Efficient sampling of reversible cross-linking polymers: Self-assembly of single-chain polymeric nanoparticles

Molecular Simulation of Covalent Adaptable Networks and Vitrimers: A Review

Covalent adaptable networks and vitrimers are novel polymers with dynamic reversible bond exchange reactions for crosslinks, enabling them to modulate their properties between those of thermoplastics and thermosets. They have been gathering interest as materials for their recycling and self-healing properties. In this review, we discuss different molecular simulation efforts that have been used over the last decade to investigate and understand the nanoscale and molecular behaviors of covalent adaptable networks and vitrimers. In particular, molecular dynamics, Monte Carlo, and a hybrid of molecular dynamics and Monte Carlo approaches have been used to model the dynamic bond exchange reaction, which is the main mechanism of interest since it controls both the mechanical and rheological behaviors. The molecular simulation techniques presented yield sufficient results to investigate the structure and dynamics as well as the mechanical and rheological responses of such dynamic networks. The benefits of each method have been highlighted. The use of other tools such as theoretical models and machine learning has been included. We noticed, amongst the most prominent results, that stress relaxes as the bond exchange reaction happens, and that at temperatures higher than the glass transition temperature, the self-healing properties are better since more bond BERs are observed. The lifetime of dynamic covalent crosslinks follows, at moderate to high temperatures, an Arrhenius-like temperature dependence. We note the modeling of certain properties like the melt viscosity with glass transition temperature and the topology freezing transition temperature according to a behavior ruled by either the Williams-Landel-Ferry equation or the Arrhenius equation. Discrepancies between the behavior in dissociative and associative covalent adaptable networks are discussed. We conclude by stating which material parameters and atomistic factors, at the nanoscale, have not yet been taken into account and are lacking in the current literature.

Unfolding of the chromatin fiber driven by overexpression of noninteracting bridging factors

Nuclear molecules control the functional properties of the chromatin fiber by shaping its morphological properties. The biophysical mechanisms controlling how bridging molecules compactify chromatin are a matter of debate. On the one side, bridging molecules could cross-link faraway sites and fold the fiber through the formation of loops. Interacting bridging molecules could also mediate long-range attractions by first tagging different locations of the fiber and then undergoing microphase separation. Using a coarse-grained model and Monte Carlo simulations, we study the conditions leading to compact configurations both for interacting and noninteracting bridging molecules. In the second case, we report on an unfolding transition at high densities of the bridging molecules. We clarify how this transition, which disappears for interacting bridging molecules, is universal and controlled by entropic terms. In general, chains are more compact in the case of interacting bridging molecules because interactions are not valence limited. However, this result is conditional on the ability of our simulation methodology to relax the system toward its ground state. In particular, we clarify how, unless using reaction dynamics that change the length of a loop in a single step, the system is prone to remain trapped in metastable, compact configurations featuring long loops.

Crowded solutions of single-chain nanoparticles under shear flow

Single-chain nanoparticles (SCNPs) are ultrasoft objects obtained through purely intramolecular cross-linking of single polymer chains. By means of computer simulations with implemented hydrodynamic interactions, we investigate for the first time the effect of the shear flow on the structural and dynamic properties of SCNPs in semidilute and concentrated solutions. We characterize the dependence of several conformational and dynamic observables on the shear rate and the concentration, obtaining a set of power-law scaling laws. The concentration has a very different effect on the shear rate dependence of the former observables in SCNPs than in simple linear chains. Whereas for the latter the scaling behaviour is marginally dependent on the concentration, two clearly different scaling regimes are found for the SCNPs below and above the overlap concentration. At fixed shear rate SCNPs and linear chains also respond very differently to crowding. Whereas, at moderate and high Weissenberg numbers the linear chains swell, the SCNPs exhibit a complex non-monotonic behaviour. We suggest that these findings are inherently related to the topological interactions preventing concatenation of the SCNPs, which lead to less interpenetration than for linear chains, and to the limitation to stretching imposed by the permanent cross-links in the SCNPs, which itself limits the ways to spatially arrange in the shear flow.

Simulating sticky particles: A Monte Carlo method to sample a stratification

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample probability distributions subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. More generally, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions.

Combinatorial-Entropy-Driven Aggregation in DNA-Grafted Nanoparticles

We use computer simulations and experiments to study the interactions between nanoparticles (NPs) grafted with self-complementary DNA strands. Each strand ends with a sticky palindromic single-stranded sequence, allowing it to associate equally favorably with strands grafted on the same particle or on different NPs. Surprisingly we find an attractive interaction between a pair of NPs, and we demonstrate that at low temperature it arises purely from a combinatorial-entropy contribution. We evaluate theoretically and verify numerically this entropic contribution originating from the number of distinct bonding patterns associated with intra- and interparticle binding. This entropic attraction becomes more favorable with decreasing inter-NP distance because more sticky ends can participate in making this choice.

Understanding, predicting, and tuning the fragility of vitrimeric polymers

Fragility is an empirical property that describes how abruptly a glass-forming material solidifies upon supercooling. The degree of fragility carries important implications for the functionality and processability of a material, as well as for our fundamental understanding of the glass transition. However, the microstructural properties underlying fragility still remain poorly understood. Here, we explain the microstructure-fragility link in vitrimeric networks, a novel type of high-performance polymers with unique bond-swapping functionality and unusual glass-forming behavior. Our results are gained from coarse-grained computer simulations and first-principles mode-coupling theory (MCT) of star-polymer vitrimers. We first demonstrate that the vitrimer fragility can be tuned over an unprecedentedly broad range, from fragile to strong and even superstrong behavior, by decreasing the bulk density. Remarkably, this entire phenomenology can be reproduced by microscopic MCT, thus challenging the conventional belief that existing first-principles theories cannot account for nonfragile behaviors. Our MCT analysis allows us to rationally identify the microstructural origin of the fragile-to-superstrong crossover, which is rooted in the sensitivity of the static structure factor to temperature variations. On the molecular scale, this behavior stems from a change in dominant length scales, switching from repulsive excluded-volume interactions to intrachain attractions as the vitrimer density decreases. Finally, we develop a simplified schematic MCT model which corroborates our microscopically founded conclusions and which unites our findings with earlier MCT studies. Our work sheds additional light on the elusive structure-fragility link in glass-forming matter and provides a first-principles-based platform for designing amorphous materials with an on-demand dynamic response.

Harnessing entropy to enhance toughness in reversibly crosslinked polymer networks

Reversible crosslinking is a design paradigm for polymeric materials, wherein they are microscopically reinforced with chemical species that form transient crosslinks between the polymer chains. Besides the potential for self-healing, recent experimental work suggests that freely diffusing reversible crosslinks in polymer networks, such as gels, can enhance the toughness of the material without substantial change in elasticity. This presents the opportunity for making highly elastic materials that can be strained to a large extent before rupturing. Here, we employ Gaussian chain theory, molecular simulation, and polymer self-consistent field theory for networks to construct an equilibrium picture for how reversible crosslinks can toughen a polymer network without affecting its elasticity. Maximisation of polymer entropy drives the reversible crosslinks to bind preferentially near the permanent crosslinks in the network, leading to local molecular reinforcement without significant alteration of the network topology. In equilibrium conditions, permanent crosslinks share effectively the load with neighbouring reversible crosslinks, forming multi-functional crosslink points. The network is thereby globally toughened, while the linear elasticity is left largely unaltered. Practical guidelines are proposed to optimise this design in experiment, along with a discussion of key kinetic and timescale considerations.

Swap-Driven Self-Adhesion and Healing of Vitrimers

Vitrimers are covalent network materials, comparable in structure to classical thermosets. Unlike normal thermosets, they possess a chemical bond swap mechanism that makes their structure dynamic and suitable for activated welding and even autonomous self-healing. The central question in designing such materials is the trade-off between autonomy and material stability: the swap mechanism facilitates the healing, but it also facilitates creep, which makes the perfectly stable self-healing solid a hard goal to reach. Here, we address this question for the case of self-healing vitrimers made from star polymers. Using coarse-grained molecular dynamics simulations, we studied the adhesion of two vitrimer samples and found that they bond together on timescales that are much shorter than the stress relaxation time. We showed that the swap mechanism allows the star polymers to diffuse through the material through coordinated swap events, but the healing process is much faster and does not depend on this mobility.

Dynamics of Vitrimers: Defects as a Highway to Stress Relaxation

We propose a coarse-grained model to investigate stress relaxation in star-polymer networks induced by dynamic bond-exchange processes. We show how the swapping mechanism, once activated, allows the network to reconfigure, exploring distinct topological configurations, all of them characterized by complete extent of reaction. Our results reveal the important role played by topological defects in mediating the exchange reaction and speeding up stress relaxation. The model provides a representation of the dynamics in vitrimers, a new class of polymers characterized by bond-swap mechanisms which preserve the total number of bonds, as well as in other bond-exchange materials.