Microscopic Theory of Long-Time Center-of-Mass Self-Diffusion and Anomalous Transport in Ring Polymer Liquids

Unified understanding of the impact of semiflexibility, concentration, and molecular weight on macromolecular-scale ring diffusion

Conformationally fluctuating, globally compact macromolecules such as polymeric rings, single-chain nanoparticles, microgels, and many-arm stars display complex dynamic behaviors due to their rich topological structure and intermolecular organization. Synthetic rings are hybrid objects with conformations that display both ideal random walk and compact globular features, which can serve as models of genomic DNA. To date, emphasis has been placed on the effect of ring molecular weight on their unusual behaviors. Here, we combine simulations and a microscopic force-level theory to build a unified understanding for how key aspects of ring dynamics depend on different tunable molecular properties including backbone rigidity, monomer concentration, degree of traditional entanglement, and molecular weight. Our large-scale molecular dynamics simulations of ring melts with very different backbone stiffnesses reveal unanticipated behaviors which agree well with our generalized theory. This includes a universal master curve for center-of-mass diffusion constants as a function of molecular weight scaled by a chemistry and thermodynamic state-dependent critical molecular weight that generalizes the concept of an entanglement cross-over for linear chains. The key physics is how backbone rigidity and monomer concentration induced changes of the entanglement length, interring packing, degree of interpenetration, and liquid compressibility slow down space-time dynamic-force correlations on macromolecular scales. A power law decay of the center-of-mass diffusion constant with inverse molecular weight squared is the first consequence, followed by an ultraslow activated hopping transport regime. Our results set the stage to address slow dynamics and kinetic arrest in different families of compact synthetic and biological polymeric systems.

Unified Understanding of the Structure, Thermodynamics, and Diffusion of Single-Chain Nanoparticle Fluids

Single-chain nanoparticles (SCNPs) are a fascinating class of soft nano-objects with promising properties and relevance to protein condensates, polymer nanocomposites, nanomedicine, bioimaging, catalysis, and drug delivery. We combine molecular dynamics simulations and equilibrium and time-dependent statistical mechanical theory to construct a unified understanding of how the internal conformational structure of SCNPs, of both a simple fractal globule-like form and more complex objects with multiple internal intermediate length scales, determines nm-scale intermolecular packing correlations, thermodynamic properties, and center-of-mass diffusion over a wide range of concentrations up to dense melts. The intermolecular pair correlations generically exhibit a distinctive deep correlation hole form due to SCNP internal connectivity structure and repulsive interparticle interactions associated with a globular-like conformation on the macromolecular scale, with concentration-dependent deviations at small separations. Unanticipated exponential-like dependences of the equation-of-state, osmotic compressibility, and center-of-mass diffusion constant on SCNP macromolecular packing fraction are theoretically predicted and confirmed via simulations. System-specific behaviors are found associated with SCNP internal structure, but overarching regularities are identified and understood based on a generalized effective globule conformation on macromolecular scales. Diffusivity slows down by 2-3 decades with increasing concentration and is understood as a consequence of a nonactivated excluded volume-driven weak-caging process associated with space-time correlated intermolecular forces experienced by the SCNP. Good agreement between the theory and simulations is established, testable predictions are made, and a quantitative comparison with viscosity measurements on a specific SCNP fluid is carried out. The basic theoretical approach can potentially be extended to treat the chemical and physical consequences of varying the structure of other classes of soft nanoparticles with distinctive internal nanoscale organization relevant in nanotechnology and nanomedicine, and the possible emergence of macromolecular kinetically arrested glasses.

Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain

Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.

Theory of the center-of-mass diffusion and viscosity of microstructured and variable sequence copolymer liquids

Biomolecular condensates formed through the phase separation of proteins and nucleic acids are widely observed, offering a fundamental means of organizing intracellular materials in a membrane-less fashion. Traditionally, these condensates have been regarded as homogeneous isotropic liquids. However, in analogy with some synthetic copolymer systems, our recent theoretical research has demonstrated that model biomolecular condensates can exhibit a microemulsion-like internal structure, contingent upon the specific sequence, inter-chain site-site interactions, and concentrated phase polymer density. Motivated by these considerations, here we present a microscopic dynamical theory for the self-diffusion constant and viscosity of a simpler class of model systems - concentrated unentangled A/B regular multiblock copolymer solutions. Our approach integrates static equilibrium local and microdomain scale structural information obtained from PRISM integral equation theory and the time evolution of the autocorrelation function of monomer scale forces at the center-of-mass level to determine the polymer diffusion constant and viscosity in a weak caging regime far from a glass or gel transition. We focus on regular multi-block systems both for simplicity and for its relevance to synthetic macromolecular science. The impact of sequence and inter-chain attraction strength on the slowing down of copolymer mass transport and flow due to local clustering enhanced collisional friction and emergent microdomain scale ordering are established. Analytic analysis and metrics employed in the study of biomolecular condensates are employed to identify key order parameters that quantity how attractive forces, packing structure, multiblock sequence, and copolymer density determine dynamical slowing down above and below the crossover to a fluctuating polymeric microemulsion state.

Non-Rouse behavior of short ring polymers in melts by molecular dynamics simulations

Short ring polymers are expected to behave nearly Rouse-like due to the little effect of topological constraints of non-knot and non-concatenation. However, this notion is questioned because of several simulation and experiment findings in recent times, which requires a further more quantitative study. Therefore, we perform a deep investigation of statics and dynamics of flexible short ring polymers (N < 2Ne) in melts via molecular dynamics simulations by further taking linear analogues as well as all-crossing ring and linear polymers with switched off topological constraints for comparisons and demonstrate the noticeable deviations from the Rouse model in terms of local and global scales. Although the overall size is compact, the subchains are swollen, which is traced back to the deeper "segmental correlation hole" effect. The same scaling relationship of the non-Gaussian deviation of the static structure factor holds, but the deviation magnitude of rings is larger than that of linear analogues. By checking the non-Gaussian parameter and autocorrelation function of center-of-mass velocity, the physical origin of anomalous sub-diffusions of short rings is identified as unscreened viscoelastic hydrodynamic interactions and not correlation hole effects, like linear analogues.

Unexpected Slow Relaxation Dynamics in Pure Ring Polymers Arise from Intermolecular Interactions

Ring polymers have fascinated scientists for decades, but experimental progress has been challenging due to the presence of linear chain contaminants that fundamentally alter dynamics. In this work, we report the unexpected slow stress relaxation behavior of concentrated ring polymers that arises due to ring-ring interactions and ring packing structure. Topologically pure, high molecular weight ring polymers are prepared without linear chain contaminants using cyclic poly(phthalaldehyde) (cPPA), a metastable polymer chemistry that rapidly depolymerizes from free ends at ambient temperatures. Linear viscoelastic measurements of highly concentrated cPPA show slow, non-power-law stress relaxation dynamics despite the lack of linear chain contaminants. Experiments are complemented by molecular dynamics (MD) simulations of unprecedentedly high molecular weight rings, which clearly show non-power-law stress relaxation in good agreement with experiments. MD simulations reveal substantial ring-ring interpenetrations upon increasing ring molecular weight or local backbone stiffness, despite the global collapsed nature of single ring conformation. A recently proposed microscopic theory for unconcatenated rings provides a qualitative physical mechanism associated with the emergence of strong inter-ring caging which slows down center-of-mass diffusion and long wavelength intramolecular relaxation modes originating from ring-ring interpenetrations, governed by the onset variable N/ND, where the crossover degree of polymerization ND is qualitatively predicted by theory. Our work overcomes challenges in achieving ring polymer purity and by characterizing dynamics for high molecular weight ring polymers. Overall, these results provide a new understanding of ring polymer physics.

Local-Average Free Volume Correlates with Dynamics in Glass Formers

Glass formers exhibit a pronounced slowdown in dynamics, accompanied by progressive heterogeneity as they approach the glass transition. There is intense debate over whether the dramatic slowdown is caused by dynamical heterogeneity and whether the enhanced dynamical heterogeneity originates from structural causes. However, the connection between dynamical heterogeneity and the spatial distribution of the single-particle free volume (a purely static structural quantity) was found to be rather weak, which raises the question of whether dynamic heterogeneity has a purely structural origin. Here, by introducing the concept of local-average free volume, we present numerical evidence that long-time dynamic heterogeneity shows significantly enhanced correlation with the average local free volume over a length scale of a few neighboring shells. Our results resolve the long-standing controversy about whether free volume plays an important role in particle rearrangements associated with the activated hopping relaxation. The concept of "local average" can be applied to other local structural descriptors to better correlate with dynamic heterogeneity in glass-forming liquids.

Theory of Transient Localization, Activated Dynamics, and a Macromolecular Glass Transition in Ring Polymer Liquids

We construct a segmental scale force level theory for the center-of-mass diffusion constant and corresponding relaxation time for globally compact unconcatenated ring polymer solutions and melts (degree of polymerization N). The approach is based on slowly decaying macromolecular scale intermolecular force dynamic correlations as the origin of their unusual dynamics. Unentangled Rouse, weakly caged, and activated regimes are predicted. The barrier of the activated regime scales linearly with N and as a power law of concentration, which drives a kinetic glass transition on the radius-of-gyration scale. The values of N at the two dynamic crossovers (Rouse to weakly caged, weakly caged to activated) are proportional, with nonuniversality entering mainly via macromolecular volume fraction and dimensionless compressibility. Quantitative comparisons with simulation data reveal good agreement. Aspects of intermediate time dynamics are analyzed, and predictions are made for the conditions required to observe a macromolecular glass transition in the laboratory and on the computer.

Effects of chain length on Rouse modes and non-Gaussianity in linear and ring polymer melts

The dynamics of ring polymer melts are studied via molecular dynamics simulations of the Kremer-Grest bead-spring model. Rouse mode analysis is performed in comparison with linear polymers by changing the chain length. Rouse-like behavior is observed in ring polymers by quantifying the chain length dependence of the Rouse relaxation time, whereas a crossover from Rouse to reptation behavior is observed in linear polymers. Furthermore, the non-Gaussian parameters of the monomer bead displacement and chain center-of-mass displacement are analyzed. It is found that the non-Gaussianity of ring polymers is remarkably suppressed with slight growth for the center-of-mass dynamics at long chain length, which is in contrast to the growth in linear polymers for both the monomer bead and center-of-mass dynamics.

Theory of polymer diffusion in polymer-nanoparticle mixtures: effect of nanoparticle concentration and polymer length

The dynamics of polymer-nanoparticle (NP) mixtures, which involves multiple scales and system-specific variables, has posed a long-standing challenge on its theoretical description. In this paper, we construct a microscopic theory for polymer diffusion in mixtures based on a combination of the generalized Langevin equation, mode-coupling approach, and polymer physics ideas. The parameter-free theory has an explicit expression and remains tractable on a pair correlation level with system-specific equilibrium structures as input. Taking a minimal polymer-NP mixture as an example, our theory correctly captures the dependence of polymer diffusion on NP concentration and average interparticle distance. Importantly, the polymer diffusion exhibits a power law decay as the polymer length increases at dense NPs and/or a long chain, which marks the emergence of entanglement-like motion. The work provides a first-principles theoretical foundation to investigate dynamic problems in diverse polymer nanocomposites.

Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids

Ring polymers in dense solutions are among the most intriguing problems in polymer physics. Because of its natural occurrence in circular form, DNA has been extensively used as a proxy to study the fundamental physics of ring polymers in different topological states. Yet, torsionally constrained-such as supercoiled-topologies have been largely neglected so far. The applicability of existing theoretical models to dense supercoiled DNA is thus unknown. Here, we address this gap by coupling large-scale molecular dynamics simulations with differential dynamic microscopy of entangled supercoiled DNA plasmids. We find that, unexpectedly, larger supercoiling increases the size of entangled plasmids and concomitantly induces an enhancement in DNA mobility. These findings are reconciled as due to supercoiling-driven asymmetric and double-folded plasmid conformations that reduce interplasmid entanglements and threadings. Our results suggest a way to topologically tune DNA mobility via supercoiling, thus enabling topological control over the (micro)rheology of DNA-based complex fluids.