Session D25: Rheology and Mechanics of Polymer Systems

Exploring the role of crystal thickness and secondary crystallization in tie molecule effectiveness and ductility

In most applications, it is immensely desirable for semicrystalline polymers to resist brittle fracture. Tie molecules (TMs) – individual polymer chains connecting adjacent crystalline lamellae – are considered a key structural feature governing this mechanical toughness, yet little research has investigated whether all TMs are equally effective at transmitting stress. Here, we study the effects of comonomer content and thermal history on ductility in semicrystalline hydrogenated polynorbornene and its random copolymers with hexylnorbornene. In quenched specimens, we find that TM content at the brittle-ductile transition (the onset of ductility) is a strong function of crystal thickness, indicating that a TM’s effectiveness depends on how firmly embedded it is within each lamella. However, in low-M_n polymers with high comonomer content, crystallization via slow-cooling promotes the formation of two distinct lamellar stacks. Counterintuitively, the stacks containing the thinner crystals can constitute the majority phase. Because the brittle-ductile transition occurs at the point where brittle fracture stress surpasses yield stress, these secondary stacks with thinner crystals govern ductility by yielding at a lesser tensile stress.   

Methodology for Characterizing Complex Strain of Polymeric Thin Films

Traditional methods for analyzing microscale mechanics of polymeric thin films are typically limited to uniaxial deformation. The increasing expansion of research in flexible electronics and soft robotics make it imperative to improve our understanding of how these films behave under a complex strain  field. With the advancement in metamaterials, non-linear microscale mechanics can be investigated to improve our understanding of how soft materials will behave in real-life conditions. This work will discuss the methodology of characterizing crazes under complex strainusing image analysis. Using a 3D printed auxetic elastomeric lattice substrate with a tailored Poission’s ratio from -0.8 to +0.8, a complex strain field is induced within the supported thin films allowing for nonlinear deformation to occur within each lattice cell. The crazing phenomena was evaluated with image analysis to qualitatively and quantitatively describe the craze propagation and density under different strain fields. The experimental results were compared to a linear elastic finite element model for predicting local stress state in the film/lattice structure. Further development of complex strain techniques can lead to more realistic evaluations of thin films in operating conditions.   

Creep in yield stress materials advances through scale-free avalanches

Amorphous solids exit the elastic regime and undergo the yielding transition when driven at their flow stress. At the critical stress and zero temperature, such systems exhibit scale-free avalanches, a pseudogap in the distribution of local stabilities, and are characterized by a robust set of nontrivial critical exponents.  Thermal activations alter this picture, gapping the stability distribution and truncating the size of mechanical avalanches [1,2].  Below the flow stress, thermally activated amorphous solids exhibit creep. Recent experiments with crumpled sheets show that creep in this system advances through very slow, self-similar, ‘thermal’ avalanches [3]. Using a mesoscale elastoplastic model (EPM) with an Arrhenius activation rule, we find good agreement with experimental data and a beautiful example of self-organized criticality. With a finite-size scaling analysis, we characterize the static and dynamic critical exponents of these thermal avalanches, both during the primary creep transient and the ultimate steady-state. I will discuss connections to the glass transition, where it was recently suggested that dynamical heterogeneity may be driven by slow thermal avalanches [4].

[1] D. Korchinski and J. Rottler. Phys. Rev. E 106, 034103 (2022).

[2] M. Popović, T. W. J. de Geus, W. Ji, and M. Wyart. Phys. Rev. E 104, 025010 (2021).

[3] D. Shohat, Y. Friedman, and Y. Lahini. Nat. Phys. 1 (2023).

[4] A. Tahaei et al., Phys. Rev. X 13, 031034 (2023).   

Onset of mechanical failure in shear-jammed dense suspensions

Dense suspensions are a broad class of matter that have the capacity for shear thickening and solidification when subject to stress, but little is known about the properties of solidified dense suspensions and the mechanisms contributing to their mechanical failure, in the form of fracture. We experimentally characterize the onset of crack formation in dense cornstarch suspensions under impact of known strain to investigate the mechanical failure of dynamically-jammed suspensions. There is a critical particle volume fraction, below which fracture will not occur. Above this critical value, the stress at which a shear-jammed solid will fracture varies with both depth and velocity of impact, suggesting that mechanical failure can occur in dynamically-jammed solids with a range of material properties.   

Particle-filled emulsion drops show flow-induced partial coalescence, but only transiently

Partial coalescence refers to a process where two or more droplets come into contact and merge, but do not recover into spherical shape. This occurs because solid-like behavior of the bulk or of the surface of the droplets resists surface tension forces that drive shape recovery. Partial coalescence can significantly impact the microstructure, stability, and rheology of multiphase materials encountered in the processing of foods, cosmetics, petroleum, and polymers. We study the partial coalescence of particle-filled droplets under flow conditions. The experiments are conducted with polyethylene oxide droplets that are filled to over 50 vol% with spherical silica particles, and the resulting yield stress resists capillary forces and prevents complete coalescence. As expected, in the initial stages of shearing, irregular, partially coalesced clusters appear as the drops collide and merge. However, as shearing continues, interesting morphological developments are observed. If shear stress dominates over yield stress, the irregular structures relax into spherical, completely coalesced droplets. If yield stress dominates, irregular structures become more compact but remain non-spherical even under extended shear. We study the evolution of these structures for different blend compositions and flow conditions. These studies provide guidance on conditions under which the formation of large-scale structures may appear in particle-containing liquid-liquid mixtures.    

Structure, solubility and solution rheology of poly(ionic liquids)

We explore the solubility, scattering properties and rheological behaviour of a poly(ionic liquid) (PIL) in 24 solvents covering a broad range of dielectric constants. The PIL is found to be soluble in polar aprotic solvents, but not in non-polar or protic ones. For high dielectric constant media, (ε ≥ 30), the correlation length scales as ξ ∼ c^-1/2, as expected by the scaling theory. The local chain conformation is approximately independent of solvent permittivity if the Bjerrum length is ≤ 1 nm. As the Bjerrum length increases beyond 1 nm, chains become less stretched because more counterions condense onto the polymer backbone, and the electrostatic blob size increases.

For solvents with intermediate permitivitties (ε ≈17-30), the correlation length scales as ξ ∼ c^-1/3, suggesting a partially collapsed (pearl necklace) conformation. We use the Dobyrnin-Rubinstein model to estimate mass per bead and bead volume fraction, establishing correlations with the solvent’s properties. In tetrahydrofuran (ε ≈ 8), the scattering and rheological behaviour matches that of neutral polymers.

The scaling model expects semidilute non-entangled  solutions to follow Rouse dynamics. The specific viscosity (η_sp) is predicted to be equal to number of correlation blobs per chain (N/(cξ³)). We compute the ratio η_spcξ³ in several solvents and find that it does not take a constant value, in disagreement with the scaling model. Our results help establish a framework to understand the solution rheology of polymerised ionic liquids.   

Gelation dynamics in elastomers with branched architecture

Elastomers with non-linear polymer architectures have drawn significant interest due to their soft, solvent free nature. Mechanical properties of such gels are highly modular through control of the molecular architecture. The competition between elastically effective crosslinkers and dangling branched side chains creates an environment where precise control of these architectural components during processing is challenging. Here, we address the impact of side chain grafting on structure formation during curing in soft elastomers. The chain dynamics and relaxation processes are resolved by transient rheological techniques. Network formation during curing is compared to the gelation of linear chain elastomer analogs, of which the dynamics are well established. We address the impact of the cure process on the gel fraction and incorporation of various chain types, which further modulates the final mechanical properties. This work illustrates the importance of understanding and controlling structure in real time to achieve predictable properties.   

Evaluation of diffusion and dethreading in blends of ring and linear polymers

Blends of linear and ring polymers can have slower dynamics and higher viscosities than the pure individual components. This is due to the threading of ring polymers by linear polymers, which introduces topological constraints that hinder chain diffusion. We simulate blends of linear and ring polymers for long time scales to study the relaxation of these topological constraints. We find that the diffusion time of a ring polymer scales like N_L^3.4N_R² in ring-linear blends. Here N_L and N_R represent the length of the linear polymer and ring polymer, respectively. In contrast, the diffusion time of a ring in a pure ring melt scales like N_R^2.8. The scaling of ring diffusion in a blend can be understood by considering the relaxation of thread constraints on the ring. Ring-linear threadings are characterized using the Gauss linking integral, which provides a quantitative measure of the degree of entanglement and can be evaluated quickly allowing for analysis of threading dynamics.   

Linking Polymer Architecture to Bubble Shape in LDPE Film Blowing through Multistage Modeling

To meet the challenge of efficient modeling of film blowing with realistic constitutive equations for commercial thermoplastic melts, we present a multistage optimization modeling framework that integrates polymerization reaction modeling, rheology modeling, and bubble-shape prediction. A direct link is thereby created between polymer architecture and the bubble shape of low-density polyethylene (LDPE) through a three-stage modeling protocol. Stage 1 aims to get complete polymer structure information from a limited set of linear and nonlinear rheological data and the measured averaged molecular weight. An optimization loop uses the Tobita algorithm for polymer reaction and the BoB model for rheology to minimize the deviation between experimental data and model predictions. Stage 2 is designed to obtain a representative reduced ensemble of LDPE in the Rolie-double-poly (RDP) model to reduce the computational cost of rheology calculations during processing. The parameters of the reduced molecular components are obtained by fitting the RDP model to a wide range of rheology data predicted by the BoB model applied to the full ensemble of polymer architectures obtained in Stage 1. In Stage 3, the reduced-ensemble RDP model is coupled to measured temperature profiles using time-temperature superposition, and the bubble shape and strain rate history of a fluid particle in the bubble are obtained by minimizing error in the momentum balance equations. With this multistage optimization strategy, we link the polymer compositions to the bubble properties during the film blowing of LDPE.   

Recent Advances in Polymer Viscoelasticity From General Rigid Bead-Rod Theory

One good way to explain the elasticity of a polymeric liquid, is to just consider the

orientation distribution of the macromolecules. When exploring how macromolecular

architecture affects the elasticity of a polymeric liquid, we find general rigid bead-rod theory

to be both versatile and accurate. This theory sculpts macromolecules using beads and rods.

Whereas beads represent points of Stokes flow resistances, the rods represent rigid

separations. In this way, how the shape of the macromolecule affects its rheological behavior

in suspension is determined. Our work shows the recent advances in polymer viscoelasticity

using general rigid bead-rod theory, including advances applied on different viruses,

including coronavirus. We calculate the rotational diffusivity of the viral suspensions, from

first principles, using general rigid bead-rod theory. We do so by beading the spherical

polymer, and then also by replacing each of its bulbous spikes with a single bead. We use

energy minimization for the spreading and positioning of the spikes, charged identically,

over the oblate or prolate capsids. We use general rigid bead-rod theory to explore the role

of ellipticity on its rotational diffusivity, the transport property around which its cell

attachment revolves.   

Calibration of Polymer Molecular Weight Using Solution Viscosity in Dilute and Semidilute Solutions

Molecular weight characterization is at the heart of modern polymer science. It relies on size-exclusion chromatography utilizing an extreme dilution of polymer fractions. Here, we present a general framework for obtaining the weight-average molecular weights of linear polymers in a broad concentration range from solution viscosity. In the dilute solution regime (c < c^*), the approach is based on the representation of solution-specific viscosity η_sp as a universal function of chain overlap concentration c* in good and θ-solvents. This approach is extended to the unentangled (Rouse) semidilute solution regime (c ≥ c^*), where we use the linear relationship between specific viscosity and number of correlation blobs per chain, η_sp(c) = N_w/g(c), where N_w is the weight-average degree of polymerization. This analysis defines a set of calibration curves for which the weight-average molecular weight can be determined from a single measurement of specific viscosity without the need for dilution.   

Linking Ultra-High Strain Rate Impact Resistance of Polymers from Nano to Macro

Understanding the failure behavior of polymers subjected to an ultra-high strain rate (UHSR) event is crucial for their applications in protective systems. As the size and energy scales associated with these systems can vary over many decades, it has been a challenging endeavor to understand how the various length scales dictate the UHSR behavior of polymers when their molecular architecture and dynamics also need to be considered. In this contribution, we experimentally investigate the UHSR behavior of polymethyl methacrylate (PMMA) by impacting targets with projectiles at the microscale using laser-induced projectile impact testing (LIPIT) and at the macroscale using a ballistic and two-stage light gas gun. We then apply dimensional analysis models based on the Buckingham-П theorem to relate the minimum perforation and residual projectile velocities over these length scales. We show that the ratio of the target thickness to projectile diameter, their density differences, and the velocity of the compressive stress wave within the target govern these scaling relationships. Using this framework, we show that our scaling relationships can be extended to polycarbonates and high-density polyethylene, demonstrating their applicability to multiple material systems to show that our scaling model can successfully predict the impact properties of polymers during UHSR events that are independent of their unique mechanical properties and failure responses.   

Multiscale Modeling of Nonlinear Rheology for Entangled Polymer Melts

Due to the growing demand for new sustainable polymers with novel molecular structures, there is a pressing need to develop a fast and reliable computational method for predicting their rheological properties, especially under real-world nonequilibrium processing conditions, based on their chemical structure. Recently, we developed a bottom-up multiscale modeling method for in-silico equilibrium rheology of entangled polymer melts. In this method, three simulation models with decreasing resolutions (namely all-atom, coarse-grained, and slip-spring) are performed to probe the polymer relaxation at increasing time and length scales, which are eventually unified to predict the full relaxation spectrum. In this talk, we will show the extension of this method to nonequilibrium rheology. As a proof of concept, we applied this method to atactic polystyrene (aPS) under nonequilibrium shear. Our method predicted the steady shear viscosity of entangled aPS melts across various molecular weights (Mw=60k~300k) and shear rates (Weissenberg number, Wi=0.1~10), demonstrated good agreement with experimental measurements, all achieved without the need for experimental data input. The presented multiscale modeling method paves the way for the rapid and efficient development of sustainable and processable polymeric materials.   

Flow-Induced Nucleation as a Stabilizing Mechanism for Polymers against Edge Fracture

We show here a universal indicator from rheology of flow-induced nucleation that gives insight into how flow enhances crystallization in semi-crystalline polymers. We study the effects of an interval of shear flow on the crystallization kinetics of a high density polyethylene (HDPE) and monodisperse polyethylene oxide (PEO) blends with a high molecular weight fraction. We characterize the crystallization of polymer using oscillatory shear linear viscoelasticity, cone & plate shear rheology, cone-partitioned plate shear rheology and capillary rheometry. We quantify crystallization by the Winter-Pogodina criterion that the storage modulus (G’) crosses the loss modulus (G”) in an oscillatory shear time sweep at a fixed angular frequency. We apply intervals of shear both above and below the melting temperature of the polymers. The intervals of shear are immediately followed by oscillatory shear time sweeps to quantify the effect of various shear intervals on crystallization kinetics when HDPE and PEO are sheared and crystallized at the same temperature. We find that applying flow at lower temperatures exhibits different crystallization kinetics than applying flow at higher temperatures. The most important take away is that flow-induced nucleation is closely connected to the first normal stress difference and acts as the universal nucleation indicator by stabilizing the melt against edge fracture which is very apparent only at high temperatures where crystals and their precursors cannot form.