Linear Stress Relaxation Research Articles

Characteristics of temperature-dependent shear flow in an ultrasonicated ferrofluid

The rheological effect of manganese zinc (Mn-Zn) ferrite ferrofluid was studied and the impact of temperature on the magnetoviscosity and viscoelastic system of manganese-zinc ferrite ferrofluid generated by co-precipitation process is investigated. At 25 ◦C, a ferrofluid structure that is both hard and elastic is produced. As the temperature rises, the fluid structure loses its elasticity and becomes semi-rigid. When a low relaxation modulus is applied, the fluid behavior, which is temperature-dependent, exhibits the development of linear stress relaxation and steady state flow. When a greater relaxation modulus is used, non-steady state flow results. At a high temperature of 50 ◦C, steady state flow is quickly obtained, whereas at a low temperature, equilibrium or steady state is attained more slowly. At low temperatures, the fluid exhibits a solid-like structure, whereas at high temperatures, a liquid-like structure forms as the fluid’s viscosity decreases. With the creation of yield stress in the region with high shear rates, shear stress increases with temperature, and yield stress increases with temperature. The viscoelastic system is underdamped, and the amount of fluid deflected at 25 ◦C is small, which prevents the disruption of the fluid’s rheology. This develops as a result of the presence of a small deflection angle, which facilitates the development of high magnetoviscosity at low temperature. High viscous effect forms at low temperatures due to the creation of low shear stress and low deflection angle at temperature 25 ◦C. The sample has a single phase and FCC structure, which X-ray diffraction research has verified.

Non-Maxwellian viscoelastic stress relaxations in soft matter.

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Anomalous Aging and Stress Relaxation in Macromolecular Physical Gels: The Case of Strontium Alginate

We investigate macromolecular physical gels (strontium alginates) in a wide range of aging times and length scales by combining linear stress relaxation and dynamic light scattering (DLS) experiments. Stress relaxation shows an early logarithmic decay followed by a stretched exponential behavior, leading to define two characteristic times, which increase as distinct power laws of gel age. The DLS clearly displays anomalous microscopic dynamics, with compressed exponential decay of autocorrelation functions and ballistic wavelength dependence of the decay time. Thus, our results demonstrate that stretched stress relaxation can coexist with compressed intensity autocorrelation functions. In addition, comparison between rheology and DLS allows for the identification of two characteristic lengths that we interpret as the typical size of collapsing pores in the gel and of avalanche-like rearrangements. We discuss this scenario in terms of some recently proposed ideas on anomalous aging, such as ultralong-ranged dynamical correlations in closely athermal systems.

Linear Stress Relaxation and Probe Reorientation: Comparison of the Segmental Dynamics of Two Glassy Polymers during Physical Aging

Segmental dynamics of glassy poly(methyl methacrylate) (PMMA) and poly(lactic acid) (PLA) have been measured over 8 h of aging via both optical probe reorientation and mechanical stress relaxation experiments performed in the linear response regime, in a temperature range between 6 and 30 K below the glass transition temperature (Tg). A clear power law relationship between relaxation times and aging times is observed in all experiments. For both PLA and PMMA glasses, the probe reorientation times are strongly correlated with stress relaxation times over the observed range of aging times and aging temperatures, with the two relaxation times related by a power law with an exponent of ∼1. Comparisons of these data sets with previously published work indicate that the relationship between the two relaxation times is not influenced by secondary relaxation processes, low levels of crosslinking, or the presence of a plasticizer. These results support the view that the probe reorientation technique is a good reporter of segmental dynamics in the glassy state.

Dynamics and Viscoelasticity of Disordered Melts of Symmetric Diblock Copolymers

Simulations of coarse-grained models are used to study relationships among chain motion, composition fluctuations, and stress relaxation in unentangled melts of symmetric diblock copolymers. Measurements of the dynamic structure factor S(q,t) are reported as a function of wavenumber q, time t, and χN, where χ is the Flory–Huggins interaction parameter and N is degree of polymerization. The function S(q,t) is found to be a nearly exponential function of time, S(q,t) ∝ e–t/τ(q), for wavenumbers similar to or less than the wavenumber q* at which the static structure factor S(q) ≡ S(q,t=0) is maximum. The relationship between the decay time τ(q) and S(q) is used to define an effective wavenumber-dependent diffusivity D(q) for fluctuations of wavenumber q. The function D(q) is shown to change very little with changes in χN and to be a monotonically decreasing function of the nondimensional wavenumber qRg, where Rg is polymer radius of gyration. The linear shear stress relaxation modulus G(t) is inferred from measurements of the shear stress autocorrelation function. At low values of χN, far from the order–disorder transition (ODT), the modulus G(t) agrees with predictions of the Rouse model. Near the ODT, G(t) develops an additional slowly decaying feature arising from slow decay of composition fluctuations with q ∼ q*. The behavior of G(t) near the ODT is predicted nearly quantitatively by a modified version of the model of Fredrickson and Larson (FL), in which the prediction of the FL theory for the slowly decaying component is added to the prediction of the Rouse theory for contributions arising from single-chain relaxation, using the independently measured behavior of S(q,t) as an input to the theory.

Simulation of the linear rheological behavior of silica-filled, star-shaped SBR compounds

The rheological behavior of star-shaped SSBR/silica 60 phr compounds with different filler surface areas was experimentally studied and simulated using constitutive modeling. Rheological behavior was characterized in small amplitude oscillatory shear (SAOS) and stress relaxation after a small step shear. Unfilled SBR and SBR filled with four different silica grades with BET surface areas of 55, 135, 160, and 195 m2/g were used. A clear trend in rheological behavior was observed with surface area. A frequency sweep in the SAOS regime indicated an increase in dynamic properties with surface area. Additionally, linear stress relaxation tests at a strain level of 0.05 showed an increase in relaxation modulus with surface area and the presence of a plateau in the relaxation modulus at large times in compounds containing silica with high surface areas. The Leonov and Simhambhatla-Leonov models, modified to incorporate multimode particle network relaxation, were successfully used to simulate the frequency dependence of the storage modulus and the time evolution of the linear relaxation modulus for all samples. However, simulations of the frequency dependence of the loss modulus showed poor results in comparison with experimental data for the filled compounds.

Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

We present unique nonlinear rheological data of well-defined symmetric Cayley-tree poly(methyl methacrylates) in shear and uniaxial extension. Earlier work has shown that their linear viscoelasticity is governed by the hierarchical relaxation of different generations, whereas the segments between branch points are responsible for their substantial strain hardening as compared to linear homopolymers of the same total molar mass at the same value of imposed stretch rate. Here, we extend that work in order to obtain further experimental evidence that will help understanding the molecular origin of the remarkable properties of these highly branched macromolecules. In particular, we address three questions pertinent to the specific molecular structure: (i) Is steady state attainable during uniaxial extension? (ii) What is the respective transient response in simple shear? and (iii) How does stress relax upon cessation of extension or shear? To accomplish our goal, we utilize state-of-the-art instrumentation, i.e., filament stretching rheometry and cone-partitioned plate shear rheometry for polymers with 3 and 4 generations, and complement it with state-of-the-art modeling predictions using the branch-on-branch (BoB) algorithm. The data indicate that the extensional viscosity reaches a steady state value, whose dependence on extensional rate is identical to that of entangled linear and other branched polymer melts. Nonlinear shear is characterized by transient stress overshoots and the validity of the Cox–Merz rule. Remarkably, nonlinear stress relaxation is much broader and slower in extension compared to shear. It is also slower at higher generation, and rate-independent for rates below the Rouse rate of the outer segment. For extension, the relaxation time is longer than that of the linear stress relaxation, suggesting a strong “elastic memory” of the material. These results are described by BoB semiquantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than three entanglements long, this is a very promising outcome that gives confidence in using BoB for understanding the key features. Moreover, the response of the segments between generations controls the rheology of the Cayley trees. Their substantial stretching in uniaxial extension appears responsible for strain hardening, whereas coupling of stretches of different parts of the polymer appears to be the origin of the slower subsequent relaxation of extensional stress. Concerning the latter effect, for which predictions are not available, it is hoped that the present experimental findings and proposed framework of analysis will motivate further developments in the direction of molecular constitutive models for branched and hyperbranched polymers.

Time, stress, and temperature-dependent deformation in nanostructured copper: Stress relaxation tests and simulations

In the present work, stress relaxation tests, high-resolution transmission electron microscopy (HRTEM), and molecular dynamics (MD) simulations were conducted on coarse-grained (cg), nanograined (ng), and nanotwinned (nt) copper at temperatures of 22 °C (RT), 30 °C, 40 °C, 50 °C, and 75 °C. The comprehensive investigations provide sufficient information for the building-up of a formula to describe the time, stress, and temperature-dependent deformation and clarify the relationship among the strain rate sensitivity parameter, stress exponent, and activation volume. The typically experimental curves of logarithmic plastic strain rate versus stress exhibited a three staged relaxation process from a linear high stress relaxation region to a subsequent nonlinear stress relaxation region and finally to a linear low stress relaxation region, which only showed-up at the test temperatures higher than 22 °C, 22 °C, and 30 °C, respectively, in the tested cg-, ng-, and nt-Cu specimens. The values of stress exponent, stress-independent activation energy, and activation volume were determined from the experimental data in the two linear regions. The determined activation parameters, HRTEM images, and MD simulations consistently suggest that dislocation-mediated plastic deformation is predominant in all tested cg-, ng-, and nt-Cu specimens in the initial linear high stress relaxation region at the five relaxation temperatures, whereas in the linear low stress relaxation region, the grain boundary (GB) diffusion-associated deformation is dominant in the ng- and cg-Cu specimens, while twin boundary (TB) migration, i.e., twinning and detwinning with parallel partial dislocations, governs the time, stress, and temperature-dependent deformation in the nt-Cu specimens.

Biomechanical Analysis of Infectious Biofilms.

The removal of infectious biofilms from tissues or implanted devices and their transmission through fluid transport systems depends in part of the mechanical properties of their polymeric matrix. Linking the various physical and chemical microscopic interactions to macroscopic deformation and failure modes promises to unveil design principles for novel therapeutic strategies targeting biofilm eradication, and provide a predictive capability to accelerate the development of devices, water lines, etc, that minimise microbial dispersal. Here, our current understanding of biofilm mechanics is appraised from the perspective of biophysics , with an emphasis on constitutive modelling that has been highly successful in soft matter. Fitting rheometric data to viscoelastic models has quantified linear and nonlinear stress relaxation mechanisms, how they vary between species and environments, and how candidate chemical treatments alter the mechanical response. The rich interplay between growth, mechanics and hydrodynamics is just becoming amenable to computational modelling and promises to provide unprecedented characterisation of infectious biofilms in their native state.

An Evaluation of the Compression Response of High-Performance Prepregs for Afp Applications

In this study, the compaction response of unidirectional out-of-an autoclave (OOA) prepreg tape has been evaluated experimentally at 25°, 45° and 65 °C. Instantaneous and incremental displacement compaction experiments have been carried out in a universal testing machine until a compressive strain of 0.42 ±0.02 was achieved. The fiber-bed stress was determined by transposing the results of displacement-controlled experiments onto data from corresponding load-controlled experiments. The material was then modelled as a viscoelastic material using a third order exponential decay function, based on a generalized Maxwell model. This procedure enabled the extraction of the relaxation time constants and the peak stress. The results highlight a linear relationship between the operating temperature and the load/stress relaxation response of the prepreg/tape, suggesting that if the fiber placement procedure is performed at 65 °C, the effect of roller stiffness on tape/fiber laying is negligible. The maximum contribution of fiber stress to the overall relaxation is approximately 6% at 45 °C and 65 °C, indicating the formability to be matrix dependent. A minimum spring-back is observed in specimens that were tested under incremental displacement conditions. The difference in thickness of the as-laid laminate and the cured laminate at 45 °C and 65 °C were similar. The linear stress relaxation model has been shown to be capable of predicting the maximum stress accurately using the viscosity values of the dashpots and the moduli of the springs.

Thermo-oxidative resistant nanocomposites containing novel hybrid-nanoparticles based on natural polyphenol and carbon nanotubes

Quercetin (Q), a natural antioxidant molecule, is physically immobilized onto multi-walled carbon nanotubes (CNTs) bearing covalently-linked long-chain alkyl functional groups, and the so obtained hybrid-nanoparticles are used to prepare Ultra High Molecular Weight PolyEthylene-based nanocomposite films with enhanced thermo-oxidation resistance. The effective immobilization of the Q molecules is confirmed by spectroscopic (micro-Raman, ATR-FTIR, and FTIR) and thermo-gravimetric analyses, and the influence of the nanoparticles on the rheological behaviour and thermo-oxidative stability of the nanocomposites are investigated. Rheological analyses (linear viscoelasticity and stress relaxation tests) and morphological observations reveal that the Q-functionalized CNTs disperse better than bare CNTs in the host matrix. Quercetin confirms to be an excellent anti-oxidant for polyethylene, but the study of the thermo-oxidation behaviour shows that a remarkable stabilizing action only emerges when Q is physically immobilized on the CNTs. In particular, a ten-fold increase of the onset of degradation phenomena in thermo-oxidative environment was found. Such an excellent result is due to a synergic effect stemming from the physical interaction between Q and CNTs, which cannot provide a similar stabilizing action if used separately. In particular, we argue that the process of physical immobilization of the Q molecules causes the formation of structural defects onto outer CNTs surfaces, thus remarkably improving the CNTs radical scavenging activity and probably promoting Q regeneration. In addition, CNTs seem acting as efficient nano-carriers for the quercetin molecules, improving the dispersion of the latter in the host matrix in spite of their poor solubility.

Viscoelastic properties of oat β-glucan-rich aqueous dispersions

C-trim is a healthy food product containing soluble dietary fibre β-glucan. The dispersion of C-trim in water is a hydrocolloid biopolymer. The linear and non-linear rheological properties of dispersions of C-trim biopolymers were investigated. The linear viscoelastic behaviours for C-trim dispersions were dependent on the β-glucan that C-trim contained. The C-trim20 and C-trim30, which have about 20% and 30% β-glucan, respectively, exhibited more fluid-like behaviours. The C-trim50 and C-trim95, which contain about 50% and 95% β-glucan, respectively, showed solid viscoelastic properties. The power law model fitting, as well as spectra, for the linear dynamic frequency sweep and stress relaxation of C-trim dispersions, suggested that the C-trim dispersions were composed of physical entanglement networks instead of chemical cross ones. The non-linear steady shearing studies for C-trim dispersions indicated that all four of the C-trim dispersions exhibited shear-thinning behaviours, which could be best described by the power law model.

Linear Viscoelasticity of Spherical SiO2 Nanoparticle-Tethered Poly(butyl acrylate) Hybrids

The melt state linear viscoelastic properties of spherical silica nanoparticles with grafted poly(n-butyl acrylate) chains of varying molecular weight were probed using linear small amplitude dynamic oscillatory measurements and complementary linear stress relaxation measurements. While the pure silica-tethered−polymer hybrids with no added homopolymer exhibit solid-like response, addition of matched molecular weight free matrix homopolymer chains to this hybrid, at low concentrations of added homopolymer, maintains the solid-like response with a lowered modulus that can be factored into a silica concentration dependence and a molecular weight dependence. While the silica concentration dependence of the modulus is strong, the dependence on molecular weight is weak. On the other hand, increasing the amount of added homopolymer changes the viscoelastic response to that of a liquid with a relaxation time that scales exponentially with hybrid concentration.

Viscoelastic Properties of Clay‐Containing Nanocomposites of Thermotropic Liquid‐Crystal Polymer

AbstractThe nanocomposites of liquid‐crystal polymer (LCP) with two different weight per cents of clay were prepared via the melt extrusion method. To investigate the properties of the materials in the linear and non‐linear viscoelastic regions, both oscillatory and rotational tests were carried out. The results showed that the nanocomposite with higher clay content exhibited an almost defectless partially cross‐linked structure compared to the nanocomposite with lower clay content or the pure LCP. The linear stress relaxation measurements revealed that the pure LCP relaxed faster than nanocomposites after imposition of a constant strain for a specific time. During the step rate relaxation test, high shear rate modified the defects in the pure LCP very quickly and probably attained almost an equilibrium position while the nanocomposite samples showed strong shear thinning behaviour.magnified image

Soft glassy rheology model applied to stress relaxation of a thermoreversible colloidal gel

Measurements of the stress relaxation modulus of a thermoreversible colloidal gel are compared with the predictions of the soft glassy rheology (SGR) model of Sollich and co-workers [Sollich et al., Phys. Rev. Lett. 78, 2020–2023 (1997); Sollich, Phys. Rev. E 58, 738–759 (1998); Fielding et al., J. Rheol. 44, 323–369 (2000)] in the linear and nonlinear regimes. The material is a 20% volume fraction suspension of organophilic silica (diameter=80nm) dispersed in the organic solvent tetradecane that gels below the critical temperature of T=23°C. We perform measurements in which prior deformation history and slip are carefully controlled. The linear stress relaxation modulus shows a significant dependence on waiting time, tw. SGR model predictions are applied to linear step strain measurements for a range of tw to assign a best fit estimate of the noise temperature, x=1.05±0.01. We then test predictions of the SGR model for the nonlinear stress relaxation modulus, G(t−tw,tw;γo), based on the linear determinat...

Pom-pom model predictions on nonlinear stress relaxation in single-step strain flow

A phenomenological pom-pom model, which utilizes linear stress relaxation data as an input, is proposed for simulating the detailed retraction behavior of a full pom-pom chain as well as the associated nonlinear stress relaxation in single-step shear flows. Specifically, the initial, Rouse-like arm and/or backbone retraction as well as the long-time, renormalized (dumbbell-like) backbone retraction is simulated at one time, and a possible coupling between linear orientation relaxation and nonlinear stretch relaxation due to diffusive or convective constraint release is self-consistently accounted for. The model’s predictions are systematically tested against nonlinear stress relaxation data on three nearly monodisperse pom-pom melts, including two six-arm pom-pom polybutadienes (PPBDs) and an H-shaped polyisoprene (PPI). The model can describe the present data reasonably well by incorporating a previously proposed effect of drag–strain coupling. Accounting further for the effect of constraint release, due primarily to arm diffusive motion and its coupling with a known polydispersity in arm molecular weight distribution, appreciably broadens the predicted nonlinear stress relaxation and substantially improves the results of theory/data comparisons. The significance of the current findings is discussed.

Linear Viscoelasticity from Molecular Dynamics Simulation of Entangled Polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation: bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Stress relaxation of bulk and ribbon glassy PdCuNiP

Abstract Detailed measurements of linear heating and isothermal stress relaxation of bulk and ribbon glassy Pd 40 Cu 30 Ni 10 P 20 below the glass transition temperature have been performed. Using the activation energy spectrum reconstructed from these measurements, the temperature dependence of the shear viscosity has been calculated. It has been found that this dependence agrees with that derived directly from the creep measurements. This provides strong support for understanding the stress relaxation as a result of the stress-oriented irreversible structural relaxation with distributed activation energies.

Rheological characterisation of salad-dressing-type emulsions stabilised by egg yolk/sucrose distearate blends

The overall objective of this work was to fully characterise the rheological behaviour of oil/water emulsions stabilised by egg yolk and a sucrose ester of intermediate hydrophilic-lipophilic balance. The influence of the egg yolk/sucrose ester weight ratio in the emulsifier blend was studied by keeping the total amount of emulsifier constant. With this aim, steady state and transient flow tests, oscillatory measurements within the linear viscoelasticity regime and stress relaxation tests were carried out. Rheological tests were complemented with droplet size measurements. The results demonstrate that the rheological response and droplet size of the emulsions studied clearly depend on the weight ratio of emulsifiers in the binary blends. Steady-state and transient viscosities, as well as the dynamic functions, significantly increase with sucrose distearate concentration in the emulsifier blend. However, the evolution of other rheological parameters related to shear-induced structural breakdown, such as the critical strain for the onset of the non-linear viscoelastic behaviour, the relative deviation of the Cox-Merz rule, the time corresponding to the stress overshoot in transient tests or the damping function indicates a more developed and resistant structural network at higher egg yolk concentrations in the emulsifier blend. These results were discussed on the basis of a gel-like continuous phase formed by the sucrose ester and the highly flocculated state favoured by egg yolk.