Molecular weight distribution of emulsion‐polymerized polyethylene

2005

Macro Materials & Eng

Summary: The molecular weight distribution (MWD), formed in emulsion polymerization that involves the polymer transfer reaction during Interval II, may approach the power‐law distribution as polymerization proceeds. The power exponent, α, of the weight fraction distribution W(M) = M−α conforms to the relationship, α = 1/Pb, where Pb is the probability that the chain end is connected to a backbone chain. The MWD of emulsion‐polymerized polyethylene reported in literature agrees reasonably well with the relationship, W(M) = M−α with α = 1/Pb. This simple relationship could be used to estimate the Pb value from the MWD data, possibly leading to determining the polymer transfer constant under well‐designed experimental conditions. Because α > 1, the number‐average MW always approaches a finite value, but the weight‐ and higher order‐averages of MWD may continue to increase as the particle grows without limit depending on the magnitude of Pb. The power‐law distributions are self‐similar, possessing the nature of fractals and lacking a characteristic scale. The i‐th moment of the MWD for the present reaction system continues to increase without limit during Interval II for Pb ≥ 1/i.Molecular weight distribution of the emulsion‐polymerized polyethylene.magnified imageMolecular weight distribution of the emulsion‐polymerized polyethylene.

“…[19,29,30] The solid curve of Figure 10 shows an example of the reported MWD profile. [19] The following conditions were reported for the experiment.…”

Section: Moments Of the Molecular Weight Distributionmentioning

confidence: 99%

Section: Moments Of the Molecular Weight Distributionmentioning

confidence: 99%

Section: Moments Of the Molecular Weight Distributionmentioning

confidence: 99%

Section: Moments Of the Molecular Weight Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scale‐Free Power‐Law Distribution of Emulsion‐Polymerized Branched Polymers: Power Exponent of the Molecular Weight Distribution

2005

Macro Materials & Eng

Monte carlo simulation of emulsion polymerization — linear, branched, and crosslinked polymers

1995

Acta Polymerica

A new Monte Carlo approach for the kinetics of emulsion polymerization is discussed. The diameters of polymer particles produced in emulsion polymerizations are in the submicrometer range; therefore, it is straightforward to simulate the formation processes of all polymer molecules in each polymer particle by application of the Monte Carlo method with a well-designed algorithm. In the Monte Carlo technique, virtually any kinetic event, such as the desorption of oligomeric radicals, chain-length-dependent reaction kinetics, branching and crosslinking reactions, can be accounted for. In principle, neither idealizations nor approximations, which are usually required in the analytical approaches, are not necessary. As a consequence one can observe the structure of each polymer molecule directly; therefore, very detailed information can be obtained easily, including the full distributions of the dead and live polymer molecular weights, and the spatial distribution of the branched and crosslinked polymer chains in the case of nonlinear polymerizations. Monte Carlo simulations promise to provide greater insight into the complex molecular processes which occur during emulsion polymerizations.

Model‐Based Reactor Design to Control Hyperbranched Polymer Architecture

Macro Reaction Engineering

2018

L is the linearly incorporated unit, one of whose two B's has reacted, and D is the dendritic unit in which both B's have already reacted. The reaction rate constant, k T is for the reaction between an A group and a B in the T unit, while k L is for the reaction between an A and a B in the L unit. The reactivity of the second B group can be represented by the reactivity ratio, r = k L /k T . The reaction systems in which the magnitude of r can be controlled from zero to infinity have been reported. [6] The DB of an HB polymer without an L unit is unity (DB = 1), and DB = 0 for the linear structure, consisting of L units with a single T unit at the chain end. The HB polymers with DB = 1 can be obtained for r = ∞. On the other hand, however, because of the randomness in the location of T units, various types of HB polymer structure can be formed even with DB = 1, as shown in Figure 2 of ref.[6]. One cannot obtain perfect dendrons even with r = ∞. The expected mean-square radii of gyration for the HB polymers having a specific chain length (degree of polymerization (DP), represented by the symbol, P in this article) are much larger than those for perfect dendrons. [7] In the kinetically controlled polymerization systems, the molecular architecture can be controlled by the residence time distribution of the given polymerization process. An example of the reactor operation to obtain HB polymers with higher DB values is the slow monomer addition method. [5,[8][9][10] In this method, monomers are added very slowly, and the slowly added monomers tend to react with the terminal groups of the HB polymers already formed, resulting in enhancing the DB values. The limiting DB of the large polymer limit, lim DB P→∞ is unchanged during the whole course of polymerization in batch polymerization, irrespective of the magnitude of r. [7] In the case of equal reactivity of both B groups, i.e., with r = 1, the limiting value is 0.5 for batch polymerization. [11][12][13] On the other hand, the value of DB for the ideal slow monomer addition method is A Monte Carlo simulation method, based on the random sampling technique in which a large number of polymers are sampled from the final product, is proposed for the continuous tanks-in-series process. The effect of the sequence of tanks with different sizes is considered for the irreversible step polymerization of AB 2 -type monomer. It is found that the tank sequence starting from a large tank followed by a number of smaller tanks is suitable to produce compact hyperbranched polymers, whose mean-square radii of gyration are much smaller than those formed in batch polymerization. Analytic formulas of the average molecular weights are presented for the tanks-in-series processes, including the post-processes to make the molecular weight distribution narrower by removing residual monomer and by introducing multifunctional core molecules. The present investigation enhances fundamental knowledge that would be useful for the model-based reactor design to control detailed branched architecture of...