(36i) A Mathematical Model Based on Artificial Neural Network for Ethylene/Norbornene Copolymerization Catalyzed By 2-(tetramethylcyclopentadienyl)-4,6-Di-Tert-Butylphenoxytitanium Dichloride

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 (T_g), 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.