Biomimetic growth in polymer gels.

By modeling gels growing in confined environments, we uncover a biomimetic feedback mechanism between the evolving gel and confining walls that enables significant control over the properties of the grown gel. Our new model describes the monomer adsorption, polymerization and cross-linking involved in forming new networks and the resultant morphology and mechanical behavior of the grown gel. Confined between two hard walls, a thin, flat "parent" gel undergoes buckling; removal of the walls returns the gel to the flat structure.

Strain-Stiffening Hydrogels with Dynamic, Secondary Cross-Linking.

Hydrogels are water-swollen, typically soft networks useful as biomaterials and in other fields of biotechnology. Hydrogel networks capable of sensing and responding to external perturbations, such as light, temperature, pH, or force, are useful across a wide range of applications requiring on-demand cross-linking or dynamic changes. Thus far, although mechanophores have been described as strain-sensitive reactive groups, embedding this type of force-responsiveness into hydrogels is unproven.

Dynamic behavior of chemically tunable mechano-responsive hydrogels.

Using theory and simulation, we model the mechanical behavior of gels that encompass loops and dangling chain ends. If the loops remain folded and dangling ends are chemically inert, then these topological features just serve as defects. If, however, the loops unfold to expose the hidden ("cryptic") binding sites and the ends of the dangling chains are reactive, these moieties can form bonds that improve the gel's mechanical properties.

Controllable growth of interpenetrating or random copolymer networks.

Interpenetrating and random copolymer networks are vital in a number of industrial applications, including the fabrication of automotive parts, damping materials, and tissue engineering scaffolds. We develop a theoretical model for a process that enables the controlled growth of interpenetrating network (IPNs), or a random copolymer network (RCN) of specified size and mechanical properties. In this process, a primary gel "seed" is immersed into a solution containing the secondary monomer and crosslinkers.

Buckling-induced interaction between circular inclusions in an infinite thin plate.

Design of slender artificial materials and morphogenesis of thin biological tissues typically involve stimulation of isolated regions (inclusions) in the growing body. These inclusions apply internal stresses on their surrounding areas that are ultimately relaxed by out-of-plane deformation (buckling). We utilize the Föppl-von Kármán model to analyze the interaction between two circular inclusions in an infinite plate that their centers are separated a distance of 2ℓ.

Harnessing biomimetic cryptic bonds to form self-reinforcing gels.

Cryptic sites, which lay hidden in folded biomolecules, become exposed by applied force and form new bonds that reinforce the biomaterial. While these binding interactions effectively inhibit mechanical deformation, there are few synthetic materials that harness mechano-responsive cryptic sites to forestall damage. Here, we develop a computational model to design polymer gels encompassing cryptic sites and a lower critical solution temperature (LCST).

Modeling the behavior of inclusions in circular plates undergoing shape changes from two to three dimensions.

Growth of biological tissues and shape changes of thin synthetic sheets are commonly induced by stimulation of isolated regions (inclusions) in the system. These inclusions apply internal forces on their surroundings that, in turn, promote 2D layers to acquire complex 3D configurations. We focus on a fundamental building block of these systems, and consider a circular plate that contains an inclusion with dilative strains.

Modeling the formation of double rolls from heterogeneously patterned gels.

Both stimuli-responsive gels and growing biological tissue can undergo pronounced morphological transitions from two-dimensional (2D) layers into 3D geometries. We derive an analytical model that allows us to quantitatively predict the features of 2D-to-3D shape changes in polymer gels that encompasses different degrees of swelling within the sample. We analyze a particular configuration that emerges from a flat rectangular gel that is divided into two strips (bistrips), where each strip is swollen to a different extent in solution.

"Patterning with loops" to dynamically reconfigure polymer gels.

The structural and mechanical properties of gels can be controlled by promoting the unfolding (and refolding) of loops (stored lengths) embedded within the networks. As a loop unfolds, the released chain length can increase the extensibility and reconfigurability of the gel. Here, we develop a theoretical model that couples the elasticity of the gel to the dynamic transitions occurring in loops that lie between the crosslinks.

Combining ATRP and FRP Gels: Soft Gluing of Polymeric Materials for the Fabrication of Stackable Gels.

Stackable gels comprised of layers of dissimilar polymers were synthesized by combining conventional free radical polymerization (FRP) and atom transfer radical polymerization (ATRP) using two approaches: (i) polymerization of a pre-gel solution containing a monomer and cross-linker introduced on top of a previously prepared gel, and (ii) simultaneous polymerization of two immiscible pre-gel solutions remaining in contact. All permutations of FRP and ATRP yielded single-piece, connected, amphiphilic gels regardless of the order of polymerization. Furthermore, multi-layer ATRP gels combining different polymers were synthesized with the FRP layer as a gluing agent.

Living Additive Manufacturing: Transformation of Parent Gels into Diversely Functionalized Daughter Gels Made Possible by Visible Light Photoredox Catalysis.

Light-initiated additive manufacturing techniques typically rely on layer-by-layer addition or continuous extraction of polymers formed via nonliving, free radical polymerization methods that render the final materials "dead" toward further monomer insertion; the polymer chains within the materials cannot be reactivated to induce chain extension. An alternative "living additive manufacturing" strategy would involve the use of photocontrolled living radical polymerization to spatiotemporally insert monomers into dormant "parent" materials to generate more complex and diversely functionalized "daughter" materials. Here, we demonstrate a proof-of-concept study of living additive manufacturing using end-linked polymer gels embedded with trithiocarbonate iniferters that can be activated by photoinduced single-electron transfer from an organic photoredox catalyst in solution.

Micromechanics of emergent patterns in plastic flows.

Crystalline solids undergo plastic deformation and subsequently flow when subjected to stresses beyond their elastic limit. In nature most crystalline solids exist in polycrystalline form. Simulating plastic flows in polycrystalline solids has wide ranging applications, from material processing to understanding intermittency of earthquake dynamics.

Coarsening in polycrystalline material using quaternions.

We develop a phase field model to study the phenomenon of recrystallization and grain coarsening in polycrystalline material. A unique feature of our model is that it can time-evolve the actual orientation field of a material, expressed in terms of quaternions, a four-dimensional non-conserved vector field. The quaternions evolve in time following a Langevin dynamics.

Predicting the coherence resonance curve using a semianalytical treatment.

Emergence of noise-induced regularity or coherence resonance in nonlinear excitable systems is well known. We explain theoretically why the normalized variance (V(N)) of interspike time intervals, which is a measure of regularity in such systems, has a unimodal profile. Our semianalytic treatment of the associated spiking process produces a general yet simple formula for V(N) , which we show is in very good agreement with numerics in two test cases, namely, the FitzHugh-Nagumo model and the chemical oscillator model.