Frequency-dependent Complex Shear Research Articles

Molecular dynamics simulation of the dynamical mechanical analysis of polybutadiene

Dynamical mechanical analysis (DMA) is an experimental technique to characterize the viscoelastic behavior of thermoplastic polymers versus the frequency, temperature, etc. However, from an atomistic simulation viewpoint, DMA has not been much investigated. In this study we propose to fill this gap. Dynamical and mechanical properties of polymers have thus been investigated using atomistic simulation to characterize the viscoelastic response of 1,4-Polybutadiene (PBD), an important synthetic rubber. For this, the dynamic moduli of the 1,4-Polybutadiene (PBD) at different regimes have been analyzed considering two different methods using molecular dynamics simulations with GPU acceleration: one based on Green-Kubo expression, and the second one on calculating stress response in a cyclic deformation. The frequency-dependent complex shear modulus and dynamic viscosity of PBD have thus been reported. Our findings will aid future research in more accurate prediction of dynamical and mechanical properties of novel viscoelastic materials.

Measurement of complex shear viscosity up to 3 GHz using an electrodeless AT-cut quartz transducer

An experimental method is proposed to determine the frequency-dependent complex shear viscosity of liquids based on the quartz crystal microbalance with dissipation method. An AT-cut quartz transducer without metal electrodes is immersed in a sample liquid and the transducer is electrically coupled to the circuit through the dielectric response of the sample itself. After correcting for the apparent change in the resonance properties due to the dielectric coupling of the sample, our method is able to determine the viscosity of liquids of high polarity and low viscosity at frequencies as high as 3 GHz. The method was then applied to ethylene glycol and the viscoelastic relaxation in the GHz regime was observed. Furthermore, it was also applied to room-temperature ionic liquids to show that the dielectric correction of the resonance properties is valid for conductive liquids.

Effect of rapeseed oil on the rheological, mechanical and thermal properties of plastic lubricants

A strong difference in the physico-chemical properties of the plastic lubricants studied was found in this study through pressure drop, thermal analysis, vibration damping, texture hardness and rheological measurements. Oxidation aging of the lubricant sample containing rapeseed oil additive was proposed. Its higher thermal sensitivity was simultaneously confirmed by frequency dependent complex shear modulus of elasticity measurements as well as by rheological testing. Rapeseed oil modified lubricant showed a higher decrease in both storage and moduli losses due to a temperature increase from 16 to 26 ° C compared to the rapeseed oil free sample. Simultaneously, the flow curves were shifted to the higher shear stresses (for plastic lubricant without rapeseed oil additive) typical for rheopectic fluids. For the rapeseed oil modified lubricant, the flow curves were shifted to the lower shear stresses, indicating its thixotropic fluid behaviour. The synthetic lubricant without rapeseed oil additive exhibited higher dissipative rheological behaviour as reflected by decreasing first resonance frequency peak position compared to the rapeseed oil modified lubricant as obtained from vibration damping measurements. It was found that the synthetic lubricant exhibited better vibration damping properties and mechanical energy dissipation into heat due to its higher viscous friction than the rapeseed oil modified lubricant under experimental conditions.

Viscoelastic shear modulus measurement of thin materials by interferometry at ultrasonic frequencies

This paper presents a technique for measuring the complex shear modulus of thin slabs of viscoelastic solids based on the measurement of the reflection and transmission of plane shear waves through a sample inserted between two delays lines. Reproducible shear wave transmission through the sample is achieved by inserting bond layers with controlled thickness between the delay lines and the sample and by characterizing beforehand the bond rheology. The frequency dependent complex shear modulus is quantitatively evaluated from the transmission and reflection coefficients using an exact model of interferences within the delay line-bond-sample-bond-delay line sandwich and by selecting the solution among the muliple solutions of the inverse problem from considerations on time of flight and sample thickness. Thanks to its reproducibility and accuracy, this method appears as an original and efficient technique for quantitatively characterizing the high frequency shear modulus of attenuating materials.

High-frequency shear viscosity and ionic mobility of solutions of polyethylene glycol in ionic liquids

The frequency-dependent complex shear viscosity of the solutions of polyethylene glycol (PEG) in various ionic liquids is measured in the frequency range of 5–205 MHz, and the ionic mobility of the corresponding solutions was also determined. The plateau viscosity in the MHz regime increases on the addition of PEG, and the relaxation in the 100 MHz regime is retarded simultaneously. The amount of the increase in the plateau viscosity correlates with that in the relaxation time, suggesting that the retardation of the relaxation is a reason for the increase in the plateau viscosity. Although the increase in the plateau viscosity is far smaller than that in the zero-frequency viscosity, these two values are correlated with each other, which can be explained as the consequence of the strength of the same kind of the solute-solvent attractive interaction. The decrease in the molar ionic conductivity also correlates with the increase in the plateau viscosity, suggesting that the plateau viscosity can be regarded as the local viscosity of ionic liquids related to the ion conduction. Based on the correlation with the Kamlet-Taft α parameter, the hydrogen bond between the ionic liquid and the oxygen atoms of PEG is suggested to be a possible origin of the increase in the plateau viscosity.

On fractional modeling of viscoelastic foams

Empiric models have been introduced to describe frequency dependence of dielectric permittivity. Simple exponential models are often not satisfactory, while advanced non-exponential models (usually referred as “anomalous relaxation”) are commonly required to better explain experimental observations of complex systems. For viscoelastic materials, the so-called fractional derivatives models are powerful for both dynamic and loss moduli prediction. In this paper, the analysis of the main models used in the characterization of dielectric and viscoelastic materials such as five-parameter fractional Zener model and empiric Havriliak–Negami model are analysed. The fractional shape parameters describing the symmetric and asymmetric broadening of the complex modulus don't have the same influence in low and high frequencies. In contrast to the five-parameter Zener model, the empiric model asymmetry parameter has an influence on complex modulus at low frequencies comparing to the loss modulus peak frequency. A no resonance technique based on a forced vibrations procedure is used to investigate the frequency dependent complex shear modulus of a polyurethane foam, not influenced by its fluid phase, in the range 0.1–500 Hz. It is shown that the Havriliak–Negami model can predict the frequency dependence for a wide frequency range.

Translation-orientation coupling and Cox-Merz rule of liquid hexane.

Equilibrium and non-equilibrium molecular dynamics simulations are performed on liquid hexane in order to clarify the origin of the Cox-Merz rule of liquids composed of chain-like molecules. The relation between the frequency-dependent complex shear viscosity and the shear-rate dependent nonlinear viscosity follows the Cox-Merz rule as expected. The slowest viscoelastic relaxation mode is explained by the translation-orientation coupling mechanism, and the saturation of the shear-induced orientational order is observed in the non-equilibrium simulation at the onset of the shear thinning. The origin of the Cox-Merz rule is discussed in terms of the translation-orientation coupling.

Dispersion in Tissue-Mimicking Gels Measured with Shear Wave Elastography and Torsional Vibration Rheometry

Dispersion, or the frequency dependence of mechanical parameters, is a primary confounding factor in elastography comparisons. We present a study of dispersion in tissue-mimicking gels over a wide frequency band using a combination of ultrasound shear wave elastography (SWE), and a novel torsional vibration rheometry which allows independent mechanical measurement of SWE samples. Frequency-dependent complex shear modulus was measured in homogeneous gelatin hydrogels of two different bloom strengths while controlling for confounding factors such as temperature, water content and material aging. Furthermore, both techniques measured the same physical samples, thereby eliminating possible variation caused by batch-to-batch gel variation, sample geometry differences and boundary artifacts. The wide-band measurement, from 1 to 1800 Hz, captured a 30%–50% increase in the storage modulus and a nearly linear increase with frequency of the loss modulus. The magnitude of the variation suggests that accounting for dispersion is essential for meaningful comparisons between SWE implementations.

I-RheoGT: Transforming from Time to Frequency Domain without Artifacts

We present a new analytical tool for educing the frequency-dependent complex shear modulus of materials from computer-aided numerical simulations of their time-dependent shear relaxation modulus, without the need of preconceived models. The rheological tool is presented in the form of an open access executable named “i-Rheo GT”, enabling its use to a broad scientific community. Its effectiveness is corroborated by analyzing the dynamics of ideal single mode Maxwell fluids and by means of a direct comparison with both bulk-rheology measurements and coarse-grained molecular dynamics simulations data transformed via a generalized Maxwell model. When adopted to transform atomistic molecular dynamics simulations data, the unbiased nature of the tool reveals new insights into the materials’ linear viscoelastic properties, especially at high frequencies, where conventional tools struggle to interpret the data and molecular dynamics simulations actually provide their most statistically accurate predictions. The w...

Comment on "A symmetrical method to obtain shear moduli from microrheology" by K. Nishi, M. L. Kilfoil, C. F. Schmidt, and F. C. MacKintosh, Soft Matter, 2018, 14, 3716.

Nishi et al. have presented a new analytical method for transforming the time-dependent materials' compliance into their frequency-dependent complex shear modulus, without the need of a preconceived fitting function nor the use of Kramers-Kronig transformations. They claim that their method significantly improves the accuracy of the outcomes, especially at high frequencies, up to "almost" the Nyquist frequency. Here, I corroborate that their method is actually able to provide a close estimation of the materials' complex shear modulus over the 'entire' range of explored frequencies (i.e. beyond the Nyquist frequency), as long as the compliance values are linearly spaced in the time-domain and its value at time zero is included as the first data point in the input file. Moreover, as a means of comparison, I employ the analytical method introduced by Tassieri et al. [New J. Phys., 2012, 14, 115032] for performing the Fourier transform of any generic time-dependent function that vanishes for negative times, is sampled at a finite rate, need not be equally spaced and extends over a finite time window. This existing method does not need preconceived fitting functions nor the use of Kramers-Kronig transformations; yet it shows a higher degree of accuracy compared to the one proposed by Nishi et al.

A complex elastographic hyperbolic solver (CEHS) to recover frequency dependent complex shear moduli in viscoelastic models utilizing one or more displacement data-sets

In this paper, we present a linear marching scheme to recover frequency-dependent complex shear moduli in viscoelastic models utilizing two sets of single component displacement data. The proposed method is designed to provide stable and accurate estimation of the tissue viscoelastic stiffness parameters by solving a first-order complex partial differential equation. To control the exponential growth of the numerical error resulting from one of the complex coefficients in the inverse equation, a modified upwind discretization is utilized on the first-order derivative terms of the target parameter. The algorithm is fully stablized when: (1) carefully chosen multiple data-sets are combined to eliminate the remaining complex coefficient that contributes to exponential error growth; and (2) a modified Tikhonov regularization is applied to the inversion method. We obtain the stability result in the norm so that the numerical scheme is convergent at fractional 1 / 2 order. Its performance is compared with the performance of the Algebraic Inversion Model previously investigated. We present shear modulus reconstructions from synthetic data, from laboratory phantom data and match frequency-dependent complex moduli from phantom data to several viscoelastic models. Since we have previously presented phase wave speed images from interference patterns, we exhibit those images here for comparison.

Ultrasound Shear Wave Viscoelastography: Model-Independent Quantification of the Complex Shear Modulus.

Ultrasound shear wave elastography methods are commonly used for estimation of mechanical properties of soft biological tissues in diagnostic medicine. A limitation of most currently used elastography methods is that they yield only the shear storage modulus ( G' ) but not the loss modulus ( G'' ). Therefore, no information on viscosity or loss tangent (tan δ) is provided. In this paper, an ultrasound shear wave viscoelastography method is developed for model-independent quantification of frequency-dependent viscoelastic complex shear modulus of macroscopically homogeneous tissues. Three in vitro tissue-mimicking phantoms and two ex vivo porcine liver samples were evaluated. Shear waves were remotely induced within the samples using several acoustic radiation force pushes to generate a semicylindrical wave field similar to those generated by most clinically used elastography systems. The complex shear modulus was estimated over a broad frequency range (up to 1000 Hz) through the analytical solution of the developed inverse wave propagation problem using the measured shear wave speed and amplitude decay versus propagation distance. The shear storage and loss moduli obtained for the in vitro phantoms were compared with those from a planar shear wave method and the average differences over the whole frequency range studied were smaller than 7% and 15%, respectively. The reliability of the proposed method highlights its potential for viscoelastic tissue characterization, which may improve noninvasive diagnosis.

Python algorithms in particle tracking microrheology.

BackgroundParticle tracking passive microrheology relates recorded trajectories of microbeads, embedded in soft samples, to the local mechanical properties of the sample. The method requires intensive numerical data processing and tools allowing control of the calculation errors.ResultsWe report the development of a software package collecting functions and scripts written in Python for automated and manual data processing, to extract viscoelastic information about the sample using recorded particle trajectories. The resulting program package analyzes the fundamental diffusion characteristics of particle trajectories and calculates the frequency dependent complex shear modulus using methods published in the literature. In order to increase conversion accuracy, segmentwise, double step, range-adaptive fitting and dynamic sampling algorithms are introduced to interpolate the data in a splinelike manner.ConclusionsThe presented set of algorithms allows for flexible data processing for particle tracking microrheology. The package presents improved algorithms for mean square displacement estimation, controlling effects of frame loss during recording, and a novel numerical conversion method using segmentwise interpolation, decreasing the conversion error from about 100% to the order of 1%.

Splinelike interpolation in particle tracking microrheology

Converting time dependent creep compliance to frequency dependent complex shear modulus is an important step in analyzing the results of particle tracking microrheology. Fitting a function to the whole time range and transforming it to calculate the shear modulus is one way of solving this problem. However, the creep compliance of many samples, such as gels of biopolymers, shows different trends under different time regimes. Fitting in these regimes segmentwise results in a function which usually cannot be transformed in a closed analytical form. In general, unlike for beta and cubic splines, also the continuity of the first derivative cannot be ensured. In this paper, we present a method for using segmentwise fitting and numerical conversion, discussing interpolation for improving the transition between the fitted ranges, and propose a dynamic sampling technique to control the accuracy of the resultant complex shear modulus.

Hydrogen Network Fluctuations of Alcohols. Evidence from Ultrasonic, Dielectric, and Shear Impedance Spectrometry

Broadband dielectric spectra (1 MHz to 40 GHz) and ultrasonic attenuation spectra (300 kHz to 3 GHz) as well as frequency-dependent complex shear viscosities (6 MHz to 120 MHz) are reported for alcohols and for their mixtures with other alcohols, with alkanes, and with water. The spectra are discussed with a view to features controlling the molecular dynamics of associating liquids. Special attention is given to (i) the rotation of terminal single-hydrogen-bonded hydroxy groups of associated structures, (ii) the dominating relaxation process of the structures, involving multiply-hydrogen-bonded hydroxy groups, (iii) the alkyl chain rotational isomerization, (iv) effects of clustering in alcohol–alkane mixtures, and (v) indications of non-critical concentration fluctuations of alcohol–water mixtures. The hydrogen network fluctuations of the alcohol systems can be consistently described in terms of a wait-and-switch model of relaxation. The concentration fluctuations are well represented by a recent “unifying” theoretical model, indicating a predominant impact of hydrophobic groups in the promotion of a micro-heterogeneous structure of mixtures with water.

Fluid substitution in rocks saturated with viscoelastic fluids

Heavy oils have high densities and extremely high viscosities, and they exhibit viscoelastic behavior. Traditional rock physics based on Gassmann theory does not apply to materials saturated with viscoelastic fluids. We use an effective-medium approach known as coherent potential approximation (CPA) as an alternative fluid-substitution scheme for rocks saturated with viscoelastic fluids. Such rocks are modeled as solids with elliptical fluid inclusions when fluid concentration is small and as suspensions of solid particles in the fluid when the solid concentration is small. This approach is consistent with concepts of percolation and critical porosity, and it allows one to model sandstones and unconsolidated sands.We model the viscoelastic properties of a heavy-oil-saturated rock sample using CPA and a measured frequency-dependent complex shear modulus of the heavy oil. Comparison of modeled results with measured properties of the heavy-oil rock reveals a large discrepancy over a range of frequencies and temperatures. We modify the CPA scheme to account for the effect of binary pore structure by introducing a compliant porosity term. This dramatically improves the predictions. The predicted values of the effective shear modulus of the rock are in good agreement with laboratory data for the range of frequencies and temperatures. This confirms that our scheme realistically estimates the frequency- and temperature-dependent properties of heavy-oil rocks and can be used as an approximate fluid-substitution approach for rocks saturated with viscoelastic fluids.

Passive and active microrheology for cross-linked F-actin networks in vitro

Actin filament (F-actin) is one of the dominant structural constituents in the cytoskeleton. Orchestrated by various actin-binding proteins (ABPs), F-actin is assembled into higher-order structures such as bundles and networks that provide mechanical support for the cell and play important roles in numerous cellular processes. Although mechanical properties of F-actin networks have been extensively studied, the underlying mechanisms for network elasticity are not fully understood, in part because different measurements probe different length and force scales. Here, we developed both passive and active microrheology techniques using optical tweezers to estimate the mechanical properties of F-actin networks at a length scale comparable to cells. For the passive approach we tracked the motion of a thermally fluctuating colloidal sphere to estimate the frequency-dependent complex shear modulus of the network. In the active approach, we used an optical trap to oscillate an embedded microsphere and monitored the response in order to obtain network viscoelasticity over a physiologically relevant force range. While both active and passive measurements exhibit similar results at low strain, the F-actin network subject to high strain exhibits non-linear behavior which is analogous to the strain-hardening observed in macroscale measurements. Using confocal and total internal reflection fluorescent microscopy, we also characterize the microstructure of reconstituted F-actin networks in terms of filament length, mesh size and degree of bundling. Finally, we propose a model of network connectivity by investigating the effect of filament length on the mechanical properties and structure.

스펙트럴유한요소법을 적용한 점탄성층 샌드위치평판의 진동해석

In this paper, a spectral finite element method for a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions has been plated. The sandwich plate consists of two isotropic and elastic face plates with a surfaced-bonded viscoelastic core. For the analysis, the in-plane and transverse energy in the face plates and only shear energy in the core are considered, respectively. To account for the frequency dependent complex shear modulus of the viscoelastic core, the Golla-Hughes-McTavish model is adopted. To evaluate the validity and accuracy of the proposed method, the frequency response function and dynamic responses of the sandwich plate with all edges simply supported subject to an impact load are calculated and compared with those calculated by a finite element method. Though these calculations, it is confirmed that the proposed method is very reliable and efficient one for vibration analysis of a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions.

Fast Fluorescence Laser Tracking Microrheometry, I: Instrument Development

To gain insight into cellular mechanotransduction pathways, we have developed a fluorescence laser tracking microrheometer (FLTM) to measure material rheological features on micrometer length scales using fluorescent microspheres as tracer particles. The statistical analysis of the Brownian motion of a particle quantifies the viscoelastic properties of the probe's environment, parameterized by the frequency-dependent complex shear modulus G*( ω). This FLTM has nanometer spatial resolution over a frequency range extending from 1 Hz to 50 kHz. In this work, we first describe the consecutive stages of instrument design, development, and optimization. We subsequently demonstrate the accuracy of the FLTM by reproducing satisfactorily the known rheological characteristics of purely viscous glycerol solutions and cross-linked polyacrylamide polymer networks. An upcoming companion article will illustrate the use of FLTM in studying the solid-like versus liquid-like rheological properties of fibroblast cytoskeletons in living biological samples.

Comparing Macrorheology and One- and Two-Point Microrheology in Wormlike Micelle Solutions

We present here a comparison between three rheological techniques to verify a recently developed optical microrheology technique. As a model viscoelastic fluid we have used wormlike micelle solutions which are well-characterized Maxwell fluids. Using the same samples, we have measured the viscoelastic response function using macroscopic rheology as well as one-particle and two-particle microrheology. With all three techniques we have obtained frequency-dependent complex shear moduli over large and overlapping frequency ranges. Excellent agreement of the results from all three techniqes was observed. This was expected given that characteristic length scales of the solution, such as persistence length and mesh size, were significantly smaller than the probe particle size. Our results provide a much needed quantitative verification of microrheology on a simple model system.