, in the soluble system (I3 − /I− ), for the gaps of 2.4 and 3.2 cm, respectively, indicating that this coefficient increases with inter-electrode space. While for copper deposition, these values were 0.00081 and 0.014, for the gaps of 2.4 and 3.2 cm. The values of this constant, a, were higher for the (I3 − /I− ) system (with diffusion coefficient of 1.12 × 10−5 cm2 s−1 ) than for the Cu(II)/Cu process (with diffusion coefficient of 5.94 × 10−6 cm2 s−1 ), suggesting that a is also favored with diffusion coefficient of electroactive specie. The constant b, associated with hydrodynamic regime, exhibits values of 0.43 and 0.33 for the gaps of 2.4 and 3.2 cm, respectively, in the system I3 − /I− , indicating that hydrodynamics on the smooth RCE diminishes according to the inter-electrode space. While for the system (Cu(II)/Cu), the values of b were 0.91 and 0.88, for the gaps of 2.4 and 3.2. These values were higher for the copper deposition than for the soluble system, due to microturbulence at the roughened (and often powdery deposits) RCE interface. For the design purposes of RCE, it is recommendable that the electrochemical engineer should obtain experimentally the corresponding mass transport correlation, because it depends on the inter-electrode gap, hydrodynamics in the smooth and rough RCE interface (given by the electrochemical reaction), transport properties of electrolyte, cell geometry, and anode and cathode arrangements. References [1] J. Low, C. Ponce de León, F.C. Walsh, Aust. J. Chem. 58 (2005) 246. [2] J.L. Nava, E. Sosa, C. Ponce de León, M.T. Oropeza, Chem. Eng. Sci. 56 (2001) 2695. [3] D.R. Gabe, G.D. Wilcox, J. González-Garcia, F.C. Walsh, J. Appl. Electrochem. 28 (1998) 759. [4] F.S. Holland, U.S. Patent 4,028,199 (1977). [5] F.C. Walsh, Pure Appl. Chem. 73 (2001) 1819. [6] J.M. Grau, J.M. Bisang, J. Chem. Technol. Biotechnol. 77 (2002) 465. [7] F.C. Walsh, in: J.D. Genders, N.L. Weinberg (Eds.), Electrochemistry for a Cleaner Environment, Electrosynthesis, New York, NY, 1992. [8] G. Chen, Sep. Purif. Technol. 38 (2004) 11. [9] F. Rivera, I. Gonzalez, J.L. Nava, Environ. Technol. 29 (2008) 817. [10] C. Madore, M. Matlosz, D. Landolt, J. Appl. Electrochem. 22 (1992) 1155. [11] N. Zech, E.J. Podlaha, D. Landolt, J. Appl. Electrochem. 28 (1998) 1251. [12] D.R. Gabe, J. Appl. Electrochem. 4 (1974) 91. [13] D.R. Gabe, F.C. Walsh, J. Appl. Electrochem. 14 (1984) 565. [14] J.M. Grau, J.M. Bisang, J. Appl. Electrochem. 35 (2005) 285. [15] A.H. Nahlé, G.W. Reade, F.C. Walsh, J. Appl. Electrochem. 25 (1995) 450. [16] F.F. Rivera, J.L. Nava, Electrochim. Acta 52 (2007) 5868. [17] I. Rodriguez, Mass transport characterization of a flow channel reactor with parallel plates used as electrodes, M.Sc. thesis, Universidad Autónoma Metropolitana-Iztapalapa, México, D.F., 2006.