A new multiscale modeling approach for the prediction of mechanical properties of polymer-based nanomaterials

A detailed knowledge about the physics and chemistry of multiphase materials on different length and time scales is essential to tailor their macroscopic physical and mechanical properties. A better understanding of these issues is also highly relevant to optimize their processing and, thus, their elucidation can be decisive for their final industrial application. In this paper, we develop a new multiscale modeling method, which combines the self-consistent field theory approach with the kinetic Monte Carlo method, to simulate the structural–dynamical evolution taking place in thermoplastic elastomers, where hard glassy and soft rubbery phases alternate. Since the early seventies, it is well established that the properties of the core nanophases in these multiphase materials considerably affect their overall mechanical properties. However, recent experimental studies have clearly demonstrated that, besides the efficient handling of the core nanophases, the appropriate treatment of their interfacial region is another major challenge one has to face on the way of target-oriented development of these materials. In this work, we set a particular focus on the complex structural–dynamical processes occurring at the interphases, and study their influence on the local structural and mechanical properties. To reach our objectives, we apply the new methodology on a thermoplastic elastomer composed of ABA triblock copolymers, subjected to a sizeable external perturbation, and determine its time-averaged internal stress and composition profile. We deduce from this investigation that, to obtain the correct local mechanical properties of these multiphase materials, their structure and dynamics need to be taken into account on an equal footing. Finally, our investigation also provides an explanation and confirms the importance of the chain-pullout mechanism in the viscoelastic and stress relaxation behavior of these materials.     

Mechanical properties of crosslinked polyurethanes

Stress–strain and stress–relaxation behavior of polyurethane elastomers based on poly(ethylene adipate), poly(ethylene maleate), polyethylene glycol, and 4,4′-diphenylmethane diisocyanate (MDI) have been studied. The elastomers were crosslinked by an excess of MDI and by dicumyl peroxide (DiCup); the latter was supposed to form additional crosslinks on the unsaturated bonds. The determined values of Young's modulus, Mooney-Rivlin elastic parameters C₁ and C₂, relaxation moduli E(10 sec) and E(100 sec), as well as relaxation speed were used to estimate the effect of MDI- and DiCup-formed crosslinks on the mechanical behavior of polyurethanes. It was found that while the elastomers crosslinked by MDI only apparently displayed viscoelastic properties, the polyurethanes additionally crosslinked by DiCup exhibited more elastic behavior. The results obtained were explained on the basis of changes in the amount of secondary bonding due to the additional network junctions formed by DiCup at nonpolar groups.     

Assessing thermomechanical properties of a reactive maleic anhydride grafted styrene-ethylene-butylene-styrene/thermoplastic polyurethane blend with temperature scanning stress relaxation method

The phenomenon of stress relaxation in thermoplastic elastomers (TPEs) is common and influences the end-use properties of polymers. Temperature scanning stress relaxation (TSSR) method extends an advanced method to study the stress relaxation of TPEs at elevated temperatures. A reactive blend system based on maleic anhydride grafted styrene-ethylene-butylene-styrene and thermoplastic polyurethane is explored for its relaxation behavior at temperature up to 200°C with TSSR meter. The relaxation spectrum revealed the transitions occurring in the blends as well as the extent of interfacial interaction present. Direct measurement of elasticity of the blends was obtained from the TSSR index (RI). Glass transition temperature of the samples was measured from dynamic mechanical analysis. The elastic nature of the blends was also pursued from the storage modulus values and results were in line with TSSR results. The density of crosslinks in the system was assessed with both TSSR and the conventional Flory-Rehner equation and a similar trend was obtained. Atomic force microscopy and scanning electron microscopy revealed the dispersed morphology of the blends.     

Exchange reactions as a basis of thermopiastic behaviour in crosslinked polymers

An attempt has been made to achieve thermoplastic behaviour in a chemically crosslinked elastomer by arranging that the crosslinks should undergo rapid exchange at high temperatures. Natural rubber was chemically modified to give pendent hydroxyl groups which were then used as crosslinking sites to form β-keto-ester or malonate crosslinks. The resultant vulcanisates showed high stress relaxation rates in the temperature range 120 to 160°C and some degree of remouldability at 180°C. The incursion of permanent crosslinking prevented quantitative correlation between stress relaxation rates and chemical exchange rates of the crosslinking systems.     

Dynamic stress relaxation behavior of nanogel filled elastomers

Long-time stress relaxation behavior of virgin elastomers, chemically crosslinked nanogels and nanogel filled elastomers was studied with the help of a dynamic mechanical analyzer. Sulfur crosslinked natural rubber and styrene butadiene rubber nanogels and nanocomposite gels were prepared and characterized using different methods. These gels were added in to the virgin elastomer matrix at different concentrations. Presence of crosslinked gels in elastomer matrix greatly influenced its stress relaxation behavior. The effect of draw ratio, gel loading and temperature on the stress relaxation behavior of elastomers was investigated in detail. It was found that virgin elastomers displayed extremely long-term relaxation processes and the time required to achieve equilibrium dramatically decreased with the increase in crosslink density in the case of gels. Time-temperature superposition studies revealed that stress relaxation process was accelerated and relaxation time reduced with a rise in temperature. Finally, experimental stress relaxation data were fitted with the empirical Chasset and Thirion equation with good agreement. From the fitting parameters, the characteristic relaxation time and the material parameter were estimated in order to understand the mechanism of the relaxation processes in the gels and the gel filled elastomers.     

Pulsed NMR study of elastomeric block copolymer under deformation

Deformation behavior of an elastomeric styrene–butadiene–styrene block copolymer (SBS) is studied by pulsed NMR techniques, and is related to lifetime distributions and the change of the microstructure in the stress relaxation process. By the measurement of spin–spin relaxation time, it is found that polybutadiene (PB) chains in the vicinity of polystyrene (PS) domains come to be in more constrained conformations with stretching than those remote from the domains mainly through the intramolecular interactions, followed by the enlargement of the constrained regions, which reflects the roles of both crosslinks and filler particles in crosslinked rubbers. In the stress relaxation process, however, the mean lifetime for SBS at the critical strain is longer than that at lower strain in contrast with the results for the crosslinked rubbers. It is estimated that the differences between the failure behaviors of SBS and those of the conventional crosslinked rubbers may be mainly caused by the characteristic change of the microstructure (the disruption of the weak interconnections between the spherical PS domains with high energy dissipation) in SBS on deformation, associated with the limited extensibility of the PB chains between the adjacent PS domains. It becomes clear that the pulsed NMR method complements the mechanical measurements with a more precise information on the heterogeneity in the rubbery polymers under deformation.     

Viscoelastic behavior of partly decrosslinked polymer networks. I. Acrylic acid anhydride-crosslinked poly(ethyl acrylate)

Acrylic acid anhydride (AAA) and tetreathylene glycol dimethacrylate (TEGDM) were employed as labile and permanent crosslinking monomers for poly(ethyl acrylate), respectively. Upon partial or total hydrolysis of the AAA crosslinks, various states of viscoelastic creep and stress relaxation were brought about. The use of chemically active monomers for crosslinking permits new polymer structures to be synthesized. In this case, decrosslinking converts a thermoset polymer into its thermoplastic counterpart. The relationship between the present decrosslinking study and a new nomenclature theory of grafted and crosslinked polymers is explored.     

Domain structure and time-dependent properties of a crosslinked urethane elastomer

The morphology of a chemically crosslinked urethane elastomer is correlated with its time-dependent mechanical properties. Evaluation of this amorphous elastomer by electron microscopy and small-angle x-ray scattering reveals that incompatible chain segments cluster into separate microphases having a periodicity in electron density of about 90 Å. This observed domain structure is similar to that seen previously in uncrosslinked, thermoplastic urethane elastomers. As in earlier studies on such linear system, thermal pretreatment of the crosslinked elastomer causes a time-dependent change in its room temperature modulus. However, the magnitude of this modulus change (about 20%) is generally less than observed previously with the linear systems. Another contrast with previous findings is that this time-dependent phenomenon is apparently not caused by thermally activated changes in microphase segregation. Rather, the observed time dependence in modulus is believed to be caused by molecular relaxation resulting in densification of amorphous packing within the hard-segment domains. The validity of this proposed mechanism is supported by differential scanning calorimetry experiments showing evidence of enthalpy relaxation during room-temperature aging of the elastomer. This relaxation is qualitatively similar to that observed previously during sub-T_g annealing of single-phase glassy polymers.     

Stress relaxation and the domain structure of thermoplastic elastomer

The relationship between the stress relaxation phenomena and domain structure of thermoplastic elastomer (TPE) was studied. Two representative thermoplastic elastomers: styrenebutadiene-styrene block copolymer (SBS) and 1,2-syndiotactic polybutadiene (1,2-PB), representing the amorphous glassy domain and crystalline domain, respectively, were tested in different atmospheres and temperatures. Results show that the structure of the domain has a significant effect on the stress relaxation curve. It is found that the way the glassy domain is formed determines the failure of the domain and hence the stress relaxation rate. In the case of crystalline domain, the history of heat treatment determines the crystal structure and, in turn, the stress relaxation rate.     

SELF-ADHESION HYSTERESIS IN POLYDIMETHYLSILOXANE ELASTOMERS

Self-adhesion hysteresis has been investigated in crosslinked poly(dimethylsiloxane) (PDMS) lenses using the Johnson, Kendall, and Roberts technique. The experimental conditions involved relatively short contact times for which interchain penetration effects across the interface are minimal. Only lenses that had been extracted in toluene displayed self-adhesion hysteresis. The same lenses demonstrated no adhesion hysteresis when pressed against tethered polystyrene substrates, indicating that hysteresis was caused by surface interactions and not bulk viscoelastic effects. Extraction produces hysteresis by removing the free chains, which normally lubricate the interface, inhibiting the adhesion mechanism. Self-adhesion hysteresis was only observed for networks with a high molecular weight between crosslinks. More tightly crosslinked networks did not display self-adhesion hysteresis, even at extended contact times under load. By inhibiting the hydrosilylation reaction between residual vinyl and silane groups in the PDMS lenses, self-adhesion hysteresis was prevented, suggesting that the formation of chemical crosslinks across the interface caused the observed hysteresis. The molecular weight dependence of the hysteresis can be interpreted in terms of the Lake-Thomas model [1] for fracture in elastomers.     

Dynamically vulcanized blends of polypropylene and ethylene octene copolymer: Influence of various coagents on thermal and rheological characteristics

The present study focuses on the influence of the three structurally different coagents, namely triallyl cyanurate (TAC), trimethylol propane triacrylate (TMPTA) and N,N′‐m‐phenylene dimaleimide (MPDM) on the thermal and rheological properties of thermoplastic vulcanizates (TPVs) based on the polypropylene (PP) and ethylene octene copolymer (EOC). Depending on the structure and reactivity, different coagents show different behaviors. All the TPV compositions were made by melt mixing method in a Haake Rheomix at 180°C. Rheological properties have also been evaluated at the same temperature. Viscoelastic properties of the TPVs were analyzed by a dynamic oscillatory rheometer in the melt state in a Rubber Process Analyzer (RPA 2000). Morphologically, TPVs consist of dense crosslinked rubber domains dispersed in a continuous thermoplastic matrix. The crosslinked rubber particles have a tendency to form agglomerates and build local clusters which undergo disintegration by shearing. A variety of rheological characteristics such as Payne effect, shear rate sensitivity, modulus recovery and dynamics of relaxation were studied by performing strain sweep, frequency sweep and stress relaxation tests. Among the various coagents taken for investigation, MPDM‐based TPVs show improved dynamic functions (complex modulus and complex viscosity) and lower rate of stress relaxation over TAC, TMPTA and the control sample without any coagent. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

A comparative study of swelling properties of hydrogels based on poly(acrylamide‐co‐methyl methacrylate) containing physical and chemical crosslinks

Poly (acrylamide‐co‐methyl methacrylate) hydrogels of different ratios were prepared by using chemical and physical crosslinks to study the effect of nature of crosslinks on swelling behavior of hydrogels. The chemically crosslinked gels were prepared by using NN′‐methylene bis acrylamide, while physically crosslinked hydrogels were prepared by precipitation polymerization method, using dioxane as solvent. Detailed swelling kinetics such as swelling ratio, transport exponent n, diffusion coefficient D and the effect of pH on equilibrium swelling studies. The study revealed that the nature of crosslinks alter the swelling characteristics of the hydrogel. In chemically crosslinked hydrogels the water transport is Fickian in nature, while in the case of the physically crosslinked hydrogels the water transport mechanism is anomalous indicating major change in relaxation mechanism due to nature of crosslinks. The results also indicate that with increasing acrylamide content the swelling ratio of the hydrogels were also increased, but the transport exponent n remains nearly constant. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 779–786, 2003     

Physical and chemical stress relaxation of elastomers

In this paper we have developed a method whereby physical and chemical relaxation processes can be distinguished, using stress relaxation experiments as a function of temperature. We assumed that there exists some temperature range above the glass transition temperature over which the chemical effects can be neglected for the time scale of the experiments. The data in this low temperature range were then used to determine the WLF constants and other physical relaxation parameters. The physical component of the stress relaxation could then be subtracted from high temperature experiments in order to extract chemical kinetic information. Based on certain reasonable assumptions, an equation was developed for the relaxation modulus of a chemically reacting system. This equation could be used to determine the time dependence of the crosslink density, or conversely could be used to predict the long term relaxation modulus from an assumed kinetic mechanism. These calculations were demonstrated for ethylene propylene and butyl elastomers.     

Thermoplastic rubber/PP elastomers toward extremely low thermal expansion

Fine regulation of the microstructure of rubber/polypropylene (PP) alloys could remarkably reduce the coefficient of linear thermal expansion (CLTE) while retaining the mechanical properties similar to those of thermoplastic elastomers. Rubber/PP elastomers with different morphologies were successfully prepared by controlling the appropriate rubber type, viscosity ratio, and processing method. The CLTE of the polymer alloy parallel to the microlayer directions was considerably reduced when the rubber domains were deformed into microlayers and co‐continuous with plastic domains. The thickness of the PP layers played a crucial role on CLTE reduction. The CLTE considerably decreased with reduced thickness of the PP layer. The sample with a co‐continuous microlayer structure exhibited good flexibility, high elongation, low hardness, and permanent deformation. Thus, low‐thermal‐expansion elastomer materials may have wide applications. Stress relaxation and strain recovery of the ethylene–propylene–diene terpolymer/PP (70/30 wt %) blend were investigated to further clarify the influence of co‐continuous microlayer structure on mechanical properties. Anisotropic mechanical properties were consistent with the morphology. Results of the stress relaxation behavior test would provide further support to the mechanism of the low thermal expansion of blends with co‐continuous microlayer structure. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43902.     

Unique shape memory behavior of polyolefinic blends with special reference to creep behavior,stress relaxation,and melt rheological study

Creep response, stress relaxation behavior, and melt rheological study of the shape memory polymer blend based on EOC‐EPDM has been studied in details. In this study, especially the effect of the crosslinks formation in presence of electron beam on the creep response, melt rheological study and stress relaxation behavior has been reported. With increase of electron beam dose, creep response becomes lower and the creep compliance value also comes down. Higher resistance creep response of the radiation crosslinked blends indicates the superior shape recovery behavior of the blends. Stress relaxation behavior of the crosslinked blend also shows the lower decay of stress value with time for higher radiation crosslinked blend. The lower relaxation ratio of the highly radiation crosslinked blend also supports the superior shape recovery behavior of the crosslinked blend. Apart from, melt rheological study shows the higher storage modulus value and higher complex viscosity of the radiation crosslinked blend which also supports the formation of higher crosslinked network structure. Tension set value also clearly indicates the better shape recovery behavior of the crosslinked blend. POLYM. ENG. SCI., 58:876–885, 2018. © 2017 Society of Plastics Engineers     

On the glassy state of multiphase and pure polymer materials

In this work we formulate a new glass theory and investigate its suitability for describing the mechanical response of thermoplastic elastomers composed of styrenic-block copolymers. These materials are composed of glassy domains of polystyrene, which physically link soft rubbery chain segments made of either polybutadiene or polyisoprene. We demonstrate that the crossover in the shift factors, observed experimentally to change from Williams-Landel-Ferry to Arrhenius behavior passing through a characteristic crossover temperature T^∗ from below, coincides with the crossover from power-law to stretched-exponential behavior of the stress relaxation found in recent tensile experiments. Moreover, we show that the characteristic crossover temperature T^∗ is identical with the underlying true equilibrium second-order phase transition temperature T₂ of the polystyrene crosslinks, predicted by the thermodynamic theory of Gibbs and Di Marzio for pure glassy polystyrene in the infinite-time limit. By combining the recently introduced theory of Di Marzio and Yang with the significant-structure theory of Eyring and Ree, we develop a new glass theory, which is capable of explaining the mechanical response of multiphase as well as pure glassy materials. Moreover, we show a clear evidence for the existence of T₂ postulated in 1950s for pure glasses and hotly debated since then.     

Applications of a two-network model for crosslinks and trapped entanglements

The dependence of stress and birefringence on strain in uniaxial extension of crosslinked rubbers can accurately be described by a model in which the properties of a network of crosslinks and a network of trapped entanglements are additive. The crosslink network is neo-Hookean and the entanglement network can conveniently be described by the Mooney-Rivlin equation. When the crosslinks are introduced in a state of strain near the glass transition temperature, the two networks have different reference undeformed states; they can be distinguished by appropriate measurements in the state of ease where their associated stresses are equal and opposite and in the state of deformation where the cross-links were introduced and make no contribution to the stress. When partial relaxation is permitted before crosslinking, trapping probabilities can be calculated for both relaxed and unrelaxed entanglements and compared with the Langley theory. The results are consistent with the terminal mechanism of relaxation in the tube theory of Doi and Edwards.     

Fatigue testing of implantable specimens: Effect of sample size and branching on the dynamic fatigue properties of polyisobutylene-based biomaterials

In this paper we present the first results on the effect of specimen size and branching on the fatigue properties of polyisobutylene-based thermoplastic elastomers measured by the hysteresis method. It was verified that smaller specimens were inherently stronger as expected; at the same loading rate microdumbbells induced higher strain rates so they can be considered as the “worst case” scenario. Microdumbbells, which can be implanted into small animals for in vivo studies, were used for dynamic fatigue testing of linear poly(styrene-b-isobutylene-b-styrene) triblock copolymers (L_SIBS) in comparison with long-chain branched (tree-like or dendritic) versions (D_SIBS). In dynamic stress relaxation studies, D_SIBS performed better than L_SIBS. Simulated physiological conditions had negligible effect on the dynamic properties.     

Elastomeric latex domain-interpenetrating polymer networks: Physical and rheological properties

The combination of rubbery and rigid polymers in a multiphase structure using staged emulsion polymerization has yielded materials with properties ranging from reinforced elastomers to high impact plastics. The many different particle morphologies that result from a two-stage latex (TSL) polymerization include core/shell, domain, interpenetrating polymer networks (IPN), and various combinations thereof. The sequence of polymerization, crosslinking, grafting, and composition are among the significant parameters that determine the particle morphology. Elastomeric TSL with soft polyacrylates (PA) as the seed particles and polystyrene (PS) as the second stage, with each stage lightly crosslinked, may yield IPN-microdomain particles. The particle morphology has been elucidated through a combination of microscopy and mechanical property analyses. The significant modulus of elastomeric latex interpenetrating polymer networks (LIPN) results from reinforcement by PS intra-particle microdomains and their significant tensile strength from a strength forming mechanism of PS inter-particle microdomains. The increase in the PA seed crosslinking increases the crosslinked PS (xPS) level of molecular mixing with, and grafting via residual unsaturation to, the crosslinked PA (xPA) network and decreases particle deformnability. At higher xPS concentrations the formation of an xPS-rich shell enhances xPS continuity in the molded material through the partial coalescence of the shells, diminishing the PA continuity, and yielding more PS-like properties. The submicron lightly crosslinked latex particles with these different morphologies flow as a pseudoplastie material through a particle slippage flow mechanism exhibiting neither a Newtonian plateau nor a yield stress at low shear rates. The deformable lightly crosslinked particles with interchangeable PS ties which disintegrate at elevated temperatures retain their identity and regain their shape at the cessation of shear. The LIPN can be processed using standard thermoplastic methods and machinery, with power law constants and shear insensitive flow activation energies that are similar to those of thermoplastics at high levels of shear. Uncrosslinked PS shells around crosslinked PA seed particles, on the other hand, completely coalesce upon molding to form a continuous thermoplastic PS matrix that may essentially flow through molecular deformation.