A Mathematical Model based on Artificial Neural Network for ethylene/norbornene copolymerization catalyzed by 2-(tetramethylcyclopentadienyl)-4,6-di-tert-butylphenoxytitanium dichloride
ABSTRACT
Ethylene/norbornene (E-N) copolymer is one of the most promising industrial thermoplastic polymers with high glass transition temperature (Tg), excellent moisture barrier properties, chemical resistance, and optical clarity. It is an attractive choice as a novel substrate material for high density data storage devices, packaging, and optical/biomedical applications.[1]
Titanium based metallocene catalysts with a pendant nitrogen donor or pendant oxygen donor on the cyclopentadienyl ring, are found to be good at catalyzing ethylene-norbornene co-polymerization with noteworthy catalytic activity and efficient norbornene incorporation for the ethylene/norbornene copolymerization.[2]
The use of neural networks (NNs) has become progressively popular for applications where the mechanistic description of the interrelation of dependent and independent variables is either obscure or very complex.[3] The neural network consists of processing neurons and information flow channels between the neurons, usually called ‘interconnects’. Each processing neuron calculates the weighted sum of all interconnected signals from the previous layer plus a bias term and then generates an output through its activation transfer function. Training is done by assigning random weights to each neuron, evaluating the output of the network and calculating the error between the output of the network and the known results by means of an error or objective function. If the error is large, the weights are adjusted and the process goes back to evaluate the output of the network. This cycle is repeated till the error is small or a stop criterion is satisfied.[4]
In this work, an artificial neural network (ANN) as a supervised back-propagation model with different architecures is implimented to investigate the effect of reaction variables for ethylene/norbornene copolymerization catalyzed by 2-(tetramethylcyclopentadienyl)-4,6-di-tert-butylphenoxytitanium dichloride. The experimental data were taken from Jianguo et al.[5] The effect of temperature, monomer to co-monomer concentration ratio and cocatalyst to catalyst concentration ratio on catalyst activity, yields, molecular weights & distribution and glass transition temperature of the copolymer has been studied using neural network approach in MATLAB® 7.10.0 (R2015a) software.[6]
References
[1] Kaminsky W., Bark A. and Arndt M., Makromol Chem Macromol Symp, 47:83, (1991).
[2] Mcknight A.L., Waymouth R.M., Macromolecules, 32:2816 (1999).
[3] Fernandes F. A. N. and Lona L. M.F., Brazilian Journal of Chemical Engineering, 22: 03, p. 401-418 (2005).
[4] Haykin, S., Neural Networks: A Comprehensive Foundation, Prentice Hall, New York (1998).
[5] Jianguo N., Chunsheng L., Yuetao Z., Zaiqun L. and, Ying M., Polymer, 49, p. 211-216. (2008)
[6] MATLAB version 7.10.0 (R2015a), computer software, Natick, Massachusetts: The MathWorks Inc., 2015.
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