The physical meaning of the Avrami equation in oligomer curing reactions

Иржак, Т. Ф.; Mezhikovskii, S.M.; Иржак, В. И.

doi:10.1134/s1560090408070117

Cited by 7 publications

(5 citation statements)

References 1 publication

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“…38 It is reported that all changes in n from 1 to 3 reect the superposition of the homogeneous (in the bulk) and heterogeneous (near the interface) components of crystallization. 39 If n ¼ 0, it indicates that the crystallization has stopped. If the phase separation rate exceeds the crystallization rates, n is close to 3; otherwise, if the crystallization rate is much higher than phase separation n approaches 1.…”

Section: Kinetics Of Crystallization and Degree Of Crystallinitymentioning

confidence: 99%

Unravelling the effects of size, volume fraction and shape of nanoparticle additives on crystallization of nanocomposite polymers

Jabbarzadeh

Halfina

2019

Nanoscale Adv.

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Unravelling the eff ects of size, volume fraction and shape of nanoparticle additives on crystallization of nanocomposite polymers Nanoparticles can be added to polymer melts to make nanocomposites. This may lead to a two-tier crystallization with an initial enhancement of crystallization that depends on the particle shape, and confi nement-induced retardation of crystallization at a later stage that depends on the interparticle free space. This interparticle free space is a function of nanoparticle size and volume fraction and governs the fi nal crystallinity in the confi nement limit. Large scale molecular simulations have revealed the eff ects of particle shape, size and volume fraction.

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Section: Kinetics Of Crystallization and Degree Of Crystallinitymentioning

confidence: 99%

Unravelling the effects of size, volume fraction and shape of nanoparticle additives on crystallization of nanocomposite polymers

Jabbarzadeh

Halfina

2019

Nanoscale Adv.

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“…However, polymerization of polyfunctional monomers proceeds via the microheterogeneous mechanism (reactive oligomers are polymerized via cross‐linked reaction), and the gel effect occurs at low conversions (1–2%) . The kinetics of such polymerization has an expressed auto‐accelerated character, and the Equation is modified to the following form:

\frac{d ([], M)}{[M]} = - d ([], {((), \frac{t}{(1 + δ) \cdot t_{p}})}^{γ}),

where γ is the contrast parameter of the composition, usually γ ≥ 2. Moreover, the monomer conversion ( P ) is described by the Avrami equation, which is widely used to consider polymerization processes:

P ((), t) = ((), 1 - \frac{[M]}{[M_{0}]}) \cdot 100 % = ((), 1 - \exp ({}, - {(\frac{t}{((), 1 + δ) \cdot t_{p}})}^{γ})) \cdot 100 %,

where [ M 0 ] is the initial concentration of the monomer.…”

Section: Main Partmentioning

confidence: 99%

“…However, polymerization of polyfunctional monomers proceeds via the microheterogeneous mechanism (reactive oligomers are polymerized via cross-linked reaction), and the gel effect occurs at low conversions (1-2%). [28,29] The kinetics of such polymerization has an expressed auto-accelerated character, [30] and the Equation (4) is modified to the following form:…”

Section: Mechanism To Control the Photopolymerization Of Uv-curable Compositions By Visible Radiationmentioning

confidence: 99%

Use of photodegradable inhibitors in UV‐curable compositions to form polymeric 2D‐structures by visible light

Mensov

Абакумов

Arsenyev

et al. 2020

J of Applied Polymer Sci

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The process of two‐wave photopolymerization of a UV‐curable composition with an optically degrading inhibitor is considered. By numerical simulation, it is shown that in the composition layer uniformly exposed to UV‐radiation, such systems allow getting segments with different conversion under the action of inhomogeneous visible light. Based on the data on the photopolymerization kinetics of the compositions from triethylene glycol dimethacrylate (TEGDMA) and bisphenol‐A glycidyl dimethacrylate (bis‐GMA) with the UV‐initiator 2,2‐dimethoxy‐2‐phenylacetophenone (DMPA), it was shown that 3,5‐di‐tert‐butyl‐o‐benzoquinone (35Q) with N,N‐dimethylaniline (DMA, “Aldrich”, 99%) can serve as an inhibitor that degrades under action of visible radiation. Combining inhomogeneous visible light generated with a conventional DLP‐projector and uniform UV‐radiation of LED (365 nm) the two‐wave lithographic process was implemented to create polymeric 2D‐structures in 20 μm layer of the compositions from TEGDMA (70)/bis‐GMA (30)/DMPA (0.05 wt%)/35Q (0.5 wt%)/DMA (1 wt%).

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“…There has also been a consistent interest in applying the Avrami model to the kinetics of crosslinking polymerization. The earliest works date back to the 1970s and 1980s [14,15]. Currently, this approach has been utilized in a number papers that have appeared to be inspired by a series of publications by Lu et al [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Problems with Applying the Ozawa–Avrami Crystallization Model to Non-Isothermal Crosslinking Polymerization

Vyazovkin

Galukhin

2022

Polymers

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Ozawa has modified the Avrami model to treat non-isothermal crystallization kinetics. The resulting Ozawa–Avrami model yields the Avrami index (n) and heating/cooling function (χ(T)). There has been a number of recent applications of the Ozawa–Avrami model to non-isothermal crosslinking polymerization (curing) kinetics that have determined n and have used χ(T) in place of the rate constant (k(T)) in the Arrhenius equation to evaluate the activation energy (E) and the preexponential factor (A). We analyze this approach mathematically as well as by using simulated and experimental data, highlighting the following problems. First, the approach is limited to the processes that obey the Avrami model. In cases of autocatalytic or decelerating kinetics, commonly encountered in crosslinking polymerizations, n reveals a systematic dependence on temperature. Second, χ(T) has a more complex temperature dependence than k(T) and thus cannot produce exact values of E and A via the Arrhenius equation. The respective deviations can reach tens or even hundreds of percent but are diminished dramatically using the heating/cooling function in the form [χ(T)]1/n. Third, without this transformation, the Arrhenius plots may demonstrate breakpoints that leads to questionable interpretations. Overall, the application of the Ozawa–Avrami model to crosslinking polymerizations appears too problematic to be justified, especially considering the existence of well-known alternative kinetic techniques that are flexible, accurate, and computationally simple.

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The physical meaning of the Avrami equation in oligomer curing reactions

Cited by 7 publications

References 1 publication

Unravelling the effects of size, volume fraction and shape of nanoparticle additives on crystallization of nanocomposite polymers

Unravelling the effects of size, volume fraction and shape of nanoparticle additives on crystallization of nanocomposite polymers

Use of photodegradable inhibitors in UV‐curable compositions to form polymeric 2D‐structures by visible light

Problems with Applying the Ozawa–Avrami Crystallization Model to Non-Isothermal Crosslinking Polymerization

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