Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Linear viscoelasticity of immiscible blends: The application of creep

A new method to characterize the long-time linear relaxation mechanisms of immiscible blends based on creep experiment was developed. Small-amplitude oscillatory shear and incomplete creep/recovery experiments were combined to characterize immiscible blends of polypropylene with dispersed droplets of polystyrene. An experimental protocol was defined such that the full creep compliance function could be obtained while minimizing morphological changes. Dynamic experiments were performed to characterize the shorter time relaxation processes, and creep and recovery measurements were used to detect the longer time portions of the relaxation spectra. Extended retardation and relaxation spectra were constructed by combining these data. It was found that using this technique, very long-time relaxation peaks which were inaccessible with dynamic experiments alone could be detected. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4720081]

Study of the influence of actin-binding proteins using linear analyses of cell deformability

The actin cytoskeleton plays a key role in the deformability of the cell and in mechanosensing. Here we analyze the contributions of three major actin cross-linking proteins, myosin II, a-actinin and filamin, to cell deformability, by using micropipette aspiration of Dictyostelium cells. We examine the applicability of three simple mechanical models: for small deformation, linear viscoelasticity and drop of liquid with a tense cortex; and for large deformation, a Newtonian viscous fluid. For these models, we have derived linearized equations and we provide a novel, straightforward methodology to analyze the experiments. This methodology allowed us to differentiate the effects of the cross-linking proteins in the different regimes of deformation. Our results confirm some previous observations and suggest important relations between the molecular characteristics of the actin-binding proteins and the cell behavior: the effect of myosin is explained in terms of the relation between the lifetime of the bond to actin and the resistive force; the presence of a-actinin obstructs the deformation of the cytoskeleton, presumably mainly due to the higher molecular stiffness and to the lower dissociation rate constants; and filamin contributes critically to the global connectivity of the network, possibly by rapidly turning over crosslinks during the remodeling of the cytoskeletal network, thanks to the higher rate constants, flexibility and larger size. The results suggest a sophisticated relationship between the expression levels of actinbinding proteins, deformability and mechanosensing.

Characterization of Non-linear Polymer Properties to Predict Process Induced Warpage and Residual Stress of Electronic Packages

Nonlinear thermo-mechanical properties of advanced polymers are crucial to accurate prediction of the process induced warpage and residual stress of electronics packages. The Fiber Bragg grating (FBG) sensor based method is advanced and implemented to determine temperature and time dependent nonlinear properties. The FBG sensor is embedded in the center of the cylindrical specimen, which deforms together with the specimen. The strains of the specimen at different loading conditions are monitored by the FBG sensor. Two main sources of the warpage are considered: curing induced warpage and coefficient of thermal expansion (CTE) mismatch induced warpage. The effective chemical shrinkage and the equilibrium modulus are needed for the curing induced warpage prediction. Considering various polymeric materials used in microelectronic packages, unique curing setups and procedures are developed for elastomers (extremely low modulus, medium viscosity, room temperature curing), underfill materials (medium modulus, low viscosity, high temperature curing), and epoxy molding compound (EMC: high modulus, high viscosity, high temperature pressure curing), most notably, (1) zero-constraint mold for elastomers; (2) a two-stage curing procedure for underfill materials and (3) an air-cylinder based novel setup for EMC. For the CTE mismatch induced warpage, the temperature dependent CTE and the comprehensive viscoelastic properties are measured. The cured cylindrical specimen with a FBG sensor embedded in the center is further used for viscoelastic property measurements. A uni-axial compressive loading is applied to the specimen to measure the time dependent Young’s modulus. The test is repeated from room temperature to the reflow temperature to capture the time-temperature dependent Young’s modulus. A separate high pressure system is developed for the bulk modulus measurement. The time temperature dependent bulk modulus is measured at the same temperatures as the Young’s modulus. The master curve of the Young’s modulus and bulk modulus of the EMC is created and a single set of the shift factors is determined from the time temperature superposition. The supplementary experiments are conducted to verify the validity of the assumptions associated with the linear viscoelasticity. The measured time-temperature dependent properties are further verified by a shadow moiré and Twyman/Green test.

Diffusion in glassy polymers

Fluid diffusion in glassy polymers proceeds in ways that are not explained by the standard diffusion model. Although the reasons for the anomalous effects are not known, much of the observed behavior is attributed to the long times that polymers below their glass transition temperature take to adjust to changes in their condition. The slow internal relaxations of the polymer chains ensure that the material properties are history-dependent, and also allow both local inhomogeneities and differential swelling to occur. Two models are developed in this thesis with the intent of accounting for these effects in the diffusion process.

In Part I, a model is developed to account for both the history dependence of the glassy polymer, and the dual sorption which occurs when gas molecules are immobilized by the local heterogeneities. A preliminary study of a special case of this model is conducted, showing the existence of travelling wave solutions and using perturbation techniques to investigate the effect of generalized diffusion mechanisms on their form. An integral averaging method is used to estimate the penetrant front position.

In Part II, a model is developed for particle diffusion along with displacements in isotropic viscoelastic materials. The nonlinear dependence of the materials on the fluid concentration is taken into account, while pure displacements are assumed to remain in the range of linear viscoelasticity. A fairly general model is obtained for three-dimensional irrotational movements, with the development of the model being based on the assumptions of irreversible thermodynamics. With the help of some dimensional analysis, this model is simplified to a version which is proposed to be studied for Case II behavior.

The short-timescale behavior of glacial ice

Glaciers are often assumed to deform only at slow (i.e., glacial) rates. However, with the advent of high rate geodetic observations of ice motion, many of the intricacies of glacial deformation on hourly and daily timescales have been observed and quantified. This thesis explores two such short timescale processes: the tidal perturbation of ice stream motion and the catastrophic drainage of supraglacial meltwater lakes. Our investigation into the transmission length-scale of a tidal load represents the first study to explore the daily tidal influence on ice stream motion using three-dimensional models. Our results demonstrate both that the implicit assumptions made in the standard two-dimensional flow-line models are inherently incorrect for many ice streams, and that the anomalously large spatial extent of the tidal influence seen on the motion of some glaciers cannot be explained, as previously thought, through the elastic or viscoelastic transmission of tidal loads through the bulk of the ice stream. We then discuss how the phase delay between a tidal forcing and the ice stream’s displacement response can be used to constrain in situ viscoelastic properties of glacial ice. Lastly, for the problem of supraglacial lake drainage, we present a methodology for implementing linear viscoelasticity into an existing model for lake drainage. Our work finds that viscoelasticity is a second-order effect when trying to model the deformation of ice in response to a meltwater lake draining to a glacier’s bed. The research in this thesis demonstrates that the first-order understanding of the short-timescale behavior of naturally occurring ice is incomplete, and works towards improving our fundamental understanding of ice behavior over the range of hours to days.

A model for nonlinear viscoelastic mechanical responses of collagenous soft tissues

Experimental observations of the time-dependent mechanical responses of collagenous tissues have demonstrated behavior that deviates from standard treatments of linear or quasi-linear viscoelasticity. In particular, time-dependent deformation can be strongly coupled to strain level, and strain-rate independence can be observed under monotonic loading, even for a tissue with dramatic stress relaxation. It was postulated that this nonlinearity is fundamentally associated with gradual recruitment of individual collagen fibrils during applied mechanical loading. Based on previously observed experimental results for the time-dependent response of collagenous soft tissues, a model is developed to describe the mechanical behavior of these tissues under uniaxial loading. Tissue stresses, under applied strain-controlled loading, are assumed to be a sum of elastic and viscoelastic stress contributions. The relative contributions of elastic and viscoelastic stresses is assumed to vary with strain level, leading to strain- and time-dependent mechanical behavior. The model formulation is examined under conditions of monotonic loading at varying constant strain rates and stress-relaxation at different applied strain levels. The model is compared with experimental data for a membranous biological soft tissue, the amniotic sac, and is found to agree well with experimental results. The limiting behavior of the novel model, at large strains relative to the collagen recruitment, is consistent with the quasi-linear viscoelastic approach. © 2006 Materials Research Society.

Comportamento reológico de géis de amido de mandioquinha salsa (Arracacia xanthorrhiza B.)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An Expansion Formula for Fractional Derivatives and its Application

An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type.

Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I-3/I-1 shows a power-law behavior with strain amplitude. In addition, I-3/I-1 and the elastic component of stress amplitude sigma(E)(0) show a very prominent maximum at the strain value where the number density (n(v)) of the Taylor vortices is maximum. A subsequent increase in applied strain (gamma) results in the distortions of the vortices and a concomitant decrease in n(v), accompanied by a sharp drop in I-3 and sigma(E)(0). The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of gamma corresponding to the peak of I-3, similar to that observed for hard-sphere glasses.

Squeeze flow viscoelasticity of electrorheological fluids based on microcrystalline cellulose

Dynamic viscoelasticity of electrorheological fluids based on microcrystalline cellulose/castor oil suspensions was experimentally investigated in squeeze flow. The dependence of storage modulus G' and loss modulus G" parallel to external electric field on electric fields and strain amplitudes is presented. The experiments show that, when external electric field is higher than the critical field, the viscoelasticity of the ER fluids converts from linear to nonlinear, and the ER fluids transfer from solid-like state to fluid state with the growth of strain amplitude. The influences of strain amplitude and oscillatory frequency on the nonlinearity of viscoelasticity were also studied.

Structure and viscoelasticity of an electrorheological fluid in oscillatory shear: computer simulation investigation

The three-dimensional molecular dynamics simulation method has been used to study the dynamic responses of an electrorheological (ER) fluid in oscillatory shear. The structure and related viscoelastic behaviour of the fluid are found to be sensitive to the amplitude of the strain. With the increase of the strain amplitude, the structure formed by the particles changes from isolated columns to sheet-like structures which may be perpendicular or parallel to the oscillating direction. Along with the structure evolution, the field-induced moduli decrease significantly with an increase in strain amplitude. The viscoelastic behaviour of the structures obtained in the cases of different strain amplitudes was examined in the linear response regime and an evident structure dependence of the moduli was found. The reason for this lies in the anisotropy of the arrangement of the particles in these structures. Short-range interactions between the particles cannot be neglected in determining the viscoelastic behaviour of ER fluids at small strain amplitude, especially for parallel sheets. The simulation results were compared with available experimental data and good agreement was reached for most of them.

Numerical study of ultrasound induced non-linear shape and size bubble oscillations in viscoelastic media

The theoretical study of forced bubble oscillations is motivated by the importance of cavitation bubbles and oscillating encapsulated microbubbles (i.e. contrast agents) in medical sciences. In more details,theoretical studies on bubble dynamics addressing the sound-bubble interaction phenomenon provide the basis for understanding the dynamics of contrast agent microbubbles used in medical diagnosis and of non-linearly oscillating cavitation bubbles in the case of high-intensity ultrasound therapy. Moreover, the inclusion of viscoelasticity is of vital importance for an accurate theoretical analysis since most biological tissues and fluids exhibit non-Newtonian behavior.