Viscoelastic Relaxation Research Articles

Effect of Strain History and Mixture Proportions on Early-Age Cement Paste and Mortar Stress Relaxation

AbstractThe influence of sand particles, aging, and water–cement (w/c) ratio on the viscoelastic relaxation modulus of cement paste and mortars was measured at early ages (1–28 days). Furthermore, ...

Post-Seismic Deformation Related to the 2016 Central Italy Seismic Sequence From GPS Displacement Time-Series.

The 2016–2017 Central Italy earthquake sequence struck the central Apennines between August 2016 and October 2016 with Mw ∈ [5.9; 6.5], plus four earthquakes occurring in January 2017 with Mw ∈ [5.0; 5.5]. We study Global Positioning System time series including near‐ and far‐field domains. We use a variational Bayesian independent component analysis technique to separate the post‐seismic deformation from signals caused by variation of the water content in aquifers at hundreds of meters of depth and of the soil moisture. For each independent component, realistic uncertainties and a plausible physical explanation are provided. We focus on the study of afterslip on the main structures surrounding the mainshock, highlighting the role played by faults that were not activated during the co‐seismic phase in accommodating the post‐seismic deformation. We report aseismic deformation occurring on the Paganica fault, which hosted the Mw 6.1 2009 L'Aquila earthquake, suggesting that static stress transfer and aseismic slip influence the recurrence time of nearby (∼50 km further south of the mainshocks) segments. A ∼2–3 km thick subhorizontal shear‐zone, clearly illuminated by seismicity, which bounds at depth the west‐dipping normal faults where the mainshocks nucleated, also shows aseismic slip. Since afterslip alone underestimates the displacement in the far‐field domain, we consider the possibility that the shear zone marks the brittle‐ductile transition, assuming the viscoelastic relaxation of the lower crust as a mechanism contributing to the post‐seismic displacement. Our results suggest that multiple deformation processes are active in the first 2 years after the mainshocks.

The dynamic viscoelastic characterisation and magnetic resonance imaging of poly(vinyl alcohol) cryogel: Identifying new attributes and opportunities

Poly(vinyl alcohol) (PVA) cryogel is a biocompatible, synthetic hydrogel, compatible with magnetic resonance (MR) imaging. It is widely used as a biomaterial in tissue scaffolds and mimics to test various diagnostic techniques. The aim of this study is to characterise the effect of varying PVA concentration, molecular weight (MW) and manufacturing protocol on the viscoelastic mechanical properties and MR T2 relaxation time. Further to this MR imaging (MRI) was investigated as a method to quantify material homogeneity. Cylindrical samples of PVA, of varying MW, concentration and number of freeze thaw cycles (FTCs), were manufactured. Dynamic mechanical analysis was performed to evaluate the storage and loss moduli between frequencies of 0.5 and 10 Hz. MR T2 relaxation maps were imaged using a 7 T MRI instrument. Storage and loss moduli were shown to increase with MW, concentration, or the number of FTCs; with storage modulus ranging from 55 kPa to 912 kPa and loss modulus ranging from 6 kPa to 103 kPa. MR T2 relaxation time was shown to increase linearly with PVA concentration. The qualitative and quantitative heterogeneity of the PVA sample were identified through MR T2 relaxation time maps. Excitingly, PVA demonstrated a composition-dependent casual correlation between the viscoelastic mechanical properties and MR T2 relaxation time. In conclusion, this research thoroughly characterised the viscoelastic mechanical properties of PVA to support its extensive use as a biomaterial, and demonstrated the use of MRI to non-invasively identify sample heterogeneity and to predict the composition-dependent viscoelastic properties of PVA.

In-vitro stress relaxation response of neonatal peripheral nerves

Characterizing the viscoelastic behavior of neonatal peripheral nerves is critical in understanding stretch-related peripheral nerve injuries (PNIs) in neonates. This study investigated the in-vitro viscoelastic stress relaxation response of neonatal piglet brachial plexus (BP) and tibial nerves at two different strain levels (10% and 20%) and stress relaxation testing durations (90- and 300-seconds). BP and tibial nerves from 20 neonatal piglets were harvested and pre-stretched to either 10% or 20% strain at a dynamic rate of 100 mm/min to simulate conditions, such as shoulder dystocia, that may lead to stretch-related PNIs in neonates. At constant strain, the reduction in stress was recorded for 90- or 300-seconds. The biomechanical data were then fit to a viscoelastic model to acquire the short- and long-term stress relaxation time-constants. Though no significant differences in the degree of stress relaxation were found between the two tested strain levels after 90 seconds in both nerve types, reduction in stress was moderately greater (p = 0.056) at 10% strain than at 20% for BP after 300 seconds. The reduction in stress was significantly higher in nerves subjected to a 300 second testing duration than 90 second for both strain levels and nerve types. When comparing BP and tibial nerve stress relaxation response, BP nerve relaxed significantly more than tibial at both strain levels after 90 seconds, but no significant differences were observed after 300 seconds. Our results confirm that neonatal peripheral nerve tissue is highly viscoelastic. These novel biomechanical data can be incorporated into finite element and computational models studying neonatal PNIs.

Conformational Freedom‐Enhanced Optomechanical Energy Conversion Efficiency in Bulk Azo‐Polyimides

AbstractAzobenzene‐doped glassy polyimides (azo‐polyimides) offer some of the most efficient optomechanical power densities to date rivaling electrostrictive polymers. Despite such potential attributes, the optomechanical efficiency remains low in comparison to other smart materials. Using high‐fidelity coarse‐grained molecular dynamics simulations, the authors reconcile both experimental and theoretical challenges to understand the limiting factors for the optomechanical conversion in photostrictive polymers. Interestingly, the ideal optomechanical efficiency of 10–24% for a single‐chain azo‐imide monomer predicted here is equal to or a little higher than experimental reports, suggesting experimental design space. The time‐dependent optomechanical efficiency of bulk azo‐polyimide is quantified, for the first time, to be strongly correlated with the initial free volumes, a measure of polymer conformational freedom. This trend is elaborated by conformational order parameters and viscoelastic relaxation moduli. Resembling the role of porosity in azobenzene‐contained metal/covalent organic frameworks to enhance the photo‐switching efficiency, a larger conformational freedom enables >10 times increase in optomechanical efficiency comparing to existing experiments. This is primarily due to facilitated viscoelastic relaxation after photo‐switching which alleviates residual stresses quickly and reduces heat dissipation. These findings suggest opportunities to improve the optomechanical performance through targeted strategies, such as porosity control and thermal annealing.

Rheological characterization of complex dynamics in Na-Zn metaphosphate glass-forming liquids.

The viscoelastic behavior and shear relaxation in supercooled [NaPO3]x[Zn(PO3)2]1-x metaphosphate liquids with 0.2 ≤ x ≤ 1.0 are investigated using a combination of small amplitude oscillatory and steady shear parallel plate rheometry, resonant ultrasound spectroscopy, and differential scanning calorimetry. The results demonstrate that these liquids are thermorheologically complex with the coexistence of a fast and a slow relaxation process, which could be attributed to the segmental motion of the phosphate chains and the Zn-O bond scission/renewal dynamics, respectively. The segmental motion of the phosphate chains is found to be the dominant process associated with the shear relaxation for all metaphosphate liquids. The compositional evolution of the calorimetric fragility of these liquids is shown to be related to the conformational entropy of the constituent phosphate chains, which is manifested by the width of the relaxation time distribution for the segmental chain motion. This entropy decreases and the temporal coupling between the chain dynamics and Zn-O bond scission-renewal increases with the increasing Zn content as the higher field strength Zn modifier ions provide more effective cross-linking between the phosphate chains.

Reuse potential of functionalized thermoplastic waste as reinforcement for thermoset polymers: Mechanical properties and erosion resistance

Two types of polymer waste materials, poly(ethylene terephthalate) (PET) and polycarbonate based Colombian Resin (CR-39), were used for the designing of fully recycled composite materials. Waste PET was employed for the synthesis of thermoset unsaturated polyester resin (UPR), while CR-39 was used as reinforcement in the UPR matrix. Prior to mixing, CR-39 particles were subjected to oxidation and chemical activation using acids/base and ethanol amine, respectively. The effect of the modifier type and variable loading of the activated CR-39 particles on mechanical and dynamic-mechanical properties of the corresponding composites was investigated. The greatest improvement in the tensile and flexural strength of UPR resin was achieved with the composite containing 0.5 wt% of amine activated filler particles, 96.0% and 62.2%, respectively. The Arrhenius equation was used to calculate the activation energy for glass transition from dynamic mechanical properties measured at various frequencies. The activation energy of the main transition for UPR resin and composites were calculated to be 173 and 350 kJ·mol−1indicating that reinforcement results in an increase in the energy barrier to macromolecules viscoelastic relaxation. In addition, erosion resistance was studied during exposure of samples to cavitation tests. According to the obtained results, these materials can be applied in construction and mining industry.

Onset of Entanglement in Aqueous Solutions of Pullulan with Narrow Molar Mass Distributions

Dynamic viscoelastic behaviors were examined for aqueous solutions of pullulan samples, which are natural polysaccharides with weight-average molar masses (Mw) of 220, 390, and 820 kg mol–1 and narrow molar mass distributions such as Mw/Mn ≤ 1.1, over a concentration range from 5.0 to 467 g L–1 and a temperature range from 1 to 30 °C. The obtained viscoelastic data at different temperatures were superposed to compose master curves for storage and loss moduli (G′ and G″) using the time–temperature superposition principle. The Arrhenius-type temperature dependencies of the shift factors necessary to compose G′ and G″ master curves provided the activation energies (Ev*) of the viscoelastic relaxation times as functions of the concentrations (c) for each pullulan sample. Fundamental viscoelastic parameters such as the average relaxation time (τw), the steady-state compliance (Je), and the zero-shear viscosity (η0) were determined as functions of c for each pullulan sample. Above the critical concentrations (cen ∝ Mw–1) demonstrating the onset of entanglement formation among pullulan molecules, the characteristic relationships, Je–1 ∝ c2, τw ∝ cα–2Mw3.5, and η0 ∝ cαMw3.5 with α = 6.0, were obtained. Although this α value was substantially greater than that for usual synthetic polymers like poly(styrene) dissolved in good solvents where α ∼ 4.5, the Mw exponent of 3.5 for τw and η0 was identical to that of synthetic polymers. The Ev* value was close to the activation energy of the solvent, water viscosity of 19 kJ mol–1, in the dilute regime and abruptly increased with increasing c. Finally, Ev* approached a constant value of ca. 39 kJ mol–1 corresponding to the activation energy necessary for pullulan molecules to release entanglements above cen irrespective of the Mw values. The observed characteristic viscoelastic behaviors of aqueous pullulan solutions are reasonably interpreted by a theoretical model for associating polymers dissolved in good solvents.

Viscoelastic Behaviour of Flexible Thermoplastic Polyurethane Additively Manufactured Parts: Influence of Inner-Structure Design Factors.

Material extrusion based additive manufacturing is used to make three dimensional parts by means of layer-upon-layer deposition. There is a growing variety of polymers that can be processed with material extrusion. Thermoplastic polyurethanes allow manufacturing flexible parts that can be used in soft robotics, wearables and flexible electronics applications. Moreover, these flexible materials also present a certain degree of viscoelasticity. One of the main drawbacks of material extrusion is that decisions related to specific manufacturing configurations, such as the inner-structure design, shall affect the final mechanical behaviour of the flexible part. In this study, the influence of inner-structure design factors upon the viscoelastic relaxation modulus, E(t), of polyurethane parts is firstly analysed. The obtained results indicate that wall thickness has a higher influence upon E(t) than other inner-design factors. Moreover, an inadequate combination of those factors could reduce E(t) to a small fraction of that expected for an equivalent moulded part. Next, a viscoelastic material model is proposed and implemented using finite element modelling. This model is based on a generalized Maxwell model and contemplates the inner-structure design. The results show the viability of this approach to model the mechanical behaviour of parts manufactured with material extrusion additive manufacturing.

What makes a hydrogel-based dressing advantageous for the prevention of medical device-related pressure ulcers.

The synergistic influences of geometrical, mechanical and thermal mismatches between a skin‐contacting medical device and the skin may cause tissue stress concentrations and sharp temperature gradients, both of which contribute to the risk for medical device‐related pressure ulcers. In this work, we developed an innovative, integrated experimental bioengineering approach encompassing mechanical stiffness, friction and thermal property studies for testing the biomechanical suitability of a hydrogel‐based dressing in prophylaxis of injuries caused by devices. We characterised the viscoelastic stress relaxation of the dressing and determined its long‐term elastic modulus. We further measured the coefficient of friction of the hydrogel‐based dressing at dressing‐device and skin‐dressing interfaces, using a tilting‐table tribometer. Lastly, we measured the thermal conductivity of the dressing, using a heat‐flow meter and infrared thermography‐based method. All measurements considered dry and moist conditions, the latter simulating skin perspiration effects. Our results revealed that the long‐term stiffness and the thermal conductivity of the hydrogel‐based dressing matched the corresponding properties of human skin for both dry and moist conditions. The dressing further demonstrated a relatively high coefficient of friction at its skin‐facing and device‐facing aspects, indicating minimal frictional sliding. All these properties make the above dressing advantageous for prevention of device‐related injuries.

Rheo-chemistry of gelation in aiyu (fig) jelly

We investigated the gelation characteristics of aiyu jelly derived from the polymeric extract obtained by washing the seeds of Ficus Pumila var. Awkeotsang. The main gel component is low methoxyl pectin, which forms crosslinks with divalent ions that bind the exuded polysaccharide chains. Unlike many fruit pectins used in jam and jellies that require heating, additional sugars, and acidic conditions to gel, the aiyu exudate gels at room temperature with just the addition of water. In this study, the time-resolved dynamics of the gelation process and the evolution of the viscoelastic relaxation spectrum with frequency and gel age are obtained via Optimally Windowed Chirp rheometry (OWCh), conventional time-sweep rheometry, and cryo-scanning electron microscope (cryo-SEM) microstructural characterization.During gelation, we observed distinctive frequency-dependent inflection points in both the time-evolving storage and loss moduli which occur nearly simultaneously in time. Close inspection of high resolution cryo-SEM images taken at different times during the gelation process showed that the gels initially form nano-fiber networks with mesh sizes on the order of tens of microns and the stiffer mature gels observed at longer times develop sub-micron mesh sizes. These observations suggest a progressive transformation between microstructures may accompany the progressive growth in the elasticity of the aiyu gels and the local inflection points in the viscoelastic moduli.We also developed a multi-species reaction kinetics model for calcium – pectin binding in aiyu gelation. By including methylesterase enzymatic conversion of pectin binding sites, combined with calcium binding and the slower formation of consecutively-bound junction zones, the distinctive inflection points in the viscoelastic moduli are captured by the kinetic gelation model. By combining rheological measurements, microstructural observations, and reaction kinetics modeling, this study not only characterizes a unique water-soluble natural extract that gels at room temperature with no additives or thermomechanical processing, it also demonstrates that the aiyu polysaccharide system is a safe and controllable model for gelation systems in which binding site activation is concurrently coupled to crosslink formation.

Fractional Order Magnetic Resonance Fingerprinting in the Human Cerebral Cortex

Mathematical models are becoming increasingly important in magnetic resonance imaging (MRI), as they provide a mechanistic approach for making a link between tissue microstructure and signals acquired using the medical imaging instrument. The Bloch equations, which describes spin and relaxation in a magnetic field, are a set of integer order differential equations with a solution exhibiting mono-exponential behaviour in time. Parameters of the model may be estimated using a non-linear solver or by creating a dictionary of model parameters from which MRI signals are simulated and then matched with experiment. We have previously shown the potential efficacy of a magnetic resonance fingerprinting (MRF) approach, i.e., dictionary matching based on the classical Bloch equations for parcellating the human cerebral cortex. However, this classical model is unable to describe in full the mm-scale MRI signal generated based on an heterogenous and complex tissue micro-environment. The time-fractional order Bloch equations have been shown to provide, as a function of time, a good fit of brain MRI signals. The time-fractional model has solutions in the form of Mittag–Leffler functions that generalise conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex heterogeneous materials. Hence, we replaced the integer order Bloch equations with the previously reported time-fractional counterpart within the MRF framework and performed experiments to parcellate human gray matter, which consists of cortical brain tissue with different cyto-architecture at different spatial locations. Our findings suggest that the time-fractional order parameters, α and β, potentially associate with the effect of interareal architectonic variability, which hypothetically results in more accurate cortical parcellation.

Exploring GPS Observations of Postseismic Deformation Following the 2012 MW7.8 Haida Gwaii and 2013 MW7.5 Craig, Alaska Earthquakes: Implications for Viscoelastic Earth Structure

AbstractThe Queen Charlotte‐Fairweather Fault (QC‐FF) system off the coast of British Columbia and southeast Alaska is a highly active dextral strike‐slip plate boundary that accommodates ∼50 mm/yr of relative motion between the Pacific and North America plates. Nine MW ≥ 6.7 earthquakes have occurred along the QC‐FF system since 1910, including a MS(G‐R)8.1 event in 1949. Two recent earthquakes, the October 28, 2012 Haida Gwaii (MW7.8) and January 5, 2013 Craig, Alaska (MW7.5) events, produced postseismic transient deformation that was recorded in the motions of 25 nearby continuous Global Positioning System (cGPS) stations. Here, we use 5+ yr of cGPS measurements to characterize the underlying mechanisms of postseismic deformation and to constrain the viscosity structure of the upper mantle surrounding the QC‐FF. We construct forward models of viscoelastic deformation driven by coseismic stress changes from these two earthquakes and explore a large set of laterally heterogeneous viscosity structures that incorporate a relatively weak back‐arc domain; we then evaluate each model based on its fit to the postseismic signals in our cGPS data. In determining best‐fit model structures, we additionally incorporate the effects of afterslip following the 2012 event. Our results indicate the occurrence of a combination of temporally decaying afterslip and vigorous viscoelastic relaxation of the mantle asthenosphere. In addition, our best‐fit viscosity structure (transient viscosity of 1.4–2.0 × 1018 Pa s; steady‐state viscosity of 1019 Pa s) is consistent with the range of upper mantle viscosities determined in previous studies of glacial isostatic rebound and postseismic deformation.

Postseismic Deformation and Afterslip Evolution of the 2015 Gorkha Earthquake Constrained by InSAR and GPS Observations

AbstractIn the past few years, space‐geodesy has measured continued postseismic deformation in the region of the 2015 Gorkha Mw 7.8 earthquake. Previous studies have suggested that the postseismic deformation is dominated by afterslip, but the spatiotemporal evolution of the afterslip, hence its cause and impact on regional seismicity are disputed, and contribution from other postseismic processes has not been well constrained. Here, we constructed an afterslip model using InSAR and GPS observations over three years after the Gorkha earthquake. First, the Sentinel‐1A satellite data were processed using Permanent Scatterer Interferometric Synthetic Aperture Radar method to extract deformational signals at high‐coherence points, and a fitting method was used to extract the postseismic displacement sequences. We then used InSAR and GPS data in a joint inversion for the evolution of afterslip, and compared its contribution to the observed postseismic displacement to that of viscoelastic relaxation and poroelastic rebound. Our results confirm that afterslip has dominated the observed postseismic deformation in the Gorkha region. Within 3 years of the Gorkha earthquake, afterslip released ∼1.20 × 1020 N m, about 14% of that released by the mainshock and the largest aftershock, or equivalent to an Mw 7.32 earthquake. The afterslip has occurred mostly downdip of the coseismic slip zone, in the ductile shear zone, apparently controlled by rheological properties. The updip shallow portion of the Main Frontal Thrust (MFT) zone has not been ruptured by coseismic slip or unlocked by afterslip, thus could potentially produce future earthquakes.

Isostasy with Love: II Airy compensation arising from viscoelastic relaxation

SUMMARY In modern geodynamics, isostasy can be viewed either as the static equilibrium of the crust that minimizes deviatoric stresses, or as a dynamic process resulting from the viscous relaxation of the non-hydrostatic crustal shape. Paper I gave a general formulation of Airy isostasy as an elastic loading problem solved with Love numbers, and applied it to the case of minimum stress isostasy. In this sequel, the same framework is used to study Airy isostasy as the long-time evolution of a viscoelastic shell submitted to surface and internal loads. Isostatic ratios are defined in terms of time-dependent deviatoric Love numbers. Dynamic isostasy depends on the loading history, two examples of which are the constant load applied on the surface in the far past and the constant shape maintained by addition or removal of material at the compensation depth. The former model results in a shape decreasing exponentially with time and has no elastic analogue, whereas the latter (stationary) model is equivalent to a form of elastic isostasy. Viscoelastic and viscous approaches are completely equivalent. If both load and shape vary slowly with time, isostatic ratios look like those of the stationary model. Isostatic models thus belong to two independent groups: the elastic/stationary approaches and the time-dependent approaches. If the shell is homogeneous, all models predict a similar compensation of large-scale gravity perturbations. If the shell rheology depends on depth, stationary models predict more compensation at long wavelengths, whereas time-dependent models result in negligible compensation. Mathematica and Fortran codes are available for computing the isostatic ratios of an incompressible body with three homogeneous layers.

Dynamic shearing resistance of hydroxyl-terminated polybutadiene (HTPB)

Hydroxyl-terminated polybutadiene (HTPB) is a widely used polymeric binder in polymer-bonded explosives (PBXs) and solid rocket propellants. Even though used in small fractions, the elastomeric binder absorbs much of the impact energy and therefore requires careful modeling of its mechanical behavior to accurately simulate the response of PBXs when they are subjected to large strains and strain rates. While the normal response of HTPB has been characterized under uniaxial stress and uniaxial strain loading, shear strength measurements under large pressures and large shear strain rates have not been made so far. Such measurements are critical for modeling localization and failure in PBXs and accurate prediction hotspot formation. In this study, pressure-shear plate impact (PSPI) experiments have been used to measure the shearing resistance of HTPB at different pressures. The shearing resistance of HTPB is found to be strongly pressure dependent. A quasi-linear viscoelastic model with pressure-dependent shear wave speeds and shearing resistance is used to describe the experimentally observed dynamic response of HTPB. The model consists of an instantaneous elastic response and viscoelastic relaxation of the elastic response.

Low Acyl Gellan as an Excipient to Improve the Sprayability and Mucoadhesion of Iota Carrageenan in a Nasal Spray to Prevent Infection With SARS-CoV-2.

The COVID-19 global pandemic, as well as the widespread persistence of influenza and the common cold, create the need for new medical devices such as nasal sprays to prevent viral infection and transmission. Carrageenan, a sulfated polysaccharide, has a broad, non-pharmacological antiviral capacity, however it performs poorly in two key areas; spray coverage and mucoadhesion. Therefore gellan, another polysaccharide, was investigated as an excipient to improve these properties. It was found that viscoelastic relaxation time was the key predictor of spray coverage, and by reducing this value from 2.5 to 0.25 s, a mix of gellan and carrageenan gave more than four times the coverage of carrageenan alone (p < 0.0001). Gellan also demonstrated enhanced adhesion to a mucus analog that increased significantly with time (p < 0.0001), suggesting the development of specific gellan–mucin interactions. This property was conferred to carrageenan on mixing the two polymers. Together, this data suggests that gellan is a promising excipient to improve both sprayability and mucoadhesion of carrageenan for use in antiviral nasal sprays.

Activity-Induced Fluidization and Arrested Coalescence in Fusion of Cellular Aggregates

At long time scales, tissue spheroids may flow or appear solid depending on their capacity to reorganize their internal structure. Understanding the relationship between intrinsic mechanical properties at the single cell level, and the tissue spheroids dynamics at the long-time scale is key for artificial tissue constructs, which are assembled from multiple tissue spheroids that over time fuse to form coherent structures. The dynamics of this fusion process are frequently analyzed in the framework of liquid theory, wherein the time scale of coalescence of two droplets is governed by its radius, viscosity and surface tension. In this work, we extend this framework to glassy or jammed cell behavior which can be observed in spheroid fusion. Using simulations of an individual-cell based model, we demonstrate how the spheroid fusion process can be steered from liquid to arrested by varying active cell motility and repulsive energy as established by cortical tension. The divergence of visco-elastic relaxation times indicates glassy relaxation near the transition toward arrested coalescence. Finally, we investigate the role of cell growth in spheroid fusion dynamics. We show that the presence of cell division introduces plasticity in the material and thereby increases coalescence during fusion.

Relationship between the Relaxation of Ionic Liquid Structural Motifs and That of the Shear Viscosity.

In a set of recent articles, we have highlighted that friction is highly inhomogeneous in a typical ionic liquid (IL) with charge networks that are stiff and charge-depleted regions that are soft. This has consequences not only for the dynamics of ILs but also for the transport properties of solutes dissolved in them. In this article, we explore whether the family of alkylimidazolium ILs coupled with bis(trifluoromethylsulfonyl)imide (with similar Coulombic interactions but different alkyl tails), when dynamically “equalized” by having a similar shear viscosity, display q-dependent structural relaxation time scales that are the same across the family. Our results show that this is not the case, and in fact, the relaxation of in-network charge alternation appears to be significantly affected by the presence of separate polar and apolar domains. However, we also find that if one was to assign weight factors to the relaxation of the structural motifs, charge alternation always contributes about the same amount (between 62.1 and 66.3%) across systems to the running integral of the stress tensor correlation function from which the shear viscosity is derived. Adjacency correlations between positive and negative moieties also contribute an identical amount if a prepeak is not present (about 38%) and a slightly smaller amount (about 28%) when intermediate range order exists. The prepeak only contributes about 6% to viscoelastic relaxation, highlighting that the dynamics of the smaller scale motifs is the most important.

Multiple power-law viscoelastic relaxation in time and frequency domains with atomic force microscopy

Complex viscoelastic materials exhibit power law (PL) relaxations, as opposed to simple materials described by exponential decays. Other interesting materials, like living cells, hold a universal double PL behavior whose exponents depend on the health and type of the cells. Usually, only dynamic assays are considered capable to study such viscoelastic relaxation mechanisms. In this work, we propose analytical responses with single or multiple power-law relaxation behavior by generalizing classical viscoelastic models in terms of fractional derivatives of arbitrary order α (0 1). In addition, we demonstrate that simple atomic force microscopy force curves are powerful methods to directly observe the viscoelastic relaxation of such complex materials. In order to validate our findings, we compare the viscoelastic relaxation exponents measured directly from simple force curves (SFCs) with those measured with dynamic techniques in both living cells and polyacrylamide gels. We believe the fractional models unveiled here describe a variety of complex materials and may be used (with SFCs) to explore sophisticated viscoelastic phenomena.