MATERIALE PLASTICE ♦ 45 ♦ Nr. 1 ♦ 2008 67 Neural Network Modelling of the Equilibrium Anionic Polymerization of Cyclic Siloxanes ALEXANDRA NISTOR 1 , CIPRIAN-GEORGE PIULEAC 1 , MARIA CAZACU 2 , SILVIA CURTEANU 1 * 1 “Gh. Asachi” Techical University, Department of Chemical Engineering, 71A, D. Mangeron Blvd., 700050, Iasi, Romania 2 Romanian Academy, “Petru Poni” Institute of Macromolecular Chemistry, 41A Gr. Ghica Voda, 700487, Iasi, Romania The kinetics of the equilibrium anionic polymerization of some cyclic siloxanes is modelled by using neural networks. Feedforward neural networks with one or two hidden layers have been used to appreciate the rates of disappearance of octamethylcyclotetrasiloxane and aminopropyl disiloxane at different catalyst concentrations (direct modelling). Alternatively, another neural model has been developed to estimate the amount of catalyst, which leads to an imposed final concentration of siloxane (inverse modelling). Experimental data for the polymerization of octamethylcyclotetrasiloxane in the presence of KOH as a catalyst and 1,3-bis(aminopropyl)tetramethyldisiloxane as a functional endblocker were used as training data sets for neural models. Satisfactory agreement between experimental data and network predictions obtained in validation phases proved that the projected models have good generalization capacities and, consequently, they describe well the process. Keywords: neural networks, direct and inverse neural modelling, polysiloxane, cyclic siloxanes, anionic ring opening polymerization The recent years proved that neural networks have become a powerful tool in chemical processes area, especially for modelling and prediction of nonlinear systems [1]. Usually, experimental and industrial practices use two types of models: mechanistic models (classical/ phenomenological models) based on the physical and chemical features and data-based empirical models. Each of these categories presents advantages and disadvantages, and, in this order, a comparison of them is necessary. The mechanistic models present the advantage to be valid upon a large area of operating conditions and reflect the process phenomenology. For this reason, whenever it is possible, the main recommendation should be to use the physic and chemical knowledge for the process. The disadvantages of these models, could be the difficulties concerning the specificity of the process and the problems in designing a system mathematical model. The difficulties regarding the chemical process refer to many aspects as follows: the absence of on-line testing (measurements), the considerable delays at testing, the possibility of many answers determined by the different operating conditions. Concerning the design of the mathematical model, several aspects can be mentioned: the complexity of reactions’ mechanisms or the fact that the phenomenology of the processes are insufficiently known, the great number of chemical species into the system, the great number of model equations and the special methods in giving the solutions. An overlooking from the studies on neural network for modelling or control allows the observation of some advantages: parallel organization permits solutions to problems where multiple constraints must be satisfied simultaneously; graceful degradation and the rules are implicit than explicit [2]. On the other hand, the disadvantages seem to be upon the necessity to obtain a perfect neural network with the experimental or operational history data. Also neural network needs large amount of good quality data for its * email: silvia_curteanu@yahoo.com training, which is normally difficult to obtain in practice. Data sparsity, ‘overfitting’ and poor generalization are other problems faced by researchers when using the basic neural network alone [3]. A special attention should be to paid to an uniform distribution of data throughout the design space [4]. In the idea of identification data which cover the whole range of the process variable, any applications prove that if properly trained and validated, these neural network models can be used to accurately predict the process behaviour, hence, leading to process optimization and control performance improvement [5]. Roy et al [6] have shown that multilayer perceptron with at most two hidden layers can solve any non-linear problem provided there are sufficient numbers of hidden nodes. An important and widely studied class of semi-organic polymers is constituted by polyorganosiloxanes. Polyorganosiloxanes possess a variety of interesting and desirable properties such as low glass transition temperatures, high lubricity, UV stability, good thermal stability, low toxicity and unique surface properties. Two general methods are well known and widely used for linear polysiloxane synthesis: polycondensation of bifunctional siloxanes and ring-opening polymerization (ROP) of cyclic oligosiloxanes [7]. ROP is the most traditionally and significant route to obtain high molar mass linear polysiloxanes, cyclic tetramer and trimer being usually the starting monomers. This polymerization may be carried out either anionically or cationically [7, 8]. In principle, any compound that can split the siloxane bond by ionic (either electrophilic or nucleophilic) mechanism can initiate polymerization of cyclosiloxanes with involvement of the positive or negative reaction centers of the growing chains. There are a wide variety of compounds that can initiate the ROP polymerization of cyclosiloxanes including strong organic and inorganic acids or bases and metal oxides [9, 10]. It is well known that, in the presence of the strong acids or bases, the Si-O bonds in both unstrained cyclosiloxanes and linear macromolecules (which have comparable