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2011
Fracture properties of model elastomeric networks of polyurethane have been investigated with a double-edge notch geometry. The networks were synthesized from monodisperse end-functionalized polypropylene glycol precursors and a trifunctional isocyanate. All reagents were carefully purified and nearly defect-free ideal networks were prepared at a stoichiometry very close to the theoretical one. Three networks were prepared: an unentangled network of short chains (M n ¼ 4 kg mol À1 ), an entangled network of longer chains (M n ¼ 8 kg mol À1 ) and a bimodal network with 8 kg mol À1 and 1 kg mol À1 chains. The presence of entanglements was found to increase significantly the toughness of the rubber, in particular at room temperature, relative to the bimodal networks and to the short chains network.
Journal of Applied Polymer Science, 2010
The crosslink density (CLD) for polyurethane elastomeric networks based on hydroxyl terminated polybutadiene and isophorone-diisocyanate was theoretically calculated with a-model equations the employing the functionality distribution and extent of reaction as input parameters. The theoretical crosslink density (m t) was compared with the CLD values computed from stress-strain data evaluated at various strain rates. The methods for the calculation of the CLD from stressstrain data were based on the Mooney-Rivlin and Young's modulus approaches. Theoretical stress-strain curves were generated on the basis of m t conforming to both phantom and affine model calculations. The experimental stressstrain plots aligned more closely to the affine model line. The deviation of the experimentally derived stress-strain curves from the theoretical affine curve was probably due to the presence of temporarily trapped physical entanglements. From the stress-strain data, the concentrations of true chemical crosslinks and physical entanglements were estimated individually. V
The crosslink density (CLD) for polyurethane elastomeric networks based on hydroxyl terminated polybutadiene and isophorone-diisocyanate was theoretically calculated with a-model equations the employing the functionality distribution and extent of reaction as input parameters. The theoretical crosslink density (m t ) was compared with the CLD values computed from stress-strain data evaluated at various strain rates. The methods for the calculation of the CLD from stressstrain data were based on the Mooney-Rivlin and Young's modulus approaches. Theoretical stress-strain curves were generated on the basis of m t conforming to both phantom and affine model calculations. The experimental stressstrain plots aligned more closely to the affine model line. The deviation of the experimentally derived stress-strain curves from the theoretical affine curve was probably due to the presence of temporarily trapped physical entanglements. From the stress-strain data, the concentrations of true chemical crosslinks and physical entanglements were estimated individually. V C 2010 Wiley Periodicals, Inc. J Appl Polym Sci 117: 920-925, 2010
Macromolecules, 1990
Poly(dioxo1ane) (PDXL) gels are prepared by an end-linking procedure upon reacting a,wdihydroxy-PDXL chains with a polyisocyanate. Mechanical and swelling measurements are carried out on various swollen samples of PDXL networks. The experimental results concerning the moduli (C) can be explained if account is taken of the contribution of trapped entanglements (Langley-Graessley model). Data arising from equilibrium swelling measurements in dioxane and in water are used to calculate the Flory-Huggins interaction parameter x12 of the system: This method of determination is independent of the type of model used to evaluate the elastic free energy. A linear dependence of x12 versus vn-the polymer volume fraction of the gel-is found. The degradation behavior of these networks in acidic aqueous media is investigated as well.
Polymer, 1994
Double torsion tests were used to evaluate the fracture toughness of a brittle organic network, poly[diethylene glycol bis(allyl carbonate)] commonly known as CR-39 resin, and to evaluate the enhancement in fracture toughness due to the incorporation of various additives. These additives were either polymerized to form a second network, an interpenetrating polymer network, or added as a second monomer which was copolymerized with the diethylene glycol bis(allyl carbonate) to form a random copolymer. The additives, which comprised two urethane acrylates, an allyl urethane and an epoxy acrylate, were found to have little effect on toughness at levels of around 2 wt% and l0 wt%. However, the stiffness of the polymer network was reduced by all four additives. Dynamic mechanical analysis revealed that all the additive agents had two competing influences on toughness. Toughening due to the lowering of an upper glass transition was counteracted by an antiplasticization effect, whereby the presence of the second network reduced the available free volume for segmental motion which caused an inherent decrease in toughness. Scanning electron microscopy revealed little evidence to support crazing as being an important mechanism in the deformation of CR-39 resins.
European Polymer Journal, 2001
Dynamic mechanical and thermal behaviour of ordered linear and crosslinked polyurethane systems based on a mesogenic diol, 4,4 H -bis(11-hydroxyundecyloxy)biphenyl (D), 2(4)-methyl-1,3-phenylene diisocyanate (DI) and poly(oxypropylene)triol (T) was investigated during network formation and in fully cured samples. The networks were prepared at various stoichiometric initial molar ratios of the reactive groups, [OH] T =[NCO] DI =[OH] D ranging from 1/1/0 to 1/12/11; for comparison, linear sample with the ratio 0/1/1 was also investigated. From our measurements it followed: (a) The power-law parameters, which are characteristic of the critical structure at the gel point (the gel strength S and relaxation exponent n), are dependent on the initial ratio of the reactive groups. With increasing content of mesogenic diol in network chain (increasing length of elastically active network chain (EANC)) both, the gel strength S and relaxation exponent n decrease. (b) Introduction of chemical junctions reduces¯exibility of the EANCs in fully cured networks and inhibits conformational rearrangements required for ordering. Increasing the content of mesogenic diol in EANCs increases the concentration of permanent physical interactions (trapped entanglements) in the systems and the intensity of the slow relaxation process in the rubbery region. Ó
Polymer Bulletin, 1982
works has shown that the trapped entanglement contribution to the equilibrium modulus is likely to occur.
Materials & Design, 2011
Polyurethane elastomer networks were designed and synthesized based on hydroxyl terminated polybutadiene/polypropyleneoxide (HTPB/PPO) mixtures, 2,4-toluene diisocyanate and 1,4-butanediol. Various networks with different molar ratio of HTPB to PPO (0/100, 25/75, 50/50, 75/25 and 100/0) had been prepared. Depending on the length of soft segment, average functionality of polyol mixtures, mechanical and thermal properties of samples were varied. Our observations confirmed that final properties of the networks can be attributed to two synergistic factors: (a) formation of chemical network (crosslinking) and (b) soft segment length. An optimum composition was found. This optimum composition shows that both physical (hard domains) and chemical network (crosslinking) have synergistic effects. Moreover, Flory-Hugins interaction parameters of soft and hard segments were calculated. Synthesized polyurethane elastomer networks have a structure similar to semi interpenetrating polymer networks, which is named pseudo-semi-IPN. These novel polyurethane elastomer networks show higher tensile strength and economic benefit than polyurethanes which are based on other non-polar polyols.
Polymer Bulletin, 1991
Elastomeric networks of polydimethylsiloxane prepared by end-linking chains having molecular weights in the range 18,500 to 220 g mo1-1 were studied from-128 to 50~ using a Rheovibron DDV Ill Viscoelastometer. In the case of the unimodal networks, the glass transition temperature Tg was generally insensitive to degree of cross-linking. The intensity of the tan 5 relaxation, however, increased by over an order of magnitude over the range of cross-link densities investigated. Bimodal networks prepared from mixtures of relatively long and very short PDMS chains also had values of Tg which were insensitive to degree of cross-linking. Finally, as expected, the intensities of the tan ~ peak for the bimodal networks could not be explained on the basis of simple additivity of contributions from the relatively long and the very short network chains.
Journal of Polymer Science Part B: Polymer Physics, 1987
The equilibrium stress-strain properties and the swelling behavior of moderately cross-linked model networks of poly(oxypropy1ene) were studied. Results were in general agreement with the theory of rubber elasticity due to Flory. However, data on the highly cross-linked networks (ac 3 725) could not be satisfactorily described by the recent theories of elasticity or swelling. This is believed to be primarily due to the marked non-Gaussian character of the very short network chains and the substantial chemical modification of the polymer by the cross-linking moiety which inevitably occurs at high cross-link densities.
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.
Polymer, 2000
Plane stress fracture toughness of amorphous films of poly(ethylene-2,6-naphthalate) (PEN) with various molecular weights (MW; characterized by the intrinsic viscosity, IV) was determined by the essential work of fracture (EWF) concept using tensile-loaded deeply double-edge notched (DDEN-T) specimens. These PENs met the basic requirement of the EWF concept: full ligament yielding, which was marked by a load drop in the force-displacement curves of the DDEN-T specimens, preceded the crack growth. This "load mark" allowed us to partition between yielding and necking. The yielding-related EWF terms were not affected by the MW of the resins and thus served for the comparison of the results. It is argued that the EWF response is governed by the entanglement network density. The role of entanglements was substantiated by showing that the "plastic" zone developed via cold drawing and not by true plastic deformation. On the other hand, MW influenced the necking related EWF terms. High MW PENs failed by stable crack growth, whereas low MW resins experienced unstable crack growth (more exactly a transition from stable to unstable crack growth) in the necking phase. This was traced to the load distribution capacity of the long entangled chains. Attempts were also made to estimate the essential and non-essential work of fracture parameters and their constituents from uniaxial tensile tests performed on dumbbells. ᭧
Journal of Polymer Science Part B Polymer Physics
A new methodology to investigate the failure of elastomers in a confined geometry has been developed and applied to model end-linked polyurethane elastomers. The experimental in situ observations show that the elastomers fail by the growth of a single cavity nucleated in the region of maximum hydrostatic stress. Tests carried out at different temperatures for the same elastomer show that the critical stress at which this crack grows is not proportional to the Young's modulus E but depends mainly on the ratio between the mode I fracture energy G IC and E. A reasonable fit of the data can be obtained with a model of cavity expansion by irreversible fracture calculating the energy release rate by finite elements with a strain hardening constitutive equation. Comparison between different elastomers shows that the material containing both entanglements and crosslinks is both tougher in mode I and more resistant to cavitation relative to its elastic modulus.
arXiv (Cornell University), 2017
John Wiley & Sons, Inc., 2019
Polyetheramine (PEA)-modified epoxies with various types of PEAs were prepared and respective effects on characteristics of epoxy networks were studied. The used PEAs were polyethylene glycol diamine (PEG-amine) and polypropylene glycol diamine (PPG-amine) with two different molecular weights (i.e., 200 and 400 g mol −1). According to mechanical tests, the structural parameters of PEAs played an important role in final properties of epoxy/amine systems. PEG 400-amine and PPG 200-amine had the highest and lowest effects on the properties of epoxy networks, respectively. Whereas 10 phr PEG 400-amine increased critical stress intensity factor (K IC) and critical strain energy release rate (G IC) of the epoxy up to 82 and 294%, the same number of PPG 200-amine chains caused to increase the K IC and G IC up to 11 and 34%. This discrepancy could be assigned to higher flexibility index (φ = 26.22), longer chain length (~27 atoms), and higher secondary interactions [δ = 9.69 (cal cm −3) 0.5 ] of PEG 400-amine in comparison with PPG 200-amine [with φ = 8.08,~10 atoms in chain, and δ = 8.98 (cal cm −3) 0.5 ]. Shear yielding as a toughening mechanism was proposed based on microscopy of the crack tips. These in-depth studies could uncover underlying structure-property relationships in a relevant class of PEA-like modifiers, shedding light on the future design of top-performing homogeneous tough polymer networks.
Journal of Applied Mechanics, 2018
The skeleton of many natural and artificial soft materials can be abstracted as networks of fibers/polymers interacting in a nonlinear fashion. Here, we present a numerical model for networks of nonlinear, elastic polymer chains with rate-dependent crosslinkers similar to what is found in gels. The model combines the worm-like chain (WLC) at the polymer level with the transition state theory for crosslinker bond dynamics. We study the damage evolution and the force—displacement response of these networks under uniaxial stretching for different loading rates, network topology, and crosslinking density. Our results suggest a complex nonmonotonic response as the loading rate or the crosslinking density increases. We discuss this in terms of the microscopic deformation mechanisms and suggest a novel framework for increasing toughness and ductility of polymer networks using a bio-inspired sacrificial bonds and hidden length (SBHL) mechanism. This work highlights the role of local network...
Bulletin of the American Physical Society, 2018
The skeleton of many natural and artificial soft materials can be abstracted as networks of fibers/ polymers interacting in a non-linear fashion. Here, we present a numerical model for networks of nonlinear, elastic polymer chains with ratedependent crosslinkers similar to what is found in gels. The model combines the worm-like chain at the polymer level with the transition state theory for crosslinker bond dynamics. We study the damage evolution and the force displacement response of these networks under uniaxial stretching for different loading rates, network topology, and crosslinking density. Our results suggest a complex non-monotonic response as the loading rate or the crosslinking density increases. We discuss this in terms of the microscopic deformation mechanisms and suggest a novel framework for increasing toughness and ductility of polymer networks using a bio-inspired Sacrificial Bonds and Hidden Length (SBHL) mechanism. This work highlights the role of local network cha...
2008
A study was made of a family of polyurethane copolymers, in which the chemical components were: a hard segment (giving, on phase separation, hard nano-scale reinforcing particles); a soft segment (giving, on phase separation, an elastomeric matrix), and a diol chain extender. The chemical compositions of all three components were varied systematically and independently, and their mechanical responses were measured in cyclic tensile tests at room temperature, up to stretches in the range 5-6. Particular attention was paid to characterizing the inelastic features – hysteresis, and stress relaxation in interrupted tests – and their variations between the materials. The same materials were also studied by wide-angle X-ray scattering (WAXS), to determine levels of crystallinity. Results showed that hysteresis was increased by increasing hard phase crystallinity. This was the case for polyurethanes based on the novel diisocyanate 4,4’-dibenzyl diiscyanate (DBDI). The extent of stress rela...
JOM, 2012
A novel atomistic simulation method is developed whereby polymer systems can undergo strain-rate-controlled deformation while bond scission is enabled. The aim is to provide insight into the nanoscale origins of fracture. Various highly cross-linked epoxy systems including various resin chain lengths and levels of nonreactive dilution were examined. Consistent with the results of physical experiments, cured resin strength increased and ductility decreased with increasing cross-link density. An analysis of dihedral angle activity shows the locations in the molecular network that are most absorptive of mechanical energy. Bond scission occurred principally at cross-link sites as well as between phenyl rings in the bisphenol moiety. Scissions typically occurred well after yield and were accompanied by steady increases in void size and dihedral angle motion between bisphenol moieties and at cross-link sites. The methods developed here could be more broadly applied to explore and compare the atomistic nature of deformation for various polymers such that mechanical and fracture properties could be tuned in a rational way. This method and its results could become part of a solution system that spans multiple length and time scales and that could more completely represent such mechanical events as fracture.
FAKIROV:COND.THERMOPLAST O-BK, 2005
Langmuir, 2004
A new cohesive zone model is developed in order to study the mechanisms of adhesive and cohesive failures of soft rubbery materials. The fracture energy is estimated here using a strategy similar to that of Lake and Thomas (LT) by considering the dissipation of stored elastic energy followed by the extension and relaxation of polymer chains. The current model, however, departs from that of LT in that the force needed to break an interfacial bond does not have a fixed value; instead, it depends on the thermal state of the system and the rate at which the force is transmitted to the bond. While the force required to rupture a chain is set by the rules of thermomechanically activated bond dissociation kinetics, extension of a polymer chain is modeled within both the linear and nonlinear models of chain elasticity. Closed form asymptotic solutions are obtained for the dependence of crack propagation speed on the energy release rate, which are valid in two regimes: (I) slow crack velocity or short relaxation time for bond dissociation; (II) fast crack velocity or long relaxation time for bond dissociation. The rate independent and the zero temperature limit of this theory correctly reduces to the fracture model of LT. Detailed comparisons are made with a previous work by Chaudhury et al. which carried out an approximate analysis of the same problem.
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