Dynamically Heterogeneous Relaxation of Entangled Polymer Chains

Retention mechanism in slalom chromatography: Perspectives on the characterization of large DNA and RNA biopolymers in cell and gene therapy

Significant progress has been made in the last two decades in producing small (<2μm), high-purity, and low-adsorption particles, columns and system hardware, for ultra-high pressure liquid chromatography (UHPLC). Simultaneously, the recent rapid expansion of cell and gene therapies for treating diseases necessitates novel analytical technologies for analyzing large (>2 kbp) plasmid double-stranded (ds) DNA (which encodes for the in vitro transcription (IVT) of single-stranded (ss) mRNA therapeutics) and dsRNAs (related to IVT production impurities) biopolymers. In this context, slalom chromatography (SC), a retention mode co-discovered in 1988, is being revitalized using the most advanced column technologies for improved determination of the critical quality attributes (CQAs) of such new therapeutics. In this review, we first recall non-exhaustively the main currently available analytical techniques (enzyme-linked immunosorbent assay (ELISA), agarose gel electrophoresis (AGE), pulse field gel electrophoresis (PFGE), capillary gel electrophoresis (CGE), mass photometry (MP), anion-exchange chromatography (AEX), ion-pairing reversed-phase liquid chromatography (IP-RPLC), hydrophobic interaction chromatography (HIC), size-exclusion chromatography (SEC), hydrodynamic chromatography (HDC), highly converging flow ultra-filtration (HCF-UF), asymmetrical flow field-flow fractionation (AF4), mass spectrometry (MS), and atomic force microscopy (AFM)) for analyzing mixtures containing large nucleic acid biopolymers, while assessing their strengths and weaknesses. We then focus comprehensively on the SC technique, report on its past applications since its birth, and review in detail the history and evolution of the proposed retention mechanisms accounting for the observations made in SC. This includes and emphasizes the latest physico-chemical insights (shear rates in packed HPLC columns, entropic elasticity and relaxation of dsDNA, dsRNA, and mRNA biopolymers) governing the retention behavior of such biopolymers in SC. Finally, based on the recent advancements in understanding the fundamentals of retention in SC, we provide some perspectives and recent proof-of-concept for the analytical characterization by SC of large dsDNAs (plasmid digests, polymerase chain reaction (PCR) verification), the separation of supercoiled/circular and linear dsDNAs (plasmid linearization), the isolation and quantification of large dsRNAs impurities present in mRNA samples produced by IVT, and the differentiation between dsRNA conformers.

Phage probes couple to DNA relaxation dynamics to reveal universal behavior across scales and regimes

Microrheology has become an indispensable tool for measuring the dynamics of macromolecular systems. Yet, its ability to characterize polymer dynamics across spatiotemporal scales, which vary among polymers and concentration regimes, is limited by the selection of probe morphologies and sizes. Here, we introduce semiflexible M13 phage as a powerful microrheological probe able to circumvent these constraints to robustly capture the dynamics of polymeric solutions across decades of concentrations, sizes, and ionic conditions. We show that phage mobility directly couples to the relaxation dynamics of DNA solutions spanning from semidilute to entangled regimes with ionic strengths varying by four orders of magnitude. Phage mobility metrics across a broad range of timescales collapse onto universal master curves that are unexpectedly insensitive to ionic strength and exhibit robust crossovers from semidilute to entangled regime scaling, not captured by current theoretical models. Our results open the door to the use of phage probes to elucidate the complex dynamics of systems exhibiting a spectrum of thermal and active relaxation processes.

Ultra-high pressure slalom chromatography: Application to the characterization of large DNA and RNA samples relevant in cell and gene therapy

Slalom chromatography (SC), initially co-discovered by Boyes and Kasai in the late 1980s, has recently re-emerged as a breakthrough technique to rapidly analyze DNA samples. With the development of cutting-edge ultra-high pressure liquid chromatography (UHPLC) systems and columns, SC now offers enhanced resolution and sensitivity for analyzing large DNA samples. By revisiting the fundamentals of the SC retention mechanism (non-equilibrium separation mode) and considering the physicochemical properties of DNA biopolymers (contour length, extension under shear flow, relaxation time), we provide analytical chemists with a general strategy and framework for selecting the most relevant applications in the expanding field of cell and gene therapy. We then present proof-of-concept data demonstrating the rapid separation (under 2 min) of plasmid digest samples containing linear double-stranded (ds) DNA macromolecules starting from 2 kbp to 25 kbp, as well as the accurate size determination (±6%) of linear dsDNAs. Additionally, we show rapid baseline separation and quantification of extensible linear dsDNAs, along with the more rigid plasmid dsDNA (supercoiled/circular/nicked circular). We also quantify dsRNA impurities present in vitro transcription (IVT) media used for producing new mRNA therapeutics and assess dsRNA structural heterogeneity (conformational isomers). These findings aim to support in a near future application chemists in addressing emerging bioanalytical challenges in cell and gene therapy by offering advanced SC columns and methods.

Theoretical predictions to facilitate the method development in slalom chromatography for the separation of large DNA molecules

Slalom chromatography (SC) re-emerged in 2024 due to the availability of low adsorption ultra-high pressure liquid chromatography (UHPLC) packed columns/instruments and large modalities being investigated in the context of cell and gene therapies. The physico-chemical principles of SC retention combined with hydrodynamic chromatography (HDC) exclusion have been recently reported. In SC, DNA macromolecules are retarded because: (1) they can be stretched to lengths comparable to the particle diameter, and (2) their elastic relaxation time is long enough to maintain them in non-equilibrium extended conformations under regular UHPLC shear flow conditions. Here, a quantitative HDC-SC retention model is consolidated. A general plate height model accounting for the band broadening of long DNA biopolymers along packed beds is also derived for supporting method development and predicting speed-resolution performance in SC. For illustration, the chromatographic speed-resolution properties in SC are predicted for the separation of specific critical pairs (4.0/4.5, 10/11, and 25/27 kbp) of linear dsDNA polymers. The calculations are performed for two available custom-made particle sizes, dp= 1.7 and 2.5μm, at a constant pressure of 10,000 psi. The predictions are directly validated from experimental data acquired using low adsorption MaxPeakTM 4.6 mm i.d. Columns packed with 1.7μm BEHTM 45 Å (15 cm long column) and 2.5μm BEH 125 Å (30 cm long column) Particles, and by injecting six linear dsDNAs (λ DNA-Hind III Digest). The LC system is very low dispersion ACQUITYTM UPLCTM I-class PLUS System, and the mobile phase is a 100 mM phosphate buffer at pH 8. Maximum resolution is always achieved when the average extended lengths of linear dsDNAs are equal to a critical length, which is proportional to the particle diameter and to the square root of the applied shear rate. Most advantageously, the experimental results reveal that the relaxation times of linear dsDNAs observed under shear flow conditions are two orders of magnitude shorter than those expected in the absence of flow: this enables the detection of the longest linear dsDNAs up to 25 kbp without irremediable loss in column performance. Finally, the retention-efficiency model elaborated in this work can be used to rapidly anticipate and develop methods (selection of particle size, column length, and operating pressure) for any targeted DNA and time-resolution constraints.

High-Electrochemical-Activity Composite Cathode Enabled by Fast Segmental Relaxation for Solid-State Lithium-Sulfur Batteries

Solid-state lithium-sulfur batteries (SSLSBs) have attracted a great deal of attention because of their high theoretical energy density and intrinsic safety. However, their practical applications are severely impeded by slow redox kinetics and poor cycling stability. Herein, we revealed the detrimental effect of aggregation of lithium polysulfides (LiPSs) on the redox kinetics and reversibility of SSLSBs. As a paradigm, we introduced a multifunctional hyperbranched ionic conducting (HIC) polymer serving as a solid polymer electrolyte (SPE) and cathode binder for constructing SSLSBs featuring high electrochemical activity and high cycling stability. It is demonstrated that the unique structure of the HIC polymer with numerous flexible ether oxygen dangling chains and fast segmental relaxation enables the dissociation of LiPS clusters, facilitates the conversion kinetics of LiPSs, and improves the battery's performance. A Li|HIC SPE|HIC-S battery, in which the HIC polymer acts as an SPE and cathode binder, exhibits an initial capacity of 910.1 mA h gS-1 at 0.1C and 40 °C, a capacity retention of 73.7% at the end of 200 cycles, and an average Coulombic efficiency of approximately 99.0%, demonstrating high potential for application in SSLSBs. This work provides insights into the electrochemistry performance of SSLSBs and provides a guideline for SPE design for SSLSBs with high specific energy and high safety.

Retention mechanism in combined hydrodynamic and slalom chromatography for analyzing large nucleic acid biopolymers relevant to cell and gene therapies

Slalom chromatography (SC) was discovered in 1988 for analyzing double-stranded (ds) DNA. However, its progress was impeded by practical issues such as low-purity particles, sample loss, and lack of a clear retention mechanism. With the rise of cell and gene therapies and the availability today of bio-inert ultra-high-pressure liquid chromatography (UHPLC) columns and systems, SC has regained interest. In SC, the elution order is opposite to that observed in hydrodynamic chromatography (HDC): larger DNA molecules are more retained than small ones. Yet, the underlying SC retention mechanism remains elusive. We provide the physicochemical background necessary to explain, at a microscopic scale, the full transition from a HDC to a SC retention mechanism. This includes the persistence length of the DNA macromolecule (representing DNA stiffness), their relaxation time (τR) from the non-equilibrium contour length to the equilibrium entropic configuration, and the relationship between the mobile phase shear rate (〈γ̇〉) in packed columns and the DNA extended length. We propose a relevant retention model to account for the simultaneous impact of hydrodynamic chromatography (HDC) and SC on the retention factors of a series of large and linear dsDNAs (ranging from 2 to 48 kbp). SC data were acquired using bio-inert MaxPeakTM Columns packed with 1.7μm BEHTM 45 Å, 1.8μm BEH 125 Å, 2.4μm BEH 125 Å, 5.3μm BEH 125 Å, and 11.3μm BEH 125 Å Particles, an ACQUITYTM UPLCTM I-class PLUS System, and either 1 × PBS (pH 7.4) or 100 mM phosphate buffer (pH 8) as the mobile phase. SC is a non-equilibrium retention mode that is dominant when the Weissenberg number (Wi=〈γ̇〉τR) is much larger than 10 and the average extended length of DNA exceeds the particle diameter. HDC, on the other hand, is an equilibrium retention mode that dominates when Wi<1 (DNA chains remaining in their non-extended configuration). Maximum dsDNA resolution is observed in a mixed HDC-SC retention mode when the extended length of the DNA is approximately half the particle diameter. This work facilitates the development of methods for characterizing various plasmid DNA mixtures, containing linear, supercoiled, and relaxed circular dsDNAs which all have different degree of molecular stiffness.

An entanglement association polymer electrolyte for Li-metal batteries

To improve the interface stability between Li-rich Mn-based oxide cathodes and electrolytes, it is necessary to develop new polymer electrolytes. Here, we report an entanglement association polymer electrolyte (PVFH-PVCA) based on a poly (vinylidene fluoride-co-hexafluoropropylene) (PVFH) matrix and a copolymer stabilizer (PVCA) prepared from acrylonitrile, maleic anhydride, and vinylene carbonate. The entangled structure of the PVFH-PVCA electrolyte imparts excellent mechanical properties and eliminates the stress arising from dendrite growth during cycling and forms a stable interface layer, enabling Li//Li symmetric cells to cycle steadily for more than 4500 h at 8 mA cm-2. The PVCA acts as a stabilizer to promote the formation of an electrochemically robust cathode-electrolyte interphase. It delivers a high specific capacity and excellent cycling stability with 84.7% capacity retention after 400 cycles. Li1.2Mn0.56Ni0.16Co0.08O2/PVFH-PVCA/Li full cell achieved 125 cycles at 1 C (4.8 V cut-off) with a stable discharge capacity of ~2.5 mAh cm-2.

Characterisation of hydrodynamic trapping in microfluidic cross-slot devices for high strain rate applications

Hydrodynamic trapping of a particle or cluster of particles based on contact and non-contact approaches has brought prominent insights to micro-nano scale applications. Of the non-contact methods, image-based real-time control in cross-slot microfluidic devices is one of the most promising potential platform for single cellular assays. Here, we report results from experiments conducted in two cross-slot microfluidic channels of different widths, with varying real-time delay of the control algorithm and different magnification. Sustained trapping of 5 μm diameter particles was achieved with high strain rates, of order 10² s^-1, higher than in any previous studies. Our experiments show that the maximum attainable strain rate is a function of the real-time delay of the control algorithm and the particle resolution (pixel/μm). Therefore, we anticipate that with further reduced time delays and enhanced particle resolution, considerably higher strain rates can be attained, opening the platform to single cellular assay studies where very high strain rates are required.

Single-Molecule Tracking of Reagent Diffusion during Chemical Reactions

Recent experiments have shown that the diffusion of reagent molecules is inconsistent with what the Stokes-Einstein equation predicts during a chemical reaction. Here, we used single-molecule tracking to observe the diffusion of reactive reagent molecules during click and Diels-Alder (DA) reactions. We found that the diffusion coefficient of the reagents remained unchanged within the experimental uncertainty upon the DA reaction. Yet, diffusion of reagent molecules is faster than predicted during the click reaction when the reagent concentration and catalyst concentration exceed a threshold. A stepwise analysis suggested that the fast diffusion scenario is due to the reaction but not the involvement of the tracer with the reaction itself. The present results provide experimental evidence on the faster-than-expected reagent diffusion during a CuAAC reaction in specific conditions and propose new insights into understanding this unexpected behavior.

Short and long-range cyclic patterns in flows of DNA solutions in microfluidic obstacle arrays

We observe regular patterns emerging across multiple length scales with high-concentration DNA solutions in microfluidic pillar arrays at low Reynolds numbers and high Deborah numbers. Interacting vortices between pillars lead to long-range order in the form of large travelling waves consisting of DNA at high concentration and extension. Waves are formed in quadratic arrays of pillars, while randomizing the position of the pillar in each unit cell of a quadratic array leads to suppression of the long-range patterns. We find that concentrations exceeding the overlap concentration of the DNA enables the waves, and exploring the behavior of the waves as a function of flow rate, buffer composition, concentration and molecular length, we identify elastic effects as central to the origin of the waves. Our work may not only help increase the low throughput that often limits sample processing in microfluidics, it may also provide a platform for further studies of the underlying viscoelastic mechanisms.

Impact of Chain Conformation on Structural Heterogeneity in Polymer Network

Polymer networks generally consist of an ensemble of single chains. However, understanding how chain conformation affects the structure and properties of polymer networks remains a challenge for optimizing their functionality. Here, we present the fabrication and comparative study of a polymer network composed of collapsed self-entangled chains (intrachain entangled network) and a standard polymer network in which random-coil chains are entangled with each other (interchain entangled network). For poly(methyl methacrylate) thin films composed of these networks, we coupled solvent vapor swelling and single-molecule tracking techniques to examine the anomalies in the dynamics of a small-molecular probe included in the system. We demonstrate that when compared to the interchain entangled network the intrachain one exhibits a more substantial structural heterogeneity, particularly under highly crowded conditions. This network also exhibits physical compactness, which keeps the heterogeneous network structure frozen over time and impedes network plasticization through solvent uptake by the film.

Statistical Dynamics of Flow-Driven Globular Polymers

The response of collapsed polymers to the effects of linear mixed flow is studied theoretically in this paper using a model of a self-interacting finitely extensible Gaussian chain that evolves stochastically in the presence of random thermal fluctuations and an external fluid velocity gradient. The interactions that produce compact chain configurations are described by a harmonic pair potential of strength κ that acts between nonbonded sites on the chain backbone. Several chain properties are calculated analytically from this model as a function of κ for elongational and shear flows, including the dependence of the chain's steady-state mean-square end-to-end distance on the Weissenberg number of the flow, the time-dependence of the chain's relaxation to equilibrium from a steady-state of given chain extension, and the nature of the force-extension curves that are obtained from the free energy change between unperturbed and flow-stretched states of the chain. For both elongational and shear flows (but to different degrees), it is found that the greater the value of κ (and the more compact the chain), the more difficult it is, in general, for the imposed flow to induce a transition between compact and extended states, in broad agreement with available data from numerical simulations. For the relaxation process, the differences between the two flow types are more marked. The characteristic decay time for relaxation from a state prepared by elongational flow is essentially independent of κ, whereas in the case of a state prepared by shear flow, it is distinctly κ-dependent, the relaxation becoming faster at larger κ.

Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions.

The relaxation dynamics of single flow-stretched polymers in semidilute to concentrated solutions

Recent experiments on the return to equilibrium of solutions of entangled polymers stretched by extensional flows [Zhou and Schroeder, Phys. Rev. Lett. 120, 267801 (2018)] have highlighted the possible role of the tube model's two-step mechanism in the process of chain relaxation. In this paper, motivated by these findings, we use a generalized Langevin equation (GLE) to study the time evolution, under linear mixed flow, of the linear dimensions of a single finitely extensible Rouse polymer in a solution of other polymers. Approximating the memory function of the GLE, which contains the details of the interactions of the Rouse polymer with its surroundings, by a power law defined by two parameters, we show that the decay of the chain's fractional extension in the steady state can be expressed in terms of a linear combination of Mittag-Leffler and generalized Mittag-Leffler functions. For the special cases of elongational flow and steady shear flow, and after adjustment of the parameters in the memory function, our calculated decay curves provide satisfactory fits to the experimental decay curves from the work of Zhou and Schroeder and earlier work of Teixeira et al. [Macromolecules 40, 2461 (2007)]. The non-exponential character of the Mittag-Leffler functions and the consequent absence of characteristic decay constants suggest that melt relaxation may proceed by a sequence of steps with an essentially continuous, rather than discrete, spectrum of timescales.

Stretching DNA to twice the normal length with single-molecule hydrodynamic trapping

Single-molecule force spectroscopy has brought many new insights into nanoscale biology, from the functioning of molecular motors to the mechanical response of soft materials within the cell. To expand the single-molecule toolbox, we have developed a surface-free force spectroscopy assay based on a high-speed hydrodynamic trap capable of applying extremely high tensions for long periods of time. High-speed single-molecule trapping is enabled by a rigid and gas-impermeable microfluidic chip, rapidly and inexpensively fabricated out of glass, double-sided tape and UV-curable adhesive. Our approach does not require difficult covalent attachment chemistries, and enables simultaneous force application and single-molecule fluorescence. Using this approach, we have induced a highly extended state with twice the contour length of B-DNA in regions of partially intercalated double-stranded (dsDNA) by applying forces up to 250 pN. This highly extended state resembles the hyperstretched state of dsDNA, which was initially discovered as a structure fully intercalated by dyes under high tension. It has been hypothesized that hyperstretched DNA could also be induced without the aid of intercalators if high-enough forces were applied, which matches our observation. Combining force application with single-molecule fluorescence imaging is critical for distinguishing hyperstretched DNA from single-stranded DNA that can result from peeling. High-speed hydrodynamic trapping is a powerful yet accessible force spectroscopy method that enables the mechanics of biomolecules to be probed in previously difficult to access regimes.

Dynamic Heterogeneity in Ring-Linear Polymer Blends

We present results from a direct statistical analysis of long molecular dynamics (MD) trajectories for the orientational relaxation of individual ring molecules in blends with equivalent linear chains. Our analysis reveals a very broad distribution of ring relaxation times whose width increases with increasing ring/linear molecular length and increasing concentration of the blend in linear chains. Dynamic heterogeneity is also observed in the pure ring melts but to a lesser extent. The enhanced degree of dynamic heterogeneity in the blends arises from the substantial increase in the intrinsic timescales of a large subpopulation of ring molecules due to their involvement in strong threading events with a certain population of the linear chains present in the blend. Our analysis suggests that the relaxation dynamics of the rings are controlled by the different states of their threading by linear chains. Unthreaded or singly-threaded rings exhibit terminal relaxation very similar to that in their own melt, but multiply-threaded rings relax much slower due to the long lifetimes of the corresponding topological interactions. By further analyzing the MD data for ring molecule terminal relaxation in terms of the sum of simple exponential functions we have been able to quantify the characteristic relaxation times of the corresponding mechanisms contributing to ring relaxation both in their pure melts and in the blends, and their relative importance. The extra contribution due to ring-linear threadings in the blends becomes immediately apparent through such an analysis.

Preparation and application of macromolecules with a fluorescence effect in polymer processing

In this study, 9-anthracenemethyl methacrylate (AMMA) and styrene (St) as monomers and benzoyl peroxide as an initiator were used to synthesize P(St-co-AMMA), a macromolecule tracer with a fluorescence effect, via free radical copolymerization. A fluorescent online detection device was built on the basis of the principle of fluorescence online detection by using the single-screw extrusion platform of a torque rheometer to explore the effect of the amount of macromolecular tracer and screw speed on the residence time distribution of polystyrene in single-screw extrusion. Fourier transform infrared spectroscopy, ¹H-NMR, thermal stability, fluorescence properties, and rheological properties show that the resulting product P(St-co-AMMA) has a degree of thermal stability, fluorescence, and rheological properties similar to polystyrene, so this product can be used to characterize the residence time distribution during single-screw extrusion. The amount of macromolecular tracer P(St-co-AMMA) does not affect the residence time distribution of polystyrene during single-screw extrusion processing, meanwhile, the minimum residence time decreases and the residence time distribution becomes narrow as the screw speed increases, that is, the axial mixing capacity of the single-screw extruder decreases as the screw speed increases.

Clustering of Entanglement Points in Highly Strained Polymer Melts

Polymer melts undergoing large deformation by elongation are studied by molecular dynamics simulations of bead-spring chains in melts. By applying a primitive path analysis to strongly deformed polymer melts, the role of topological constraints in highly entangled polymer melts is investigated and quantified. We show that the overall, large scale conformations of the primitive paths (PPs) of stretched chains follow affine deformation while the number and the distribution of entanglement points along the PPs do not. Right after deformation, PPs of chains retract in both directions parallel and perpendicular to the elongation. Upon further relaxation we observe a long-lived clustering of entanglement points. Together with the delayed relaxation time this leads to a metastable inhomogeneous distribution of topological constraints in the melts.

Optical Tweezers Microrheology Maps the Dynamics of Strain-Induced Local Inhomogeneities in Entangled Polymers

Optical tweezers microrheology (OTM) offers a powerful approach to probe the nonlinear response of complex soft matter systems, such as networks of entangled polymers, over wide-ranging spatiotemporal scales. OTM can also uniquely characterize the microstructural dynamics that lead to the intriguing nonlinear rheological properties that these systems exhibit. However, the strain in OTM measurements, applied by optically forcing a microprobe through the material, induces network inhomogeneities in and around the strain path, and the resultant flow field complicates the measured response of the system. Through a robust set of custom-designed OTM protocols, coupled with modeling and analytical calculations, we characterize the time-varying inhomogeneity fields induced by OTM measurements. We show that homogenization following strain does not interfere with the intrinsic stress relaxation dynamics of the system, rather it manifests as an independent component in the stress decay, even in highly nonlinear regimes such as with the microrheological large-amplitude-oscillatory-shear (MLAOS) protocols we introduce. Our specific results show that Rouse-like elastic retraction, rather than disentanglement and disengagement, dominates the nonlinear stress relaxation of entangled polymers at micro- and mesoscales. Thus, our study opens up possibilities of performing precision nonlinear microrheological measurements, such as MLAOS, on a wide range of complex macromolecular systems.

Ring polymer dynamics and tumbling-stretch transitions in planar mixed flows

The properties of dilute polymer solutions are governed by the conformational dynamics of individual polymers which can be perturbed in the presence of an applied flow. Much of our understanding of dilute solutions comes from studying how flows manipulate the molecular features of polymer chains out of equilibrium, primarily focusing on linear polymer chains. Recently there has been an emerging interest in the dynamics of nonlinear architectures, particularly ring polymers, which exhibit surprising out-of-equilibrium dynamics in dilute solutions. In particular, it has been observed that hydrodynamics can couple to topology in planar elongational and shear flows, driving molecular expansion in the nonflow direction that is not observed for linear chains. In this paper, we extend our understanding of dilute ring polymer dynamics to mixed flows, which represent flow profiles intermediate between simple shear or planar elongation. We map the conformational behaviors at a number of flow geometries and strengths, demonstrating transitions between coiled, tumbling, and stretched regimes. Indeed, these observations are consistent with how linear chains respond to mixed flows. For both linear and ring polymers, we observe a marked first-order-like transition between tumbling and stretched polymers that we attribute to a dynamic energy barrier between the two states. This manifests as bimodal extension distributions in a narrow range of flow strengths and geometries, with the primary difference between rings and linear chains being the presence of molecular expansion in the vorticity direction.

Effect of molecular architecture on ring polymer dynamics in semidilute linear polymer solutions

Understanding the dynamics of ring polymers is a particularly challenging yet interesting problem in soft materials. Despite recent progress, a complete understanding of the nonequilibrium behavior of ring polymers has not yet been achieved. In this work, we directly observe the flow dynamics of DNA-based rings in semidilute linear polymer solutions using single molecule techniques. Our results reveal strikingly large conformational fluctuations of rings in extensional flow long after the initial transient stretching process has terminated, which is observed even at extremely low concentrations (0.025 c*) of linear polymers in the background solution. The magnitudes and characteristic timescales of ring conformational fluctuations are determined as functions of flow strength and polymer concentration. Our results suggest that ring conformational fluctuations arise due to transient threading of linear polymers through open ring chains stretching in flow.