Knowledge-based prediction of pore diameter of nanoporous anodic aluminum oxide

Journal of Electroanalytical Chemistry 705 (2013) 57–63

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Knowledge-based prediction of pore diameter of nanoporous anodic aluminum oxide Mahdi Mohajeri a,b,c, Hamed Akbarpour d,⇑ a

Faculty of Engineering, Tarbiat Modares University, Tehran, Iran Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran c Nanotechnology Division, Research Institute of Petroleum Industry, Tehran, Iran d Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran b

a r t i c l e

i n f o

Article history: Received 27 March 2013 Received in revised form 13 July 2013 Accepted 18 July 2013 Available online 31 July 2013 Keywords: Artificial neural network Nanoporous anodic aluminum oxide Pore diameter

a b s t r a c t Using nanostructured materials, especially nanoporous aluminum oxide, becomes more popular in recent years. The main purpose of this paper is developing an artificial neural network (ANN) model and conducting an experiment to predict the pore diameter of nanoporous aluminum oxide membrane. For this reason, a total of 32 experimental data are collected and used to develop the proposed model. The process parameters such as electrolyte concentration, temperature and anodization potential are considered as input, while the pore diameter is accounted for output. A comparison of ANN, experimental study and two previous empirical formulas indicates that ANN has a good predictive capability of the pore diameter. It can also forecast the experimental result with an acceptable error. The results also reveal that both empirical formulas are too conservative. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction In recent years, using nanostructured materials becomes more popular in several applications such as magnetic, photonic, electronic, gas separation due to their unique and invaluable structural properties [1–6]. These modern technological applications need precise control of dimension and geometry of nanostructured surfaces. They also require a considerable attention on developing simple, elegant and inexpensive methods in nanostructured materials synthesis. Compared with the conventional methods, template-assisted ones are good candidate for fabrication of nanostructured materials such as nanowires and nanotubes [7– 21]. Nanoporous anodic alumina (NPAA) membrane is the most versatile template which is prepared by a self-organized two-step anodizing of aluminum in acidic electrolytes [22–26]. The self-organized two-step anodization process consists of the periodic concave patterns on aluminum surface by initial anodizing and the subsequent chemical etching. Then, ordered nanopores have formed on the generated nucleation sites in the second anodization step [27–30]. Fig. 1 illustrates a two-step anodization process schematically. Adjusting anodizing conditions including: potential, temperature and process duration can easily control the characteristic parameters of NPAA membranes such as interpore distance,

⇑ Corresponding author. Tel.: +98 (21) 64542220. E-mail address: [email protected] (H. Akbarpour). 1572-6657/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jelechem.2013.07.026

pore diameter, thickness and density. Fig. 2 shows the characteristic parameters NPAA membranes. From an economical point of view, it is essential to produce reliable and durable NPAA membranes with the least geometric tolerance in templates. The influence of different applied voltage, anodization duration, temperature and type of electrolyte on the characteristic parameters of NPAA membranes was investigated separately in the literature. Later studies present the pore diameter empirically dependent on anodizing potential. O’Sullivan and Wood [31] suggested a proportional linear relationship between pore diameter and potential as follows:

Dp ¼ kp  U

ð1Þ

where the proportionality constant (kp) is approximately 1.29 nm V1; U and Dp denotes potential (V) and pore diameter (nm), respectively. Palibroda et al. [32] reported Eq. (2) for the pore diameter.

Dp ¼ 4:986 þ 0:709  U

ð2Þ

Nowadays, the importance of experimental studies in conjunction with knowledge-based procedures is recognized clearly. The most common approaches to date are used as the knowledgebased systems are artificial neural networks (ANNs), which finding out the best representation of database with a set of rules. There are several studies which use ANNs in various engineering applications [33–38].

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Nomenclature ANN Dp U kp BP Hj Wij Xi biasj F ILW ILB

artificial neural network pore diameter (nm) applied voltage (V) constant (1.29 nm V1) back-propagation algorithm activity level generated at the jth hidden neuron weights on the connections to the hidden layer of neurons input value transmitted from the xth input neuron bias at the jth hidden neuron activation function input layer weight input layer bias

HLW HLB MAE MAPE RMS R2 COR ti Oi N O t

hidden layer weight hidden layer bias mean absolute error mean absolute percentage error root mean square error absolute fraction of variance correlation coefficient desired pore diameter predicted output total number of data records in each set of data mean value of predictions mean value of observations

The aim of this research is to present an artificial neural network in conjuction with an experimental study to predict the pore diameter of NPAA membranes at the synthesis conditions. As far as the earliest researches showed the influence of three important factors including: potential, temperature and electrolyte concentration on the average pore diameter [39–41], these factors are considered as input layer neurons. It is noted that a total of 32 experimental data are used to develop an ANN model. The results show that the outputs of the ANN have good agreement with their corresponding experimental records. All results are also compared with two above-mentioned empirical formulas which it reveals that the proposed ANN model is more accurate than the empirical formulas. 2. Experimental study An aluminum foil (99.9%, 0.2 lm thickness) is used as the working substrate. It is precut in a coupon (0.5 cm  2 cm) and annealed

Fig. 1. Schematic of a two-step anodization process.

Fig. 2. The characteristic parameters of NPAA membranes.

at 450 °C in air for 3 h. In order to attain a remarkable decrease of surface roughness and oxide layer removal, the chemical polishing solution of NaOH (1 mol/dm3 (M)) is used where polishing duration is 3 min. Then the coupon is immersed in ethanol and subsequently in deionized water. The counter electrode is an Al sheet with a 1-cm2 effective surface (0.5 cm  2 cm) and the separation distance between the two electrodes is kept at 3 cm. A self-organized two-step anodization procedure is used for fabrication of NPAA film. This is carried out in double-walled electrochemical cell with magnetic stirrer (600 r.p.m.). In the anodizing cell, current is monitored by a data acquisition board in conjunction with the LabVIEW program. An oxalic acid solution (0.3 M) is used as an electrolyte and a high power chiller in a closed circuit is applied to keep the temperature constant during the anodization process. The anodization is done twice under a constant DC voltage of 40 V for 3 h at the temperature of 1 °C. After the first anodization, the aluminum oxide layer is removed by soaking the coupon in a vigorously stirred mixture of 6 wt% phosphoric acid and 1.8 wt% chromic acid at 75 °C for 1 h. Then, the coupon is anodized at the same experimental conditions again. X-ray diffraction (XRD) instrument (Philips Analytical PC-APD) is used to characterize the NPAA film. The sample morphology is investigated by a field emission scanning electron microscope (Hitachi S-4160, Japan). The Image J 1.37v software is used for estimation of the pore diameter of NPAA film.

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59

of 31 experimental studies from the literature and the above-mentioned work done by the authors [24,39,42–51]. The distribution of effecting factors on the proposed model is shown in Fig. 3.

4. Artificial neural network

Fig. 3. Distribution of anodization parameters in pore diameter database.

3. Data collection The purpose of this study is to establish an ANN model for prediction of the pore diameter of NPAA membrane. In order to provide the community for training, validating and testing the model, a pore size database is collected. This includes the results

Artificial neural networks are information processing techniques based on the way biological nervous systems process information. The basic concept of ANNs is the structure of the information processing system. ANNs are configured for specific applications such as data classification or pattern recognition through a learning process which is called training. In fact, ANNs can solve complex problems with acceptable errors [52]. An ANN consists of three layers including input, hidden and output layers. Input data are presented to the network through the input layer where there are some nodes that their numbers are equal to the number of independent input variables [53]. In this paper, three effecting factors on the pore diameter of NPAA are considered as the input variables including: concentration, temperature and potential. The output layer involves neurons representing desired problem solutions. In this research, the pore

Fig. 4. Schematic architecture of the proposed ANN model.

Fig. 5. The current density–time curve for anodic oxidation process.

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Fig. 6. X-ray diffraction pattern of NPAA membrane after second anodizing process.

diameter is selected as the target variable. Thus, the output layer has only one neuron. These two above-mentioned layers are separated with one or more hidden layers which are connected each other through some weighted interconnections. It is noted that there is no general rule for determining the hidden layer size. Some researchers carried out many try and error studies to provide an algorithm for predicting the hidden layer size. It is suggested that the upper bond on the number of hidden neurons is limited to twice the input variables plus one [54]. After trying some networks, the number of hidden neurons is selected as five herein setting in a one hidden layer. Back propagation (BP) is known to be the most powerful and widely used technique to train a network. To obtain some desired outputs, weights which represent connection strengths between neurons and biases are adjusted using a number of training inputs and the corresponding target values. The network error, that is the difference between the predicted and expected target patterns, is then back propagated from the output layer to the input layer for updating the network weights and biases. The process of adjusting the weights and biases is conducted until the network error arrives at a specific level of accuracy. For this aim, this algorithm, at first, develops an activity level (Hj) and then uses a transfer function (f) to compute the relationship between inputs and output in the network. A multilayer feed-forward network is typically uses a sigmoid function in its hidden layer. The activity level and activation function are given in Eqs. (3) and (4) [53,55,56]. It is noted that the structure of the proposed ANN model is illustrated in Fig. 4 schematically.

Hj ¼

N X W ij X i þ biasj

ð3Þ

HLW ¼ j 1:0088 0:3846 0:55104 0:15674 0:7964 j ð7Þ HLB ¼ j0:0478j

5. Model assessment Five indexes are used to compare the predicted and actual target values in the ANN. These determine errors between the desired

Fig. 7. FE-SEM top-view image of NPAA after the second step of anodization at constant-potential (40 V) and temperature (1 °C) in 0.3 M oxalic acid.

i¼1

f ðHj Þ ¼

1 1 þ eðHj Þ

ð4Þ

where Hj is activity level which is generated at jth hidden neuron; Wij are weights on the connections to hidden neurons; Xi is an input which is transmitted from xth input neuron; biasj is the bias at jth hidden neuron; and f is an activation function. In this part all weights, useful parameters of the hidden layer and the model predictions are derived and presented. The input layer weights (ILWs), input layer biases (ILB), hidden layer weights (HLWs) and hidden layer biases (HLB) of the proposed ANN model are given in the following equations.

   1:1001 2:7023 3:2269 0:43189 1:8146      ILW ¼  0:4518 0:00182 0:42961 3:54622 1:843     3:8176 0:30431 0:91926 1:39774 0:37519  ð5Þ ILBT ¼ j 3:25343 2:0803 0:12913 2:37079 1:9678 j

ð8Þ

ð6Þ Fig. 8. Comparison of the ANN and empirical formulas [31,32].

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values and model predictions. On the other hand, these factors show the capability of model and are as follows: N 1X MAE ¼ jOi  t i j N i¼1

MAPE ¼

1 N

N X i¼1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X RMSE ¼ t ðOi  t i Þ2 N i¼1

ð9Þ R2 ¼ 1 

jOi  ti j  100 ti

PN

2 i¼1 ðOi  t i Þ PN 2 i¼1 ðOi Þ

ð11Þ

! ð12Þ

ð10Þ

Table 1 Statistical values for pore diameter of the ANN and empirical equations. Data set

Model type

MAE

MAPE

RMSE

R2

COR

Training

ANN O’Sullivan equation [31] Palibroda equation [32]

1.73356 6.30875 16.59648

3.75374 13.80904 32.76291

2.26088 8.55706 19.81160

0.99795 0.96892 0.59790

0.99392 0.92014 0.92014

Validating

ANN O’Sullivan equation [31] Palibroda equation [32]

1.26852 2.40000 11.50733

3.92603 8.34909 30.42066

1.94232 2.62548 13.61714

0.99762 0.99547 0.72454

0.99452 0.99290 0.99290

Testing

ANN O’Sullivan equation [31] Palibroda equation [32]

1.91886 3.26667 11.41067

4.91019 9.12969 28.15225

2.54038 3.68137 13.72406

0.99667 0.99297 0.77009

0.99720 0.98918 0.98918

Fig. 9. Comparison of the ANN outputs and actual data for (a) training, (b) validating, and (c) testing.

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PN  i¼1 ðOi  Oi Þðt i  t i Þ ffi COR ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 PN  2 i¼1 ðOi  Oi Þ i¼1 ðt i  t i Þ

ð13Þ

where ti is the desired pore diameter; Oi is the estimated output; N is the total number of samples in each set; O is the average value of the predictions and t is the average value of the observations.

6. Results and discussion In this research, an ANN model is described along with an experimental study. Both analyses consider three important factors including: concentration, temperature and anodizing potential to study the pore size of NPAA membranes. In experimental study-which is carried out to verify the knowledge-based model predictions – a two-step anodization process is performed in 0.3 M oxalic acid at 40 V for 3 h. Fig. 5 shows the current–time curve for a constant-voltage anodization process. It is illustrated detailed information on the oxidation process of NPAA membranes. The horizontal axis shows anodization time (s) and vertical axis is referred to the current density in mA cm2. Applying voltage brings an initial high current density about immediately due to double-layer charging. In fact, the formation of a barrier layer of NPAA increases the electrode resistance which is observed by a rapid current density drop. After that, initial dissolution of the insulated NPAA layer is locally promoted by local heating. Slow increasing is observed in the current–time curve is observed which is resulted from local heating. This local heating comes from the field-assisted effect and the resistance leading to the promotion of the local dissolution of insulated barrier layer [57,58]. It is noted that as the rate at which aluminum oxide forms is equal to the local dissolution rate of the barrier layer the current reaches a constant value.

Table 2 Comparison of experimental and predicted results. Sample no.

C

U

T

DpExp:

DpANN

DpO’Sullivan

DpPalibroda

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.31 0.31 0.31 0.53 0.53 0.76 1.1 2.4 0.18 1.1 0.3 0.34 0.4 0.3 0.4 0.4

20 25 30 55 60 20 25 30 35 60 25 30 35 40 45 50 12.5 15 20 12.5 15 12.5 12.5 12.5 25 25 40 40 80 40 30 40

313 313 313 313 313 318 318 318 318 318 323 323 323 323 323 323 273 273 273 273 273 273 273 273 283 278 293 288 298 290 290 275

24 30 34 69 71 30 33 37 42 76 39 43 59 60 67 82 19.9 21.6 24 19.1 21.4 19 18.4 13.7 24 36 50 60 80 55 38 54

24.47 29.44 34.67 68.69 73.43 27.81 32.31 37.02 42.66 78.64 42.37 47.41 53.57 61.22 70.13 79.48 18.47 20.06 24.30 19.94 22.64 19.14 16.89 13.67 24.62 35.99 53.27 56.19 79.02 54.04 39.07 59.32

25.80 32.25 38.70 70.95 77.40 25.80 32.25 38.70 45.15 77.40 32.25 38.70 45.15 51.60 58.05 64.50 16.13 19.35 25.80 16.13 19.35 16.13 16.13 16.13 32.25 32.25 51.60 51.60 103.20 51.60 38.70 51.60

19.17 22.71 26.26 43.98 47.53 19.17 22.71 26.26 29.80 47.53 22.71 26.26 29.80 33.35 36.89 40.44 13.85 15.62 19.17 13.85 15.62 13.85 13.85 13.85 22.71 22.71 33.35 33.35 61.71 33.35 26.26 33.35

The NPAA is also examined by XRD analysis. The powder sample on a cut quartz crystal substrate is evaluated by scanning at a rate of 2h° min1 using copper Ka radiation. In Fig. 6, XRD results show a complete amorphous trace and no crystalline phases are observed. It is referred to a good chemical stability of NPAA membranes in a corrosive environment [59,60]. The surface of NPAA is examined by FESEM to measure the pore diameter (Fig. 7). Fig. 7 shows a highly ordered nanoporous alumina where nanopores on the surface have the same diameter with a negligible tolerance. In addition to experimental study, an artificial neural network modeling is also studied here. In the model, 20, 6 and 6 data are selected for training, validating and testing, respectively. The statistical values for each sets of data and the above-mentioned empirical formulas [31,32] are given in Table 1. As mentioned earlier, both empirical formulas [31,32] described pore diameter as a function of potential solely, but this research focuses on how other factors influence the pore size. In this regard, the ANN is proposed and the results show it is more accurate than empirical formulas. The performance of the ANN and empirical formulas [31,32] are shown in Fig. 8. In Fig. 8, the horizontal and vertical axes present the sample number and ratio of experimental to predicted ones, respectively. All results prove that the ANN has good predictive capacity to determine pore diameter with acceptable errors. With respect to Fig. 8 and Table 1, ANN is better and more accurate than empirical formulas [31,32]. Fig. 8 also shows that empirical formulas predict the pore diameter with considerable errors which is due to considering only the applied voltage. It is clear that other effecting parameters affect the pore diameter significantly, where for Palibroda formula [32], the predicted values reach twice time of its corresponding experimental data. Although O’Sullivan and Wooed formula [31] foretold pore diameter better than another empirical equation, but the ANN result is more accurate than others. The performance of the ANN for training, validating and testing is depicted in Fig. 9 and Table 2. In Fig. 9, the ANN results are compared with experimental records. The horizontal and vertical axes are the sample number and pore diameter (nm), respectively. The results prove that ANN has capability of learning the relationship between inputs and outputs. In addition, it can generalize inputs and outputs. Finally it can foresee the pore diameter of NPAA membrane accurately. Fig. 7 shows the FE-SEM image of nanoporous anodic alumina, which indicates with the concentration, temperature and applied voltage of 0.3 M, 274 °K and 40 V, respectively, the pore diameter equals to 55 nm. The experimental study is evaluated with the proposed ANN and two empirical formulas [31,32]. The ANN predicts the pore diameter with acceptable errors. The results of ANN, O’Sullivan and Wooed- and Palibroda-equations are 54.04, 51.6 and 33.35 nm, respectively. It is revealed that the ANN presents the closest result to experimental study. All samples results are given in Table 2. A comparison between the ANN and empirical formulas shows that the ANN can predict the pore diameter with an acceptable error.

7. Conclusion Using nanostructured materials becomes more popular in different fields of engineering in recent years. Thus, conducting an investigation on geometry of their surface is allocated as an important problem. For this reason, a prediction of pore diameter of NPAA membrane has obtained some attractions recently. The aim of this research is to carry out an experimental study on the synthesis conditions of the pore diameter of NPAA along with

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providing an artificial neural network. The computer-based model predictions are very close to experimental results. The mean absolute error, mean absolute percentage error, root mean square error and correlation coefficient are stated to express the accuracy of the ANN. In addition, the results are compared with the above-mentioned empirical formulas. These empirical equations consider only the applied voltage as the effecting factor, but the ANN also involves concentration and temperature. The results show that the effect of other parameters is significant. As mentioned earlier, an experimental study is also carried out and its results are verified with the ANN and empirical formulas [31,32]. The results show that the ANN can predict the desired outputs successfully. References [1] M.M.A. Imran, Journal of Alloys and Compounds 455 (2008) 17–20. [2] L. Guo, X. Wang, C. Zhong, L. Li, Journal of Alloys and Compounds 534 (2012) 6– 8. [3] X. Huang, Y. Yang, X. Dou, Y. Zhu, G. Li, Journal of Alloys and Compounds 461 (2008) 427–431. [4] K.R. Pirota, D. Navas, M. Hernández-Vélez, K. Nielsch, M. Vázquez, Journal of Alloys and Compounds 369 (2004) 18–26. [5] Y. Shen, T. Yamazaki, Z. Liu, D. Meng, T. Kikuta, N. Nakatani, M. Saito, M. Mori, Sensors and Actuators B: Chemical 135 (2009) 524–529. [6] L. Patil, M. Shinde, A. Bari, V. Deo, Sensors and Actuators B: Chemical 143 (2009) 270–277. [7] F.E. Atalay, H. Kaya, S. Atalay, S. Tari, Journal of Alloys and Compounds 469 (2009) 458–463. [8] S. Dabboussi, H. Elhouichet, C. Bouzidi, G.K. Maliarevich, N.V. Gaponenko, M. Oueslati, Applied Surface Science 255 (2009) 4255–4258. [9] R. Inguanta, M. Butera, C. Sunseri, S. Piazza, Applied Surface Science 253 (2007) 5447–5456. [10] R. Inguanta, S. Piazza, C. Sunseri, Applied Surface Science 255 (2009) 8816– 8823. [11] A. Jagminas, J. Kuzmarskyt, G. Niaura, Applied Surface Science 201 (2002) 129– 137. [12] K.-Z. Li, J. Wei, H.-J. Li, Y.-L. Zhang, C. Wang, D.-S. Hou, Applied Surface Science 253 (2007) 7365–7368. [13] C.L. Liao, M.T. Wu, J.H. Yen, I.C. Leu, K.Z. Fung, Journal of Alloys and Compounds 414 (2006) 302–309. [14] S. Massou, L. Masson, I. Ozerov, E. Moyen, K. Sengupta, M. Hanbücken, Applied Surface Science 256 (2009) 395–398. [15] K. Rana, G. Kucukayan-Dogu, E. Bengu, Applied Surface Science 258 (2012) 7112–7117. [16] X. Tan, Journal of Alloys and Compounds 477 (2009) 648–651. [17] W. Wang, H. Ke, J. Rao, J. Feng, M. Feng, D. Jia, Y. Zhou, Journal of Alloys and Compounds 509 (2011) 4722–4725. [18] W. Wang, D. Li, M. Tian, Y.-C. Lee, R. Yang, Applied Surface Science 258 (2012) 8649–8655. [19] H.-Y. Wu, Y. Zhao, Q.-Z. Jiao, Journal of Alloys and Compounds 487 (2009) 591– 594. [20] C.-L. Xu, H. Li, G.-Y. Zhao, H.-L. Li, Applied Surface Science 253 (2006) 1399– 1403. [21] W. Zhang, D. Zhang, Y. Le, L. Li, B. Ou, Applied Surface Science 255 (2008) 2671–2674. [22] G.S. Huang, X.L. Wu, G.G. Siu, P.K. Chu, Solid State Communications 137 (2006) 621–624. [23] H. Akbarpour, M. Mohajeri, M. Moradi, Computational Materials Science 79 (2013) 75–81. [24] G.D. Sulka, A. Brzózka, L. Zaraska, M. Jaskuła, Electrochimica Acta 55 (2010) 4368–4376.

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