Ein Modell zur Beschreibung reversibler Copolymerisationen

Krüger, Hartmut; Bauer, Jörg; Rübner, Joachim

doi:10.1002/macp.1987.021880913

Cited by 35 publications

(38 citation statements)

References 11 publications

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“…These new equations reduce to the expressions for the same quantities derived by Krüger et al [3] and used by Palmer et al [9] and Badeen and Dubé [10] when only terminal kinetics are considered (s 1 ¼ s 2 ¼ 1). They can be used along with Equation (6), (7), and (12) to solve for polymer composition and k p,copo for a copolymerization system with depropagation and penultimate unit effects.…”

mentioning

confidence: 87%

“…Lowry Case 1, which assumes that depropagation is only important when a depropagating monomer is attached to the same monomer type, i.e., depropagation by diad end groups, becomes a special case of Wittmer's model when only one of the homopropagation reactions is reversible. Krüger et al [3] modified the solution approach to Wittmer's model by defining the propagation probabilities. More recently, Kukulj and Davis [4] have derived an expression for average propagation rate coefficient (k p,copo ) by using terminal kinetics and the Lowry Case 1 model.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, a system of equations describing instantaneous copolymer composition and k p,copo are developed for the full reversible reaction scheme based on penultimate kinetics, expanding on the formulation given by Krüger et al [3] for terminal kinetics. The model predictions for styrene /butyl methacrylate (BMA), a system in which only one monomer depropagates, are examined to demonstrate the interaction between depropagation and the penultimate unit effect.…”

Section: Introductionmentioning

confidence: 99%

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High Temperature Free Radical Copolymerization with Depropagation and Penultimate Kinetic Effects

Leiza

Hutchinson

2005

Macro Theory & Simulations

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Summary: Methacrylate copolymers produced under higher temperature starved‐feed conditions are affected by depropagation, and some binary systems also experience a penultimate effect. In this work a generalized set of equations has been developed to describe the combined effect of depropagation and penultimate copolymerization kinetics on instantaneous copolymer composition and average copolymerization rate coefficients. Limiting cases applicable to the methacrylate/styrene system are examined. When combined with depropagation, penultimate kinetics not only decrease the effective propagation rate coefficient but also deviate from terminal model predictions of polymer composition.Copolymerization chain growth with penultimate kinetics and depropagation.magnified imageCopolymerization chain growth with penultimate kinetics and depropagation.

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mentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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High Temperature Free Radical Copolymerization with Depropagation and Penultimate Kinetic Effects

Leiza

Hutchinson

2005

Macro Theory & Simulations

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“…Lowry Case I is a special case of Wittmer's model when only the homopropagation of monomer type 2 is reversible (k dp 11 k dp 12 k dp 21 0). Krüger et al [38] introduced a slightly modified approach compared to Wittmer's model by defining propagation probabilities, as recently updated by Badeen and Dubé [39]. An experimental study examining the influence of BMA depropagation on ST/BMA copolymer composition found that the Lowry Case I description of depropagation is applicable, i.e., BMA only depropagates when BMA is also present as the penultimate unit of the polymer chain [40].…”

Section: Copolymerizationmentioning

confidence: 97%

Free‐Radical Acrylic Polymerization Kinetics at Elevated Temperatures

Wang

Hutchinson

2010

Chem Eng & Technol

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Free-radical acrylic homo-and copolymerization kinetics are reviewed, focusing on secondary reactions that impact the polymerization rate and polymer molecular weight (MW) under industrially-relevant synthesis conditions. Dependent on the monomer type (acrylate, methacrylate, styrene), mechanisms that must be considered include chain-end depropagation, monomer self-initiation, formation and reaction of midchain radicals, and incorporation of macromonomers formed by b-scission of midchain radicals. The relative importance of these reactions varies with temperature and, for copolymerization, monomer composition. A comprehensive treatment of these complexities has been completed for polymerizations conducted up to 180°C, but further work is required to extend the applicability of the model to even higher temperatures. IntroductionThe production of low-density polyethylene and associated copolymers at 200-300°C and high pressure is perhaps the bestknown example of high-temperature free-radical polymerization (FRP). However, an increasing number of acrylic resins, produced from a mixture of monomers selected from the methacrylate, acrylate, and styrene families, are also manufactured under higher temperature conditions (>120°C) in homogeneous solution. Low-molecular-weight acrylic resins are the base polymer components for many automotive coatings due to their excellent resistance to chemicals, solvents, ultraviolet light, and abrasion, as well as their exterior durability after crosslinking on the surface of the vehicle [1]. High-temperature conditions are used to produce a variety of other materials for coatings, adhesives, and paints [2]. These conditions are chosen to increase production rates and to decrease (or eliminate) the solvent employed in the formulation while maintaining reasonable solution viscosity [2][3][4].While commercially advantageous, the high polymerization temperatures greatly promote the occurrence of secondary reactions that have a strong impact on polymerization rate and polymer MW, such as monomer self-initiation, chain depropagation, and the formation and subsequent reaction of midchain radicals and unsaturated polymer chains (macromonomers). These reactions occur in addition to the well-known and well-understood set of basic FRP mechanisms consisting of initiation, propagation, termination, and chain transfer [5,6]. This article provides an overview and summarizes recent experimental and modeling efforts by our group and other researchers to improve the understanding of these mechanisms. As most high-temperature acrylic polymerization processes involve multiple monomers, the complexities of including these reactions in copolymerization will also be addressed. An accurate treatment of high-temperature FRP kinetics is a critical component of larger-scale process models used to predict the influence of the operating conditions on reaction rate and polymer properties, guide the selection and optimization of standard operating conditions for existing and new polymer grades, and guide process ...

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“…Because of this mathematical difficulty, it was until 1987 that the first systematic treatment of first-order terminal models with depropagation was given by Kruger et.al. [14]. Kruger's approach was based on the key assumption that the copolymer sequence can be described as a first-order Markov chain (Eq.…”

Section: Introductionmentioning

confidence: 99%

A general theory of kinetics and thermodynamics of steady-state copolymerization

Shu

Song

Ou-Yang

et al. 2015

J. Phys.: Condens. Matter

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Kinetics of steady-state copolymerization has been investigated since 1940s. Irreversible terminal and penultimate models were successfully applied to a number of comonomer systems, but failed for systems where depropagation is significant. Although a general mathematical treatment of the terminal model with depropagation was established in 1980s, penultimate model and higher-order terminal models with depropagation have not been systematically studied, since depropagation leads to hierarchically-coupled and unclosed kinetic equations which are hard to be solved analytically. In this work, we propose a truncation method to solve the steady-state kinetic equations of any-order terminal models with depropagation in an unified way, by reducing them into closed steady-state equations which give the exact solution of the original kinetic equations. Based on the steady-state equations, we also derive a general thermodynamic equality in which the Shannon entropy of the copolymer sequence is explicitly introduced as part of the free energy dissipation of the whole copolymerization system.

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Ein Modell zur Beschreibung reversibler Copolymerisationen

Cited by 35 publications

References 11 publications

High Temperature Free Radical Copolymerization with Depropagation and Penultimate Kinetic Effects

High Temperature Free Radical Copolymerization with Depropagation and Penultimate Kinetic Effects

Free‐Radical Acrylic Polymerization Kinetics at Elevated Temperatures

A general theory of kinetics and thermodynamics of steady-state copolymerization

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