Controlled free‐radical polymerization of vinyl chloride

Owing to the importance of poly(vinyl chloride) (PVC) as the second‐largest plastic in volume after the polyolefins and above styrene polymers, the control of the free‐radical polymerization of vinyl chloride (VC) is of high industrial and academic interest. But still the term “controlled” polymerization is not yet clearly defined. Often it is used for quasi‐living polymerizations with equilibrium reactions in the initiation and/or termination step or for the control of the molecular weight distribution (MWD), but it can also be applied to several structural aspects such as stereochemistry, branching, or special technical properties. In the present article, the control of chain growth and chain transfer is discussed. It has been well known for many years that the propagation step in the VC polymerization is terminated to a large degree by the rather frequent and temperature‐dependent chain transfer of the growing macromolecules to the monomer. Therefore, the degree of polymerization is strongly governed by the polymerization temperature. However, this transfer step does not result in a controlled or a narrow MWD. By means of free‐radical nitroxide‐mediated polymerization of VC in suspension, PVC with a narrower MWD can be obtained also at higher polymerization temperatures. The resulting PVC with nitroxide end groups can act as a macro‐initiator for various monomers, resulting in two‐block copolymers, which are, e.g., interesting compatibilizers in blends with PVC. J. VINYL ADDIT. TECHNOL., 11:86–90, 2005. © 2005 Society of Plastics Engineers     

An analytical solution of the molecular weight distribution of reversible step growth polymerization in homogeneous continuous flow stirred tank reactors

Mole balance for the molecular weight distribution in homogeneous continuos-flow stirred tank reactors (HCSTRs) for reversible step-growth polymerization has been written. The relation for the moment generating function G is found to be a nonlinear ordinary differential equation and has been solved analytically. The solution of the MWD of the polymer formed is shown to be valid even if the condensation product is removed. At equilibrium, the solution reduces to the Flory distribution. The computations show that the polydispersity of the polymer first increases with the residence time θ of the reactor, but, for large θ, it reduces to the equilibrium value after undergoing a maximum.     

An efficient algorithm of computation of molecular weight distributions and its moments for reversible step growth polymerization in homogeneous continuous flow stirred tank reactors

The reversible step growth polymerization in homogeneous continuous flow stirred tank reactors (HCSTRs), in which the condensation product (W) leaves the reactor through flashing, has been analyzed. The molecular weight distribution (MWD) of the polymer formed is governed by nonlinear coupled algebraic relations to be solved simultaneously. To find the MWD numerically a large number of these are normally solved simultaneously using a suitable iterative procedure. In this paper, these have been decoupled using the technique proposed in our earlier works (1, 2) and the MWD can now be obtained sequentially without any trial and error. This leads to considerable saving in computation time compared to methods currently used. To demonstrate the efficacy of the algorithm, the polycondensation step of the poly(ethylene terephthal-ate) (PET) formed in HCSTRs has been analyzed. The MWD, the average chain length and the polydispersity index of the polymer have been computed and it takes 0.1 CPU seconds on a DEC 1090 as opposed to the earlier method which would take seventy minutes for similar computations. The simple model of the HCSTR for the PET formation gives the effect of reactor temperature and pressure and the quantitative results have been presented in this paper.     

Modeling of molecular weight distribution of propylene slurry phase polymerization on supported metallocene catalysts

A mathematical model of the molecular weight distribution (MWD) based on a particle growth model and the kinetic scheme is developed to simulate the MWD of the slurry phase propylene polymerization on a silica-supported metallocene catalyst by means of the equations of moments. The model is used to predict molecular weight distribution, including the number-average molecular weight, the weight-average molecular weight, and the polydispersity index. The results show that the mass transfer has great influence on the polymerization reaction, and it can broaden the MWD especially; moreover, the MWD can be evaluated by simulation; the average molecular weight increases as pressure or temperature, and MWD shifts to long chain lengths as the effective diffusion coefficient increasing thought the influence is not remarkable; furthermore, the MWD's simulation results are calculated, which fit greatly with the experimental data.     

Analysis of multiphase polycarbonate polymerization in a semibatch reactor

A physical and chemical model that describes the interfacial condensation of bisphenol-A to polycarbonate in a multiphase gas-liquid-liquid semi-batch reactor is presented. The particular polymerization kinetics model consists of initiation, propagation and termination reactions between dissolved bisphenol-A monomer, phosgene gas, a phenolic polymer chain growth stopper and various resulting polymer species. Using these kinetics, a physical model for a semi-batch stirred tank reactor is developed. The model accounts for finite liquid-liquid and gas-liquid mass transfer resistances and includes either plug-flow or complete backmixing of the gas bubbles as options for the gas flow pattern. The model equations are solved using the z-transform method from which the polymer MWD and the moments of the polymer MWD are obtained. The utility of the model as a quantitative means of assessing the effect of various kinetic and transport parameters on the polymer MWD is examined for a particular case.     

A multi-thread parallel computation method for dynamic simulation of molecular weight distribution of multisite polymerization

Molecular weight distribution (MWD) is an important quality index of polymer products. Many methods have been proposed to dynamically simulate the MWD of polymerization, but these methods are normally designed for serial computations. In this paper, a multi-thread parallel computation method was proposed for multisite free-radical polymerization. Analysis of the relationship among different subtasks revealed a combined parallel strategy by fully exploiting the parallel feature of the process. A good performance was obtained to accelerate the dynamic simulation of MWD based on Flory method. We theoretically analyzed the speedup ratio (SR) and parallel efficiency (PE). Results showed that software algorithm and hardware configuration exhibited a good match. The efficiency of the proposed parallel method was presented through industrial slurry processes that used high-density polyethylene (HDPE).     

Modeling of molecular weight distribution of gas‐phase polymerization of butadiene

A mathematical model of the molecular weight distribution (MWD) based on a multilayer model and an improved intrinsic kinetics model was proposed to simulate the MWD of the gas‐phase polymerization of butadiene with a heterogeneous catalyst. Intrinsic kinetics and heat and mass‐transfer resistances based on the multilayer model of a polymeric particle were considered in the modeling of the MWD. The effects of the reaction conditions, catalyst particle size, mass‐transfer resistance, deactivation of active sites, and transfer of the polymer chain on the molecular weight and MWD were simulated. The results show that the effects of the deactivation of active sites and transfer of the polymer chain on the average molecular weight are significant and that the effect of the catalyst particle size on the MWD is not significant. The simulation results of the molecular weight and MWD are compared with the experimental results. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 88–103, 2003     

Evaluation of rate constants from experimental batch reactor data for anionic polymerization of poly(methyl methacrylate) at high temperatures

At high temperatures, in anionic polymerization, depolymerization and autocyclization reactions cannot be ignored and the molecular weight distribution (MWD) results based on irreversible polymerization give erroneous results. In this article, we have developed a semianalytical solution for the MWD of the polymer for a general complex mechanism. We then show that the various rate constants can be directly determined from the experimental data on MWD. After evaluating these, it is possible to model the anionic polymerization more rationally, as we have demonstrated using the experimental data from the literature. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65:845–859, 1997     

Prediction of molar mass distribution,number and weight average degree of polymerization and branching of low density polyethylene

An extended mathematical model of an autoclave reactor for the high pressure polymerization of ethylene is presented. It allows one to predict not only the conversion but also the molar mass distribution, short and long chain branching, number and weight average degree of polymerization as a function of the synthesis conditions. The model includes the initiation step, chain growth, chain termination by disproportionation and combination, chain transfer to the monomer, polymer and modifier, and intramolecular chain transfer in the polymer radical. Number and weight average degrees of polymerization were computed by means of generating functions. For the calculation of the molar mass distribution recursion formulae are given. The performance of the model is shown by the good agreement of the predicted values with the experimental data.     

Ethylene polymerization over supported titanium‐magnesium catalysts: Effect of polymerization parameters on the molecular weight distribution of polyethylene

The data on the effects of polymerization duration, cocatalyst, and monomer concentrations upon ethylene polymerization in the absence of hydrogen, and the effect of an additional chain transfer agent (hydrogen) on the molecular weight (MW), molecular weight distribution (MWD), and content of vinyl terminal groups for polyethylene (PE) produced over the supported titanium‐magnesium catalyst (TMC) are obtained. The effects of these parameters on nonuniformity of active sites for different chain transfer reactions are analyzed by deconvolution of the experimental MWD curves into Flory components. It has been shown that the polymer MW grows, the MWD becomes narrower and the content of vinyl terminal groups in PE increases with increasing polymerization duration. It is assumed to occur due to the reduction of the rate of chain transfer with AlEt₃ with increasing polymerization duration. The polydispersity of PE is found to rise with increasing AlEt₃ concentration and decreasing monomer concentration due to the emergence of additional low molecular weight Flory components. The ratios of the individual rate constants of chain transfer with AlEt₃, monomer and hydrogen to the propagation rate constant have been calculated. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Evolution to similarity solutions for polymerization and depolymerization with microwave radiation

The kinetics of polymerization and depolymerization are critical in understanding the stability and characterization of polymers. The kinetics of simultaneous polymerization and degradation of poly(methyl methacrylate) have been investigated by varying the initiator concentration and monomer concentration under the influence of microwave energy. Microwave radiation initially polymerizes the monomer, then degrades the resulting polymer and the polymer attains an equilibrium molecular weight distribution with a polydispersity of two. To understand more fully the kinetics, the molecular weight distribution (MWD) is represented as a gamma distribution; the random degradation rate coefficient is assumed to vary linearly with molecular weight and the polymerization rate coefficient is assumed to be independent of molecular weight. The change of the MWD with time is studied by continuous distribution kinetics; the solutions obtained depict the change of the average molecular weight, polydispersity and the gamma distribution parameters with time. Experimental data indicate that reaction rates are enhanced by microwave radiation and the MWD approaches a similarity solution within 10 min for all the investigated cases. The model satisfactorily predicts the change of the MWD with time. © 2001 Society of Chemical Industry     

Mathematical modeling of the full molecular weight distribution in ATRP techniques

In this work the molecular weight distribution (MWD) of several atom transfer radical polymerization (ATRP) techniques has been derived and solved using the Reduced Stiffness by Quasi Steady State Approximation (RSQSSA) methodology. The Quasi Steady State Approximation has been validated on the living radicals for normal, Simultaneous Reversible and Normal Initiation and Activators Regenerated by Electron Transfer (ARGET), and it is shown that the information lost due to its application is negligible. According to these results, RSQSSA shows the best performance in terms of wall‐clock time and required memory in comparison to implicit techniques and Predici. In the case of the ARGET technique, the model predictions show good agreement with experimental data. Finally, an analysis on the impact of the slow and fast activation of the initiator on the MWD using ARGET has been carried out, indicating that the optimal initiator to control the MWD should exhibit activation‐deactivation rates very similar to those of the polymeric equilibrium. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2762–2777, 2016     

Algorithm for computation of molecular weight distribution and its moments in reversible step-growth polymerization in batch reactors

The differential equations governing the molecular weight distribution (MWD) in step-growth polymerization are coupled and nonlinear and a large number of them must be solved simultaneously to keep the truncation error low. In this work, these equations have been decoupled so that they can be solved sequentially. The solution of these is independent of the truncation error and there is considerable saving of computation time. To demonstrate the efficiency of the algorithm, the formation of polyethylene terephthalate (PET) in batch reactors with ethylene glycol evaporating has been analyzed. The feed to the reactor is taken as polymer with its oligomers present according to the Flory's distribution. The effect of pressure and temperature of the reactor on the progress of polymerization has been modelled and evaluated. The amount of ethylene glycol distilled, the concentrations of the first five oligomers Q₁ to Q₅, the number average chain length, and the polydispersity index of the polymer have been determined. It is shown that the reduced pressure and increased temperature reduce the concentration of the condensation product in the reaction mass, thus pushing the polymerization in the forward direction. Lastly the CPU time on Dec 1090 using this algorithm is only 0.40 s compared to about 10 min for similar computations using other existing methods.     

Transport equations for distillation of ethanol and water from the entropy production rate

We have derived a set of transport equations for heat and mass transfer across a liquid-vapour interface in distillation columns. We have used the entropy production rate on each tray, and integrated through the interface, when the liquid is not in equilibrium with the vapour. The set, that defines overall coefficients of transport, includes contributions from the interface, from the vapour film, and from the liquid film. It is shown, using data for a rectifying column that separates ethanol and water, that the coefficients can be determined by fitting the transport equations to the entropy production rate, with the constant thickness of one of the films as the only adjustable variable. Almost all of the entropy production is due to mass transfer between the phases. Coefficient values were determined for a large and a small value for the film thickness ratio as a function of temperature. The distribution of the entropy production rate between the phases depends largely on the film thickness, but its distribution between mass and heat transfer contribution does not depend on this variable. A contribution from the Soret or Dufour effect is found for large liquid films. The driving force for mass transfer, calculated with coefficients and rates, compared well with average values, which were calculated from the experimental data. The set of equations was compared to the Maxwell-Stefan equation set. Since it contains the interface contribution and coupling, it can be used to asses common approximations.     

Simulation of reversible nylon-66 polymerization in homogeneous continuous-flow stirred tank reactors

Experimental data of Ogata¹ has been curve-fitted to obtain the forward and reverse rate constants for nylon-66 polymerization. Its molecular weight distribution (MWD) has been simulated in homogeneous continuous-flow stirred tank reactors (HCSTR) for 11 h of residence time when the reaction mass is very close to equilibrium. The set of algebraic equations have been solved using Brown's algorithm,² which was found to be more efficient compared to the Gauss-Jordon techniques of solution. The MWD thus obtained is compared with our earlier simulation of the molecular weight distribution from batch reactors³ and was found to differ significantly. In HCSTR, the weight fraction distribution does not undergo a maximum and the polydispersity index ρ of the polymer formed is much higher than that obtained from batch reactors. The number and weight average of the polymer formed in HCSTR is found to be significantly lower.     

Modeling of molecular weight and copolymer composition distributions for ethylene-propylene solution copolymerization

A comprehensive computational fluid dynamics (CFD) model was developed to investigate spatial distributions of molecular weight distribution (MWD) and copolymer composition distribution (CCD) for ethylene-propylene (EPM) copolymers in a bubble column reactor. The CFD approach incorporated Euler–Euler two-fluid model, copolymerization kinetics, and copolymer microstructural distribution model together by user-defined functions for ethylene-propylene heterogeneous copolymerization process. MWD and CCD distributions were calculated by introducing Flory's distribution and Stockmayer's distribution, respectively. CFD model results were validated with literature data. The multiphase hydrodynamics, interphase mass transfer, spatial–temporal variations of MWD and CCD distributions were analyzed. Both distributions are wider at the inlet of reactor for the inefficient mixing, but narrower at the outlet due to fully developed flow and polymerization. This model is beneficial to the improvement of polymer products and process control in industrial EPM reactor.     

The influence of reactor type and operating conditions on the molecular weight distribution in vinyl acetate polymerization

The vinyl acetate polymerization system was investigated with respect to the breadth of the molecular weight distribution (MWD) in batch, continuous segregated, and continuous micromixed reactors. Models were developed employing a complex kinetic scheme including polymer transfer and terminal double bond polymerization, without neglecting initiation and termination steps. Inclusion of a gel effect for terminal double bond polymerization gave better agreement with experimental molecular weight data in suspension polymerization. Simulation results showed the MWD order in the three reactor types is not fixed, but a function of reactant concentrations and the importance of chain branching. In some cases changing the initiator type and concentration will change the MWD order.     

Kinetic model for lonic polymerization initiated by difunctional initiator with monomer transfer

The kinetics of difunctional ionic polymerization with monomer transfer and without assumption of instantaneous initiation is studied theoretically. The set of kinetic differential equations is rigorously solved by way of graphical theory. Expressions for the molecular weight distribution (MWD) function, the number- and weight-average degrees of polymerization, and the distribution of functionality are obtained. A procedure is proposed for calculating the MWD curve and the values of other molecular parameters.     

Modelling of reversible poly(ethylene terephthalate) reactors

The second stage of batch poly(ethylene terephthalate) (PET) reactor with bis(2-hydroxyethyl) terephthalate (BHET) as the feed has been simulated. In this stage, the overall polymerization is not diffusion limited and is known to be a complex reaction. In this work it has been assumed to consist of polycondensation, reaction with monofunctional compounds (cetyl alcohol), redistribution, and cyclization reactions. The forward and reverse steps of each of these have been modelled in terms of the rate constants involving functional groups and the reacted bonds. The equations for the calculation of the molecular weight distribution (MWD) in batch reactors have been written and solved numerically. The MWD reported in this work is assumed to include the monofunctional products only, and, for the case where ethylene glycol is not removed from the reaction mass, it was found to be unaffected by the choice of the redistribution rate constant (k_r). Since the removal of ethylene glycol is not mass transfer controlled, its concentration in the reaction mass is assumed be given by the vapor–liquid equilibrium existing at the pressure applied on the reactor. In this work, the level of ethylene glycol concentration, y_g (?[G]/[P₁]₀), has been taken as a parameter, and, on application of vacuum, the MWD results were found to vary with k_r with the sensitivity increasing with y_g. It was then shown that the importance of the redistribution reaction is enhanced when the cyclization reaction also occurs. The effect of vacuum on the performance of the reactor has been studied by varying y_g. For y_g less than 0.01, the change in the MWD of the polymer becomes very small. The effects of polymerization temperature and initial concentration of monofunctional compounds on MWD were found to be small.     

Radical thermo‐ and sonopolymerization of methyl methacrylate initiated by iodobenzene 1,1‐diacetate

The efficiency of iodobenzene 1,1‐diacetate or (diacetoxyiodo)benzene (DAIB) as a thermo‐ and sono‐initiator of methyl methacrylate (MMA) in radical bulk polymerization is tested. The polymerization kinetics and molecular‐mass characteristics support an assumption for a combined polymerization mechanism including a classical bimolecular termination with chain transfer reaction and iniferter quasi‐living polymerization. In addition to the equilibrium formation and degradation of the ‘dormant’ polymer ends, other possible decomposition reactions of the hypervalent iodine bond are the probable reason for the deviation of this polymerization from the iniferter polymerization mechanism. These reactions bear some similarity to the two‐step addition–fragmentation chain transfer mechanism of controlled radical polymerization. The application of the poly(MMA) obtained as a macroinitiator is evidence of ‘dormant’ chain end formation. © 2001 Society of Chemical Industry