Controllable Power-Law Distribution in Free-Radical Vinyl/Divinyl Copolymerization by Using a Continuous Stirred Tank Reactor,Macromolecular Theory and Simulations

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Controllable Power-Law Distribution in Free-Radical Vinyl/Divinyl Copolymerization by Using a Continuous Stirred Tank Reactor
Macromolecular Theory and Simulations ( IF 1.8 ) Pub Date : 2021-07-10 , DOI: 10.1002/mats.202100030
Hidetaka Tobita ₁

Affiliation

It has been believed that the power-law molecular weight distribution is formed at the gel point, and the power exponent falls in a category of universality in critical phenomena, and therefore, it cannot be changed. It is found that the power-law weight fraction distribution W(P) ∝ P^−α, capable of controlling the exponent α, can be synthesized by using a continuous stirred tank reactor (CSTR). The exponent is governed by a single non-dimensional parameter, ξ that is equivalent to the Damköhler number, representing the ratio of timescales between the mean residence time and the crosslinking reaction. For small ξ’s, the non-critical transition of the weight-average molecular weight to infinity is observed, and the exponent approaches α = 2. For large ξ’s, the system shows similar behavior to that in a closed system and the exponent is the same as for the batch polymerization, with α = 1.5. At the gel point, the product of the average crosslinking density

\bar{ρ}

and the weight-average primary chain length

{\bar{P}}_{wp}

satisfies the relationship,

\bar{ρ} {\bar{P}}_{wp} ≅ 0.43 ξ / (1 + ξ) + 0.57

. The crosslinking density of the gel molecule at the gel point is found to be

ρ_{g} = 2 / {\bar{P}}_{wp}

.

中文翻译：

使用连续搅拌釜反应器控制自由基乙烯基/二乙烯基共聚中的幂律分布

人们一直认为，幂律分子量分布是在凝胶点形成的，幂指数属于临界现象中的普适性范畴，因此不能改变。发现幂律重量分数分布W ( P ) ∝ P ^{- α}能够控制指数α，可以通过使用连续搅拌釜反应器 (CSTR) 合成。指数由一个单一的无量纲参数ξ 控制，它相当于 Damköhler 数，代表平均停留时间和交联反应之间的时间尺度比。对于小ξ的，观察到重均分子量到无穷大的非临界转变，指数接近α = 2。对于大的ξ，系统表现出与封闭系统相似的行为，指数是与间歇聚合相同，α = 1.5。在凝胶点，平均交联密度的乘积