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 singlechain 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.

Coiled-coil domains can direct the assembly of protein block copolymers into physically crosslinked, viscoelastic hydrogels. Here we describe the use of fluorescence recovery after photobleaching (FRAP) to probe chain mobility in reversible hydrogels assembled from engineered proteins bearing terminal coiled-coil domains. We show that chain mobility can be related to the underlying dynamics of the coiled-coil domains by application of a 3-state "hopping" model of chain migration. We further show that genetic programming allows the effective mobility of network chains to be varied 500-fold through modest changes in protein sequence. Destabilization of the coiled-coil domains by site-directed mutagenesis increases the effective diffusivity of probe chains. Conversely, probe mobility is reduced by expanding the hydrophobic surface area of the coiled-coil domains through introduction of the bulky leucine surrogate homoisoleucine. Predictions from the 3-state model imply asymmetric sequential binding of the terminal domains. Brownian Dynamics simulations suggest that binding asymmetry is a general feature of reversible gels, arising from a loss in entropy as chains transition to a conformationally restricted bridged state.

The unique pressure exerted by active particles -the "swim" pressure -has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an extremely negative surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure is not a true pressure. At a boundary or interface, the reduction in particle swimming generates a net active force density -an entirely self-generated body force. The pressure at the boundary, which was previously identified as the swim pressure, is in fact an elevated (relative to the bulk) value of the traditional particle pressure that is generated by this interfacial force density. Recognizing this unique mechanism for stress generation allows us to define a much more physically plausible surface tension. We clarify the utility of the swim pressure as an "equivalent pressure" (analogous to those defined from electrostatic and gravitational body forces) and the conditions in which this concept can be appropriately applied. arXiv:1912.11727v1 [cond-mat.soft]

Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.

We study associating polymer gels under steady shear using Brownian dynamics simulation to explore the interplay between the network structure, dynamics, and rheology. For a wide range of flow rates, we observe the formation of shear bands with a pronounced difference in shear rate, concentration, and structure. A striking increase in the polymer pressure in the gradient direction with shear, along with the inherently large compressibility of the gels, is shown to be a crucial factor in destabilizing homogeneous flow through shear-gradient concentration coupling. We find that shear has only a modest influence on the degree of association, but induces marked spatial heterogeneity in the network connectivity. We attribute the increase in the polymer pressure (and polymer mobility) to this structural reorganization. DOI: 10.1103/PhysRevLett.119.117801 Associating polymers (APs) in dilute solution can aggregate into multichain clusters when the "sticker" (the physically associating moiety) attraction energy exceeds the thermal energy kT. Near the overlap concentration, sticker clusters can be bridged by polymer strands and form an interconnected volume spanning networka physical gel [1][2][3]. Such gels are found in both natural and synthetic systems, and display a striking array of rheological behavior, including strain stiffening [4], negative normal stresses [5], shear thickening [6,7], shear thinning [8], and shear banding [9][10][11][12][13][14][15].Despite the ubiquity and versatility of physical gels, a fundamental understanding of the interplay between their microstructure, dynamics, and rheological properties remains a challenging and open problem. For instance, while experiments and simulations of associative networks (including both AP [13][14][15] and colloidal [16] gels) under simple shear have observed spatial inhomogeneities in both shear rate and density, suggesting some form of sheargradient concentration coupling (SCC) [17][18][19][20], the microscopic mechanism for the instability is unclear. Mean-field based models [21] of AP rheology have largely focused on chain elasticity and have not accounted for density inhomogeneity (e.g., chain migration) which would require a constitutive relation describing the solute pressure (the driving force for chain migration) as a function of shear rate and concentration. To date, no such relation has been explored for physical gels-largely due to the experimental difficulty in measuring the pressure of a single species in solution under shear [22]. Furthermore, the observation of SCC in both AP and colloidal gels suggests that the common physics between the gels-such as network connectivity and transient particle localization-may play a key role in driving the instability.In this Letter, we report results from Brownian dynamics simulations of an AP gel under steady shear in the nonlinear, shear-thinning, regime. The polymers we study have multiple associating sticker groups along the backbone, a prevalent building block of natural and synthetic gels. Our stud...

External fields can decidedly alter the free energy landscape of soft materials and can be exploited as a powerful tool for the assembly of targeted nanostructures and colloidal materials. Here, we use computer simulations to demonstrate that nonequilibrium internal fields or forces -forces that are generated by driven components within a system -in the form of active particles can precisely modulate the dynamical free energy landscape of a model soft material, a colloidal gel. Embedding a small fraction of active particles within a gel can provide a unique pathway for the dynamically frustrated network to circumvent the kinetic barriers associated with reaching a lower free energy state through thermal fluctuations alone. Moreover, by carefully tuning the active particle properties (the propulsive swim force and persistence length) in comparison to those of the gel, the active particles may induce depletion-like forces between the constituent particles of the gel despite there being no geometric size asymmetry between the particles. These resulting forces can rapidly push the system toward disparate regions of phase space. Intriguingly, the state of the material can be altered by tuning macroscopic transport properties such as the solvent viscosity. Our findings highlight the potential wide-ranging structural and kinetic control facilitated by varying the dynamical properties of a remarkably small fraction of driven particles embedded in a host material.Advances in materials chemistry have opened new and exciting vistas for designing colloidal and nanoparticle building blocks, resulting in materials endowed with unique structures and accompanying properties. 1-4 Particle shape 5,6 and surface chemistry (e.g., decorating the particle surface with sticky "patches" 7,8 of organic or biological molecules 9-11 ) allow for exquisite control of the directionality of particle interactions, unlocking a multitude of structures with wide-ranging symmetries. The attractive particle interactions that are often used to stabilize these structures may also introduce a free energy landscape replete with barriers associated with particle rearrangement which can significantly delay or even preclude reaching the globally stable configuration. Indeed, the traditional pathways for homogeneous suspensions of particles to phase separate into dilute and dense phases, including spinodal decomposition and nucleation, can be exceedingly long and in practice can be the limiting factor in the experimental observation of ordered colloidal and nanoparticle-based materials. 12,13The classical system that demonstrates this issue of kinetic frustration is perhaps also the simplest: a colloidal suspension of spheres with short-range isotropic attractive interactions. While the equilibrium phase diagram of this system predicts fluid-solid coexistence for interaction strengths as little as a few times the thermal energy k B T , in practice the system is found to form a long-lived space-spanning network, a gel, for nearly the entire coexistence regio...

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