A simulation model for long-chain branching in vinyl acetate polymerization: 1. Batch polymerization

A new simulation model for the kinetics of long-chain branching formed via chain transfer to polymer and terminal double-bond polymerization is proposed. This model is based on the branching density distribution of the primary polymer molecules. The theory of branching density distribution is that each primary polymer molecule experiences a different history of branching and provides information on how each primary polymer molecule is connected with other chains that are formed at different conversions, therefore making possible a detailed analysis on the kinetics of the branched structure formation. This model is solved by applying the Monte Carlo method and a computer-generated simulated algorithm is proposed. The present model is applied to a batch polymerization of vinyl acetate, and various interesting structural changes occurring during polymerization (i.e., molecular weight distribution, distribution of branch points, and branching density of the largest polymer molecule) are calculated. The present method gives a direct solution for the Bethe lattice formed under nonequilibrium conditions; therefore, it can be used to examine earlier theories of the branched structure formation. It was found that the method of moments that has been applied successfully to predict various average properties would be considered a good approximation at least for the calculation of not greater than the second-order moment in a batch polymerization. © 1994 John Wiley & Sons, Inc.     

Branched structure formation in free radical polymerization of vinyl acetate

The branched structure formation during free radical polymerization of vinyl acetate is investigated in detail by application of the computer simulations on the basis of the Monte Carlo sampling technique. Simulations are made for the whole molecular weight distribution (MWD), the MWDs for polymer molecules containing 0, 1, 2, 3, etc., branch points, the branching density as functions of both size and the number of branch points, the spatial distribution of the branched chains, etc. It was found that the effect of polyradicals on the formed MWD could be neglected for batch polymerizations of the present reaction system. A large number of relatively small branch chains are formed due to both chain transfer to polymer (CTP) and the terminal double-bond polymerization (TDBP). The radius of gyration at a Θ state is found to agree satisfactorily with the Zimm-Stockmayer equation for random branching in spite of the heterogeneous branched structure formed in the polymerization. The present investigation reveals important characteristics of the complex molecular structure formation during free radical polymerization that involves both CTP and TDBP. © 1996 John Wiley & Sons, Inc.     

Molecular weight distribution in nonlinear emulsion polymerization

A modelistic study of the molecular weight distribution (MWD) formed in emulsion polymerization that involves chain transfer to polymer is conducted, by focusing our attention to the effect of very small reaction volume on the formed MWD. In emulsion polymerization, a polymer radical that causes polymer transfer reaction must choose the partner only within the same particle, which makes the expected size of the polymer molecule to be chosen smaller compared with the corresponding polymerization system that involves an infinitely large number of polymeric species. The usual assumption for homogeneous polymerization that the rate of chain transfer to a particular polymer molecule is proportional to its chain length cannot be used, except when branching frequency is low and particle size is large enough. This fact invalidates the direct use of models developed for homogeneous nonlinear polymerizations to emulsion polymerizations. Model equations that could be used to assess the significance of the limited space effects on the MWD under a given polymerization condition are also proposed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1515–1532, 1997     

Long-chain branching in free-radical polymerization due to chain transfer to polymer

The Monte Carlo sampling technique is used to investigate the branched structure formation during free-radical polymerization that involves chain transfer to polymer. This method accounts for the history of the generated branched structure and can provide virtually any structural information, because one can observe each polymer molecule directly. In this paper, we investigate the whole molecular weight distribution (MWD) for both pre- and postgelation periods, the MWDs for polymer molecules containing 0, 1, 2, 3, … branch points, the branching density of polymer molecules as functions of both size and the number of branch points, the spatial distribution of the branched chains at the theta state, etc. Contrary to the term ‘long-chain’ branching, many branch chains are relatively small, and the branched structures formed are significantly different from those usually depicted to introduce ‘branched polymers’ in many introductory textbooks. The radii of gyration at the theta state can be approximated by the Zimm-Stockmayer equation for random branching, in spite of various violations against the assumptions used in deriving the equation © 1995 John Wiley & Sons, Inc.     

Simultaneous long‐chain branching and random scission: I. Monte Carlo simulation

In free‐radical olefin polymerizations, the polymer transfer reactions could lead to chain scission as well as forming long‐chain branches. For the random scission of branched polymers, it is virtually impossible to apply usual differential population balance equations because the number of possible scission points is dependent on the complex molecular architecture. On the other hand, the present problem can be solved on the basis of the probability theory by considering the history of each primary polymer molecule in a straightforward manner. The random sampling technique is used to solve this problem and a Monte Carlo simulation method is proposed. In this simulation method, one can observe the structure of each polymer molecule formed in this complex reaction system, and virtually any structural information can be obtained. In the illustrative calculations, the full molecular weight distribution development, the gel point determination, and examples of two‐ and three‐dimensional polymer structure are shown. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 391–403, 2001     

Molecular weight distribution of metallocene polymerization with long chain branching using a binary catalyst system

In metallocene polymerization, termination by β-hydride elimination generates polymer chains containing unsaturated vinyl groups at their chain ends. Further polymerization of these macromonomers produces branched polymers. Material properties of the branched polymers not only depend on molecular weight and branching density, but also on chain structure. This work presents analytical expressions to predict the bivariate distribution of molecular weight and branching density for polymer chains having dendritic and comb structures. It is shown that when a single metallocene catalyst is used the formation of dendritic polymers is favored with only a very small fraction of highly branched chains assuming comb structure. The use of a binary catalyst system is therefore proposed to obtain high content of comb polymers. One catalyst generates macromonomers and the other yields in-situ branching. It is found that the comb polymers give much narrower molecular weight distributions than dendritic polymers with same branching densities.     

Molecular weight distribution and molecular structure of polyethylene produced by radiation-induced polymerization

The molecular weight distribution of polyethylene produced by radiation was calculated according to a kinetic scheme. The calculated molecular weight distribution was compared with the results deduced from gel-permeation chromatography. The observed distribution curve from GPC was broader and showed a lower degree of polymerization than the calculated one. Discrepancies between observed and calculated curves can be explained if the polymer contains nonsteady-state products and if the reaction mechanism includes chain transfer to dead polymer. By this reaction long-chain branching would occur. Several long-chain branches per polymer molecule were indeed found, as inferred from solution properties.     

Molecular Weight Development during Simultaneous Chain Scission,Long‐Chain Branching and Crosslinking, 1

A general matrix formula is proposed for the weight‐average molecular weights of the polymer systems formed through simultaneous scission, branching and crosslinking of N types of chains, assuming the chain connection statistics are Markovian. For the polymerization systems in which chains are generated consecutively, such as for free‐radical polymerization, the present theory can be applied by increasing the number of chain types N to infinity, by considering the chains formed at different times as different types of chains. The gel point determination reduces to the eigenvalue problem and the present theory extends the classical gelation theory to non‐random, history‐dependent reaction systems. From the mathematical point of view, this theory is capable of describing complex molecular build‐up processes through end‐linking, T‐ and H‐shaped chain connections, irrespective of reaction/reactor types used.

Schematic representation of the 0^th generation segment and the connection to the 1^st generation segments.     

Simulation model for network formation in free-radical crosslinking copolymerization: Pregelation period

A new simulation model for network formation in free-radical copolymerization of vinyl and divinyl monomers is proposed. This model is based on the crosslinking density distribution of the primary polymer molecules that results from a kinetically controlled network formation. The crosslinking density distribution provides information on how each chain is connected to other chains and therefore, a detailed analysis of the kinetics of network formation becomes possible by application of Monte Carlo simulations. In this method, not only averages but also various distributions, such as molecular weight distribution and distribution of crosslinked units as well as of unreacted pendant double bonds among various polymer molecules, can be calculated. The present theory is a direct solution for the Bethe lattice formed under nonequilibrium conditions, and therefore, it can be used to examine the applicability of the earlier theories of network formation to kinetically controlled systems. The present method is quite general and can be applied to various complex reactions systems that involve crosslinking, branching, cryclization and degradation in a nonequilibrium system.     

Dimensions of branched polymers formed in simultaneous long‐chain branching and random scission

In free‐radical olefin polymerizations, the polymer‐transfer reactions could lead to chain scission as well as the formation of long‐chain branches. The Monte Carlo simulation for free‐radical polymerization that involves simultaneous long‐chain branching and random scission is used to investigate detailed branched structure. The relationship between the mean‐square radius of gyration 〈s²〉 and degree of polymerization P as well as that between the branching density and P is the same for both with and without random scission reactions—at least for smaller frequencies of scission reactions. The 〈s²〉 values were larger than those calculated from the Zimm–Stockmayer (Z‐S) equation in which random distribution of branch points is assumed, and therefore, the Z‐S equation may not be applied for low‐density polyethylenes. The elution curves of size exclusion chromatography were also simulated. The molecular weight distribution (MWD) calibrated relative to standard linear polymers is much narrower than the true MWD, and high molecular weight tails are clearly underestimated. A simplified method to estimate the true MWD from the calibrated MWD data is proposed. The MWD obtained with a light scattering photometer in which the absolute weight‐average molecular weight of polymers at each retention volume is determined directly is considered a reasonable estimate of the true MWD. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2960–2968, 2001     

Simulation model for the molecular weight distribution in emulsion polymerization

A Monte Carlo simulation model for the kinetics of emulsion polymerization is proposed. In the present model, the formation of each polymer molecule is simulated by the use of only a couple of probability functions; therefore, the calculation can be handled well even on personal computers. It is straightforward to account for virtually any kinetic event, such as the desorption of oligomeric radicals and chain length dependence of kinetic parameters, and as a consequence very detailed information such as the full distributions of the dead polymer molecular weights and the macroradicals among various polymer particles can be obtained. When bimolecular terminations are the dominant chain stoppage mechanism, the instantaneous molecular weight distribution (produced in a very small time interval) becomes broader than that for homogeneous polymerizations due to a higher possibility that short and long polymer radicals react with each other if bimolecular reactions are fast enough. The increase in the polydispersity of the MWD is fairly large, especially when bimolecular termination by disproportionation is significant; however, the gel permeation chromatography (GPC) may not be a suitable analytical technique to detect such broadening since oligomeric peaks may not be observed in the elution curve. The present simulation method provides greater insight into the complicated phenomena of emulsion polymerizations. © 1995 John Wiley & Sons, Inc.     

脉冲激光引发自由基聚合的动力学研究

处理了无链转移时脉冲激光引发自由基聚合中的动力学问题:推导出聚合产物数均和重均分子量的严格数学表达式,给出了链自由基、死聚物及总的聚合产物的归一化的分子量分布函数,计算结果表明:随着单体转化率的上升,各种分子参数,例如数均和重均分子量,以及多分散指数的数值周期性地振荡,且振幅逐渐下降,分子量分布曲线则包含一些特征峰,且随着每次脉冲激光产生的初级自由基浓度的降低,分布曲线峰的数目增加,另外,与歧化终止相比,偶合终止使产物的分子量分布略为变窄.     

Dual bimodal polyethylene prepared by intercalated silicate with nickel diimine complex

The ethylene polymerization was catalyzed by the intercalated montmorillonite with the nickel complex, [ArN?C(Me)? C(Me)?NAr]NiBr₂ (Ar = 2,6‐C₆H₃ (i‐Pr)₂). Polymer with low melting point and high molecular weight was produced at the early stage of polymerization followed by formation of polymer with high melting point and low molecular weight. It is proposed that the gallery of silicate lowers the propagation rate of polymerization and frequency of “chain walking” process of nickel complex anchored inside the gallery, which produces polymer with low molecular weight and low branching, whereas the nickel complex immobilized on the surface of silicate generates polymer with high molecular weight and high branching. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5506–5511, 2005     

Branching kinetics in copolymerization of styrene with a chain-transfer monomer

In an earlier work it was shown that a random long-chain branching structure can be incorporated in polystyrene by copolymerizing styrene with a small amount of monomer that contains a chain transfer group. The use of vinylbenzylthiol as the chain transfer monomer produced a polystyrene with low number-average molecular weight and a degree of branching lower than expected. In this study polymerization kinetics were used to compute the theoretical molecular weight and degree of branching. The results show that if the chain-transfer constant of the chain transfer monomer is as high as that for vinylbenzylthiol the expected molecular weight and degree of branching will indeed be as low as those found experimentally. The theory also predicts that if the chain transfer constant is near one a highly branched bushy structure will result.     

Determination of Monomer Transfer Constants in Emulsion Polymerization

The monomer transfer constant, C_m can be determined from the chain length distribution (CLD) under conditions in which the monomer transfer reaction rate is much larger than the other chain termination processes. Such reaction conditions are feasible in emulsion polymerization where bimolecular termination reactions are relatively less important. We conducted theoretical investigations aimed at finding the necessary reaction conditions to apply the CLD method to emulsion polymerization. The number of polymer chains per polymer particle needs to be large enough in order to keep the effects of unknown chain lengths to a minimum, i.e., the unknown chains formed during the nucleation period and those which stop growing when the polymerization is stopped for sampling. In emulsion polymerization, the polymer concentration at the polymerization locus is higher than the corresponding bulk polymerization as long as monomer droplets exist, and the polymer transfer reaction may possess significant effects under conditions where monomer transfer reactions are important. The Monte Carlo (MC) simulation results have shown that although the CLD profile becomes broader due to the polymer transfer reactions, they do not significantly change the slope, from which C_m is determined. According to the present simulation results, the CLD method is considered applicable even when the polymer transfer reaction cannot be neglected. The MC simulation method can be used to find the experimental conditions where the CLD method is applicable.     

High‐density polyethylene fractionation with supercritical propane

During the development of column extraction techniques, two methods of separation were identified. The first method is based on altering polymer solubility by varying the ratio of solvent in a solvent/nonsolvent mixture at a constant temperature above the polymer melting point (gradient solvent elution fractionation). This method fractionates polymers according to molecular weight. The second method is based on altering polymer solubility by varying solvent temperature (temperature rising elution fractionation—TREF). TREF fractionates semicrystalline polymers with respect to their crystallizability, independently of molecular weight effects. In the present article, supercritical propane will be used to fractionate a high‐density polyethylene sample by molecular weight and short chain branching. The main advantage of supercritical fluid fractionation is that large polymer fractions with narrow molecular weight distributions (isothermal fractionation) or narrow short chain branching distributions (isobaric fractionation) can be obtained without using hazardous organic chlorinated solvents. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 553–560, 1999     

Short-chain branching in γ-radiation-induced polymerization of ethylene

In an attempt to elucidate the mechanism of chain-branch formation in the polymerization of ethylene, the effect of reaction conditions on short-chain branching in γ-radiationinduced polymerization of ethylene was investigated by using infrared spectroscopy. The concentration of methyl groups, i.e., the frequency of short-chain branching, increases with temperature and pressure and is independent of ethylene conversion to polymer and radiation intensity. The number of methyl groups per polymer molecule increases almost proportionally with the degree of polymerization. These facts indicate that short-chain branching occurs mainly by the mechanism of intramolecular hydrogen transfer. The effect of pressure on the rate of chain branching can be postulated by considering the transition state to be six-membered rings in hydrogen transfer reactions. The activation energy of chain branching is found to exceed that of propagation by 6 kcal./mole.