Ensemble Of Meso-regions Research Articles

A viscoelastic model for predicting viscoelastic functions of polymer and polymer nanocomposites

In the present work, a time-dependent constitutive equation, established in the literature, is further elaborated to describe a variety of viscoelastic functions. The viscoelastic model under investigation is based on the assumption that the network of chains is thought to be an ensemble of meso-regions, linked to each other. The neighboring chains on the basis of cooperative motions, change their positions, and the time-dependent response is determined by the distribution of meso‑regions with varying energy barriers. In the present work, the Gaussian distribution was selected to be followed by the activation energies. The constitutive equation was solved for dynamic mechanical, stress-relaxation and creep experiments. It has been shown that starting from one viscoelastic function in the frequency (time) domain, all viscoelastic functions in the time (frequency) domain could hereafter be evaluated, with the same parameter values. The proposed treatment was proved to be flexible enough, to predict viscoelastic functions of various polymeric materials and polymer nanocomposites.

The effect of impurities on the viscoelastic response of polycarbonate reinforced with short glass fibers

Observations are reported in oscillatory torsion tests at room temperature on unfilled and fiber-reinforced polycarbonates melt-blended with impurities (acronitrile–butadiene–styrene, high-impact polystyrene, low-density polyethylene, poly(ethylene terephthalate) and Nylon 6,6). Constitutive equations are derived for the viscoelastic behavior of glassy polymers. With reference to the theory of cooperative relaxation, a polymer is treated as an ensemble of meso-regions with arbitrary shapes and sizes. The time-dependent response of the ensemble is attributed to rearrangement of meso-domains. The rearrangement events occur at random times, when meso-regions are excited by thermal fluctuations. Stress–strain relations are derived by using the laws of thermodynamics. The governing equations are determined by four adjustable parameters that are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. The study focuses on the effects of the concentration of impurities and glass fibers on material parameters.

The effect of temperature on the viscoelastic response of semicrystalline polymers

Three series of isothermal torsion relaxation tests were performed at various temperatures ranging from room temperature to T = 120°C on isotactic polypropylene, low-density polyethylene, and linear low-density polyethylene. Constitutive equations are derived for the viscoelastic behavior of a semicrystalline polymer at small strains. A polymer is treated as an equivalent network of strands bridged by temporary junctions (entanglements, physical crosslinks on the surfaces of crystallites, and lamellar blocks). The network is thought of as an ensemble of mesoregions with various activation energies for detachment of active strands from their junctions. The time-dependent response of the ensemble reflects thermally induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). Stress–strain relations are developed by using the laws of thermodynamics. The governing equations involve five adjustable parameters that are found by fitting the experimental data. This study focuses on the influence of temperature and crystalline morphology of polyolefins on the material parameters in the constitutive relations. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 9–23, 2004

Linear thermo-viscoelasticity of isotactic polypropylene

Observations are reported on injection-molded isotactic polypropylene in torsion oscillation tests at various temperatures from room temperature to T=150 °C, as well as in torsion relaxation and bending creep tests in the range of temperatures between 30 and 80 °C. Constitutive equations are derived for the viscoelastic response of a semicrystalline polymer at three-dimensional deformations with small strains. A polymer is treated as an equivalent transient network of strands connected by junctions (entanglements, physical cross-links on the surfaces of crystallites and lamellar blocks). The network is thought of as an ensemble of meso-regions with various activation energies for rearrangement of strands. The distribution of meso-domains is described by a generalized Gaussian function. The time-dependent behavior of the ensemble reflects separation of active strands from their junctions and merging of dangling strands with the network. The rearrangement events occur at random times, when the strands are excited by thermal fluctuations. Stress–strain relations involve five material constants that are found by fitting the experimental data. Good agreement in demonstrated between the observations and the results of numerical simulation. The study concentrates on the effect of temperature on the adjustable parameters.

The effect of temperature on the viscoelastic behavior of linear low-density polyethylene

Observations are reported on linear low-density polyethylene in isothermal torsional oscillation and relaxation tests at various temperatures ranging from room temperature to 110 ∘C. Constitutive equations are derived for the viscoelastic response of a semicrystalline polymer at small strains. The polymer is treated as an equivalent network of strands bridged by junctions (entanglements, physical cross-links on the surfaces of crystallites and lamellar blocks). The network is thought of as an ensemble of meso-regions with various potential energies for rearrangement of strands. Two types of meso-domains are introduced: active, where strands separate from temporary junctions as they are excited by thermal fluctuations, and passive, where detachment of strands is prevented by the surrounding macromolecules. The time-dependent behavior of the ensemble reflects separation of active strands from their junctions and merging of dangling strands with the network. Stress–strain relations are developed by using the laws of thermodynamics. The governing equations involve six material constants that are found by fitting the experimental data. The study focuses on the effects of (i) temperature, (ii) the deformation mode (torsion versus bending), and (iii) the loading program (oscillations versus relaxation) on the adjustable parameters.

The viscoelastic and viscoplastic behavior of polymer composites: polycarbonate reinforced with short glass fibers

Observations are reported on polycarbonate filled with various amounts of short glass fibers (i) in tensile tests with a constant strain rate and (ii) in oscillatory torsion tests at room temperature. Constitutive equations are derived for the viscoelastic and viscoplastic responses of a polymer composite. The composite is treated as an equivalent 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 theory of cooperative relaxation, the viscoelastic response is attributed to rearrangement of meso-domains that occurs at random times when the regions are thermally activated. The viscoplastic behavior is associated with displacements of meso-regions with respect to each other. The rate of sliding of meso-domains is proportional to the rate of macro-deformation. Constitutive equations for isothermal deformation of a polymer composite are derived by using the laws of thermodynamics. The stress–strain relations are determined by five adjustable parameters that are found by fitting the experimental data. The effect of the filler content on the material parameters is studied in detail.

The effect of annealing on the elastoplastic and viscoelastic responses of isotactic polypropylene

Observations are reported on isotactic polypropylene (i) in a series of tensile tests with a constant strain rate on specimens annealed for 24 h at various temperatures in the range from 110 to 150 °C, (ii) in two series of creep tests in the subyield region of deformations on samples not subjected to thermal treatment and on specimens annealed at 140 °C, and (iii) in a series of tensile relaxation tests on non-annealed specimens. Constitutive equations are derived for the elastoplastic and non-linear viscoelastic responses of semicrystalline polymers. A polymer is treated as an equivalent transient network of macro-molecules bridged by junctions (physical cross-links, entanglements and lamellar blocks). The network is assumed to be highly heterogeneous, and it is thought of as an ensemble of meso-regions with different activation energies for separation of strands from temporary nodes. The elastoplastic behavior is modelled as sliding of junctions in meso-domains with respect to their reference positions driven by macro-deformation. The viscoelastic response is attributed to detachment of active strands from temporary junctions and attachment of dangling chains to the network. Constitutive equations for isothermal deformations with small strains are derived by using the laws of thermodynamics. Adjustable parameters in the stress–strain relations are found by fitting the experimental data.

Model for the viscoelastic and viscoplastic responses of semicrystalline polymers

AbstractConstitutive equations are derived for the time‐dependent behavior of semicrystalline polymers at isothermal loading with small strains. A semicrystalline polymer at temperatures above the glass‐transition point for its amorphous phase is thought of as a network of macromolecules bridged by junctions (physical crosslinks, entanglements, and crystalline lamellae) that can slide with respect to their reference positions in the bulk material under straining. The network is assumed to be highly inhomogeneous, and it is modeled as an ensemble of mesoregions (MRs) with various strengths of interchain interaction. Two types of MRs are distinguished: passive, where these interactions prevent detachment of strands from junctions; and active, where active strands separate from junctions and dangling strands merge with the network at random times as they are thermally agitated. The viscoelastic response of a semicrystalline polymer reflects reformation of strands in active MRs, whereas its viscoplastic behavior is associated with sliding of junctions. Stress–strain relations for uniaxial deformation are developed by using the laws of thermodynamics. Adjustable parameters in the constitutive equations are found by fitting experimental data for isotactic polypropylene in a tensile test with a constant strain rate and in tensile relaxation tests at various strains. Fair agreement is demonstrated between the observations and the results of numerical simulation. It is revealed that the viscoplastic flow of junctions strongly affects the rearrangement process in active MRs, whose rate reaches a threshold value in the vicinity of the apparent yield point. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1438–1450, 2003

The Nonlinear Time‐Dependent Response of Semicrystalline Polymers: Correlations Between the Configurational Entropy and the Rate of Rearrangement of Chains

Two series of tensile creep tests are performed on isotactic poly(propylene) in the sub-yield region of deformations at room temperature. In the first series, injection-molded specimens are used as produced, whereas in the other series the samples are preloaded (five loading-unloading cycles with the maximal strain 0.01). A constitutive model is derived for the viscoelastic and elastoplastic behavior of semicrystalline polymers. A polymer is treated as an equivalent transient network of chains bridged by junctions. Active chains separated from their junctions and dangling chains merge with the network at random times when they are thermally activated. The network id modelled as an ensemble of meso-regions (MRs) with various activation energies for detachment of chains from temporary nodes ( a distribution function for the activation energies entirely determines the configurational entropy of the ensemble). Rearrangement of chains in the network reglects the viscoelastic response. The elastoplastic behavior is attributed to sliding of junctions with respect to their reference positions and to changes in the distribution of activation energies (driven by fine and coarse slip of lamellar blocks. Stress-strain relations for a semicrystalline polymer are determined by four adjustable parameters that are found by fitting the experimental data. It is demonstrated that the attempt rate for detachment of active chains from their nodes is proportional to the configurational entropy of the ensemble of MRs.

Finite Viscoelasticity of Particle-Reinforced Elastomers: the Effect of Filler Content

Constitutive equations are derived for the time-dependent behavior of particle-reinforced rubbers at isothermal loading with finite strains. An elastomer is thought of as a network of macromolecules bridged by junctions that slip with respect to the bulk material under straining. A filled rubber is treated as an ensemble of meso-regions where sliding of junctions occurs at different rates. Two types of domains are distinguished: passive, where slippage of junctions is prevented by intermolecular links, and active, where the sliding process is not affected by interchain forces. Activation of passive meso-regions under loading is modelled as mechanically-induced breakage of van der Waals links between strands. Stress–strain relations are developed using the laws of thermodynamics. For tensile relaxation tests, these equations are determined by four adjustable parameters that are found by fitting experimental data on gum rubber, unfilled rubber, and carbon black-filled natural rubber at longitudinal strains in the range from 100 to 250%. It is revealed that the rate of sliding and the concentration of active meso-regions are noticeably affected by stretching, whereas the distribution of potential energies for sliding of junctions is independent of strains, but is severely influenced by the filler content.