Interpenetrated and Bridged Nanocylinders from Self-Assembled Star Block Copolymers.

The design of functional polymeric materials with tunable response requires a synergetic use of macromolecular architecture and interactions. Here, we combine experiments with computer simulations to demonstrate how physical properties of gels can be tailored at the molecular level, using star block copolymers with alternating block sequences as a paradigm. Telechelic star polymers containing attractive outer blocks self-assemble into soft patchy nanoparticles, whereas their mirror-image inverted architecture with inner attractive blocks yields micelles. In concentrated solutions, bridged and interpenetrated hexagonally packed nanocylinders are formed, respectively, with distinct structural and rheological properties. The phase diagrams exhibit a peculiar re-entrance where the hexagonal phase melts upon both heating and cooling because of solvent-block and block-block interactions. The bridged nanostructure is characterized by similar deformability, extended structural coherence, enhanced elasticity, and yield stress compared to micelles or typical colloidal gels, which make them promising and versatile materials for diverse applications.

Adsorption characteristics of Janus tadpole polymers.

The shape of Janus particles is directly connected to their adsorption behavior. Janus tadpole polymers offer a unique topological architecture that includes competition between entropic, enthalpic, and topological terms in the adsorption free energy; accordingly, non-trivial adsorption behavior patterns are expected. We study the surface adsorption of Janus tadpole polymers by means of Monte Carlo simulations, finding that, depending on which part of the tadpole polymers is preferentially adsorbing on the surface, very different types of behavior for both the adsorbed polymeric phase and of the brush arise. The adsorbed phase and the brush mutually influence each other, leading to a variety of phenomena such as nematic ordering of the adsorbed stiff tadpole tails and intriguing changes in the territoriality of adsorbed ring polymers on the surface. We analyze in detail our findings, revealing the mechanisms behind the organization and ordering, and opening up new possibilities to tune and control the structure of such systems.

Reply to the 'Comment on "Effects of topological constraints on linked ring polymers in solvents of varying quality"' by M. Tsige and H. Guo, Soft Matter, 2024, 20, DOI: 10.1039/D3SM01614E.

In the preceding Comment, Drs Tsige and Guo compare their findings about the θ-temperatures of linear chains, ring polymers and poly[n]catenanes with those of previous work by us [Z. A. Dehaghani, I. Chubak, C. N. Likos and M. R. Ejtehadi, Soft Matter, 2020, 16, 3029-3038] and point out that the ordering they obtain for these three quantities is, for large degrees of polymerisation, the reverse of the one we had found in our own investigations. We thank the authors of the Comment for their remarks and we appreciate their detailed investigations, which emphasise the importance of understanding the properties of topological polymers and their behaviour under varying solvent quality. We point out, however, that the discrepancy found by Tsige and Guo is only apparent because it pertains to the Θ-temperature of rings and poly[n]catenanes with the same overall molecular weight, whereas in our work we compared the Θ-temperature of a constituent ring of the poly[n]catenane with that of the entire mechanically linked macromulecule.

Supercoiled ring polymers under shear flow.

We apply monomer-resolved computer simulations of supercoiled ring polymers under shear, taking full account of the hydrodynamic interactions, accompanied, in parallel, by simulations in which these are switched off. The combination of bending and torsional rigidities inherent in these polymers, in conjunction with hydrodynamics, has a profound impact on their flow properties. In contrast to their flexible counterparts, which dramatically deform and inflate under shear [Liebetreu et al., Commun. Mater. 2020, 1, 4], supercoiled rings undergo only weak changes in their overall shape and they display both a reduced propensity to tumbling (at fixed Weissenberg number) and a much stronger orientational resistance with respect to their flexible counterparts. In the presence of hydrodynamic interactions, the coupling of the polymer to solvent flow is capable of bringing about a topological transformation of writhe to twist at strong shear upon conservation of the overall linking number.

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.

Engineering Ultrasoft Interactions in Stiff All-DNA Dendrimers by Site-Specific Control of Scaffold Flexibility.

A combined experimental and theoretical study of the structural correlations in moderately concentrated suspensions of all-DNA dendrimers of the second generation (G2) with controlled scaffold rigidity is reported here. Small-angle X-ray scattering experiments in concentrated aqueous saline solutions of stiff all-DNA G2 dendritic constructs reveal a novel anomalous liquid-like phase behavior which is reflected in the calculated structure factors as a two-step increase at low scattering wave vectors. By developing a new design strategy for adjusting the particle's internal flexibility based on site-selective incorporation of single-stranded DNA linkers into the dendritic scaffold, it is shown that this unconventional type of self-organization is strongly contingent on the dendrimer's stiffness. A comprehensive computer simulation study employing dendritic models with different levels of coarse-graining, and two theoretical approaches based on effective, pair-potential interactions, remarkably confirmed the origin of this unusual liquid-like behavior. The results demonstrate that the precise control of the internal structure of the dendritic scaffold conferred by the DNA can be potentially used to engineer a rich palette of novel ultrasoft interaction potentials that could offer a route for directed self-assembly of intriguing soft matter phases and experimental realizations of a host of unusual phenomena theoretically predicted for ultrasoft interacting systems.

Glassy phases of the Gaussian core model.

We present results from molecular dynamics simulations exploring the supercooled dynamics of the Gaussian Core Model in the low- and intermediate-density regimes. In particular, we analyse the transition from the low-density hard-sphere-like glassy dynamics to the high-density one. The dynamics at low densities is well described by the caging mechanism, giving rise to intermittent dynamics. At high densities, the particles undergo a more continuous motion in which the concept of cage loses its meaning. We elaborate on the idea that these different supercooled dynamics are in fact the precursors of two different glass states.

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.

Multi-particle collision dynamics for a coarse-grained model of soft colloids applied to ring polymers.

The simulation of polymer solutions often requires the development of methods that accurately include hydrodynamic interactions. Resolution on the atomistic scale is too computationally expensive to cover mesoscopic time and length scales on which the interesting polymer phenomena are observed. Therefore, coarse-graining methods have to be applied. In this work, the solvent is simulated using the well-established multi-particle collision dynamics scheme, and for the polymer, different coarse-graining methods are employed and compared against the monomer resolved Kremer-Grest model by their resulting diffusion coefficients. This research builds on previous work [Ruiz-Franco et al., J. Chem. Phys. 151, 074902 (2019)], in which star polymers and linear chains in a solvent were simulated and two different coarse-graining methods were developed, in order to increase computational efficiency. The present work extends this approach to ring polymers and seeks to refine one of the authors' proposed model: the penetrable soft colloid model. It was found that both proposed models are not well suited to ring polymers; however, the introduction of a factor to the PSC model delivers satisfying results for the diffusion behavior by regulating the interaction intensity with the solvent.

Cluster Formation in Solutions of Polyelectrolyte Rings.

We use molecular dynamics simulations to explore concentrated solutions of semiflexible polyelectrolyte ring polymers, akin to the DNA mini-circles, with counterions of different valences. We find that the assembly of rings into nanoscopic cylindrical stacks is a generic feature of the systems, but the morphology and dynamics of such a cluster can be steered by the counterion conditions. In general, a small addition of trivalent ions can stabilize the emergence of clusters due to the counterion condensation, which mitigates the repulsion between the like-charged rings. Stoichiometric addition of trivalent ions can even lead to phase separation of the polyelectrolyte ring phase due to the ion-bridging effects promoting otherwise entropically driven clustering. On the other hand, monovalent counterions cause the formation of stacks to be re-entrant with density. The clusters are stable within a certain window of concentration, while above the window the polyelectrolytes undergo an osmotic collapse, disfavoring ordering. The cluster phase exhibits characteristic cluster glass dynamics with arrest of collective degrees of freedom but not the self-ones. On the other hand, the collapsed phase shows arrest on both the collective and single level, suggesting an incipient glass-to-glass transition, from a cluster glass of ring clusters to a simple glass of rings.

Effective Interactions between Double-Stranded DNA Molecules in Aqueous Electrolyte Solutions: Effects of Molecular Architecture and Counterion Valency.

A computational investigation of the effects of molecular topology, namely, linear and circular, as well as counterion valency, on the ensuing pairwise effective interactions between DNA molecules in an unlinked state is presented. Umbrella sampling simulations have been performed through the introduction of bias potential along a reaction coordinate defined as the distance between the centers-of-mass of pairs of DNA molecules, and effective pair interaction potentials have been computed by employing the weighted histogram analysis method. An interesting comparison can be drawn between the different DNA topologies studied here, especially with regard to the contrasting effects of divalent counterions on the effective pair potentials: while DNA-DNA repulsion in short center-of-mass distances decreases significantly in the presence of divalent counterion-ions (as compared to monovalent ions) for linear DNA, the opposite effect occurs for the DNA minicircles. This can be attributed to the fact that linear DNA fragments can easily adopt relative orientations that minimize electrostatic and steric repulsions by rotating relative to one another and by exhibiting more pronounced bending due to the presence of free ends.

To thread or not to thread? Effective potentials and threading interactions between asymmetric ring polymers.

We use computer simulations to study a system of two unlinked ring polymers, whose length and bending stiffness are systematically varied. We derive the effective potentials between the rings, calculate the areas of minimal surfaces of the same, and characterize the threading between them. When the two rings are of the same kind, threading of a one ring through the surface of the other is immanent for small ring-ring separations. Flexible rings pierce the surface of the other ring several times but only shallowly, as compared to the stiff rings which pierce less frequently but deeply. Typically, the ring that is being threaded swells and flattens up into an oblate-like conformation, while the ring that is threading the other takes a shape of an elongated prolate. The roles of the threader and the threaded ring are being dynamically exchanged. If, on the other hand, the rings are of different kinds, the symmetry is broken and the rings tend to take up roles of the threader and the threaded ring with unequal probabilities. We propose a method how to predict these probabilities based on the parameters of the individual rings. Ultimately, our work captures the interactions between ring polymers in a coarse-grained fashion, opening the way to large-scale modelling of materials such as kinetoplasts, catenanes or topological brushes.

Electroosmotic Flow Induced Lift Forces on Polymer Chains in Nanochannels.

A major objective of research in nanofluidics is to achieve better selectivity in manipulating the fluxes of nano-objects and in particular of biopolymers. Numerical simulations allow one to better understand the physical mechanisms at play in such situations. We performed hybrid mesoscale simulations to investigate the properties of polymers under flows in slit pores at the nanoscale. We use multiparticle collision dynamics, an algorithm that includes hydrodynamics and thermal fluctuations, to investigate the properties of fully flexible and stiff polymers under several types of flow, showing that Poiseuille flows and electroosmotic flows can lead to quantitatively and qualitatively different behaviors of the chain. In particular, a counterintuitive phenomenon occurs in the presence of an electroosmotic flow: When the monomers are attracted by the solid surfaces through van der Waals forces, shear-induced forces lead to a stronger repulsion of the polymers from these surfaces. Such focusing of the chain in the middle of the channel increases its flowing velocity, a phenomenon that may be exploited to separate different types of polymers.

Validity of Effective Potentials in Crowded Solutions of Linear and Ring Polymers with Reversible Bonds.

We perform simulations to compute the effective potential between the centers-of-mass of two polymers with reversible bonds. We investigate the influence of the topology on the potential by employing linear and ring backbones for the precursor (unbonded) polymer, finding that it leads to qualitatively different effective potentials. In the linear and ring cases the potentials can be described by Gaussians and generalized exponentials, respectively. The interactions are more repulsive for the ring topology, in analogy with known results in the absence of bonding. We also investigate the effect of the specific sequence of the reactive groups along the backbone (periodic or with different degrees of randomness), establishing that it has a significant impact on the effective potentials. When the reactive sites of both polymers are chemically orthogonal so that only intramolecular bonds are possible, the interactions become more repulsive the closer to periodic the sequence is. The opposite effect is found if both polymers have the same types of reactive sites and intermolecular bonds can be formed. We test the validity of the effective potentials in solution, in a broad range of concentrations from high dilution to far above the overlap concentration. For this purpose, we compare simulations of the effective fluid and test particle route calculations with simulations of the real all-monomer system. Very good agreement is found for the reversible linear polymers, indicating that unlike in their nonbonding counterparts many-body effects are minor even far above the overlap concentration. The agreement for the reversible rings is less satisfactory, and at high concentration the real system does not show the clustering behavior predicted by the effective potential. Results similar to the former ones are found for the partial self-correlations in ring/linear mixtures. Finally, we investigate the possibility of creating, at high concentrations, a gel of two interpenetrated reversible networks. For this purpose we simulate a 50/50 two-component mixture of reversible polymers with orthogonal chemistry for the reactive sites, so that intermolecular bonds are only formed between polymers of the same component. As predicted by both the theoretical phase diagram and the simulations of the effective fluid, the two networks in the all-monomer mixture do not interpenetrate, and phase separation (demixing) is observed instead.

Glass quantization of the Gaussian core model.

We use the replica method to study the dynamical glass transition of the Gaussian core model, a system of ultrasoft repulsive spheres interacting via a Gaussian potential, focusing on low temperatures and low-to-moderate densities. At constant temperature, an amorphous glassy state is entered upon a first compression but this glass melts as the density is further increased. In addition to this reentrant transition, a second, smooth transition is discovered between a continuous and a discretized glass. The properties of the former are continuous functions of temperatures, whereas the latter exhibits a succession of stripes, characterized by discontinuous jumps of the glassiness parameters. The glass physics of ultrasoft particles is hence richer than that of impenetrable particles for reasons that can be attributed to the ability of the former to create and break out-of-equilibrium clusters of overlapping particles.

Blunt-End Driven Re-entrant Ordering in Quasi Two-Dimensional Dispersions of Spherical DNA Brushes.

We investigate the effects of crowding on the conformations and assembly of confined, highly charged, and thick polyelectrolyte brushes in the osmotic regime. Particle tracking experiments on increasingly dense suspensions of colloids coated with ultralong double-stranded DNA (dsDNA) fragments reveal nonmonotonic particle shrinking, aggregation, and re-entrant ordering. Theory and simulations show that aggregation and re-entrant ordering arise from the combined effect of shrinking, which is induced by the osmotic pressure exerted by the counterions absorbed in neighbor brushes and of a short-range attractive interaction competing with electrostatic repulsion. An unconventional mechanism gives origin to the short-range attraction: blunt-end interactions between stretched dsDNA fragments of neighboring brushes, which become sufficiently intense for dense and packed brushes. The attraction can be tuned by inducing free-end backfolding through the addition of monovalent salt. Our results show that base stacking is a mode parallel to hybridization to steer colloidal assembly in which attractions can be fine-tuned through salinity and, potentially, grafting density and temperature.

Active Topological Glass Confined within a Spherical Cavity.

We study active topological glass under spherical confinement, allowing us to exceed the chain lengths simulated previously and determine the critical exponents of the arrested conformations. We find a previously unresolved "tank-treading" dynamic mode of active segments along the ring contour. This mode can enhance active-passive phase separation in the state of active topological glass when both diffusional and conformational relaxation of the rings are significantly suppressed. Within the observational time, we see no systematic trends in the positioning of the separated active domains within the confining sphere. The arrested state exhibits coherent stochastic rotations. We discuss possible connections of the conformational and dynamic features of the system to chromosomes enclosed in the nucleus of a living cell.

Self assembling cluster crystals from DNA based dendritic nanostructures.

Cluster crystals are periodic structures with lattice sites occupied by several, overlapping building blocks, featuring fluctuating site occupancy, whose expectation value depends on thermodynamic conditions. Their assembly from atomic or mesoscopic units is long-sought-after, but its experimental realization still remains elusive. Here, we show the existence of well-controlled soft matter cluster crystals. We fabricate dendritic-linear-dendritic triblock composed of a thermosensitive water-soluble polymer and nanometer-scale all-DNA dendrons of the first and second generation. Conclusive small-angle X-ray scattering (SAXS) evidence reveals that solutions of these triblock at sufficiently high concentrations undergo a reversible phase transition from a cluster fluid to a body-centered cubic (BCC) cluster crystal with density-independent lattice spacing, through alteration of temperature. Moreover, a rich concentration-temperature phase diagram demonstrates the emergence of various ordered nanostructures, including BCC cluster crystals, birefringent cluster crystals, as well as hexagonal phases and cluster glass-like kinetically arrested states at high densities.

Effect of softness on glass melting and re-entrant solidification in mixtures of soft and hard colloids.

We present a systematic investigation of the structure and dynamic properties of model soft-hard colloidal mixtures. Results of a coarse-grained theoretical model are contrasted with rheological data, where the soft and hard colloids are mimicked by large star polymers with high functionality as the soft component and smaller stars with ultrahigh functionality as the hard one. Previous work by us revealed the recovery of the ergodicity of glassy soft star solutions and subsequent arrested phase separation and re-entrant solid transition upon progressive addition of small hard depletants. Here, we use different components to show that a small variation in softness has a significant impact on the state diagram of such mixtures. In particular, we establish that rendering the soft component more penetrable and modifying the size ratio bring about a remarkable shift in both the phase separation region and the glass-melting line so that the region of restored ergodicity can be notably enhanced and extended to much higher star polymer concentrations than for pure systems. We further rationalize our findings by analyzing the features of the depletion interaction induced by the smaller component that result from the interplay between the size ratio and the softness of the large component. These results demonstrate the great sensitivity of the phase behavior of entropic mixtures to small changes in the molecular architecture of the soft stars and point to the importance of accounting for details of the internal microstructure of soft colloidal particles for tailoring the flow properties of soft composites.

Multiscale Approaches for Confined Ring Polymer Solutions.

We apply a hierarchy of multiscale modeling approaches to investigate the structure of ring polymer solutions under planar confinement. In particular, we employ both monomer-resolved (MR-DFT) and a coarse-grained (CG-DFT) density functional theories for fully flexible ring polymers, with the former based on a flexible tangent hard-sphere model and the latter based on an effective soft-colloid representation, to elucidate the ring polymer organization within slits of variable width in different concentration regimes. The predicted monomer and polymer center-of-mass densities in confinement, as well as the surface tension at the solution-wall interface, are compared to explicit molecular dynamics (MD) simulations. The approaches yield quantitative (MR-DFT) or semiquantitative (CG-DFT) agreement with MD. In addition, we provide a systematic comparison between confined linear and ring polymer solutions. When compared to their linear counterparts, the rings are found to feature a higher propensity to structure in confinement that translates into a distinct shape of the depletion potentials between two walls immersed into a polymer solution. The depletion potentials that we extract from CG-DFT and MR-DFT are in semiquantitative agreement with each other. Overall, we find consistency among all approaches as regards the shapes, trends, and qualitative characteristics of density profiles and depletion potentials induced on hard walls by linear and cyclic polymers.