Compact structure and non-Gaussian dynamics of ring polymer melts

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.

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.

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.

Conformation of Network Strands in Polymer Gels

Small angle neutron scattering was used to measure single chain radii of gyration of end-linked polymer gels before and after cross-linking to calculate the prestrain, which is the ratio of the average chain size in a cross-linked network to that of a free chain in solution. The prestrain increased from 1.06 ± 0.01 to 1.16 ± 0.02 as gel synthesis concentration decreased near the overlap concentration, indicating that the chains are slightly more stretched in the network than in solution. Dilute gels with higher loop fractions were found to be spatially homogeneous. Form factor and volumetric scaling analyses independently confirmed that elastic strands stretch by 2-23% from Gaussian conformations to create a space-spanning network, with increased stretching as network synthesis concentration decreases. Prestrain measurements reported here serve as a point of reference for network theories that rely on this parameter for the calculation of mechanical properties.

Decoding polymer self-dynamics using a two-step approach

The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. We show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a "two-step" approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.

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.

Melt rheology of tadpole-shaped polystyrenes with different ring sizes

In this study, linear melt rheology of a single-tail tadpole-shaped polystyrene, ST-30/80, having ring and linear sizes of MR ∼ 30 kg mol-1 and ML ∼ 80 kg mol-1, respectively, was examined, and the effect of the ring size on rheological properties of tadpole polymers was discussed by comparing with the data of the previously reported tadpole samples having MR ∼ 60 kg mol-1. ST-30/80 exhibits an entanglement plateau and shows a clearly slower terminal relaxation than that of its component ring and linear polymers. When the zero-shear viscosity η0 for ST-30/80 is plotted against the molecular weight of a linear tail chain, the data point lies on the single curve of η0 for 4- and 6-arm star polymers and the single-tail tadpoles with MR ∼ 60 kg mol-1. These results suggest that the tadpole molecule in this study spontaneously forms a characteristic entanglement network, i.e., the intermolecular ring-linear threading, in the same manner as the previous tadpole samples, even though the size of the ring part is just slightly larger than the entanglement molecular weight (i.e., MR ∼ 1.8Me).

Local Effects of Ring Topology Observed in Polymer Conformation and Dynamics by Neutron Scattering-A Review

The physical properties of polymers depend on a range of both structural and chemical parameters, and in particular, on molecular topology. Apparently simple changes such as joining chains at a point to form stars or simply joining the two ends to form a ring can profoundly alter molecular conformation and dynamics, and hence properties. Cyclic polymers, as they do not have free ends, represent the simplest model system where reptation is completely suppressed. As a consequence, there exists a considerable literature and several reviews focused on high molecular weight cyclics where long range dynamics described by the reptation model comes into play. However, this is only one area of interest. Consideration of the conformation and dynamics of rings and chains, and of their mixtures, over molecular weights ranging from tens of repeat units up to and beyond the onset of entanglements and in both solution and melts has provided a rich literature for theory and simulation. Experimental work, particularly neutron scattering, has been limited by the difficulty of synthesizing well-characterized ring samples, and deuterated analogues. Here in the context of the broader literature we review investigations of local conformation and dynamics of linear and cyclic polymers, concentrating on poly(dimethyl siloxane) (PDMS) and covering a wide range of generally less high molar masses. Experimental data from small angle neutron scattering (SANS) and quasi-elastic neutron scattering (QENS), including Neutron Spin Echo (NSE), are compared to theory and computational predictions.

Dynamics of poly[n]catenane melts

Inspired by advances in the chemical synthesis of interlocking polymer architectures, extensive molecular dynamics simulations have been conducted to study the dynamical properties of poly[n]catenanes-polymers composed entirely of interlocking rings-in the melt state. Both the degree of polymerization (number of links) and the number of beads per ring are systematically varied, and the results are compared to linear and ring polymers. A simple Rouse-like model is presented, and its analytical solution suggests a decomposition of the dynamics into "ring-like" and "linear-like" regimes at short and long times, respectively. In agreement with this picture, multiple sub-diffusive regimes are observed in the monomer mean-squared-displacements even though interchain entanglement is not prevalent in the system. However, the Rouse-type model does not account for the topological effects of the mechanical bonds, which significantly alter the dynamics at intermediate length scales both within the rings and at the chain segment scales. The stress relaxation in the system is extremely rapid and may be conveniently separated into ring-like and linear-like contributions, again in agreement with the Rouse picture. However, the viscosity has a non-monotonic dependence on the ring size for long chains, which disagrees strongly with theoretical predictions. This unexpected observation cannot be explained in terms of chain disentanglement and is inconsistent with other measures of polymer relaxation. Possible mechanisms for this behavior are proposed and implications for materials design are discussed.

On the diffusivity of ring polymers

A free volume theory of linear polyethylene (PE) melts [Soft Matter, 2019, 15, 9300-9309] was used to describe the crossover in the size dependence of the center-of-mass diffusion coefficients of ring PE melts from Dcm ∼ N-1.03±0.15 to Dcm ∼ N-1.88±0.14 at Nc ≈ 100. Parameters in the theory were determined theoretically by either the polymer reference interaction site model (PRISM) theory or molecular dynamics (MD) simulation data. The former method is computationally less expensive, whereas the latter gives more accurate results in calculating the temperature dependence of Dcm as different intermolecular and intramolecular potentials were explicitly included in the equation of motion. Both approaches were able to describe the dynamics below and above the crossover in the size dependence of Dcm.

Threading of Unconcatenated Ring Polymers at High Concentrations: Double-Folded vs Time-Equilibrated Structures

Unconcatenated ring polymers in concentrated solutions and melt are remarkably well described as double-folded conformations on randomly branched primitive trees. This picture though contrasts recent evidence for extensive intermingling between close-by rings in the form of long-lived topological constraints or threadings. Here, we employ the concept of ring minimal surface to quantify the extent of threadings in polymer solutions of the double-folded rings vs rings in equilibrated molecular dynamics computer simulations. Our results show that the double-folded ring polymers are significantly less threaded compared to their counterparts at equilibrium. Second, threadings form through a slow process whose characteristic time-scale is of the same order of magnitude as that of the diffusion of the rings in solution. These findings are robust, being based on universal (model-independent) observables as the average fraction of threaded length or the total penetrations between close-by rings and the corresponding distribution functions.

Synthesis of macrocyclic poly(ethylene oxide)s containing a protected thiol group: a strategy for decorating gold surfaces with ring polymers

Macrocyclic poly(ethylene oxide)s containing a protected thiol group are able to attach to gold substrates without thiol deprotection enabling surface modification.

Intermolecular structural correlations in model globular and unconcatenated ring polymer liquids

We employ the field theoretic polymer integral equation theory to construct a segment-level theory for the thermodynamics and pair structure of dense liquids of interpenetrating ring polymers and a simple globule model. The latter is defined by a fractal mass distribution on all internal length scales with an exponent equal to the spatial dimension (dF = ds = 3). In an isochoric ensemble the dimensionless compressibility and pressure is predicted to vary exponentially with macromolecular volume fraction. An intermolecular correlation hole exists down to small length scales. This model appears to be useful for a recently studied experimental soft nanoparticle suspension, and also serves as a reference system for our analysis of ring liquids. Motivated by simulations, a two-fractal exponent ring model is adopted for the intramolecular structure factor. At smaller lengths it describes chain-like macromolecules, while on larger scales it corresponds to a space-filling object in the sense that dF = ds = 3. The crossover between these two regimes is of order the entanglement length of the linear chain analog. Based on a constant compressibility ensemble, the effective volume fraction grows at intermediate values of degree of polymerization (N), and crosses over to a very slow logarithmic growth at large N. A weaker intermolecular correlation hole is predicted. The number of nearest neighbor rings increases dramatically at small N, akin to linear chain melts, but then tends to saturate at large N, in accord with simulations. The tools developed may be relevant for other partially interpenetrating soft objects such as core-shell nanogels or microgels.

Topological free volume and quasi-glassy dynamics in the melt of ring polymers

Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first construct a phenomenological free energy which enables one to quantify the degree of topological crowding measured by the coordination number. Then we pinpoint a key role of the cooperative dynamics of neighboring rings, which is responsible for an anomalous dependence of the global structural relaxation (diffusion) time on ring length. Predictions on molecular weight dependence of both static (ring size, coordination number) and dynamic (relaxation time, diffusion coefficient) quantities are in very good agreement with reported numerical simulations. Throughout the discussion, the entanglement length Ne is assumed to be a unique characteristic length for the topological constraint, and hence, all the physical quantities are universally described in terms of the rescaled chain length N/Ne. Finally, we discuss how the dense solution of rings is analogous to yet different from ordinary glassy systems.

Viscoelastic Properties of Unentangled Multicyclic Polystyrenes

We report on the viscoelastic properties of linear, monocyclic, and multicyclic polystyrenes with the same low molecular weight. All polymers investigated were found to exhibit unentangled dynamics. For monocyclic polymers without inner loops, a cyclic-Rouse model complemented by the contribution of unlinked chains (whose fraction was determined experimentally) captured the observed rheological response. On the other hand, multicyclic polymers with inner loops were shown to follow a hierarchical cyclic-Rouse relaxation with the outer loops relaxing first, followed by the inner loop relaxation. The influence of unlinked linear chains was less significant in multicyclic polymers with inner loops. The isofrictional zero-shear viscosity decreased with increasing number of constrained segments on the coupling sites, which was attributed to the decreasing loop size and the dilution effect due to the hierarchical relaxation.

Scaling Laws for the Conformation and Viscosity of Ring Polymers in the Crossover Region around Me from Detailed Molecular Dynamics Simulations

We present results from detailed, atomistic molecular dynamics (MD) simulations of pure, strictly monodisperse linear and ring poly(ethylene oxide) (PEO) melts under equilibrium and nonequilibrium (shear flow) conditions. The systems examined span the regime of molecular weights (M_w) from sub-Rouse (M_w < M_e) to reptation (M_w ∼ 10 M_e), where M_e denotes the characteristic entanglement molecular weight of linear PEO. For both PEO architectures (ring and linear), the predicted chain center-of-mass self-diffusion coefficients D_G as a function of PEO M_w are in remarkable agreement with experimental data. From the flow simulations under shear, we have extracted and analyzed the zero-shear viscosity of ring and linear PEO melts as a function of M_w.

Glassiness and Heterogeneous Dynamics in Dense Solutions of Ring Polymers

Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and, yet, they display a large number of topological constraints. To understand their role, here we systematically probe the response of solutions of rings at various densities to "random pinning" perturbations. We show that these perturbations trigger non-Gaussian and heterogeneous dynamics, eventually leading to nonergodic and glassy behavior. We then derive universal scaling relations for the values of solution density and polymer length marking the onset of vitrification in unperturbed solutions. Finally, we directly connect the heterogeneous dynamics of the rings with their spatial organization and mutual interpenetration. Our results suggest that deviations from the typical behavior observed in systems of linear polymers may originate from architecture-specific (threading) topological constraints.

On the tree-like structure of rings in dense solutions

One of the most challenging problems in polymer physics is providing a theoretical description for the behaviour of rings in dense solutions and melts. Although it is nowadays well established that the overall size of a ring in these conditions scales like that of a collapsed globule, there is compelling evidence that rings may exhibit ramified and tree-like conformations. In this work I show how to characterise these local tree-like structures by measuring the local writhing of the rings' segments and by identifying the patterns of intra-chain contacts. These quantities reveal two major topological structures: loops and terminal branches which strongly suggest that the strictly double-folded "lattice animal" picture for rings in the melt may be replaced by a more relaxed tree-like structure accommodating loops. In particular, I show that one can identify hierarchically looped structures whose degree increases linearly with the size of a ring, and that terminal branches are found to store about 30% of the whole ring mass, irrespectively of its length. Finally, I draw an analogy between rings in the melt and slip-linked chains, where contact points are enforced by mobile slip-links and for which a field-theoretic treatment can be employed to get some insight into their typical conformations. These findings are ultimately discussed in the light of recent works on the static structure of rings and on the existence of inter-ring threadings.

DNA as a Model for Probing Polymer Entanglements: Circular Polymers and Non-Classical Dynamics

Double-stranded DNA offers a robust platform for investigating fundamental questions regarding the dynamics of entangled polymer solutions. The exceptional monodispersity and multiple naturally occurring topologies of DNA, as well as a wide range of tunable lengths and concentrations that encompass the entanglement regime, enable direct testing of molecular-level entanglement theories and corresponding scaling laws. DNA is also amenable to a wide range of techniques from passive to nonlinear measurements and from single-molecule to bulk macroscopic experiments. Over the past two decades, researchers have developed methods to directly visualize and manipulate single entangled DNA molecules in steady-state and stressed conditions using fluorescence microscopy, particle tracking and optical tweezers. Developments in microfluidics, microrheology and bulk rheology have also enabled characterization of the viscoelastic response of entangled DNA from molecular levels to macroscopic scales and over timescales that span from linear to nonlinear regimes. Experiments using DNA have uniquely elucidated the debated entanglement properties of circular polymers and blends of linear and circular polymers. Experiments have also revealed important lengthscale and timescale dependent entanglement dynamics not predicted by classical tube models, both validating and refuting new proposed extensions and alternatives to tube theory and motivating further theoretical work to describe the rich dynamics exhibited in entangled polymer systems.

Microscopic Dynamics and Topology of Polymer Rings Immersed in a Host Matrix of Longer Linear Polymers: Results from a Detailed Molecular Dynamics Simulation Study and Comparison with Experimental Data

We have performed molecular dynamics (MD) simulations of melt systems consisting of a small number of long ring poly(ethylene oxide) (PEO) probes immersed in a host matrix of linear PEO chains and have studied their microscopic dynamics and topology as a function of the molecular length of the host linear chains. Consistent with a recent neutron spin echo spectroscopy study (Goossen et al., Phys. Rev. Lett. 2015, 115, 148302), we have observed that the segmental dynamics of the probe ring molecules is controlled by the length of the host linear chains. In matrices of short, unentangled linear chains, the ring probes exhibit a Rouse-like dynamics, and the spectra of their dynamic structure factor resemble those in their own melt. In striking contrast, in matrices of long, entangled linear chains, their dynamics is drastically altered. The corresponding dynamic structure factor spectra exhibit a steep initial decay up to times on the order of the entanglement time τe of linear PEO at the same temperature but then they become practically time-independent approaching plateau values. The plateau values are different for different wavevectors; they also depend on the length of the host linear chains. Our results are supported by a geometric analysis of topological interactions, which reveals significant threading of all ring molecules by the linear chains. In most cases, each ring is simultaneously threaded by several linear chains. As a result, its dynamics at times longer than a few τe should be completely dictated by the release of the topological restrictions imposed by these threadings (interpenetrations). Our topological analysis did not indicate any effect of the few ring probes on the statistical properties of the network of primitive paths of the host linear chains.

Minimal Surfaces on Unconcatenated Polymer Rings in Melt

In order to quantify the effect of mutual threading on conformations and dynamics of unconcatenated and unknotted rings in the melt we computationally examine their minimal surfaces. We found a linear scaling of the surface area with the ring length. Minimal surfaces allow for an unambiguous algorithmic definition of mutual threading between rings. Based on it, we found that, although ring threading is frequent, majority of cases correspond to short loops. These findings explain why approximate theories that neglect threading are so unexpectedly successful despite having no small parameter justification. We also examine threading dynamics and identify the threading order parameter that reflects the ring diffusivity.

A topologically driven glass in ring polymers

The static and dynamic properties of ring polymers in concentrated solutions remains one of the last deep unsolved questions in polymer physics. At the same time, the nature of the glass transition in polymeric systems is also not well understood. In this work, we study a novel glass transition in systems made of circular polymers by exploiting the topological constraints that are conjectured to populate concentrated solutions of rings. We show that such rings strongly interpenetrate through one another, generating an extensive network of topological interactions that dramatically affects their dynamics. We show that a kinetically arrested state can be induced by randomly pinning a small fraction of the rings. This occurs well above the classical glass transition temperature at which microscopic mobility is lost. Our work both demonstrates the existence of long-lived inter-ring penetrations and realizes a novel, topologically induced, glass transition.

Celebrating Soft Matter's 10th Anniversary: Topology matters: structure and dynamics of ring polymers

Considering topology among all polymer architectures polymer rings are unique, as they are the simplest closed structures without ends. In this review we present recent experimental advances addressing the structure and dynamics of rings. We focus mainly on neutron scattering results that reveal experimental insight on a molecular scale. We first briefly reflect on the progress in ring chemistry that made the experimental access possible. Structural investigations characterizing rings as compact objects in the melts are put into theoretical context. In contrast to the plateau regime common for all other high molecular weight polymer systems, the dynamic modulus of pure ring systems is characterized by a power law decay, while the viscosity displays a much weaker molecular weight dependence as a corresponding linear melt. The dynamics of ring melts is uniquely addressed by neutron spin-echo spectroscopy. The sub-diffusive center of mass motion at short times agrees well with simulation as well as theoretical concepts. In the internal dynamics the basic length scale of the ring molecule, the loop size, manifests itself clearly. The experiments reveal strong evidence for loop motions and call for further theoretical work describing them. Finally, small fractions of ring molecules in linear melts turn out to be very sensitive probes in order to scrutinize the dynamics of the host with the potential to reveal fundamental aspects of the dynamics of branched polymer systems.

Sensing Polymer Chain Dynamics through Ring Topology: A Neutron Spin Echo Study

Using neutron spin echo spectroscopy, we show that the segmental dynamics of polymer rings immersed in linear chains is completely controlled by the host. This transforms rings into ideal probes for studying the entanglement dynamics of the embedding matrix. As a consequence of the unique ring topology, in long chain matrices the entanglement spacing is directly revealed, unaffected by local reptation of the host molecules beyond this distance. In shorter entangled matrices, where in the time frame of the experiment secondary effects such as contour length fluctuations or constraint release could play a role, the ring motion reveals that the contour length fluctuation is weaker than assumed in state-of-the-art rheology and that the constraint release is negligible. We expect that rings, as topological probes, will also grant direct access to molecular aspects of polymer motion which have been inaccessible until now within chains adhering to more complex architectures.

Segregated structures of ring polymer melts near the surface: a molecular dynamics simulation study

We study structural properties of a ring polymeric melt confined in a film in comparison to a linear counterpart using molecular dynamics simulations. Local structure orderings of ring and linear polymers in the vicinity of the surface are similar to each other because the length scale of surface-monomer excluded volume interactions is smaller than the size of an ideal blob of the ring. In a long length scale, while the Silberberg hypothesis can be used to provide the physical origin of the confined linear polymer results, it no longer holds for the ring polymer case. We also present different structural properties of ring and linear polymers in a melt, including the size of polymers, the adsorbed amount, and the coordination number of a polymer. Our observation reveals that a confined ring in a melt adopts a highly segregated conformation due to a topological excluded volume repulsion, which may provide a new perspective to understand the nature of biological processes, such as territorial segregation of chromosomes in eukaryotic nuclei.

Influence of the Solvent Quality on Ring Polymer Dimensions

We present a systematic investigation of well-characterized, experimentally pure polystyrene (PS) rings with molar mass of 161 000 g/mol in dilute solutions. We measure the ring form factor at θ- and good-solvent conditions as well as in a polymeric solvent (linear PS of roughly comparable molar mass) by means of small-angle neutron scattering (SANS). Additional dynamic light scattering (DLS) measurements support the SANS data and help elucidate the role of solvent quality and solution preparation. The results indicate the increase of ring dimensions as the solvent quality improves. Furthermore, the experimental form factors in both θ-solvent and linear matrix behave as ideal rings and are fully superimposable. The nearly Gaussian conformations of rings in a melt of linear chains provide evidence of threading of linear chains through rings. The latter result has implications for the dynamics of ring-linear polymer mixtures.

Molecular scale dynamics of large ring polymers

We present neutron scattering data on the structure and dynamics of melts from polyethylene oxide rings with molecular weights up to ten times the entanglement mass of the linear counterpart. The data reveal a very compact conformation displaying a structure approaching a mass fractal, as hypothesized by recent simulation work. The dynamics is characterized by a fast Rouse relaxation of subunits (loops) and a slower dynamics displaying a lattice animal-like loop displacement. The loop size is an intrinsic property of the ring architecture and is independent of molecular weight. This is the first experimental observation of the space-time evolution of segmental motion in ring polymers illustrating the dynamic consequences of their topology that is unique among all polymeric systems of any other known architecture.

Mechanochemistry of Topological Complex Polymer Systems

Although existing since the concept of macromolecules, polymer mechanochemistry is a burgeoning field which attracts great scientific interest in its ability to bias conventional reaction pathways and its potential to fabricate mechanoresponsive materials. We review here the effect of topology on the mechanical degradation of polymer chains and the activation of mechanophores in polymer backbones. The chapter focuses on both experimental and theoretical work carried out in the past 70 years. After a general introduction (Sect. 1), where the concept, the history, and the application of polymer mechanochemistry are briefly described, flow fields to study polymer mechanochemistry are discussed (Sect. 2), results of mechanochemistry study are presented for linear polymers (Sect. 3), cyclic polymers (Sect. 4), graft polymers (Sect. 5), star-shaped polymers (Sect. 6), hyperbranched polymers and dendrimers (Sect. 7), and systems with dynamic topology (Sect. 8). Here we focus on (1) experimental results involving the topological effect on the coil-to-stretch transition and the fracture of the polymer chains, (2) the underlying mechanisms and the key factor that determines the mechanical stability of the macromolecules, (3) theoretical models that relate to the experimental observations, and (4) rational design of mechanophores in complex topology to achieve multiple activations according to the existing results observed in chain degradation.