Linear viscoelasticity of polymer melts filled with nano-sized fillers

The linear dynamic rheology of polymer melts filled with nano-sized fillers is investigated in relation to a proposed two phase model. A common principle is disclosed for nanofilled polymers exhibiting either fluid- or solid-like behaviors with increasing filler volume fraction. The bulky polymer phase far away from the filler inclusions in the nanocomposites behaves the same as in the unfilled case while its contribution to the composite modulus is enlarged due to strain amplification effect. The filler forms aggregates together with polymer chains absorbed on the filler surface, which is termed as the “filler phase” in the proposed model. The dynamics of the “filler phase” slow down with increasing filler concentration. The applicability of the proposed two phase model is discussed in relation to the well-known structural inhomogeneity of nanofilled polymers as well as the strain amplification and the filler clustering effects.     

Effects of molecular weight distribution and branching on rheological properties of polyolefin melts

The objective of this work was to determine the relationships among molecular and melt parameters of polyolefins. The polyolefins studied are polypropylene, poly-1-butene, poly-1-hexene, poly-1-dodecene, these have regularly spaced short-chain branches. Conclusions from previous work, as well as some new data, on polyethylene are given. As the molecular weight increases, the critical shear rate decreases but the melt viscosity and non-Newtonian ratio increase. As the molecular weight distribution broadens, the critical shear rate decreases, whereas the normal forces and the non-Newtonian ratio increase. Increasing the number of short-chain branches increases the energy of activation and the melt viscosity but decreases the non-Newtonian ratio. As the length of the short-chain branches increases, the non-Newtonian ratio increases, but the melt viscosity, critical shear rate, and energy of activation decrease. Increasing the number of long-chain branches decreases the non-Newtonian ratio, but the normal forces and the melt viscosity increase. Such information allows the polymer chemist to design a polyolefin molecule having the critical melt properties required for a given production technique.     

Prediction of linear viscoelastic response for entangled polyolefin melts from molecular weight distribution

The linear viscoelastic properties of polymer melts depend strongly and systematically on the molecular weight distribution. A molecular theory relating dynamic modulus and molecular weight distribution for linear polymers, developed and confirmed earlier with data for three other polymer species, is applied here to commercial samples of isotactic polypropylene and high density polyethylene. Experimental master curves are compared with predictions based on only the fundamental rheological parameters of the species and molecular weight distributions as obtained by the methods of size exclusion chromatography. Agreement is fairly good for the two polypropylene samples, about the same as had been found earlier for the other species, but it is highly variable for the ten polyethylene samples. We attribute this variability to differences among high density polyethylenes in the frequency, length, and type of long-chain branching. However, we could find surprisingly little supporting evidence for this from such supposed signatures of long branches in polyethylene as the flow activation energy E_a. Measured values of E_a agreed well with the literature results for linear polyethylene; none showed the elevation in E_a that would be expected for polyethylene with long branches.     

Effect of dispersion of particles on viscoelasticity of CaCo3-filled polypropylene melts

Viscoelastic properties of polypropylene melts filled with small (0.15 μm) and large (4.0 μm) CaCO₃ particles have been measured. The effects of particle size, loading, and rheological history on the dispersion of particles have been investigated. The dispersion of particles was found to decisively influence the viscoelastic properties of these filled polymers. The systems filled with large particles exhibit a relatively stable viscoelastic behavior. The small particle-filled polymers with low loading are stable similarly to the large particle-filled system. For the system filled with 30 wt% small particles, there appears a “second plateau” in the storage modulus G′ curve in low frequency region and the height of the second plateau depends strongly on the rheological history. The results are interpreted in terms of the formation of an internal structure of particles. It was found that the internal structure of particles is broken up by a steady shear flow and the dispersion of particles is changed.     

Influence of side‐chain structures on the viscoelasticity and elongation viscosity of polyethylene melts

Metallocene‐catalyzed, low‐density and linear low‐density polyethylenes with similar melt indexes were used to investigate how side‐chain structures influence the elongation viscosity and viscoelastic properties. The viscoelastic properties were determined with a rotation rheometer, while the elongation viscosities were acquired by using isothermal fiber spinning. The Phan‐Thien‐Tanner (PTT) model was also used to understand how the side‐chain structure affects the elongation behavior. Experimental results demonstrate that the log G′ vs. log G″ plot can qualitatively describe the effects of the side chain branch on the rheological properties of polyethylene melts. According to the results determined by the PTT model, low‐density polyethylene (LDPE) has low elongation viscosities at high strain rates. This low elongation viscosity can be attributed to the fact that LDPE has high shear thinning behavior. The long‐chain branching tends to increase entanglements, thereby enhancing the storage modulus, elongation viscosity and shear‐thinning behaviors. Uniform side‐chain distribution lowers the entanglements, which results in a low storage modulus, elongation viscosity and shear‐thinning behavior.     

Correlation between viscoelasticity,microstructure, and molecular properties of zein and pennisetin melts

Cereals are a large source of biopolymers, where mainly the starch is used for food and feed. A rapidly growing cereal application is the production of biofuel, mainly produced from corn in the US. The starch is fermented to ethanol leaving spent grain rich in cereal proteins as a by-product. The corn protein zein is currently extracted on a large scale and used in, for example, material applications. Similarly, pennisetin can be extracted from pearl millet, a crop critical for food security in sub-Saharan Africa. The formation of viscoelastic melts is crucial for (bio)plastics production and the viscoelasticity, microstructure, and molecular properties of zein and pennisetin melts were determined here. The proteins were mixed with plasticizers (polyethyleneglycol or glycerol/citric acid) to form melts. The melts displayed a phase separated microstructure with protein-rich and plasticizer-rich regions with distinctly separate T_gs. The pennisetin melts formed cross-links at temperatures above 60°C, which could be related to the high content of cysteine and methionine, as compared to zein. As a consequence, pennisetin melts showed a more thermocomplex behavior than zein melts. For zein melts, the mixture of glycerol and citric acid interacted with protein in addition to being a plasticizer causing a high-molecular weight shoulder in the molecular weight distribution. The study showed that, although both zein and pennisetin form viscoelastic melts, the choice of plasticizer strongly affects both melt structure and physical properties. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Model description of the nonlinear viscoelasticity of oriented polyethylene terephthalate and polycaproamide fibres

The possibility of quantitatively describing and predicting the nonlinear viscoelasticity of fibres in the region of low strains based on a mechanical model is demonstrated. __________ Translated from Khimicheskie Volokna, No. 3, pp. 12–15, May–June, 2006.     

Constitutive equations in nonlinear viscoelasticity of glassy polymers based on the concept of traps

Constitutive equations are derived for the nonlinear viscoelastic response of amorphous polymers. The model treats a glassy polymer as an ensemble of independent relaxing regions that randomly hop in their cages being thermally activated. Rearrangement occurs when a flow unit reaches some liquid‐like state. Stress‐strain relations are verified using experimental data in tensile relaxation tests for polyester resins with two types of flexibilizers. Fair agreement is demonstrated between observations and results of numerical simulation.     

Dynamic viscoelasticity and phenomenological model of electrorheological elastomers

Electrorheological elastomers (EREs) present a tunable viscoelasticity with the application of an electric field. For their application, it is necessary to investigate the viscoelasticity of the EREs under various loading conditions and establish an accurate constitutive model. In this study, anisotropic silicone‐rubber‐based EREs with 30 vol % TiO₂–urea core–shell particles were prepared under an orientation electric field. We evaluated their viscoelasticities by testing their shear stress–shear strain hysteresis loops under various electric fields, frequencies, and strain amplitudes. On the basis of the experimental data, a nonlinear, revised Bouc–Wen phenomenological model was established, and the parameters in the model were identified. The results indicate that the revised model could accurately describe the viscoelastic properties of the EREs within a low frequency. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45407.     

The onset of nonlinear viscoelasticity in multiaxial creep of glassy polymers: A constitutive model and its application to PMMA

A physically based, isostructural, constitutive model is described for simulating the onset of nonlinear viscoelasticity in multiaxial creep of glassy polymers, as needed in stress analyses of load-bearing components. In the linear viscoelastic limit, shear response reduces to that of a generalized Maxwell model, while hydrostatic response is Hookean. Nonlinearity enters through Eyring-type rate process kinetics. The equations of the model are solved numerically using a pseudo-linear approximation through each time step, leading to an incremental equation for stress that would be convenient for use in finite element analyses. The model and its assumptions were tested using tension, shear and combined tension/shear creep experiments on well-aged poly(methyl methacrylate) at 70°C. Reproducibility tests confirmed the assumption of constant glass structure for strains up to ～ 1.5 × 10^?2. Shear and pressure activation volumes were obtained by fitting the dependence of the shear compliance on stress invariants. The data showed unequivocally that shear activation volumes vary with log(relaxation time), and excellent agreement was obtained for a linear variation, consistent with the “compensation rule” of polymer thermo-viscoelasticity. The activation volumes are large (many monome units), indicating the cooperative nature of the elementary flow process. Interestingly, they are of the same order as those applying to yield and plastic flow. Although the model finds success in simulating creep, it fails to describe so accurately the strain recovery on unloading. Possible explanations are suggested.     

Optimizing selection of a model of the viscoelasticity of synthetic fibres

A method was obtained for numerical solution of the problem concerning the resolvent of the determining integral relaxation and creep equations for the case of nonlinearity of the viscoelastic properties of synthetic fibres. Numerical rotation of the integral relaxation and creep kernels and the corresponding normalized functions in the form of the normalized arctangent of the logarithm of the reduced time allows drawing a conclusion concerning the validity of the choice of a given function as the basis for the model of the viscoelastic properties. The optimality criteria for selection of the mathematical model of the viscoelasticity of synthetic fibres are reported. __________ Translated from Khimicheskie Volokna, No. 6, pp. 58–60, November–December, 2006.     

Development of industrial polyolefin blends using melt rheology data

The review of current knowledge of the composition dependence of polymer-blend processability and morphology shows that development of industrial blends requires use of a semiempirical approach, based on the particular rheological composition (PRC) concept. Selecting blend composition in the close proximity to PRC and employing factorial experiments for the mixing process allows the development of successful industrial polyethylene/polypropylene blends designed for film and blow-molding applications.     

Modeling of nonlinear extensional and shear rheology of low-viscosity polymer melts

The hierarchical multi-mode molecular stress function (HMMSF) model developed by Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheol. 60, 625–636 (2016)] for linear and long-chain branched (LCB) polymer melts were used to analyze the set of transient elongational and shear viscosity data of two LCB low-density polyethylenes (1840H and 2426 k), and a linear poly-(ethylene-co-α-butene), PEB A-780090 as reported by [Li et al. J. Rheol. 64, 177 (2020)], who had developed a new horizontal extensional rheometer to extend the lower limits of elongational viscosity measurements of polymer melts. Comparison between model predictions and elongational stress growth data reveals excellent agreement within the experimental window, and good consistency with shear stress growth data, based exclusively on the linear-viscoelastic relaxation spectrum and only two nonlinear model parameters, the dilution modulus G_D for extensional flows, and in addition a constraint release parameter for shear flow.     

A numerical approach for obtaining nonlinear viscoelasticity parameters of polymeric materials and composites

A least-squares fitting procedure is developed for application to determine the parameters of the power law for nonlinear creep and recovery behavior of polymeric materials. The nonlinear power law, developed by Schapery from thermodynamic principles, is linearized, and an iterative approach is used to determine the desired parameters. The iteration is stopped after the standard deviation of the calculated points with respect to the fitted points reaches a minimum value. The purpose of this method is to avoid the inherent ambiguities present in the more familiar graphical fitting procedure. In order to study the sensitivity and limitations of an experimental approach for determining the viscoelastic parameters, sets of artificial experimental data points were generated for use as a control. These points were obtained by varying the theoretical functional values with normally-distributed random numbers within a preset error band.     

用低烟无卤阻燃剂聚烯烃材料制造复合编织布研究

概述:传统的塑料包装布主要是聚烯烃塑料编织布,其中的高聚物属易燃、可燃材料,在燃烧时热释放速率大、热值高、火焰传播速度快、不易自熄、延燃性强,燃烧时还会产生浓烟或有毒、有害、有腐蚀性的气体,对环境造成二次性危害,对人的生命安全带来巨大的威胁。此种编织布遇火极易引起燃烧,故适用范围受到限制。     

Interaction of nonhomogeneous shear,nonlinear viscoelasticity,and yield of a solid polymer

A constitutive equation for small strain viscoelastic response is considered in which stress relaxation. occurs faster as strain increases. The constitutive equation is of single integral type and has a psuedo- or material time function which is calculated from a strain dependent shift function. First, it is shown that such a constitutive equation can account for yield as observed in polymers for a number of different stress and strain histories. Next, the constitutive equation is used in the analysis of the problem in which a hollow cylinder is fixed at its inner surface and a moment history is applied to its outer surface. This causes the cylindrical surfaces to rotate about the central axis, thereby inducing a radial shear strain distribution. It is shown that there is a time when the material near the inner support begins to yield and a layer of large shear strain gradient begins to grow rapidly. It is also shown that the stress or strain history at a material element will generally not be one of the standard histories used to study yield.     

聚烯烃织物背胶干燥特性及干燥模型研究

研究了聚烯烃织物背胶在不同干燥温度和风速时的干燥曲线、干燥速率曲线、水分有效扩散系数(Deff)以及干燥活化能(Ea),建立了干燥的数学模型。研究结果表明:聚烯烃织物背胶的整个干燥过程属于降速干燥,干燥温度和风速的升高都有利于缩短干燥时间;Page模型能较好描述聚烯烃织物背胶的干燥过程,并且Deff为(2.46~4.15)×10-8m2/s,Ea为26.95 kJ/mol。