skip to main content


Title: Method of Moments Applied to Most-Likely High-Temperature Free-Radical Polymerization Reactions
Many widely-used polymers are made via free-radical polymerization. Mathematical models of polymerization reactors have many applications such as reactor design, operation, and intensification. The method of moments has been utilized extensively for many decades to derive rate equations needed to predict polymer bulk properties. In this article, for a comprehensive list consisting of more than 40 different reactions that are most likely to occur in high-temperature free-radical homopolymerization, moment rate equations are derived methodically. Three types of radicals—secondary radicals, tertiary radicals formed through backbiting reactions, and tertiary radicals produced by intermolecular chain transfer to polymer reactions—are accounted for. The former tertiary radicals generate short-chain branches, while the latter ones produce long-chain branches. In addition, two types of dead polymer chains, saturated and unsaturated, are considered. Using a step-by-step approach based on the method of moments, this article guides the reader to determine the contributions of each reaction to the production or consumption of each species as well as to the zeroth, first and second moments of chain-length distributions of live and dead polymer chains, in order to derive the overall rate equation for each species, and to derive the rate equations for the leading moments of different chain-length distributions. The closure problems that arise are addressed by assuming chain-length distribution models. As a case study, β-scission and backbiting rate coefficients of methyl acrylate are estimated using the model, and the model is then applied to batch spontaneous thermal polymerization to predict polymer average molecular weights and monomer conversion. These predictions are compared with experimental measurements.  more » « less
Award ID(s):
1803215
NSF-PAR ID:
10192002
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Processes
Volume:
7
Issue:
10
ISSN:
2227-9717
Page Range / eLocation ID:
656
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Mechanical initiation of polymerization offers the chance to generate polymers in new environments using an energy source with unique capabilities. Recently, a renewed interest in mechanically controlled polymerization has yielded many techniques for controlled radical polymerization by ultrasound. However, other types of polymerizations induced by mechanical activation are rare, especially for generating high‐molecular‐weight polymers. Herein is an example of using piezoelectric ZnO nanoparticles to generate free‐radical species that initiate chain‐growth polymerization and polymer crosslinking. The fast generation of high amounts of reactive radicals enable the formation of polymer/gel by ultrasound activation. This chemistry can be used to harness mechanical energy for constructive purposes in polymeric materials and for controlled polymerizations for bulk‐scale reactions.

     
    more » « less
  2. Abstract

    Mechanical initiation of polymerization offers the chance to generate polymers in new environments using an energy source with unique capabilities. Recently, a renewed interest in mechanically controlled polymerization has yielded many techniques for controlled radical polymerization by ultrasound. However, other types of polymerizations induced by mechanical activation are rare, especially for generating high‐molecular‐weight polymers. Herein is an example of using piezoelectric ZnO nanoparticles to generate free‐radical species that initiate chain‐growth polymerization and polymer crosslinking. The fast generation of high amounts of reactive radicals enable the formation of polymer/gel by ultrasound activation. This chemistry can be used to harness mechanical energy for constructive purposes in polymeric materials and for controlled polymerizations for bulk‐scale reactions.

     
    more » « less
  3. The advantageous material properties that arise from combining non-polar olefin monomers with activated vinyl monomers have led to considerable progress in the development of viable copolymerization strategies. However, unfavorable reactivity ratios during radical copolymerization of the two result in low levels of olefin incorporation, and an abundance of deleterious side reactions arise when attempting to incorporate many polar vinyl monomers via the coordination–insertion pathway typically applied to olefins. We reasoned that design of an activated monomer that is not only well-suited for radical copolymerization with polar vinyl monomers ( e.g. , acrylates) but is also capable of undergoing post-polymerization modification to unveil an olefin repeat unit would allow for the preparation of statistical olefin-acrylate copolymers. Herein, we report monomers fitting these criteria and introduce a post-polymerization modification strategy based on single-electron transfer (SET)-induced decarboxylative radical generation directly on the polymer backbone. Specifically, SET from an organic photocatalyst (eosin Y) to a polymer containing redox-active phthalimide ester units under green light leads to the generation of reactive carbon-centered radicals on the polymer backbone. We utilized this approach to generate statistical olefin-acrylate copolymers by performing the decarboxylation in the presence of a hydrogen atom donor such that the backbone radical is capped by a hydrogen atom to yield an ethylene or propylene repeat unit. This method allows for the preparation of copolymers with previously inaccessible comonomer distributions and demonstrates the promise of applying SET-based transformations to address long-standing challenges in polymer chemistry. 
    more » « less
  4. null (Ed.)
    Heterogeneous phase astrochemistry plays an important role in the synthesis of complex organic matter (COM) as found on comets and rocky body surfaces like asteroids, planetoids, moons and planets. The proposed catalytic model is based on two assumptions: (a) siliceous rocks in both crystalline or amorphous states show surface-exposed defective centers such as siloxyl (Si-O•) radicals; (b) the second phase is represented by gas phase CO molecules, an abundant C 1 building block found in space. By means of quantum chemistry; (DFT, PW6B95/def2-TZVPP); the surface of a siliceous rock in presence of CO is modeled by a simple POSS (polyhedral silsesquioxane) where a siloxyl (Si-O•) radical is present. Four CO molecules have been consecutively added to the Si-O• radical and to the nascent polymeric CO (pCO) chain. The first CO insertion shows no activation free energy with ΔG 200 K = −21.7 kcal/mol forming the SiO-CO• radical. The second and third CO insertions show Δ G 200 K ‡ ≤ 10.5 kcal/mol. Ring closure of the SiO-CO-CO• (oxalic anhydride) moiety as well as of the SiO-CO-CO-CO• system (di-cheto form of oxetane) are thermodynamically disfavored. The last CO insertion shows no free energy of activation resulting in the stable five member pCO ring, precursor to 1,4-epoxy-1,2,3-butanone. Hydrogenation reactions of the pCO have been considered on the SiO oxygen or on the carbons and oxygens of the pCO chains. The formation of the reactive aldehyde SiO-CHO on the siliceous surface is possible. In principle, the complete hydrogenation of the (CO) 1−4 series results in the formation of methanol and polyols. Furthermore, all the SiO-pCO intermediates and the lactone 1,4-epoxy-1,2,3-butanone product in its radical form can be important building blocks in further polymerization reactions and/or open ring reactions with H (aldehydes, polyols) or CN (chetonitriles), resulting in highly reactive multi-functional compounds contributing to COM synthesis. 
    more » « less
  5. Abstract

    Polymer‐grafted inorganic particles (PGIPs) are attractive building blocks for numerous chemical and material applications. Surface‐initiated controlled radical polymerization (SI‐CRP) is the most feasible method to fabricate PGIPs. However, a conventional in‐batch reaction still suffers from several disadvantages, including time‐consuming purification processes, low grafting efficiency, and possible gelation problems. Herein, a facile method is demonstrated to synthesize block copolymer–grafted inorganic particles, that is, poly(poly(ethylene glycol) methyl ether methacrylate) (PPEGMEMA)‐b‐poly(N‐isopropylacrylamide) (PNIPAM)–grafted silica micro‐particles using continuous flow chemistry in an environmentally friendly aqueous media. Immobilizing the chain transfer agent and subsequent SI‐CRP can be accomplished sequentially in a continuous flow system, avoiding multi‐step purification processes in between. The chain length (MW) of the grafted polymers is tunable by adjusting the flow time or monomer concentration, and the narrower molar mass dispersity (Р< 1.4) of the grafted polymers reveals the uniform polymer chains on the particles. Moreover, compared with the in‐batch reaction at the same condition, the continuous system also suppresses possible gelation problems.

     
    more » « less