Graph theoretical approach to the mechanical strength of polymers

Gündüz, Güngör; Dernaika, M.; Dikencik, G.; Fares, Mohammad M.; Aras, Leyla

doi:10.1080/08927020701868367

Cited by 4 publications

(3 citation statements)

References 81 publications

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“…Besides structural information, the size distribution of linear fragments plays an important role in the elasticity of polymeric networks [15,32]. The numberaverage length of linear fragments strongly depends on the conversion; it increases at early stages of the reaction and eventually decreases to almost to 1.…”

Section: Discussion/application To Linseed Oil Networkmentioning

confidence: 99%

“…Although the MCMC scheme (15) provides only a means of approximate sampling, it possesses one very important feature: it is not necessary to compute all the elements of matrix P i,j but only certain selected values. This feature allows to considerably save on computational resources for large adjacency matrices.…”

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confidence: 99%

“…The downside of MCMC is that one has to ensure that the Markov chain (15) operates in a stationary regime before terminating it and accepting the final values as a random sample that mimics samples from P i,j .…”

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confidence: 99%

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Random Graph Approach to Multifunctional Molecular Networks

Kryven

Duivenvoorden

Hermans

et al. 2016

Macromol. Theory Simul.

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one must realize that such simulations imply an enormous spread of length and time scales: even the simple case of a linear polymer exhibits geometrical structures from the scale of a chemical bond to the scale of the gyration radius, to the collective length scales that might be much larger in dense materials. [ 1 ] Moreover, our drive for modelling is not limited to linear polymers but also is directed at tree-like branched structures, cross-linked polymers, and even infinite molecular networks, i.e., gels. In this paper we propose a strategy that draws a consensus between what can be computed on the one hand and pursuing fundamental roots of the matter at hand on the other.The process of assembly or polymerization of molecular networks usually goes through a few temporal stages: disconnected monomers, linear polymer, branched polymer, and gel (an infi nite network). Furthermore, the gel itself should not be perceived as a single, fi nal state of polymer topology. After the gel point the connectivity patterns of the network continue to evolve. [2][3][4] In fact, in many cases a major part of the whole polymerization process may occur in the gel regime. [ 5 ] In view of extremely long time scales associated with polymerization, namely, the time scales that might well exceed hours for some industrial processes, [ 6 ] or even years (drying of oil paint [ 7 ] ), direct atomistic simulation Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The process does not account for spatial positions of the monomers explicitly, yet the Euclidean distances between the monomers are derived from the topological information by applying self-avoiding random walks. This allows favoring reactivity of monomers that are close to each other, and to disfavor the reactivity for monomers obscured by the surrounding. As a result, the model is applicable to large time scales. The phenomena of conversion-dependent reaction rates, gelation, microgelation, and structural inhomogeneity are predicted by the model. Resulting nonhomogeneous network topologies are analyzed to extract such descriptors as: size distribution, crosslink distances, and gel-point conversion. Furthermore, new to the molecular simulation community descriptors are suggested that are especially useful when explaining evolution of the gel as being a single molecule: local clustering coeffi cient, network modularity, cluster size distribution.

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Section: Discussion/application To Linseed Oil Networkmentioning

confidence: 99%

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confidence: 99%

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Random Graph Approach to Multifunctional Molecular Networks

Kryven

Duivenvoorden

Hermans

et al. 2016

Macromol. Theory Simul.

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Topological structure and mechanics of glassy polymer networks

Elder

Sirk

2017

Soft Matter

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The influence of chain-level network architecture (i.e., topology) on mechanics was explored for unentangled polymer networks using a blend of coarse-grained molecular simulations and graph-theoretic concepts. A simple extension of the Watts-Strogatz model is proposed to control the graph properties of the network such that the corresponding physical properties can be studied with simulations. The architecture of polymer networks assembled with a dynamic curing approach were compared with the extended Watts-Strogatz model, and found to agree surprisingly well. The final cured structures of the dynamically-assembled networks were nearly an intermediate between lattice and random connections due to restrictions imposed by the finite length of the chains. Further, the uni-axial stress response, character of the bond breaking, and non-affine displacements of fully-cured glassy networks were analyzed as a function of the degree of disorder in the network architecture. It is shown that the architecture strongly affects the network stability, flow stress, onset of bond breaking, and ultimate stress while leaving the modulus and yield point nearly unchanged. The results show that internal restrictions imposed by the network architecture alter the chain-level response through changes to the crosslink dynamics in the flow regime and through the degree of coordinated chain failure at the ultimate stress. The properties considered here are shown to be sensitive to even incremental changes to the architecture and, therefore, the overall network architecture, beyond simple defects, is predicted to be a meaningful physical parameter in the mechanics of glassy polymer networks.

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Tensile Bond Strength of a Highly Cross-Linked Denture Tooth to the Compression-Molded and Injection-Molded Denture Base Polymers

Doğan

Korkmaz

Doğan

et al. 2009

The Journal of Adhesion

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This study compared tensile bond strengths between conventional compressionmolded heat (HC)-, auto (AP)-, and microwave-polymerized (MC) poly(methyl methacrylate)-based denture resins and a relatively new injection-molded, microwave-polymerized polyurethane based resin (MI) bonded to a highly cross-linked denture tooth. In the first part of the experiments, denture teeth were used as received. In the second part, they were treated with dichloromethane to see its effect on bonding of conventional denture bases (HCS and APS). Bond strength was tested in tension according to ADA specification No.15. The results showed that the HC group failed cohesively because of higher interface bonding (49.95 MPa) compared with those of the others (AP: 25.41 MPa; MC: 22.06 MPa; MI: 20.02 MPa). The application of dichloromethane improved bond strengths of HCS and APS groups (60.61 and 32.03 MPa, respectively). It was suggested that dichloromethane could be applied on the denture teeth ridge lap area prior to denture base processing to enhance adhesion between the tooth=resin.

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Graph theoretical approach to the mechanical strength of polymers

Cited by 4 publications

References 81 publications

Random Graph Approach to Multifunctional Molecular Networks

Random Graph Approach to Multifunctional Molecular Networks

Topological structure and mechanics of glassy polymer networks

Tensile Bond Strength of a Highly Cross-Linked Denture Tooth to the Compression-Molded and Injection-Molded Denture Base Polymers

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