Victor V. Yashin

Theoretical and computational modeling of self-oscillating polymer gels

The authors model wave propagation in swollen, chemoresponsive polymer gels that are undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction. To carry out this study, they first modify the Oregonator model for BZ reactions in simple solutions to include the effect of the polymer on the reaction kinetics. They then describe the gel dynamics through the framework of the two-fluid model. The polymer-solvent interactions that are introduced through the BZ reaction are captured through a coupling term, which is added to the Flory-Huggins model for polymer-solvent mixtures. The resulting theoretical model is then used to develop the gel lattice spring model (gLSM), which is a computationally efficient approach for simulating large-scale, two-dimensional (2D) deformations and chemical reactions within a swollen polymer network. The 2D calculations allow the authors to probe not only volume changes but also changes in the samples shape. Using the gLSM, they determine the pattern formation and shape changes in 2D rectangular BZ gels that are anchored to a solid wall. They demonstrate that the dynamic patterns depend on whether the gel is expanded or contracted near the wall, and on the samples dimensions. Finally, they isolate a scenario where the detachment of the gel from the wall leads to macroscopic motion of the entire sample.

Shape- and size-dependent patterns in self-oscillating polymer gels

Polymeric hydrogels that exhibit autonomous, coupled chemical and mechanical oscillations are a unique example of synthetic, active soft matter. Here, we explore the effects of gel aspect ratio and absolute dimensions on pattern formation in hydrogels undergoing the Belousov-Zhabotinsky (BZ) reaction. We synthesize and analyze N-isopropylacrylamide gels containing covalently bound BZ catalyst and polyacrylamide-silica gel composites containing physically associated BZ catalyst. Through both experiments and computational simulations, we demonstrate that the oscillating chemical patterns within BZ gels can be altered by changing the shape and size of the gel, and that these patterns evolve over long timescales. In our simulations, we utilize an improved Oregonator model, which explicitly accounts for the total concentration of the catalyst grafted onto the polymer network. We find that the three-dimensional simulations of the BZ gels successfully reproduce patterns, oscillation periodicity, and catalyst concentration-dependence observed in experiments. Together, these findings validate our theoretical and computational approaches for modeling chemomechanical coupling in active, chemo-responsive gels, and enable future studies that exploit the shape- and size-confinement effects of self-oscillating reactions.

Designing communicating colonies of biomimetic microcapsules.

Using computational modeling, we design colonies of biomimetic microcapsules that exploit chemical mechanisms to communicate and alter their local environment. As a result, these synthetic objects can self-organize into various autonomously moving structures and exhibit ant-like tracking behavior. In the simulations, signaling microcapsules release agonist particles, whereas target microcapsules release antagonist particles and the permeabilities of both capsule types depend on the local particle concentration in the surrounding solution. Additionally, the released nanoscopic particles can bind to the underlying substrate and thereby create adhesion gradients that propel the microcapsules to move. Hydrodynamic interactions and the feedback mechanism provided by the dissolved particles are both necessary to achieve the collective dynamics exhibited by these colonies. Our model provides a platform for integrating both the spatial and temporal behavior of assemblies of “artificial cells,” and allows us to design a rich variety of structures capable of exhibiting complex, cooperative behavior. Due to the cell-like attributes of polymeric microcapsules and polymersomes, material systems are available for realizing our predictions.

Exploiting gradients in cross-link density to control the bending and self-propelled motion of active gels

Oscillating polymer gels undergoing the Belousov–Zhabotinsky (BZ) reaction provide an ideal medium for probing the interplay between chemical energy and mechanical action. Inspired by recent experiments, we use computational modeling to determine how gradients in crosslink density across the width of a sample can drive long, thin BZ gels to both oscillate and bend, and thereby undergo concerted motion. Free in solution, these samples move forward (in the direction of lower cross-link density) through a rhythmic bending and unbending. Our simulations allow us to not only isolate optimal ranges of parameters for achieving this distinctive behavior but also provide insight into the dynamic coupling between chemical and mechanical energy that is needed to produce the self-sustained motion. We then model samples that are mechanically constrained by their attachment to a flat, rigid surface. By varying the concentration of the reagents in the solution, we show that the undulations of the samples free end can be significantly modified, so that the overall motion can be directed either upwards or downwards. The findings from these studies provide guidelines for creating autonomously moving objects, which can be used for robotic or microfluidic applications.

Controlling the dynamic behavior of heterogeneous self-oscillating gels

Polymer gels undergoing the Belousov–Zhabotinsky (BZ) reaction exhibit autonomous, coupled chemical and mechanical oscillations. The ruthenium catalyst that contributes to the rhythmic swelling and deswelling of the gel is chemically grafted to the backbones of the polymer chains. Using both experiments and computer simulations, we examine films of heterogeneous BZ gels where the catalyst is localized in distinct sub-millimeter sized patches, and these BZ patches are surrounded by a non-reactive polymer network. The photo-polymerization method for sample fabrication permits control over the size of the disk-shaped patches, the ruthenium concentration in each of the disks, and arrangement of the disks in the non-reactive matrix. We first consider two distinct disks of the BZ gel that differ in size or the concentration of catalyst, [Ru]. By varying the separation between the disks, we isolated conditions necessary for the synchronization between the chemo-mechanical oscillations within these BZ patches. We then considered an arrangement of four disks and demonstrated that the two-dimensional propagation of the traveling wave within the film could be controlled by tailoring the size and [Ru] in the patches. Subsequently, we present results on the computational modeling of such heterogeneous self-oscillating gels. We demonstrate that the simulations capture the experimentally observed effects of the catalyst concentration, patch size, and inter-patch distance on the synchronization of oscillations in the neighboring BZ gels. Taken together, the experimental and computational studies reveal how the synchronization effects can be utilized to control the dynamical behavior of the entire system.

Modeling the response of dual cross-linked nanoparticle networks to mechanical deformation

We develop a hybrid computational model for the behavior of a network of cross-linked polymer-grafted nanoparticles (PGNs). The individual nanoparticles are composed of a rigid core and a corona of grafted polymers that encompass reactive end groups. With the overlap of the coronas on adjacent particles, the reactive end groups can form permanent or labile bonds, which lead to the formation of a “dual cross-linked” network. To capture these multi-scale interactions, our approach integrates the essential structural features of the polymer grafted nanoparticles, the interactions between the overlapping coronas, and the kinetics of bond formation and rupture between the reactive groups on the chain ends. Via this model, we determine the tensile properties of the dual cross-linked samples. We find that the mechanical behavior of the network can be tailored by altering the bond energies of the labile bonds, the fraction of permanent bonds in the network and the thickness of the polymer corona. In particular, for a network with weaker labile bonds, an increase in fraction of permanent bonds and the contour length of the chain can yield a tough network that behaves like a polymeric material, which exhibits cold drawing/necking. On the other hand, similar changes to the network with stronger labile bonds lead to an increase in toughness, with the network characteristics being similar to that of a purely ductile material. Variations in the ratio between the strain rate and the bond rupture rate are also found to affect the response of the networks. Our model provides a powerful approach for predicting how critical features of the system affect the performance of cross-linked polymer-grafted nanoparticles.

Computational Design of Active, Self-Reinforcing Gels

Many living organisms have evolved a protective mechanism that allows them to reversibly alter their stiffness in response to mechanical contact. Using theoretical modeling, we design a mechanoresponsive polymer gel that exhibits a similar self-reinforcing behavior. We focus on cross-linked gels that contain Ru(terpy)(2) units, where both terpyridine ligands are grafted to the chains. The Ru(terpy)(2) complex forms additional, chemoresponsive cross-links that break and re-form in response to a repeated oxidation and reduction of the Ru. In our model, the periodic redox variations of the anchored metal ion are generated by the Belousov-Zhabotinsky (BZ) reaction. Our computer simulations reveal that compression of the BZ gel leads to a stiffening of the sample due to an increase in the cross-link density. These findings provide guidelines for designing biomimetic, active coatings that send out a signal when the system is impacted and use this signaling process to initiate the self-protecting behavior.

Global signaling of localized impact in chemo-responsive gels

A vital function performed by skin is to send a chemical alarm signal throughout the system in response to irritation or damage. Using our 3D model for chemo-responsive gels, we design a coating that can perform an analogous, biomimetic function. Our system consists of a polymer gel undergoing the Belousov–Zhabotinsky (BZ) reaction. We show that such coatings respond to a spatially localized mechanical force by exhibiting a range of signaling behavior. For example, an initially stationary gel can emit transient waves in response to a sufficiently weak, localized impact. A stronger localized impact, however, can generate a global signal, which encompasses both chemical waves and surface ripples that propagate across the entire sample. This complex dynamical response persists even after the force is lifted. Furthermore, the spatial patterns formed by these oscillating gels reveal the location and magnitude of the applied force. Our findings open up the possibility of harnessing BZ gels for a range of applications, such as creating sensors that transmit a global signal in response to a local mechanical impact.

Theoretical model of interfacial polymerization

We present a theoretical description for the creation of a thin polymeric layer through the interfacial polymerization of two immiscible, low molecular weight liquids. The theory specifically takes into account the effects of polydispersity on the formation of the polymer film at the liquid-liquid interface. Consequently, we can describe the structure of the growing film and the molecular weight distribution of the resultant polymer chains. We focus on a model system where alternating AB copolymers are formed at the interface between phase-separated, low molecular weight species A and B. It is assumed that any A(B) unit can reversibly attach to any available B(A) unit or B(A)-ended chain. The formation of the copolymer layer is described by a system of reaction-diffusion equations, which detail the chemical evolution and diffusive dynamics of the polydisperse mixture of AB copolymers around the interface, and the evolution of the interface itself. Using this model, we determine the effects of the chemical reaction rates and the initial conditions on the kinetics of forming the AB copolymer layer and the structure of this film.

Designing self-propelled microcapsules for pick-up and delivery of microscopic cargo

Using computational modeling, we design a system of active polymeric microcapsules that pick-up, convey and drop-off a cargo between locations on a patterned surface. To create this system, we harness “signaling” and “target” capsules, which release nanoparticles into the surrounding solution. These nanoparticles bind to the underlying surface and thereby create adhesion gradients that trigger the spontaneous motion of the capsules. One signaling and two target capsules are found to form a stable triad, which can transport a cargo of four target capsules. Guided by an adhesive stripe on the surface, the triad and cargo form a “train” that moves autonomously along the substrate. The stripe is designed to encompass a small region with a lower adhesive strength. Through the aid of this patch, the triad can deposit its cargo and move on to potentially pick up a new payload at another location. Since the microcapsules can encase a wide variety of compounds, the system could provide an effective means of autonomously transporting a broad range of substances within microfluidic devices.