Solubility prediction of 21 azo dyes in supercritical carbon dioxide using wavelet neural network

doi:10.1016/j.dyepig.2005.12.003

Dyes and Pigments

Volume 73, Issue 2, 2007, Pages 230-238

https://doi.org/10.1016/j.dyepig.2005.12.003 Get rights and content

Abstract

The solubility of 21 azo dyes in supercritical carbon dioxide was related to the six descriptors over a wide range of pressures (100–355 bar) and temperatures (308–413 K). The wavelet neural network (WNN) model was constructed with six descriptors as an input layer, eight neurons as a hidden layer and a neuron as an output layer. The descriptors consisted of temperature, pressure, LUMO energy, polarizability, volume of the molecule and number of unsaturated bonds and they were selected based on stepwise feature selection from different descriptors using multiple linear regression (MLR) method. The WNN architecture and its parameters were optimized simultaneously. The data were randomly divided into the training, prediction and validation sets. The RMSE and mean absolute errors in WNN model were 0.220 and 0.158 for prediction set and 0.156 and 0.114 for validation set. In addition, the prediction ability of the model was also evaluated for five azo dyes, the molecules and data of which were not in any previous data sets.

The performance of the WNN model was also compared with artificial neural network (ANN) and MLR models.

Introduction

Supercritical fluid dyeing (SFD) is an alternative dyeing process, which is able to replace the conventional wet process. In this process, water, surfactants, dispersing agents and drying process are eliminated. Therefore, this method will not deliver a lot of wastewater to the environment. Moreover, a lot of energy (roughly 50%) can be saved [1], [2], [3], [4], [5]. However, in order to apply this technique, the knowledge of the solubility of disperse dyes in supercritical carbon dioxide (SC-CO₂) is required. The solubility measurements of dyes in SC-CO₂ have been conducted by many researchers [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. These experimental data are commonly to correlate with theoretical or semi-empirical models [25], [26], [27], [28], [29], [30], [31], [32], [33], [34]. In addition to those hard modeling methods, some software methods such as artificial neural network (ANN) [35] and wavelet neural network (WNN) [36] have also been used for the prediction of solubility in supercritical conditions.

The purpose of this work is (1) prediction of solubility of various azo dyes in supercritical carbon dioxide using WNN, (2) simultaneous optimization of the WNN architecture and its parameters, and (3) evaluation of the performance of the model using two data sets; a validation set, in which data were not used in construction of the model and a data set consisted of five azo dyes, the molecules and data of which were new for the model. This model can be used to predict the solubility of newly synthesized azo dyes in SC-CO₂ as a primary estimation.

Section snippets

Wavelet

Wavelet is a type of transformation that retains both time and frequency information of the signal [37]. In chemical studies, the time domain can be replaced by other domains such as wavelength. In Fourier transform, only the sine and cosine functions can be chosen as the basis functions. However, wavelet transformation (WT) has versatile basis functions to be selected based on the type of the signal analyzed. In WT, all basis function $ψ_{a, b} (x)$ can be derived from a mother wavelet $ψ (x)$ through

Data set

The structures of the 21 azo dyes with the references to their experimental solubility values are given in Table 1.

Descriptor selection and calculations

HyperChem (version 6) software was used to calculate the quantum chemical and geometrical descriptors. Before calculation of the descriptors, optimization of the molecular structures was carried out by semi-empirical AM1 method using the Fletcher–Reeves algorithm until the root mean square gradient of 0.01 was obtained. The calculated descriptors were electronic energy, nuclear

Results and discussion

The data set consisted of experimental values of the solubility of the 21 azo dyes at different temperatures and pressures. The data set of 16 azo dyes was randomly divided into three data sets; training, prediction and validation sets. These sets consist of 139, 30 and 82 data, respectively. It is necessary to emphasize that the data of the validation set have not contributed to the optimization of the model and is only used for evaluation of the performance of the model.

Conclusions

Only one WNN model was constructed to predict the solubility of 16 azo dyes in supercritical carbon dioxide over a wide range of pressures (100–355 bar) and temperatures (308–413 K). The performance of the model was evaluated by the validation set and also with a data set, the molecules and data of which were new for the model. The ability of the WNN model was also compared with ANN and MLR models. It was demonstrated that WNN is superior to ANN and ANN has a better performance than MLR.

Acknowledgement

The authors acknowledge the Research Council of Isfahan University of Technology and Center of Excellency in Chemistry of Isfahan University of Technology for the support of this work.

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Solubility prediction of 21 azo dyes in supercritical carbon dioxide using wavelet neural network

Abstract

Introduction

Section snippets

Wavelet

Data set

Descriptor selection and calculations

Results and discussion

Conclusions

Acknowledgement

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