Collapse of telechelic star polymers to watermelon structures

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.

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

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

Aggregation shapes of amphiphilic ring polymers: from spherical to toroidal micelles

The self-assembly of Janus ring polymers is studied via a coarse-grained molecular dynamics employing a bead spring model including bending rigidity contributions to the Hamiltonian. We examine the formation and the morphology of amphiphilicity-driven clusters in the system using the number density ρN, the temperature T, the fraction of solvophobic monomers α, and the stiffness of the polymer rings κ as control parameters. We present a quantitative analysis of several characteristics for the formed clusters of Janus rings. Measured quantities include the distribution of the cluster size MC and the shape of the clusters in the form of the prolate/oblate factor Q and shape factors sf. We demonstrate Janus rings form polymorphic micelles that vary from a spherical shape, akin to that known for linear block copolymers, to a novel type of toroidal shape, and we highlight the role played by the key physical parameters leading to the stabilization of such structures.

Self-Organization and Flow of Low-Functionality Telechelic Star Polymers with Varying Attraction

We combine state-of-the art synthesis, simulations, and physical experiments to explore the tunable, responsive character of telechelic star polymers as models for soft patchy particles. We focus on the simplest possible system: a star comprising three asymmetric block copolymer arms with solvophilic inner and solvophobic outer blocks. Our dilute solution studies reveal the onset of a second slow mode in the intermediate scattering functions as the temperature decreases below the θ-point of the outer block, as well as the size reduction of single stars upon further decreasing temperature. Clusters comprising multiple stars are formed and their average dimensions, akin to the single star size, counterintuitively decrease upon cooling. A similar phenomenology is observed in simulations upon increasing attraction between the outer blocks and is rationalized as a result of the interplay between interstar associations and steric repulsion between the star cores. Since our simulations are able to describe the experimental findings reliably, we can use them with confidence to make predictions at conditions and flow regimes that are inaccessible experimentally. Specifically, we employ simulations to investigate flow properties of the system at high shear rates, revealing shear thinning behavior caused by the breakup of interstar associations under flow. On the other hand, the zero-shear viscosity obtained experimentally exhibits a rather weak activation energy, which increases upon rising star concentration. These findings demonstrate the unusual properties of telechelic star polymers even in the dilute regime. They also offer a powerful toolbox for designing soft patchy particles and exploring their unprecedented responsive properties further on.

Self-organization of gel networks formed by block copolymer stars

The equilibrium properties of block copolymer star networks (BCS) are studied via computer simulations. We employ both molecular dynamics and multiparticle collisional dynamics simulations to investigate the self-organization of BCS with f = 9 functionalized arms close to their overlap concentrations under conditions of different fractions of functionalization and varying attraction strength. We find three distinct macroscopic self-organized states depending on fraction of attractive end-monomers and the strength of the attraction. At weak attractions, ergodic, diffusive liquids result, with short-lived bonds between the stars. As the attraction strength grows, the whole system forms a percolating cluster, while at the same time the individual molecules are diffusive. Finally, arrested gels emerge when the attractions become strong. The conformation of the BCS in these solutions is found to be strongly affected by the concentration, with the stars assuming typically spherical, open configurations in seeking to maximize inter-star associations as opposed to the inter-star collapse that results at infinite dilution, giving rise to strongly aspherical shapes and reduced sizes.

Self-assembly of magnetically functionalized star-polymer nano-colloids

We explore the potential of star-polymers that carry super-paramagnetic nano-particles as end-groups with respect to the single-molecule self-assembly process. With the aid of molecular dynamics simulation, the configurations of these macromolecules are analyzed as a function of functionality, magnetic interaction strength, and the length of the polymeric arms. By means of an external magnetic field the nano-particles can be controlled to form static or dynamic dipolar chains, resulting in conformations of isolated stars that can be characterized by the average number of chains and length. The single-molecule conformation diagram in the plane of magnetic interaction strength vs. the star-functionality is obtained. Further, the molecules are characterized by means of various shape and size order parameters.

Network formation and gelation in telechelic star polymers

We investigate the efficiency of gelation and network formation in telechelic star polymer melt, where the tips of polymer arms are dipoles while the rest of the monomers are uncharged. Our work is motivated by the experimental observations [A. Kulkarni et al., Macromolecules 48, 6580 (2015)] in which rheological studies of telechelic star polymers of poly-(L-lactide), a bio-degradable polymer, showed a drastic increase in elastic properties (up to 2000 times) compared to corresponding star polymers without the telechelic arm ends. In contrast to previous studies, we avoid using effective attractive Lennard-Jones potentials or dipolar potentials to model telechelic interactions. Instead we use explicit Coulomb positive and negative charges at the tip of polymer-arms of our bead-spring model of star polymers. By our simulations we show that the dipoles at the tip of star arms aggregate together to form clusters of dipoles. Each cluster has contributions from several stars, and in turn each star contributes to several clusters. Thus the entire polymer melt forms a connected network. Network forming tendencies decrease with a decrease of the value of the effective charge constituting the dipole: this can be experimentally realized by choosing a different ionomer for the star tip. We systematically varied the value of dipole charges, the fraction of star-arms with dipoles at the tip, and the length of the arms. The choice of explicit charges in our calculations enables us to make better quantitative predictions about the onset of gelation; moreover we get qualitatively distinct results about structural organization of dipoles within a dipole-cluster.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

Artistic representation of limited valance units consisting of a soft core (in blue) and a small number of flexible bonding patches (in orange).

Self-assembly and glass-formation in a lattice model of telechelic polymer melts: Influence of stiffness of the sticky bonds

Telechelic polymers are chain macromolecules that may self-assemble through the association of their two mono-functional end groups (called "stickers"). A deep understanding of the relation between microscopic molecular details and the macroscopic physical properties of telechelic polymers is important in guiding the rational design of telechelic polymer materials with desired properties. The lattice cluster theory (LCT) for strongly interacting, self-assembling telechelic polymers provides a theoretical tool that enables establishing the connections between important microscopic molecular details of self-assembling polymers and their bulk thermodynamics. The original LCT for self-assembly of telechelic polymers considers a model of fully flexible linear chains [J. Dudowicz and K. F. Freed, J. Chem. Phys. 136, 064902 (2012)], while our recent work introduces a significant improvement to the LCT by including a description of chain semiflexibility for the bonds within each individual telechelic chain [W.-S. Xu and K. F. Freed, J. Chem. Phys. 143, 024901 (2015)], but the physically associative (or called "sticky") bonds between the ends of the telechelics are left as fully flexible. Motivated by the ubiquitous presence of steric constraints on the association of real telechelic polymers that impart an additional degree of bond stiffness (or rigidity), the present paper further extends the LCT to permit the sticky bonds to be semiflexible but to have a stiffness differing from that within each telechelic chain. An analytical expression for the Helmholtz free energy is provided for this model of linear telechelic polymer melts, and illustrative calculations demonstrate the significant influence of the stiffness of the sticky bonds on the self-assembly and thermodynamics of telechelic polymers. A brief discussion is also provided for the impact of self-assembly on glass-formation by combining the LCT description for this extended model of telechelic polymers with the Adam-Gibbs relation between the structural relaxation time and the configurational entropy.

Soft self-assembled nanoparticles with temperature-dependent properties

The fabrication of versatile building blocks that reliably self-assemble into desired ordered and disordered phases is amongst the hottest topics in contemporary materials science. To this end, microscopic units of varying complexity, aimed at assembling the target phases, have been thought, designed, investigated and built. Such a path usually requires laborious fabrication techniques, especially when specific functionalisation of the building blocks is required. Telechelic star polymers, i.e., star polymers made of a number of f di-block copolymers consisting of solvophobic and solvophilic monomers grafted on a central anchoring point, spontaneously self-assemble into soft patchy particles featuring attractive spots (patches) on the surface. Here we show that the tunability of such a system can be widely extended by controlling the physical and chemical parameters of the solution. Indeed, under fixed external conditions the self-assembly behaviour depends only on the number of arms and on the ratio of solvophobic to solvophilic monomers. However, changes in temperature and/or solvent quality make it possible to reliably change the number and size of the attractive patches. This allows the steering of the mesoscopic self-assembly behaviour without modifying the microscopic constituents. Interestingly, we also demonstrate that diverse combinations of the parameters can generate stars with the same number of patches but different radial and angular stiffness. This mechanism could provide a neat way of further fine-tuning the elastic properties of the supramolecular network without changing its topology.

Lattice model of linear telechelic polymer melts. I. Inclusion of chain semiflexibility in the lattice cluster theory

The lattice cluster theory (LCT) for the thermodynamics of polymer systems has recently been reformulated to treat strongly interacting self-assembling polymers composed of fully flexible linear telechelic chains [J. Dudowicz and K. F. Freed, J. Chem. Phys. 136, 064902 (2012)]. Here, we further extend the LCT for linear telechelic polymer melts to include a description of chain semiflexibility, which is treated by introducing a bending energy penalty whenever a pair of consecutive bonds from a single chain lies along orthogonal directions. An analytical expression for the Helmholtz free energy is derived for the model of semiflexible linear telechelic polymer melts. The extension provides a theoretical tool for investigating the influence of chain stiffness on the thermodynamics of self-assembling telechelic polymers, and for further exploring the influence of self-assembly on glass formation in such systems.

Determination of the interaction parameter and topological scaling features of symmetric star polymers in dilute solution

Star polymers provide model architectures to understand the dynamic and rheological effects of chain confinement for a range of complex topological structures like branched polymers, colloids, and micelles. It is important to describe the structure of such macromolecular topologies using small-angle neutron and x-ray scattering to facilitate understanding of their structure-property relationships. Modeling of scattering from linear, Gaussian polymers, such as in the melt, has applied the random phase approximation using the Debye polymer scattering function. The Flory-Huggins interaction parameter can be obtained using neutron scattering by this method. Gaussian scaling no longer applies for more complicated chain topologies or when chains are in good solvents. For symmetric star polymers, chain scaling can differ from ν=0.5(d(f)=2) due to excluded volume, steric interaction between arms, and enhanced density due to branching. Further, correlation between arms in a symmetric star leads to an interference term in the scattering function first described by Benoit for Gaussian chains. In this work, a scattering function is derived which accounts for interarm correlations in symmetric star polymers as well as the polymer-solvent interaction parameter for chains of arbitrary scaling dimension using a hybrid Unified scattering function. The approach is demonstrated for linear, four-arm and eight-arm polyisoprene stars in deuterated p-xylene.

Customizing wormlike mesoscale structures via self-assembly of amphiphilic star polymers

We examine the phase behavior of end-functionalized diblock copolymer stars by means of Grand Canonical Monte Carlo simulations. We focus on solutions of diblock copolymer stars with a solvophobic outer block shorter than the solvophilic inner block, which are expected to nucleate microphase aggregates. By tuning the temperature and rigidity of the molecules, we target specific mesoscale structures, which can act as powerful rheology modifiers. In particular, we control the hierarchical self-assembly of single micelles in a "pearl-necklace" fashion, which eventually merge into elongated, wormlike supermicelles.

Soft-patchy nanoparticles: modeling and self-organization

We consider a novel class of patchy particles inspired by polymer-based complex units where the limited valence in bonding is accompanied by soft interactions and incessant fluctuations of the patch positions, possibly leading to reversible modifications of the patch number and size. We introduce a simple model that takes into account the aforementioned features and we focus on the role played by the patch flexibility on the self-organization of our patchy units in the bulk, with particular attention to the connectivity properties and the morphology of the aggregated networks.

Telechelic star polymers as self-assembling units from the molecular to the macroscopic scale

By means of multiscale molecular simulations, we show that telechelic-star polymers are a simple, robust, and tunable system, which hierarchically self-assembles into soft-patchy particles and mechanically stabilizes selected, open crystalline structures. The self-aggregating patchy behavior can be fully controlled by the number of arms per star and by the fraction of attractive monomeric units at the free ends of the arms. Such self-assembled soft-patchy particles while forming, upon augmenting density, gel-like percolating networks, preserve properties as particle size, number, and arrangement of patches per particle. In particular, we demonstrate that the flexibility inherent in the soft-patchy particles brings forward a novel mechanism that leads to the mechanical stability of diamond and simple cubic crystals over a wide range of densities, and for molecular sizes ranging from about 10 nm up to the micrometer scale.

Aggregation phenomena in telechelic star polymer solutions

Telechelic star polymers are macromolecules with functionalized, mutually attractive end groups. We employ computer simulations on a lattice to investigate the phase behavior of trifunctional telechelic stars as a function of the fraction lambda of attractive terminal monomers. We find macrophase separation that disappears at some value 0.4<lambda<0.5 , at which point it is replaced by self-organization into interconnected micelles. We supplement the thermodynamics with a morphometric analysis that provides insight into the mesostructure of the resulting aggregates.

Pathway to copolymer collapse in dilute solution: uniform versus random distribution of comonomers

Monte Carlo simulations show that copolymers with uniformly (or periodically) distributed sticky comonomers collapse "cooperatively," abruptly forming a compact intermediate comprising a monomer shell surrounding a core of the aggregated comonomers. In comparison, random copolymers collapse through a relatively less-compact intermediate comprising a comonomer core surrounded by a fluffy monomer shell that densifies over a wide temperature range. This difference between the collapse pathways for random and uniform copolymers persists to higher chain lengths, where uniform copolymers tend to form multiple comonomer cores. In this paper, we describe the formation of such an intermediate state, and the subsequent collapse, by recognizing that these arise from the expected balance between comonomer aggregation enthalpy and loop formation entropy dictated by the chain microstructure.

Effective nonadditive pair potential for lock-and-key interacting particles: The role of the limited valence

Theoretical studies of self-assembly processes and condensed phases in colloidal systems are often based on effective interparticle potentials. Here we show that developing an effective potential for particles interacting with a limited number of "lock-and-key" selective bonds (due to the specificity of biomolecular interactions) requires-in addition to the nonsphericity of the potential-a (many body) constraint that prevents multiple bonding on the same site. We show the importance of retaining both valence and bond selectivity by developing, as a case study, a simple effective potential describing the interaction between colloidal particles coated by four single-strand DNA chains.