Detailed Structural Analysis of the Hyperbranched Polymers Formed in Self‐Condensing Vinyl Polymerization

2019

Processes

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Design and control of hyperbranched (HB) polymer architecture by way of reactor operation is key to a successful production of higher-valued HB polymers, and it is essential in order to clarify the fundamental structural characteristics formed in representative types of reactors. In this article, the irreversible step growth polymerization of AB2 type monomer is investigated by a Monte Carlo simulation method, and the calculation was conducted for a batch and a continuous stirred-tank reactor (CSTR). In a CSTR, a highly branched core region consisting of units with large residence times is formed to give much more compact architecture, compared to batch polymerization. The universal relationships, unchanged by the conversion levels and/or the reactivity ratio, are found for the mean-square radius of gyration Rg2, and the maximum span length LMS. For batch polymerization, the g-ratio of Rg2 of the HB molecule to that for a linear molecule conforms to that for the random branched polymers represented by the Zimm-Stockmayer equation. A single linear equation represents the relationship between Rg2 and LMS, both for batch and CSTR. Appropriate process control in combination with the chemical control of the reactivity of the second B-group promises to produce tailor-made HB polymer architecture.

Section: Batch Polymerizationmentioning

confidence: 90%

Universal Relationships in Hyperbranched Polymer Architecture for Batch and Continuous Step Growth Polymerization of AB2-Type Monomers

2019

Processes

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“…Theory Simul. 2020, 29,1900057 For perfect dendron polymers, the following linear relationship was found [11,12] Rg L 0.5 2 for perfect dendrons…”

Section: Relationship Between Rg 2 and L Msmentioning

confidence: 99%

“…Interestingly, a ≈ 0.18 holds true also for the hyperbranched polymers formed in a continuous stirred-tank reactor (CSTR), for which formed branched architecture is much more compact compared with that formed in a batch reactor. [11,12] At present, the origin of the present linear relationship is an open question. Why does a linear relationship apply for various types of branched architecture?…”

Section: Relationship Between Rg 2 and L Msmentioning

confidence: 99%

“…Hyperbranched polymers formed in step-growth polymerization of AB 2 -type monomer with/without substitution effect, conducted in a batch reactor or in a CSTR 0.18 [12] Hyperbranched polymers formed in self-condensing vinyl polymerization (SCVP) conducted in a batch reactor or in a CSTR 0.18 [11] Perfect dendron 0.5 [11,12]…”

Section: Polymer Typementioning

confidence: 99%

“…In addition to Rg 2 , the maximum span length L MS , which is the longest end-to-end path length represented by the number of monomeric units, is considered. [6,[9][10][11][12] For linear chains, L MS is directly equal to the chain length. It is expected that the magnitude of L MS has a significant effect on Rg 2 , and in this article, a linear relationship between Rg 2 and L MS will be reported, as already found for the hyperbranched polymers [11,12] and for the long-chain branched polymers with a heterogenous distribution of branch points.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Random Branching of Polymer Chains with Schulz–Zimm Distribution. 2. Radius of Gyration and Maximum Span Length

Macro Theory & Simulations

2020

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Mean‐square radius of gyration Rg2 and the maximum span length LMS of each polymer molecule are investigated for the random branching of primary chains that follow the Schulz–Zimm distribution, by using the Monte Carlo simulation method. It is found that the expected g‐ratio of Rg2 of the branched molecule to that of a linear molecule for a given number of branch points k does not change with the branching density. The expected g‐ratio becomes larger for the primary chains with broader distribution. An approximate formula for the relationship between g‐ratio and k that accounts for the distribution breadth is proposed. The relationship between the weight fraction of the maximum span chain LMS/(degree of polymerization) and k shows the analogous behavior with that for g‐ratio and k. The magnitude of Rg2 is proportional to LMS, with Rg2 = 0.18 LMS, irrespective of the breadth of the primary polymer chain length distribution.

Dimension of heterogeneous network architecture formed in emulsion cross‐linking copolymerization

2023

Can J Chem Eng

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The mean‐square radius of gyration Rg2 and the graph diameter D of highly heterogeneous network polymers formed in emulsion vinyl/divinyl copolymerization are investigated to find a linear relationship, Rg2 = a D. The proportionality coefficient, a, is dominated by the cycle (circuit) rank, kc, or the number of intramolecular cross‐links. The magnitude of a is slightly larger than that for the random cross‐linked network polymers, but the functional form of a (kc) is simply proportional to that for the random networks proposed earlier. This relationship makes it possible to determine Rg2 based on D and kc, enabling quick estimation of Rg2 for large network polymers. It is found that the contraction factor g of the present heterogeneous network polymer is larger than that for the homogeneous networks formed through random cross‐linking of polymer chains. The ratio of these two contraction factors is kept constant, irrespective of the magnitude of kc.