Effect of cyclic chain architecture on properties of dilute solutions of polyethylene from molecular dynamics simulations

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.

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.

Conformational behavior and self-assembly of disjoint semi-flexible ring polymers adsorbed on solid substrates

The conformational behavior and spatial organization of self-avoiding semi-flexible ring polymers, that are fully adsorbed on solid substrates, are investigated via systematic coarse-grained molecular dynamics simulations. Our results show that both conformations and spatial organization of the polymers depend strongly on their bending stiffness, κ, and on their areal number density, ρ. For ρ < ρ*, where ρ* is the overlap density, and for low values of κ, thermal fluctuations lead to weakly anisotropic instantaneous conformations of the polymers. The interplay between thermal fluctuations and polymer stiffness leads to a non-monotonic dependence of the polymers elongation on κ with a maximum elongation at some intermediate κ. Regardless of κ, the polymers elongation is almost independent of ρ for ρ ⪅ ρ*, then increases with ρ. At ρ ≈ ρ* and high κ, the almost circularly-shaped polymers self-assemble into a triangular lattice with quasi-long range order. For ρ above ρ* and high κ, crowding of the polymers leads to their self-assembly into liquid-crystalline phases. In particular, for ρ moderately above ρ* and high κ, the polymer conformations are obround and self-assemble into domains with smectic-A-like order. At higher densities, the polymer have a biconcave geometry and self-assemble into domains with smectic-C-like order.

Hydrogels Generated from Cyclic Poly(2-Oxazoline)s Display Unique Swelling and Mechanical Properties

Cyclic macromolecules do not feature chain ends and are characterized by a higher effective intramolecular repulsion between polymer segments, leading to a higher excluded-volume effect and greater hydration with respect to their linear counterparts. As a result of these unique properties, hydrogels composed of cross-linked cyclic polymers feature enhanced mechanical strength while simultaneously incorporating more solvent with respect to networks formed from their linear analogues with identical molar mass and chemical composition. The translation of topology effects by cyclic polymers into the properties of polymer networks provides hydrogels that ideally do not include defects, such as dangling chain ends, and display unprecedented physicochemical characteristics.

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.

Functional Nanoassemblies of Cyclic Polymers Show Amplified Responsiveness and Enhanced Protein-Binding Ability

The physicochemical properties of cyclic polymer adsorbates are significantly influenced by the steric and conformational constraints introduced during their cyclization. These translate into a marked difference in interfacial properties between cyclic polymers and their linear counterparts when they are grafted onto surfaces yielding nanoassemblies or polymer brushes. This difference is particularly clear in the case of cyclic polymer brushes that are designed to chemically interact with the surrounding environment, for instance, by associating with biological components present in the medium, or, alternatively, through a response to a chemical stimulus by a significant change in their properties. The intrinsic architecture characterizing cyclic poly(2-oxazoline)-based polyacid brushes leads to a broad variation in swelling and nanomechanical properties in response to pH change, in comparison with their linear analogues of identical composition and molecular weight. In addition, cyclic glycopolymer brushes derived from polyacids reveal an enhanced exposure of galactose units at the surface, due to their expanded topology, and thus display an increased lectin-binding ability with respect to their linear counterparts. This combination of amplified responsiveness and augmented protein-binding capacity renders cyclic brushes invaluable building blocks for the design of "smart" materials and functional biointerfaces.

Topological Polymer Chemistry Enters Materials Science: Expanding the Applicability of Cyclic Polymers

Polymer-topology effects can alter technologically relevant properties when cyclic macromolecules are applied within diverse materials formulations. These include coatings, polymer networks, or nanostructures for delivering therapeutics. While substituting linear building blocks with cyclic analogues in commonly studied materials is itself of fundamental interest, an even more fascinating observation has been that the introduction of physical or chemical boundaries (e.g., a grafting surface or cross-links) can amplify the topology-related effects observed when employing cyclic polymer-based precursors for assembling multidimensional objects. Hence, the application of cyclic polymers has enabled the fabrication of coatings with enhanced biorepellency and superior lubricity, broadened the tuning potential for mechanical properties of polymer networks, increased the thermodynamic stability, and altered the capability of loading and releasing drugs within polymeric micelles.

Effects of topological constraints on linked ring polymers in solvents of varying quality

We investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their θ-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. Using molecular dynamics simulations, we study the scaling of the poly[n]catenane's radius of gyration in a good solvent, assuming in general that Rg∼mμnν and we find that μ = 0.65 ± 0.02 and ν = 0.60 ± 0.01 for the range of n and m considered. These findings are further rationalized with the help of a mean-field Flory-like theory yielding the values of μ = 16/25 and ν = 3/5, consistent with the numerical results. We show that individual rings within catenanes feature a surplus swelling due to the presence of NL topological links. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its θ-temperature in comparison to isolated linear and ring chains with the following ordering: T > T > T. Finally, we show that the presence of links similarly raises the θ-temperature of a single linked ring in comparison to an unlinked one, bringing its θ-temperature close to the one of a poly[n]catenane.

Surface Density Variation within Cyclic Polymer Brushes Reveals Topology Effects on Their Nanotribological and Biopassive Properties

While topology effects by cyclic polymers in solution and melts are well-known, their translation into the interfacial properties of polymer "brushes" provides new opportunities to impart enhanced surface lubricity and biopassivity to inorganic surfaces, above and beyond that expected for linear analogues of identical composition. The impact of polymer topology on the nanotribological and protein-resistance properties of polymer brushes is revealed by studying linear and cyclic poly(2-ethyl-2-oxazoline) (PEOXA) grafts presenting a broad range of surface densities and while shearing them alternatively against an identical brush or a bare inorganic surface. The intramolecular constraints introduced by the cyclization provide a valuable increment in both steric stabilization and load-bearing capacity for cyclic brushes. Moreover, the intrinsic absence of chain ends within cyclic adsorbates hinders interpenetration between opposing brushes, as they are slid over each other, leading to a reduction in the friction coefficient (μ) at higher pressures, a phenomenon not observed for linear grafts. The application of cyclic polymers for the modification of inorganic surfaces generates films that outperform both the nanotribological and biopassive properties of linear brushes, significantly expanding the design possibilities for synthetic biointerfaces.

Aggregation of cyclic polypeptoids bearing zwitterionic end-groups with attractive dipole–dipole and solvophobic interactions: a study by small-angle neutron scattering and molecular dynamics simulation

The aggregation behavior of cyclic polypeptoids has been studied using experiments and simulations.

A convergent approach to ring polymers with narrow molecular weight distributions through post dilution in ring expansion cationic polymerization

In this paper, we demonstrate a convergent approach to convert “fused” ring chains obtained via ring expansion cationic polymerization of vinyl ether with a hemiacetal ester (HAE)-based ring initiator (1) into “sing” ring ones of narrow MWDs.

Marked difference in conformational fluctuation between giant DNA molecules in circular and linear forms

We performed monomolecular observations on linear and circular giant DNAs (208 kbp) in an aqueous solution by the use of fluorescence microscopy. The results showed that the degree of conformational fluctuation in circular DNA was ca. 40% less than that in linear DNA, although the long-axis length of circular DNA was only 10% smaller than that of linear DNA. Additionally, the relaxation time of a circular chain was shorter than that of a linear chain by at least one order of magnitude. The essential features of this marked difference between linear and circular DNAs were reproduced by numerical simulations on a ribbon-like macromolecule as a coarse-grained model of a long semiflexible, double-helical DNA molecule. In addition, we calculated the radius of gyration of an interacting chain in a circular form on the basis of the mean field model, which provides a better understanding of the present experimental trend than a traditional theoretical equation.

Cluster Glasses of Semiflexible Ring Polymers

We present computer simulations of concentrated solutions of unknotted nonconcatenated semiflexible ring polymers. Unlike in their flexible counterparts, shrinking involves a strong energetic penalty, favoring interpenetration and clustering of the rings. We investigate the slow dynamics of the centers-of-mass of the rings in the amorphous cluster phase, consisting of disordered columns of oblate rings penetrated by bundles of prolate ones. Scattering functions reveal a striking decoupling of self- and collective motions. Correlations between centers-of-mass exhibit slow relaxation, as expected for an incipient glass transition, indicating the dynamic arrest of the cluster positions. However, self-correlations decay at much shorter time scales. This feature is a manifestation of the fast, continuous exchange and diffusion of the individual rings over the matrix of clusters. Our results reveal a novel scenario of glass formation in a simple monodisperse system, characterized by self-collective decoupling, soft caging, and mild dynamic heterogeneity.

Architecture-Induced Size Asymmetry and Effective Interactions of Ring Polymers: Simulation and Theory

We investigate, by means of Monte Carlo simulations, the role of ring architecture and topology on the relative sizes of two interacting polymers as a function of the distance between their centers-of-mass. As a general rule, polymers swell as they approach each other, irrespectively of their topologies. For each mutual separation, two identical linear polymers adopt the same average size. However, unknotted rings at close separations adopt different sizes, with the small one being "nested" within the large one over long time intervals, exchanging their roles in the course of the simulation. For two rings of different architectures and identical polymerization degree, the knotted one is always smaller, penetrating the unknotted one. On the basis of these observations, we propose a phenomenological theory for the effective interactions between rings, modeling them as unequal-sized penetrable spheres. This simple approximation provides a good description of the simulation results. In particular, it rationalizes the non-Gaussian shape and the short-distance plateau observed in the effective potential between unknotted ring polymers and pairs of unequal-sized unknotted/knotted ones. Our results demonstrate the crucial role of the architecture on both the effective interactions and the molecular size for strongly interpenetrating polymers.

Effects of Knots on Ring Polymers in Solvents of Varying Quality

We employ extensive computer simulations to investigate the conformations and the interactions of ring polymers under conditions of worsening solvent quality, in comparison with those for linear polymers. We determine the dependence of the Θ-temperature on knotedness by considering ring polymers of different topologies. We establish a clear decrease of the former upon changing the topology of the polymer from linear to an unknotted ring and a further decrease of the same upon introducing trefoil- or 5-fold knots but we find no difference in the Θ-point between the two knotted molecules. Our results are based on two independent methods: one considering the scaling of the gyration radius with molecular weight and one based on the dependence of the effective interaction on solvent quality. In addition, we calculate several shape-parameters of the polymers to characterize linear, unknotted, and knotted topologies in good solvents and in the proximity of the Θ-point. The shape parameters of the knotted molecules show an interesting crossover at a degree of polymerization that depends on the degree of knottedness of the molecule.

Cyclic poly(alpha-peptoid)s and their block copolymers from N-heterocyclic carbene-mediated ring-opening polymerizations of N-substituted N-carboxylanhydrides

N-Heterocyclic carbene (NHC)-mediated ring-opening polymerization (ROP) of N-substituted N-carboxylanhydride ((N)R-NCA) yields cyclic poly(alpha-peptoid)s with controlled molecular weights (M(n) = 3-30 kg mol(-1)) and narrow molecular weight distributions (PDI = 1.04-1.12). The reactions exhibit characteristics of a living polymerization with minimal chain transfer. This enables the facile synthesis of cyclic diblock copoly(alpha-peptoid)s through sequential monomer addition. The cyclic polymer architectures were verified by MALDI-TOF mass spectrometry and intrinsic viscosity measurements. Mark-Houwink-Sakurada plot analyses revealed that cyclic poly(alpha-peptoid)s prepared from NHC-mediated polymerizations exhibit lower intrinsic viscosities than their linear analogues prepared from primary amine-initiated polymerizations. The ratio of their intrinsic viscosities is consistent with the former being mostly cyclic.

DNA closed nanostructures: a structural and Monte Carlo simulation study

DNA nanoconstructs are obtained in solution by using six unique 42-mer DNA oligonucleotides, whose sequences have been designed to form a pseudohexagonal structure. The required flexibility is provided by the insertion of two non-base-paired thymines in the middle of each sequence that work as flexible hinges and constitute the corners of the nanostructure when formed. We show that hexagonally shaped nanostructures of about 7 nm diameter and their corresponding linear open constructs are formed by self-assembly of the specifically designed linear oligonucleotides. The structural and dynamical characterization of the nanostructure is obtained in situ for the first time by using dynamic light scattering (DLS), a noninvasive method that provides a fast dynamic and structural analysis and allows the characterization of the different synthetic DNA nanoconstructs in solution. A validation of the LS results is obtained through Monte Carlo (MC) simulations and atomic force microscopy (AFM). In particular, a mesoscale molecular model for DNA, developed by Knotts et al., is exploited to perform MC simulations and to obtain information about the conformations as well as the conformational flexibilities of these nanostructures, while AFM provides a very detailed particle analysis that yields an estimation of the particle size and size distribution. The structural features obtained by MC and AFM are in good agreement with DLS, showing that DLS is a fast and reliable tool for characterization of DNA nanostructures in solution.

Conformation of circular DNA in two dimensions

The conformation of circular DNA molecules of various lengths adsorbed in a 2D conformation on a mica surface is studied. The results confirm the conjecture that the critical exponent nu is topologically invariant and equal to the self-avoiding walk value (in the present case nu=3/4), and that the topology and dimensionality of the system strongly influence the crossover between the rigid regime and the self-avoiding regime at a scale L approximately 7l{p}. Additionally, the bond correlation function scales with the molecular length L as predicted. For molecular lengths L<or=5l{p}, circular DNA behaves like a stiff molecule with an approximately elliptic shape.

Universality in the phase behavior of soft matter: a law of corresponding states

We show that the phase diagram of substances whose molecular structure changes upon varying the thermodynamic parameters can be mapped, through state-dependent scaling, onto the phase diagram of systems of molecules having fixed structure. This makes it possible to identify broad universality classes in the complex phase scenario exhibited by soft matter, and enlightens a surprisingly close connection between puzzling phase phenomena and familiar behaviors. The analysis presented provides a straightforward way for deriving the phase diagram of soft substances from that of simpler reference systems. This method is applied here to study the phase behavior exhibited by two significative examples of soft matter with temperature-dependent molecular structure: thermally responsive colloids and polymeric systems. A region of inverse melting, i.e., melting upon isobaric cooling, is predicted at relatively low pressure and temperature in polymeric systems.

Studies on the behavior of nanoconfined homopolymers with cyclic chain architecture

We have performed Monte Carlo simulations to study the effect of cyclic architecture on the behavior of homopolymer chains under several conditions of confinement. The collapse of the rings in two stages, a coil-to-globule and a liquidlike-to-solidlike transition, was observed even at extreme confinement. Both transitions were observed at lower temperatures than for linear chains of the same length, 2%-5% lower for unconfined systems, and 10%-15% lower for wall separations below three bond lengths due to the effect of confinement. When the plates separation approached the two-dimensional regime, the coil-to-globule transition shifted to lower temperatures. The inverse trend was observed when the chain length was increased. In the collapsed state, the average size and conformations of linear and cyclic molecules of same length were similar independently of confinement. At temperatures near the coil-to-globule transition, the radius of gyration of unconfined linear chains, [R(g)(2)](linear), became larger than for the cyclic chains, [R(g)(2)](cyclic), and this difference increased considerably with confinement. The radius of gyration ratio [R(g)(2)](linear)/[R(g)(2)](cyclic) in this region decreased rapidly. The decrease was more pronounced and occurred at lower temperatures for slit width confinements. At higher temperatures, in the coil state, the radius of gyration ratio became nearly constant for a given separation, and varied from 0.56 for unconfined systems to 0.47 when the chain was completely confined between the walls. This reduction was attributed to the higher increase in the average size of linear chains with confinement when compared with cyclic chains, due to architectural restrictions.