Thermodynamics and Structure of Poly[n]catenane Melts

Shape and size tunability of sheets of interlocked ring copolymers

Mechanically bonded membranes of interlocked ring polymers are a significant generalization of conventional elastic sheets, where connectivity is provided by covalent bonding, and represent a promising class of topological meta-materials. In this context, two open questions regard the large-scale reverberations of the heterogeneous composition of the rings and the inequivalent modes of interlocking neighboring rings. We address these questions with Langevin dynamics simulations of chainmails with honeycomb-lattice connectivity, where the rings are block copolymers with two segments of different rigidity. We considered various combinations of the relative lengths of the two segments and the patterns of the over- and under-passes linking neighboring rings. We find that varying ring composition and linking patterns have independent and complementary effects. While the former sets the overall size of the chainmail, the latter defines the shape, enabling the selection of starkly different conformation types. Notably, one of the considered linking patterns favors saddle-shaped membranes, providing a first example of spontaneous negative Gaussian curvature in mechanically bonded sheets. The results help establish the extent to which mechanically bonded membranes can differ from conventional elastic ones, particularly for the achievable shape and size tunability.

Polycatenanes Formed of Self-Assembled Metal-Organic Cages

Poly-[n]-catenanes (PCs) self-assembled of three-dimensional (3D) metal organic cages (MOCs) (hereafter referred to as PCs-MOCs) are a relatively new class of mechanically interlocked molecules (MIMs) that combine the properties of MOCs and polymers. The synthesis of PCs-MOCs is challenging because of the difficulties associated with interlocking MOCs, the occurrence of multiple weak supramolecular electrostatic interactions between cages, and the importance of solvent templating effects. The high density of mechanical bonds interlocking the MOCs endows the MOCs with mechanical and physical properties such as enhanced stability, responsive dynamic behavior and low solubility, which can unlock new functional properties. In this Minireview, we highlight the benefit of interlocking MOCs in the formation of PCs-MOCs structures as well as the synthetic approaches exploited in their preparation, from thermodynamic to kinetic methods, both in the solution and solid-states. Examples of PCs-MOCs self-assembled from various types of nanosized cages (i.e., tetrahedral, trigonal prismatic, octahedral and icosahedral) are described in this article, providing an overview of the research carried out in this area. The focus is on the structure-property relationship with examples of functional applications such as electron conductivity, X-ray attenuation, gas adsorption and molecular sensing. We believe that the structural and functional aspects of the reviewed PCs-MOCs will attract chemists in this research field with great potential as new functional materials in nanotechnological disciplines such as gas adsorption, sensing and photophysical properties such as X-ray attenuation or electron conductivity.

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.

Effects of Linking Topology on the Shear Response of Connected Ring Polymers: Catenanes and Bonded Rings Flow Differently

We perform computer simulations of mechanically linked (poly[2]catenanes, PC) and chemically bonded (bonded rings, BR) pairs of self-avoiding ring polymers in steady shear. We find that BRs develop a novel motif, termed gradient tumbling, rotating around the gradient axis. For the PCs the rings are stretched and display another new pattern, termed slip tumbling. The dynamics of BRs is continuous and oscillatory, whereas that of PCs is intermittent between slip-tumbling attempts. Our findings demonstrate the interplay between topology and hydrodynamics in dilute solutions of connected polymers.

Single-molecule analysis of solvent-responsive mechanically interlocked ring polymers and the effects of nanoconfinement from coarse-grained simulations

In this study, we simulate mechanically interlocked semiflexible ring polymers inspired by the minicircles of kinetoplast DNA (kDNA) networks. Using coarse-grained molecular dynamics simulations, we investigate the impact of molecular topological linkage and nanoconfinement on the conformational properties of two- and three-ring polymer systems in varying solvent qualities. Under good-quality solvents, for two-ring systems, a higher number of crossing points lead to a more internally constrained structure, reducing their mean radius of gyration. In contrast, three-ring systems, which all had the same crossing number, exhibited more similar sizes. In unfavorable solvents, structures collapse, forming compact configurations with increased contacts. The morphological diversity of structures primarily arises from topological linkage rather than the number of rings. In three-ring systems with different topological conformations, structural uniformity varies based on link types. Extreme confinement induces isotropic and extended conformations for catenated polymers, aligning with experimental results for kDNA networks and influencing the crossing number and overall shape. Finally, the flat-to-collapse transition in extreme confinement occurs earlier (at relatively better solvent conditions) compared to non-confined systems. This study offers valuable insights into the conformational behavior of mechanically interlocked ring polymers, highlighting challenges in extrapolating single-molecule analyses to larger networks such as kDNA.

Structure and dynamics of double-stranded DNA rotaxanes

A DNA rotaxane, with its unique mechanically interlocked architecture consisting of a circular DNA molecule threaded onto a linear DNA axle, holds promise as a fundamental component for nanoscale functional devices. Nevertheless, its structural and dynamic behaviors, essential for advancing molecular machinery, remain largely unexplored. Using extensive all-atom molecular dynamics simulations, we investigated the behaviors of double-stranded DNA (dsDNA) rotaxanes, concentrating on the effects of shape distortion induced by torsional stress in small circular dsDNA containing 70-90 base pairs. We analyzed structural characteristics, including shape, intermolecular distances, and tilt angles, while also exploring dynamic properties such as translational diffusion and toroidal rotation. Our results indicate that shape distortion brings the circular and linear dsDNA components into closer proximity and causes a slight increase in translational diffusion yet a minor decrease in toroidal rotation. Nevertheless, there is no apparent evidence of coupling between translation and rotation. Overall, the insights from this study indicate that such shape distortion does not significantly alter their structure and dynamics. This finding provides flexibility for the design of DNA rotaxanes in nanoscale applications.

A thermally driven rotaxane-catenane interconversion with a dynamic bis(hindered amino) disulfide

We have developed a versatile and simple synthetic method to produce a [3]catenane. Heating a rotaxane with bis(hindered amino) disulfide groups at both ends spontaneously and selectively produces the [3]catenane. The successful polymerization of the obtained [3]catenane provides a platform for the synthesis of various interlocking polymers.

Sliding Dynamics of a Small Charged Ring Chain on the Diblock Polyelectrolyte in Poly[2]catenane in the Presence of Counterions

In this study, we investigate the sliding dynamics of small charged ring chains along the rigid central cyclic diblock polyelectrolyte of AnBn in radial charged poly[2]catenane in the presence of counterions using molecular dynamics simulations and the Lifson-Jackson formula, and our aim is to study the effects of electrostatical interaction strength, the size of the charged small ring chain, and the rigid block length of the diblock polyelectrolyte on the sliding dynamics of a small ring chain threaded on the rigid diblock polyelectrolyte. The mean-square displacement g3(t) of a small ring chain sliding along the rigid diblock polyelectrolyte of A10B10 exhibits oscillating behavior at short time scales for the moderate electrostatical interaction strength, while for the weak or strong electrostatic interactions, it is normal subdiffusion at short time scales. For n = 1, the diffusion coefficient D of the small ring chain sliding along the rigid diblock polyelectrolyte of A1B1 decreases monotonically as the relative electrostatic interaction strength A increases from A = 0.25-4. However, for n ≠ 1, the diffusion coefficient D of the small ring chain sliding along the rigid diblock polyelectrolyte of AnBn first decreases and then increases with the increase of A, and the nonmonotonous relationship between D and A becomes more obvious for larger n. In view of the free energy potential, the sliding diffusion of a small ring chain is governed by both the width of the free energy potential well and the height of the free energy potential barrier. According to the potential of mean force (PMF) of the small ring chain sliding along the rigid diblock polyelectrolyte, we find that our results are in good agreement with the theoretical analysis using the Lifson-Jackson formula. These results may help us to understand the diffusion motion of a ring chain in radial poly[n]catenanes from a fundamental point of view and control the sliding dynamics in molecular designs.

Mixing Linear Polymers with Rings and Catenanes: Bulk and Interfacial Behavior

We derive and parameterize effective interaction potentials between a multitude of different types of ring polymers and linear chains, varying the bending rigidity and solvent quality for the former species. We further develop and apply a density functional treatment for mixtures of both disconnected (chain-ring) and connected (chain-polycatenane) mixtures of the same, drawing coexistence binodals and exploring the ensuing response functions as well as the interface and wetting behavior of the mixtures. We show that worsening of the solvent quality for the rings brings about a stronger propensity for macroscopic phase separation in the linear-polycatenane mixtures, which is predominantly of the demixing type between phases of similar overall particle density. We formulate a simple criterion based on the effective interactions, allowing us to determine whether any specific linear-ring mixture will undergo a demixing phase separation.

Spatial Organization of Slit-Confined Melts of Ring Polymers with Nonconserved Topology: A Lattice Monte Carlo Study

We present Monte Carlo computer simulations for melts of semiflexible randomly knotted and randomly concatenated ring polymers on the fcc lattice and in slit confinement. Through systematic variation of the slit width at fixed melt density, we explore the influence of confinement on single-chain conformations and interchain interactions. We demonstrate that confinement makes chains globally larger and more elongated while enhancing both contacts and knottedness propensities. As for multichain properties, we show that ring-ring contacts decrease with the confinement, yet neighboring rings overlap more as confinement grows. These aspects are accompanied by a marked decrease in the links formed between pairs of neighboring rings. In connection with the quantitative relation between links and entanglements in polymer melts recently established by us [Ubertini M. A.; Rosa A.Macromolecules2023, 56, 3354-3362], we propose that confinement can be used to set polymer networks that act softer under mechanical stress and suggest a viable experimental setup to validate our results.

Topological Entanglement of Linear Catenanes: Knots and Threadings

We used molecular dynamics simulations to investigate the self-entanglements of the collapsed linear catenanes. We found two different types of topologically complex states. First, we observed numerous long-lived knotting events of the catenane backbone. However, comparison with conventional polymers reveals that knots are suppressed in catenanes. Next, we observed topologically complex states with no analogue in polymers, where a concatenated ring was threaded by other near or distal rings sliding through it. Differently from knots, these threaded states can disentangle by becoming fully tightened. A detailed thermodynamic and microscopic analysis is employed to rationalize the persistence of threaded states, which can survive significant internal reorganizations of the entire catenane. We finally discuss the broader implications of these previously unreported types of entanglements for other systems, such as noncollapsed and interacting catenanes.

Structure and Thermodynamics of Linear, Ring, and Catenane Polymers in Solutions and at Liquid-Liquid Interfaces

In recent decades, advances in the syntheses of mechanically interlocked macromolecules, such as catenanes, have led to much greater interest in the applications of these complexes, from molecular motors and actuators to nanoscale computational memory and nanoswitches. Much remains to be understood, however, regarding how catenated ring compounds behave as a result of the effects of different solvents as well as the effects of solvent/solvent interfaces. In this work, we have investigated, using molecular dynamics simulations, the effects of solvation of poly(ethylene oxide) chains of different topologies─linear, ring, and [2]catenane─in two solvents both considered favorable toward PEO (water, toluene) and at the water/toluene interface. Compared to ring and [2]catenane molecules, the linear PEO chain showed the largest increase in size at the water/toluene interface compared to bulk water or bulk toluene. Perhaps surprisingly, observations indicate that the tendency of all three topologies to extend at the water/toluene interface may have more to do with screening the interaction between the two solvents than with optimizing specific solvent-polymer contacts.

The effect of thread-like monomer structure on the synthesis of poly[n]catenanes from metallosupramolecular polymers

The main-chain poly[n]catenane consists of a series of interlocked rings that resemble a macroscopic chain-link structure. Recently, the synthesis of such intriguing polymers was reported via a metallosupramolecular polymer (MSP) template that consists of alternating units of macrocyclic and linear thread-like monomers. Ring closure of the thread components has been shown to yield a mixture of cyclic, linear, and branched poly[n]catenanes. Reported herein are studies aimed at accessing new poly[n]catenanes via this approach and exploring the effect the thread-like monomer structure has on the poly[n]catenane synthesis. Specifically, the effect of the size of the aromatic linker and alkenyl chains of the thread-like monomer is investigated. Three new poly[n]catenanes (with different ring sizes) were prepared using the MSP approach and the results show that tailoring the structure of the thread-like monomer can allow the selective synthesis of branched poly[n]catenanes.

Polycatenanes: synthesis, characterization, and physical understanding

Chemical composition and architecture are two key factors that control the physical and material properties of polymers. Some of the more unusual and intriguing polymer architectures are the polycatenanes, which are a class of polymers that contain mechanically interlocked rings. Since the development of high yielding synthetic routes to catenanes, there has been an interest in accessing their polymeric counterparts, primarily on account of the unique conformations and degrees of freedom offered by non-bonded interlocked rings. This has lead to the synthesis of a wide variety of polycatenane architectures and to studies aimed at developing structure-property relationships of these interesting materials. In this review, we provide an overview of the field of polycatenanes, exploring synthesis, architecture, properties, simulation, and modelling, with a specific focus on some of the more recent developments.

Distinctive features and challenges in catenane chemistry

From being an aesthetic molecular object to a building block for the construction of molecular machines, catenanes and related mechanically interlocked molecules (MIMs) continue to attract immense interest in many research areas. Catenane chemistry is closely tied to that of rotaxanes and knots, and involves concepts like mechanical bonds, chemical topology and co-conformation that are unique to these molecules. Yet, because of their different topological structures and mechanical bond properties, there are some fundamental differences between the chemistry of catenanes and that of rotaxanes and knots although the boundary is sometimes blurred. Clearly distinguishing these differences, in aspects of bonding, structure, synthesis and properties, between catenanes and other MIMs is therefore of fundamental importance to understand their chemistry and explore the new opportunities from mechanical bonds.

Flatness and intrinsic curvature of linked-ring membranes

Recent experiments have elucidated the physical properties of kinetoplasts, which are chain-mail-like structures found in the mitochondria of trypanosome parasites formed from catenated DNA rings. Inspired by these studies, we use Monte Carlo simulations to examine the behavior of two-dimensional networks ("membranes") of linked rings. For simplicity, we consider only identical rings that are circular and rigid and that form networks with a regular linking structure. We find that the scaling of the eigenvalues of the shape tensor with membrane size are consistent with the behavior of the flat phase observed in self-avoiding covalent membranes. Increasing ring thickness tends to swell the membrane. Remarkably, unlike covalent membranes, the linked-ring membranes tend to form concave structures with an intrinsic curvature of entropic origin associated with local excluded-volume interactions. The degree of concavity increases with increasing ring thickness and is also affected by the type of linking network. The relevance of the properties of linked-ring model membranes to those observed in kinetoplasts is discussed.

Topological and physical links in soft matter systems

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.

Complementarity of 2,6-Dimethanolpyridine and Di(ethylene glycol) in the Complexation of Na+ Ions: Attaching Multiple Copies of [2]Catenane Branches to Isophthalaldehyde-Containing Cores

In this study we found that 2,6-dimethanolpyridine displays good complementarity toward di(ethylene glycol) for the complexation of Na⁺ ions, allowing us to use this recognition system for the efficient synthesis of hetero[2]catenanes; indeed, it allowed us to attach multiple copies of [2]catenanes to branched systems presenting multiple isophthalaldehyde units. When we attempted to form a catenane from a preformed macrocycle featuring only a single di(ethylene glycol) unit, reacting it with a di(ethylene glycol) derivative presenting two amino termini, isophthalaldehyde, and templating Na⁺ ions [i.e., with the aim of using di(ethylene glycol)·Na⁺·di(ethylene glycol) recognition to template the formation of the interlocked imino macrocycle], the yields of the hetero[2]catenane and homo[2]catenane, comprising two imino macrocyclic units, were both poor (14% and 7%, respectively). In contrast, when one or two 2,6-dimethanolpyridine units were present in the preformed macrocycles, their reactions with the same diamine, dialdehyde, and Na⁺ ions provided the hetero[2]catenanes with high selectivity and efficiency (44% and 64% yields, respectively), with minimal formation of the competing homo[2]catenane. The high complementary of the 2,6-dimethanolpyridine·Na⁺·di(ethylene glycol) ligand pair allowed us to synthesize [2]catenane dimers and trimers directly from corresponding isophthalaldehyde-presenting cores, with yields, after subsequent reduction and methylation, of 42% and 31%, respectively.

Double Asymptotic Structures of Topologically Interlocked Molecules

The mean square size of topologically interlocked molecules (TIMs) is presented as a linear combination of contributions from the backbone and subcomponents. Using scaling analyses and extensive molecular dynamics simulations of polycatenanes as a typical example of TIMs, we show that the effective exponent ν(m) for the size dependence of the backbone on the monomer number of subcomponent m is asymptotic to a value ν (∼0.588 in good solvents) with a correction of m^-0.47, which is the same as for the covalently linked polymer. However, the effective exponent for the size dependence of subcomponents on m is asymptotic to the same value ν but with a new correction of m^-1.0. The different corrections to the scaling on the backbone and subcomponent structure induce a surprising double asymptotic behavior for the architecture of the TIMs. The scaling model that takes into account the double asymptotic behavior is in good quantitative agreement with the simulation result that the effective exponent for the size dependence of TIMs on m increases with the subcomponent number n. The full scaling functional form of the size dependence on m and n for polycatenanes in a good solvent is well described by a simple sum of two limiting behaviors with different corrections.

Effect of metallosupramolecular polymer concentration on the synthesis of poly[n]catenanes

Poly[n]catenanes are a class of polymers that are composed entirely of interlocked rings. One synthetic route to these polymers involves the formation of a metallosupramolecular polymer (MSP) that consists of alternating units of macrocyclic and linear thread components. Ring closure of the thread components has been shown to yield a mixture of cyclic, linear, and branched poly[n]catenanes. Reported herein are investigations into this synthetic methodology, with a focus on a more detailed understanding of the crude product distribution and how the concentration of the MSP during the ring closing reaction impacts the resulting poly[n]catenanes. In addition to a better understanding of the molecular products obtained in these reactions, the results show that the concentration of the reaction can be used to tune the size and type of poly[n]catenanes accessed. At low concentrations the interlocked product distribution is limited to primarily oligomeric and small cyclic catenanes . However, the same reaction at increased concentration can yield branched poly[n]catenanes with an ca. 21 kg mol-1, with evidence of structures containing as many as 640 interlocked rings (1000 kg mol-1).

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.

Sliding dynamics of multi-rings on a semiflexible polymer in poly[n]catenanes

The sliding dynamics of one- or multi-ring structures along a semiflexible cyclic polymer in radial poly[n]catenanes is investigated using molecular dynamics simulations. The fixed and fluctuating (non-fixed) semiflexible central cyclic polymers are considered, respectively. With increasing bending energy of the central cyclic polymer, for the fixed case, the diffusion coefficient increases monotonically due to the reduction of the tortuous sliding path, while for the fluctuating case, the diffusion coefficient decreases. This indicates that the contribution of the polymer fluctuation is suppressed by a further increase in the stiffness of the central cyclic chain. Compared with the one ring case, the mean-square displacement of the multiple rings exhibits a unique sub-diffusive behavior at intermediate time scales due to the repulsion between two neighboring rings. In addition, for the multi-ring system, the whole set of rings exhibit relatively slower diffusion, but faster local dynamics of threading rings and rotational diffusion of the central cyclic polymer arise. These results may help us to understand the diffusion motion of rings in radial poly[n]catenanes from a fundamental point of view and control the sliding dynamics in molecular designs.

The influence of arm composition on the self-assembly of low-functionality telechelic star polymers in dilute solutions

We combine synthesis, physical experiments, and computer simulations to investigate self-assembly patterns of low-functionality telechelic star polymers (TSPs) in dilute solutions. In particular, in this work, we focus on the effect of the arm composition and length on the static and dynamic properties of TSPs, whose terminal blocks are subject to worsening solvent quality upon reducing the temperature. We find two populations, single stars and clusters, that emerge upon worsening the solvent quality of the outer block. For both types of populations, their spatial extent decreases with temperature, with the specific details (such as temperature at which the minimal size is reached) depending on the coupling between inter- and intra-molecular associations as well as their strength. The experimental results are in very good qualitative agreement with coarse-grained simulations, which offer insights into the mechanism of thermoresponsive behavior of this class of materials.

Hydrodynamic interactions in topologically linked ring polymers

Despite decades of interdisciplinary research on topologically linked ring polymers, their dynamics remain largely unstudied. These systems represent a major scientific challenge as they are often subject to both topological and hydrodynamic interactions (HI), which render dynamical solutions either mathematically intractable or computationally prohibitive. Here we circumvent these limitations by preaveraging the HI of linked rings. We show that the symmetry of ring polymers leads to a hydrodynamic decoupling of ring dynamics. This decoupling is valid even for nonideal polymers and nonequilibrium conditions. Physically, our findings suggest that the effects of topology and HI are nearly independent and do not act cooperatively to influence polymer dynamics. We use this result to develop highly efficient Brownian dynamics algorithms that offer enormous performance improvements over conventional methods and apply these algorithms to simulate catenated ring polymers at equilibrium, confirming the independence of topological effects and HI. The methods developed here can be used to study and simulate large systems of linked rings with HI, including kinetoplast DNA, Olympic gels, and poly[n]catenanes.

Cluster prevalence in concentrated ring-chain mixtures under shear

Semiflexible ring polymers are known to exhibit clustering behavior and form stacks in concentrated solutions. Recently, weak shear was suggested to re-orient these stacks with flow, a phenomenon more easily visible in more concentrated solutions [Liebetreu et al., ACS Appl. Polym. Mater., 2020, 2(8), 3505-3517, DOI: 10.1021/acsapm.0c00522]. In this work, we investigate the impact of mixing linear chains and rings in a similar system under shear, studying clustering in the presence of semiflexible, rod-like chains. We present a correlation between chain monomer fraction and clustering behavior as linear chains take up less space, thus decreasing the system's effective density and, subsequently, clustering. However, we suggest mixtures with a low chain concentration to maintain or potentially enhance clustering at equilibrium while this effect is destroyed under shear. The mixing of chains and rings may therefore be used to create more strongly organized structures susceptible to reorientation via weak shear.

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.