Viscoelastic Relaxation Behavior Research Articles

Effects of blend phase ratio upon thermomechanical, viscoelastic relaxation and strain recovery behavior of crosslinked LDPE/EVA foams

Effects of blend phase ratio upon thermomechanical, viscoelastic relaxation and strain recovery behavior of crosslinked LDPE/EVA foams

Linear viscoelastic shear and bulk relaxation moduli in poly(tetramethylene oxide) (PTMO) using united-atom molecular dynamics

A quantitative understanding and prediction of the viscoelastic relaxation behavior of polymer melts is required to build up predictive multiscale models, which can be utilized for the practical design of viscoelastic materials. We report the application of the Green–Kubo method to compute the common shear relaxation modulus and the rarely reported bulk relaxation modulus for a realistic united atom model of poly(tetramethylene oxide) (PTMO), which is one key components of the segmented polyurethane (PU) elastomers. The temperature and molecular weight dependent viscoelastic behavior is investigated in detail by computing the bulk relaxation modulus K(t) along with shear relaxation modulus G(t). Our results provide new rheological data for PTMO melt based on the united atom model, which incorporates the chemical details of the polymer backbone. The predicted stress relaxation are mapped onto master curves using the time–temperature superposition principle with horizontal and vertical shift factors. The computed shift factors agree with the Williams–Landel–Ferry equation and appear to be similar for the shear and bulk relaxation modulus. The underlying dynamics for the shear and bulk relaxation modulus appear to stem from the same mechanistic origin as both processes seem to sample similar kinetic signature of the reference time scale of the underlying thermally activated processes in the liquid. Our results demonstrate furthermore, that MD simulations with the chemical details beyond coarse-grained models can sample the Rouse dynamics and the transitions towards entanglement, which is evident by the emergence of a plateau in shear relaxation modulus and scaling relations in the diffusion behavior of the monomer at larger molecular weights.

3D printable hybrid acrylate-epoxy dynamic networks

Polymer networks with dynamic bonds, also known as covalent adaptable networks (CANs) combine the superior mechanical properties and chemical resistance of thermosets with the ability to be reprocessed, a feat formerly attributed only to thermoplastics. Inspired by an evergrowing body of research on dynamic poly(β-hydroxy ester) networks, a polyacrylate/epoxy-acid thermoset was designed, which contains a high concentration of β-hydroxy ester bonds that partake in transesterification reactions that facilitate the repair and recycle of the cured material at feasible temperatures. Firstly, liquid formulations are subjected to UV light to initiate acrylate homopolymerization to obtain the intermediate, partially-cured material. A subsequent thermal treatment triggers the epoxy-acid reaction, which improves the mechanical properties and helps increase the likelihood of transesterifications as new β-hydroxy ester groups are formed. The effect of thermal post-treatment and the choice of catalyst on viscoelastic properties and stress relaxation behavior of these materials is studied. Results show that, transesterification reactions reach equilibrium in less than 4 h at 180 °C during which time the overall cross-linking density increases further. As to the choice of catalyst, a commonly used zinc acetylacetonate outperforms an imidazole-type base. Thanks to the dynamic bonds, damaged samples can be repaired fully using simple procedures. Recyclability is tested by grinding pristine samples and re-molding them under pressure and temperature. Practically complete recovery of viscoelastic properties is confirmed.

Modeling and experimental study of the needle indentation into a brain phantom

In some surgical operations, a needle is inserted into the patient’s brain to perform the necessary manipulations (for instance, a biopsy). In this context, the study of the interaction between the needle and the brain tissue is an important task. One of common ways to perform experimental study of such interaction is through the use brain phantoms. In this work, a series of experiments is performed on indentation of a biopsy needle into a phantom manufactured of the agar gel. During these experiments, the force of interaction between the needle and the phantom tissue was measured for different indentation speeds and depths. An analytical mathematical model is proposed that describes this force. The model takes into account such effects as viscoelastic and plastic properties and relaxation behavior of the material, as well as the presence of a surface film. Parameters of the model are identified based on the obtained experimental data. It is shown that the results of numerical simulation using this model are in good agreement with the experimental data. Such a model is general and can be used not only for solving problems of biomechanics.

Drying Kinetics from Micrometer- to Nanometer-Scale Polymer Films: A Study on Solvent Diffusion, Polymer Relaxation, and Substrate Interaction Effects.

The drying behavior of two different polymers [polyvinyl pyrrolidone (PVP) and polyisobutylene (PIB)] with different glass transition temperatures are investigated and compared as a function of film thickness from micrometer (∼3 μm) to nanometer scale (∼10 nm). The focus of this study is to distinguish between solvent diffusion, polymer relaxation, and substrate confinement of polymer chain mobility toward the interface as the dominating mechanism of drying kinetics. Relaxation kinetics becomes more dominant when the film thickness is reduced, which is shown experimentally for the first time for nanometer-scale film thicknesses. Identical drying curves regardless of the film thickness of PVP/methanol indicate the limitation of solvent transport by relaxation kinetics. The viscoelastic relaxation behavior of the polymer/solvent film is modeled by a Maxwell element. The results are in accordance with the experimental drying curves and allow for the determination of the characteristic relaxation time. Relaxation limitation becomes relevant at high diffusion Deborah numbers when the relaxation time-which is a function of the deployed material and the polymer/solvent composition-is higher than the characteristic diffusion time in the film. The latter is a function of the polymer/solvent composition and the thickness of the film. Drying curves of PIB/toluene films show additional effect in a substrate-near region of about 5 nm in which polymer chain mobility is confined, resulting in decelerated solvent diffusion. Although this effect near the substrate interface is expected to be present regardless of the film thickness, it becomes more dominant when the substrate-near region represents a significant fraction of the total film thickness. The key to the derived methodology for characterization of the polymer/solvent drying process is to vary dry film thickness from micrometers to a few nanometers which allows us to determine the dominating mechanism of drying kinetics.

Dynamics of the Topological Network Formed by Movable Crosslinks: Effect of Sliding Motion on Dielectric and Viscoelastic Relaxation Behavior

We investigated the dynamics of the topological network formed by rotaxane-type movable crosslinks consisting of a poly(ethyl acrylate) backbone threaded through peracetylated cyclodextrins, which ...

Modeling and Characterization of Cure-Dependent Viscoelasticity of Molded Underfill in Ultrathin Packages

Warpage control of an ultrathin package is critical in the semiconductor industry because of the large volume of molded underfill (MUF) encapsulated in such packages and because of the low stiffness of the entire package structure. The viscoelastic relaxation behavior that is observed during the MUF curing process results in a major warpage change and thus should be investigated. First, the material model of the cure-dependent viscoelasticity of MUF in the time domain and the curing kinetics model of MUF were successfully established based on the characterization results. Then, a finite-element (FE) model integrated with the material model for package warpage prediction was successfully developed. The final prediction results of package warpage obtained using a novel process modeling approach are in agreement with the experimental data measured using thermal shadow Moire. Furthermore, the effects of MUF volume change observed by changing the die size and thickness in an ultrathin package were studied using the warpage prediction model. The results indicate that package warpage can be effectively reduced by decreasing the die size and increasing the die thickness.

The effects of solid solution and oxide dispersion alloying on the viscoelastic behavior of Au alloy thin films

The effects of solid solution and oxide dispersion alloying on viscoelastic relaxation behavior of Au alloy films were investigated by using gas pressure bulge testing in the temperature range of 20–80 °C. Three sets of 500 nm thick films were fabricated for the study: nominally pure Au, Au-V solid solution alloys with V concentration ranging from 0.89 to 5.4 at% V, and a Au-V2O5 nanoparticle dispersion alloy with a V concentration of 5.4 at%. The residual stress, unrelaxed plane strain modulus, and normalized time-dependent effective modulus were determined as a function of alloy type and temperature. Both alloying approaches resulted in a refined grain size that was thermally stable. As expected, the fractional modulus decay measured after 3 h was greater at higher temperatures for all cases. Solid solution strengthening and dispersion strengthening were both effective at reducing the 3-h modulus decay, and the Au-V2O5 films showed the largest resistance to relaxation at all temperatures studied. Activation energy analysis reveals a value of approximately 0.11 eV, matching the Peierls barrier height, for pure Au and the two alloys. The results are consistent with a viscoelastic stress relaxation mechanism based on reversible dislocation bowing, weak solid solution hardening through elastic solute/dislocation interactions, and strong dislocation pinning associated with oxide nanoparticles.

Emergent structure-dependent relaxation spectra in viscoelastic fiber networks in extension

Viscoelasticity plays an important role in the mechanical behavior of biological tissues undergoing dynamic loading. Exploring viscoelastic relaxation spectra of the tissue is essential for predicting its mechanical response. Most load-bearing tissues, however, are also composed of networks of intertwined fibers and filaments of, e.g., collagen, elastin. In this work, we show how non-affine deformations within fiber networks affect the relaxation behavior of the material leading to the emergence of structure-dependent time scales in the relaxation spectra. In particular, we see two different contributions to the network relaxation process: a material contribution due to the intrinsic viscoelasticity of the fibers, and a kinematic contribution due to non-affine rearrangement of the network when different fibers relax at different rates. We also present a computational model to simulate viscoelastic relaxation of networks, demonstrating the emergent time scales and a pronounced dependence of the network relaxation behavior on whether components with different relaxation times percolate the network. Finally, we observe that the simulated relaxation spectrum for Delaunay networks is comparable to that measured experimentally for reconstituted collagen gels by others. Statement of SignificanceViscoelasticty plays an important role in the mechanical behavior of biological tissues undergoing dynamic loading. Stress relaxation tests provide a convenient way to explore the viscoelastic behavior of the material, while providing an advantage of interrogating multiple time scales in a single experiment. Most load bearing tissues, however, are composed of networks of intertwined fibers and filaments. In the present study, we analyze how the network structure can affect the viscoelastic relaxation behavior of a tissue leading to the emergence of structure-based time scales in the relaxation spectra.

The effect of grain size on viscoelastic relaxation behavior of Au thin films

The effect of grain size on viscoelastic relaxation behavior of Au thin films was investigated by using gas pressure bulge testing to measure the changing normalized plane-strain modulus as a function of time. We observed more rapid and extensive relaxation with increasing grain sizes. The normalized modulus of the Au films is shown to be linearly dependent on the square of the in-plane grain size. Transmission electron microscopy suggests that an increase in grain size allows a higher fraction of mobile dislocation segments to bow under an applied stress, resulting in a proportional increase of the relaxation of coarser-grained films.

Effect of Zr content on damping property of Mg–Zr binary alloys

The damping property expressed by internal friction tan⁡φ of as-cast Mg–Zr binary alloys with Zr content from 0.6 to 5.0% was experimentally measured under conditions of changing temperature from ambient temperature Tam to 600 K (327 °C), vibration frequency f from 1.0 to 10.0 Hz, strain ε from 1.0 × 10–6 to 1.0 × 10–3, and heating rate ν from 2 to 5 K/min. The experimental results indicate that the damping property of prepared as-cast Mg–Zr binary alloys can be effectively promoted by increasing either heating rate ν or strain ε. Increasing vibration frequency f can effectively decrease the damping property, however increasing vibration frequency f has little effect on the plots of internal friction tan⁡φ against temperature T, i.e., T–tanφ curve, under the condition of f > 5.0 Hz. The optimal Zr content of the as-cast Mg–Zr binary alloys with better performance of damping property is recommended to be 0.6 mass % in a range of Zr content from 0.6 to 5.0%. Furthermore, the effect of strain ε on damping property for the as-cast Mg–Zr binary alloys can be ideally explained by dislocation pinning theory or the G–L model, while the influence of temperature T on damping property for the as-cast Mg–Zr binary alloys complies with the viscoelastic relaxation behaviour.

Rheology and Microscopic Heterogeneity of Poly(ethylene oxide) Solid Polymer Electrolytes

Lack of precise thermal control in poly(ethylene oxide) (PEO)‐based solid polymer electrolytes (SPEs) with molar masses well above M > 104 g mol−1 during preparatory stage often demonstrates molar mass dependence on thermal properties and ionic conductivities. In the earlier study, PEO‐based SPEs were heated under inert atmosphere above the melting temperature of PEO and then cooled down for subsequent isothermal crystallization. The system demonstrates insignificant variation with respect to molar mass of PEO at constant salt concentration for thermal properties, ionic conductivity and intermolecular interaction. Here, we report the subsequent results of rheology and microscopic heterogeneity as a function of PEO molar mass (Mɳ = 3 × 105 and 4 × 106 g mol−1) and lithium salt concentration (0–13 wt.%). Above the solubility limit of PEO, the glass transition studied using differential scanning calorimetry shows the presence of microscopic heterogeneity of the systems as indicated by the change in enthalpy of endothermic overshoot near the endset of glass transition. Rheological parameters were measured over a wide range of frequency (0.01 to 100 Hz) at different temperatures (30, 60 and 80 °C) using parallel plate geometry. Melt rheology system reveals that neat PEO at 80 °C exhibits restriction in the long‐range motion of the chains. When incorporated with salt, it exhibits further deviation from the terminal viscoelastic relaxation behaviour. This study agrees with our previous findings that influence of molar mass of PEO in this range is insignificant on the melt rheology and microscopic heterogeneity at constant salt concentration.

3D printing of an interpenetrating network hydrogel material with tunable viscoelastic properties

Interpenetrating network (IPN) hydrogel materials are recognized for their unique mechanical properties. While IPN elasticity and toughness properties have been explored in previous studies, the factors that impact the time-dependent stress relaxation behavior of IPN materials are not well understood. Time-dependent (i.e. viscoelastic) mechanical behavior is a critical design parameter in the development of materials for a variety of applications, such as medical simulation devices, flexible substrate materials, cellular mechanobiology substrates, or regenerative medicine applications. This study reports a novel technique for 3D printing alginate-polyacrylamide IPN gels with tunable elastic and viscoelastic properties. The viscoelastic stress relaxation behavior of the 3D printed alginate-polyacrylamide IPN hydrogels was influenced most strongly by varying the concentration of the acrylamide cross-linker (MBAA), while the elastic modulus was affected most by varying the concentration of total monomer material. The material properties of our 3D printed IPN constructs were consistent with those reported in the biomechanics literature for soft tissues such as skeletal muscle, cardiac muscle, skin and subcutaneous tissue.

Monitoring Nanoscale Deformations in a Drawn Polymer Melt with Single-Molecule Fluorescence Polarization Microscopy.

Elongating a polymer melt causes polymer segments to align and polymer coils to deform along the drawing direction. Despite the importance of this molecular response for understanding the viscoelastic properties and relaxation behavior of polymeric materials, studies on the single-molecule level are rare and were not performed in real time. Here we use single-molecule fluorescence polarization microscopy for monitoring the position and orientation of single fluorescent perylene diimide molecules embedded in a free-standing thin film of a polymethyl acrylate (PMA) melt with a time resolution of 500 ms during the film drawing and the subsequent stress relaxation period. The orientation distribution of the perylene diimide molecules is quantitatively described with a model of rod-like objects embedded in a uniaxially elongated matrix. The orientation of the fluorescent probe molecules is directly coupled to the local deformation of the PMA melt, which we derive from the distances between individual dye molecules. In turn, the fluorescence polarization monitors the shape deformation of the polymer coils on a length scale of 5 nm. During stress relaxation, the coil shape relaxes four times more slowly than the mechanical stress. This shows that stress relaxation involves processes on length scales smaller than a polymer coil. Our work demonstrates how optical spectroscopy and microscopy can be used to study the coupling of individual fluorescent probe molecules to their embedding polymeric matrix and to an external mechanical stimulus on the single-molecule level.

Deformation and relaxation of grafted polymer layers at elevated temperatures

The mechanical deformation and relaxation behaviour of thin-grafted polymer layers is investigated by a scanning force microscope (SFM) in contact mode. The layers were considerably plastically deformed at different temperatures. By scratching across the surface, a ripple structure is created. The temperature- and time-dependent relaxation of the ripple structure is followed directly by SFM and discussed in comparison to classical viscoelastic relaxation behaviour and time-temperature superposition of bulk material. In contrast to classical viscoelastic behaviour, here, the strong plastic deformation of the grafted layers accelerates the relaxation behaviour.

A preliminary investigation of the dynamic viscoelastic relaxation of bovine cortical bone

A new experimental approach is proposed to characterize the dynamic viscoelastic relaxation behaviour of cortical bone. Theoretical models are presented to show that a linear viscoelastic material, when allowed to relax between two long elastic bars, will produce stress, strain and strain rate histories that contain characteristic features. Furthermore, typical experimental results are presented to show that these characteristic features are observed during split Hopkinson bar tests on bovine cortical bone using a Cone-in-Tube striker. The interpretation of this behaviour in the context of a standard linear viscoelastic model is discussed.

Precision Glass Molding: Validation of an FE Model for Thermo‐Mechanical Simulation

In precision glass molding process, the required accuracy for the final size and shape of the molded lenses as well as the complexity of this technology calls for a numerical simulation. The current paper addresses the development of an FE model for thermo‐mechanical simulation of the precision glass molding process including heating, pressing, and cooling stages. Temperature‐dependent viscoelastic and structural relaxation behavior of the glass material are implemented through a FORTRAN material subroutine (UMAT) into the commercial FEM program ABAQUS, and the FE model is validated with a sandwich seal test. Subsequently, precision molding of several glass rings is performed at three different pressing temperatures, and the experimental deformation of the glass rings at the end of the molding is compared with the predicted ones from FE simulation. Furthermore, the transient and residual stress distribution inside the glass rings are calculated by the developed FE model, and the effects of some important process parameters such as interface friction and mold temperature on the FE results are assessed. The developed FE model can be employed to predict the deformation behavior, final size/shape, and the residual stress state inside the glass lenses in a precision glass molding process.

Evaluation of the viscoelastic behaviour and glass/mould interface friction coefficient in the wafer based precision glass moulding

Recent improvements in the manufacturing process of camera lenses have introduced the use of a new technology involving wafer based precision glass moulding. The utilization of this technology has some important advantages such as cost reduction, supply chain simplification and higher image quality. However, the required accuracy for the final size and shape of the moulded lenses as well as the complexity of this technology call for a high level of process understanding and numerical simulation is a very important part of achieving this goal. The viscoelastic parameters of the optical glass as well as the glass/mould interface friction coefficient play a key role in deformation behaviour and stress distribution of the moulded glass lens. Therefore, a proper evaluation of these parameters is the first important step in numerical modelling of the precision glass moulding process.The current paper deals with characterization of the interfacial glass/mould friction coefficient and viscoelastic behaviour of the L-BAL42 glass material above the glass transition temperature. Several glass rings are pressed at three different temperatures to various thicknesses and the experimental force, displacements, internal diameter and thickness of the rings are measured during the tests. Viscoelastic and structural relaxation behaviour of the glass are implemented into the ABAQUS FEM software through a FORTRAN material subroutine (UMAT) and the FE model is validated with a sandwich seal test. Then, by FE simulation of the ring compression test and comparison of the experimental creep with the simulated one in an iterative procedure, viscoelastic parameters of the glass material are characterized. Finally, interfacial glass/mould friction coefficients at different temperatures are determined through FEM based friction curves combined with experimental data points. The obtained viscoelastic parameters and interfacial friction coefficients can later be employed for prediction of the final shape/size as well as the stress distribution in the glass wafer during a real wafer based precision glass moulding process.

A transdermal device from 2-hydroxyethyl methacrylate grafted carboxymethyl guar gum–multi-walled carbon nanotube composites

A hydrophobic and biocompatible transdermal device has been developed from 2-hydroxyethyl methacrylate (HEMA) grafted carnboxymethyl guar gum (CMG)-functionalized multi-walled carbon nanotube (MWCNT) in situ composite membranes. The developed composites may be used for sustained delivery of diclofenac sodium. Supreme matrix–MWCNT interaction at 0.5 and 1 wt% MWCNT concentrations induces excellent copolymer-adsorbed fibrillar orientation of MWCNT compared to that at 2 and 3 wt%. It successively leads to efficient encapsulation and more sustained release of the drug molecules at these compositions (65% vs. 17% at 1 wt%). Analyses show that the releases are dominated by the viscoelastic relaxation behavior (power law indices 0.75 and 0.80 and extremely high Deborah numbers) of the devices. Conversely, for the latter, the releases are comparatively less sustained and more swelling controlled (indices are 0.5 and 0.6 and low Deborah numbers). However, all devices have significantly increased the half life period of the drug molecules (2.5 h vs. 47 h at 1 wt%).

Modeling of the nonlinear viscoelasticity of polyoxymethylene in tension and compression

An optical measurement technique was used to measure the axial and transverse strain of polyoxymethylene in various uniaxial tensile and compressive loadings. The 3d nonlinear viscoelastic model of Schapery was chosen to describe the time-dependent mechanical behavior. The model equation is solved using a recursive technique, which is used in a nonlinear optimization algorithm to identify model parameters by fitting experimental data. It is shown that the Schapery model is capable of describing the nonlinear viscoelastic relaxation behavior in tension and compression. Furthermore, it is verified that the model determined using stress relaxation data can accurately predict the response to creep and cyclic stress histories. A bending stress relaxation test serves as an exemplary test of a structure with simultaneously occurring compressive and tensile stresses. The model is used in a finite-element simulation of this test to demonstrate its performance in this more complex application.