Shear-Induced Heterogeneity in Associating Polymer Gels: Role of Network Structure and Dilatancy

Sequence and gelation in supramolecular polymers

Supramolecular polymer networks exhibit unique and tunable thermodynamic and dynamic properties that are attractive for a wide array of applications, such as adhesives, rheology modifiers, and compatibilizers. Coherent states (CS) field theories have emerged as a powerful approach for describing the possibly infinite reaction products that result from associating polymers. Up to this point, CS theories have focused on relatively simple polymer architectures. In this work, we develop an extension of the CS framework to study polymers with reversible bonds distributed along the polymer backbone, opening a broad array of new materials that can be studied with theoretical methods. We use this framework to discern the role of reactive site placement on sol-gel phase behavior, including the prediction of a microstructured gel phase that has not been reported for neutral polymer gels. Our results highlight the subtleties of thermodynamics in supramolecular polymers and the necessity for theories that capture them.

Structural and dynamic heterogeneity in associative networks formed by artificially engineered protein polymers

This work investigates static gel structure and cooperative multi-chain motion in associative networks using a well-defined model system composed of artificial coiled-coil proteins. The combination of small-angle and ultra-small-angle neutron scattering provides evidence for three static length scales irrespective of protein gel design which are attributed to correlations arising from the blob length, inter-junction spacing, and multi-chain density fluctuations. Self-diffusion measurements using forced Rayleigh scattering demonstrate an apparent superdiffusive regime in all gels studied, reflecting a transition between distinct "slow" and "fast" diffusive species. The interconversion between the two diffusive modes occurs on a length scale on the order of the largest correlation length observed by neutron scattering, suggesting a possible caging effect. Comparison of the self-diffusive behavior with characteristic molecular length scales and the single-sticker dissociation time inferred from tracer diffusion measurements supports the primarily single-chain mechanisms of self-diffusion as previously conceptualized. The step size of the slow mode is comparable to the root-mean-square length of the midblock strands, consistent with a single-chain walking mode rather than collective motion of multi-chain aggregates. The transition to the fast mode occurs on a timescale 10-1000 times the single-sticker dissociation time, which is consistent with the onset of single-molecule hopping. Finally, the terminal diffusivity depends exponentially on the number of stickers per chain, further suggesting that long-range diffusion occurs by molecular hopping rather than sticky Rouse motion of larger assemblies. Collectively, the results suggest that diffusion of multi-chain clusters is dominated by the single-chain pictures proposed in previous coarse-grained modeling.

Mechanical theory of nonequilibrium coexistence and motility-induced phase separation

Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both nonequilibrium and equilibrium systems. Here, we present a general mechanical theory for phase separation rooted in ideas explored nearly a half-century ago in the study of inhomogeneous fluids. The core idea is that the mechanical forces within the interface separating two coexisting phases uniquely determine coexistence criteria, regardless of whether a system is in equilibrium or not. We demonstrate the power and utility of this theory by applying it to active Brownian particles, predicting a quantitative phase diagram for motility-induced phase separation in both two and three dimensions. This formulation additionally allows for the prediction of novel interfacial phenomena, such as an increasing interface width while moving deeper into the two-phase region, a uniquely nonequilibrium effect confirmed by computer simulations. The self-consistent determination of bulk phase behavior and interfacial phenomena offered by this mechanical perspective provide a concrete path forward toward a general theory for nonequilibrium phase transitions.

Learning heterogenous reaction rates from stochastic simulations

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning nonhomogeneous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution.

Irreversible Shear-Activated Gelation of a Liquid Crystalline Polyelectrolyte

We report irreversible, shear-activated gelation in liquid crystalline solutions of a rigid polyelectrolyte that forms rodlike assemblies (rods) in salt-free solution. At rest, the liquid crystalline solutions are kinetically stable against gelation and exhibit low viscosities. Under steady shear at, or above, a critical shear rate, a physically cross-linked, nematic gel network forms due to linear growth and branching of the rods. Above a critical shear rate, the time scale of gelation can be tuned from hours to nearly instantaneously by varying the shear rate and solution concentration. The shear-activated gels are distinct in their structure and rheological properties from thermoreversible gels. At a fixed concentration, the induction time prior to gelation decreases exponentially with the shear rate. This result indicates that shear-activated thermalization of the electrostatically stabilized rods overcomes the energy barrier for rod-rod contact, enabling rod fusion and subsequent irreversible network formation.

Mechanisms of Diffusion in Associative Polymer Networks: Evidence for Chain Hopping

Networks assembled by reversible association of telechelic polymers constitute a common class of soft materials. Various mechanisms of chain migration in associative networks have been proposed; yet there remains little quantitative experimental data to discriminate among them. Proposed mechanisms for chain migration include multichain aggregate diffusion as well as single-chain mechanisms such as "walking" and "hopping", wherein diffusion is achieved by either partial ("walking") or complete ("hopping") disengagement of the associated chain segments. Here, we provide evidence that hopping can dominate the effective diffusion of chains in associative networks due to a strong entropic penalty for bridge formation imposed by local network structure; chains become conformationally restricted upon association with two or more spatially separated binding sites. This restriction decreases the effective binding strength of chains with multiple associative domains, thereby increasing the probability that a chain will hop. For telechelic chains this manifests as binding asymmetry, wherein the first association is effectively stronger than the second. We derive a simple thermodynamic model that predicts the fraction of chains that are free to hop as a function of tunable molecular and network properties. A large set of self-diffusivity measurements on a series of model associative polymers finds good agreement with this model.