Equivalent Circuit Analog to an Electrochemical Cell for Anodic Growth of Titania Nanotube Array

Jhon Alexander Peñafiel Castro1, a and Rafael Quintero-Torres1,b 1Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México

Boulevard Juriquilla 3001, Juriquilla, Querétaro 76230, México

ajapenafiel@fata.unam.mx, brquintero@fata.unam.mx

Submitted: August 30, 2010; revised: October 26, 2010; accepted: November 22, 2010

Keywords: Titanium oxide, nanotube, electrochemical, circuit equivalent.

Abstract. The behavior of an electrochemical cell for anodic formation of titanium oxide nanotubes is calculated from an electrical model obtained from the DC Current-time plot. The result can predict the behavior beyond the voltage source used in the experiment and in conditions that are impossible to achieve in a real experiment. This clarifies the speculation around the cell voltage versus cell current limited experimental data and its behavior is explained in terms of the source used in the experiment.

Introduction

The TiO2 physicochemical properties are modified as a result of quantum confinement and geometrical arrangement at nanometric scale, in particular the anodic surface obtained over titanium presents both and we referred to it as a nanostructured profile.

The intensive work and results provided by the Schmuki [1-6] and Grimes [7-10] groups allowed the improvement of the morphology and properties described by the different generations of materials and the control of final properties of such surfaces. Disregarding the fact that such material is relatively new, the achievements in the final morphology are remarkable, however a whole knowledge of the mechanisms that define the formation of such structures is poorly understood [10].

All the accepted models that explain the oxide formation include a first stage identified by the formation of an initial oxide barrier, followed by a superficial activation of defects in the oxide as a result of its chemical dissolution by fluorine ions, enhanced by the electric field. The next stage consists of the selective dissolution at the bottom of the tube making it longer. Despite the basic understanding of the processes involved, the self organization is the most elusive part.

The usual approach for the study of the growth mechanism comprises techniques such as XPS, in parallel with SEM and TEM, which are much slower, and more expensive when compared to an equivalent electrical circuit of an electrochemical cell. This is a technique that allows the study of the charge movement phenomenology; physical movement as in ohm’s law and electric displacement as in capacitance studies, this is carried out in the bulk and at the interfaces. From this information it is possible to infer the change of conductivity in the whole system and correlate it with the physical phenomena involved, such as chemical reactions and charge transport. As a result a proposed model for the understanding of the different stages of TiO2 production has been described [6].

The general conclusion obtained from systems where an anodic oxide grows as a thin film is based on the underlying mechanisms required to produce the oxide; charge transport in the different phases and exchange of charge due to chemical reactions that take place at the interfaces oxide-electrode and oxide-electrolyte.

Journal of Nano Research Vol. 14 (2011) pp 39-45Online available since 2011/Apr/14 at www.scientific.net© (2011) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/JNanoR.14.39

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Inorganic matter presents itself via the equilibrium state, the forces present in TiO2 nanoestructured profile involve: gravity and kinematic forces, random Brownian movement and electrostatic forces. The oxide nanotubular surfaces over metallic materials bear a hexagonal honeycomb structure, defined by electrostatic forces and the screening of ions due to its solvation.

Experimental details

The experimental results used for this work were the product of a series of designed experiments to obtain information from electrochemical impedance spectroscopy (EIS) to relate them with the initial evolution of anodic nanotubes [11]. In this work, conditions at corrosion potential will be extended to have oxidation-reduction events in different electrodes and electrically similar in all the physicochemical processes of the nanotubes formation. The model used to adjust the data is presented in Fig. 1.

Fig. 1 Electrical circuit equivalent to the electrochemical cell corresponding to a single electrochemical reaction and used to best fit the experimental data. Equations from the electrical circuit used for the analysis.

The different redox processes needed to form the nanotubes include the electrically equivalent next three routes: Oxidation of titanium:

Anodic reaction: −+ +→ eTiTi 44

Cathodic reaction: −− +→+ OHHeOH 22 2

1

Titanium dissolution:

Anodic reaction: −+ +→ eTiTi 44

R2

R1

C

R0

Vf

Icell Vcell

Cell 210 )( CR

V

RRC

VV

dt

dV ccfc −+

−=

10 RR

VVI cf

cell +−

=

cellccell IRVV 1+=

40 Journal of Nano Research Vol. 14

Cathodic reaction: )(6)(3)(666 324 aqNHgHaqFeFNH ++→+ −−

Titanium dioxide dissolution:

Anodic reaction: )(64)(6)( 42

2642 aqNHOeaqTiFFNHsTiO +−− +++→+

Cathodic reaction: )(4)(24)(4 324 aqNHgHeaqNH +→+ −+

These reactions form the Faradic current represented by the variable R2 [12], R1 represents the local ohmic impedance and C represents the interfacial capacitance.

Table 1. Oxide NTA growth conditions.

Sample Voltage

[V]

Water

[% vol]

NH4F

[% mass]

Time

[h]

T1 30 0 0.25 14

T2 60 0 0.25 34

T3 60 3 0.25 14

T4 30 3 0.25 34

T5 30 0 0.5 34

T6 30 3 0.5 14

T7 60 0 0.5 14

T8 60 3 0.5 34

Table 2 Elements that best fit the data. Sample Water

[% vol]

R1 [Ω] C2 [mF] R2 [Ω] R2 [Ω] Range

T1 0 15000 100 200000 200000

T2 0 10000 100 100000 100000

T3 3 6000 5 317001 tk + 1000-80000

T4 3 15000 1 tk 14001 + 1000-448000

T5 0 9000 50 80000 80000

T6 3 7000 10 tk 7001 + 1000-224000

T7 0 3500 100 70000 70000

T8 3 3000 10 317001 tk + 1000-80000

The substrates used in this work were titanium foils (0.25mm thickness, 99.7% purity, Sigma Aldrich). Each sample was degreased in acetone for 10 minutes by standard ultrasonic cleaning, and then rinsed with deionized water and air dried. Anodization for all experiments was carried out

Journal of Nano Research Vol. 14 41

in a home-made two-electrode electrochemical cell containing a platinum sheet as counterelectrode. The voltage for anodic growth was delivered by a direct current (DC) power supply and an electrometer (Keithley Model 6517) was used to monitor the current in the electrochemical cell. The samples were anodized in ethylene glycol (99.8 % purity Sigma Aldrich) and NH4F was the source of fluoride ions. A mixture of ethylene glycol and water was used as electrolyte in some cases (see Table 1).

What is clear is the reduction in the initial resistance with the water added to the electrolyte. It is well known that the ethylene glycol can be purified by electrical power and that ethylene glycol resistance is a sensor of the amount or water dissolved.

The large value of capacitance observed in table 2 is not geometrical rather it is due to charge displacement C= dQ/dV, indicating that a large amount of ions are available at the interface with the electrodes.

Figures 2 and 3 present the results for the current circulating in the electrochemical cell with titanium area of half centimeter square, if a constant voltage is applied, as indicated in table 1.

Fig. 2 Results for all the samples that include water in the electrolyte. (a) Experimental data plot. (b) Adjusted plots, with the electrical circuit in fig. 1 and the data from table 2.

Fig. 3 Results for all the samples without water in the electrolyte (a), Experimental data plots. (b) Adjusted plots, with the electrical circuit in fig. 1 and the data from table 2.

Sample 1 and 2

30

5000200001

VR −= (1a)

(a) (b)

(a) (b)

42 Journal of Nano Research Vol. 14

30

1000003000002

VR −= (1b)

Sample 3 and 4

30

9000240001

VR −= (2a)

22 69.104.048.4165592400 tEVttVR −−−+−= (2b)

With eq. 1 or 2 and a small program in MatLab® to solve the electrical circuit numerically, it is possible to predict the behavior of the circuit in any desired condition. Samples 5 & 7 are similar in behavior to eq. 1 and samples 6 & 8 are similar in behavior to eq. 2.

Fig. 4 Simulation results for step source voltage and samples 3-4 (a) Cell current versus time, (b) Cell current versus cell voltage.

Fig. 5 Simulation results for ramp source voltage and samples 3-4 (a) Cell current versus time, (b) Cell current versus cell voltage.

Discussion

When the steady-state condition (constant anodic current) is attained at a shorter time, the nanotube length was correspondingly shorter. Prior to achieving this condition, longer nanotubes were formed at longer growth time. Elsewhere has been discussed [11] here it is only mentioned that an absence of water in the growth medium contributes to non-uniform NTA growth on the surface of Ti

(a) (b)

(a) (b)

Journal of Nano Research Vol. 14 43

substrate and with poor adhesion. The thickest nanotube walls were secured at higher anodization voltages during growth. Concomitantly the thinnest nanotube wall dimension occurred at high fluoride ion level and short growth time and/or low voltage and longer growth time.

Figure 4 presents the electrochemical cell behavior when a step function in the source voltage is used, from zero to 10, 25, 40 and 55 volts. The current through the cell decreases continuously and the voltage in the cell changes very little getting closer to the source voltage.

Figure 5 presents the transition from slow increase in voltage to a sharp transition in voltage similar to the one used in fig. 4. In this figure it is possible to identify a similar initial slope for all plots, in the middle region the plateau at different current level is clear as well and the decrease of current when the ramp is fast enough is visible also. The analysis of the current cell versus the voltage cell presents a similar behavior as the experiment allows and this completes the picture with results beyond experimental possibilities.

Conclusion

Equivalent circuit model for NTA growth is possible to be produced with a limited number of experimental trials, from this information it is possible to generate a complete behavior of the cell. Access to the physicochemical process is gain with this exercise and identifies the redox reactions involved in the electrochemical cell.

Acknowledgments

We acknowledge CONACYT for the scholarship of one of us (JAPC) and the financial assistance via DGAPA-UNAM under grant PAPIIT IN107009.

References

[1] R. Beranek, H. Hildebrand, and P. Schmuki. Electrochemical and Solid-State Letters Vol. 6(3) (2003), p. B12-B14.

[2] L. V. Taveira, J. M. Macák, H. Tsuchiya, L. F. P. Dick, and P. Schmuki. Journal of The Electrochemical Society Vol. 152(10) (2005), p. B405-B410.

[3] J. M. Macák, H. Tsuchiya, and P. Schmuki. High-Aspect-Ratio TiO2 Nanotubes by anodization of titanium. Angew. Chem. Int. Ed. Vol. 44 (2005), p. 2100-2102.

[4] J. M. Macák, H. Tsuchiya, L.V. Taveira, S. Aldabergerova, and P. Schmuki. Angew. Chem. Int. Ed. Vol. 44 (2005), p. 7463-7465.

[5] K. Yasuda, J. M. Macak, S. Berger, A. Ghicov, and P. Schmuki. Journal of The Electrochemical Society Vol. 154 (9) (2007), p. C472-C478.

[6] J.M. Macak, H. Hildebrand, U. M. Jahns, P. Schmuki. Journal of Electroanalytical Chemistry Vol. 621 (2008), p. 254–266.

[7] D. Gong, C. A. Grimes, O. K. Varghese, W. Hu, R.S. Singh, Z. Chen, E. C. Dickey. J. Mater. Res. Vol. 16 (2001), p. 3331-3334.

[8] C. Ruan, M. Paulose, O. K. Varghese, G. K. Mor, and C. A. Grimes. J. Phys. Chem. B Vol. 109 (2005), p. 15754-15759.

44 Journal of Nano Research Vol. 14

[9] M. Paulose, K. Shankar, S. Yoriya, H. E. Prakasam, O. K. Varghese, G. K. Mor, T. A. Latempa, A. Fitzgerald, and C. A. Grimes.. J. Phys. Chem. B Vol. 110 (2006), p. 16179-16184.

[10] M. Paulose, H. E. Prakasam, O. K. Varghese, L. Peng, K. C. Popat, G. K. Mor, T. A. Desai, and C. A. Grimes. J. Phys. Chem. C Vol. 111 (2007), p. 14992-14997.

[11] J. A. Peñafiel, R. Quintero-Torres, N. R. de Tacconi, K. Rajeshwar, and W. Chanmanee. J. Electrochem. Soc., Volume 158, Issue 2, pp. D84-D90 (2011)submitted to Journal of electrochemical Society. 2010.

[12] M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy, The Electrochemical Society Series, J. Wiley & Sons, New York, (2008).

Journal of Nano Research Vol. 14 45

Journal of Nano Research Vol. 14 10.4028/www.scientific.net/JNanoR.14 Equivalent Circuit Analog to an Electrochemical Cell for Anodic Growth of Titania Nanotube Array 10.4028/www.scientific.net/JNanoR.14.39

DOI References

[1] R. Beranek, H. Hildebrand, and P. Schmuki. Electrochemical and Solid-State Letters Vol. 6(3) (2003), p.

B12-B14.

doi:10.1149/1.1545192 [2] L. V. Taveira, J. M. Macák, H. Tsuchiya, L. F. P. Dick, and P. Schmuki. Journal of The Electrochemical

Society Vol. 152(10) (2005), p. B405-B410.

doi:10.1149/1.2008980 [5] K. Yasuda, J. M. Macak, S. Berger, A. Ghicov, and P. Schmuki. Journal of The Electrochemical Society

Vol. 154 (9) (2007), p. C472-C478.

doi:10.1149/1.2749091 [6] J.M. Macak, H. Hildebrand, U. M. Jahns, P. Schmuki. Journal of Electroanalytical Chemistry Vol. 621

(2008), p.254–266.

doi:10.1016/j.jelechem.2008.01.005 [7] D. Gong, C. A. Grimes, O. K. Varghese, W. Hu, R.S. Singh, Z. Chen, E. C. Dickey. J. Mater. Res. Vol. 16

(2001), pp.3331-3334.

doi:10.1557/JMR.2001.0457 [8] C. Ruan, M. Paulose, O. K. Varghese, G. K. Mor, and C. A. Grimes. J. Phys. Chem. B Vol. 109 (2005),

pp.15754-15759.

doi:10.1021/jp052736u [9] M. Paulose, K. Shankar, S. Yoriya, H. E. Prakasam, O. K. Varghese, G. K. Mor, T. A. Latempa, A.

Fitzgerald, and C. A. Grimes. J. Phys. Chem. B Vol. 110 (2006), pp.16179-16184.

doi:10.1021/jp064020k [10] M. Paulose, H. E. Prakasam, O. K. Varghese, L. Peng, K. C. Popat, G. K. Mor, T. A. Desai, and C. A.

Grimes. J. Phys. Chem. C Vol. 111 (2007), pp.14992-14997.

doi:10.1021/jp075258r [11] J. A. Peñafiel, R. Quintero-Torres, N. R. de Tacconi, K. Rajeshwar, and W. Chanmanee. J. Electrochem.

Soc., Volume 158, Issue 2, pp. D84-D90 (2011)submitted to Journal of electrochemical Society. (2010).

doi:10.1149/1.3251305 [12] M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy, The Electrochemical Society

Series, J. Wiley & Sons, New York, (2008).

doi:10.1002/9780470381588