Using nanoporous anodic aluminum oxide thin layer becomes more popular in recent years due to its capability to be a membrane in some engineering applications. The main purpose of this paper is to investigate the synthesis conditions at the interpore distance of nanoporous anodic aluminum oxide through an experimental study, an artificial neural network (ANN), and a multiple linear regression (MLR) model. A total of 33 experimental data used to establish both models. The models have three inputs including the concentration of electrolyte, temperature, and applied voltage. The interpore distance of nanoporous anodic aluminum oxide is considered as output in the models. The results of the models are compared with the results of experimental study and an empirical formula proposed by Nielsch. The results reveal that the proposed models have good prediction capability with acceptable errors. However, in this research, the proposed ANN model is accurate than the MLR analysis and both of them are better than empirical formula. The proposed models can also predict the results of experimental study successfully.
Nanoporous anodic aluminum oxide (AAO) had attracted intensive interest due to its potential to use as a membrane in some applications such as the gas separation [1], [2], [3] and [4], drug delivery [5] and [6], and bone fixation [7]. Anodizing aluminum in an acidic electrolyte resulted in a thin layer of compact aluminum oxide, following by an ordered array of nanopores [8], [9] and [10]. The synthesis process led to mechanically robust and thermally durable [3] and inert, wide and variety of pore size distribution, which showed unique capability for biomolecule separation process [11] and hemodialysis [12], [13], [14] and [15].
The geometry of aluminum oxide layer executed important role for a separation process which could lead to maximize permeation and flux across nanoporous anodic aluminum oxide membrane. For example, as a hemodialysis membrane, a pore size was desirable which had capability to clear urea, creatinine, vancomycin and inulin as a waste product with small and middle of molecular weight while maintaining large molecular weight solutes (albumin) [16], [17], [18], [19], [20] and [21].
The geometry of nanoporous anodic aluminum oxide had grown through anodization was represented schematically in Fig. 1.
Full-size image (51 K)
Fig. 1.
The schematic geometry of nanoporous anodic aluminum oxide layer and aluminum substrate.
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Many equations were suggested for correlation between the geometry of aluminum oxide layer and conditions of anodized aluminum [22], [23], [24] and [25]. According to Nielsch et al. [22], the interpore distance (Dc) in nanometer (nm) was linearly proportional to the applied voltage (U) in volts (V) of the steady-state growth of oxide layer as follows:
equation(1)
View the MathML sourceDc=λcU(λc≈2.5nmV-1)
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where λc is a proportional constant in nm V−1.
It was assumed that the pore diameter was a function of applied voltage. The other efforts showed that anodizing temperature and concentration of electrolyte cause changing the interpore distance [23], [24] and [25]. In this regard, three important effecting parameters on the interpore distance of nanoporous aluminum oxide were identified as following:
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Concentration of electrolyte (C) in mol/dm3.
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Anodizing temperature (T) in K.
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Applied voltage (U) in V.
In general, these parameters had a considerable effect on the interpore distance of nanoporous aluminum oxide, but the contribution of each parameter separately was studied a little. Nowadays, computer-based methods such as artificial neural networks (ANNs) and multiple linear regression analysis have attracted some attentions to be replaced with high-cost experimental studies. The above-mentioned techniques were used in different fields of engineering applications such as civil engineering [26], [27], [28] and [29], chemical engineering [30] and [31] and material science [32], [33], [34] and [35].
The artificial neural networks (ANNs) are known as the important and successful simulating tools of input–output datasets. The most fundamental part of such networks is the training process. The ANN model is trained with some relevant experimental results and then can predict the output with an accepted error.
This paper presents an artificial neural network (ANN) and a multiple linear regression (MLR) model accompanished with an experimental study to investigate the synthesis conditions at the interpore distance of nanoporous anodic aluminum oxide. In this regard, a total of 33 experimental records are used with three factors each. The results reveal that output in the models have an agreement with experimental records. In addition, all results are compared with output of formula proposed by Nielsch [22]. It is clear that ANN is more accurate than formula proposed by Nielsch [22] and MLR model.
The synthesis conditions at the interpore distance of nanoporous anodic aluminum oxide thin layer are important problems in recent years. In this regard, some computer-based techniques such as artificial neural networks (ANNs) and multiple linear regressions are good tools for determining the results of these complicated problems. The main purpose of this study is to develop artificial neural network and multiple linear regression models for predicting the interpore distance of nanoporous anodic aluminum oxide. The models’ predictions are very close to the experimental desired results for training, validating, and testing. The mean absolute error, mean absolute percentage error, root mean square error, and the correlation coefficient are presented to show the accuracy of models. Moreover, the results of models are compared with empirical formula proposed by Nielsch et al. [22]. It is noted that the models consider three effecting factors on the interpore distance while the empirical formula just considers the applied voltage as the effecting parameter. In fact, the proposed models investigate also the effect of other parameters including the concentration of electrolyte and temperature more than the potential.
In addition, an experimental study is carried out and the results are verified with other models and formula proposed by Nielsch et al. [22]. The results show that models can predict the desired output successfully.
In this study, it is shown that ANN model is better than another model and formula proposed by Nielsch et al. [22]. The results also reveal that ANN and MLR can predict the interpore distance of nanoporous anodic aluminum oxide successfully. The proposed models can save time and avoid carrying some high-cost experimental studies out due to their more accurate predictions with acceptable errors.
