Linear Viscoelastic Properties Research Articles

Dynamics of entangled metallosupramolecular polymer networks combining stickers with different lifetimes

We study the linear viscoelastic properties of polymeric networks formed by poly(n-butyl acrylate) telechelic stars end-capped with 2,2:6,2″-terpyridine (Star-PnBA-tpy4) and two types of metal-ligand cross-links with different lifetimes. The influence of interactions, mediated by temperature, nature of metal ions, and ion content, on the linear viscoelastic behavior of both single and double dynamics transient networks is systematically investigated by small amplitude oscillatory shear and creep rheometry. The experimental results reveal that the dynamics of networks with two different metal-ligand cross-links is much faster than expected, characterized by the average sticker lifetime rather than a discrete contribution of each metal-ligand complex. We model the dynamics with the help of our modified tube-based time marching algorithm by accounting for both association/dissociation dynamics of metal-ligand coordination and the entanglement dynamics. Two parameters are defined in the model, namely, the proportion of dangling ends and the average time during which a sticker is free. This allows us to quantify the transient dynamics of the network and, in particular, to determine how the sticker dynamics depend on temperature and ion content.

Tailoring the linear viscoelastic response of industrial double dynamics networks through the interplay of associations

We investigate the linear viscoelastic properties of industrial pressure sensitive adhesives comprising double networks with an entangled acrylate-based polymer and two types of intermolecular associations (crosslinking), permanent (epoxide) and reversible (metal-chelate), having different compositions. A combination of shear rheometry and an appropriately modified version of the Time Marching Algorithm (TMA) allows to probe and analyze the behavior of the different double dynamic networks, in particular, the effects of the type and amount of crosslinks on their linear viscoelastic spectra. To this end, the dynamics of the double networks are compared with the respective individual responses of the polymeric component without crosslinks and the single networks (possessing only physical or only chemical crosslinks), in order to quantify their contributions to the relaxation mechanisms, particularly the interplay between disentanglement and bond association/dissociation processes. With the help of the TMA model, we also examine the respective roles of the lifetime of stickers, polydispersity, and molar mass. Triggered by the good comparison between predictions and experimental data, we propose a framework to tune material parameters in order to obtain a desired viscoelastic behavior.

Inter-conversion of the generalized Kelvin and generalized Maxwell model parameters via a continuous spectrum method

• Constructed the continuous spectra ( H τ and L ρ ) via the direct and indirect methods. • Obtained the optimal ranges of retardation time and relaxation time. • Proposed a spectrum method to establish the inter-conversion between E k and D j Accurate determination of the Prony series parameters of the generalized Maxwell (GM) model and the generalized Kelvin (GK) model is crucial to the characterization of linear viscoelastic (LVE) properties of asphalt mixture and the prediction of in-service performance of asphalt pavement. However, existing methods may not be able to provide satisfactory accuracy due to their weakness of fully complying with the LVE theory or the involvement of unsolvable high-order nonlinear systems. To identify the Prony series parameters more efficiently and accurately, this paper developed a continuous spectrum method to establish the inter-conversion between the GM and GK model parameters. In the newly developed method, the complex modulus mater curves are first constructed through the conventional master curve models. The continuous relaxation and retardation spectra are then established using the proposed direct or indirect methods. The time and strength constants of the GM and GK models are subsequently calculated via an extended search method, based on which the Prony series parameters and the LVE variables of the asphalt mixture can be finally determined. Accuracy of the new method in determining the LVE variables was validated through a comparison of the calculated and measured LVE variables of asphalt mixture, while the equivalence between the GM and GK models established based on the new method was verified in different domains. Besides, the success implementation of the new method to the generalized Sigmodal model demonstrates the universality of the newly developed continuous spectrum method in determining the LVE variables of asphalt mixture.

Evaluating fatigue resistance based on viscoelastic properties of asphalt mixtures

ABSTRACT In this study, the fatigue resistance of different asphalt mixture types subjected to the same aging condition was evaluated using linear viscoelastic properties of asphalt mixtures. The relaxation spectra were determined from the dynamic modulus test based on the linear viscoelastic theory, and the relationship between the parameters of relaxation spectra and the parameters of the storage modulus master-curves were developed. The Texas overlay test was conducted to evaluate the fatigue resistance with the number of load cycle to failure used as the measure of fatigue resistance. From the corresponding results, it is shown that the inflection point frequency of the dynamic modulus master-curves could be used to assess the fatigue resistance compared to other parameters. The Glover-Rowe parameter also exhibited a fair relationship with the fatigue resistance of the asphalt mixtures. The effect of the shape parameter (γ) of the dynamic modulus master-curves was quantified but seemed not very sensitive to fatigue resistance for the asphalt mixtures evaluated. In the study, a new parameter (VECIndex) was developed to evaluate the fatigue resistance, which considered the inflection point frequency and shape of the dynamic modulus master-curves, both of which influence the linear viscoelastic properties and fatigue resistance of asphalt mixtures.

An improved method to establish continuous relaxation spectrum of asphalt materials

The relaxation spectrum plays a vital role in the study of linear viscoelastic (LVE) properties of asphalt materials; however, the current developed using methods are not accurate enough to characterize the LVE properties of asphalt materials. This paper aims to develop an improved method to determine the continuous relaxation spectrum of asphalt materials. A modified Christensen–Anderson–Marasteanu (CAM) model is first selected as the master curve model of the storage modulus, upon which the master curve model of loss modulus is then established using the numerical form of the exact Kramers-Kronig relation between the storage modulus and loss modulus. According to LVE conversions between the relaxation spectrum and storage modulus, the model of the continuous relaxation spectrum is subsequently derived and finally determined based on the same model parameters of the storage modulus and loss modulus models. This study demonstrates that the relaxation spectrum of both mixtures and binders constructed by the proposed method is compliant with LVE theory and physical causality. The generated relaxation spectrum is verified to be accurate enough to compare the storage modulus and loss modulus values recalculated by the relaxation spectrum and the corresponding values predicted by master curve models. The results also show that the approximate Kramers-Kronig relation between the storage modulus and loss modulus cannot be used to establish the relaxation spectrum of asphalt materials, especially for asphalt binders. In addition, the generated relaxation spectrum was utilized to construct the relaxation modulus of mixtures and to develop the stiffness modulus of binders, respectively. Since the relaxation modulus and creep stiffness are determined from the relaxation spectrum, both are consistent with LVE theory and physical causality.

Viscoelastic Characterization of Corn Starch Paste: (I) The First Normal Stress Difference of a Cross-Linked Waxy Corn Starch Paste with Sucrose

Experimental viscoelastic data and the corresponding theoretical analysis of corn starch paste in the past 30 years indicate an evident deficiency of the viscoelastic characterization of the paste. The purposes of the study are to check the capability of a recent model on describing the viscoelasticity of the paste and to improve the viscoelastic analysis. The linear viscoelastic property; the steady shear viscosity and the first normal stress difference (N1) of a cross-linked waxy corn starch paste mixed with sucrose experimentally reported in 2003 were characterized with a structuralized viscoelastic constitutive equation in the present paper. The structuralized parameter f in the equation was obtained using the viscosities in the dynamic and steady shear experiment. Both a power law strain model and a linear strain model were proposed to describe the normal component in the strain matrix. Three kinds of viscoelastic properties of the paste can be described well with the structuralized equation. Both the power law and the linear strain model can yield reasonable calculations of N1. The maximum deviation of N1 calculated by two strain models is about 10%. The theoretical model adopted is available for describing the complex viscoelastic behaviors of corn starch paste usually appearing in the processing of corn starch.

Determining with High Accuracy the Relaxation Modulus and Creep Compliance of Asphaltic Materials in the Form of Sums of Exponential Functions from Mathematical Master Curves of Dynamic Modulus

According to the physical causality principle, the two components of complex modulus are not independent yet interrelated to each other via Kramers-Kronig relationships. Using two mathematical functions to predict simultaneously the dynamic modulus (DM) and phase angle (PA) generally leads to the violation of the causality principle. Therefore, the calculation of one component based on the other one is a vital task for using mathematical models to predict the linear viscoelastic (LVE) behavior of asphaltic materials. In addition, the relaxation modulus (RM) or the creep compliance (CC) in the form of sums of exponential functions (SEFs) is necessary for the efficient resolution of the stress–strain relationship in the time domain. This paper presented a novel method for calculating with high accuracy the RM and CC in the form of SEFs based on the input DM master curve. First, the midpoint integration scheme was used to calculate the PA based on the exact relationship between the PA and DM. After that, the storage modulus and compliance were computed and decomposed with high accuracy into SEFs using a special technique. Then, the closed-form formula of the RM and CC were derived thanks to the special form function of the storage modulus and compliance. Finally, the special technique was used once again to decompose with high accuracy the RM and CC into SEFs for possible uses in finite-element method (FEM) analysis in the time domain. The results showed that the relative errors of all LVE properties computed were lower than 0.1 percent at all calculating points.

Microscopic Dynamics and Viscoelasticity of Vitrimers

We implement a hybrid molecular dynamics/Monte Carlo simulation to study the microscopic dynamics and the macroscopic rheology of vitrimers with a fast bond exchange rate. We show that the linear viscoelastic properties and mean squared displacement of the vitrimers collapse onto master curves by applying the same shift factors that follow the Williams–Landel–Ferry equation at low temperatures and Arrhenius-like behavior at high temperatures. The linkage between the microscopic dynamics and the linear rheology of vitrimers is established using the generalized Stokes–Einstein relationship, which efficiently extends the timescale of simulations and predicts the viscoelasticity. The values of the shift factors are related to the characteristic decay time of the intermediate scattering function, which is accessible in scattering experiments. The same results hold in the case of an all-atom model of an ionic liquid. Our methodology provides a microscopic basis for the time-superposition principle and predicts the macroscopic rheology of thermo-rheologically simple vitrimers.

Dynamics and Rheology of Supramolecular Assemblies at Elevated Pressures.

A methodology to investigate the linear viscoelastic properties of complex fluids at elevated pressures (up to 120 MPa) is presented. It is based on a dynamic light scattering (DLS) setup coupled with a stainless steel chamber, where the test sample is pressurized by means of an inert gas. The viscoelastic spectra are extracted through passive microrheology. We discuss an application to hydrogen-bonding motif 2,4-bis(2-ethylhexylureido)toluene (EHUT), which self-assembles into supramolecular structures (tubes and filaments) in apolar solvents dodecane and cyclohexane. High levels of pressure (roughly above 20 MPa) are found to slow down the terminal relaxation process; however, the increases in the entanglement plateau modulus and the associated persistence length are not significant. The concentration dependence of the plateau modulus, relaxation times (fast and slow), and correlation length is practically the same for all pressures and exhibits distinct power-law behavior in different regimes. Within the tube phase in dodecane, the relative viscosity increment is weakly enhanced with increasing pressure and reaches a plateau at about 60 MPa. In fact, depending on concentration, the application of pressure in the tube regime may lead to a transition from a viscous (unentangled) to a viscoelastic (partially entangled to well-entangled) solution. For well-entangled, long tubes, the extent of the plateau regime (ratio of high- to low-moduli crossover frequencies) increases with pressure. The collective information from these observations is summarized in a temperature-pressure state diagram. These findings provide ingredients for the formulation of a solid theoretical framework to better understand and exploit the role of pressure in the structure and dynamics of supramolecular polymers.

Polylactic acid/polycaprolactone bionanocomposites containing zinc oxide nanoparticles: Structure, characterization and cytotoxicity assay

In the present study, zinc oxide nanoparticles (ZnO-NPs) were synthesized by a hydrothermal method followed by the fabrication of polylactic acid/polycaprolactone blend (PLA/PCL, 80/20 wt/wt) at various loadings of ZnO-NPs (2, 4, and 6 wt%) via melt mixing. FTIR and XRD patterns confirmed that the ZnO-NPs were successfully synthesized. The ZnO-NPs with an average diameter of about 46–73 nm were observed by the FESEM analysis. The effect of ZnO-NPs on morphological, thermal, UV absorption, mechanical, photochemical degradation, rheological and cell viability properties of PLA/PCL blend were investigated. FESEM micrographs of bionanocomposites demonstrated that polycaprolactone was dispersed as a droplet to the Polylactic acid matrix phase. DSC analysis showed that the addition of ZnO-NPs increased the degree of crystallinity and melting temperature of the PLA. Mechanical assessment of the bionanocomposites reveals that the addition of 2, 4 and 6 wt.% of ZnO-NPs into the blend sample leads to increase in the tensile modulus by about 5.4, 11 and 24%. The MTT assay results implied that cell viability of the both filled and unfilled samples is greater than 90% indicating their biocompatibility to the fibroblast cells. It is observed that the melt linear viscoelastic properties of the prepared bionanocomposites are under control of LA/PCL chain degradation and hydrodynamic nanoparticles interaction.

Linear viscoelasticity of nanocolloidal suspensions from probe rheology molecular simulations

We use molecular dynamics (MD) simulations in conjunction with the probe rheology technique to investigate the linear viscoelasticity of nanocolloidal suspensions. A particulate model of the solvent is used in which the hydrodynamics is governed by interparticle interactions. Active and passive probe rheology molecular simulations are performed on the colloidal suspensions of different volume fractions ranging from 0.30 to 0.45 to determine the linear viscoelastic properties of these systems. The viscoelastic modulus of the suspensions is obtained by analyzing the probe motion using continuum mechanics. In active rheology, the distribution of colloid particles around the probe is observed to be symmetric indicating that the system is in the linear regime at all conditions investigated. In passive rheology, the mean-squared displacement of the probe covers the range of motion from ballistic to diffusive regimes. The dynamic modulus and the reduced complex viscosity values obtained from probe rheology simulations are in good agreement with the results from the oscillatory nonequilibrium MD (NEMD) simulations and the literature theoretical predictions. At low frequency values, accounting for artificial hydrodynamic interactions between the probe and its periodic images improves the quantitative accuracy of the modulus values obtained from simulations. Simulations carried out using probes of different sizes indicate that only the probes that are larger than the colloids yield viscoelastic modulus values that are in good agreement with the NEMD values at all volume fractions investigated.

A highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials

In this paper, a highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials is proposed based on micromechanics and homogenization method in the time domain. The deformation first is additively divided into volumetric and deviatoric parts and then the viscoelastic behaviors are decomposed into the time-dependent and time-independent parts. Finite element simulations based on representative volume element models are utilized to numerically verify the constitutive model. The effects of the void-shape, porosity, elastic and viscous parameters of the matrix, strain rate, and angular frequency on the effective linear viscoelastic responses are studied. The results demonstrate that the constitutive model can provide accurate estimation of the effective linear viscoelastic properties for the closed-cell porous materials in both time and frequency domains. The 3D printed nylon porous materials with various porosities are employed to experimentally validate the constitutive model through simple uniaxial compression tests, stress relaxation uniaxial compression tests, and uniaxial compression tests with different strain rates. The results reveal that the constitutive model can also predict well the behaviors of linear viscoelastic closed-cell porous materials with different porosities in the time domain under various loading conditions.

Measuring biological materials mechanics with atomic force microscopy - Determination of viscoelastic cell properties from stress relaxation experiments.

Cells are complex, viscoelastic bodies. Their mechanical properties are defined by the arrangement of semiflexible cytoskeletal fibers, their crosslinking, and the active remodeling of the cytoskeletal network. Atomic force microscopy (AFM) is an often-used technique for the study of cell mechanics, enabling time- and frequency-dependent measurements with nanometer resolution. Cells exhibit time-dependent deformation when stress is applied. In this work, we have investigated the stress relaxation of HeLa cells when subjected to a constant strain. We have varied the applied force (1, 2, 4, and 8 nN) and pause time (1, 10, and 60 s) to check for common assumptions for the use of models of linear viscoelasticity. Then, we have applied three models (standard linear solid, five element Maxwell, power law rheology) to study their suitability to fit the datasets. We show that the five element Maxwell model captures the stress relaxation response the best while still retaining a low number of free variables. This work serves as an introduction and guide when performing stress relaxation experiments on soft matter using AFM. RESEARCH HIGHLIGHTS: Cells exhibit linear viscoelastic properties when subjected to stress relaxation measurements at the studied different forces and times. The stress relaxation is best described by a five element Maxwell model. All three used models capture a softening and fluidization of cells when disrupting actin filaments.

Effect of corneal collagen crosslinking on viscoelastic shear properties of the cornea

The cornea is responsible for most of the refractive power in the eye and acts as a protective layer for internal contents of the eye. The cornea requires mechanical strength for maintaining its precise shape and for withstanding external and internal forces. Corneal collagen crosslinking (CXL) is a treatment option to improve corneal mechanical properties. The primary objective of this study was to characterize CXL effects on viscoelastic shear properties of the porcine cornea as a function of compressive strain. For this purpose, corneal buttons were prepared and divided into three groups: control group (n = 5), pseudo-crosslinked group (n = 5), and crosslinked group (n = 5). A rheometer was used to perform dynamics torsional shear experiments on corneal disks at different levels of compressive strain (0%–40%). Specifically, strain sweep experiments and frequency sweep tests were done in order to determine the range of linear viscoelasticity and frequency dependent shear properties, respectively. It was found that the shear properties of all samples were dependent on the shear strain magnitude, loading frequency, and compressive strain. With increasing the applied shear strain, all samples showed a nonlinear viscoelastic response. Furthermore, the shear modulus of samples increased with increasing the frequency of the applied shear strain and/or increasing the compressive strain. Finally, the CXL treatment significantly increased the shear storage and loss moduli when the compressive strain was varied from 0% to 30% (p < 0.05); larger shear moduli were observed at compressive 40% strain but the difference was not significant (P = 0.12).

Effect of Organic-Montmorillonite on rheological performance of Bio-Asphalt composites with various oxidative aging

Several previous studies have demonstrated that bio-asphalt derived from Waste Cooking Oil (WCO) displays superior performance in cracking resistance at low and medium temperature, but inferior in high temperature rutting resistance. This study aims to further improve the rutting resistance of WCO based bio-asphalt by a compound modification with Organized Montmorillonite (OMMT). One neat asphalt binder with penetration grade of 90 is selected in this study. The WCO based bio-oils are firstly mixed with neat binders followed by further modified with the OMMT additives. The frequency sweep, linear amplitude sweep (LAS) and multiple stress creep recovery (MSCR) tests are respectively conducted for evaluation of the linear viscoelastic properties, fatigue and rutting resistance. Experimental results demonstrate again that the fatigue resistances of bio-binders are improved compared to the base asphalt whereas the addition of bio-oil obviously reduces the binder rutting resistance at high temperature. However, the OMMT addition into the bio-asphalt is found to effectively enhance the rutting resistance when increasing the OMMT content without compromising the fatigue performance. Therefore, it can be preliminary concluded that the Bio/OMMT compound modification approach can be utilized to address the rutting potential concern of WCO based bio-binders at high temperature. Furthermore, the Response Surface Methodology (RSM) is employed to model the rheological properties of Bio/OMMT compound modified binder under various modifier weights, in which the damage characteristic and performance index can be effectively estimated.

Linear viscoelastic properties of the vertex model for epithelial tissues.

Epithelial tissues act as barriers and, therefore, must repair themselves, respond to environmental changes and grow without compromising their integrity. Consequently, they exhibit complex viscoelastic rheological behavior where constituent cells actively tune their mechanical properties to change the overall response of the tissue, e.g., from solid-like to fluid-like. Mesoscopic mechanical properties of epithelia are commonly modeled with the vertex model. While previous studies have predominantly focused on the rheological properties of the vertex model at long time scales, we systematically studied the full dynamic range by applying small oscillatory shear and bulk deformations in both solid-like and fluid-like phases for regular hexagonal and disordered cell configurations. We found that the shear and bulk responses in the fluid and solid phases can be described by standard spring-dashpot viscoelastic models. Furthermore, the solid-fluid transition can be tuned by applying pre-deformation to the system. Our study provides insights into the mechanisms by which epithelia can regulate their rich rheological behavior.

Linear viscoelasticity of PP/PS/MWCNT composites with co-continuous morphology

In this work, a study of the linear viscoelastic properties of co-continuous polypropylene/polystyrene blends filled with multiwall carbon nanotubes (MWCNTs) is presented. The YZZ rheological model [W. Yu et al., Polymer 51, 2091–2098 (2010)] is employed to correlate the rheological behavior of the blends with their microstructure and electrical properties. A test design involving a sequence of small amplitude oscillatory shear and a time sweep (simulating thermal annealing) is used to evaluate the morphology and evolution of electrical properties. It was shown that the YZZ rheological model could be successfully modified to be able to quantify a co-continuous morphology of filled composites. The calculated characteristic domain size was found to be in good agreement with the experimental data obtained via scanning electron microscopy. Furthermore, it is shown that the characteristic domain size slightly decreased after 30 min of thermal annealing. It was shown, as well, that thermal annealing promoted a reduction in the electrical percolation threshold (wt. % MWCNT) from 0.28 to 0.06.

Equilibrium and non-equilibrium molecular dynamics approaches for the linear viscoelasticity of polymer melts

Viscoelastic properties of polymer melts are particularly challenging to compute due to the intrinsic stress fluctuations in molecular dynamics (MD). We compared equilibrium and non-equilibrium MD approaches for extracting the storage (G′) and loss moduli (G″) over a wide frequency range from a bead-spring chain model in both unentangled and entangled regimes. We found that, with properly chosen data processing and noise reduction procedures, different methods render quantitatively equivalent results. In equilibrium MD (EMD), applying the Green−Kubo relation with a multi-tau correlator method for noise filtering generates smooth stress relaxation modulus profiles from which accurate G′ and G″ can be obtained. For unentangled chains, combining the Rouse model with a short-time correction provides a convenient option that circumvents the stress fluctuation challenge altogether. For non-equilibrium MD (NEMD), we found that combining a stress pre-averaging treatment with discrete Fourier transform analysis reliably computes G′ and G″ with a much shorter simulation length than previously reported. Comparing the efficiency and statistical accuracy of these methods, we concluded that EMD is both reliable and efficient, and is suitable when the whole spectrum of linear viscoelastic properties is desired, whereas NEMD offers flexibility only when some frequency ranges are of interest.

Spherical indentation test for quasi-non-destructive characterisation of asphalt concrete

The indentation test is a promising technique for the viscoelastic characterisation of asphalt concrete (AC). Indentation measurements are primarily influenced by the material properties in the direct vicinity of the indenter-specimen contact point. Accordingly, it may become a useful alternative for the characterisation of thin asphalt layers as well as for a quasi-non-destructive AC characterisation in the field. In this study, the spherical indentation test is used to measure the linear viscoelastic properties of AC mixtures extracted from a road test section. The measured complex moduli are compared to those obtained by the shear box test and are found to exhibit a linear correlation. The measurements are further analysed using the Gaussian mixture model to assign each indentation test to either aggregate-dominated or mastic-dominated response. The measurements attributed to mastic-dominated response are found to be more sensitive to the temperature and AC’s binder properties as compared to the average measurements. Accordingly, the proposed test method may provide a promising tool to measure AC viscoelastic properties and monitor the changes in AC binder phase in a non-destructive manner. A finite element micromechanical model is used to identify a representative scale for the response measured in mastic-dominated tests as well as to quantify the effect of measured properties on the AC damage propensity.

Effect of Base Oil and Thickener on Texture and Flow of Lubricating Greases: Insights from Bulk Rheometry, Optical Microrheology and Electron Microscopy

The structure and flow behavior of lubricating greases depend on the base oil and the type and concentration of the dissolved thickener. In this study, the linear viscoelastic properties of greases were characterized by combining oscillatory shear and squeeze flow covering a broad frequency range (0.1–105 rad s−1). Multiple-particle tracking (MPT) microrheology and scanning electron microscopy (SEM) provided further insight into local viscoelastic properties and sample structure on a submicron-length scale. The type and viscosity of the base oil did not affect the absolute value of the complex viscosity and the filament shape formed by a given thickener. High-frequency shear modulus data, however, indicated that the thickener lithium 12-hydroxystearate formed stiffer networks/filaments in poly-α-olefins than in mineral oils. As expected, the viscosity increased with increased thickener concentrations, but microscopy and high-frequency rheometry revealed that the thickness, length, and stiffness of the individual filaments did not change. In mineral oil, the 12-hydroxystearate thickeners yielded higher viscosity than the corresponding stearates with the same metal ion. The filamentous lithium thickeners created stronger networks than the roundish aggregates formed by magnesium and zinc stearate. Network mesh sizes varying between approximately 100 nm and 300 nm were consistently determined from SEM image analysis and MPT experiments. The MPT experiments further disclosed the existence of gel-like precursors of approximately 130 µm at thickener concentrations far below the critical value at which a sample-spanning network resulting in a characteristic grease texture is formed.