Finite Element Based Micro-mechanical Modeling of Interphase in Filler Reinforced Elastomers

Characteristic properties of elastomers can be tailored by embedding them with filler particles. Along with enhancing the overall properties of the composite, filler particles also induce some inelastic effects. In this paper, a finite element computational model is used to study the effect of microstructure morphology in filled elastomers, on its macroscopic large deformation behavior. A multiphase material model that accounts for the hypothesis of shift in glass transition temperature in the vicinity of the filler particle is developed to simulate the interphase between the fillers and the matrix. It also accounts for the breakdown and re-aggregation of filler networks under cyclic loading. Examples at the microstructural level, demonstrating the dynamics of the interphase using the developed multiphase model have been successfully simulated. The obtained results are in good qualitative agreement with the Mullins effect. Therefore, computational experiments using this methodology enable the prediction of the experimentally observed softening behavior in filled elastomers based on its microstructure evolution.     

Influence of the crosslink network structure on stress‐relaxation behavior: Viscoelastic modeling of the compression set experiment

A viscoelastic approach of the compression set test is addressed in this work. This test measures the ability of rubber compounds to retain elastic properties after prolonged action of compressive stresses. Elastic properties were tested by recording the normal stress under a constant deformation of 25% with a laboratory rheometer. Considering the Boltzmann superposition principle, compression set data were modeled from the relaxation of Young's modulus, described by a Maxwell spectrum plus a constant E_∞ defining the elastic properties at the long times. This approach was developed with the copolymer of ethylene and vinyl acetate (EVA) networks crosslinked by radical chemistry and by an exchange reaction between acetate groups and silane compounds as crosslinking agents. Regarding the recovery of the elastic properties, radical chemistry provided better results than the exchange reaction for the identical crosslinking density of the network. Then, the Curro–Pincus molecular approach was developed to understand the influence of the microstructure of the EVA network on the elastic properties. The difference of the elastic properties between the two networks crosslinked by two different chemistry means was accounted for by considering the probability of having a dangling end of n units for a random crosslinking process. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1779–1790, 2003     

Magneto‐sensitive Elastomers in a Homogeneous Magnetic Field: A Regular Rectangular Lattice Model

A theory of mechanical behaviour of the magneto‐sensitive elastomers is developed in the framework of a linear elasticity approach. Using a regular rectangular lattice model, different spatial distributions of magnetic particles within a polymer matrix are considered: isotropic, chain‐like and plane‐like. It is shown that interaction between the magnetic particles results in the contraction of an elastomer along the homogeneous magnetic field. With increasing magnetic field the shear modulus, G, for the shear deformation perpendicular to the magnetic field increases for all spatial distributions of magnetic particles. At the same time, with increasing magnetic field the Young's modulus, E, for tensile deformation along the magnetic field decreases for both chain‐like and isotropic distributions of magnetic particles and increases for the plane‐like distribution of magnetic particles.

     

Thermo‐Viscoelastic Response of Polycarbonate Reinforced with Short Glass Fibers

Observations are reported for oscillatory torsion tests at several temperatures ranging from room temperature to 100 °C on a polymer composite consisting of a polycarbonate matrix reinforced with short glass fibers. Constitutive equations are derived for the linear viscoelastic behavior of the polymer composite, which is treated as an equivalent heterogeneous network of chains bridged by junctions (entanglements and glass fibers). The network is thought of as an ensemble of meso‐regions with arbitrary shapes and sizes. With reference to the concept of cooperative relaxation, the time‐dependent response of an ensemble is associated with the rearrangement of meso‐domains. The rearrangement events occur at random times as meso‐regions are agitated by thermal fluctuations. Stress–strain relations for isothermal deformation of an ensemble of meso‐domains are derived by using the laws of thermodynamics. The governing equations are determined by five adjustable parameters that are found by fitting the experimental data. The effects of temperature and filler content on the material parameters are studied in detail.

The shear modulus G GPa versus the content of short glass fibers ν wt.‐%. Symbols: treatment of observations in oscillatory torsion tests at T = 25 (unfilled circles) and T = 100 °C (filled circles). Solid lines: approximation of the experimental data by Equation (27). Curve 1: G₀ = 1.05, G₁ = 3.83 × 10⁻². Curve 2: G₀ = 0.91, G₁ = 3.65 × 10⁻².     

Application of the Christensen‐Lo Model to the Reinforcement of Elastomers by Fractal Fillers

This paper is concerned with the development of a hydrodynamic model for the reinforcement of rubber by colloidal fillers such as silica and carbon black. Each fractal aggregate is replaced by an equivalent effective sphere, and the reinforcing ability of the latter is estimated using the Christensen‐Lo solution of the “three‐phase composite sphere model”. With a single adjustable parameter, the model allows a quantitative interpretation of the small‐strain modulus of rubber loaded with up to 50 PHR of N234 carbon black, which falls just below the filler overlap concentration. No additional contributions to the small‐strain modulus by filler–filler “interactions” are needed to interpret the data.

A branched filler aggregate made up of spherical primary particles (black) and the effective sphere replacing it (gray).     

Effect of side groups of polymer glycol on microphase‐separated structure and mechanical properties of polyurethane elastomers

The effect of side methyl and dimethyl groups of the soft segment component on the microphase‐separated structure and mechanical properties of polyurethane elastomers (PUEs) was investigated. Poly(oxytetramethylene) glycol (PTMG), and PTMG incorporating dimethyl groups (PTG‐X) and methyl side groups (PTG‐L) were used as a polymer glycol, which forms a soft segment in the PUEs. The PUEs were synthesized with 4,4′‐dipheylmethane diisocyanate [1,1′‐methylenebis(4‐isocyanatobenzene)], 1,4‐butane diol, and 1,1,1‐trimethylol propane by a prepolymer method. The degree of microphase separation of the PUEs became weaker with increasing side group content in polymer glycols. Dynamic viscoelastic properties measurement showed reorganized‐crystallization and melting of the soft segment for the PUEs based on PTMG, PTG‐L, and PTG‐X with a lower content of the side groups, but not for a PTG‐L and PTG‐X with higher content of the side groups. Tensile testing revealed that increasing methyl group concentration made the PUEs soften and weaken. The PTMG‐based PUEs obviously exhibited strain‐induced crystallization of the soft segment chains during elongation process. In contrast, for the PTG‐L and PTG‐X‐based PUEs, crystallinity decreased with increasing side group content, and the PUEs with PTG‐L and PTG‐X with highest methyl group content did not crystallize even at a large strain. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2054–2063, 2008     

Manipulating Latex Polymer Microstructure Using Chain Transfer Agent and Cross‐Linker to Modify PSA Performance and Viscoelasticity

Two series of butyl acrylate (BA)/acrylic acid (AA)/2‐hydroxy ethyl methacrylate latexes were produced via starved seeded semi‐batch emulsion polymerization. The first series, five latexes with gel contents ranging from 0 to 75 wt.‐%, were generated by varying the amount of chain transfer agent (CTA, n‐dodecyl mercaptan) in the absence of cross‐linker. The second series, two latexes with gel contents of 49 and 74 wt.‐%, were obtained by manipulating the amount of CTA in the presence of a constant cross‐linker (allyl methacrylate) concentration. Latexes with similar gel contents, one from each series, were compared with respect to their microstructure, viscoelastic properties and pressure‐sensitive adhesive performance. At similar gel contents, latexes obtained in the absence of cross‐linker had larger sol polymer molecular weight ($\overline {M} _{{\rm w}} $ ) and molecular weight between cross‐linking points (M_c), compared to the latexes generated using both CTA and cross‐linker. The different microstructures of latexes with similar gel contents resulted in significantly different viscoelastic properties and shear strength of the pressure‐sensitive adhesive films cast from the latexes.

     

Toughening of poly(L‐lactide)/multiwalled carbon nanotubes nanocomposite with ethylene‐co‐vinyl acetate

Poly(L ‐lactide)/multiwalled carbon nanotubes (PLLA/MWCNTs) nanocomposite recently attracts much attention because of its excellent comprehensive properties including improved thermostability, tensile strength, and conductivity. However, the nanocomposite exhibits similar brittleness compared with unmodified PLLA. In this work, a polar elastomer, that is, ethylene‐co‐vinyl acetate (EVA), was introduced into PLLA/MWCNTs nanocomposite. The selective distribution of MWCNTs and the effects of EVA on crystalline structure of PLLA were investigated using scanning electron microscope, transmission electron microscope, differential scanning calorimetry, and wide angle X‐ray diffraction. The results show that the presence of EVA induces the change of the distribution of MWCNTs in the nanocomposites, and consequently, the cold crystallization of PLLA is prevented. With the increase of EVA content, both the ductility and the impact resistance of PLLA/FMWCNTs are improved greatly, indicating the toughening effect of EVA on PLLA/MWCNTs nanocomposite. The decreased tensile strength and modulus can be compensated through annealing treatment. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Conductive Elastomers with Autonomic Self‐Healing Properties

Healable, electrically conductive materials are highly desirable and valuable for the development of various modern electronics. But the preparation of a material combining good mechanical elasticity, functional properties, and intrinsic self‐healing ability remains a great challenge. Here, we design composites by connecting a polymer network and single‐walled carbon nanotubes (SWCNTs) through host–guest interactions. The resulting materials show bulk electrical conductivity, proximity sensitivity, humidity sensitivity and are able to self‐heal without external stimulus under ambient conditions rapidly. Furthermore, they also possess elasticity comparable to commercial rubbers.     

Modeling the Viscoelastic Response of Suspension of Particles in Polymer Solution: The Effect of Polymer‐Particle Interactions

A conceptual model is proposed for the viscoelastic response of dilute polymer solutions containing well‐dispersed low volume fraction spherical particles. The equilibrium structure of the reversibly adsorbed polymer layer on the particle surface was characterized by a scaling theory. The dynamics of the polymer chains were studied by a Maxwell type kinetic model. At the limit of small particle size, our results show that the monomer‐filler energetic affinity, particle volume fraction and surface friction strongly affect the overall viscoelastic response of the filled solutions and lead to unusual viscoelastic properties that have been observed experimentally. These properties include a dramatic increase in shear viscosity, intense shear thinning, and solid‐like behavior at low frequency domains.

     

Lightly crosslinked,mesomorphic networks obtained through the reaction of dimeric,liquid‐crystalline epoxy–imine monomers and heptanedioic acid

We reacted various dimeric, liquid‐crystalline epoxy–imine monomers, differing in the length of the central aliphatic spacer or the dipolar moments, with heptanedioic acid. The resulting systems showed a liquid‐crystalline phase in some cases, depending on the dimer and on the reaction conditions. The systems were characterized with respect to their mesomorphic properties and then were submitted to dynamic mechanical thermal analysis in both fixed‐frequency and frequency‐sweep modes in the shear sandwich configuration. The arrangement in the liquid‐crystalline phase seemed to be mainly affected both by the polarization of the mesogen and by the reaction temperature, which favored the liquid‐crystalline arrangement when it was lying in the range of stability of the dimer mesophase. In agreement with other recent literature data, dynamic mechanical thermal analysis results suggested that the presence of the mesogen directly incorporated into the main chain increased the lifetimes of the elastic modes both in the isotropic phase and in the liquid‐crystalline phase with respect to side‐chain liquid‐crystalline elastomers and that the time–temperature superposition principle did not hold through the liquid‐crystalline‐to‐isotropic transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44:6270–6286, 2006     

On the relevance of the 8‐chain model and the full‐network model for the deformation and failure of networks formed through photopolymerization of multifunctional monomers

Crosslinked networks were synthesized by copolymerization of mono‐functional tert‐butyl acrylate (tBA) with diethyleneglycol dimethacrylate (DEGDMA) or polyethylene glycol dimethacrylates (PEGDMA). By varying the chain length and concentration of the difunctional PEGDMA, we obtained tBA‐PEGDMA copolymer networks while by varying the concentration of difunctional DEGDMA, we obtained tBA‐DEGDMA crosslinked networks. The various materials were submitted to large deformations through uniaxial tension tests. For moderate weight percent of crosslinking agent, up to 20%, the networks showed standard S‐shape stress–strain curves, characteristic of rubber‐like elasticity. Two macromolecular models, the 8‐chain model and the full‐network model, were applied to fit the uniaxial tensile response of the materials. Both models provide good representations of the overall uniaxial stress–strain response of each material. After fitting to stress–strain data, the network models were employed to predict the shear modulus and the elongation at break. Neither the 8‐chain nor the full network model were capable of predicting the failure strain or shear modulus, indicating these models are best used to describe stress–strain relations rather than predict mechanical properties for the network polymers considered here. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1226–1234, 2008     

Adhesion curves between two viscoelastic materials by a point‐contact method in a crossed‐cylinder geometry

We investigated an evaluation method of adhesion between two cylindrical viscoelastic materials by a point contact in a crossed‐cylinder geometry. The shape of the adhesion curve obtained in this technique is characterized not only by the maximum adhesion force, F_A, but also by the adhesion force at complete separation, F_S. To clarify the factors that determine the characteristic properties of the adhesion curve, the adhesion forces of a highly crosslinked polydimethylsiloxane were measured as a function of the separation velocity. As a result, F_A and F_S strongly depended on the separation velocity. To understand the experimental results, a simulation of the separation behavior was carried out using the Generalized Maxwell model, which could qualitatively reproduce the experimental observations. From these results, we discussed the factors that determine the adhesion curve and clarified the uniqueness and advantages of this evaluation method. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1778–1788, 2009     

Direct 3D Visualization of the Phase‐Separated Morphology in Chlorinated Polyethylene/Nylon Terpolyamide Based Thermoplastic Elastomers

Blends of chlorinated polyethylene and nylon‐6/‐6,6/‐12 terpolyamide were prepared. The ratio of the two components was systematically varied within the blends. The mechanical behavior of the samples was analyzed with tensile tests and dynamical mechanical analysis showing that, for several ratios, materials with improved mechanical properties typical of thermoplastic elastomers were obtained. In such a mechanical regime, a co‐continuous phase‐separated morphology was clearly evidenced at the microscopic scale by 3D laser scanning confocal fluorescent microscopy (LSCFM). At blend compositions where plastic tensile behavior is observed, LSCFM reveals dispersed spheres of one component in the other.     

Viscoelasticity of nanobubble‐inflated ultrathin polymer films: Justification by the coupling model

The nanobubble inflation method is the only experimental technique that can measure the viscoelastic creep compliance of unsupported ultrathin films of polymers over the glass–rubber transition zone as well as the dependence of the glass transition temperature (T_g) on film thickness. Sizeable reduction of T_g was observed in polystyrene (PS) and bisphenol A polycarbonate by the shift of the creep compliance to shorter times. The dependence of T_g on film thickness is consistent with the published data of free‐standing PS ultrathin films. However, accompanying the shift of the compliance to shorter times, a decrease in the rubbery plateau compliance is observed. The decrease becomes more dramatic in thinner films and at lower temperatures. This anomalous viscoelastic behavior was also observed in poly(vinyl acetate) and poly (n‐butyl methacrylate), but with large variation in the change of either the T_g or the plateau compliance. By now, well established in bulk polymers is the presence of three different viscoelastic mechanisms in the glass–rubber transition zone, namely, the Rouse modes, the sub‐Rouse modes, and the segmental α‐relaxation. Based on the thermorheological complexity of the three mechanisms, the viscoelastic anomaly observed in ultrathin polymer films and its dependence on chemical structure are explained in the framework of the Coupling Model. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Theoretical modeling of the relationship between Young's modulus and formulation variables for segmented polyurethanes

We describe a new modeling approach to prediction of Young's modulus of segmented polyurethanes. This approach combines micromechanical models with thermodynamic considerations based on the theory of block copolymers. The resulting model predicts both the equilibrium morphology and the “ideal” Young's modulus of a segmented polyurethane polymer as a function of its formulation (hard segment chemical structure, hard segment weight fraction, soft segment equivalent weight) and temperature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2123–2135, 2007     

Synthesis,characterization, and properties of polyurethanes containing 1,4:3,6‐dianhydro‐D‐sorbitol

Two‐ and three‐component polyurethanes containing 1,4:3,6‐dianhydro‐D ‐sorbitol (isosorbide) derived from glucose were synthesized using n‐BuSn(?O)OH·H₂O as a catalyst, and the thermal properties (T_g, T_d) of the polymers were investigated by differential scanning calorimetry and thermogravimetric analysis. We carried out molds for polyurethanes, the molds of polyurethanes were obtained. The dynamic mechanical analyzes showed that the storage modulus values of the three‐component polymers were constant to a higher temperature than those of the two‐component polymers. The storage moduli (E′), loss moduli (E″), and values of tan δ for the polymers were obtained. The rigidity of three‐component polymers was increased by the introduction of bisphenol A and diphenylmethane group to two‐component polymer. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6025–6031, 2009