International Journal of Scientific & Engineering Research, Volume 6, Issue 3, March-2015 84

ISSN 2229-5518

Artifficial Neural Network Modeling for AC

conductivity Behaviour of PVA/acid salt Polymer

Electrolyte

Mahmoud Y. El-Bakry1∗, Reda Khalil2∗∗

1Department of Physics, Faculty of Science, University of Tabuk, KSA

2Department of Physics, Faculty of Science, University of Benha, Egypt r.khalil@fsc.bu.edu.eg

Abstract— Levenberg-Marquardt algorithm (LM) and neural networks (NN) are combined to study the electrical properties of PVA /Acid Salt Polymer Electrolytes (PVA)(1-x) (MgBr 2 ) x/2 (H3 PO4 ) x/2 . The obtained function from NN model calculates and simulates the relation between the AC conductivity and the frequency for PVA/acid salt at different temperatures. The simulation results from NN-based model are compared with the experimental data. The obtained function of NN model has proven matching better for the experimental data. The results show that NNs are able to produce accurate results of the electrical properties for PVA/acid salt polymer electrolytes.

Index Terms— Artificial Neural Network (ANN), AC conductivity, Acid Salt, Polymer, Electrolytes, Levenberg-Marquardt algorithm and PVA.

1 INTRODUCTION

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olid Polymer Electrolytes (SPEs) in the highly ionic con- ducting, electrochemical stability and in the flexible film form have been attracting great deal of attentions in the recent years because of their potential technological applica- tion relevance's in developing all-solid-state electrochemical devices viz. batteries, fuel cells, super capacitors, ECDs etc. [1,
2].
Extensive studies have been undertaken to investigate ion
conduction behavior on polymer materials. Impedance spec-
troscopy is employed to establish the conduction mechanism
observing the contribution of the polymeric chain mobility
and carrier generation processes. One of the most characteris-
tic features of electrical conduction in disordered solid systems is the dispersion of conductivity with frequency. In the low frequency regime, almost found to be frequency independent - the plateau value - and it is equal to true dc conductivity.
While in the high frequency region, closer to the relaxation times, the mobility of the charge carriers is high and hence, the conductivity increases with frequency and varying approxi- mately as a power of frequency [3–6]. Different approaches have been used for the interpretation of the conductivity per- formance of these disordered composites.
All these models can be broadly categorized in two catego- ries, namely microscopic and macroscopic models. The micro- scopic model [7] assumes disorder on atomic length scale and the conductivity is due to either hopping or tunneling through the localized states. Whereas the macroscopic model [8] as- sumes disorder on length scales large enough that a local con- ductivity may be defined and the conductivity is explained on the basis of either effective medium approximation (EMA) or

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* Permenent Address: Department of Physics, Faculty of Education, Ain

Shams University

percolation path approximation (PPA).

In this connection, the neural network (NN)[9-11] has been studied and designed to study the AC conductivity (σ) and frequency for PVA/acid salt polymer electrolytes (PVA)R(1-x) R(MgBrR2R)Rx/2R(HR3RPOR4R)Rx/2R. AC conductivity is calculated by min- imizing the differences between measured and model- generated results. The Levenberg-Marquardt algorithm is used to a measure of the quality of the match between the ex- perimental data and model calculated. Modeling tools play an important role in Solid State Physics. Neural network ap- proaches provide an effective tool [12, 13] for such modeling.

In the present work, we illustrate the experimental tech- nique to prepare the PVA/acid salt electrolytes. Following sections provide a brief introduction of ANN to model the relationship between AC conductivity (σ) and frequency for PVA/acid salt and discuss the results.

2 EXPERIMENT DETAILS

The preparation of polymer complexes has been described elsewhere [2]. The polymer films were kept in desiccators for further drying. In order to study the amorphous character of PVA complexes with different weight percentages of MgBrR2R and HR3RPOR4R, the XRD patterns of the samples were recorded at room temperature with a Philips X’Pert instrument, which employs a CuKa X-radiation.

To study the ionic conductivity of the samples, impedance spectroscopy was performed using a HIOKI 3532 program- mable automatic LCR bridge interfaced to a computer for data acquisition. The study was carried out in the frequency range
100 Hz to 100 kHz. The thin polymer electrolyte films were sandwiched between two stainless steel disk electrodes, which acted as a blocking electrode for ions. The temperature- dependent ionic conductivity was performed in the tempera-

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International Journal of Scientific & Engineering Research, Volume 6, Issue 3, March-2015 85

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ture range between 30 and 150 oC. The conductivity, σ, of each sample was calculated using equation σ = t/(Rb A), where t is
the thickness of the film, Rb is the bulk impedance and A is the area of the cross-section of the film. The value of Rb was con- firmed by comparing with the 1/Rb value obtained from a
complex admittance graph.

3 NEURAL NETWORK MODEL

Soft computing is a practical alternative for solving complex problems through the use of human expertise and a prior knowledge about the problem in hand. Neural network is made up of many simple and highly interconnected computa- tional elements [14-16], called artificial neurons or nodes.
The net input into jth layer node [in (j)] is equal to the sum of weighted outputs from the prior ith layer [out (i)]
in[j] = ∑wij out [i] (1)
where, wij is the weight factor.
The neurons of hidden layers and the weight factors of the
links between them play a critical role during the learning
process. A simple neuron structure is shown in the fig. (1)
The transfer function ( ϕ) of processing nodes is used to de-
conventional gradient decent techniques. The adjustment for
the weights (Δw) is done by the following equation
Δw = (jTj + μ I )-1jTe (2)
where j is the Jacobin matrix of derivatives of each error
with respect to each weight, jT is the transposed matrix of j, (I)
is the identity matrix that has the same dimensions as those of
jTj, (μ) is a scalar changed adaptively by the algorithm and e is an error vector. Also Δw is a measure for the rate of learning of the network.

4 RESULTS

The proposed neural network model for AC conductivity (σ) have two inputs: frequency (f) and temperature (T), one out- put (σ) and three hidden layers which consists of 10, 10 and 7 neurons respectively as shown in fig. (3).
The transfer function where chosen to be a tan sigmoid func- tion [(enet – e-net)/(en + e-n)] for the hidden layer and a pure line function (linear function) for the output layer. Using this in- put-output arrangement and connecting weights (Iw, Lw) are trained using LM for the given experimental data as described in sec 2. It is interesting to note that the training reached a zero sum square error which means that an exact fitting for the ex- perimental data as seen in fig. (4). Appendix shows the final NN weights after training of 2000 Epochs and stopped after

Fig. 1. Neuron structure.


termine the output value of the node based on the total net input from nodes in prior layer. The neuron has a bias (bk ), which is summed with the weighted inputs to form the net
input to transfer function (ϕ). Multilayer network, shown in
fig(2), consists of one or more layers of neurons, called hidden
layer, between input and output layer. The network is called
fully connected when every neuron in one layer is connected
to every neuron of the next layer.
The proposed ANN model was trained using Levenberg-
Marquardt (LM) optimization technique [17-19].

This optimization technique is more powerful than the

Fig. 3. Representation of ANN Modeling for AC conductivity (σ).


19th iteration. Also in appendix the obtained function for AC conductivity (σ) using NN model which calculate the relation between AC conductivity and the frequency for PAV/acid salt polymer electrolytes (PVA)x (MgBr2 )x/2 (H3 PO4) x/2 .
Fig (4) illustrates the simulation results of σ as a function of frequency at given temperature. The proposed σ based ANN model was tested after training on:

Fig. 2. General architecture of a multilayer perceptron.

Fig. 4. Representation of ANN Modeling for AC Conductivity (σ).

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International Journal of Scientific & Engineering Research, Volume 6, Issue 3, March-2015 86

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1. 80% data sets used in training (to assure the simulation capability of the proposed ANN).
2. 20% data sets not used in the training (to assure the predic- tion capability of the proposed ANN).
Results of σ as in fig.(4) based ANN model showed good fit- ting to the experimental data. This gives the ANN the provsion of wide usage in modeling of solid state physics.
Appendix A:
The equation which describes the relation between the AC
conductivity and frequency is given by:

σ = Pureline [{net.LW (4,3). tan sigmoid {net . LW(3,2). tan

sigmoid {net . LW(2,1). tan sigmoid {net.IW(1,1)β + net.b(1)} +

net.b(2)} + net.b(3)} + net.b(4)}]

Where, β is the input which is (Temp, f(Hz)).

net.LW (4,3) linked weight between the third hidden layer and the

output layer.

net.LW (3,2) linked weight between the third hidden layer and the second hidden layer .

net.LW (2,1) linked weights between the first and the second hidden layer.

net.IW (1,1)linked weights between the input layer and the first hid- den layer.

net.b (1) is the bias of the first hidden layer. net.b (2) is the bias of the second hidden layer. net.b (3) is the bias of the third hidden layer. net.b (4) is the bias of the output layer.

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