Simulation of Fracture Nucleation in Cross-Linked Polymer Networks (original) (raw)
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Molecular modeling of deformation and fracture of polymer networks
We propose a simulation methodology for subjecting atomistic bulk computational specimens to uniaxial fracture tensile tests with a strain rate conforming to the ASTM-D412 standard. An amorphous, unflawed polyethylene melt is crosslinked and characterized dynamically and mechanically. The spectrum of relaxation times permits sampling the equilibrium stress-strain law with Molecular Dynamics simulations. The elongation and stress at break are predicted by a stochastic description of bond scission.
Molecular Dynamics Simulations of a Cross-linked Epoxy-resin Sample
2022
because of their excellent physical properties such as mechanical strength, electrical insulation, heat resistance, and solvent resistance. [1] These properties result from their highly cross-linked network structures, which comprise phenolic and methy lene units. In these structures, three methylenes can connect to a phenolic ring such that one can be at the para (p) and two can be at the ortho (o) positions that are adjacent to the hydroxyl group of the phenolic ring, as shown in Figure 1. To further improve these properties, characterization of the relation between the network structure and the physical properties is one of the most important issues. However, this relation has not been completely understood experimentally because a fully cured resin is insoluble and infusible, which makes structural analysis difficult. In such cases, for studying cross-linked phenolic and other thermosetting resins that hold experimental constraints for structural analysis, a theoretical approach based on molecular dynamics (MD) simulations is expected to be effective. [2] Fueled by the evolution of computational sciences in polymer physics and the computational performance of desktop computers over the past two decades, many studies of epoxy resins using atomistic and coarse-grained MD simulations have been reported and the modeling methodology of cross-linked epoxy resins has been refined through these studies, revealing numerous molecularlevel findings that cannot be experimentally obtained. [2-12] Progress in the computational studies of epoxy resins over the last two decades has mainly been the result of rapid industrial growth of carbon-fiber reinforced plastics that use epoxy resins as matrix resins. However, detailed reports on atomistic simulations of cross-linked phenolic resins have been limited compared with the studies of epoxy resins. [13-17] We have investigated the application of atomistic MD simulation methods of epoxy resins to phenolic resins and were the first to propose a simple modeling method to generate highly cross-linked structures from a relaxed structure of phenolic oligomers. In the proposed method, a pair of nearest reactive carbons on the phenolic rings was connected via a newly inserted methylene unit, and this cross-linking reaction was repeated until a target degree of cross-linking was reached. [13] The structure modeling was successful, and a highly cross-linked structure (cross-linking degree of 0.92) was obtained. However, Molecular Dynamics Simulations A new molecular modeling algorithm for conducting large-scale molecular dynamics simulation studies of cross-linked phenolic resins is developed using a united-atom model. A phenol-formaldehyde polycondensation system is simulated by a pseudoreaction algorithm taking into consideration (i) the difference in the experimental reaction rate constants at ortho and para positions of phenolic units and (ii) the geometry of the reactants. To avoid formation of locally strained cross-linked structures that can be generated in a typical cutoffdistance-based reaction scheme, a geometrical judgment constraint is applied in the reaction procedure. With this algorithm, cross-linked network structures of phenolic resins with a maximum conversion (α) of 0.90 are obtained from 10 000 phenols. The density and the tensile modulus of the structure with α of 0.90 at 300 K are 1.2 g cm −3 and 5.4 GPa, respectively. This is in good agreement with experimental values. The strain-free, highly cross-linked network structures of phenolic resins exhibit a higher density and tensile modulus compared with structures generated in the absence of the geometrical cutoff. This result demonstrates that the geometrical judgment constraint can effectively avoid the formation of distorted and strained local structures and is necessary for accurate modeling of highly cross-linked phenolic resins.
Atomistic molecular simulations of structure and dynamics of crosslinked epoxy resin
Polymer, 2007
Many excellent thermal and mechanical performances of cured epoxy resin products can be related to their specific network structure. In this work, a typical crosslinked epoxy resin was investigated using detailed molecular dynamics (MD) simulations, in a wide temperature range from 250 K to 600 K. A general constant-NPT MD procedure widely used for linear polymers failed to identify the glass transition temperature (T g ) of this crosslinked polymer. This can be attributed to the bigger difference in the time scales and cooling rates between the experiments and simulations, and specially to the highly crosslinked infinite network feature. However, by adopting experimental densities appropriate for the corresponding temperatures, some important structural and dynamic features both below and above T g were revealed using constant-NVT MD simulations. The polymer system exhibited more local structural features in case of below T g than above T g , as suggested by some typical radial distribution functions and torsion angle distributions. Non-bond energy, not any other energy components in the used COMPASS forcefield, played the most important role in glass transition. An abrupt change occurring in the vicinity of T g was also observed in the plots of the mean squared displacements (MSDs) of the crosslinks against the temperature, indicating the great importance of crosslinks to glass transition. Rotational dynamics of some bonds in epoxy segments were also investigated, which exhibited great diversity along the chains between crosslinks. The reorientation functions of these bond vectors at higher temperatures can be well fitted by KohlrauscheWilliamseWatts (KWW) function.
Atomistic Modeling of Cross-linked Epoxy Polymer
52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2011
Molecular Dynamics simulations are used to study cross-linking of an epoxy polymer. OPLS force field parameters are used for modeling a 2:1 stoichiometric mixture of epoxy resin and the cross-linking agent. The model has 17,928 united atoms and a static cross-linking method is used along with molecular minimization and molecular dynamics techniques to achieve two different cross-link densities. The crosslinked models can be used for understanding various phenomenon occurring in cross-linked epoxy resins at the atomic scale. Glass-transition temperature ranges of two differently cross-linked samples have been predicted using the models. These models will be used for studying aging behavior at the atomic level in epoxy materials and understanding the influence of aging on mechanical properties. I. Introduction poxy Resins are prime constituents in adhesives, sealants, and aircraft composite structural components. A wide range of studies have focused on epoxy-based materials to establish physical and mechanical properties. 1-3 The excellent specific-stiffness and specific-strength properties of epoxy-based composite materials are due to the complex microstructure of their constituent materials. There is significant interest in understanding the aging response of these material systems due to their widespread use in commercial aircraft. A. Computational Studies on Epoxy Polymers Epoxy resins are formed when epoxy monomers react with compounds known as cross-linking or curing agents with active hydrogens such as amines and anhydrides. 4 A trial-and-error approach to experimentally optimize the processing conditions of epoxy materials can become time-consuming and expensive. With the advancement of computational technology, computational modeling has provided an efficient route to study these polymer resins. 5-14,4,15 Molecular dynamics (MD) simulations based on the bead-spring model 10,11 and Monte-Carlo simulations based on the bond-fluctuation model 16,8,9 have been used in the last two decades for studying epoxy materials. The beadspring models did not take into account the details of the molecular structures and thus cannot predict the influence of specific groups of atoms on the physical properties. In the last few years, MD at the atomic scale has been quite successful in exploring different phenomena occurring at pico-to nano-second time scales in epoxy resins. 14 Many researchers have studied the formation of cross-linked epoxy resins using different approaches of simulated cross-linking. Doherty et al. 5 modeled PMA networks using lattice-based simulations in a polymerization MD scheme. Yarovsky and Evans 15 discussed a cross-linking technique which they used to crosslink low molecularweight, water-soluble, phosphate-modified epoxy resins (CYMEL 1158). The cross-linking reactions were carried out simultaneously (static cross-linking process). Dynamic cross-linking of epoxy resins was performed by Xu et al. 4
Macromolecules 40(22) : 8104–8113, 2007
This paper presents a new computational method for simulating polymer network formation. There are four separate procedures involved in the methodology for this multiscale simulation: (i) mapping of the polymerizing monomers onto a coarse-grained model, (ii) cross-linking the monomers by applying Monte Carlo simulation to the coarse-grained model, (iii) reverse mapping of the coarse-grained model to a fully atomistic representation, and (iv) simulation of the atomistic model through standard molecular dynamics technique. Molecular dynamics simulations and experimental studies are carried out to check the algorithm on the basis of the determination of the physical properties of the cycloaliphatic epoxy resin which is prepared from 3,4-epoxycyclohexylmethyl-3,4-epoxycyclohexanecarboxylate as resin monomers and 4-methylhexahydrophthalic anhydride as curing agents. Depending on the effective conversion and temperature, we determine the density, the glass transition temperature, and the thermal expansion coefficient of the cross-linked epoxy system. An increase in the degree of cross-linking is found to increase the glass transition temperature. Good agreement between computer simulation and experimental results is achieved for highly cross-linked networks, thereby showing that the simulation model is basically valid.
Computer simulation of structure and properties of crosslinked polymers: application to epoxy resins
Polymer, 2002
In this work, a methodology has been developed for construction of atomistic models of crosslinked polymer networks. The methodology has been applied to low molecular weight water soluble epoxy resins crosslinked with different curing agents that are being considered for use as a primer coating on steel. The simulations allowed the crosslink density and the amount of free crosslinking sites in the coatings to be predicted. Shrinkage of the resin upon curing was reproduced by the simulation. In addition, the barrier properties of the model coatings were estimated. The interface between an inorganic substrate and cured epoxy resin has been constructed and the strength and molecular mechanisms of adhesion have been revealed. The developed methodology has a potential to signi®cantly impact on the design and development of new coatings with improved barrier and adhesion properties. q
Atomistic molecular modelling of crosslinked epoxy resin
Polymer, 2006
In the present study, a new method was developed to construct atomistic molecular models of crosslinked polymers based on commercially important epoxy resin. This method employed molecular dynamics/molecular mechanics schemes and assumed close proximity. The generic Dreiding2.21 force-field and advanced compass force-field were used for the construction of models and prediction of properties, respectively. A polymer network with conversion up to 93.7% was successfully generated by this method. Density and elastic constants of the system were calculated from the equilibrated structure for the validation of the generated models. The simulated results compared reasonably with experimental data available. The developed method would hold great promise in further molecular simulations for structure and properties of epoxy resin or other cured systems.
Journal of the American Chemical Society, 2021
The fracture of rubbery polymer networks involves a series of molecular events, beginning with conformational changes along the polymer backbone and culminating with a chain scission reaction. Here, we report covalent polymer gels in which the macroscopic fracture "reaction" is controlled by mechanophores embedded within mechanically active network strands. We synthesized poly(ethylene glycol) (PEG) gels through the end-linking of azide-terminated tetra-arm PEG (M n = 5 kDa) with bisalkyne linkers. Networks were formed under identical conditions, except that the bis-alkyne was varied to include either a cis-diaryl (1) or cis-dialkyl (2) linked cyclobutane mechanophore that acts as a mechanochemical "weak link" through a force-coupled cycloreversion. A control network featuring a bis-alkyne without cyclobutane (3) was also synthesized. The networks show the same linear elasticity (G′ = 23-24 kPa, 0.1-100 Hz) and equilibrium mass swelling ratios (Q = 10-11 in tetrahydrofuran), but they exhibit tearing energies that span a factor of 8 (3.4 J, 10.6, and 27.1 J•m -2 for networks with 1, 2, and 3, respectively). The difference in fracture energy is well-aligned with the force-coupled scission kinetics of the mechanophores observed in single-molecule force spectroscopy experiments, implicating local resonance stabilization of a diradical transition state in the cycloreversion of 1 as a key determinant of the relative ease with which its network is torn. The connection between macroscopic fracture and a small-molecule reaction mechanism suggests opportunities for molecular understanding and optimization of polymer network behavior.
PLoS ONE, 2012
The construction of molecular models of crosslinked polymers is an area of some difficulty and considerable interest. We report here a new method of constructing these models and validate the method by modelling three epoxy systems based on the epoxy monomers bisphenol F diglycidyl ether (BFDGE) and triglycidyl-p-amino phenol (TGAP) with the curing agent diamino diphenyl sulphone (DDS). The main emphasis of the work concerns the improvement of the techniques for the molecular simulation of these epoxies and specific attention is paid towards model construction techniques, including automated model building and prediction of glass transition temperatures (T g ). Typical models comprise some 4200-4600 atoms (ca. 120-130 monomers). In a parallel empirical study, these systems have been cast, cured and analysed by dynamic mechanical thermal analysis (DMTA) to measure T g . Results for the three epoxy systems yield good agreement with experimental T g ranges of 200-220uC, 270-285uC and 285-290uC with corresponding simulated ranges of 210-230uC, 250-300uC, and 250-300uC respectively.