D'hooge, Dagmar

Duchateau, Jan

Hernández Ortiz, Julio César

Marin, Guy

Remerie, Klaas

Reyniers, Marie-Françoise

Schreurs, Fons

Toloza, Carolina

Van Steenberge, Paul

Vaz, Ana Luisa

Ghent University Academic Bibliography

Laboratory for Chemical Technology, Ghent Universityhttp://www.lct.UGent.beA tracking of the complete microstructural evolution of individual polymer chains during polymer modification reactionsJulio César Hernández Ortiz,1 Paul H. M. Van Steenberge,1Jan N. E. Duchateau2, Klass Remerie2, Carolina Toloza2, Ana L. Vaz2, Fons Schreurs2, Marie-Francoise Reyniers1, Guy B. Marin1, Dagmar R. D’hooge1,31ICCK, Chicago, USA, 22/05/20171 Laboratory for Chemical Technology, Ghent Universityhttp://www.lct.UGent.be2 SABIC, PO Box 319 / 6160 AH Geleen, The Netherlands3 Department of Textiles, hent UniversityOutline• Functional polymers• Modeling by kMC• Model development: Module A and Module B• Results (Module A and Module B)• Effect of diffusional limitations• Conclusions2ICCK 2017, Chicago, 21-25 May 20173ICCK 2017, Chicago, 21-25 May 2017Functional polymersSource of free radicals+Monomer4ICCK 2017, Chicago, 21-25 May 2017Mechanism of free-radical induced graftingGrafting “from”5ICCK 2017, Chicago, 21-25 May 2017Mechanism of free-radical induced graftingCrosslinkingCrosslinkingCrosslinkingGrafting “to”Grafting “from”Grafting “to”Homopolymerization6ICCK 2017, Chicago, 21-25 May 2017Mechanism of free-radical induced graftingCrosslinkingCrosslinkingCrosslinkingHomopolymerizationGrafting “to”Grafting “from”Grafting “to”Kinetic Monte Carlo in PRE7ICCK 2017, Chicago, 21-25 May 2017Stochastic methodsDeterministic methodsComplete numericalsolutionMethod of momentsFixed pivot techniqueGalerkin methodsKinetic Monte CarloMonte Carlo random samplingAnalytical solutionKinetic Monte Carlo (kMC)Modeling inPREKinetic Monte Carlo (kMC) Algorithm8ICCK 2017, Chicago, 21-25 May 2017𝑎𝑗 𝑿 = 𝑘𝑗,𝑚𝑖𝑐𝑋𝑎𝑋𝑏𝑎0 𝑿 = 𝑗=1𝑀𝑎𝑗 𝑿 𝑓𝜏 =1𝑎0 𝑿ln1𝑟1 𝑗=1𝜇−1𝑎𝑗 𝑿 ≤ 𝑟2𝑎0 𝑿 ≤ 𝑗=1𝜇𝑎𝑗 𝑿Find 𝜇𝑿 ← 𝑿 + 𝝊𝒋𝑡 ← 𝑡 + 𝜏𝑓𝑡 > 𝑡𝑒𝑛𝑑𝑓NoEndYesStart𝑡 = 𝑡𝑜𝑿 = 𝑿𝟎𝑓Results: Reaction propertiesMicrostructural polymer propertiesKinetic Monte Carlo (kMC) Algorithm9ICCK 2017, Chicago, 21-25 May 2017When will a reaction take place?Which reaction will take place?Microscopic reaction rates as a function of the number of molecules of reactants𝑎𝑗 𝑿 = 𝑘𝑗,𝑚𝑖𝑐𝑋𝑎𝑋𝑏𝑎0 𝑿 = 𝑗=1𝑀𝑎𝑗 𝑿 𝑓𝜏 =1𝑎0 𝑿ln1𝑟1 𝑗=1𝜇−1𝑎𝑗 𝑿 ≤ 𝑟2𝑎0 𝑿 ≤ 𝑗=1𝜇𝑎𝑗 𝑿Find 𝜇𝑿 ← 𝑿 + 𝝊𝒋𝑡 ← 𝑡 + 𝜏𝑓𝑡 > 𝑡𝑒𝑛𝑑𝑓NoEndYesStart𝑡 = 𝑡𝑜𝑿 = 𝑿𝟎𝑓Results: Reaction propertiesMicrostructural polymer propertiesUpdate of the number of molecules10Non-macromolecular speciesReactant ProductXI= XI -1X𝑅𝑖𝑛∗= X𝑅𝑖𝑛∗+2X𝑅𝑖𝑛∗= X𝑅𝑖𝑛∗Efficiency factor f𝑅𝑛∗ +𝑀𝑘𝑝𝑅𝑛+1∗Reactant ProductXM= XM -1𝑋𝑅𝑛+1∗ = 𝑋𝑅𝑛+1∗ +1𝑋𝑅𝑛∗= 𝑋𝑅𝑛∗ -1𝑟𝑝 = 𝑘𝑝,𝑚𝑎𝑐 𝑀  𝑛=1𝑁𝑅𝑛∗Update of the number of moleculesMacromolecular speciesEvery update for macromolecular species would require to make a sum of N elementsUsually, NThis increment of +2 will be executed only with a probability fevery time this reaction event is sampled𝐼𝑓,𝑘𝑑2 𝑅𝑖𝑛∗ICCK 2017, Chicago, 21-25 May 2017Binary trees11ICCK 2017, Chicago, 21-25 May 2017Sampling based on mass fraction12Monomer unitsRandom sampling base on mass fraction𝑅𝐻 = 𝑘𝐻𝑛𝐶𝑃𝑛𝐶𝑅𝑖𝑛𝑚𝑃𝑛 = 𝑛𝐶𝑃𝑛ICCK 2017, Chicago, 21-25 May 2017Description of complex architectures13It is possible to track average properties of the reactive system, as average grafting “from” density, average grafting “to” density,average crosslinking density, etc.,but the information for the distribution of this properties is mixed anddifficult to track.It is not possible to calculate the chain length of every graft or the chain length of the vinylsegments between crosslinking pointsComplex architecture: Several grafted chains and several crosslinking points per macromoleculeICCK 2017, Chicago, 21-25 May 2017kMC simulation: Module A and B14Link between binary trees and arrays158 11 7 5 3 2 2 119 12 5 38313912 34 75 69 10 11 12 13 14 151 2 3 4 5 6 7 8Every leaf node provides the information of the chain length and the number of macromolecules with that specific chain lengthi CL_R*(i)1 12 13 14 15 16 17 18 19 210 211 212 213 214 215 216 217 218 219 2. .. .. .39 1Chain-length array for macroradicalsChain-length binary tree for macroradicalsArray containing 8macroradicals of chain length equal to 1, according to the information of the leaf node 888Arrays in Module B16ICCK 2017, Chicago, 21-25 May 2017Results obtained with Module A17kH (dm3·mol-1·s-1) 𝐾𝑒𝑞 (mol·dm-3)ICCK 2017, Chicago, 21-25 May 2017𝑘𝑝𝑒𝑓𝑓 = 𝑘𝑝 1 −𝐾𝑒𝑞𝑀18Results obtained with Module AICCK 2017, Chicago, 21-25 May 2017CLD of homopolymerCLD of polyolefin19Results obtained with Module BICCK 2017, Chicago, 21-25 May 2017CLD of grafts20Results obtained with Module BICCK 2017, Chicago, 21-25 May 2017Bivariate distribution: Copolymer composition-CLDInitial CLD of polyolefin21Results obtained with Module BICCK 2017, Chicago, 21-25 May 2017Reaction event distribution Initial CLD of polyolefinDiffusional effects22ICCK 2017, Chicago, 21-25 May 2017Concluding remarks• Comprehensive model for the description of microstructural properties of individual chains with complex topology was developed.• A mass-weighted CLD needs to be considered to properly account for the chain length dependence of the hydrogen abstraction reactivity. • Diffusional limitations need to be accounted for to accurately represent the grafting kinetics.23ICCK 2017, Chicago, 21-25 May 201724

A tracking of the complete microstructural evolution of individual polymer chains during polymer modification reactions

https://biblio.ugent.be/publication/8537429/file/8537432

A tracking of the complete microstructural evolution of individual polymer chains during polymer modification reactions

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