Linear and non-linear viscoelastic rheology of hybrid nanostructured materials from block copolymers with gold nanoparticles

A polystyrene-b-poly-4-vinypyridine (PS-b-P4VP) diblock copolymer is modified with a gold precursor to obtain an organic–inorganic (hybrid) block copolymer in bulk with gold nanoparticles selectively incorporated in the P4VP block. In the linear viscoelastic regime, temperature sweep tests over a series of these hybrid block copolymer systems revealed consistent shifts (ΔT) in the glass transition temperatures (both T _g\text-PS_{\rm g\text{-}PS} and T _g\text-P4VP_{\rm g\text{-}P4VP}) of the hybrid materials in comparison to the pristine polymers. Studying different volume fractions of the pyridine block, a level-off point was found for block copolymers with f _P4VP > 0.26, where the shifts in T _g\text-P4VP_{\rm g\text{-}P4VP} consistently increased up to ΔT = 25°C. By artificially increasing the volume fraction of the pyridine block, the nanoparticles reduce the transition regime determined in master curves. At higher volume fractions of the pyridine block, crossover frequencies were not detected after the entanglement regime, indicating that the material does not relax from topological constraints (entanglements and nanoparticles) into the terminal regime. Above a specific volume fraction of nanoparticles (Φ _P = 0.05), the flow behaviour of the hybrid materials becomes increasingly elastic, exhibiting wall-slip from the geometry at lower strain values in comparison to the pristine material. In the non-linear viscoelastic regime, Fourier-transformed rheology was used to analyse the raw signals from strain sweep experiments. It was clearly demonstrated the nanoparticle effect by following the second and third harmonic (I _2/1, I _3/1) of the stress response. Comparing the behaviour of the third and second harmonics provided an unambiguous fingerprint for the effect of the nanoparticles.     

Linear viscoelastic properties of emulsions and suspensions with thermodynamic and hydrodynamic interactions

We present a new approach to describe the rheological properties of dispersions with non-hydrodynamic interactions (steric, electrostatic and Van der Waals interactions) in the linear viscoelastic domain. Our model is based on the calculation of additional stresses resulting from interaction potentials between spheres and Brownian motion. We start from the statistical mechanical approaches which have been developed by Batchelor and Green and later Lionberger and Russel, to model the viscoelastic properties of emulsions and suspensions. We have extended their calculations to the more general case of viscoelastic deformable inclusions in a viscoelastic matrix. Our contribution lies in the computation of the hydrodynamic functions involved in the term describing interaction stresses. This computation is based on Palierne's results on the deformation field around a viscoelastic inclusion embedded in a viscoelastic matrix. We have also rewritten the conservation equation in the case of interest, over the whole frequency domain. We finally express the complex shear modulus of the dispersion as the sum of two terms : Palierne's complex shear modulus gives the purely hydrodynamic contribution; the interaction contribution depends on both the hydrodynamic properties and the interaction potential.     

Linear viscoelastic master curves of neat and laponite-filled poly(ethylene oxide)–water solutions

Aqueous solutions composed of dispersed nanoparticles and entangled polymers are shown to exhibit common viscoelasticity over a range of particle and polymer concentrations. Time–temperature superposition and time–concentration superposition are applied to generate rheological master curves for neat and laponite-filled aqueous solutions of poly(ethylene oxide). The shift factors were correlated in terms of temperature and concentration and are found to differ from previous reports for ideal polymer solutions, which can be rationalized with a molecular interpretation of the structure of the laponite–polymer solutions. Laponite addition to the concentrated polymer solution is observed to increase the relaxation time but decrease the elastic modulus, which is a consequence of polymer adsorption and bridging. The addition of small amounts of laponite to stable PEO–water solutions also leads to ageing on the time scale of days.     

Unsteady motion of a non-linear viscoelastic fluid

In this paper, we study the unsteady flow of a generalized second grade fluid. Specifically, we solve numerically the linear momentum equations for the flow of this viscoelastic shear-thinning (shear-thickening) fluid surrounding a solid cylindrical rod that is suddenly set into longitudinal and torsional motion. The equations are made dimensionless. The results are presented for the shear stresses at the wall, related to the drag force; these are physical quantities of interest, especially in oil-drilling applications.     

树脂基三维编织复合材料粘弹性性能的有限元分析

根据材料的细观结构,采用APDL语言分别建立了纤维束和三维编织复合材料两级单胞的参数化几何模型;推导了Prony级数表示的树脂粘弹性本构方程,对模型进行了组分材料参数设置;对纤维束单胞模型进行扫掠式网格划分,对三维编织复合材料单胞模型进行线-面-体式网格划分;对两级单胞模型均施加合理的边界条件,使单胞边界上的位移满足周期性和连续性。以有限元模型为基础,计算了三维编织复合材料的粘弹性能,并给出了材料粘弹性效应随工艺参数变化的规律。计算结果表明:三维编织复合材料编织方向的粘弹性效应随编织角的增大而增强,随纤维体积比的增大而减弱。该结果与已有实验结论一致。     

Effect of ionic interaction on linear and nonlinear viscoelastic properties of ethylene based ionomer melts

The effect of ionic interaction on linear and nonlinear viscoelastic properties was investigated using poly(ethylene-co-methacrylic acid) (E/MAA) and its ionomers which were partially neutralized by zinc or sodium. Dynamic shear viscosity and step-shear stress relaxation studies were performed. Stress relaxation moduli G(t, y) of the E/MAA and its sodium or zinc ionomers were factorized into linear relaxation moduli G°(t) and damping functions h(y). The relaxation modulus at the smallest strain in each ionomer agreed with the linear relaxation modulus calculated from storage modulus G and loss modulus G. In the linear region, the ionic interaction shifted the relaxation time longer with keeping the same relaxation time distribution as E/MAA. In the nonlinear region, the ionic interaction had no influence on h(y) when the ion content was low. At higher ion content, however, the ion bonding enhanced the strain softening of h(y).     

Limitations of the Phan-Thien non-linear network viscoelastic model

The failure of the Phan-Thien non-linear network viscoelastic model to predict realistic stress-strain relationships under certain conditions is illustrated in two examples. Care in the application of the model when applied in situations where high shear rates are expected is indicated.     

Inflation of a bonded non-linear viscoelastic toroidal membrane

The inflation of a bonded viscoelastic toroidal membrane under finite deformations is considered. Three new variables, viz. the two principal stretch ratios and the angle between the normal vector of a deformed membrane and the axis of symmetry are introduced as dependent variables. The governing equations are reduced thereafter to a set of three first-order partial differential integral equations. The constitutive equation developed by Pipkin and Rogers for the non-linear response of a viscoelastic material is used. The creep phenomenon for an inflated viscoelastic toroidal membrane under a constant pressure is presented.     

Mechanical and optical characterization of cellulose acetate

To obtain the basic relations for photo-viscoelastoplastic stress analysis using cellulose acetate, the effect of strain rate as well as room temperature on mechanical and optical properties was precisely investigated by the uniaxial tension test. As a result, the nonlinear stress-strain, the non-linear-stress-fringe order and the nonlinear-fringe-order strain relations were uniquely reoresented in their nondimensional forms regardless of strain rate and room temperature. Young's modulus, yield stress and the yield fringe order were linearly related both to room temperature and to logarithm of strain rate. The effect of strain rate on these relations has caused great difficulties in experimental stress analysis with respect to photoplasticity. However, it was found in this work that the value of the strain rate at any points in the model can be determined by the fringe-order rate measured. Therefore, it is possible to estimate not only the distribution of strain rate but that of stress or strain in the photo-viscoelastoplastic model with cellulose acetate.     

Domain switching and non-linear coupling of ferroelectric composites

One of the most notable characteristics of ferroelectric materials is that they could undergo spontaneous polarization and spontaneous strain changes by applied fields. Reorientation of the spontaneous polarization and spontaneous polarization strain of ferroelectric inclusions in ferroelectric composites can change microstructures and affect effective electroelastic properties of ferroelectric composites. Based on orientation distribution function and its evolution as well as switching criterion, non-linear electromechanical coupling behaviour of ferroelectric composites is studied by application of micromechanics. A constitutive model of ferroelectric composites is developed. Comparison between analytical and experimental results shows that the model presented can describe many non-linear electromechanical coupling problems of ferroelectric composites such as polarization or depolarization, etc.     

Linear and non-linear rheology of linear polydisperse polyethylene

Rheological techniques, size-exclusion chromatography, and molecular spectroscopy are the most widely used tools for describing polymer molecular structure in polyolefins. The detection of long-chain branching, and to some extent, its quantification, have been based on quantifying the deviation of polyethylene??s (PE) rheological behavior from that of a linear reference. Although metallocene-based PE has been extensively studied, linear polydisperse originating from Ziegler or Chromium-based catalysts are not often thoroughly considered, despite their high industrial importance. Within this work, we study the linear and non-linear rheology of a set of polydisperse PEs, for which the topological linearity is confirmed by GPC-MALLS measurements. Thus, we can safely quantify the effect of broad molecular weight distribution, high and ultra-high molecular weight fractions on rheological quantities and model parameters. Specifically, the zero-shear viscosity, ?? ₀ vs. M _w, relaxation spectra, phase lag vs. the complex modulus plot (van Gurp?CPalmen method) were applied and significant deviations from the ??rheologically linear?? behavior were observed, attributed only to M _w, M _z and polydispersity. Since the elongational viscosity was typical of linear PE, large-amplitude oscillatory shear and FT-Rheology were applied to quantify the non-linear rheological behavior. The latter was described by a single parameter, $Q=I_{3/1}/\gamma_0^2$ , which for linear polydisperse PE was correlated to the high molecular weight fraction and was constant over a broad range of applied Deborah numbers for the respective excitation frequencies. Since we need to correlate structural features such as broad MWD and HMW to polymer performance under processing conditions, we have to extend the analysis of linear rheological parameters, such as zero-shear viscosity, to non-linear parameters, e.g., the Q parameter quantified and used here.     

Linear and non-linear nature of the flow of polypropylene filled with ferrite particles: from low to concentrated composites

The flow behavior of a filled suspension consisting of ferrite particles suspended in a polypropylene matrix with and without the addition of a commercial dispersant (Solplus DP310) was studied. The composites were filled with 10, 20, 30, and 40 vol.%. Both capillary and parallel disk rotational flows were employed. On the one hand, dynamic results confirm general trends found for highly concentrated systems. The higher is the filler level, the lower is the linear viscoelastic domain. When adding the dispersant agent, it was shown a larger linear viscoelastic domain, lower moduli values and thus, lower viscosity. Also, the critical strain, G′ and G′′ showed a power law dependency on the volume fraction. On the other hand, the capillary results showed no dependency of the flow properties on the die. Thus, no slip of the suspension at the wall was observed. Actually, this experimental finding elucidated that the significant decrease on viscosity produced by the addition of the dispersant agent at 40 vol.% is principally due to lubricant effects and not at all to slip contributions. The results also reveal three distinct flow regimes. Low, moderate, and high shear rates lead to different microstructure under flow.     

Characterisation of non-linear viscoelastic foods by the indentation technique

A method to determine the non-linear viscoelastic constitutive constants from indentation force–displacement data corresponding to different indentation speeds has been developed. The method consists of two parts. In the first part, the force–displacement data is expressed as two functions which represent the strain and the time-dependent responses, respectively. From these functions, the time-dependent constants and the instantaneous force–displacement response are obtained. In the second part, the strain-dependent variables are determined from the instantaneous force–displacement response through an inverse analysis based on the Levenberg–Marquardt method. The method was verified by numerical experiments using the properties of cheese as examples.     

Effect of time dependent compressibility on non-linear viscoelastic wave propagation

The work presented consists essentially of two parts: the first deals with the development of a non-linear constitutive equation for a three-dimensional viscoelastic material with instantaneous and time dependent compressibility; the second deals with the solution of some specific wave propagation problems for three simple three-dimensional geometries. The constitutive equation is based on the existence of elastic and creep potentials and is expressed in terms of single memory integrals with non-linear kernels. The wave propagation problems are solved by numerical integration along the characteristics of the governing equations. The primary conclusion drawn deals with the effect of time dependent compressibility on the dynamic stress, strain and velocity fields. Results indicate that the dynamic response of even slightly time dependent compressible materials varies dramatically from those assumed to have only an instantaneous elastic compressibility.     

Linear viscoelastic behavior of asphalt and asphalt based mastic

The rheological properties of an asphalt mastic and its matrix are investigated. For the purpose of comparison a sample of thermal aged asphalt matrix is also considered. Dynamic and creep shear measurements are reported. The reduced shear rate concept proposed by Ohl and Gleissle is used to correlate mechanical properties of the three materials at the same temperature. We found that the concept gives only qualitative trends. A similar conclusion is found concerning the applicability of the time-temperature superposition principle for each sample. Our experimental results show also that the increase in viscosity due to thermal treatment or to the inclusion of solid particles is not uniform with temperature. The differences in the increase of the Vogel temperature from the asphalt to the mastic, or to the thermally aged asphalt, relate to the different mechanisms involved. Sedimentation of steel spheres in asphalt and mastic, is studied next. The Newtonian wall correction factor for the Stokes drag law holds for the three samples. Despite the similar behavior observed in conventional shear tests, Stokes' law gives the correct trend for the two asphalts although it overestimates the experimental settling velocity by a factor of approximately two in the case of the mastic. Received: 8 June 1999/Accepted: 19 October 1999     

Instability of steady shearing flows in a non-linear viscoelastic fluid

This paper proves the non-existence of global smooth solutions to an equation for a viscoelastic fluid shearing flow. The non-existence of smooth solutions is interpreted physically as the formation of a vortex sheet and an instability in the fluid motion.Dedicated to Clifford Truesdell on the occasion of his sixtieth birthday