concepts of chemical recycling: part 1...log-mmd evolution frp de smit et. al., reac. chem. eng....

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This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement N° 820687.

The MMAtwo project results presented reflect only the author's view.

The Commission is not responsible for any use that may be made of the information it contains.

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Second Generation MethylMethAcrylate

Concepts of Chemical Recycling:

Part 1

MMAtwo

workshop

15/09/2020

Dr. Yoshi W. Marien

DOI: 10.13140/RG.2.2.36058.98241

https://www.researchgate.net/deref/http%3A%2F%2Fdx.doi.org%2F10.13140%2FRG.2.2.36058.98241?_sg%5B0%5D=K3CXEzc_He2M2nq3y1N2I5Q5H_5iy7GNxRZD1ahp9BM56bS3vH1K-Oc9edB4_bP20z_iv7bDalJOY2WV9fGBphavoQ.wzSCbbt2MiKRxbMuP620RQWUNgn5dkoAqRcfkVvtOZ5scs07wSFNhxHTrKq4KjMrMXdF-gUOfNguRvWekoT77w

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2MMAtwo workshop – 15/09/2020

Introduction

Moens et al., Polymers 2020, 12, 1667

Ragaert et. al., Waste Management 2017, 69, 24

Raw materials

Synthesis of

polymeric materials

Polymer processing

Application and

service life

Mechanical

recycling

Chemical

recycling

Re-usage

Plastic/polymer

waste

Landfilling Energy recovery

Energy

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3

Outline

• Introduction

• Overview of depolymerization kinetic models

• Application of matrix based kinetic Monte Carlo to PMMA depolymerization

• The role of defects & functionalities to initiate depolymerization

• How defects & functionalities are introduced during free radical polymerization

• Modeling of free radical polymerization

• Modeling of depolymerization

• Conclusions

MMAtwo workshop – 15/09/2020

4


4

• Global conversion based models

• Global average chain length based models

• Elementary reaction step based models


Depolymerization kinetic

models

5



𝑑𝛼

𝑑𝑡= 𝑘𝑓 𝛼 = 𝐴 𝑒𝑥𝑝 −

𝐸

𝑅𝑇𝑓 𝛼 𝜶: conversion

𝑑𝛼

𝑑𝑇=𝐴

𝛽𝑒𝑥𝑝 −

𝐸

𝑅𝑇𝑓 𝛼

ln 𝛽𝑑𝛼

𝑑𝑇= ln 𝐴 𝑓 𝛼 −

𝐸

𝑅𝑇

𝑑 ln𝑑𝛼𝑑𝑇

𝑑1𝑇 𝛼

= −𝐸

𝑅 𝛼+

𝑑 ln 𝑓 𝛼

𝑑1𝑇

𝛼

𝑑𝛼

𝑑𝑡=𝑑𝛼

𝑑𝑇

𝑑𝑇

𝑑𝑡=𝑑𝛼

𝑑𝑇𝛽

Global conversion based

models


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6


models• Global conversion based models


𝑑1𝑇

𝛼

= −𝐸

𝑅 𝛼+

𝑑 ln 𝑓 𝛼

𝑑1𝑇

𝛼


ln 1 −1

𝑥𝑛,0− ln 1 −

1

𝑥𝑛= 𝑘𝑖𝑟𝑡


➢ Deterministic

➢ Stochastic


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7

Deterministic elementary

reaction based models

Population balances

𝑑[𝑃𝑖]

𝑑𝑡= − 𝑖 − 1 𝑘𝑓 𝑃𝑖 +⋯ 𝑖 = 1, 𝑖𝑚𝑎𝑥

Balances for moments only

𝑑µ𝑚

𝑑𝑡= −𝑘𝑓(µ𝑚+1 − µ𝑚) + ⋯ 𝑚 = 0, 1, 2


𝑥𝑛 =µ1

µ0𝑥𝑚 =

µ2

µ1Ð =

𝑥𝑚

𝑥𝑛

𝑃𝑖𝑘𝑓𝑅𝑖−𝑗 + 𝑅𝑗

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8


models• Global conversion based models


𝑑1𝑇

𝛼

= −𝐸

𝑅 𝛼+

𝑑 ln 𝑓 𝛼

𝑑1𝑇

𝛼


ln 1 −1

𝑥𝑛,0− ln 1 −

1

𝑥𝑛= 𝑘𝑖𝑟𝑡


➢ Deterministic

➢ Stochastic

✓ Tree based kinetic Monte Carlo

✓ Matrix based kinetic Monte Carlo


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Stochastic elementary

reaction based models• Stochastic sampling of reactions via kinetic Monte Carlo (kMC)

• Probability 𝑃 to sample reaction υ is proportional to its microscopic reaction rate 𝑅 [s-1]

𝑅 υ = 𝑘𝑎𝑝𝑝,𝑀𝐶υ 𝑛𝐴𝑛𝐵

𝑃 υ = 𝑅 υ

υ

𝑅 υ

−1

υ=1

υ=μ−1

𝑃 υ < 𝑟1 ≤

υ=1

υ=μ

𝑃 υ

• Update of reaction time via

𝑡 = 𝑡 +𝑙𝑛

1

𝑟2

συ 𝑅 υ


𝑟1

Van Steenberge et al., Macromolecules 2012, 45, 8519

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Tree based kMC

MMAtwo workshop – 15/09/2020 Van Steenberge et al., Chem. Eng. Sci. 2014, 110, 185

Trigilio et. al., Ind. Eng. Chem. Res. 2020, doi.org/10.1021/acs.iecr.0c03888

1

# # # #####

2 3

4 5 6 7

i=1 i=3 i=4 i=5 i=6 i=7i=2 i=8

Chain length tree

# # # #####

1

2 3

4 5 6 7

C=0 C =2 C=3 C=4 C=5C=1

Copolymer composition tree

Monomer unit A Monomer unit B

https://doi.org/10.1021/acs.iecr.0c03888

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11

Matrix based kMC


Propagation event with monomer unit A

Propagation event with monomer unit B

Activation eventDeactivation event

Termination event

Copolymer CompositionReaction event history

Lab

eled

co

po

lym

er c

hai

n

Deadcopolymer

Dormantcopolymer

Van Steenberge et al., Macromolecules 2012, 45, 8519



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12

Tree vs. matrix based

kMC


Complexity and macromolecular structural detail

log (molar mass (kg mol-1))

w (

log m

ola

r m

ass)

Univariate tree based Bivariate tree based Matrix based

Num

ber

Fra

ctio

n (

-)

Num

ber

Fra

ctio

n (

-)

m / z (Da)

Time (h)

Mm

[kg m

ol-1

]

3D 2D

D‘hooge et al., Prog. Polym. Sci. 2016, 58, 59



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13

Outline

• Introduction







• Conclusions


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PMMA depolymerization

reactions

Initiation of depolymerization depends on the presence of structural defects and

functionalities → also chain-by-chain visualization of polymerization needed


De Smit et. al., Reac. Chem. Eng. 2020, 10.1039/D0RE00266F

https://doi.org/10.1039/D0RE00266F

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MMA free radical

polymerization reactionsInitiator dissociation

Chain initiation initiator radical Chain initiation monomeric radical

Propagation

Chain transfer to monomer

Termination

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Diffusional limitations in

FRP

Buback et. al., Macromol. Chem. Phys. 1994, 195, 2117

Achilias et. al., Macromol. Theory. Simul. 2007, 16, 319

D‘hooge et al., Macromol. React. Eng. 2009, 3, 185

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Glass effect

1

𝑘𝑝,𝑎𝑝𝑝𝑖

=1

𝑘𝑝,𝑐ℎ𝑒𝑚𝑖

+1

𝑘𝑝,𝑑𝑖𝑓𝑓𝑖

𝑘𝑝,𝑑𝑖𝑓𝑓𝑖 = 𝑘𝑝,𝑑𝑖𝑓𝑓 = 4𝜋𝜎𝑝𝑁𝐴𝐷𝑡𝑟,𝑀

𝐷𝑡𝑟,𝑀 = 𝐷𝑀,0 𝑒−𝐸𝑎,𝑀𝑅𝑇 −𝑉𝑀

∗𝑀𝑗,𝑀

𝑤𝑚𝑀𝑗,𝑀

+𝑤𝑝𝑀𝑗,𝑀

Τ𝑉𝐹𝐻 𝜆

Parallel encounter pair model

Smoluchowski equation

Free volume theory

Vrentas et al., J. Polym. Sci. Part A-2, Polym. Phys. 1984, 22, 459

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Gel effect

for 𝑖 < 𝑖gel and 𝑖 < 𝑖SL: 𝑘t,iiapp

= 𝑘t,11app

𝑖−𝛼s

for 𝑖 < 𝑖gel and 𝑖 ≥ 𝑖SL: 𝑘t,iiapp

= 𝑘t,11app

𝑖SL𝛼l−𝛼s𝑖−𝛼l

for 𝑖 ≥ 𝑖gel and 𝑖 < 𝑖SL: 𝑘t,iiapp

= 𝑘t,11app

𝑖gel

𝛼gel−𝛼s𝑖−𝛼gel

for 𝑖 ≥ 𝑖gel and 𝑖 < 𝑖SL: 𝑘t,iiapp

= 𝑘t,11app

𝑖SL𝛼l−𝛼s𝑖

gel

𝛼gel−𝛼l𝑖−𝛼gel

Johnston-Hall et al., J. Polym. Sci. Part A: Polym. Chem. 2008, 46,

3155

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Cage effect

𝑓𝑎𝑝𝑝 =𝐷𝐼

𝐷𝐼 + 𝐷𝑡𝑒𝑟𝑚

𝐷𝐼 = 𝐷0,𝐼 𝑒−𝐸𝑎,𝐼𝑅𝑇 −

Τ𝑤𝑚𝑉𝑚∗𝜉𝑐𝑝 𝜉𝑚𝑝 + 𝑤𝑝𝑉𝑝

∗𝜉𝑐𝑝Τ𝑉𝐹𝐻 𝜆

Apparent initiator efficiency as a function of monomer conversion

Free volume theory

Buback et al., Macromol. Chem. Phys. 1994, 195, 2117

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Importance diffusional

limitations in FRP

Intrinsic + gel effect + glass effect + cage effect



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363 K and [AIBN]0:[MMA]0=0.003 343 K and [AIBN]0:[MMA]0=0.003

323 K and [AIBN]0:[MMA]0=0.003 323 K and [AIBN]0:[MMA]0=0.002

Model validation FRP



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log-MMD evolution FRP



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Depolymerization at 625 K

PMMA made via FRP at 343 K

and with [AIBN]0= 0.027 mol L-1



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Evolution of functionalities

Polymerization Depolymerization



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25

Outline

• Introduction







• Conclusions


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Conclusions

• Chemical recycling (depolymerization) allows to recover monomeric building

blocks

• Depolymerization processes are characterized by a large number of competing

elementary reactions such as fission, scission and termination reactions

• Elementary reaction step based models are key to improve the knowledge of

depolymerization mechanisms and kinetics

• Matrix based kinetic Monte Carlo tools allow to track individual chains during both

polymerization and depolymerization

• The initial molar mass distribution and the presence of defects and functionalities

strongly affect the depolymerization kinetics

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Second Generation MethylMethAcrylate

This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement N° 820687.

The MMAtwo project results presented reflect only the author's view.

The Commission is not responsible for any use that may be made of the information it contains.

[email protected]

www.mmatwo.eu

concepts of chemical recycling: part 1...log-mmd evolution frp de smit et. al., reac. chem. eng....

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