Continuum Model for the Phase Behavior, Microstructure, and Rheology of Unentangled Polymer Nanocomposite Melts

Elucidating the rheological implications of adding particles in blood

In the past few decades, nanotechnology has been employed to provide breakthroughs in the diagnosis and treatment of several diseases using drug-carrying particles (DCPs). In such an endeavor, the optimal design of DCPs is paramount, which necessitates the use of an accurate and trustworthy constitutive model in computational fluid dynamics (CFD) simulators. We herein introduce a continuum model for elaborating on the rheological implications of adding particles in blood. The model is developed using non-equilibrium thermodynamics to guarantee thermodynamic admissibility. Red blood cells are modeled as deformed droplets with a constant volume that are able to aggregate, whereas particles are considered rigid spheroids. The model predictions are compared favorably against rheological data for both spherical and non-spherical particles immersed in non-aggregating blood. It is expected that the use of this model will allow for the testing of DCPs in virtual patients and for their tailor-design in treating various diseases.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00397-021-01289-x.

A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions

Red blood cells (RBCs) can deform substantially, a feature that allows them to pass through capillaries that are narrower than the largest dimension of an undeformed RBC. Clearly, to understand how they transport through our microcirculation, we need a constitutive model able of accurately predicting the deformability of RBCs, which seems currently unavailable. To address this void, we herein propose a new model that accounts for the deformability of RBCs by modeling them as deformed droplets with a constant volume. To make sure the model is by construction thermodynamically admissible we employ non-equilibrium thermodynamics as our tool. Since RBCs are merely droplets with the inner fluid exhibiting a higher viscosity than that of the outer one, RBCs are described by a conformation tensor constrained to have a constant determinant (volume). The model predicts the second normal stress coefficient in steady-state simple shear flow to first shear thicken and then shear thin, which is an unexpected behavior; however, we cannot judge whether such a prediction is aphysical or not due to unavailable experimental rheological data in the literature. We show that the new model is capable of addressing the deformability of isolated (very low hematocrit) RBCs in simple shear and the shear viscosity of non-aggregating blood. As derived the model addresses only non-aggregating blood, but can very easily be generalized to account for aggregating blood.

A nonequilibrium thermodynamics perspective of thixotropy

We propose a new description of elasto-viscoplastic fluids by relating the notion of thixotropy directly to internal viscoelasticity and network structures through a general, thermodynamically consistent approach. By means of non-equilibrium thermodynamics, a thermodynamically admissible elasto-viscoplastic model is derived which introduces self-consistently and effortlessly thixotropic effects and reproduces at both low and high shear rates experimental data usually fitted with empirical constitutive equations, such as the Bingham and Herschel-Bulkley models. The predictions of the new model are in very good agreement with available steady-state shear rheological data for soft colloidal pastes and blood, i.e., systems exhibiting a yield stress, and with time-dependent rheological data for blood, i.e., during a triangular time-dependent change in the shear rate, exhibiting a hysteresis. The proposed approach is expected to provide the means to improve our understanding of thixotropic fluids.

Multiscale Molecular Simulations of Polymer-Matrix Nanocomposites: or What Molecular Simulations Have Taught us About the Fascinating Nanoworld

Following the substantial progress in molecular simulations of polymer-matrix nanocomposites, now is the time to reconsider this topic from a critical point of view. A comprehensive survey is reported herein providing an overview of classical molecular simulations, reviewing their major achievements in modeling polymer matrix nanocomposites, and identifying several open challenges. Molecular simulations at multiple length and time scales, working hand-in-hand with sensitive experiments, have enhanced our understanding of how nanofillers alter the structure, dynamics, thermodynamics, rheology and mechanical properties of the surrounding polymer matrices.

Tailoring the alignment of string-like nanoparticle assemblies in a functionalized polymer matrix via steady shear

This work reports the steady shear induced aligning behaviour of nanoparticle strings in a functionalized polymer matrix.

How the flow affects the phase behaviour and microstructure of polymer nanocomposites

We address the issue of flow effects on the phase behaviour of polymer nanocomposite melts by making use of a recently reported Hamiltonian set of evolution equations developed on principles of non-equilibrium thermodynamics. To this end, we calculate the spinodal curve, by computing values for the nanoparticle radius as a function of the polymer radius-of-gyration for which the second derivative of the generalized free energy of the system becomes zero. Under equilibrium conditions, we recover the phase diagram predicted by Mackay et al. [Science 311, 1740 (2006)]. Under non-equilibrium conditions, we account for the extra terms in the free energy due to changes in the conformations of polymer chains by the shear flow. Overall, our model predicts that flow enhances miscibility, since the corresponding miscibility window opens up for non-zero shear rate values.

The filler-rubber interface in styrene butadiene nanocomposites with anisotropic silica particles: morphology and dynamic properties

Silica-styrene butadiene rubber (SBR) nanocomposites were prepared by using shape-controlled spherical and rod-like silica nanoparticles (NPs) with different aspect ratios (AR = 1-5), obtained by a sol-gel route assisted by a structure directing agent. The nanocomposites were used as models to study the influence of the particle shape on the formation of nanoscale immobilized rubber at the silica-rubber interface and its effect on the dynamic-mechanical behavior. TEM and AFM tapping mode analyses of nanocomposites demonstrated that the silica particles are surrounded by a rubber layer immobilized at the particle surface. The spherical filler showed small contact zones between neighboring particles in contact with thin rubber layers, while anisotropic particles (AR > 2) formed domains of rods preferentially aligned along the main axis. A detailed analysis of the polymer chain mobility by different time domain nuclear magnetic resonance (TD-NMR) techniques evidenced a population of rigid rubber chains surrounding particles, whose amount increases with the particle anisotropy, even in the absence of significant differences in terms of chemical crosslinking. Dynamic measurements demonstrate that rod-like particles induce stronger reinforcement of rubber, increasing with the AR. This was related to the self-alignment of the anisotropic silica particles in domains able to immobilize rubber.