Intramolecular Reactions in Randomly End-Linked Polymer Networks and Linear (Co)polymerizations

Lang, Michael; Göritz, D.; Kreitmeier, Stefan

doi:10.1021/ma049025z

Cited by 41 publications

(92 citation statements)

References 49 publications

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“…The model has been proven to be successful for simulating cross-linked polymers [26][27][28][29]. In order to investigate the gelation properties in detail, we map the cross-linking process into a percolation problem on the 2D lattice of grafting points.…”

Section: Introductionmentioning

confidence: 99%

Gelation threshold of cross-linked polymer brushes

2011

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The cross-linking of polymer brushes is studied using the bond-fluctuation model. By mapping the cross-linking process into a two-dimensional (2D) percolation problem within the lattice of grafting points, we investigate the gelation transition in detail. We show that the particular properties of cross-linked polymer brushes can be reduced to the distribution of bonds which are formed between the grafted chains, and we propose scaling arguments to relate the gelation threshold to the chain length and the grafting density. The gelation threshold is lower than the percolation threshold for 2D bond percolation because of the longer range and broad distribution of bonds formed by the cross-linking process. We term this type of percolation problem star percolation. We observe a broad crossover from mean-field to critical percolation behavior by analyzing the cluster size distribution near the gelation threshold.

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Section: Introductionmentioning

confidence: 99%

Gelation threshold of cross-linked polymer brushes

2011

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“…Unlike dangling chains, which can be readily quantified via titration or spectroscopy, there are no known methods for quantification of primary loops. Their prevalence is estimated from pregel measurements or variations between the properties of a given material and theoretical model networks (2,4,(7)(8)(9)(12)(13)(14)(15)(16)(17). These molecular-level mechanical imperfections could critically impact modern applications of polymer networks and gels (18-28), especially those built on an end-linked network architecture (29-33).…”

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confidence: 99%

Counting primary loops in polymer gels

Zhou¹,

Woo²,

Cok³

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

198

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Much of our fundamental knowledge related to polymer networks is built on an assumption of ideal end-linked network structure. Real networks invariably possess topological imperfections that negatively affect mechanical properties; modifications of classical network theories have been developed to account for these defects. Despite decades of effort, there are no known experimental protocols for precise quantification of even the simplest topological network imperfections: primary loops. Here we present a simple conceptual framework that enables primary loop quantification in polymeric materials. We apply this framework to measure the fraction of primary loop junctions in trifunctional PEG-based hydrogels. We anticipate that the concepts described here will open new avenues of theoretical and experimental research related to polymer network structure.responsive materials | topology | network disassembly spectrometry | tetrazine T he properties of all known polymer networks, from commodity materials like nylon, rubber, and plastics, to biological tissues such as the extracellular matrix (ECM) and cartilage, are defined by the network's chemical composition and structural topology (1-3). Much of our fundamental knowledge related to polymer materials, e.g., theories of elasticity and gelation, was built more than half a century ago upon an assumption of ideal end-linked network structure (Fig. 1A) (2, 4-7). Real networks invariably possess imperfections such as first-order elastically inactive dangling chains and primary loops (Fig. 1B), and higher-order elastic loop structures and chain entanglements; modifications of classical network theories have been developed to account for these defects (8-11).First-order network imperfections (Fig. 1B) have the most direct negative impact on the mechanical properties of materials. Dangling chains can be minimized if efficient end-linking reactions are used between functional groups present at 1:1 ratio. In contrast, kinetic constraints demand that primary loops exist regardless of functional group conversion (12). Unlike dangling chains, which can be readily quantified via titration or spectroscopy, there are no known methods for quantification of primary loops. Their prevalence is estimated from pregel measurements or variations between the properties of a given material and theoretical model networks (2,4,(7)(8)(9)(12)(13)(14)(15)(16)(17). These molecular-level mechanical imperfections could critically impact modern applications of polymer networks and gels (18-28), especially those built on an end-linked network architecture (29-33).Here we present a simple conceptual framework called network disassembly spectrometry (NDS) that enables facile, simultaneous quantification of the fraction of primary loops and the numbers and structures of dangling chains in end-linked materials via site-selective network disassembly. We apply this framework to degradable PEG hydrogels, which are similar to materials frequently used in tissue engineering applications (29,32).

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“…26,31,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] In the present study we use MD simulations to reproduce the swelling/deswelling of a polymer network after preparation. The Obukhov-Rubinstein-Colby model depicts the influence that swelling/deswelling has on elasticity, but its physical picture is too complicated to be sufficiently validated by experiment.…”

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confidence: 99%

“…26,31,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] In the present study we use MD simulations to reproduce the swelling/deswelling of a polymer network after preparation. 26,31,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] In the present study we use MD simulations to reproduce the swelling/deswelling of a polymer network after preparation.…”

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Supercoiling transformation of chemical gels

et al. 2015

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The swelling/deswelling behavior of chemical gels has been an unsolved problem disputed over for a long time. The Obukhov-Rubinstein-Colby model depicts the influence that swelling/deswelling has on elasticity, but its physical picture is too complicated to be sufficiently validated by experiment. In this study, we use molecular dynamics simulation to verify the validity of the molecular picture of network strands predicted by the Obukhov-Rubinstein-Colby model. We conclude that the physical picture of the Obukhov-Rubinstein-Colby model is reasonable, and furthermore the simulation can reveal the details of conformational changes in network strands during the supercoiling transformation. Our findings not only reveal the validity, but also give a better understanding of the dynamics of the swelling/deswelling behavior of chemical gels.

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Intramolecular Reactions in Randomly End-Linked Polymer Networks and Linear (Co)polymerizations

Cited by 41 publications

References 49 publications

Gelation threshold of cross-linked polymer brushes

Gelation threshold of cross-linked polymer brushes

Counting primary loops in polymer gels

Supercoiling transformation of chemical gels

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