Estimation of Polymerization Conditions Needed to Make Ethylene/1-olefin Copolymers with Specific Microstructures Using Artificial Neural Networks

Abstract

their molecular weight distribution (MWD) and chemical composition distribution (CCD) that depend on copolymerization conditions and catalyst type. [ 1 ] Polymers with narrow MWDs can be synthesized with single-site-type metallocene catalysts. [ 2 ] A combination of two metallocene catalysts can be used to control polyolefi n structures with versatility and fl exibility. [3][4][5][6] Polymerization kinetics models for ethylene/1-olefi n copolymerization with two metallocenes are expressed as a system of ordinary differential or algebraic equations. These model can be used to estimate chain microstructures from a specifi c set of polymerization conditions; [ 7 ] they cannot, however, be used to determine polymerization conditions to yield desired microstructures because these models cannot be inverted.Artifi cial neural networks (ANNs) can be used to solve highly nonlinear problems. ANNs mimic the pattern recognition process of neural systems by learning from examples. Only input and output datasets are used in ANNs-phenomenological models for the process Two artifi cial neural network models (forward and inverse) are developed to describe ethylene/1olefi n copolymerization with a catalyst having two site types using training and testing datasets obtained from a polymerization kinetic model. The forward model is applied to predict the molecular weight and chemical composition distributions of the polymer from a set of polymerization conditions, such as ethylene concentration, 1-olefi n concentration, cocatalyst concentration, hydrogen concentration, and polymerization temperature. The results of the forward model agree well with those from the kinetic model. The inverse model is applied to determine the polymerization conditions to produce polymers with desired microstructures. Although the inverse model generates multiple solutions for the general case, unique solutions are obtained when one of the three key process parameters (ethylene concentration, 1-olefi n concentration, and polymerization temperature) is kept constant. The proposed model can be used as an effi cient tool to design materials from a set of polymerization conditions.

On the Robustness of Forward and Inverse Artificial Neural Networks for the Simulation of Ethylene/1‐Butene Copolymerization

“…However, although the existence of multiple solutions precludes us to find the conditions we used in the training set to make a copolymer with a given M n , M w , CC, and Y , in practice these multiple solutions are an advantage. If we can identify a multiple set of polymerization conditions that produce polymers with the same desired microstructure, we can then select the conditions that are most viable from technical and economical points of view . We may also constrain the solution space for the inverse problem to eliminate solutions that we know are technically unfeasible or undesirable, such as too high or too low polymerization temperatures, for instance.…”

“…This approach may be used to solve highly nonlinear and complex problem by finding the optimum learning patterns of relationship between input and output variables . ANN models have been applied in various polymer applications as a predictive model for polymer properties and polymerization kinetics …”

“…Recently, our research group developed forward and inverse ANN models to describe the copolymerization of ethylene and 1‐butene with two single‐site catalysts . The forward model predicted the MWD and CCD, while the inverse model estimated the polymerization conditions required to make copolymers with the desired MWD and CCD.…”

Heuristic Search Strategy for Transforming Microstructural Patterns to Optimal Copolymerization Recipes

“…In the above summation equations, the subscript j denotes the site type, m ( j ) is the mass fraction of polymer produced on site type j , M w refers to molecular weight, w (‐) ( j ) denotes the weight fraction (distribution) of molecular weight and/or chemical composition of polymer produced on site type j , W (‐) denotes the total weight (distribution) of molecular weight and/or chemical composition, N s is the total number of active site types on the catalyst, and F 1 is the molar fraction of ethylene monomer in the copolymer. More information on the derivation of these equations can be found elsewhere . Despite the fact that the above equations are capable of precisely predicting the variations of MWD and CCD for a wide range of operational conditions (moving from X to Y), the establishment of structure–property relationships in such systems needs continuous update due to the fact that the interrelationships between copolymerization conditions and microstructural patterns are severely nonlinear (moving in an inverse manner, i.e., from Y to X).…”

“…Second, the predefined target copolymer with preset MWD and CCD patterns is directly received by the computer code. As per previous work in the literature, 15 data points on both MWD and CCD microstructural patterns are specified by equally spaced slicing of input patterns, which is shown to be adequate for reflecting the behavior of such distribution curves . Then, in the third step, an initial population of chromosomes (i.e., copolymerization recipes) is generated randomly.…”