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論文10. Application of Artificial Neural Network for the Estimation of Solubility of New Blowing and Cleaning Agents

Shingo Urata*, Jun Irisawa* and Akira Takada*

　The Artificial Neural Network (ANN) technique was applied to the solubility
estimation in order to screen new alternative blowing and cleaning agents. In this study, two solubility estimation studies were carried out. One was the n - eicosane (n - C10H22) solubility estimation in hydrofluoroethers (HFEs), hydrofluoroketones (HFKs), and chlorine containing compounds, and the other was the estimation of HFEs solubility in polyol PE - 315 (aromatic polyol, OH value = 315mgKOH/g). Information on the intermolecular interactions was evaluated using the molecular simulation technique with the code ‘Cerius2/Blends (MSI)’, and was used as a descriptor. The computationally calculated fractional charges of atoms in solute, and several measured physical properties, such as liquid density, molecular volume, and molecular weight were also prepared as descriptors, and several of these descriptors were selected empirically in each study. In both studies, the optimal thresholds for training of ANN were determined, in order to avoid over - fitting using the cross validation test, and two accurate ANNs were constructed. Finally, the two constructed ANNs were applied to screen new alternatives, and CHF2CF2OCHF2 (HFE - 236pc) was consequently discovered to be a new candidate for a blowing agent.


目次
	1. Introduction
	2. Methodology
	3. Results and Discussion
	4. Conclusion

1.Introduction

Chlorofluorocarbons (CFCs)and hydrochloro fluoro - carbons (HCFCs)have been extensively utilized as refrigerants, blowing agents, and cleaning agents. However, since these compounds have the potential to deplete the ozone layer, they should be replaced with alternative compounds. For this purpose, we have mainly developed hydrofluoroethers (HFEs)and hydrofluoro - ketones (HFKs)as new alternatives to CFCs and HCFCs^{（1
）}, because they show almost zero ozone depletion potential (ODP)^{（2
）}and low global warming potential (GWP)^{（3 ）-（6
）}, and, moreover, have physical properties similar to those of CFCs and HCFCs.^{（1 ）}
　Solubility is one of the most important physical properties in selecting suitable compounds for each type of practical use. For example, the high solubility of oil is required in the use of cleaning agents, and solubility in polyol is important for use
in blowing, because low solubility in polyol negatively influences the performance of polyurethane foam. In our project, the solubility of n - eicosane (n - C20H42)was measured as an index of ability as cleaning agents, and the solubility in polyol PE - 315 (aromatic polyol, OH value = 315mgKOH/g)was measured to confirm the performance as blowing agents .^（7）^、（8）
　However, it is difficult to measure the solubility of all HFEs and HFKs, because they have a lot of isomers. In such cases, molecular simulation techniques or empirical estimation methods like quantitative structure property relationships (QSPR)are powerful enough to use to accelerate the screening of candidates, without the necessity of conducting laborious experiments. Nowadays, molecular simulation techniques have certainly become useful tools, but they require long CPU times, which are still insufficient to quantitatively estimate the properties of complex mixtures. However, empirical estimation methods are rapid and effective if there is enough observed data. Therefore, we tried to estimate solubilities empirically in this work.
　One of our objectives in this study was to estimate the n - eicosane solubilities in HFEs or HFKs, and the other was to estimate the solubilities of HFEs in PE - 315. These studies were carried out by means of the Artificial Neural Network (ANN). The three - layered feed forward type ANN was used, and was optimized by using the general back - propagation learning algorithm.^（9） As the descriptors of ANN, information on intermolecular interactions evaluated by using the Monte Carlo technique and several basic physical properties such as molecular weight, molecular volume, and liquid density, were empirically selected.

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2.Methodology

2.1 Artificial Neural Network
　The three - layered feed forward type ANN, in which one output neuron is used, was applied in this study. In this three - layered neural network, signals x(i), which are input parameters of ANN, are transferred from the input layer to the output layer through the hidden layer. These layers consist of several units called neurons. The neurons of the hidden layer y(j)are described by the sigmoidal transfer functions as follows:

where w12 (i , j)are the connections between the input and the hidden neurons, and αis an adjustable parameter for the non - linearity of sigmoidal transfer functions. The neuron in the output layer z is represented by the linear summation of y(j).

where w23 (j)are the connections between the hidden and output neurons. In this work, the input parameters were normalized between 0.1 and 0.9, and the output values were normalized between 0.0 and 1.0.
　The training of ANN was carried out using a general back propagation algorithm^{（9 ）}. This training procedure was repeated until error E, given by eq. (3), fell under threshold Eth.

where T(p)is the training value set number p. In order to avoid the over - fitting, the predictability of the constructed ANN was confirmed by means of the cross - validation test method at various Eth, and the optimal threshold was decided. As the cross - validation test, we applied the “leave - one - out ”test method, in which one set of the training data is removed, and the rest are used for training. After training, the estimated value and training value for the dataset left out are compared. This test method was applied to all datasets.

2.2 Descriptor Generation
　 The information on the intermolecular interaction used as a descriptor of ANN was evaluated using the code “Cerius2/Blends (MSI)”^{（10
）} , which is the Monte Carlo program combined with a modified Flory - Huggins theory^（11）. In this software, the distribution of intermolecular energy Eij is evaluated from a lot of random configurations of two molecules, and the coordination number of molecule j around molecule i (Zij)is also available. In addition, the interaction parameter χis directly calculated using these parameters as follows:

These values can be calculated from only the molecular structure of two compounds. In this work, 100, 000 random configurations were generated to estimate Eij, and Zij was calculated as an average value of 500 samples. The geometry of each molecule was optimized by using the ab initio molecular orbital calculation at the HF/6 - 31G* level.
The intermolecular interaction was represented by van der Waals and the electrostatic interactions. The van der Waals interaction was evaluated by using Dreiding 2.21^（12）as a force field. In order to calculate electrostatic interaction, the fractional charge of each atom in the molecule was optimized at the B3LYP/6 - 31+G**//HF/6 - 31G*level with the CHELPG^（13） method. All molecular orbital calculations were carried out by means of the Gaussian94 suite of programs^（14）.
　We also used several basic physical properties, such as molecular weight (MW), molecular volume (V), and liquid density (ρ)as descriptors. The liquid densities are observed values near room temperature. The molecular volume was given by MW/ρ. However, such observed liquid densities would not be useful for the screening of new compounds. Therefore, liquid densities were simplified to one decimal place in [ g/cm³ ] and were used as input parameters, in accordance with the predictable accuracy of liquid density. Such precision of liquid density is predictable by using a combination of the conventional methods^（15）or ANN estimation methods^（16）^{, （17）}from the formula of compounds.

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3.Results and Discussion

3.1 Solubility of n - eicosane
　In order to estimate the solubility of n - eicosane, we selected the interaction parameter χcalculated by using eq. (4)as a descriptor of ANN. In the calculation of this χparameter, n - eicosane was represented by a combination of two n - decanes (n - C10H22), since its size was too long to be represented by one segment (Fig.1).In addition to interaction parameter χ, other presumably important properties, such as molecular weight and liquid density, were chosen as descriptors empirically. A schematic diagram of the constructed ANN is shown in Fig.2. For the input layer, we used the three descriptors described above and a bias neuron, which always puts out unit value. Four neurons were used in the hidden layer, whose a value was 2.5.
　The observed solubility values of 31 compounds, which were measured at 297 K, were used as training values to construct the ANN. In the training procedure, the logarithmic values of the volume fraction of these solubility data were used, since there were differences in figures between the fluorinated and chlorinated compounds.
　As a beginning, the relation between threshold
Eth and the average of the absolute deviation (AAD) of the predicted values were studied to avoid over - fitting. Figure 3 shows the relation between threshold and predictability. Consequently, it was revealed that over - fitting occurred when Eth was set under 0.1.Therefore, the training of ANN using all 31 data was carried out until error E became 0.1.Here, error E was calculated using outputs normalized from 0 to 1, with the following to eq.(3).
　The results of the training and leave - one - out test at Eth =0.1 are graphically shown in Fig.4, and these values and input parameters are listed in Table 1. The correlation coefficients (R)of the trained and estimated values were 0.976 and 0.948 respectively, and the AAD for trained and estimated values were 0.209 and 0.296.This result shows that the proposed estimation method using ANN is accurate enough to estimate solubility, and that the parameters used were suitable as descriptors.

3.2 Solubility in polyol PE - 315
　The constitution of ANN, which succeeded in estimating the solubility of n - eicosane, failed to estimate the HFEs ’solubilities in PE - 315. We reasoned that the failure was due to the high polarity of PE - 315, since the χparameter only represented the uniformly averaged information of intermolecular interactions. To overcome that problem, two new parameters were introduced instead of the χparameter. First, the change of the most stable interaction energy between before and after mixing (ΔEmin), which was defined by eq. (5), was used as a descriptor.

where Eij^min is the minimum interaction energy between molecules i and j. The most stable configurations were selected from 100, 000 configurations generated by the Blends code^（12）. In this calculation, a simplified structure of PE - 315 was used (Fig.5). This parameter may represent the ease of mixing. Secondly, the maximum fractional charge of hydrogen of each solute was added to the descriptors to represent the interaction between solute and the polar chain of PE - 315. We found that most of the conformations given minimum interaction energy were specific arrangements (Fig.6). Therefore, it seems to be difficult to represent the intermolecular interaction between solute and PE - 315 by using only the parameter (ΔEmin )defined as eq. (5). In addition to
these two parameters, liquid density and molecular volume were chosen as descriptors in the same way with the n - eicosane solubility study.Figure 7 shows a schematic diagram of used ANN. For the input layer, we used the four descriptors described above and a bias neuron. The hidden layer was composed of four neurons whose a value was 2.0. The observed solubilities of 25 compounds are listed in Table 2. Since the solubilities were roughly observed, we used the center value of each observed data as the training values.
　At first, the relation between threshold Eth and predictability in the leave - one - out cross validation test was studied to avoid over - fitting. In this case, over - fitting was observed when Eth was set under 0.17 (Fig.8). Thus, we set Eth on 0.18 to avoid over - fitting in the training procedure using all 25 data. Here, error E was also calculated using outputs normalized from 0 to 1. The results of the training and leave - one - out test are graphically shown in Fig.9, and these values and input parameters are listed
in Table 2. Consequently, the correlation coefficients R for the trained and estimated values were 0.935 and 0.827, respectively. And their AAD was 5.5 wt%and 10.1 wt%. The predictability was a little worse than the accuracy of trained values. However, it was accurate enough to select the new candidates, which will have high solubility, if the accuracy of observation is considered. From this result, it was concluded that these selected input parameters are reasonable as descriptors, and the proposed method is useful in the estimation of solubility for the polar compounds.

3.3 Application for screening
　 Since the purpose of this study is not only the construction of the solubility estimation method but also the screening of alternative compounds for CFCs or HCFCs, we tried to estimate the solubility by using two constructed ANNs for unobserved compounds. Here, estimated liquid densities were used for the new compounds ’input parameters by means of the ANN estimation method^{（16 ）, （17 ）} .In the
estimation of the n - eicosane solubility, there was no compound that showed high solubility, however, for the solubility with PE - 315, we could find four promising HFEs. They were listed in Table 3. HFE - 236pc as a new candidate for the blowing
agents among them. After our computer estimation, we measured the HFE - 236pc solubility with PE - 315, and it was revealed that HFE - 236pc had solubility over 60wt%. This result indicated that this constructed ANN is useful enough to screen alternative compounds without further experimental work.

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4.Conclusion

　A couple of solubility estimation studies were carried out by means of the Artificial Neural Network technique. One of them was the estimation of n - eicosane solubilities in HFEs, HFKs and chlorine containing compounds, and the other was the estimation of solubilities of HFEs in polyol PE - 315. The former solubility estimation was studied by using the interaction parameter c evaluated by the Monte Carlo technique, with the observed liquid density and molecular weight as descriptors. In the later study, the change of minimum interaction energy between before and after mixing (ΔEmin), the maximum fractional charge of hydrogen in solute, the observed liquid density, and the molecular volume were selected as descriptors empirically. The change of minimum interaction energy was evaluated by using the Monte Carlo technique. The maximum fractional charge of hydrogen was calculated by using molecular orbital calculation. In both studies, the most suitable threshold of the learning procedure was decided, and the predictability in the leave - one - out cross validation test was considered. Owing
to such procedures, over - fitting was avoided, and accurate estimation methods were constructed.
　Finally, we tried to screen new candidates for cleaning and blowing agents using constructed ANNs. In this way, we were able to find a promising compound, HFE - 236pc (CHF2CF2OCHF2), as a new blowing agent.

－Acknowledgements －
　We would like to thank Mr. Ryouichi Tamai (Central Glass Co. , Ltd. ), Yuji Kurokawa (Kanto Denka Kogyo Co. , Ltd. )and Akira Sekiya (National Institute of Advanced Industrial Science and Technology)for their support on this study, in addition we are greatful to Dr. Hiroshi Yamamoto (Asahi Glass Co. , LTD. )for his helpful discussions on molecular simulation and the artificial neural network. This research was carried out under the
project “Department for the New Refrigerant and Other Substances Research (F. Y. 1994 - 2001, in Japan)”conducted by the Research Institute of Innovative Technology for the Earth (RITE)with financial support from the New Energy and Industrial Technology Development Organization (NEDO).

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