Re-visiting the “consequences of grafting density on the linear viscoelastic behavior of graft polymers”
Not provided.
Polymer Science↗
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Time–Concentration Superposition for Linear Viscoelasticity of Polymer Solutions
The concentration dependence of linear viscoelastic properties of polymer solutions is a well-studied topic in polymer physics. Dynamic scaling theories allow qualitative predictions of polymer solution rheology, but quantitative predictions are still limited to model polymers. Meanwhile, the scaling properties of non-model polymer solutions must be determined experimentally. In present paper, the time–concentration superposition (TCS) of experimental data is shown to be a robust procedure for studying the concentration scaling properties of binary and ternary polymer solutions. TCS can not only identify whether power law scaling may exist or not, and over which concentration range, but also unambiguously estimate the concentration scaling exponents of linear viscoelastic properties for a range of non-model polymer solutions.
42 ENGINEERING↗
Linear viscoelastic measurements of commerical therapy putties for design and intuition
This dataset complements the publication Mapping Linear Viscoelasticity for Design and Tactile Intuition (Corman & Ewoldt, 2019). It contains rigorous shear rheometry measurements for six commercial silicone putties, including creep recovery, SAOS, LAOS, and stress relaxation. Additional, unpublished data was generated as part of a graduate rheology course taught by Randy Ewoldt at University of Illinois Urbana-Champaign. Together, these datasets provide a comprehensive example of linear viscoelasticity of a commercial material. The collection is intended both as a pedagogical resource for developing physical intuition in linear viscoelasticity and as a reference dataset for data interpretation, model fitting, and comparative rheological analysis.
C. Marsh, Maxwell↗
Linear Viscoelastic Properties of Putative Cyclic Polymers Synthesized by Reversible Radical Recombination Polymerization (R3P)
Linear viscoelastic properties in both melt and solution states are reported for a series of poly(3,6-dioxa-1,8-octanedithiol) (polyDODT) made by reversible radical recombination polymerization (R 3 P) under conditions designed to produce linear (LDODT), cyclic (RDODT) and linear-cyclic mixtures (LRDODT). PolyDODT is amorphous (T g < -50 °C) and highly flexible (entanglement molecular weight M e,lin ≈ 1850 g/mol for LDODT). PolyDODT’s low T g and low M e,lin enable characterization over a wide dynamic range and a wide range of dimensionless weight-average molecular weight Z w = M w /M e,lin . Measurements at temperatures from -57 °C to 100 °C provide up to 18 deades of reduced frequency, which is necessary to characterize RDODT melts with Z w from 23 to 300. The two highest molecular weight polymers in the present RDODT series have such high M w (406k and 556k g/mol) that mass spectrometry, NMR spectroscopy, and even chemical assays for chain ends are unable to rule out up to 2 mol% linear contaminant. By studying the samples in solution (using dilution to reduce Z w ) we could compare their dynamics with those of previously established high-purity polystyrene (PS) rings (limited to Z w ≤ 13.6). RDODT solutions with Z w < 15 (concentrations <5wt% for RDODT-406k and 556k) have dynamic moduli G^* that accord with LCCC-purified PS rings in terms of the frequency dependence (including the absence of a plateau), the progression of shapes of G* as a function of Z w , and the linear scaling of their zero-shear viscosity η0 with M w . The shape of G* as a function of Z w for solutions of RDODT-406k and -556k also accord with lower M w RDODT melts (which have ≤ 1.3mol% linear contaminant). Thus, measurement of the linear viscoelastic properties of appropriate concentrations of high M w (>200k g/mol) putative cyclic polymers, in which linear chains evade spectroscopic detection, may provide an alternative means (though not fully proven) of validation of sample purity. When Z w > 15 (including all seven RDODT melts and eight of their solutions), G* has a rubbery plateau. This suggests that the onset of entanglement-like behavior in rings requires 4-5-fold greater Z w than is required for linear chains. Further, the plateau moduli of RDODT samples are indistinguishable from G N o of the corresponding LDODT (melt or matched-concentration solutions). In entangled linear polymers, the observation that G N o is independent of Z w follows from limitations on lateral fluctuations due to neighboring chains becoming independent of position along a given chain. The present results for RDODT suggest that this holds for sufficiently long endless chains, too. While the RDODT have the same G N o as entangled LDODT, when Z w > 60 the terminal relaxation, if reached at all, of RDODT extends to orders of magnitude lower frequency than an entangled linear polymer of the same Z w . Consequently, the viscosity of RDODT with Z w > 60 increases with Z w much more strongly than the 3.4-power observed for entangled linear polymers. Lastly, these novel polymers, with disulfide-linked backbone and broad relaxation time distribution may prove important in relation to biodegradable elastomers and materials with exceptional low-frequency dissipation, extending at least 12 decades below the onset of the rubbery plateau.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Linear viscoelastic characterization of electrically conductive adhesives used as interconnect in photovoltaic modules
Electrically conductive adhesives (ECAs) are incorporated into recent designs of photovoltaic (PV) modules and replace the traditional metallic solders as interconnects. This transition depicts a significant material change, and a proper understanding of the interconnects' mechanical response has not yet been established. However, such an understanding is necessary to (a) identify the driving forces for module degradation and failure, (b) allow for module design optimization, and (c) enable accurate lifetime predictions. This study summarizes the framework for the mechanical materials characterization and modeling of ECAs for PV applications. Only high-fidelity material models are able to capture the rate and temperature dependency of the ECA interconnect and allow for accurate modeling of the materials response. Furthermore, a linear viscoelastic representation is found to describe the mechanical response of the ECAs sufficiently well. The effects of curing conditions and environmental exposure are investigated, and material models for a variety of ECAs are reported and prepared for the use in numerical simulations. Overall, a finite element simulation of a generic submodel of a shingled cell module is used to highlight the need for high-fidelity material models and demonstrates the error made in the predicted stress states by using less sophisticated models.
14 SOLAR ENERGY↗
Modified error-in-constitutive-relation (MECR) framework for the characterization of linear viscoelastic solids
Not provided.
Materials Science↗
Collaborative Research: Polymer Macrocycles: A novel topology to control dynamics of rubbery materials
Understanding the dynamics of polymers of different topologies is an important field of study and one of the most important unanswered questions in this field is "how do circular polymers move," particularly in the melt state. New information suggests that molecular topology, specifically circular rings, impacts the response of materials in nanometer- scale confinement. The work performed here tackles these subjects through a collaboration in which specialists in polymer synthesis, polymer rheology and scattering methods, and in the physics of nanoconfinement work together to investigate the thermophysical behavior of circular macromolecules. The project goals are to use a novel synthesis method of "green" oxidative polymerization to produce high purity macrocycles and to investigate their linear viscoelastic behavior in order to fully characterize the dynamics of circular macromolecules to sizes that correspond to linear molecule entanglement densities higher than previously obtainable with synthetic polymers. Chemical chain end characterization and critical edge fractionation coupled with direct visualization of the prepared polymers through the use of polymer amplification methods are proposed in order to quantify the numbers of circular and linear molecules in each sample. The study of the linear viscoelastic response of blends of linear and circular molecules is also to be undertaken in the project. Nonlinear viscoelastic measurements, including extensional viscosity, are to be made. Strong differences in behavior between linear chains and circular ones also provides an important opportunity for new technology to break the "magic triangle" for tires: it is believed that improving one of the three key attributes - traction, wear, rolling resistance - necessarily sacrifices at least one of the others. Rubber made from cyclic polymers has the potential to break out of this triangle by reducing the so-called Payne effect in reinforced rubbers because circular macromolecules are less sensitive to nanoconfinement than their linear counterparts. The work has as one objective to characterize the impact of nanoconfinement on the behavior of large circular macromolecules. In addition, the dynamics of carbon black filled circular macromolecules are to be studied to test the hypothesis that the resulting rubbery materials will exhibit a reduced Payne effect.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
pyvisco [SWR-22-30]
pyvisco is a Python library that supports the identification of Prony series parameters for linear viscoelastic materials described by a Generalized Maxwell model. The necessary material model parameters are identified by fitting a Prony series to the experimental measurement data. pyvisco allows for the identification of Prony series parameters from experimental data measured in either the frequency-domain (via Dynamic Mechanical Thermal Analysis) or time-domain (via relaxation measurements). The experimental data can be provided as raw measurement sets at different temperatures or as pre-processed master curves. An optional minimization routine is included to reduce the number of Prony elements. This routine is helpful in Finite Element simulations where reducing the computational complexity of the linear viscoelastic material models can shorten the simulation time. See also, https://pypi.org/project/pyvisco/
Springer, Martin↗
Rheology and Gelation of Hyaluronic Acid/Chitosan Coacervates
Hyaluronic acid (HA) and chitosan (CHI) are biopolyelectrolytes which are interesting for both the medical and polymer physics communities due to their biocompatibility and semi-flexibility, respectively. In this work, we demonstrate by rheology experiments that the linear viscoelasticity of HA/CHI coacervates depends strongly on the molecular weight of the polymers. Moduli for coacervates were found significantly higher than those of individual HA and CHI physical gels. A remarkable 1.5-fold increase in moduli was noted when catechol-conjugated HA and CHI were used instead. This was attributed to the conversion of coacervates to chemical gels by oxidation of 3,4-dihydroxyphenylalanine (DOPA) groups in HA and CHI to di-DOPA crosslinks. These rheological results put HA/CHI coacervates in the category of strong candidates as injectable tissue scaffolds or medical adhesives.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Quasi‐dynamic breathing model of the lung incorporating viscoelasticity of the lung tissue
Abstract We advanced a novel model to calculate viscoelastic lung compliance and airflow resistance in presence of mucus, accounting for the quasi‐linear viscoelastic stress–strain response of the parenchyma (alveoli) tissue. We adapted a continuum‐based numerical modeling approach for the lung, integrating the fluid mechanics of the airflow within individual generations of the bronchi and alveoli. The model accounts for elasticity of the deformable bronchioles, resistance to airflow due to the presence of mucus within the bronchioles, and subsequent mucus flow. Simulated quasi‐dynamic inhalation and expiration cycles were used to characterize the net compliance and resistance of the lung, considering the rheology of the mucus and viscoelastic properties of the parenchyma tissue. The structure and material properties of the lung were identified to have an important contribution to the lung compliance and airflow resistance. The secondary objective of this work was to assess whether a higher frequency and smaller volume of harmonic air flow rate compared to a normal ventilator breathing cycle enhanced mucus outflow. Results predict, lower mucus viscosity and higher excitation frequency of breathing are favorable for the flow of mucus up the bronchi tree, towards the trachea.
60 APPLIED LIFE SCIENCES↗
Yielding Behavior of Bottlebrush and Linear Block Copolymers
Block copolymers can exhibit a pronounced yield stress, but the impact of molecular architecture, chemistry, and self-assembly on macroscopic rheology remains poorly understood. Here, we study the linear-viscoelastic and yield-stress fluid behavior of two architectures—bottlebrush copolymers (with statistical or blocky sequences) and linear diblocks—that self-assemble into body-centered cubic (BCC) spheres and hexagonally close-packed cylinders (HEX). The dynamic properties of these polymers were probed by oscillatory frequency and amplitude sweeps at temperatures well below the order–disorder transition (TODT) to furnish insights into the yielding transition. All BCC-forming polymers have a similar signature of yielding: smaller yield strains (γ yBCC ≈ 0.053 < γ y,HEX ≈ 0.18), sharper solid–liquid transitions, and better reversibility than HEX. Statistical bottlebrushes show the most frequency-independent structural modulus (G 0 ) and no signs of defect relaxation. A simple power-law relationship captures the dependence of the normalized structural modulus (G 0 /RT) on the inter-micelle distance (d) across different architectures and morphologies [G 0 /(RT) = 1.31 × 10 4 (nm 2.6 mol/m 3 ) d –2.6 ]. These studies establish quantitative structure–property relationships that are relevant in contemporary applications, for example, extrusion-based 3D printing.
36 MATERIALS SCIENCE↗
The nonlinear rheology of complex yield stress foods
Many foods have a yield stress that allows them to retain a desired shape at rest, but transition into a viscous fluid when being served or consumed. The determination of the yield stress of the food dictates how the foods are formed and packaged, how they are served, and how they are perceived when being eaten. Oscillatory shearing provides an ideal test protocol to map the rheology across a range of time and flow strength scales. We couple oscillatory shearing and an iterative recovery procedure to show that the yielding process is a continuous transition for two common yield stress foods. We show that unrecoverable processes from oscillatory tests are equivalent to the steady shear flow behavior. We show that this yielding behavior can be well approximated by a recently published model that treats yield stress materials as continuous viscoelastic fluids with a rate-dependent relaxation time and has parameters that can be obtained from the linear viscoelastic oscillatory frequency sweep and the steady shear flow curve.
Griebler, James J.↗
Microstructural characterization of a star-linear polymer blend under shear flow by using rheo-SANS
We present an investigation into the dynamic relaxation mechanisms of a polybutadiene blend composed of a four-arm star (10 wt. %) and a linear polymer matrix in the presence of an applied shear flow. Our focus was the response of the star polymer, which cannot be unambiguously assessed via linear viscoelastic measurements since the signature of the star polymer can barely be detected due to the dominant contribution of the linear matrix. By utilizing small-angle neutron scattering (SANS) coupled with a Couette shear device and a deuterated matrix polymer, we investigated the dynamics of the minority star component of the blend. Our results confirm that the stars deform anisotropically with increasing shear rate. We have compared the SANS data with predictions from the well-established scattering adaptation of the state-of-the-art tube model for entangled linear polymer melts undergoing shear, i.e., Graham, Likhtman, Milner, and McLeish (GLaMM) approach, appropriately modified following earlier studies in order to apply to the star. This modified model, GLaMM-R, includes the physics necessary to understand stress relaxation in both the linear and nonlinear flow regimes, i.e., contour length fluctuations, constraint release, convective constraint release, and chain retraction. The full scattering signal is due to the minority star component and, although the contribution of the linear chains is hidden from the neutron scattering, they still influence the star polymer molecular dynamics, with the applied shear rate ranging from approximately 8 to 24 s –1 , below the inverse relaxation time of the linear component. This study provides another confirmation that the combination of rheology and neutron scattering is an indispensable tool for investigating the nonlinear dynamics of complex polymeric systems.
36 MATERIALS SCIENCE↗
Gelation and Re-entrance in Mixtures of Soft Colloids and Linear Polymers of Equal Size
Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions of soft colloids having the same hydrodynamic size yields a liquid-togel-to-re-entrant liquid transition. In particular, the dynamic state diagram of 1,4-polybutadiene star-linear polymer mixtures was determined with the help of linear viscoelastic and small-angle Xray scattering experiments. While keeping the star polymers below their nominal overlap concentration, a gel was formed upon increasing the linear polymer content. Further addition of linear chains yielded a re-entrant liquid. This unexpected behavior was rationalized by the interplay of three possible phenomena: (i) depletion interactions, driven by the size disparity between the stars and the polymer length scale which is the mesh size of its entanglement network; (ii) colloidal deswelling due to the increased osmotic pressure exerted onto the stars; and (iii) a concomitant progressive suppression of the depletion efficiency on increasing the polymer concentration due to reduced mesh size, hence a smaller range of attraction. Our results unveil an exciting new way to tailor the flow of soft colloids and highlight a largely unexplored path to engineer soft colloidal mixtures.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Orthotropic Viscoelastic Modeling of Polymeric Battery Separator
The separator is one of the most important components for battery safety since its failure can cause short-circuit that may lead to thermal runaway. As such, understanding the mechanical behaviors of separators is critical to improve battery safety. Nevertheless, modeling the mechanical behaviors of separators is challenging since they usually depend on multiple factors such as orientation, temperature and strain rate due to the microstructure of separators. Here we develop an orthotropic linear viscoelastic model for separators, which takes both anisotropy and strain rate effects into account. This model is the first step of a future model that considers more factors such as temperature and large deformation. The model has been implemented as a user material model in a finite element package, where a discretization algorithm is developed to evaluate the stiffness-based hereditary integral with a kernel of Prony series. The user model has been applied to a polypropylene (PP) separator Celgard ® 2400. The simulation results agree well with experimental data, which include the rate dependent uniaxial tensile behavior of the separator in the two in-plane material directions and in shear, and the strain contour patterns of every strain component during biaxial tension.
25 ENERGY STORAGE↗
Experimental workflow to estimate model parameters for evaluating long term viscoelastic response of CO2 storage caprocks
Understanding the time-dependent behavior of reservoir and sealing formations is critical to assessing risks associated with geological carbon storage since time-dependent deformation strongly influences mechanical responses of some rock types. Many studies have evaluated the risk of CO2 leakage and induced seismicity by assuming poroelastic rheology in sealing formations. Few have considered viscoelastic or other time-dependent responses, where the existing literature adopts 1D models to represent long-term time-dependent responses. This is primarily because to date, the general form of a reasonable 3D time-dependent model for rocks remains unclear. In this paper, we address this unclear issue by proposing a new workflow to select constitutive modeling parameters to evaluate if a 3D viscoelastic model is reasonable using several-hour-long experimental data and a power-law response to extrapolate to the decades-long time frames of interest in geologic carbon storage. To provide experimental data, we conducted multi-level loading/unloading triaxial relaxation tests with four rock types. The experimental results showed that the maximum load relaxation observed is approximately 49%, with some rock types showing as little as 1.4%. Using a simple linear viscoelastic model, parameters were chosen such that a maximum deviation of 1.5 MPa in axial stress and 7 MPa in radial stress was attained with the extrapolated 30-year data. We found that a reasonable parameter range for the normalized elastic modulus is 0.1~2 for rocks with significant time-dependent responses and 0.01~0.06 for those with small time-dependent responses. No matter how significant time-dependent responses are for rocks considered, our results showed that the relaxation time has a general range of 1~10^10 s, whose time scale can be one or two orders higher than a time frame typically envisioned for CO2 injection projects.
Stress relaxation, 3D time-dependent model, viscoe↗
On the inference of viscoelastic constants from stress relaxation experiments
Several constitutive theories have been proposed in the literature to model the viscoelastic response of materials, including widely used rheological constitutive models. These models are characterized by certain parameters ("time constants") that define the time scales over which the material relaxes. These parameters are primarily obtained from stress relaxation experiments using curve-fitting techniques. However, the question of how best to estimate these time constants remains open. As a step towards answering this question, we propose an optimal experimental design approach based on ideas from information geometry, namely Fisher information and Kullback-Leibler divergence. The material is modeled as a spring element in parallel with multiple Maxwell elements and described using a one- or two-term Prony series. Treating the time constants as unknowns, we develop expressions for the Fisher information and Kullback-Leibler divergence that allow us to maximize information gain from experimental data. Based on the results of this study, we propose that the largest time constant estimated from a stress relaxation experiment for a linear viscoelastic material should be at most one-fifth of the total time of the experiment in order to maximize information gain. Our results also provide confirmation that the equilibrium modulus of the material cannot be reliably determined from curve-fitting to data from a stress relaxation experiment.
Fisher information↗
Experimental and modeling studies of IPDI-based polyurea elastomers – The role of hard segment fraction
Segmented polyureas (PUa) are industrially important class of polymers widely used in coatings, sealant, and adhesive applications. Here, in this paper, we report synthesis, characterization, and modeling of Isophorone Diisocyanate-Diethyl-Toluene-Diamine-Polyether amine (IPDI-DETDA-PO PUa) with varied hard segment contents of 20, 30, and 40 weight percent. For each of the three materials, we study its structure and phase behavior using FTIR, DSC, and TEM, and clearly show the presence of microphase separation between the hard and soft nanodomains. We then measure the linear viscoelastic response of the PUa-s using DMA (frequency sweeps at multiple temperatures). The DMA data are shown to obey the time-temperature superposition. Finally, we develop a new micromechanical model describing the DMA results; the model describes a phase-separated PUa as two “Fractional-order Maxwell gels” branches, connected in parallel, with the first FMG branch representing the “percolated hard phase" and the second one modeling the “filled soft phase". In agreement with the earlier thermodynamic theories, the volume-fraction of the percolated hard phase is related to the hard segment weight-fraction (HSWF), defined as the combined mass of IPDI and DETDA normalized to the total mass of the polymer. The data and model are found to be in a good qualitative and quantitative agreement.
36 MATERIALS SCIENCE↗