Small-diameter parallel plate rheometry: a simple technique for measuring rheological properties of glass-forming liquids in shear

The rheological characterization of glass-forming liquids is challenging due to their extreme temperature dependence and high stiffness at low temperatures. This study focuses on the special precautions that need to be taken to accommodate high sample stiffness and torsional instrument compliance in shear rheological experiments. The measurement errors due to the instrument compliance can be avoided by employing small-diameter parallel plate (SDPP) rheometry in combination of numerical instrument compliance corrections. Measurements of that type demonstrate that accurate and reliable rheological data can be obtained by SDPP rheometry despite unusually small diameter-to-gap (d/h) ratios. Specimen preparation for SDPP requires special attention, but then experiments show excellent repeatability. Advantages and some current applications of SDPP rheometry are briefly reviewed. SDPP rheometry is seen as a simple and versatile way to measure rheological properties of glass-forming liquids especially near their glass transition temperature.     

Strain-induced low-frequency relaxation in colloidal DGEBA/SiO2 suspensions

Diglycidyl ether of bisphenol A (DGEBA) is widely exploited as an epoxy resin in adhesives and coatings. In this paper, it is used as an oligomer matrix for silica-filled nanocomposites. Rheological measurements show that the pure matrix obeys power-law relaxation dynamics in the vicinity of the dynamic glass transition of this low-molecular-weight glass former. In the filled systems, a low-frequency relaxation appears additionally to the structural α-process of the matrix. Considering the nanocomposites as Newtonian hard-sphere suspensions at low angular frequencies (or high temperatures), the modified terminal regime behavior of the matrix can be linked to strain-induced perturbations of the isotropic filler distributions. While in the low-frequency regime hydrodynamic stresses relax instantaneously, the Brownian stress relaxation is viscoelastic and can be evidenced by dynamic rheological measurements. At higher angular frequencies, the α-process of the matrix superimposes on the Brownian stress relaxation. In particular, we were able to depict the low-frequency anomaly for concentrated, semi-dilute, and even for dilute suspensions.     

Gelation of a radiation crosslinked model polyethylene

A radiation crosslinked model linear low-density polyethylene (LLDPE) exhibits power-law relaxation,G(t) =St ^–n at its gel point (GP). The relaxation exponent has a value of about 0.46. The relaxation behavior is dominated by power laws, not only directly at GP, but in a very broad vicinity of GP and in a frequency window, which narrows with distance from the gel point. The power law exponent decreases with increasing radiation dose (increasing extent of crosslinking). Independent measurements of the gel fraction and the molecular-weight distribution of the radiated samples' soluble fraction support the rheological observations.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

A model of acoustic absorption in fluids based on a continuous distribution of relaxation times

This work extends the quasi-equilibrium relaxation theory of sound absorption in liquids to the case of continuous distribution of relaxation times. Such extension is needed when absorption mechanisms are not confined to the action of viscosity and heat conduction, but are mainly due to the excitation of a large number of internal molecular degrees of freedom. In this case the conventional Navier-Stokes equations are not sufficient to describe the fluid motion, and additional equations are required to model normal relaxation stresses. When relaxation frequencies form a sufficiently dense distribution, as is the case for many biological fluids, it makes sense to consider the limit of continuously distributed relaxation frequencies, in order to obtain the required equation for normal relaxation stresses.In contrast to its discrete counterparts, the proposed method avoids the use of a potentially infinite number of relaxation equations for a given set of distinct relaxation frequencies. Instead, these are replaced by a single evolution equation of Boltzmann type whose right-hand side is a linear combination of the time derivatives of density and entropy. The rheological functions appearing before these derivatives are expressed in terms of the absorption coefficient. Since the dependence of absorption coefficient on sound frequency is measurable experimentally, these rheological coefficients can be recovered from experimental data.The key feature of the present study is that a closed system of equations of motion can be formulated directly from absorption measurement data on the basis of the theory proposed for the very wide range of absorption laws that can occur in practice.As an illustration of the generality of the present method, a number of absorption laws documented in the experimental literature are considered in detail, in order to derive the coefficients of the related systems of equations of motion for these liquids. For example, the methodology based on modelling of acoustic absorption in biologically soft tissue by the employment of fractional derivatives, which has been recently developed in the literature, is shown to be a special case of the proposed theory.     

Rheological changes in the bitumen caused by heating and interaction with rubber during asphalt–rubber production

The demand for more safe and durable roads, combined with the need to preserve the environment, led to the production and application of asphalt–rubber (AR) on roads. Nevertheless, this complex material needs further study in order to better distinguish among the phenomena that take place during AR production, as they impact on the final product characteristics. Here, we effectively quantify the rheological changes related to bitumen aging due to diffusion of small molecules of bitumen into the rubber particles and to the release of fillers from rubber into the bitumen during AR production. “A sphere AR production simulator” was developed to assess AR aging independently. The comparison of the characteristic relaxation times of both AR and simulated AR shows that the aging alone cannot explain the rheological changes during AR production. The extent of the changes related to the combined effects of aging and filler release increases as the bitumen used to produce AR is softer.     

Further remarks on numerical investigation on gas displacement of a shear-thinning liquid and a visco-plastic material in capillary tubes

In this note, we present some results concerning the gas displacement of power-law liquids and visco-plastic Papanastasiou’s materials improving the understanding of the problem considered in Sousa et al. (2007) [1]. Specifically, we present: the fraction of mass attached to the wall for a viscosity-thickening power-law fluid, different transition patterns between by pass and full-recirculating flow regimes, expressions for the critical (in the sense proposed by Soares and Thompson (2009) [2]) fraction of residual mass as a function of the rheological parameter of interest, and fields of yielded and unyielded zones for the visco-plastic material.     

Thermorheological properties near the glass transition of oligomeric poly(methyl methacrylate) blended with acrylic polyhedral oligomeric silsesquioxane nanocages

Two distinct oligomeric species of similar mass and chemical functionality (M _w≈2,000 g/mol), one a linear methyl methacrylate oligomer (radius of gyration R _g≈1.1 nm) and the other a hybrid organic–inorganic polyhedral silsesquioxane nanocage (methacryl-POSS, r≈1.0 nm), were subjected to thermal and rheological tests to compare the behaviors of these geometrically dissimilar molecules over the entire composition range. The glass transition temperatures of the blends varied monotonically between the glass transition temperatures of the pure oligomer (T _g=−47.3°C) and the pure POSS (T _g=−61.0°C). Blends containing high POSS contents (with volume fraction φ _POSS≥0.90) exhibited enhanced enthalpy relaxation in differential scanning calorimetry (DSC) measurements, and the degree of enthalpy relaxation was used to calculate the kinetic fragility indices m of the oligomeric MMA (m=59) and the POSS (m=74). The temperature dependences of the viscosities were fitted by the free-volume based Williams–Landel–Ferry (WLF) and Vogel–Fulcher–Tammann (VFT) framework and a dynamic scaling relation. The calculated values of the fragility from the WLF–VFT fits were similar for the POSS (m=82) and for the oligomer (m=76), and the dynamic scaling exponent was similar for the oligomeric MMA and the POSS. Within the range of known fragilities for glass-forming liquids, the temperature dependence of the viscosity was found to be similarly fragile for the two species. The difference in shape of the nanocages and oligomer chains is unimportant in controlling the glass-forming properties of the blends at low volume fractions (φ _POSS<0.20). However, at higher volume fractions, adjacent POSS cages begin to crowd each other, leading to an increase in the fractional free volume at the glass transition temperature and the observed enhanced enthalpy relaxation in DSC.     

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

A modified fractional model to describe the entire viscoelastic behavior of polybutadienes from flow to glassy regime

The dynamic mechanical behavior of a series of monodisperse polybutadienes has been investigated from the flow regime to the glassy state. Assuming a linear superposition of the entanglement and glass behavior a mathematical model of the spectrum of relaxation times is developed. It consists in a self-similar spectra for the entanglement contribution and a Fractional Maxwell Fluid (FMF) for the glassy contribution. The model closely represents the master curves of dynamic moduli over 15 logarithmic decades of frequency with three parameters for the flow regime (GN ⁰ _{N 0} and a cut-off parameter _max) and four parameters for the FMF. It is shown that one of the parameter of the FMF is similar to the power-law exponent of a self-similar spectra previously proposed in the literature to model the transition to glass.     

The structure and properties of long-chain branching poly(trimethylene terephthalate)

A multifunctional epoxide chain extender (ADR4370S) was used to increase the molecular weight of poly(trimethylene terephthalate) (PTT). And the effects of ADR4370S content on the molecular structure, melt viscosity, and rheological properties of PTT were studied. It is found that a star-type topological structure is formed in PTT by introduction of ADR4370S, and the balance torque, intrinsic viscosity, and molecular weight are increased by increasing ADR4370S dosage. The rheological measurement results show that the elastic modulus, complex viscosity, and shear thinning behavior of long-chain branching PTT are increased with the concentration of ADR4370S. The presence of broadened relaxation time spectrum and a long relaxation time mode for the PTT with 1.50 wt% ADR4370S demonstrate that the cross-linking reaction occurs, and the gel forms in the PTT system.     

On the modeling of fluidity loss phenomena in Couette and Poiseuille flows of elastic liquids

Some effects of the possible relaxation transition from viscoelastic liquid state to highly elastic solid state were theoretically and numerically investigated in the shear situations, within the approach proposed in papers [1, 2, 5, 16]. It was found that for a single Maxwellian model the constitutive equations developed in [1, 2, 5] are not valid at elevated shear stresses. Some new aspects of the possible rheological behavior of elastic liquids in subcritical (before transition) and supercritical (after transition) regimes were demonstrated. The mechanism of fluidity loss studied in this paper could serve as a possible trigger mechanism for the melt flow instabilities.     

An empirical constitutive law for concentrated colloidal suspensions in the approach of the glass transition

Concentrated, non-crystallizing colloidal suspensions in their approach of the glass state exhibit distinct dynamics patterns. These patterns suggest a powerlaw rheological constitutive model for near-glass viscoelasticity, as presented here. The rheological parameters used for this model originate in the mode-coupling theory. The proposed constitutive model provides explicit expressions for the steady shear viscosity, the steady normal stress coefficient, the modulus-compliance relation, and the α peak of G″. The relaxation pattern distinctly differs from gelation.     

A model for the thermorheological behavior of viscoelastic fluids

Using a power-law ansatz for the temperature dependence of the shear modulus on the level of internal variables, the thermorheological behavior is modeled for viscoelastic fluids of a special group of rheological constitutive equations (rate-type models). The model parameter introduced characterizes thermoelastic contributions. The relation between the model parameter and the physical quantities appearing in deformation processes is discussed. Based on the chosen temperature dependence of the shear modulus, thermodynamically consistent equations like the nonlinear rheological constitutive equation and the temperature equation are derived. The special cases of entirely entropy and energy elastic fluids are also considered. The thermorheological behavior (exo-, - or endothermal processes) of a viscoelastic fluid in a stress-growth experiment followed by relaxation is analyzed with respect to the model parameter.     

Relaxational interactions and viscoelasticity of polymer melts. Part I: model development

Rheological equations of state for the concentrated solutions and melts of high polymers are derived by applying a structural approach. The dynamics of a macromolecule are considered on the basis of the fundamental model of the polymer chain, e.g., the bead-spring model. The drag forces describing correlations of motion macromolecules are determined by means of the relaxation equations. The oscillatory shearing flow of the melts is studied on the basis of the equations derived. Expressions for the dynamic modulus and relaxation times are determined. As can be judged from the form of the dependence of the dynamic modulus on frequency, the relaxation time distribution is the same as in real materials. The relaxation spectrum of high polymers has a terminal zone with abnormally long relaxation times.     

Relaxation and power spectra of low-frequency fluctuations in foams

The dynamics of foam formation in a water-glycerin solution was studied to establish the relationship between the relaxation characteristics and the fluctuation power spectrum for a stochastic process. Foaming occurred during the dissociation of the gas-saturated solution and during bubbling of the solution through a porous filter. Two types of relaxation of the foam—exponential and power-law—were revealed. The power-law type of relaxation was observed upon exposure to ultrasound. Relationships between the type of relaxation and the distribution of lowfrequency fluctuations and power spectra was established.     

Creep response of bituminous mixtures—rheological model and microstructural interpretation

The main failure mechanisms of flexible pavements, such as low-temperature cracking, fatigue failure, and rutting are strongly influenced by the viscoelastic properties of asphalt. These viscoelastic properties originate from the thermorheological behavior of bitumen, the binder material of asphalt. In this paper, the bitumen behavior is studied by means of a comprehensive experimental program, allowing the identification of viscoelastic parameters of a power-law type creep model, indicating two time scales (short-term and long-term) within the creep deformation history of bitumen. Moreover, these characteristics of the creep deformation transfer towards bitumen-inclusion mixtures, as illustrated for mastic, consisting of bitumen and filler. For this purpose, the aforementioned power-law creep model is implemented into a micromechanical framework. Finally, the activation of the different creep mechanisms as a function of the loading rate is discussed, using viscoelastic properties obtained from both static and cyclic creep tests.     

高聚物玻璃化的不平衡性及流变行为

高聚物在玻璃化转变前后表现出截然不同的力学、物理及流变特性,并在玻璃态下继续松弛。本文介绍了有关经典理论的形成和发展,最后从热力学、统计力学、动理学(kinetics)3方面联合考虑提出了3维空间(PVT/PST)数学表象,这是目前处理这方面问题较完善的理论。      

Yield stress fluids and ageing

Many high-concentration multiphase materials that are industrially and academically important do not reach thermodynamic equilibrium because of kinetic constraints originating from the structurally arrested microstructure. However, owing to thermal or elastic energy of the constituents, their microstructure progressively reorganizes to form thermodynamically more stable states. In this physical ageing process, the whole spectrum of relaxation times evolves that makes relaxation dynamics increasingly sluggish. In a process of rejuvenation, deformation field increases mobility, but non-trivially alters the shape of relaxation time spectrum. Interestingly, this class of materials also demonstrates yield stress, whose origin could be closely related to physical aging, and as a result, it depends on time and deformation history. In this review, we present an overview of experimental behaviors and theoretical advances that indicate a complex coupling between ageing and rejuvenation for this class of materials having diverse microstructures.     

聚合物分子模型的Brown动力学模拟

介绍了研究聚合物分子模拟流变性质的Brown动力学模拟方法,综述了有关这方面的研究工作．在通常情况下,将分子模型的数值模拟与求解流动守恒方程的数值解法相结合,便有可能用分子模型去代替连续介质力学的本构方程,来模拟聚合物流体的复杂流动．本文介绍了这一方法的产生背景、最新进展以及优点．