Average functionalities of macromolecules in stepwise polyfunctional polymerization

General expressions are derived for the average functionalities of macromolecules in stepwise polyfunctional polymerization, in particular for systems composed of monomers endowed with both A and B coreactive functional groups. Knowing the molecular distribution functions the weight average functionalities are calculated directly, on the basis of a new method using the propagation expectation.     

Substitution effects and average molecular weights in non-linear stepwise polymerization

The authors' method of calculating average molecular weights, in the pre-gel region, for stepwise polymerization of polyfunctional monomers, is extended to systems where the functional groups exhibit unequal reactivities induced by substitution effects in the course of the reaction.     

Estimation of molecular weight distribution parameters for free-radical polymerization

A method is described which allows the precise estimation of molecular weight distribution parameters p and A which pertain to free-radical polymerizations. Thus, expressions are developed which allow the estimation of (1 ? p) by means of a programmable calculator using molecular weight distribution data derived from GPC. Values of A may subsequently be calculated by means of a plot of one of the expressions given. Values of (1 ? p) and A obtained in this paper were checked using theoretical values as well as by a comparison between calculated and observed values. The agreement between calculated and theoretical or experimental values indicates that the method presented for the estimation of (1 ? p) and A is both reliable and relatively rapid. Previously reported methods for the estimation of (1 ? p) and A have involved curve-fitting trial calculations as well as more precise interpolation procedures. However, the latter are based on single-peak maximum values.     

Intrinsic unequal reactivity and average molecular weights in non-linear stepwise polymerization

The general expressions of average molecular weights in the pre-gel region, for stepwise polymerization of polyfunctional monomers endowed with both A and B coreactive functional groups, are extended to systems where some or all of the B groups react at different rates. The method of calculation is always based on the propagation expectation and the presence of by-product in the reactions is taken into account.     

Calculation method of molecular weight averages in polymerization with chain-length-dependent termination

A systematic method for calculating the molecular weight distribution moments in free radical polymerization where termination rate depends on the size of the participating radicals, is presented. The central part of the method is the evaluation of the distribution of termination rates in the balance equations. From an adopted functional form of the termination rate constant, the moment equations are derived. For evaluating the moments of the termination rate distribution an approximate reconstruction of the radical chain length distribution using Laguerre polynomials is proposed. The calculation method can handle termination by disproportionation and combination simultaneously and allows easily to take into account diffusioncontrolled initiation, propagation and chain transfer reactions. The usefulness of the method is illustrated by simulating the bulk polymerization of methyl methacrylate and styrene. The calculated results of conversion, molecular weight averages (M _n,M _w,M _z and M _z+1) and polydispersity are in good agreement with the reported experimental data.     

Bulk polymerization of styrene in presence of polybutadiene: Calculation of molecular macrostructure

In our previous publication the detailed molecular macrostructure generated in a solution polymerization of styrene (St) in the presence of polybutadiene (PB) at 60°C, was theoretically calculated. In this work, an extended kinetic mechanism that incorporates monomer thermal initiation, chain transfer to the rubber, chain transfer to the monomer, and the gel effect is proposed, with the aim of simulating a bulk high-impact polystyrene (HIPS) process. The mathematical model enables the calculation of the bivariate weight chainlength distributions (WCLDs) for the total copolymer and for each of the generated copolymer topologies and the univariate WCLDs for the free polystyrene (PS), the residual PB, and the crosslinked PB topologies. These last topologies are characterized by the number of initial PB chains per molecule; copolymer topologies are characterized by the number of PS and PB chains per molecule. The model was validated with published literature data and with new pilot plant experiments that emulate an industrial HIPS process. The literature data correspond to a dilute solution polymerization at a constant low temperature with chemical initiation and a bulk polymerization at a constant high temperature with thermal initiation. The new experiments consider different combinations of prepolymerization temperature, initiator concentration, and solvent concentration. One of the main conclusions is that most of the initial PB is transformed into copolymer. For example, for a prepolymerization temperature of 120°C with addition of initiator, the experimental measurements indicate that the final total rubber mass is approximately three times higher than the initial PB. Also, according to the model predictions, the final weight fractions are: free PS, 0.778; graft copolymer, 0.220; initial PB, 0.0015; and purely crosslinked PB, 0.0005. The final graft copolymer exhibits the following characteristics: average molecular weights, M _n,C = 492,000 and M _w,C = 976,000; average weight fraction of St, 0.722; and average number of PS and PB branches per molecule, 5.19 and 1.13, respectively. © 1996 John Wiley & Sons, Inc.     

Calculation of molecular weight distribution in styrene polymerization initiated by a binary initiator system

A computational scheme is presented for the calculation of molecular weight distribution in styrene polymerization initiated by a binary initiator system. In this paper, the method of finite molecular weight moment is presented by calculation of the polymer chain length distribution. This method is compared with the method of integrating an infinite number of polymer population balance equations. The results of the two methods show a reasonably good agreement. It is possible to produce polymer having the same molecular weight distribution.     

Absolute online monitoring of a stepwise polymerization reaction: Polyurethane synthesis

The feasibility of using a recently introduced method for continuous, absolute online monitoring for step‐growth polymerization was demonstrated, and polyurethane synthesis was chosen for the demonstration. The previously reported use of this method was for monitoring free‐radical initiated chain‐growth polymerization. The technique involves continuously withdrawing a small stream of reaction liquid from the polymerization reactor and pumping it through a series of light scattering and viscosity detectors. This permits the absolute weight‐average molecular weight and reduced viscosity to be simultaneously monitored as the reaction proceeds. The final weight‐average molecular weights of the polyurethane samples were compared to the separate light scattering measurements of the final products. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 2070–2077, 2001     

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     

General expressions of average molecular weights in condensation polymerisation of polyfunctional monomers

A new method, using the propagation expectation defined by Case, is presented to compute directly and simply the general expressions of average molecular weights for condensation polymerisation of polyfunctional monomers. In particular, the weight average molecular weight in systems composed of monomers endowed with both A and B coreactive functional groups is derived.     

A molecular model for solid-state polymerization of nylon 6

Transport properties of antioxidants in polymers have a very important role in their effectiveness. Lifetime of a product is strongly influenced by the physical loss of the stabilizer. The diffusion coefficient (D) and solubility (S) of Irganox 1010 in low-density polyethylene (LDPE) were studied at 45 and 80°C, changing the physical state of the antioxidant in the additive source. Irganox 1010 is a polymorphous material; its actual morphology depends on the thermal history. It was proved that the morphology of the additive has a determining effect on the measured D and S values. Contradictions in the literature data can be explained by the differences in the experimental conditions, i.e., in the physical state of the penetrant in the additive source and the crystallinity and orientation of the polymer.     

Synthesis of well-defined star-branched polymers by stepwise iterative methodology using living anionic polymerization

This article reviews the synthesis of regular and asymmetric star-branched polymers with well-defined structures by methodologies using living anionic polymerization, especially focusing on the synthetic approaches accessible for precisely controlled architectures of star-branched polymers concerning molecular weight, molecular weight distribution, arm number, and composition. The reason for selecting living anionic polymerization from many living/controlled polymerization systems so far developed is that this living polymerization system is still the best to meet the strict requirements for the precise structures of star-branched polymers. Furthermore, we herein mainly introduce a novel and quite versatile stepwise iterative methodology recently developed by our group for the successive synthesis of many-armed and multi-compositional asymmetric star-branched polymers. The methodology basically involves only two sets of the reaction conditions for the entire iterative synthetic sequence. The reaction sequence can be, in principle, limitlessly iterated to introduce a definite number of the same or different polymer segments at each stage of the iteration. As a result, a wide variety of many-armed and multi-compositional asymmetric star-branched polymers can be synthesized.     

自由基聚合制备甲基丙烯酸甲酯-苯乙烯嵌段共聚物

以偶氮二异丁腈为引发剂,乙二硫醇（EDT）为链转移剂进行甲基丙烯酸甲酯（MMA）的自由基聚合,得到了含有残余巯基的聚甲基丙烯酸甲酯大分子链转移剂（HS-PMMA）,继而以HS-PMMA作为大分子链转移剂进行苯乙烯的自由基聚合,采用普通自由基聚合方法合成了结构可以设计的嵌段共聚物。     

General expressions of average molecular weights in polycondensation of polyfunctional monomers involving condensation by-product

In this paper, the general expressions of average molecular weights for condensation polymerisation involving eliminat species are derived in the pre-gel region especially for systems composed of monomers endowed with both A and B coreactive functional groups. The weight average molecular weights are calculated directly according to a new method using the propagation expectation.     

Optimal operation of ethylene polymerization reactors for tailored molecular weight distribution

This work presents a comprehensive steady‐state model of the high‐pressure ethylene polymerization in a tubular reactor able to calculate the complete molecular weight distribution (MWD). For this purpose, the probability generating function technique is employed. The model is included in an optimization framework, which is used to determine optimal reactor designs and operating conditions for producing a polymer with tailored MWD. Two application examples are presented. The first one involves maximization of conversion to obtain a given MWD, typical of industrial operation. Excellent agreement between the resulting MWD and the target one is achieved with a conversion about 5% higher than the ones commonly reported for this type of reactor. The second example consists in finding the design and operating conditions necessary to produce a polymer with a bimodal MWD. The optimal design for this case involves a split of the initiator, monomer, and modifier feeds between the main stream and two lateral injections. To the best of our knowledge, this is the first work dealing with the optimization of this process in which a tailored shape for the MWD is included. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Influence of irradiation parameters on the polymerization of ceramic reactive suspensions for stereolithography

Stereolithography is an additive manufacturing process which makes it possible to fabricate useful complex 3D ceramic parts, with a high dimensional resolution and a good surface finish. Stereolithography is based on the selective UV polymerization of a reactive system consisting in a dispersion of ceramic particles in a curable monomer/oligomer resin. In order to reach a homogeneous polymerization in the green part, and to limit the risk of cracking and/or deformation during subsequent stages of debinding and sintering due to internal stresses, the influence of various fabrication parameters (laser power, scanning speed, number of irradiations) on the degree of polymerization was investigated. In addition, the impact of the irradiation of the subsequent upper layers onto the previously deposited and irradiated layers was evaluated. The degree of conversion was determined by Fourier Transform Infrared Spectroscopy (FTIR). Raman spectroscopy was also used and a brief comparison between these two methods is given.