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.
The use of PBS, 10% FBS or 10% CS as media for SI‐ATRP is reported. Controlled/living SI‐ATRP of MeOEGMA in PBS is achieved leading to better control than in water. The livingness is confirmed by chain extension with MeOEGMA or carboxybetaine acrylamide. This technique is successfully adopted for the polymerization of MeOEGMA in 10% FBS or CS as models for complex biological media with reasonable control of the brush growth. All prepared brushes show excellent antifouling properties.
We developed an analytical solution to describe how the CLD of polymers made with coordination polymerization catalysts vary as a function of time for very short polymerization times before the CLD becomes completely developed. We compared the analytical solution with a dynamic Monte Carlo model for validation, obtaining excellent agreement. Our analytical solution can be used to determine when the steady‐state hypothesis, commonly used in polymerization models, becomes valid as a function of polymer chain length. We also extended our model to describe polymerization with multiple‐site‐type catalysts. Depending on the polymerization kinetic parameters of the different site types on the catalyst, the fully developed CLD is reached through very different intermediate CLDs. This modeling approach, although rather simplified, can be used to interpret results from short polymerization time experiments such as the ones done in stopped‐flow reactors.
Styrene polymerization literature is reviewed and a model with dicumyl peroxide and benzoyl peroxide initiators is developed. Nine parameters are selected for estimation using statistical methods that account for the influence of parameters on model predictions, correlated effects of parameters and uncertainties of initial literature values. Updated parameters result in improved fits to conversion and molecular weight data from three research groups, reducing the least‐squares objective function by 73%. Use of industrial data from 19 batch reactor runs increases the number of estimable parameters to 16. Good predictions are obtained for validation runs with temperature ramps using both initiators.
A mathematical model is developed for condensation polymerization of 1,3‐propanediol to produce Cerenol polyether. The effect of the super‐acid catalyst is considered explicitly in the proposed reaction mechanism. The main reactions include protonation/deprotonation equilibrium, polycondensation, carbocation formation, end degradation, and transetherification. Formation of propanal and secondary hydroxyl ends is also considered. Mass transfer of water, propanal, and monomer from the liquid phase into nitrogen bubbles is included in the model. The proposed model predicts the time evolution of number average molecular weight and concentrations of water, propanal, monomer, and unsaturated end groups, along with evaporation rates of small molecules. Data from isothermal batch experiments are used to estimate model parameters. Steep upward trends in degree of polymerization and in concentration of unsaturated ends are not predicted well at long reaction times based on the current model.
Batch and semibatch styrene polymerizations are carried out using a heterogeneous ATRP catalyst system that provides excellent molecular‐weight control. The observed initiator efficiency is lower for semibatch operation due to the high initiator concentrations required to make a low‐MW polymer. Experiments verified that the insoluble metal complex does not participate in the polymerization and that Cu(I) solubility is an order of magnitude higher than that of Cu(II). A mechanistic model, using kinetic coefficients from literature and the solubility data from this study, provides a good representation of the experimental results.
We developed an analytical solution to describe how the chain length distribution (CLD) of polymers made with coordination polymerization catalysts vary as a function of time for very short polymerizations considering non‐instantaneous site activation. This solution is an extension of our previous analytical expression for instantaneous site activation. We validated the analytical solution with dynamic Monte Carlo simulation and obtained excellent agreement. Simulation results indicate that, unless the catalyst activation rate is much lower than the propagation rate, it will have only a minor effect on the initial shape of the CLD of polymers made in stopped‐flow reactors (SFR). We also show how incorrect polymerization kinetic parameters may be estimated when assuming instantaneous site activation when this hypothesis is not applicable to the polymerization data under investigation.
The use of pressure‐drop and constant‐pressure dilatometry for obtaining rate data for liquid propylene polymerization in filled batch reactors was examined. The first method uses reaction temperature and pressure as well as the compressibility of the reactor contents to calculate the polymerization rate; in the second, the polymerization rate is calculated from the monomer feed rate to the reactor. Estimated polymerization rates compare well to those obtained using the well‐developed isoperibolic calorimetry technique, besides pressure‐drop dilatometry provides more kinetic information during the initial stages of the polymerization than the other methods.
Kinetic Monte Carlo simulations are performed to investigate the capability of ICAR ATRP for the synthesis of well‐defined poly(isobornyl acrylate‐b‐styrene) block(‐like) copolymers using one‐pot semi‐batch and two‐pot batch procedures. The block copolymer quality is quantified via a block deviation (〈BD〉) value. For 〈BD〉 values lower than 0.30, the quality is defined as good and for well‐chosen polymerization conditions the formation of homopolymer chains upon addition of the second monomer can be suppressed. A better block quality is obtained when isobornyl acrylate is polymerized first. For lower Cu levels a one‐pot semi‐batch procedure allows a much faster ATRP and better control over the polymer properties than a two‐pot batch procedure.
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.
Fundamental measurements in online polymerization reaction monitoring and control seek to avoid empirical and inferential models in data interpretation. One such approach making use of multiple detectors is automatic continuous online monitoring of polymerization reactions (ACOMP), wherein a continuous reactor stream is automatically, continuously diluted and conditioned to where measurements reflect intrinsic particle properties and not the interactions that can dominate measurements in concentrated media. Examples where dilute regime measurements are needed include static and dynamic light scattering, and reduced viscosity. This review focuses on ACOMP to illustrate a number of reaction contexts where fundamental measurements are used to gain a comprehensive picture of reaction characteristics.
Two initiators containing a cleavable ester bond were compared in the lipase‐catalyzed ROP of CL and PDL. The results show that transesterification reactions are present at high rates throughout the enzymatic ROP and start at low conversion. HEA and HEMA displayed similar reaction efficiencies as initiators (acyl acceptors) in the enzymatic ROP. However, transacylation reactions on the HEA‐initiated polyesters were found to be 15 times faster. While in both cases the amount of HEA‐ and HEMA‐initiated polymers could be maximized by short reaction times, a well‐defined (meth)acrylation by this approach was not possible. Our results show that transesterification reactions have to be considered when performing an enzyme‐catalyzed ROP.
A mathematical model was developed to account for the evolution of polymer product attributes in the emulsion polymerization of styrene. The effects of transfer agent, surfactant, initiator and temperature were investigated. Polymerization rate, and particle size decreased with increasing concentration of the transfer agent. The polymerization rate increased with increasing surfactant and initiator concentrations, while an increase in temperature led to a decrease of molecular weight but an increase of polymerization rate and particle size. Chain extension was successfully achieved in the presence of our RAFT agent. The model predictions compared well with our experimental results.
The use of a tubular reactor for conducting living radical polymerizations by atom transfer radical polymerization (ATRP) was investigated. Solution polymerization experiments were performed with styrene and butyl acrylate to elucidate the influence of a continuous reaction process on conversion, molecular weight, and polydispersity compared to batch polymerization experiments. The continuous polymerizations were well controlled. Initial conversion was found to be slightly higher in the tubular reactor than in a batch polymerization run at similar conditions, while number average molecular weight and polydispersity are comparable between the continuous and batch processes. Residence time distribution studies showed the reactor exhibits nearly plug flow behavior.
NMRP is a controlled polymerization technique with the ability to produce polymers with a highly controlled microstructure. The properties of the thus obtained polymers make it desirable to scale this technique to an industrial level, but there are still some challenges to be faced, e.g., to develop emulsion NMRP at low temperatures (lower than about 100 °C) with inexpensive, commercially available nitroxides such as TEMPO. Here, the emulsion NMRP of styrene using TEMPO at temperatures lower than 100 °C is described. An optimal control of molecular weights and polydispersities and a fast polymerization rate are obtained.
Polymerization strategies aiming at further reducing the environmental impact of the already “green” emulsion polymerization process were investigated. Life cycle assessment showed that non‐isothermal strategies starting at low temperature resulted in an environmental impact lower than the isothermal ones. Nevertheless, the major part of the environmental impact was due to raw materials. The effect of the polymerization strategy on polymer microstructure was investigated.
The RPPFM is employed to describe the gas‐phase catalytic polymerization of ethylene in the presence of supported or self‐supported Z‐N catalysts. Numerical simulations are carried out to analyze the effect of the catalyst type on the polymerization rate, particle overheating and the average molecular polymer properties of the polyolefin. It is shown that non‐porous, self‐supported Ziegler‐Natta catalysts exhibit higher particle growth rates and lower particle overheating. The average molecular weight of polyethylene produced by both catalysts is almost identical. Depending on particle size and polymer crystallinity, the average monomer solubility and the effective monomer diffusivity can significantly vary.
