Molecular scale dynamics of large ring polymers

The Topology of Polymer Brushes Determines Their Nanoscale Hydration

Time-of-flight neutron reflectometry (ToF-NR) performed under different relative humidity conditions demonstrates that polymer brushes constituted by hydrophilic, cyclic macromolecules exhibit a more compact conformation with lower roughness as compared to linear brush analogues, due to the absence of dangling chain ends extending at the polymer-vapor interface. In addition, cyclic brushes feature a larger swelling ratio and an increased solvent uptake with respect to their linear counterparts as a consequence of the increased interchain steric repulsions. It is proposed that differences in swelling ratios between linear and cyclic brushes come from differences in osmotic pressure experienced by each brush topology. These differences stem from entropic constraints. The findings suggest that to correlate the equilibrium swelling ratios at different relative humidity for different topologies a new form of the Flory-like expression for equilibrium thicknesses of grafted brushes is needed.

Comparison of Cyclic and Linear Poly(lactide)s Using Small-Angle Neutron Scattering

Small-angle neutron scattering (SANS) experiments were conducted on cyclic and linear polymers of racemic and l-lactides (PLA) with the goal of comparing chain configurations, scaling, and effective polymer-solvent interactions of the two topologies in acetone-d ₆ and THF-d ₈. There are limited reports of SANS results on cyclic polymers due to the lack of substantial development in the field until recently. Now that pure, well-defined cyclic polymers are accessible, unanswered questions about their rheology and physical conformations can be better investigated. Previously reported SANS experiments have used cyclic and linear polystyrene samples; therefore, our work allowed for direct comparison using a contrasting (structurally and sterically) polymer. We compared SANS results of cyclic and linear PLA samples with various microstructures and molecular weights at two different temperatures, allowing for comparison with a wide range of variables. The results followed the trends of previous experiments, but much greater differences in the effective polymer-solvent interaction parameters between cyclic and linear forms of PLA were observed, implying that the small form factor and hydrogen bonding in PLA allowed for much more compact conformations in the cyclic form only. Also, the polymer microstructure was found to influence polymer-solvent interaction parameters substantially. These results illustrate how the difference in polymer-solvent interactions between cyclic and linear polymers can vary greatly depending on the polymer in question and the potential of neutron scattering as a tool for identification and characterization of the cyclic topology.

Superstretchable Elastomer from Cross-linked Ring Polymers

The stretchability of polymeric materials is critical to many applications such as flexible electronics and soft robotics, yet the stretchability of conventional cross-linked linear polymers is limited by the entanglements between polymer chains. We show using molecular dynamics simulations that cross-linked ring polymers are significantly more stretchable than cross-linked linear polymers. Compared to linear polymers, the entanglements between ring polymers do not act as effective cross-links. As a result, the stretchability of cross-linked ring polymers is determined by the maximum extension of polymer strands between cross-links, rather than between trapped entanglements as in cross-linked linear polymers. The more compact conformation of ring polymers before deformation also contributes to the increase in stretchability.

Intrinsic structure and dynamics of monolayer ring polymer melts

We present the general structural and dynamical characteristics of flexible ring polymers in narrowly confined two-dimensional (2D) melt systems using atomistic molecular dynamics simulations. The results are further analyzed via direct comparison with the 2D linear analogue as well as the three-dimensional (3D) ring and linear melt systems. It is observed that dimensional restriction in 2D confined systems results in an increase in the intrinsic chain stiffness of the ring polymer. Fundamentally, this arises from an entropic penalty on polymer chains along with a reduction in the available chain configuration states in phase space and spatial choices for individual segmental walks. This feature in combination with the intermolecular interactions between neighboring ring chains leads to an overall extended interpenetrated chain configuration for the 2D ring melt. In contrast to the generally large differences in structural and dynamical properties between ring and linear polymers in 3D melt systems, relatively similar local-to-global chain structures and dynamics are observed for the 2D ring and linear melts. This is attributed to the general structural similarity (i.e., extended double-stranded chain conformations), the less effective role of the chain ends, and the absence of complex topological constraints between chains (i.e., interchain entanglement and mutual ring threading) in the 2D confined systems compared with the corresponding 3D bulk systems.

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.

Synthesis, Properties, and Applications of Bio-Based Cyclic Aliphatic Polyesters

Cyclic polymers have long been reported in the literature, but their development has often been stunted by synthetic difficulties such as the presence of linear contaminants. Research into the synthesis of these polymers has made great progress in the past decade, and this review covers the synthesis, properties, and applications of cyclic polymers, with an emphasis on bio-based aliphatic polyesters. Synthetic routes to cyclic polymers synthesized from bioderived monomers, alongside mechanistic descriptions for both ring closure and ring expansion polymerization approaches, are reviewed. The review also highlights some of the unique physical properties of cyclic polymers together with potential applications. The findings illustrate the substantial recent developments made in the syntheses of cyclic polymers, as well as the progress which can be made in the commercialization of bio-based polymers through the versatility this topology provides.

Self-Similar Dynamics of Large Polymer Rings: A Neutron Spin Echo Study

This work clarifies the self-similar dynamics of large polymer rings using pulsed-field gradient nuclear magnetic resonance and neutron spin echo spectroscopy. We find center of mass diffusion taking place in three dynamic regimes starting (i) with a strongly subdiffusive domain ⟨r^{2}(t)⟩_{com}∼t^{α} (0.4≤α≤0.65); (ii) a second subdiffusive region ⟨r^{2}(t)⟩_{com}∼t^{0.75} that (iii) finally crosses over to Fickian diffusion. While the t^{0.75} range previously has been found in simulations and was predicted by theory, we attribute the first to the effect of cooperative dynamics resulting from the correlation hole potential. The internal dynamics at scales below the elementary loop size is well described by ring Rouse motion. At larger scales the dynamics is self-similar and follows very well the predictions of the scaling models with preference for the self-consistent fractal loopy globule model.

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.

Self-Similar Polymer Ring Conformations Based on Elementary Loops: A Direct Observation by SANS

We report small angle neutron scattering (SANS) results on very large polyethylene-oxide (PEO) rings in the melt. Major findings are (i) the observation of a cross over in the SANS pattern from a strong Q-dependence at intermediate Q to a Q^-2 dependence at higher Q that is independent of the ring size. Summing up scattering amplitudes in a minimal model that contains the ring closure and a cross over from Gaussian statistics at short distances to more compact structures at larger distances, we identify the cross over to occur at a distance along the ring of N_e,0 = 45 ± 2.5. We consider this finding as a clear signature of the theoretically predicted elementary loops that build up the ring conformation. Their size is in the range of an entanglement strand for linear PEO melts and they are characterized by Gaussian statistics. (ii) The chain length dependence of the radius of gyration R_g follows rather closely the prediction of Obukhov's decorated ring model. (iii) Other than extracted from numerous simulations that are interpreted in terms of a cross over to mass fractal behavior around N ≅ 10N_e,0 with a fractal dimension d_f = 3 and exponent ν = 1/3, we do not observe such a cross over, but R_g(N) ∼ N^ν=0.39 holds over the entire size range.

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.

Orientational relaxation of ring polymers in dilute solutions

The segmental relaxation dynamics of ring polymers in dilute solutions is investigated via optimized Rouse-Zimm theory. To the best of our knowledge, this is the first study that characterizes the orientational relaxation dynamics of ring polymers in dilute solutions. The orientational time autocorrelation functions are governed by two major processes that span a broad range of timescales: (i) local segmental motion at short times, independent of the ring size, and (ii) overall motion of the ring at long times that depends on the limiting ring size. Smaller rings relax faster than larger rings and their respective linear analogues. The hydrodynamic interactions decrease the higher relaxation rates corresponding to the local relaxation modes and increase the smaller relaxation rates which correspond to the collective relaxation modes. The spectral density is independent of frequency in the low frequency regime while it decreases with increasing frequency. Regardless of the ring size, the spin-lattice relaxation rate exhibits a single characteristic maximum as a function of frequency that shifts to a lower value with increasing strength of hydrodynamic interactions.

Unexpected Stretching of Entangled Ring Macromolecules

In the melt state at equilibrium, entangled nonconcatenated ring macromolecules adapt more compact conformations compared to their linear analogs and do not form an entanglement network. We show here that, when subjected to uniaxial stretching, they exhibit a unique response, which sets them apart from any other polymer. Remarkably, whereas both linear and ring polymers strain-harden, the viscosity of the rings increases dramatically (the melt thickens) at very low stretch rates due to the unraveling of their conformations along the stretching direction. At high rates, stretching leads to viscosity thinning similar to that of entangled linear polymers, albeit with subtle differences.

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.

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.

Effect of chain stiffness on the structure of single-chain polymer nanoparticles

Polymeric single-chain nanoparticles (SCNPs) are soft nano-objects synthesized by purely intramolecular cross-linking of single polymer chains. By means of computer simulations, we investigate the conformational properties of SCNPs as a function of the bending stiffness of their linear polymer precursors. We investigate a broad range of characteristic ratios from the fully flexible case to those typical of bulky synthetic polymers. Increasing stiffness hinders bonding of groups separated by short contour distances and increases looping over longer distances, leading to more compact nanoparticles with a structure of highly interconnected loops. This feature is reflected in a crossover in the scaling behaviour of several structural observables. The scaling exponents change from those characteristic for Gaussian chains or rings in θ-solvents in the fully flexible limit, to values resembling fractal or 'crumpled' globular behaviour for very stiff SCNPs. We characterize domains in the SCNPs. These are weakly deformable regions that can be seen as disordered analogues of domains in disordered proteins. Increasing stiffness leads to bigger and less deformable domains. Surprisingly, the scaling behaviour of the domains is in all cases similar to that of Gaussian chains or rings, irrespective of the stiffness and degree of cross-linking. It is the spatial arrangement of the domains which determines the global structure of the SCNP (sparse Gaussian-like object or crumpled globule). Since intramolecular stiffness can be varied through the specific chemistry of the precursor or by introducing bulky side groups in its backbone, our results propose a new strategy to tune the global structure of SCNPs.

Marginally compact fractal trees with semiflexibility

We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness, the self-contact density gets drastically reduced.

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.

Onset of static and dynamic universality among molecular models of polymers

A quantitatively accurate prediction of properties for entangled polymers is a long-standing challenge that must be addressed to enable efficient development of these materials. The complex nature of polymers is the fundamental origin of this challenge. Specifically, the chemistry, structure, and dynamics at the atomistic scale affect properties at the meso and macro scales. Therefore, quantitative predictions must start from atomistic molecular dynamics (AMD) simulations. Combined use of atomistic and coarse-grained (CG) models is a promising approach to estimate long-timescale behavior of entangled polymers. However, a systematic coarse-graining is still to be done for bridging the gap of length and time scales while retaining atomistic characteristics. Here we examine the gaps among models, using a generic mapping scheme based on power laws that are closely related to universality in polymer structure and dynamics. The scheme reveals the characteristic length and time for the onset of universality between the vastly different scales of an atomistic model of polyethylene and the bead-spring Kremer-Grest (KG) model. The mapping between CG model of polystyrene and the KG model demonstrates the fast onset of universality, and polymer dynamics up to the subsecond time scale are observed. Thus, quantitatively traceable timescales of polymer MD simulations can be significantly increased.

Effects of precursor topology and synthesis under crowding conditions on the structure of single-chain polymer nanoparticles

By means of molecular dynamics simulations, we investigate the formation of single-chain nanoparticles through intramolecular cross-linking of polymer chains, in the presence of their precursors acting as purely steric crowders in concentrated solution. In the case of linear precursors, the structure of the resulting SCNPs is weakly affected by the density at which the synthesis is performed. Crowding has significant effects if ring precursors are used: higher concentrations lead to the formation of SCNPs with more compact and spherical morphologies. Such SCNPs retain in the swollen state (high dilution) the crumpled globular conformations adopted by the ring precursors in the crowded solutions. Increasing the concentration of both the linear and ring precursors up to 30% leads to faster formation of the respective SCNPs, prior to deceleration expected at higher densities. The results presented here propose promising new routes for the synthesis of globular SCNPs, which are usually elusive by conventional methods.

Marginally compact hyperbranched polymer trees

Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution ρ_pair(r) or the shear-stress relaxation modulus G(t), are investigated theoretically and by means of computer simulations. We emphasize that albeit the self-contact density diverges logarithmically with the total mass N, this effect becomes rapidly irrelevant with increasing spacer length S. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time τ_p of mode p must scale as τ_p ∼ (N/p)^5/3 rather than the usual square power law for linear chains.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers

The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a and is related to the hopping diffusion of NPs in the entanglement network. In contrast to the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled nonconcatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.

Influence of chain topology on polymer crystallization: poly(ethylene oxide) (PEO) rings vs. linear chains

The absence of entanglements, the more compact structure and the faster diffusion in melts of cyclic poly(ethylene oxide) (PEO) chains have consequences on their crystallization behavior at the lamellar and spherulitic length scales. Rings with molecular weight below the entanglement molecular weight (M < M_e), attain the equilibrium configuration composed from twice-folded chains with a lamellar periodicity that is half of the corresponding linear chains. Rings with M > M_e undergo distinct step-like conformational changes to a crystalline lamellar with the equilibrium configuration. Rings melt from this configuration in the absence of crystal thickening in sharp contrast to linear chains. In general, rings more easily attain their extended equilibrium configuration due to strained segments and the absence of entanglements. In addition, rings have a higher equilibrium melting temperature. At the level of the spherulitic superstructure, growth rates are much faster for rings reflecting the faster diffusion and more compact structure. With respect to the segmental dynamics in their semi-crystalline state, ring PEOs with a steepness index of ∼34 form some of the "strongest" glasses.

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.

Miscibility phase diagram of ring-polymer blends: A topological effect

The miscibility of polymer blends, a classical problem in polymer science, may be altered, if one or both of the component do not have chain ends. Based on the idea of topological volume, we propose a mean-field theory to clarify how the topological constraints in ring polymers affect the phase behavior of the blends. While the large enhancement of the miscibility is expected for ring-linear polymer blends, the opposite trend toward demixing, albeit comparatively weak, is predicted for ring-ring polymer blends. Scaling formulas for the shift of critical point for both cases are derived. We discuss the valid range of the present theory, and the crossover to the linear polymer blends behaviors, which is expected for short chains. These analyses put forward a view that the topological constraints could be represented as an effective excluded-volume effects, in which the topological length plays a role of the screening factor.

Concentrated Solutions of Single-Chain Nanoparticles: A Simple Model for Intrinsically Disordered Proteins under Crowding Conditions

By means of large-scale computer simulations and small-angle neutron scattering (SANS), we investigate solutions of single-chain nanoparticles (SCNPs), covering the whole concentration range from infinite dilution to melt density. The analysis of the conformational properties of the SCNPs reveals that these synthetic nano-objects share basic ingredients with intrinsically disordered proteins (IDPs), as topological polydispersity, generally sparse conformations, and locally compact domains. We investigate the role of the architecture of the SCNPs in their collapse behavior under macromolecular crowding. Unlike in the case of linear macromolecules, which experience the usual transition from self-avoiding to Gaussian random-walk conformations, crowding leads to collapsed conformations of SCNPs resembling those of crumpled globules. This behavior is already found at volume fractions (about 30%) that are characteristic of crowding in cellular environments. The simulation results are confirmed by the SANS experiments. Our results for SCNPs--a model system free of specific interactions--propose a general scenario for the effect of steric crowding on IDPs: collapse from sparse conformations at high dilution to crumpled globular conformations in cell environments.