Radii of Gyration of Ring-Shaped Polystyrenes with High Purity in Dilute Solutions

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 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 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.

PolyDODT: a macrocyclic elastomer with unusual properties

Reversible Radical Recombination Polymerization (R3P) using triethylamine (TEA), H2O2 and air is a scalable and green method for the synthesis of biodegradable polysulfides.

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.

Dimensions of catenated ring polymers in dilute solution studied by Monte-Carlo simulation

Interaction between two simple ring chains catenated in a molecule was estimated by a Metropolis Monte Carlo simulation, and the result was compared with a model. We employed catenated ring chains in this study; they were composed of two simple ring chains, and the topology was kept as 2 1 2 . The temperature dependence of the distance between two ring chains in a molecule was discussed using Flory's scaling exponent, ν, in R _g ∝ N ^ν , where R _g is the radius of gyration of a simple ring chain catenated in a molecule. In the simulation, the topology of the component rings and their links were kept because chain crossing was prohibited. The excluded volume of chains was screened by the attractive force between polymer segments, and the strength of the attractive force depends on temperature, T. At the θ temperature for trivial ring polymers, where the condition ν = 1/2 holds, their trajectories can be described statistically as a closed-random walk, i.e., a closed-phantom chain model. The temperature at which interaction between trivial ring polymers, i.e., inter-molecular interaction, is repulsive; trivial ring polymer molecules show the excluded volume generated with keeping their own topology, 0₁. A catenated molecule is composed of two simple rings, and so forth a component ring can be affected by the existence of the counterpart rings. Under that temperature, the mean-square distance between two rings in a catenated molecule, ⟨L ²⟩, was obtained and compared with that of the simple model composed of two circles in three-dimensions, where interaction between circles is set as zero. It has been found that the simulated ⟨L ²⟩ values were constantly larger than those of the model owing to the excluded volume of rings in a molecule.

Macromolecular 'size' and 'hardness' drives structure in solvent-swollen blends of linear, cyclic, and star polymers

In this paper, we apply molecular simulation and liquid state theory to uncover the structure and thermodynamics of homopolymer blends of the same chemistry and varying chain architecture in the presence of explicit solvent species. We use hybrid Monte Carlo (MC)/molecular dynamics (MD) simulations in the Gibbs ensemble to study the swelling of ∼12 000 g mol^-1 linear, cyclic, and 4-arm star polystyrene chains in toluene. Our simulations show that the macroscopic swelling response is indistinguishable between the various architectures and matches published experimental data for the solvent annealing of linear polystyrene by toluene vapor. We then use standard MD simulations in the NPT ensemble along with polymer reference interaction site model (PRISM) theory to calculate effective polymer-solvent and polymer-polymer Flory-Huggins interaction parameters (χ^eff) in these systems. As seen in the macroscopic swelling results, there are no significant differences in the polymer-solvent and polymer-polymer χ^eff between the various architectures. Despite similar macroscopic swelling and effective interaction parameters between various architectures, the pair correlation function between chain centers-of-mass indicates stronger correlations between cyclic or star chains in the linear-cyclic blends and linear-star blends, compared to linear chain-linear chain correlations. Furthermore, we note striking similarities in the chain-level correlations and the radius of gyration of cyclic and 4-arm star architectures of identical molecular weight. Our results indicate that the cyclic and star chains are 'smaller' and 'harder' than their linear counterparts, and through comparison with MD simulations of blends of soft spheres with varying hardness and size we suggest that these macromolecular characteristics are the source of the stronger cyclic-cyclic and star-star correlations.

Scaling behavior of knotted random polygons and self-avoiding polygons: Topological swelling with enhanced exponent

We show that the average size of self-avoiding polygons (SAPs) with a fixed knot is much larger than that of no topological constraint if the excluded volume is small and the number of segments is large. We call it topological swelling. We argue an "enhancement" of the scaling exponent for random polygons with a fixed knot. We study them systematically through SAP consisting of hard cylindrical segments with various different values of the radius of segments. Here we mean by the average size the mean-square radius of gyration. Furthermore, we show numerically that the topological balance length of a composite knot is given by the sum of those of all constituent prime knots. Here we define the topological balance length of a knot by such a number of segments that topological entropic repulsions are balanced with the knot complexity in the average size. The additivity suggests the local knot picture.

Statistical and Dynamical Properties of Topological Polymers with Graphs and Ring Polymers with Knots

We review recent theoretical studies on the statistical and dynamical properties of polymers with nontrivial structures in chemical connectivity and those of polymers with a nontrivial topology, such as knotted ring polymers in solution. We call polymers with nontrivial structures in chemical connectivity expressed by graphs "topological polymers". Graphs with no loop have only trivial topology, while graphs with loops such as multiple-rings may have nontrivial topology of spatial graphs as embeddings in three dimensions, e.g., knots or links in some loops. We thus call also such polymers with nontrivial topology "topological polymers", for simplicity. For various polymers with different structures in chemical connectivity, we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We evaluate the ratio of the gyration radius to the hydrodynamic radius, which we expect to be universal from the viewpoint of the renormalization group. Furthermore, we show that the short-distance intrachain correlation is much enhanced for real topological polymers (the Kremer⁻Grest model) expressed with complex graphs. We then address topological properties of ring polymers in solution. We define the knotting probability of a knot K by the probability that a given random polygon or self-avoiding polygon of N vertices has the knot K. We show a formula for expressing it as a function of the number of segments N, which gives good fitted curves to the data of the knotting probability versus N. We show numerically that the average size of self-avoiding polygons with a fixed knot can be much larger than that of no topological constraint if the excluded volume is small. We call it "topological swelling".

Ring-expansion cationic polymerization of vinyl ethers

Ring-expansion cationic polymerization of vinyl ethers with a hemiacetal ester-embedded cyclic initiator allows precise syntheses of ring-based architectures due to the controlled propagation as well as the monomer pendant design.

A versatile flash cyclization technique assisted by microreactor

An innovative and versatile flash cyclization technique assisted by microreactor (or micromixer) is presented. The cyclization of linear poly(ethylene oxide) (l-PEO) with high efficiency can be instantly and completely realized in a micromixer.

The effect of size and concentration of nanoparticles on the glass transition temperature of polymer nanocomposites

Here we use model nanocomposites based on polystyrene and polyphenylene dendrimers to show both theoretically and experimentally that inclusion of rigid nanoparticles of 2.3–5 nm size into the polymer leads to a negligible glass transition temperature (T_g) increase.

Interfacial diffusion of a single cyclic polymer chain

Lateral diffusion of cyclic polystyrene at the interface between fused silica and dichloromethane is investigated at the single-molecular level. Narrowly distributed cyclic polystyrene (c-PS) of high purity with molecular weights spanning nearly an order of magnitude is prepared via atom transfer radical polymerization (ATRP) and Cu-catalyzed azide/alkyne cycloaddition (CuAAC) click reaction. The diffusion coefficients (D) of c-PS and its linear analogue (l-PS) on the surface are measured by fluorescence correlation spectroscopy (FCS). The diffusion coefficient of c-PS is discovered to have an inverse dependence on molecular weight, D ∼ M^-1, in contrast to the case of linear polystyrene, which reproduces a stronger molecular weight dependence, D ∼ M^-3/2. The slower interfacial motion of cyclic chains is attributed to their stronger binding to the surface and more importantly, the unique surface diffusion mechanism due to the absence of free chain ends.

Confinement Effects with Molten Thin Cyclic Polystyrene Films

The surface fluctuations of a melt film of a low molecular weight cyclic polystyrene (CPS) manifest confinement effects for a film thickness (14R_g) much larger than that for which a melt film of the linear chain analog manifests confinement. This is true both in terms of absolute thickness and thickness relative to chain size, R_g. In fact, the linear analog polymer does not manifest confinement effects even at a thickness of 7R_g. Both types of films have a strongly adsorbed layer at the substrate that plays a role in slowing the surface fluctuations for the thinnest films. This layer is 70% thicker for the cyclic chains than for the linear chains. At the interface with the substrate the packing of the cyclic chains is perturbed much more strongly than is the packing of the linear chains.

Interactions of complex polymers with nanoporous substrate

With the advance of polymer synthesis, polymers that possess unique architectures such as stars or cyclic chains, and unique chemical composition distributions such as block copolymers or statistical copolymers have become frequently encountered. Characterization of these complex polymer systems drives the development of interactive chromatography where the adsorption of polymers on the porous substrate in chromatography columns is finely tuned. Liquid Chromatography at the Critical Condition (LCCC) in particular makes use of the existence of the Critical Adsorption Point (CAP) of polymers on solid surfaces and has been successfully applied to characterization of complex polymer systems. Interpretation and understanding of chromatography behaviour of complex polymers in interactive chromatography motivates theoretical/computational studies on the CAP of polymers and partitioning of these complex polymers near the CAP. This review article covers the theoretical questions encountered in chromatographic studies of complex polymers.