Graduation Year

2022

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Physics

Major Professor

Robert S. Hoy, Ph.D.

Committee Member

Martin Muschol, Ph.D.

Committee Member

Ivan Oleynik, Ph.D.

Committee Member

David Simmons, Ph.D.

Keywords

Crazing, Entanglement, Polymer Mechanics, Rheology, Semiflexible Polymers

Abstract

This dissertation is devoted to the computational study of model semiflexible polymers using a coarse-grained bead-spring approach and molecular dynamics (MD) simulations. Much of the work presented here is motivated by the need to derive predictive models for describing polymeric materials’ macroscopic mechanical response from the underlying local structure or local chain parameters. This dissertation describes polymeric materials in the context of granular media, melts, and glasses with a focus on relating characteristics such as chain stiffness and local structure to systems’ solidification, rheology, and fracture mechanisms.

Chain stiffness κ and structural properties like chains’ characteristic bond angle θ0 are tunable parameters that govern the physics of polymeric materials on a wide range of length scales. Varying either θ0 or κ and fixing the other, we can employ coarse-grained bead-spring models to describe the crossover from fully flexible coil-like to stiff rod-like behavior. As chains stiffen (becoming more rod-like), the number of entanglement points between neighboring chains increases, resulting in qualitative and quantitative changes in these systems’ dynamics and fracture mechanisms. These relationships are explored in detail in the following chapters.

Starting in Chapter 1, we briefly introduce related key ideas and topics for understanding the mechanics, entanglement, and fracture mechanisms of the polymer systems discussed in this work. In Chapter 2, we first examine how local and large-scale chain structures affect solidification mechanisms when semiflexible granular polymer systems are compressed quasistatically. Unlike in dynamic compression protocols, we have found that chain entanglement is a precursor to the onset of athermal solidification or jamming. Our findings highlight the importance of local chain bending and stretching modes, as these interactions are fundamental to stability in fiber networks. In short, low aspect-ratio polymer systems are likely to exhibit a stronger fatigue resistance, as these systems tend to collapse locally with relative ease. On the other hand, high aspect-ratio polymers will likely exhibit better energy storage and dissipation properties, as they are more capable of long-range stress-transmission through their contact networks. Materials that combine high energy dissipation with high fatigue resistance are especially attractive for shock-absorption applications.

Moving forward, in Chapter 3, we turn to another class of material and discuss a new equilibration protocol we have developed and used to prepare long-chain, well-entangled semiflexible polymer melts with chain stiffnesses up to the isotropic-nematic transition. Prior to our method, it was computationally impractical or unfeasible to prepare stiffer polymer melt samples due to these systems’ slow dynamics and higher energy barriers. As discussed in this chapter, our algorithm combines Monte-Carlo (MC) topological-chain-switching moves with core-softened Lennard-Jones interactions to equilibrate melts faster than previously published methods. We evaluate the performance of our algorithm by employing topological analysis methods and calculating entanglement-related quantities that are highly sensitive to systems’ non-equilibrium structures.

In Chapter 4, we study and employ these well-equilibrated samples to validate and refine a recently developed analytic model for describing entanglement properties of dense polymer melts. We find that the functional forms of these expressions are robust against changing the topological analysis method and entanglement length Ne-estimator, provided that pathological estimators are avoided. We demonstrate the utility of the Kremer-Grest bead-spring model by showing good agreement between bead spring data and experimental measurements of the plateau modulus for melts of varying chemistry. Additionally, we find that the revised expressions semiquantitatively match all available experimental data for flexible, semiflexible, and stiff polymer melts (including new data for conjugate polymers that lie in a previously unpopulated intermediate stiffness regime) and outperform all previously proposed expressions.

Continuing the work presented in Chapters 3 and 4, in Chapter 5, we cool our equilibrated melts to form semiflexible polymer glasses (SPG) and study these systems’ fracture mechanisms. We have found, contrary to the well-established Kramer picture for glassy-polymeric crazing, SPGs with their entanglement length equal to their Kuhn length can form stable crazes and are perhaps less brittle than previously thought. Moreover, we have found that their craze extension ratio λcraze and fracture stretch λfrac, rather than being 1 as predicted by Kramer, can be quantitatively predicted by recognizing that chains can stretch at the Kuhn-segment scale. We speculate that these systems’ enhanced ductility may be attributed to having a high rate of void nucleation and a relatively low rate of void growth that mechanically stabilize these glasses.

A large fraction of our findings discussed in Chapter 4 rely heavily on the topological analysis results obtained from both primitive path analysis (PPA) and the unpublished Z1+ algorithm. In Chapter 6, we describe and provide Z1+, the successor of the Z- and Z1-codes for topological analyses of mono- and polydisperse entangled linear polymeric systems. We use Z1+ to show that it yields entanglement lengths that agree quantitatively with the results discussed in Chapter 4. Finally, we will show that the associated theoretical expressions discussed in Chapter 4, which express reduced entanglement-related quantities in terms of the geometric parameter Λ, need not describe results for model polymer solutions of different chemistries, (i.e. different angular and dihedral interactions but the same Λ).

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