Session U35: Rheology and Dynamics of Polymers and Polyelectrolytes

Polyelectrolyte solutions in complex macro- and micro-scale flows

Studying the behavior of polymer and polyelectrolyte solutions under complex hydrodynamic flow conditions is of interest to a variety of processes, such as extrusion, coating, and flocculation. Often these flow fields include combinations of both shear and extension flows, requiring characterization of the shear and extensional rheology for optimized materials processing. Here, the behavior of polymer solutions in two flow fields will be discussed: Taylor-Couette flows and microfluidic flow-focusing. First, in Taylor-Couette flow, which is flow between two concentric, rotating cylinders, the complex solutions are subjected to a wide variation of hydrodynamic flow states. The addition of non-Newtonian polymer solutions increases the solution’s elasticity, which in turn can modify flow states that are typically dominated by inertial forces. In this study, a cationic polyacrylamide was used to modify the elasticity of the solution, and with varying concentrations of NaCl to alter the ionic strength of the solution. The coil conformation and relaxation times of charged polymers changes depending on the ionic strength, from a more rigid conformation at low ionic strengths to a more flexible conformation at high ionic strengths, resulting in different non-Newtonian responses to shear. The effect of polymer conformation as a result of varying solution ionic strength on TC flows with co- and counter-rotation of the cylinders will be discussed. Second, microfluidic geometries will be used to characterize the extensional properties of low molecular weight, low viscosity polymer and polyelectrolyte solutions. Specifically, filament stretching using a cross-slot microfluidic channel will be used to resolve extensional properties of polyelectrolyte solutions at varying NaCl concentrations.   

Measuring packing length in simulations for different polymer architectures

The packing length p is the range over which the density near a given monomer is dominated by monomers from the same chain. Bulky, flexible polymers have larger p while thin, stiff polymers have smaller p. The packing length figures prominently in scaling predictions of the entanglement length and bulk modulus for polymer melts and solutions. p has been argued to scale as the ratio V/R^2 of chain displaced volume V and mean-square end-to-end distance R^2. This scaling works for several cases, but it is not obvious how to apply it to chains with side groups, in particular how to estimate the diameter of such a chain.
In this work, we measure the packing length, as the typical distance of closest approach of two polymer strands in a simulated bead-spring melt. We use the intermolecular correlation function to measure the distance up to which a given polymer strand dominates the volume fraction. We compare this measured packing length to our recent measurements of the entanglement length in simulations. Using our measured packing length, we find good agreement of entanglement properties with the Lin-Noolandi ansatz for flexible polymers of different architectures, which we explore by varying chain stiffness and sidegroup lengths.   

Influence of Sodium Salts on the Swelling and Rheology of Hydrophobically Crosslinked Hydrogels Determined by QCM-D

Hydrophobically modified copolymers provide a versatile platform of hydrogel materials for diverse applications, but the influence of salts on the swelling and material properties of this class of hydrogels has not been extensively studied. Here, we investigate model hydrogels with three different sodium salts with anions chosen from the classic Hofmeister series to determine how these counterions influence the swelling and mechanical properties of neutral hydrogels. Our measurements utilize a quartz crystal microbalance with dissipation (QCM-D) to quantify both swelling and rheological properties of these gels. Overall, the observed trends are broadly consistent with more kosmotropic ions causing diminished solubility (‘salting out’) and strongly chaotropic ions causing improved solubility (‘salting in’), a trend characteristic of the Hoffmeister series governing the solubility of many proteins and synthetic water soluble polymers, but trends in the shear stiffness with gel swelling are clearly different from those normally observed in chemically cross-linked gels.   

Effects of humidity on the rheology of supramolecular organogels

It is known that organic oils typically contain tiny amountss of water (0.01% by weight) which can influence the self-assembly as well as the macroscopic properties of supramolecular gelators. We explore here the rheological consequences of this phenomenon which has been overlooked. Specifically, we investigate the properties of biphenyl tricarboxamides (BPTA) in dodecane which exhibit structural transitions with varying temperature. The driving force behind these transitions is the fact tat the humidity content of the supramolecular polymer changes with temperature. We perform shear rheological measurements under controlled humidity conditions in both humid (~60% relative humidity) and dry (~5% relative humidity) conditions and observe that in a humid environment the linear and nonlinear rheological properties are ubstantially affected by the temperature. At temperatures where the systems strongly interacts with water the plateau modulus is lower, the relaxation faster and there is absolutely no sign of strain hardening behaviour. These findings are discussed in the context of existing theories of living polymers. It is concluded that humidity effects cannot be ignored when working in oily environments.
Work in collaboration with N.J. Van Zee and E.W. Meijer (T. U. Eindhoven).   

Rheology of Jammed Silicone Microgels

Colloidal and granular-scale hydrogel particles have been widely used to study jammed and glassy matter in systems with soft inter-particle potentials. Aqueous microgels are most commonly used for these investigations and a diversity of chemical formulations have been developed for controlling inter-particle interactions, microgel size, and particle stiffness. However, there are numerous industrial applications of non-aqueous microgels, creating the need for the fundamental understanding of the rheology of jammed non-aqueous microgels. In this presentation, we will describe our investigations of polydimethylsiloxane (PDMS) microgels. We synthesize PDMS microgels using several different silicone formulations and swell them to a jammed state in silicone oil. The size and the shape of the microgels are varied during synthesis and the resulting effect on the rheological properties of the microgels are studied. By independently varying microgel composition and solvent viscosity, we can independently tune the yield stress and flow characteristics of this jammed system.   

Predicting the plateau modulus from molecular parameters of conjugated polymers

The relationship between Kuhn length b, packing length p, and plateau modulus G_N^° initially proposed by Graessley and Edwards and experimentally investigated by Everaers, while well-studied for flexible and stiff polymers, has a large gap in experimental data between the flexible and stiff regimes. This gap prevents the validation of theoretical models of the crossover between flexible and stiff polymers and therefore, the prediction of mechanical properties from chain structure of any polymer in this region. Given the chain architecture, including a semiflexible backbone and side chains, conjugated polymers are an ideal class of material to study this cross-over region. Using small angle neutron scattering (SANS), static light scattering (SLS), and oscillatory shear rheology along with the freely rotating chain model we have shown that nine non-crystalline conjugated polymers and three aromatic polymers not only populate a large part of this gap, but that they follow the proposed relationship between b, p, and G_N^° as well. We have also experimentally validated the freely rotating chain model for various conjugated polymers using SANS and SLS and find good agreement in Kuhn length values from 1.7 nm in aromatic polymers up to 23.2 nm in conjugated polymers.   

Accessing Viscoelasticity of PDMS at MHz Frequencies: Physically Intuitive Continuum Mechanics Model for QCM Able to Treat Film Resonance Region

Quartz crystal microbalance (QCM) is increasingly applied as a MHz-rheometer to measure viscoelastic properties of films beyond the simple Sauerbrey equation relating frequency shifts to mass loading of the crystal. For films, the range of harmonics available is often limited by needing higher harmonics to access where frequency shifts become sensitive to the film’s viscoelasticity, while avoiding the film resonance region where shifts and dissipation become large. Film resonance corresponds to the harmonics that form standing acoustic waves in the film. Most QCM modeling applies simplifications assuming small resonance shifts, like the small load approximation, which are not valid under film resonance. This limits the range of film thicknesses whose viscoelasticity can be accurately measured, especially for rubbery films where film resonance occurs at lower harmonics. We present a physically intuitive continuum mechanics model with no small frequency-shift approximations that can numerically treat film resonance, accessing a wider range of film thicknesses. Fits for polydimethylsiloxane (PDMS) films, including film resonance conditions, give shear modulus values in good agreement with interpolated literature values from kHz and GHz frequencies.   

Viscoelastic properties of tightly entangled polymeric systems

The rheology of semiflexible polymer solutions has attracted much attention now because it provides a basis for fundamental understanding the physical properties of cellulose nanofibers, which have been considered to be a new material for sustainalbe society. This talk describes recent experimental findings on the rheology of semiflexible polymers including cellulose derivatives and DNA. In addition to the orientational stress of the viscoelastic segment, the bending and tension modes of the segment contribute to the viscoelasticity of the semiflexible polymer solution. In particular, in tightly entangled systems, where the entanglement length is shorter than the persistent length, the bending mode significunlty contributes to the viscoelasticity of the rubbery plateau region. In this talk, by combining simultenous mesurement of strain-induced birefringence, the mode separation of orientation, bending, and tension is carried out on on the linear viscoelasticity of the model materials, and the contribution of each mode is quantitatively discussed.   

Microphase Separation in Entangled Polymeric Solutions in Extensional Flows

Recent NEMD simulations of an entangled polyethylene melt revealed that within intermediate extensional rates, entangled melts could undergo a coil-stretch transition, and exhibit bimodal configurational distributions with peaks corresponding to coiled and stretched configurations. Furthermore, it was shown that through a configurational microphase separation, the coiled molecules develop distinct domains surrounded by stretched molecules. On the other hand, various experimental studies have shown that the response of entangled polymeric melts to elongational flow fields could be very different from those of entangled solutions depending on the solvent molecule architecture. Such complexities bring up many questions about the coil-stretch transition in entangled polymeric liquids. Do entangled solutions undergo a coil-stretch transition? Do they experience any configurational or chemical microphase separation?
To address these questions, we performed a series of NEMD simulations for entangled C₁₀₀₀H₂₀₀₂ polyethylene solutions in oligomeric C₁₆H₃₂ and benzene solvents. The solutions were subject to planar elongational flows within a wide range of extension rates. The simulations revealed both similarities and differences between entangled melts and solutions that will be discussed.   

Predicting the Microstructure of Bottlebrush Copolymers

The unique structure of bottlebrush polymers, a typically linear polymer backbone with densely grafted polymer side-chains, allows for the creation of interesting and unique morphologies. By combining structurally dissimilar backbone and grafts, copolymer bottlebrushes serve as candidates for materials with unique combinations of properties. An example includes polymers with a mechanically rigid backbone and conductive grafts, which can be useful as membranes in battery applications. In this talk, we present a field-theoretic model for the structure of bottlebrush copolymers. We systematically explore the transition from the comb to the bottlebrush regime and show how this modulates the phase diagram of the bottlebrush copolymers. Finally, we show how the chain conformations change in the various microphases in the comb and bottlebrush limits. We accomplish this via our recently developed theoretically informed Langevin dynamics (TILD) package for LAMMPS, in which field-based self-consistent forces are calculated in lieu of pair-wise interactions.   

Interactions between two knots in a stretched DNA molecule

Knots in DNA serve as a model system with which to study the physics of polymer entanglement, and are known to affect the function of genomic sequencing devices. We use microfluidic devices to stretch viral genomic DNA molecules in an elongational electric field, and observe the molecules using fluorescence microscopy. Previously, we have reported the effects that knots have on the relaxation and elasticity of single molecules, as well as the mechanisms by which knots translate along molecules and untie. Here, we discuss molecules that have two knots, and the interactions between the knots. It has been predicted computationally that in a doubly-knotted molecule an attraction exists between the knots, with a minimum in the free energy occurring when the two knots are intertwined. We see long range attraction of knots towards each other from opposite ends of the molecule over tens of seconds, in contrast to the end-migrating behavior of single knots. At short distances, pairs of knots fluctuate in and out of visual contact, remaining in proximity for tens of seconds to minutes. The distribution of intraknot distances can be used to measure free energy landscapes for the knot-knot interactions, which are qualitatively and quantitatively similar to previous computational studies.   

Diffusion of knots in DNA molecules confined in nanochannels

Knots formed in DNA influence biological processes (e.g., DNA replication) and the accuracy of genomics technologies. Knot diffusion, which destroys knots in linear DNA molecules when the knot reaches the chain end, is a key step to understanding these processes. We present experimental data on the diffusion of knots in single DNA molecules via a combination of a nanofluidic "knot factory" device and fluorescence microscopy. Knots are first generated using pressure-driven flow, which compresses single DNA molecules against slit barriers in nanochannels. The knots are identified as bright spikes in intensity profiles of DNA backbone and their motions are tracked for 8 minutes. The ensembled-averaged data for the mean-squared displacement produce a scaling exponent that indicates that confined knots undergo subdiffusion. This result supports the theory that the knot breathing mechanism, where knot diffusion originates from a local motion of knot region, dominates knot diffusion in long polymer chains.   

Dynamics of DNA-bridged particle dumbbells in well-entangled, shear-banding polymer solutions under large amplitude oscillatory shear (LAOS)

Despite accumulation of experimental evidence for shear-banding flows in highly entangled polymer solutions over the last two decades, the current understanding of the conformational changes that induce shear banding remains incomplete. To elucidate the microscopic dynamics of entangled chains in shear-banding flows, we study the dynamics of DNA-bridged particle dumbbells in the shear-banding flow of well-entangled double-stranded DNA (dsDNA) solutions under LAOS using a rheo-confocal shear cell. First, we confirm that the velocity profiles of the entangled dsDNA solutions become inhomogeneous and strong shear-banding flows arise at high Weissenberg number. We then analyze the translation and orientation of particle dumbbells in the co-existing high- and low-shear rate bands. The orientational distribution of dumbbells exhibits clear difference in the co-existing bands. Moreover, we find that the coupling between sudden reorientation and rapid translational motion of dumbbells occurs exclusively in the high-shear rate band. Quantitative investigation of the spatially distinct dynamics of such dsDNA-bridged dumbbells provides new insights into the microscopic structural origin of shear-banding flows in entangled polymer solutions.