Fourier Transform Rheology Research Articles

Characterization of yield stress and slip behaviour of skin/hair care gels using steady flow and LAOS measurements and their correlation with sensorial attributes

Gels made with three different polymers widely used as rheology modifiers in cosmetic formulations (cross-linked poly(acrylic acid), cross-linked poly(maleic acid-alt-methyl vinyl ether) copolymer and cross-linked poly(acrylic acid-co-vinyl pyrrolidone) copolymer) were characterized by rheological and sensory evaluation methods to determine the relationship between sensorial perception and corresponding rheological parameters. Both conventional rheological characterization methods and a more recent method, Fourier Transform Rheology with Large Amplitude Oscillatory Flow data (LAOS), were utilized to characterize the material with and without wall slip. Sensorial analyses were implemented in vivo to evaluate the perceived ease of initial and rub-out spreadability, cushion, pick-up and slipperiness attributes of the gels. Results were statistically analysed by both variance (ANOVA) and principle component analysis (PCA). Sensorial panel testing characteristics discriminated the three materials, and PCA analyses revealed that sensory attributes could be well predicted by rheological methods. Rheological experiments, without wall slip, revealed that gel strength in the linear viscoelastic region (LVR) and yield stress of these materials are similar, but exhibit significantly different wall slip and thixotropy behaviour in the low shear rate region under wall slip conditions. Above the critical shear rate, which corresponds to the yield stress, all tested materials did not slip and behaved as conventional, shear thinning polymeric fluids. In particular, the rheological parameters and sensorial perception of the 1% cross-linked vinyl pyrrolidone/acrylic acid copolymer were significantly affected by wall slip and/or thixotropy-related shear banding phenomena.

A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS): Application to theoretical nonlinear models

The nonlinear yielding responses of three theoretical models, including the Bingham, a modified Bingham, and Giesekus models, to large-amplitude oscillatory shear are investigated under the framework proposed recently by Rogers et al. (2011). Under this framework, basis states are allowed to wax and wane throughout an oscillation, an approach that conflicts directly with the assumptions of all Fourier-like linear algebraic approaches. More physical yielding descriptions of the nonlinear waveforms are attained by viewing the responses as representing purely elastic to purely viscous sequences of physical processes. These interpretations are compared with, and contrasted with, results obtained from linear algebraic analysis methods: Fourier-transform rheology; and the Chebyshev description of the so-called elastic and viscous stress components σ′ and σ″. Further, we show that the discrepancies between the built-in model responses and parameters, and the interpretations of the Chebyshev and Fourier coefficients are directly related to misinterpretations of σ′ and σ″ as being the elastic and viscous stress contributions. We extend these ideas and discuss how every linear algebraic analysis is likely to conflate information from predominantly elastic and viscous processes when a material yields.

Method of Calculation of Instantaneous Shear Stress of Polymer Melts Extruding Through a Capillary under Vibration

A calculation method for the instantaneous shear stress of polymer melts extruding through a capillary under vibration is developed. Although directly applied to a multifunction and all-electric rheometer (MAR) designed by the authors, it is believed to be generally applied. The method of determination of each parameter's value is given. The influence of compressibility is discussed. A quantitive determination method is given to judge whether the influence of compressibility can be ignored or not. According to the magnitude range of the three terms of the shear stress formula, the gravity effect can be ignored when the polymer melt rheological behavior is studied with MAR, and the inertia effect can normally be ignored under certain conditions. Therefore, the formula can be reduced to two terms normally or to one term under certain conditions. The application example indicates that this calculation method is convenient and feasible. The instantaneous shear stress can be further analyzed by the methods that are used to analyze the nonlinear behavior in oscillatory experiments, such as Fourier-transform rheology (FT-rheology) and general stress decomposition (GSD). The further analyzed results can be related to some information of the polymer melts at high shear rate. The factors that depend on the shear rate and influence the viscoelastic properties can be studied by this method.

Fourier Transform Rheology as a universal non-linear mechanical characterization of droplet size and interfacial tension of dilute monodisperse emulsions

A new protocol to gain interfacial tension and droplet size of dilute monodisperse emulsions from Fourier Transform Rheology (FTR), is proposed. Specifically, a universal dimensionless quantity E was found at small strain amplitudes to correlate with the droplet size of the emulsion where E is inversely related to the square of the capillary number Ca and directly proportional to the relative intensities of the fifth and third harmonics, I5/I3. The limiting value E0 at small strain deformations can be used as a universal parameter to calculate different emulsion properties. Different morphological constitutive models for emulsions were used to establish the universality of the parameter E0. Preliminary analysis on experimental data confirms the validity of this approach for the characterization of emulsion properties, including the estimation of interfacial tension and droplet radius.

Correlations between local flow mechanism and macroscopic rheology in concentrated suspensions under oscillatory shear

An optical visualization apparatus has been designed to measure the particle velocity of concentrated particle suspensions in a stress controlled rheometer equipped with a quartz parallel-plate. Suspensions with high and low matrix viscosity were used to investigate the nonlinear rheology and the local flow mechanism, as well as the correlations between particle velocity profiles and transition behaviors. Herein, it is shown that the sedimentation has great effects on the flow behavior of suspensions and on the particle velocity profiles. Local flow behaviors e.g. shear banding, drift in the center position of oscillatory shear and dynamic wall slip, have been studied comprehensively. By Fourier-transform rheology (FTR) analysis, the shear banding phenomenon is proved to be strongly linked with the nonlinear rheology of suspensions.

Yielding processes in a colloidal glass of soft star-like micelles under large amplitude oscillatory shear (LAOS)

The understanding of yielding and flow of a colloidal glass under large amplitude oscillatory shear (LAOS) represents a motivating challenge. Monitoring the higher harmonics in the stress signal by Fourier-transform (FT) rheology may provide useful insight on the progressive transition from linear to nonlinear viscoelastic response. However, the physical interpretation of FT-rheology data is still not obvious. Here we study the process of yielding in a colloidal glass formed by star-like block copolymer micelles with LAOS experiments and interrogate the nonlinear intracycle stress response by FT analysis and decomposition to an orthogonal set of Chebyshev polynomials [Ewoldt, R. H., et al. J. Rheol. 52(6), 1427–1458 (2008)]. Such approach provides a robust framework enabling us to map out a rich phenomenology of intracylce nonlinearities that may relate to distinct physical mechanisms. We find that the nonlinearities during yielding are represented by intracylce shear thickening/thinning and strain harden...

Dynamic rheological properties of wood polymer composites: from linear to nonlinear behaviors

The microstructure of wood plastic composite (WPC) with respect to wood particle content and maleic anhydride-grafted polypropylene (MAHPP) compatibilizer is studied by both linear and nonlinear rheological methods in this article. The complete long characteristic relaxation behavior in linear region, which is closely related to the structure of wood particle aggregates and MAHPP compatibilizing effect at the interface, is limited by observing time. Fortunately, the Fourier transform rheology (FTR) by the stress control mode is found to be an effective method for further investigating the structure with long relaxation time in WPC system. The plateau value of I31 at high stress and the range of ϕ31 are proved to be corresponding to the content of wood particle agglomerates in the WPC melts and the type of interfacial hydrodynamic interaction. The interesting outcomes suggest that MAHPP do has the effect on changing the properties of the heterogeneous interface and confirm the difference of the structure with long relaxation time in WPC can be easily captured by the high sensitive FTR indeed.

Structural and mechanical characterization of κ/ι-hybrid carrageenan gels in potassium salt using Fourier Transform rheology

The mechanical and structural properties of κ/ι-hybrid carrageenan gels obtained at various concentrations in the presence of 0.1 m KCl were studied with Fourier Transform rheology (FTR) and cryoSEM imaging. FTR data show that gels formed at concentration below 1.25 wt% exhibit a strain hardening behavior. The strain hardening is characterized by a quadratic increase of the scaled third harmonic with the strain and a third harmonic phase angle of zero degree. Both features are weakly depending on the concentration and conform to predictions from a strain hardening model devised for fractal colloidal gels. However, the phase angle of the third harmonic reveals that κ/ι-hybrid carrageenan gels obtained at higher concentrations show shear thinning behavior. Colloidal gel models used to extract structural information from the concentration scaling of gel equilibrium shear modulus G 0 and the strain dependence of FTR parameters suggest that κ/ι-hybrid carrageenan gels are built from aggregating rod-like strands (with fractal dimension x = 1.13) which essentially stretch under increasing strain. The mechanically relevant structural parameters fairly match the gel fractal dimension ( d = 1.66) obtained from the cryoSEM analysis.

Establishing a New Mechanical Nonlinear Coefficient Q from FT-Rheology: First Investigation of Entangled Linear and Comb Polymer Model Systems

The nonlinear response of monodisperse linear and comb polymer melts has been investigated under oscillatory shear with Fourier-transform rheology (FT-rheology). The relative intensity of the third harmonics (I3/1), which quantify nonlinearity, was found to depend on the strain amplitude (γ0) at small and medium strain amplitudes quadratically regardless of the excitation frequency, temperature, and polymer topology. From these results, for the first time, we proposed new nonlinear coefficient Q, which is defined as Q ≡ I3/1/γ02, and we also defined zero-strain nonlinearity, Q0, as a constant value at relatively small strain amplitude (limγ0→0 Q ≡ Q0; e.g., the zero shear viscosity). In the case of the linear polymer melt, the Q value displays a constant value at small and medium strain amplitude. At large strain amplitude, we detect that the value of Q is finally reduced (Q(γ0) is decreasing). The investigated comb polymer shows very different behavior; the value of Q displays an overshoot (Q(γ0) is incr...

Control on the topological structure of polyolefin elastomer by reactive processing

The feasibility of preliminary tailoring of the long chain branched (LCB) polymer through complex flow field was evaluated in the torque rheometer, for the reaction of melt polyolefin elastomer (POE) with peroxides at elevated temperatures. With the compensation of temperature, the strength of complex shear flow could be the only factor affecting the reaction kinetics and mechanism. The results of sample characterization by the rheological and dilute polymer solution methods indicated that the degradation mainly made the length of LCB arm shorter and shorter as the rotational speed increases. Extremely, a certain amount of LCB degraded to be linear chains again due to the scission approaching the branching point at intense mixing condition. One new LCB index (DLCB) was defined from nonlinear oscillatory shear, and a nearly linear relationship between it and long chain branching index (LCBI) was found, which can be a map to quantify LCB level by Fourier Transform Rheology (FTR).

Dynamic response of block copolymer wormlike micelles to shear flow

The linear and nonlinear dynamic response to an oscillatory shear flow of giant wormlikemicelles consisting of Pb–Peo block copolymers is studied by means of Fourier transformrheology. Experiments are performed in the vicinity of the isotropic–nematic phasetransition concentration, where the location of isotropic–nematic phase transition lines isdetermined independently. Strong shear-thinning behaviour is observed due to criticalslowing down of orientational diffusion as a result of the vicinity of the isotropic–nematicspinodal. This severe shear-thinning behaviour is shown to result in gradient shear banding.Time-resolved small-angle neutron scattering experiments are used to obtain an insightinto the microscopic phenomena that underlie the observed rheological response.An equation of motion for the order parameter tensor and an expression of thestress tensor in terms of the order parameter tensor are used to interpret theexperimental data, both in the linear and nonlinear regimes. Scaling of the dynamicbehaviour of the orientational order parameter and the stress is found when criticalslowing down due to the vicinity of the isotropic–nematic spinodal is accountedfor.

Fourier Transform Rheology of Dilute Immiscible Polymer Blends: A Novel Procedure To Probe Blend Morphology

Morphological characterization of polymer blends is important for tailoring final properties of plastic products based on these systems. A novel technique to estimate the characteristic dimension and size distribution of a polymer blend is proposed and tested. The procedure is based on Fourier transform rheology (FTR) and large-amplitude oscillatory shear experiments and exploits their sensitivity to microstructural properties. The inference protocol requires that the experimental data are analyzed with a model capable of describing the blend dynamics. This novel technique is applicable to immiscible polymer blends of practical industrial interest. The procedure is successfully tested on a model system (an immiscible polymer blend of PDMS in PIB) by treating the polymer blends with the Maffettone–Minale model coupled with the Batchelor theory.

Rheological discrimination and characterization of carrageenans and starches by Fourier transform-rheology in the non-linear viscous regime

Classical rheological methods are often insufficient to characterize and to differentiate the non-linear rheological behavior of polysaccharide systems such as carrageenan or starch. In this article the non-linear rheological method of characteristic functions is used to discriminate between the different polysaccharides. This method is based on the Fourier transform-rheology (FT-rheology). The response of a sample is decomposed using simple characteristic functions. We show that there are differences in the response of a number of carrageenan and starch samples, which are not distinguishable with classical rheometry.

Evaluation on the degrading behavior of melt polyolefin elastomer with dicumyl peroxide in oscillatory shear flow by Fourier transform rheology

The degradation of melt polyolefin elastomer (POE) at the presence of dicumyl peroxides (DCP) was estimated at elevated temperature in oscillatory shear flow. Large amplitude oscillatory shear (LAOS) experiments followed by Fourier transform rheology (FTR) were carried out to detect and evaluate the branching architecture of the products. The third complex harmonic (I3∗) and other two parameters, small strain elastic shear modulus (M) and large strain elastic shear modulus (L), which describe the nonlinearity and elasticity of a material obtained from FTR, are mainly used to characterize the topological structure of polymer chains. The results indicate the degradation appeared just after a large amount of the long chain branches (LCB) created rather than as soon as the reaction started when the strain was applied within the linear viscoelastic regime of the original POE at high frequencies. This is different from our previous result that the dominant reaction was coupling in linear shear flow. The threshold strain for degradation decreased with the oscillatory frequency, and the frequency owned a different acting mechanism from the strain amplitude to cause the degradation reaction. Moreover, there is a kind of selectivity of shear rate on the polymer chains for degradation. Low frequency results in short linear scission segments and a long branched chain suffers from degradation more than once. At high frequency, the possibility of degradation at the sites near the branching points of LCB increases.

Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts

Nonlinear response of linear and branched polymers has been investigated under medium strain amplitude oscillatory shear (strain amplitude range from 10% to 100%) with Fourier-transform rheology. A power law relationship was found between the relative third intensity (I3∕I1), which is an indicator of nonlinearity, and the strain amplitude at low and medium strain amplitudes. On a log-log plot, the intercept and slope of I3∕I1 were investigated at different excitation frequencies and temperatures. Simulation results with three different constitutive equations [Giesekus, exponential Phan-Thien Tanner (E-PTT), pom-pom model] were also compared. Experimental results show that the intercept was affected by the excitation frequency and temperature, and the slope of I3∕I1 for linear polymer remained constant regardless of molecular weight, molecular weight distribution, and excitation frequency in accordance with the predictions of the constitutive equations (Giesekus and E-PTT). It should be noted that the slope of I3∕I1 for branched polymer was lower than that of linear polymer, unlike the prediction of the pom-pom model. Among the molecular architecture and processing parameters (e.g., molecular weight, molecular weight distribution, frequency, and temperature), the slope of I3∕I1 under medium amplitude oscillatory shear was found to depend only on the long chain branching, which means that it can be used as a measure of the degree of branching. The failure of the pom-pom model in predicting the nonlinear shear behavior was also pointed out.

Detection and quantification of industrial polyethylene branching topologies via Fourier-transform rheology, NMR and simulation using the Pom-pom model

The significance of sparse long-chain branching in polyolefines towards mechanical properties is well-known. Topology is a very important structural property of polyethylene, as is molecular weight distribution. The method of Fourier-transform rheology (FTR) and melt state nuclear magnetic resonance (NMR) is applied for the detection and quantification of branching topology (number of branches per molecule), for industrial polyethylenes of various molecular weight and molecular weight distributions. FT rheology consists of studying the development of higher harmonics contribution of the stress response to a large amplitude oscillatory shear deformation. In particular, when applying large-amplitude oscillatory shear (LAOS), one observes the development of mechanical higher harmonic contributions at 3ω 1, 5ω 1,..., in the shear stress response. We correlate the relative intensity, I 3/1, and phase Φ 3 of these harmonics with structural properties of industrial polyethylene, i.e. polymer topology and molecular weight distribution. Experiments are complemented by numerical simulations, using a multimode differential Pom-pom constitutive model (DCPP formulation), by fitting to the experimental linear and nonlinear viscoelastic behaviours. Simulation results in the nonlinear regime are correlated with molecular properties of the “pom-pom” macromolecular architecture. Qualitative agreement is found between predicted and experimental FT rheology results.

Degree of branching of polypropylene measured from Fourier-transform rheology

In this study, linear and branched polypropylenes (PP) were compared under medium strain amplitude oscillatory shear (usually strain amplitude range from 10 to 100%) with Fourier-transform rheology (FT rheology). On a log–log diagram, the third relative intensity (I3/I1), which is a parameter to represent nonlinearity, shows a linear relationship with the strain amplitude in the range of medium strain amplitude. The slope of I3/I1 of linear PP with various molecular weight and molecular weight distribution was 2 as most constitutive equations predict, while that of branched PP was 1.64, which is lower than that of linear PP. When the linear and branch PP were blended, the slope of I3/I1 was proportional to the composition of the branch PP. Therefore, it is suggested that the degree of branching can be defined in terms of the slope of I3/I1 under medium amplitude oscillatory shear.

Fourier Transform Rheology of Branched Polyethylene: Experiments and Models for Assessing the Macromolecular Architecture

Fourier transform rheology (FTR) consists of analyzing the frequency spectrum of the nonlinear torque response obtained during large-amplitude oscillatory shear. In the present work, the analysis has been carried out in the whole complex space and was especially focused on the study of the third complex harmonic I*3/I1 (= I*(3ω1)/I1, where I1 is the spectrum intensity at the fundamental frequency ω1), the intensity I3/I1 (= |I*3/I1|), and the phase shift Φ3 of I*3/I1. The accuracy of FTR to characterize the architecture of linear, sparsely, and densely branched polyethylene regarding the number of branches and their length has been shown. A modified Wagner integral model and a differential multimode pompom model were used to simulate FTR experiments. Nonlinear parameters of each model were determined by fitting the curve of the third complex harmonic I*3/I1 versus the strain amplitude γ0 with the experimental data. Good results have been obtained with the modified Wagner model. Whereas, the pompom model accounts for the experimental intensity of the third harmonic, discrepancies remain for the phase shift behavior Φ3 for the polymers showing the highest nonlinear behavior regarding the level of I3/I1. Nevertheless, when fitting was possible, the results have been correlated with the supposed structure expected from the type of synthesis.

Non Linear Rheology for Long Chain Branching characterization, comparison of two methodologies : Fourier Transform Rheology and Relaxation.

In this study we compare three rheological ways for Long Chain Branching (LCB) characterization of a broad variety of linear and branched polyethylene compounds. One method is based on dynamical spectrometry in the linear domain and uses the van Gurp Palmen plot. The two other methods are both based on non linear rheology (Fourier Transform Rheology (FTR) and chain orientation/relaxation experiments). FTR consists in the Fourier analysis of the shear stress signal due to large oscillatory shear strains. In the present work we focus on the third and the fifth harmonics of the shear stress response. Chain orientation/relaxation experiment consists in the analysis of the polymer relaxation after a large step strain obtained by squeeze flow. In this method, relaxation is measured by dynamical spectrometry and is characterized by two relaxation times related to LCB. All methods distinguish clearly the group of linear polyethylene from the group of branched polyethylene. However, FTR and Chain orientation/relaxation experiments show a better sensitivity than the van Gurp Palmen plot. Non linear experiments seem suitable to distinguish long branched polyethylene between themselves.

Fourier-transform rheology experiments and finite-element simulations on linear polystyrene solutions

Large amplitude oscillatory shear strain was applied to anionically synthesized linear polystyrene solutions in dioctylphthalate. The resulting torque was analyzed in Fourier space with respect to frequency, magnitude, and phase (Fourier-transform rheology). The concentration of the solutions was varied to achieve different degrees of entanglement. In addition, numerical simulations were performed using the Giesekus constitutive equation fitted on the basis of linear viscoelastic data. We found a good qualitative agreement between experiments and predictions; a quantitative agreement was reached for intermediate strain amplitudes. Some deviations were observed at very low strain amplitudes. We present a descriptive relation for the relative magnitude of the third harmonic as a function of strain amplitude using a modified damping function. From this relation we obtained a universal parameter that describes the scaling behavior law for the increasing non-linearity (e.g., measured by the relative intensity ...