Multi‐Objective Optimization of Semi‐Batch Copolymerization Reactors Using Adaptations of Genetic Algorithm

Summary: The polymerization of styrene‐acrylonitrile (SAN) random copolymers in semi‐batch reactors is optimized using multiple objective functions that are often conflicting and non‐commensurate in nature. These include the average composition of the copolymer product, its number‐average molecular weight, its polydispersity index, and the conversion of monomers attained in the reactor. Two decision/control variables are used, namely, the rate of continuous addition of a monomer‐solvent‐initiator mixture (having a specified and fixed composition) and the history of the temperature in the reactor. The elitist non‐dominated sorting genetic algorithm, NSGA‐II, is adapted and used for decision variables that are functions of time (trajectory optimization). This robust, AI (artificial intelligence)‐based technique, enables the solution of far more complex optimization problems than those reported in the literature. A set of several non‐dominating (equally good) Pareto optimal solutions was obtained. These provide insights into the conflicting nature of the objective functions. An engineer (decision maker) can then use his judgment (often intuitive) to choose the preferred solution from among these possibilities.

Pareto set of optimal solutions and some corresponding state variables for a Reference Problem.     

Molecular Dynamics Simulation of the Formation of Polymer Networks

The random end linking of different amounts of trifunctional crosslinkers with 3 000 prepolymer linear chains, with length varying from 10 to 30 monomers, to form networks at different system number densities was dynamically simulated by the molecular dynamics method. Investigation of the crosslinking kinetics shows that, with a stoichiometric number of crosslinkers present, the time evolution of free ends fraction decays as a power law in time t^−3/4. This scaling behavior is different from the one in a dense polymer melt. Structural analyses of the resulting networks indicate that the imperfections of the network structure strongly depend on the initial synthesis conditions including the initial system number density and the ratio of crosslinkers to precursor polymer chain ends.

     

Dynamic Monte Carlo Simulation of Olefin Polymerization in Stopped-Flow Reactors

Stopped-flow reactors are very useful to estimate olefin polymerization rate constants and to investigate particle morphology development. Because the residence time in these reactors is comparable to the life time of the polymer chains, very narrow molecular weight distributions are obtained and the number average molecular weight is proportional to reactor residence time. In this case, traditional models for olefin polymerization in industrial reactors can not be applied. In this contribution, we derived analytical solutions and performed Monte Carlo simulations to describe the time evolution of the molecular weight distribution of polyolefins made with single- and multiple-site catalysts in stopped-flow reactors.     

Computational Analysis of Mixing and Scale-Up in Emulsion Polymerization Reactors

Summary: A hybrid multi-zonal/computational fluid dynamics (CFD) framework is currently being developed to aid in the scale-up of high solid content latex production and processing. Poly3D, a commercial laminar CFD code tailored to modelling the mixing of non-Newtonian fluids, has been coupled to a population balance model via a customized interface. CFD is used to generate flow fields inside a series of reactors; this information is then transferred to a multi-zone population balance model to assess the impact of non-homogenous mixing on the evolution of the latex particle size distribution (PSD) when concentrated latex suspension is altered via the addition of a coagulant. The rheological properties of high solid content latexes are sensitive to changes in the PSD, so the flow field is periodically updated if significant changes in the rheological properties of the latex are detected in any of the zones. The details of the models comprising the framework are presented and the utility of the framework is demonstrated.     

Thermodynamic Modeling of Polymer Solution Interface

A new method is presented to characterize the interfacial concentration field and interfacial tension between equilibrium polymer solution phases, using readily accessible equilibrium concentration data. The new method is tested and validated using experimental data from different polystyrene solutions and it consists of i) calculation of a universal expression for the concentration gradient coefficient based on the Cahn‐Hilliard model and the Wolf interfacial tension master equation, and ii) development of a highly accurate algebraic function (Kappa distribution) that, for a given equilibrium polymer concentration set, yields the essentially exact interfacial profile predicted by the classical gradient theory for polymer solutions.

     

Fabricating Triple‐Sensitive Polymer Nano‐Aggregates via an Aqueous Iminoboronate Multicomponent Reaction

A triple‐sensitive polymer of poly(ethylene glycol)‐iminoboronate nitrobenzyl ethanediol chelate (PEG‐INEC) is efficiently fabricated via the convenient aqueous iminoboronate multi‐component reaction (MCR) of methoxypolyethylene glycol amine (mPEG‐NH₂), 2‐formylphenylboronic acid (FPBA), and bis(2‐nitrophenyl) ethanediol (BNPE, a photo‐cleavable nitrobenzyl alcohol derivate). The aqueous MCR synthetic procedure is followed using ¹H NMR and turbidity analysis. It is shown that polymer nano‐aggregates of PEG‐INEC in aqueous solution can be dissociated through the stimuli responsive reactions of the hydrophobic iminoboronate nitrobenzyl ethanediol chelates (INECs) when exposed to UV light, acid, and H₂O₂, respectively. Furthermore, upon the stimulation of combined triggers, the dissociation of polymer nano‐aggregates can be accelerated to different extents, resulting in the synergistic release of encapsulated hydrophobic molecules in water. The proposed facile and general method is quite desirable and of great importance in practical applications like drug and gene delivery.

     

Novel Two‐Compartment Micelles Formed by Self‐Assembly of Linear Pentablock Copolymers in Selective Solvents

In this work, the formation of two‐compartment micelles from symmetric pentablock copolymers in selective solvents was studied using the dissipative particle dynamics simulation technique, and the effects of block lengths and solvent quality were investigated. The simulations revealed several new morphologies and their formation mechanisms were elucidated at the molecular level, providing useful information that may contribute to the future rational design and synthesis of novel multicompartment micelles with tailored structures.

     

Prediction of Chain Length Distribution of Polystyrene Made in Batch Reactors with Bifunctional Free‐Radical Initiators Using Dynamic Monte Carlo Simulation

The objective of this paper is to present a dynamic Monte Carlo model that is able to simulate the polymerization of styrene with bifunctional free‐radical initiators in a batch reactor. The model can predict the dynamic evolution of the chain length distribution of polystyrene in the reactor. The model includes all relevant polymerization mechanistic steps, including chemical and thermal radical generation, and diffusion‐controlled termination. The model was applied to styrene polymerization and the Monte Carlo estimates for chain length averages were compared to those obtained with the method of moments. Excellent agreement was obtained between the two methods. Although styrene polymerization was used as a case study, the proposed methodology can be easily extended to any other polymer type made by free‐radical polymerization.

     

Gradient Copolymers by ATRP in Semibatch Reactors: Dynamic Monte Carlo Simulation

We developed a dynamic Monte Carlo model for ATRP in semibatch reactors. Semibatch reactors can be used to produce gradient copolymers even if the difference between the reactivity ratios of the comonomers is not significant by using different comonomer feed policies. The model was used to predict average molecular weights, polydispersity index, copolymer composition and complete distributions of molecular weight, chemical composition, and comonomer sequence length at any polymerization time. Two case studies, poly[styrene‐co‐(methyl methacrylate)] and poly[acrylonitrile‐co‐(methyl methacrylate)], were chosen to demonstrate the effect of comonomer feed compositions on the final chemical composition distribution of the copolymer.

     

Molecular Dynamics Simulations of Polymer Translocations

Summary: Molecular dynamics simulation studies of the translocation of charged homopolymers of length, N, driven by an electric potential gradient through a channel have been performed. We find that the translocation time, τ, displays an inverse power dependence on the temperature of the simulation τ ∼ (T − T₀)^−7/4, which is in very good agreement with experimental results. In addition, the dependence of τ on the driving field strength and the velocity of translocation on the polymer length N have also been obtained. The results suggest that such minimalist models are useful in modelling biological processes and that the molecular dynamics method is a suitable approach for carrying out these simulations.

Snapshot of the polymer during the simulation.     

Modeling and Simulation of Liquid Phase Propylene Polymerizations in Industrial Loop Reactors

Liquid phase tubular loop polymerization reactors are widely used in the polyolefin industries because of their capabilities to promote high mixing of reactants in the reaction vessel and to allow for high heat transfer rates with the cooling jacket due to their high aspect ratio. Previous works on this subject focused on the modeling of the polymerization system, but only a few compared their results with real industrial data. A literature review about the propylene production in loop reactors shows that the validation of a distributed model with actual industrial data is yet to be presented. A distributed mathematical model is presented for industrial liquid phase loop polypropylene reactors and validated with actual industrial data for the first time. The model is able to represent the dynamic trajectories of production rates, MFI and XS values during grade transitions within the experimental accuracy. The model indicates that the polymer quality can change significantly along the reactor train and that manipulation of feed flow rates can be successfully used for production of more homogeneous polymer products.     

Pre-Averaged Sampling On the Entanglement Kinetics for Polymer Dynamics

A new model for entangled polymer dynamics based on pre-averaged sampling of the entanglement structure is proposed. Although it has been reported that sliplink simulations are powerful and promising to predict entangled polymer dynamics, it is still unpractical to calculate polymers with many entanglements. In the present study, a possible approach to achieve fast calculation is proposed by pre-averaged sampling of entanglement structure with skipping detail kinetics of entanglements dominated by chain ends in conventional sliplink models. To achieve time development of the chain conformation and entanglement structure, i) number of entanglement per chain and number of monomers for each segment are randomly obtained from the equilibrium distribution proposed by Schieber [J. Chem. Phys. 2003 , 118, 5162] and ii) the renewed entanglement structure is mechanically equilibrated. The established power-laws on molecular weight dependence of chain dimension, the longest relaxation time and self-diffusion coefficient were reasonably reproduced. Comparison on linear viscoelastic response is also discussed.     

Modeling and Simulation of the Crystallization Behavior of Polymer Melts in the Hollow‐Profile Extrusion Process Using the Coexistence Model of Spherulite and Shish‐Kebab

The thermally and flow induced crystallization behavior of polymer melts has been investigated by using penalty finite element‐finite difference simulation with a decoupled solving algorithm. The coexistence model of spherulite and shish‐kebab is proposed to describe the evolution of crystallization kinetics process. The Schneider equation and Eder equation are adopted to discriminate the relative roles of the thermal and the flow effect on the crystallization behavior. The proposed mathematical model and numerical method have been successfully applied to the investigation of crystallization behavior in the hollow‐profile extrusion process. Both the evolution of crystalline size within the extrusion die and the effects of processing conditions on the crystallization kinetics process are discussed.