Frequency Dependence Of Modulus Research Articles

Setting Material Function Design Targets for Linear Viscoelastic Materials and Structures

Rheologically complex materials are described by function-valued properties with dependence on a timescale (linear viscoelasticity), input amplitude (nonlinear material behavior), or more generally both (nonlinear viscoelasticity). This complexity presents a difficulty when trying to utilize these material systems in engineering designs. Here, we focus on linear viscoelasticity and a methodology to identify the desired viscoelastic behavior. This is an early-stage design step to optimize target (function-valued) properties before choosing or synthesizing a real material. In linear viscoelasticity, it is not obvious which properties can be treated as independent design variables. Thus, it is nontrivial to select the most design-appropriate constitutive model, to be as general as possible, but not violate fundamental restrictions. We use the Kramers–Kronig constraint to show that frequency-dependent moduli (e.g., shear moduli G′(ω) and G″(ω)) cannot be treated as two independent design variables. Rather, a single function such as the relaxation modulus (e.g., K(t) for force-relaxation or G(t) for stress relaxation) is an appropriate function-valued design variable. A simple case study is used to demonstrate the framework in which we identify target properties for a vibration isolation system. Viscoelasticity improves performance. Different parameterizations of the kernel function are optimized and compared for performance. While parameterization may limit the generality of the kernel function, we do include a nonobvious representation (power law) that is found in real viscoelastic material systems and in the spring-dashpot paradigm would require an infinite number of components. Our methodology provides a means to answer the question, “What viscoelastic properties are desirable?” This ability to identify targeted behavior will be useful for subsequent stages of the design process including the selection or synthesis of real materials.

Effects of temperature and frequency on dynamic mechanical properties of glass/epoxy composites

Under extreme services conditions, the dynamic mechanical properties of polymer matrix composites play an important role in controlling the durability of composite structures. Temperature–frequency-dependent dynamic mechanical properties of glass/epoxy composites were studied under different loading modes by dynamic mechanical analysis. The temperature-dependent modulus and temperature–frequency-dependent modulus models of epoxy resin and glass/epoxy composites were developed. The physical meaning and how to determine the values of parameters in the model were discussed. All the model predictions showed good agreements with the experimental results.

Self-healing poly(N-isopropylacrylamide) hydrogels

Substitution the covalently crosslinked polymer chains by supramolecular ones is a promising strategy to design self-healing hydrogels. Approaches for the synthesis of supramolecular poly(N-isopropylacrylamide) (PNIPAAm) hydrogels with the ability to self-heal are rare because of the bulky side groups of the polymer hindering formation of strong cooperative secondary interactions. Herein, we describe, for the first time to our knowledge, preparation of PNIPAAm hydrogels with autonomous self-healing ability. Strong hydrophobic interactions were used to physically crosslink PNIPAAm chains in a micellar solution. The hydrogels were prepared by micellar copolymerization of N-isopropylacrylamide (NIPAAm) with 2mol% stearyl methacrylate (C18) in 0.25M NaBr solution of cetyltrimethylammonium bromide (CTAB). The physical gels exhibit frequency-dependent dynamic moduli and a loss factor above 0.1 due to the temporary nature of the hydrophobic associations in the presence of surfactant micelles. Cyclic mechanical tests show significant mechanical hysteresis and reversible loading/unloading cycles up to large maximum strains indicating that the damage done to the gel samples during the loading is recoverable in nature. The hydrogels indeed have autonomous self-healing ability with an efficiency of up to 100%. After swelling in water, the hydrogels undergo a significant change in their internal dynamics and lose their ability to self-heal due to the strengthening of hydrophobic associations in the absence of CTAB. By incorporating acrylic acid (AAc) units within the supramolecular PNIPAAm network, self-healing in swollen PNIPAAm hydrogels is achieved due to the fixing of CTAB in the gel phase by complexation with AAc units.

Nonlocal description of sound propagation through an array of Helmholtz resonators

A generalized macroscopic nonlocal theory of sound propagation in rigid-framed porous media saturated with a viscothermal fluid has been recently proposed, which takes into account both temporal and spatial dispersion. Here, we consider applying this theory capable to describe resonance effects, to the case of sound propagation through an array of Helmholtz resonators whose unusual metamaterial properties such as negative bulk moduli, have been experimentally demonstrated. Three different calculations are performed, validating the results of the nonlocal theory, relating to the frequency-dependent Bloch wavenumber and bulk modulus of the first normal mode, for 1D propagation in 2D or 3D periodic structures.

A single charge in the actin binding domain of fascin can independently tune the linear and non-linear response of an actin bundle network.

Actin binding proteins (ABPs) not only set the structure of actin filament assemblies but also mediate the frequency-dependent viscoelastic moduli of cross-linked and bundled actin networks. Point mutations in the actin binding domain of those ABPs can tune the association and dissociation dynamics of the actin/ABP bond and thus modulate the network mechanics both in the linear and non-linear response regime. We here demonstrate how the exchange of a single charged amino acid in the actin binding domain of the ABP fascin triggers such a modulation of the network rheology. Whereas the overall structure of the bundle networks is conserved, the transition point from strain-hardening to strain-weakening sensitively depends on the cross-linker off-rate and the applied shear rate. Our experimental results are consistent both with numerical simulations of a cross-linked bundle network and a theoretical description of the bundle network mechanics which is based on non-affine bending deformations and force-dependent cross-link dynamics.

Effect of Zn(NO3)2 filler on the dielectric permittivity and electrical modulus of PMMA

Composite films consisting of polymethyl methacrylate (PMMA) and Zn(NO 3) 2 were developed in the laboratory through the sol casting technique. These films were characterized using X-ray diffraction (XRD) and Fourier transform infrared (FTIR) spectroscopy. The morphological analysis was carried out by scanning electron microscopy (SEM). These analyses revealed the homogeneous and semi-crystalline behaviour of the films. The dielectric response measurement was conducted in the frequency range from 100 Hz to 5 MHz. The real and imaginary part of the dielectric permittivity decreased with the increase in frequency but increased with temperature. The electrical conductivity measurement showed a plateau-like behaviour in the low-frequency region and dispersion in the high-frequency region. The frequency-dependent electrical modulus obeyed Arrhenius law, and it showed an increase in the dipolar interaction with the temperature due to thermal activation. The activation energy of the film specimen was estimated to be about 0.448 eV. Thus the polymeric composite PMMA–Zn(NO 3) 2 is one of the appropriate candidate for numerous technical applications such as supercapacitors, high-speed computers and gate dielectric material for organic FETs.

Relaxation mechanism of (x)Mn0.45Ni0.05Zn0.50Fe2O4 + (1 − x)BaZr0.52Ti0.48O3 multiferroic materials

Polycrystalline (x)Mn0.45Ni0.05Zn0.50Fe2O4 + (1 − x)BaZr0.52Ti0.48O3 (with 0.2 ≤ x ≤ 0.8) multiferroic materials were prepared by the standard solid state reaction technique and samples prepared from these composites were sintered at 1200 °C. The impedance, electrical modulus, ac conductivity and dielectric permittivity were investigated over a wide range of frequencies (20 Hz–1 MHz) and at various temperatures (room temperature to 600 °C) to understand the relaxation phenomenon in these materials. X-ray diffraction patterns confirm the presence of a simple cubic spinel structure for the ferromagnetic phase and tetragonal peroveskite for the ferroelectric phase. Frequency-independent conductivity was observed in the low frequency region, which shifts to a higher frequency and dominates over a wide range of frequency (up to 1 MHZ) at higher temperature (600 °C). The transition temperature (∼675 °C) of these composites is higher than that of ferrite and ferroelectric phases. The frequency response electric modulus graphs for some composites show two maxima in the relaxation process. The first relaxation process appears at lower temperature and higher frequency with a lower value of activation energy for the composites containing more than 20% ferrimagnetic phase. This relaxation process is due to the first ionization energy of oxygen vacancies. The second relaxation process appears at all temperatures and at lower frequency, which shifts to higher frequency with increasing temperature, possessing a comparatively higher value of activation energy. This relaxation process is attributed to the Maxwell–Wagner–Sillars relaxation phenomenon. The frequency-dependent impedance and modulus plots exhibit a non-coincidence of relaxation peaks, indicating the deviation from the Debye-type relaxation process.

Frequency-dependent dielectric permittivity and electric modulus studies and an empirical scaling in (100−x)BaTiO3/(x)La0.7Ca0.3MnO3 composites

We have studied the dielectric permittivity and electrical modulus behavior in (100−x)BaTiO3/(x)La0.7Ca0.3MnO3 (x = 20, 30, 40, 50, 60 %) composites over a frequency range from 42 Hz to 5 MHz at room temperature. The dielectric permittivity data have been well interpreted using the Curie–Von Schweidler function adding the conduction contribution. The electric modulus data have been analyzed by invoking the decay relaxation function. Both formalisms describing a non-Debye type relaxation have been obtained in the composites. The electric modulus formalism indicates the Maxwell–Wagner–Sillars relaxation involved in the composite. In the scaled coordinate, the dielectric permittivity and electrical modulus for different x fall on a single master curve, indicating the existence of a general scaling formalism. The empirical scaling also signifies that the relaxation mechanism is independent of composition. In addition, we have proposed an Arrhenius-like equation for x-dependent dc conductivity and characteristic peak frequency in this composite system.

Curcumin-Encapsulated Hexagonal Liquid Crystalline Formed by Brij 97/NaDC Mixtures

The phase diagram of a five-components Brij 97-NaDC/IPM-PEG 400/H2O system was determined at 25°C. The hexagonal liquid crystalline phase (H1) was found in this system. By use of small-angle x-ray scattering (SAXS), polarization microscopy, and rheology techniques, the influence of composition, temperature, and addition of curcumin on H1 phase was studied. It is shown that: 1) the investigated hexagonal liquid crystals exhibit a strong shear thinning behavior and viscoelasticity and the strength of the network of H1 phase becomes weaker with increasing oil content; 2) the frequency-dependent moduli of H1 samples decreases as the temperature increases and the steady-state limiting viscosity of the hexagonal samples shows an Arrhenius-like dependence on temperature; and 3) samples in H1 phase containing curcumin retained their organized hexagonal structure. The SAXS results show that the curcumin molecules may be solubilized both into the apolar core of cylinders together with IPM and in the polar domain coexisting with PEG 400 between the cylinders. When curcumin is encapsulated in samples with low oil content, there is a significant decrease in the frequency-dependent moduli. The tendency of frequency behavior for samples incorporating curcumin as a function of temperature is weakened.

Dielectric studies of Poly (Ethylene glycol)-Polyurethane/Poly (Methylmethacrylate)/Montmorillonite Composite

Semi Inter penetrating Polymer Network (IPN) of [poly (ethylene glycol)-polyurethane-polymethylmethacrylate] [60:40]-montmorillonite (MMT) nanocomposites with different weight percentages of MMT are synthesized. The formation of the composite and its structural properties are characterized by Fourier transform infrared, X-ray diffraction pattern (XRD) and scanning electron microscopy (SEM) images. Differential scanning calorimetry (DSC) and XRD patterns show the amorphous nature of the composites. The Thermo Gravimetric Analysis (TGA) shows the enhanced thermal stability of the composite compared with the semi IPN without fillers. The conductivity behavior, frequency dependent modulus properties and dielectric properties of these prepared composites are studied by using ac impedance spectroscopy (EIS) in the frequency range 1Hz-1MHz. It is found from the impedance results that conductivity increases from 2.17×10−7 S/cm to 2.32×10−6 S/cm with increase of MMT concentration up to 5wt % and it decreases with further increase of MMT content. The dielectric analysis shows that dielectric permittivity (ɛ′) and dielectric loss (ɛ″) values decreases with increase in frequency at lower frequency region whereas frequency independent behavior is observed in the high frequency region. The electrical modulus representation shows a peak in the imaginary component. The ionic conduction relaxation times of the composites obtained from this peak maximum are in good correlation with the electrode polarization relaxation time and conductivity values.

Viscoelasticity of Ells River bitumen sand and 4D monitoring of thermal enhanced oil recovery processes

Samples of Ells River bitumen sand from Alberta, Canada were measured at low frequencies (0.2–205 Hz) to determine the temperature and frequency dependence of velocities and attenuations. The samples were first measured “as received” where the pore space is mostly filled with bitumen but also contains small amounts of air and water. With residual air in the pores, at 5°C, there is strong dispersion in the P-wave modulus and a peak in attenuation at seismic frequencies. The frequency-dependent moduli and attenuations shift by three orders of magnitude in frequency as temperature is increased from 5°C to 48°C, consistent with the bitumen viscosity. Samples were then saturated so any empty pore space is filled with water. After saturation, at 1 Hz, increasing temperature from 5°C to 49°C causes a 30% reduction in the saturated P-wave modulus, a 34% reduction in the saturated bulk modulus, and a 6% reduction in the shear modulus. This behavior can only be explained by the temperature-dependent bulk modulus of bitumen. The results enable predictions regarding the P-velocities that can be expected during seismic monitoring of thermal enhanced oil recovery processes. Velocities for cold bitumen sand are near [Formula: see text] at reservoir pressure and temperature. Following steam injection, velocities should be very low (near [Formula: see text]) in heated zones more than 50°C with a free gas phase, which could be steam or gas. There will be a progressive reduction in velocities, i.e., [Formula: see text] at 25°C and [Formula: see text] at 49°C, in areas of formation heating, but without steam or gas in the pores. Albeit smaller than the effect of steam, the effect of formation heating alone is large enough to be easily detected by today’s 4D surveys. With local rock physics calibration, it should be possible to map the areal extent of formation heating using 4D seismic data.

Shear mechanical properties of the porcine pancreas: Experiment and analytical modelling

We provide the first account of the shear mechanical properties of porcine pancreas using a rheometer both in linear oscillatory tests and in constant strain-rate tests reaching the non-linear sub-failure regime. Our results show that pancreas has a low and weakly frequency-dependent dynamic modulus and experiences a noticeable strain-hardening beyond 20% strain. In both linear and non-linear regime, the viscoelastic behaviour of porcine pancreas follows a four-parameter bi-power model that has been validated on kidney, liver and spleen. Among the four solid organs of the abdomen, pancreas proves to be the most compliant and the most viscous one.

Strain Measures for Transfer Function Approaches to Resonant Column Testing

Abstract This paper presents strain measures to accompany a recently developed transfer function approach for resonant column testing of soils using a free-free apparatus. Although a number of past studies have proposed the use of random excitation or transfer functions in various forms, the new approach is unique in that the transfer function does not involve the current or voltage from the electromagnetic drive system. Consequently, the approach eliminates the need for many device-dependent calibrations and properties, including the torque-current calibration factor, stiffness of the torsional spring connecting the active and passive beams, and mass moments of inertia for the active platen and active beam. A brief review is given of the frequency domain transfer function approach for determining the shear modulus and damping of soil and rock, and a new theoretical formulation is presented for the associated strains in the soil specimen in terms of the measured boundary motion. It is demonstrated that higher modes can possess zero arithmetic average strains; therefore, a root-mean-square strain is proposed and derived as an alternative strain metric that will be non-zero for any frequency at which a specimen is undergoing deformation. Excellent agreement is found between experimental data and the newly derived strain measures. The concepts presented herein are valid for use with harmonic or stepped-sine testing as well as broadband random excitation, whereby strains are obtained for a range of frequencies spanning multiple modes of vibration. The approach provides a rigorous theoretical model that accurately describes the physics of the experiment over a broad frequency range spanning multiple modes. Additionally, the modulus and damping can be arbitrary functions of the frequency parameter without a loss of generality in the theoretical formulation, enabling studies of frequency-dependent modulus and damping.

Natural rubber protein as interfacial enhancement for bio‐based nano‐fillers

ABSTRACTNatural rubber was enhanced with soy protein nano‐aggregates and carbon black using a hybrid process. The rubber composites reinforced with an optimum amount of soy protein or soy protein/carbon black showed useful tensile properties. The stress‐strain behaviors were analyzed with a micro‐mechanical model that describes the stress–strain measurements well. The model analysis provides insight into filler network characteristics and entanglement modulus. The composites were also analyzed with both linear and nonlinear viscoelastic properties. Temperature and frequency dependent modulus as well as the model analysis of stress softening effect describe the ability of soy protein to constraint polymer chains in the highly filled composites. For the composites reinforced with soy protein, the good tensile properties are attributed to good filler‐polymer adhesion through the compatibilization effect of natural rubber protein. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 2188–2197, 2013

Reinforcement effect of biomass carbon and protein in elastic biocomposites

AbstractBiomass carbon (BC) and soy protein (SP) were used to reinforce natural rubber (NR) biocomposites. The particle size of BC was reduced and characterized with elemental analysis, X‐ray diffraction, infrared spectroscopy, and particle size analysis. The rubber composite reinforced with the BC/SP and the composite reinforced with the BC of higher carbon content show useful tensile properties at an optimum filler fraction. The model analysis of the stress–strain behaviors provides insight into filler network characteristics. For the highly filled composites, the BC have less constraint on the polymer chains as shown by the temperature and frequency dependent modulus as well as the model analysis of stress softening effect. The presence of NR protein improves the filler–polymer adhesion for the composites reinforced with BC/SP. POLYM. COMPOS., 2013. © 2013 Society of Plastics Engineers

Bayesian characterization of Young's modulus of viscoelastic materials in laminated structures

This paper addresses an inverse approach to estimate the frequency-dependent Young's modulus of a viscoelastic polymer layer in a laminated structure. The Young's modulus is parameterized by a fractional derivative model and examined from a Bayesian perspective with the consideration of measurement and modeling uncertainties. The probabilistic Bayesian identification is carried out based on an efficient surrogate model through the use of Markov Chain Monte Carlo sampling methods. The proposed approach is experimentally validated on laminated glass.

Dynamic Response Analysis of a SRM Incorporating Frequency-Dependent Modulus Using Iterative Approach

Mode-based, dynamic analysis of a Solid Rocket Motor (SRM), during transportation, is performed, while considering frequency-dependent modulus of viscoelastic materials. The modulus of viscoelastic materials depends on vibration frequency, which however cannot be modified during the mode-based response analysis. An iterative approach is proposed, to extract mode-based stress response of a SRM. The material modulus used to get response, is based on frequency that is the same as the motor’s eigenfrequency. In order to do modal summation of mode responses, two methods are used in the analysis. Results show that in both the Eigenfrequency extraction and in the subsequent stress response analysis, the used material evaluation frequency is in complete agreement with the eigenfrequency.

Linear Viscoelastic Response of Dendronized Polymers

We investigate the linear rheology of well-defined dendronized polymers (DPs). They consist of polymethacrylate backbones with tree-like branches (dendrons) of different generations, from zeroth to fourth, grafted at each monomer and a methyleneoxycarbonyl spacer between the polymerizable group and the dendritic substituent. The degrees of polymerization for the different generation polymers are almost constant, allowing for systematic studies as a function of generation. Because of the synthetic approach, these macromolecules possess tert-butoxycarbonyl (Boc) groups which promote hydrogen bonding, whereas the benzene groups allow for weaker bonding (π-stacking) as well. The master curves of frequency-dependent storage and loss moduli of these macromolecular structures were obtained via time–temperature superposition of dynamic frequency sweeps at various temperatures. To access slow relaxations, creep measurements were performed at long times and converted to frequency-dependent moduli. For the first generation, it was possible to detect relaxation processes suggesting an approach to the terminal regime (flow). On the other hand, the zeroth and second to fourth generation polymers exhibited a solid-like behavior throughout a wide range of frequencies. The fast relaxations reflect the coupling of segmental friction and hydrogen bonding and render the WLF-type analysis nontrivial. On the basis of the molecular structure of these unique materials as revealed by molecular dynamics simulations and complementary studies with their linear analogues poly(methyl methacrylate) and poly(tert-butyl)methacrylate, we propose that DPs resemble weakly interpenetrating elongated core–shell systems. As generation increases, their enhanced rigidity and intermolecular hydrogen bonding, which occurs primarily toward the outer surface of the DPs, appear to dominate the dynamics. PG0 is not a DP and has an open structure that promotes intermolecular bonding. These results provide design guidelines for ultrahigh-molecular-weight responsive polymers with possibilities for multifunctional substitution and tailoring Frheological response from liquid-like to solid-like.

Application of resonant acoustic spectroscopy to asphalt concrete beams for determination of the dynamic modulus

In this paper, a new application of resonant acoustic spectroscopy (RAS) is examined for constructing asphalt concrete mastercurves from seismic testing. The frequency-dependent material properties can be characterized from multiple modes of vibration through the use of RAS. Beam-shaped asphalt specimens are tested at multiple temperatures to determine the resonance frequencies of the specimens. The resonance frequencies are estimated by applying a small load impulse and measuring the resulting acceleration through the specimens. Using RAS, the material properties of the specimens are determined numerically using the measured resonance frequencies. The results presented show that the frequency-dependent dynamic modulus of the asphalt concrete specimens can be characterized using several modes of vibration at each testing temperature.

Concentration effect of BMIMTf on P(VdF-HFP)/MgTf-based solid polymer electrolyte system

Abstract