Theory of phase transition in polymer gels

Critical Conditions Regulating the Gelation in Macroionic Cluster Solutions

The critical gelation conditions observed in dilute aqueous solutions of multiple nanoscale uranyl peroxide molecular clusters are reported, in the presence of multivalent cations. This gelation is dominantly driven by counterion-mediated attraction. The gelation areas in the corresponding phase diagrams all appear in similar locations, with a characteristic triangle shape outlining three critical boundary conditions, corresponding to the critical cluster concentration, cation/cluster ratio, and the degree of counterion association with increasing cluster concentration. These interesting phrasal observations reveal general conditions for gelation driven by electrostatic interactions in hydrophilic macroionic solutions.

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. Polymerization and cross-linking in the confined parent generates the next stage of growth, forming a random copolymer network (RCN). When the walls are removed, the RCN remains in the buckled state, simultaneously "locking in" these patterns and increasing the Young's modulus by two orders of magnitude. Confinement of thicker gels between harder or softer 3D walls leads to controllable mechanical heterogeneities, where the Young's modulus between specific domains can differ by three orders of magnitude. These systems effectively replicate the feedback between mechanics and morphology in biological growth, where mechanical forces guide the structure formation throughout stages of growth. The findings provide new guidelines for shaping "growing materials" and introducing new approaches to matching form and function in synthetic systems.

Onset of criticality in hyper-auxetic polymer networks

Against common sense, auxetic materials expand or contract perpendicularly when stretched or compressed, respectively, by uniaxial strain, being characterized by a negative Poisson's ratio ν. The amount of deformation in response to the applied force can be at most equal to the imposed one, so that ν = - 1 is the lowest bound for the mechanical stability of solids, a condition here defined as "hyper-auxeticity". In this work, we numerically show that ultra-low-crosslinked polymer networks under tension display hyper-auxetic behavior at a finite crosslinker concentration. At this point, the nearby mechanical instability triggers the onset of a critical-like transition between two states of different densities. This phenomenon displays similar features as well as important differences with respect to gas-liquid phase separation. Since our model is able to faithfully describe real-world hydrogels, the present results can be readily tested in laboratory experiments, paving the way to explore this unconventional phase behavior.

Putting the Squeeze on Phase Separation

Phase separation is a ubiquitous process and finds applications in a variety of biological, organic, and inorganic systems. Nature has evolved the ability to control phase separation to both regulate cellular processes and make composite materials with outstanding mechanical and optical properties. Striking examples of the latter are the vibrant blue and green feathers of many bird species, which are thought to result from an exquisite control of the size and spatial correlations of their phase-separated microstructures. By contrast, it is much harder for material scientists to arrest and control phase separation in synthetic materials with such a high level of precision at these length scales. In this Perspective, we briefly review some established methods to control liquid-liquid phase separation processes and then highlight the emergence of a promising arrest method based on phase separation in an elastic polymer network. Finally, we discuss upcoming challenges and opportunities for fabricating microstructured materials via mechanically controlled phase separation.

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. After the latter species are absorbed into the primary network, the absorbed monomers are polymerized to form the secondary polymer chains, which then can undergo further crosslinking to form an IPN, or undergo inter-chain exchange with the existing network to form a RCN. The swelling and elastic properties of the IPN and RCN networks can be tailored by modifying the monomer and crosslinker concentrations in the surrounding solution, or by tuning the enthalpic interactions between the primary polymer, secondary monomer and solvent through a proper choice of chemistry. This process can be used repeatedly to fabricate gels with a range of mechanical properties from stiff, rigid materials to soft, flexible networks, allowing the method to meet the materials requirements of a variety of applications.

Application of a Clapeyron-Type Equation to the Volume Phase Transition of Polymer Gels

The applicability of the Clapeyron equation to the volume phase transition of cylindrical poly(N-isopropylacrylamide)-based gels under external force is reviewed. Firstly, the equilibrium conditions for the gels under tension are shown, and then we demonstrate that the Clapeyron equation can be applied to the volume phase transition of polymer gels to give the transition entropy or the transition enthalpy. The transition enthalpy at the volume phase transition obtained from the Clapeyron equation is compared with that from the calorimetry. A coefficient of performance, or work efficiency, for a gel actuator driven by the volume phase transition is also defined. How the work efficiency depends on applied force is shown based on a simple mechanical model. It is also shown that the force dependence of transition temperature is closely related to the efficiency curve. Experimental results are compared with the theoretical prediction.

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). LCST gels swell with a decrease in temperature, thereby generating internal stresses within the sample. The gels also encompass loops held together by the cryptic sites, as well as dangling chains with chemically reactive ends. A decrease in temperature or an applied force causes the loops to unfold and expose the cryptic sites, which then bind to the dangling chains. We show that these binding interactions act as "struts" that reinforce the network, as indicated by a significant decrease in the volume of the gel (from 44% to 80%) and shifts in the volume phase transition temperature. Once the temperature is increased or the deformation is removed, the latter "cryptic bonds" are broken, allowing the loops to refold and the gel to return to its original state. These findings provide guidelines for designing polymer networks with reversible, mechano-responsive bonds, which allow gels to undergo a self-stiffening behavior in response to a temperature-induced internal stress or external force. When applied as a coating, these gels can prevent the underlying materials from undergoing damage and thus, extend the lifetime of the system.

Adhesion and Particle Removal from Surface-Tethered Poly(N-Isopropylacrylamide) Coatings Using Hydrodynamic Shear Forces

Thermally responsive coatings of poly(N-isopropylacrylamide), or poly(NIPAAm), have a volume phase transition temperature (VPTT) near 32 °C. Below this temperature, the coating imbibes water and swells. Above this temperature, the coating rejects water and collapses. Herein, a spinning disk method is used to determine the hydrodynamic shear stress necessary to remove 10 μm polystyrene (PS) microspheres capped with either carboxylic acid (COOH) functionality or immunoglobulin (IgG) proteins from the coatings as a function of coating thickness and temperature. In the case of the PS-COOH, the hydrodynamic shear stress necessary to remove the microspheres was consistently larger below the VPTT than above the VPTT of the poly(NIPAAm) coating. In the case of PS-IgG, the trend was reversed, in which the hydrodynamic shear stress necessary to remove the microspheres was consistently smaller below the VPTT than above the VPTT. Simple scaling relationships were developed to explain the findings within the Johnson-Kendall-Roberts (JKR) model of contact mechanics, which illustrates the delicate interplay between the pull-off force and contact radius (as determined by the coating shear modulus) in governing particle removal from soft surfaces with hydrodynamic forces.

Effect of responsive graft length on mechanical toughening and transparency in microphase-separated hydrogels

Effective remote control of mechanical toughening can be achieved by using thermo-responsive grafts such as poly(N-isopropylacrylamide) (PNIPAm) in a hydrophilic covalently cross-linked polymer network. The weight ratio of PNIPAm grafts in the network may impart such a thermo-responsive mechanical reinforcement. Here, we show that the network topology - especially graft length - is likewise crucial. A series of covalently cross-linked poly(N,N-dimethylacrylamide) (PDMA) gels grafted with PNIPAm side-chains of different lengths were designed and studied on both sides of phase separation temperature T_c, at a fixed overall polymer concentration of 16.7 wt% and constant PDMA/PNIPAm weight ratio. Phase-separated PNIPAm organic micro-domains were expected to act as responsive fillers above T_c and to generate a purely organic nanocomposite (NC). In contrast to conventional NC gels where dissipative processes take place at the solid nanoparticle/matrix interface, here dissipation originates from the disruption of the filler itself by the unravelling of the PNIPAm grafts embedded in collapsed domains. Results show that PNIPAm graft length is a key parameter to enhance - reversibly and on-demand - the mechanical response. The longer the graft is, the more effective the mechanical toughening is. Interestingly, for long PNIPAm grafts, above T_c, the hydrogels combine perfect transparency together with both increased stiffness and fracture toughness (up to 150 J m^-2) at constant macroscopic volume. As a proof of concept, stimuli-responsive adhesion and shape-memory properties were designed to probe the inter-chain bridging efficiency (in bulk or bridging the interface).

How to Force Polymer Gels to Show Volume Phase Transitions

Relatively few polymer gels are known to show volume phase transition where the gels undergo an abrupt change in the degree of swelling by passing through a three-phase equilibrium. Characteristic for such transition is the existence of van der Waals (vdW) loop on the dependence of solvent chemical potential versus polymer concentration. For the χ-induced transition, the existence of vdW loop is determined by the concentration dependence of the interaction function. It is shown that expansive mechanical strains can assist in development of the vdW loop. Systems characterized by continuous change of the degree of swelling transform upon such strain into ones where the degree of swelling changes much and abruptly. Also, expansive modes of strain can make the transition wider and more robust in gels where transition is already observed under free swelling condition. The possibility to induce the volume phase transition by external stresses can be utilized for finding other stimuli sensitive gels, strengthening of gel response, and in modeling of properties of gel constructs by Finite Element Method.

Controlling deformations of gel-based composites by electromagnetic signals within the GHz frequency range

Using theoretical and computational modeling, we focus on dynamics of gels filled with uniformly dispersed ferromagnetic nanoparticles subjected to electromagnetic (EM) irradiation within the GHz frequency range. As a polymer matrix, we choose poly(N-isopropylacrylamide) gel, which has a low critical solution temperature and shrinks upon heating. When these composites are irradiated with a frequency close to the Ferro-Magnetic Resonance (FMR) frequency, the heating rate increases dramatically. The energy dissipation of EM signals within the magnetic nanoparticles results in the heating of the gel matrix. We show that the EM signal causes volume phase transitions, leading to large deformations of the sample for a range of system parameters. We propose a model that accounts for the dynamic coupling between the elastodynamics of the polymer gel and the FMR heating of magnetic nanoparticles. This coupling is nonlinear: when the system is heated, the gel shrinks during the volume phase transition, and the particle concentration increases, which in turn results in an increase of the heating rates as long as the concentration of nanoparticles does not exceed a critical value. We show that the system exhibits high selectivity to the frequency of the incident EM signal and can result in a large mechanical feedback in response to a small change in the applied signal. These results suggest the design of a new class of soft active gel-based materials remotely controlled by low power EM signals within the GHz frequency range.

"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. Using this model, we show that a thermally-induced swelling of the gel generates an internal strain, which unfolds the loops and thereby further increases the degree of gel swelling. We exploit this cooperative behavior to reconfigure the gel by patterning the location of the loops within the sample. Through this approach, we convert flat, two-dimensional layers into three-dimensional forms and introduce architectural features into uniform 3D slabs. At a fixed temperature, an applied force produces analogous structural transformations. The shape-changes are reversible: the systems return to their original structure when the temperature is reset or the force is removed. The findings provide guidelines for creating materials that interconvert thermal, chemical and mechanical energy to perform work. Such systems could be useful for designing soft robotic materials that convert environmental stimuli into useful functionality.

Designing polymer gels and composites that undergo bio-inspired phototactic reconfiguration and motion

Inspired by the adaptive behavior of photo-responsive biological organisms, we develop analytical and computational models to design polymer gels and composites that can be dynamically reconfigured and driven to move with the application of light. We focus on gels formed from poly(N-isopropylacrylamide) and functionalized with spirobenzopyran (SP) chromophores, which become hydrophobic under blue light in acidic aqueous solution. Using our modeling approaches, we irradiate the gels through photomasks and demonstrate that the shapes of the samples can be reversibly and remotely 'remolded' by varying the apertures in the masks. By simulating the effect of repeatedly moving the light across the sample, we also show that the gel can undergo directed motion. We then examine gels that contain both SP chromophores and the ruthenium catalysts that drive the oscillatory Belousov-Zhabotinsky reaction. These dual-functionalized gels undergo spontaneous, self-sustained motion even when the lights are held stationary. We also simulate the behavior of composites formed from SP-functionalized fibers embedded in the poly(N-isopropylacrylamide) gel. With the SP-functionalization confined to the fibers, light and heat act as orthogonal stimuli and thus the composites display distinctly different modes of movement when the different cues are applied to the samples. Overall, our findings provide guidelines for using light to controllably reconfigure the shape and drive the movement of gel-based materials and thus, tailor the material to display different functionalities.

Thermoresponsive Toughening with Crack Bifurcation in Phase-Separated Hydrogels under Isochoric Conditions

A novel mode of gel toughening displaying crack bifurcation is highlighted in phase-separated hydrogels. By exploring original covalent network topologies, phase-separated gels under isochoric conditions demonstrate advanced thermoresponsive mechanical properties: excellent fatigue resistance, self-healing, and remarkable fracture energies. Beyond the phase-transition temperature, the fracture proceeds by a systematic crack-bifurcation process, unreported so far in gels.

Two-dimensional magnetic colloids under shear

Complex rheological properties of soft disordered solids, such as colloidal gels or glasses, inspire a range of novel applications. However, the microscopic mechanisms of their response to mechanical loading are not well understood. Here, we elucidate some aspects of these mechanisms by studying a versatile model system, i.e. two-dimensional superparamagnetic colloids in a precessing magnetic field, whose structure can be tuned from a hexagonal crystal to a disordered gel network by varying the external field opening angle θ. We perform Langevin dynamics simulations subjecting these structures to a constant shear rate and observe three qualitatively different types of material response. In hexagonal crystals (θ = 0°), at a sufficiently low shear rate, plastic flow occurs via successive stress drops at which the stress releases due to the formation of dislocation defects. The gel network at θ = 48°, on the contrary, via bond rearrangement and transient shear banding evolves into a homogeneously stretched network at large strains. The latter structure remains metastable after switching off of the shear. At θ = 50°, the external shear makes the system unstable against phase separation and causes a failure of the network structure leading to the formation of hexagonal close packed clusters interconnected by particle chains. At a microcopic level, our simulations provide insight into some of the mechanisms by which strain localization as well as material failure occur in a simple gel-like network. Furthermore, we demonstrate that new stretched network structures can be generated by the application of shear.

Designing Dual-functionalized Gels for Self-reconfiguration and Autonomous Motion

Human motion is enabled by the concerted expansion and contraction of interconnected muscles that are powered by inherent biochemical reactions. One of the challenges in the field of biomimicry is eliciting this form of motion from purely synthetic materials, which typically do not generate internalized reactions to drive mechanical action. Moreover, for practical applications, this bio-inspired motion must be readily controllable. Herein, we develop a computational model to design a new class of polymer gels where structural reconfigurations and internalized reactions are intimately linked to produce autonomous motion, which can be directed with light. These gels contain both spirobenzopyran (SP) chromophores and the ruthenium catalysts that drive the oscillatory Belousov-Zhabotinsky (BZ) reaction. Importantly, both the SP moieties and the BZ reaction are photosensitive. When these dual-functionalized gels are exposed to non-uniform illumination, the localized contraction of the gel (due to the SP moieties) in the presence of traveling chemical waves (due to the BZ reaction) leads to new forms of spontaneous, self-sustained movement, which cannot be achieved by either of the mono-functionalized networks.

Modeling Chemoresponsive Polymer Gels

Stimuli-responsive gels are vital components in the next generation of smart devices, which can sense and dynamically respond to changes in the local environment and thereby exhibit more autonomous functionality. We describe recently developed computational methods for simulating the properties of such stimuli-responsive gels in the presence of optical, chemical, and thermal gradients. Using these models, we determine how to harness light to drive shape changes and directed motion in spirobenzopyran-containing gels. Focusing on oscillating gels undergoing the Belousov-Zhabotinksy reaction, we demonstrate that these materials can spontaneously form self-rotating assemblies, or pinwheels. Finally, we model temperature-sensitive gels that encompass chemically reactive filaments to optimize the performance of this system as a homeostatic device for regulating temperature. These studies could facilitate the development of soft robots that autonomously interconvert chemical and mechanical energy and thus perform vital functions without the continuous need of external power sources.

Mechano-chemical oscillations and waves in reactive gels

We review advances in a new area of interdisciplinary research that concerns phenomena arising from inherent coupling between non-linear chemical dynamics and mechanics. This coupling provides a route for chemical-to-mechanical energy transduction, which enables materials to exhibit self-sustained oscillations and/or waves in both concentration and deformation fields. We focus on synthetic polymer gels, where the chemo-mechanical behavior can be engineered into the material. We provide a brief review of experimental observations on several types of chemo-mechanical oscillations in gels. Then, we discuss methods used to theoretically and computationally model self-oscillating polymer gels. The rest of the paper is devoted to describing results of theoretical and computational modeling of gels that undergo the oscillatory Belousov-Zhabotinsky (BZ) reaction. We discuss a remarkable form of mechano-chemical transduction in these materials, where the application of an applied force or mechanical contact can drive the system to switch between different dynamical behavior, or alter the mechanical properties of the material. Finally, we discuss ways in which photosensitive BZ gels could be used to fabricate biomimetic self-propelled objects. In particular, we describe how non-uniform illumination can be used to direct the movement of BZ gel 'worms' along complex paths, guiding them to bend, reorient and turn.

Surface instabilities in ultrathin, cross-linked poly(N-isopropylacrylamide) coatings

Near-the-surface instabilities with a cusplike morphology were observed in ultrathin photo-cross-linked poly(N-isopropylacrylamide) coatings upon swelling in water. The characteristic wavelength of the instability was approximately 25 times the dry thickness and scaled linearly with coating thickness between 30 and 1200 nm. Above 1200 nm, slippage of the coating along the confining substrate led to reticulated patterns with a much larger wavelength. To help interpret the origin of the instability, the coatings were also exposed to a solvent slightly worse than water (acetone) and a solvent slightly better than water (isopropanol). In all cases, the characteristic wavelength scaled linearly with respect to the swelling induced by each solvent. Both water and isopropanol produced well-defined cusps or folds in the gel surface, while acetone produced semiordered blisters that grew into one another. The features produced in acetone may be a consequence of swelling being close to the threshold value for the loss of planar stability. Through the use of a first-order linear perturbation of the Flory-Rehner model, it is shown that the emergence of a characteristic wavelength is consistent with an inhomogeneous distribution of solvent that results from diffusion of solvent into a dry coating.

Viscoelastic response of photo-cross-linked poly(N-isopropylacrylamide) coatings by QCM-D

The viscoelastic behavior of surface-tethered poly(N-isopropylacrylamide), or poly(NIPAAm), networks in contact with aqueous solutions was characterized by the quartz crystal microbalance with dissipation (QCM-D). To avoid ambiguities in the data analysis, four integer multiples of the dry thickness (h = k x 36 nm, where k = 1, 2, 3, 4) were analyzed at the third through ninth overtones of the QCM-D signal. At the third overtone, the networks resembled rigid films and the viscoelastic behavior could not be ascertained. With increasing overtones, however, the films showed deviation from the rigid film limit, allowing for analysis of the viscoelastic parameters. As the network collapsed over the temperature range of 15-40 degrees C, the shear modulus of the network increased by a factor of 24 (from 5 to 120 MPa); the shear viscosity, on the other hand, increased only by a factor of 2 (from 40 to 80 cP). The high values of the shear modulus suggest the QCM-D probes a regime where the polymer mesh does not adequately relax, and the high values of the shear viscosity suggest significant polymer-polymer coil overlap above and below the demixing temperature. Finally, the influence of NaCl on the viscoelastic response was measured. Interestingly, NaCl affects the shear modulus of the networks but not the dynamics.

Oscillatory dynamics induced in polyelectrolyte gels by a non-oscillatory reaction: a model

We develop a general model and the associated numerical algorithm to compute the swelling dynamics of chemo-responsive polyelectrolyte gels immersed in a reactive ionic solution kept at a non equilibrium stationary state by a permanent feed of fresh reactants. Using an autocatalytic bistable but nonoscillatory reaction, namely, the bromate-sulfite reaction, we predict that a piece of hydrogel that swells/shrinks as a function of pH can exhibit spontaneous mechanical and chemical oscillations. This constitutes the extension to realistic and experimentally feasible conditions of results previously obtained on a toy model with artificial swelling conditions.

Chemomechanical synchronization in heterogeneous self-oscillating gels

Using computational modeling, we introduce patches of self-oscillating gels undergoing the Belousov-Zhabotinsky (BZ) reaction into a nonreactive polymer network and thereby demonstrate how these BZ gels can be harnessed to impart remarkable functionality to the entire system. By first focusing on two adjacent patches of BZ gels, we show that the patches' oscillations can become synchronized in phase or out of phase, with the oscillation frequency depending on the synchronization mode and the spatial separation between these domains. We then apply these results to an array of five adjacent BZ patches and by varying the distance between these pieces, we dramatically alter the dynamical behavior of the patterned gel. For example, the sample can be made to exhibit a unidirectional traveling wave or display a concerted expansion and contraction, properties that are valuable for creating gel-based devices, such as micropumps and microactuators. The findings point to a "modular" design approach, which can impart different functionality simply by arranging identical pieces of BZ gels into distinct spatial arrangements within a polymer matrix.

Formation of double helical and filamentous structures in models of physical and chemical gels

This discusses two recent models, one that captures physical network formation starting from the molecular architecture of its constituents and another that contains the basic features of phase separation in cross-linked polymer gels: A) the Janus chain (multibead bead-spring type) model exhibiting semiflexibility and induced curvature and B) a stretched elastic network of Lennard-Jones particles. The length scales and related structures predicted by the two generic models are different. Model B, a generic soft solid model, exhibits hysteresis and the formation of filamentous structures in two dimensions. The Janus chain model A is able to describe the process of the formation of double helical superstructures, will be operated in three dimensions, and its internal parameters are directly deduced from atomistic simulation. Both models rely on classical ingredients which have been separately studied extensively: i) the Lennard-Jones particle system, ii) the elastic solid, and iii) the FENE-B model for semiflexible, finitely extendable nonlinear elastic (FENE) polymer chains. While model A combines i) and iii), model B combines i) and ii). This aspect of technical simplicity, however, is contrasted by the rich phenomenology observed for these models. The Janus model even resolves structure formation on the molecular scale. Intriguingly, the coarse dynamical models capture a wide range of superstructures known for polymeric networks and therefore clearly serve to understand their underlying physical mechanisms.

Modeling self-assembly and phase behavior in complex mixtures

Using a variety of computational techniques, I investigate how the self-assembly of complex mixtures can be guided by surfaces or external stimuli to form spatially regular or temporally periodic patterns. Focusing on mixtures in confined geometries, I examine how thermodynamic and hydrodynamic effects can be exploited to create regular arrays of nanowires or monodisperse, particle-filled droplets. I also show that an applied light source and chemical reaction can be harnessed to create hierarchically ordered patterns in ternary, phase-separating mixtures. Finally, I consider the combined effects of confining walls and a chemical reaction to demonstrate that a swollen polymer gel can be driven to form dynamically periodic structures. In addition to illustrating the effectiveness of external factors in directing the self-organization of multicomponent mixtures, the selected examples illustrate how coarse-grained models can be used to capture both the equilibrium phase behavior and the dynamics of these complex systems.

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 sample's 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 sample's dimensions. Finally, they isolate a scenario where the detachment of the gel from the wall leads to macroscopic motion of the entire sample.

Pattern Formation and Shape Changes in Self-Oscillating Polymer Gels

We developed an efficient model for responsive gels that captures large-scale, two-dimensional (2D) deformations and chemical reactions within a swollen polymer network. The 2D calculations allowed us to probe not only volume changes but also changes in sample shape. By focusing on gels undergoing the oscillatory Belousov-Zhabotinsky reaction, we observed traveling waves of local swelling that form a rich variety of dynamic patterns and give rise to distinctive oscillations in the gel's shape. The observed patterns depend critically on the gel's dimensions. The approach provides a useful computational tool for probing the dynamics of chemomechanical processes and uncovering morphological transformations in responsive gels.

Solvent control of crack dynamics in a reversible hydrogel

The resistance to fracture of reversible biopolymer hydrogels is an important control factor of the textural characteristics of food gels (such as gummy candies and aspic preparations). It is also critical for their use in tissue engineering, for which mechanical protection of encapsulated components is needed. Its dependence on loading rate and, recently, on the density and strength of crosslinks has been investigated. But, so far, no attention has been paid to solvent or to environment effects. Here we report a systematic study of crack dynamics in gels of gelatin in water/glycerol mixtures. We show in this model system that increasing solvent viscosity slows down cracks; moreover soaking with solvent markedly increases gel fragility; finally tuning the viscosity by adding a miscible liquid affects crack propagation through diffusive invasion of the crack tip vicinity. The results highlight the fact that fracture occurs by viscoplastic chain pull-out. This mechanism, as well as the related phenomenology, should be common to all reversibly crosslinked (physical) gels.

Effect of chemical structure on the volume-phase transition in neutral and weakly charged poly(N-alkyl(meth)acrylamide) hydrogels studied by ultrasmall-angle x-ray scattering

Neutral poly(N-isopropylacrylamide) (PIPAAm), poly(N,N-diethylacrylamide) (PDEAAm), and poly(N-isopropylmethacrylamide) (PIPMAm) hydrogels and their weakly charged counterparts prepared by copolymerizing with sodium methacrylate (x(MNa)=0,0.025,0.05) were studied using ultrasmall-angle x-ray scattering. The volume-phase transition in hydrogels was observed as an increase in the inhomogeneity correlation length of the networks. The change in inhomogeneity correlation length was abrupt in neutral PIPAAm and PIPMAm gels with increase in temperature but was continuous in neutral PDEAAm gels. Addition of ionic comonomer to the network backbone suppressed the volume-phase transition in poly(N-alkylacrylamide)s but not in PIPMAm. The observed differences in temperature-induced volume change of these three polymers in water cannot be rationalized based on their relative hydrophobicity and are instead explained by considering the hydrogen-bonding constraints on their thermal fluctuations. Both PIPAAm and PDEAAm undergo volume collapse since their thermal fluctuations are constrained by hydrogen bonding with water to an extent that beyond a critical temperature they seek entropic compensation. Although thermal fluctuations in both PIPAAm and PIPMAm are equally constrained, thermal energy of the latter can be relaxed via the rotation of alpha-methyl groups allowing it greater flexibility. Compared to N-alkylacrylamides, N-alkylmethacrylamide can thus sustain hydrogen bonding to relatively higher temperatures before seeking entropic compensation by undergoing volume collapse.

Low-voltage-driven electromechanical effects of swollen liquid-crystal elastomers

We experimentally investigate, in detail, electromechanical effects in liquid-crystal elastomers (LCEs) previously swollen with low-molecular-weight liquid crystals (LMWLCs). Both polydomain (POLY) and monodomain (MONO) LCEs were studied. We used a well known LMWLC, 4-n-pentyl-4-cyanobiphenyl (5CB) as a solvent. After swelling POLY and MONO LCEs (LSCE) with 5CB, shape changes were measured by recording the displacement of the edge of the swollen LCE at different voltages, V, and temperature. With 100 microm distance between electrodes, measurable shape changes (approximately 1-20 microm) are observed with small voltages (V approximately 0.5-10 V). In particular, we note that, compared to unswollen L(S)CEs, a dramatic approximately 200 times decrease of the threshold field was found for electromechanical effects in swollen L(S)CEs. While swollen MONO LCEs showed electromechanical effects in the planar geometry, homeotropic MONO swollen with homeotropically oriented 5CB did not. This is easy to understand because, in the homeotropic case, the liquid-crystal preferred axis is already aligned with the field so the field has no reorienting effect. The inverse of the response time when the field was switched on in both POLY and MONO was proportional to E2, which is the same field dependence as the response time of LMWLCs. When the field was switched off, the relaxation time showed a field dependence different from that of LMWLCs that we attribute to relaxation of the LCE network.