Solubility prediction of 21 azo dyes in supercritical carbon dioxide using wavelet neural network
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 can be derived from a mother wavelet 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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2018, Journal of the Taiwan Institute of Chemical EngineersCitation Excerpt :With regard to a commercial application purpose of this technology, the solubility behavior of different dye solutes in the hydrophobic medium of supercritical carbon dioxide fluid plays a fundamental and important role in the dye selection, color matching, process design and control, and the improvement of process efficiency for achieving some desired shades from customers, etc. [3,10–13]. During the last decades, numerous researches have been carried out to investigate the solubilities or phase behaviors of different dye solutes, even as well as various other organic compounds [14–17] in supercritical carbon dioxide medium for facilitating the application of this technology in practice [2,5,12,18–25]. Particularly, most of those researches are mainly concentrated on disperse organic dyes.