The dynamics of polymer solutions: Effects of concentration, chain architecture, and flow

Young, Charles D.

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https://hdl.handle.net/2142/112953 Copy

Description

Title

The dynamics of polymer solutions: Effects of concentration, chain architecture, and flow

Author(s)

Young, Charles D.

Issue Date

2021-05-27

Director of Research (if dissertation) or Advisor (if thesis)

Sing, Charles E

Doctoral Committee Chair(s)

Sing, Charles E

Committee Member(s)

• Schroeder, Charles M
• Ewoldt, Randy H
• Rogers, Simon A

Department of Study

Chemical & Biomolecular Engr

Discipline

Chemical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Polymer dynamics
• Molecular simulation

Abstract

The dynamics and rheology of polymer solutions are crucial to understanding and designing a broad range of polymer processing applications and biological systems. The microscopic conformational dynamics of polymers are directly related to the rheological response of solutions in processing flows. Additionally, the non-equilibrium conformations which result from these flows often determine the continuum level material properties of the end product, such as the tensile strength of polymeric fibers and the power conversion efficiency of organic solar cells. Despite the importance of the polymer dynamics, a quantitative understanding of the relationship between non-equilibrium conformations and solution flow behavior remains incomplete. Thus, we are motivated to perform a fundamental study of the dynamics of polymer solutions. In particular, we are interested in the influence of polymer concentration and chain architecture in processing flows. There are many variables to tune in the design of processing applications, including molecular weight, solvent quality, and crosslinking reactions. While each of these effects have been investigated independently, in practice multiple variables often need to be adjusted at once due to limitations of the polymer synthesis or the processing equipment. We aim to understand the concurrent influence of concentration, chain architecture, and flow. It is well known that polymer center of mass diffusion decreases as concentration increases above the overlap concentration c* into the semidilute regime due to intermolecular excluded volume (EV) and solvent-mediated hydrodynamic interactions (HI). At higher concentrations, polymer dynamics further slow down as entanglement effects emerge. Upon application of strong flows, polymer are deformed from their equilibrium conformations. The response to flow in dilute solutions and polymer melts has been widely studied. These systems are computationally and theoretically tractable because intermolecular interactions can be neglected in the dilute limit, and HI and EV are screened in the concentrated limit. However, in the semidilute regime, where intra and intermolecular HI and EV are important, there has been significantly less progress, particularly for polymers of non-linear architectures. Theoretical challenges are caused by the limitations of traditional mean-field and preaveraging methods and computational challenges by the orders of magnitude of separation in the relevant time and length scales. Experimental studies are also lacking because of the difficulty in synthesizing polymers of monodisperse architecture and molecular weight. The goal of this work is to elucidate the conformational dynamics in this regime by molecular simulations. When possible, simulations are performed in collaboration with single molecule experiments. Throughout the dissertation, we use a coarse-grained bead-spring model of a polymer at the level of an individual Kuhn step. The solvent is modeled implicitly by a noise term and a diffusion tensor incorporating solvent-mediated HI. The systems of interest are at low Reynolds number, allowing us to significantly simplify the governing Langevin equation of motion for the polymer beads to the overdamped limit, commonly referred to as Brownian dynamics (BD) simulation. The Stokes flow approximation is used for HI, and the thermal fluctuations are coupled to the HI by the fluctuation-dissipation theorem. We first use traditional BD simulations to investigate the influence of chain architecture in planar mixed flows. We simulate for linear and ring or circular polymers (polymers lacking free ends) across a wide range of flow rates and values of the flow parameter alpha which controls the degree of extension versus rotation. We find both linear and ring polymers exhibit similar tumbling-stretch dynamical transitions, although the rings possess a unique open-loop conformation due to flow-architecture coupling. Despite the utility of BD simulations in spanning the time and length scales associated with polymer dynamics, they remain computationally challenging due to the need to calculate the matrix square root of the diffusion tensor in evaluation of the coupled Brownian noise. To overcome this limitation, we introduce an iterative conformational averaging (CA) method for dilute polymer solutions, in which the hydrodynamics and noise are replaced by averaged quantities. These averages are obtained by from an iterative process starting with an initial guess for the HI and noise and directly sampling the polymer conformations by BD simulation. We first investigate the validity of the method in the dilute limit and find excellent agreement with traditional BD simulations at significantly reduced computational cost. While the dilute CA method is useful, it is less successful for semidilute solutions in which there are large fluctuations in the diffusion tensor as polymers diffuse. To overcome this limitation, we replace the diffusion tensor calculation with a more accurate method, using a conformational average for the intramolecular HI and a grid-space tabulated HI for intermolecular interactions. The Brownian noise is still determined by a conformational average, so we retain the computational acceleration of the dilute CA method. Thus, we are able to quantitatively reproduce the polymer diffusion constant and zero-shear viscosity as a function of concentration and molecular weight. We then extend the semidilute CA method to non-equilibrium systems by introducing appropriate flowing boundary conditions and generalizing the Brownian noise average to account for the time-dependent polymer conformations on startup of planar extensional flow. We again find quantitative agreement in the conformational dynamics and solution rheology as compared to traditional BD simulations. We then utilize the CA method to explore the broad parameter space of concentration, architecture, and flow. First, we show that semidilute linear polymer solutions exhibit enhanced conformational diversity on startup of flow due to intermolecular HI. At steady state, these HI lead to larger conformational fluctuations and even complete retraction and tumbling. We also observe flow-induced intermolecular hooking interactions at concentrations significantly below the equilibrium entanglement concentration c_e. However, these hooking events are rare in pure linear polymer solutions. Finally, we extend the CA method to non-linear architectures, including comb and ring polymers. We find a number of unique and unexpected results, many of which are supported by direct visualization of single polymers in flow via confocal fluorescence microscopy of labeled DNA in microfluidic devices. In particular, we find a non-monotonic trend in the relaxation of comb polymers in a semidilute background of linear chain. As combs are added to the backbone, the relaxation time initially decreases despite the increase in molecular weight, in contrast to established results for dilute solutions and melts. Simulations reveal that this is due to a local dilution of the comb backbone's environment, thus reducing the hydrodynamic drag. In the case of semidilute ring-linear blends in extensional flow, we observe a distinct departure from the expected coil-stretch transition. Sub-populations of individual ring trajectories undergo extension overshoots on startup of flow due to intermolecular ring-linear hooks. At steady state, rings exhibit large conformational fluctuations due to intermolecular HI with the background linear chains. In particular the disparity in the size and relaxation time of ring and linear polymers is the driving force for ring fluctuations. We probe these effects as a function of applied flow rate and mass fraction of ring versus linear polymers, revealing a broad range of previously unknown dynamics. Overall, we have developed a method for accelerated molecular simulation of polymer solutions and applied it to a number of systems of interest. Our results elucidate the importance of polymer concentration and chain architecture in flow and provide guidance for designing the dynamical response of a polymer in a given environment. We provide several pathways forward for generalizing these results to polydisperse solutions of varying concentration. We also discuss applications to semidilute planar mixed flows and crossover behavior towards the semidilute entangled regime.

Graduation Semester

2021-08

Type of Resource

Thesis

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http://hdl.handle.net/2142/112953

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Copyright 2021 Charles D. Young

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