Nonlinear elasticity and cavitation of a triblock copolymer gel

Needle-induced cavitation: A method to probe the local mechanics of brain tissue

Traditional mechanical characterization of extremely soft tissues is challenging given difficulty extracting tissue, satisfying geometric requirements, keeping tissues hydrated, and securing the tissue in an apparatus without slippage. The heterogeneous nature and structural complexity of brain tissues on small length scales makes it especially difficult to characterize. Needle-induced cavitation (NIC) is a technique that overcomes these issues and can mechanically characterize brain tissues at precise, micrometer-scale locations. This small-scale capability is crucial in order to spatially characterize diseased tissue states like fibrosis or cancer. NIC consists of inserting a needle into a tissue and pressurizing a fluid until a deformation occurs at the tip of the needle at a critical pressure. NIC is a convenient, affordable technique to measure mechanical properties, such as modulus and fracture energy, and to assess the performance of soft materials. Experimental parameters such as needle size and fluid flowrate are tunable, so that the end-user can control the length and time scales, making it uniquely capable of measuring local mechanical properties across a wide range of strain rates. The portable nature of NIC and capability to conduct in vivo experiments makes it a particularly appealing characterization technique compared to traditional methods. Despite significant developments in the technique over the last decade, wide implementation in the biological field is still limited. Here, we address the limitations of the NIC technique specifically when working with soft tissues and provide readers with expected results for brain tissue. Our goal is to assist others in conducting reliable and reproducible mechanical characterization of soft biomaterials and tissues.

Temperature- and strain-dependent transient microstructure and rheological responses of endblock-associated triblock gels of different block lengths in a midblock selective solvent

Endblock associative ABA gels in midblock selective solvents are attractive due to their easily tunable mechanical properties. Here, we present the effects of A- and B-block lengths on the rheological properties and microstructure of ABA gels by considering three low and one high polymer concentrations. The triblock polymer considered is poly(methyl methacrylate)-poly(n-butyl acrylate)-poly(methyl methacrylate) [PMMA-PnBA-PMMA] and the midblock solvent is 2-ethyl-1-hexanol. The gelation temperature has been found to be strongly dependent on the B-block (PnBA) length, as longer B-blocks facilitate network formation resulting in higher gelation temperature even with lower polymer chain density. Longer A-blocks (PMMA chains) make the endblock association stronger and significantly increase the relaxation time of gels. Temperature-dependent microstructure evolution for the gels with high polymer concentration reveals that the gel microstructure does not change significantly after the gel formation takes place. The dynamic change of microstructure in an applied strain cycle was captured using RheoSAXS experiments. The microstructure orients with the applied strain and the process is reversible in nature, indicating no significant A-block pullout. Our results provide new understandings regarding the temperature and strain-dependent microstructural change of ABA gels in midblock selective solvents.

Multicolor Nitrogen-Doped Carbon Quantum Dots for Environment-Dependent Emission Tuning

Carbon quantum dots (CQDs) have potential applications in many fields such as light-emitting devices, photocatalysis, and bioimaging due to their unique photoluminescence (PL) properties and environmental benignness. Here, we report the synthesis of nitrogen-doped carbon quantum dots (NCQDs) from citric acid and m-phenylenediamine using a one-pot hydrothermal approach. The environment-dependent emission changes of NCQDs were extensively investigated in various solvents, in the solid state, and in physically assembled PMMA-PnBA-PMMA copolymer gels in 2-ethyl-hexanol. NCQDs display bright emissions in various solvents as well as in the solid state. These NCQDs exhibit multicolor PL emission across the visible region upon changing the environment (solutions and polymer matrices). NCQDs also exhibit excitation-dependent PL and solvatochromism, which have not been frequently investigated in CQDs. Most CQDs are nonemissive in the aggregated or solid state due to the aggregation-caused quenching (ACQ) effect, limiting their solid-state applications. However, NCQDs synthesized here display a strong solid-state emission centered at 568 nm attributed to the presence of surface functional groups that restrict the π-π interaction between the NCQDs and assist in overcoming the ACQ effect in the solid state. NCQD-containing gels display significant fluorescence enhancement in comparison to the NCQDs in 2-ethyl hexanol, likely because of the interaction between the polar PMMA blocks and NCQDs. The application of NCQDs-Gel as a solid/gel state fluorescent display has been presented. This research facilitates the development of large-scale, low-cost multicolor phosphor for the fabrication of optoelectronic devices, sensing, and bioimaging applications.

Cavitation induced fracture of intact brain tissue

Nonpenetrating traumatic brain injuries (TBIs) are linked to cavitation. The structural organization of the brain makes it particularly susceptible to tears and fractures from these cavitation events, but limitations in existing characterization methods make it difficult to understand the relationship between fracture and cavitation in this tissue. More broadly, fracture energy is an important, yet often overlooked, mechanical property of all soft tissues. We combined needle-induced cavitation with hydraulic fracture models to induce and quantify fracture in intact brains at precise locations. We report here the first measurements of the fracture energy of intact brain tissue that range from 1.5 to 8.9 J/m2, depending on the location in the brain and the model applied. We observed that fracture consistently occurs along interfaces between regions of brain tissue. These fractures along interfaces allow cavitation-related damage to propagate several millimeters away from the initial injury site. Quantifying the forces necessary to fracture brain and other soft tissues is critical for understanding how impact and blast waves damage tissue in vivo and has implications for the design of protective gear and tissue engineering.

Biomimetic Strain-Stiffening in Chitosan Self-Healing Hydrogels

The strain-stiffening and self-healing capabilities of biological tissues enable them to preserve the structures and functions from deformation and damage. However, biodegradable hydrogel materials with both of these biomimetic characteristics have not been explored. Here, a series of strain-stiffened, self-healing hydrogels are developed through dynamic imine crosslinking of semiflexible O-carboxymethyl chitosan (main chain) and flexible dibenzaldehyde-terminated telechelic poly(ethylene glycol) (crosslinker). The biomimetic hydrogels can be reversibly stiffened to resist the deformation and can even recover to their original state after repeated damages. The mechanical properties and stiffening responses of the hydrogels are tailored by varying the component contents (1-3%) and the crosslinker length (4 or 8 kDa). A combinatorial system of in situ coherent small-angle X-ray scattering with rheological testing is developed to investigate the network structures (in sizes 1.5-160 nm) of hydrogels under shear strains and reveals that the strain-stiffening originates from the fibrous chitosan network with poly(ethylene glycol) crosslinking fixation. The biomimetic hydrogels with biocompatibility and biodegradability promote wound healing. The study provides an insight into the nanoscale design of biomimetic strain-stiffening self-healing hydrogels for biomedical applications.

Mechanical Characterization of Multilayered Hydrogels: A Rheological Study for 3D-Printed Systems

We describe rheological protocols to study layered and three-dimensional (3D)-printed gels. Our methods allow us to measure the properties at different depths and determine the contribution of each layer to the resulting combined properties of the gels. We show that there are differences when using different measuring systems for rheological measurement, which directly affects the resulting properties being measured. These methods allow us to measure the gel properties after printing, rather than having to rely on the assumption that there is no change in properties from a preprinted gel. We show that the rheological properties of fluorenylmethoxycarbonyl-diphenylalanine (FmocFF) gels are heavily influenced by the printing process.

Achieving High-Speed Retraction in Stretchable Hydrogels

Hydrogels mimicking elastomeric biopolymers such as resilin, responsible for power-amplified activities in biological species necessary for locomotion, feeding, and defense have applications in soft robotics and prosthetics. Here, we report a bioinspired hydrogel synthesized through a free-radical polymerization reaction. By maintaining a balance between the hydrophilic and hydrophobic components, we obtain gels with an elastic modulus as high as 100 kPa, stretchability up to 800%, and resilience up to 98%. Such properties enable these gels to catapult projectiles. Furthermore, these gels achieve a retraction velocity of 16 m s^-1 with an acceleration of 4 × 10³ m s^-2 when released from a stretched state, and these values are comparable to those observed in many biological species during a power amplification process. By utilizing and tuning the simple synthetic strategy used here, these gels can be used in soft robotics, prosthetics, and engineered devices where power amplification is desired.

Cavitation in soft matter

Cavitation is the sudden, unstable expansion of a void or bubble within a liquid or solid subjected to a negative hydrostatic stress. Cavitation rheology is a field emerging from the development of a suite of materials characterization, damage quantification, and therapeutic techniques that exploit the physical principles of cavitation. Cavitation rheology is inherently complex and broad in scope with wide-ranging applications in the biology, chemistry, materials, and mechanics communities. This perspective aims to drive collaboration among these communities and guide discussion by defining a common core of high-priority goals while highlighting emerging opportunities in the field of cavitation rheology. A brief overview of the mechanics and dynamics of cavitation in soft matter is presented. This overview is followed by a discussion of the overarching goals of cavitation rheology and an overview of common experimental techniques. The larger unmet needs and challenges of cavitation in soft matter are then presented alongside specific opportunities for researchers from different disciplines to contribute to the field.

Rheological properties and failure of alginate hydrogels with ionic and covalent crosslinks

Polysaccharide-based hydrogels are being used in a wide variety of applications ranging from tissue engineering to food products due to their biocompatibility and the ease of gel formation. In real-life applications, hydrogels can undergo large strain deformation, which may result in structural damage leading to failure. Here, we report the nonlinear rheological properties and failure behavior of alginate hydrogels, a class of polysaccharide hydrogels, synthesized via ionic and covalent crosslinking. Gels with ionic crosslinks or ionic alginate hydrogels are prepared by addition of Ca2+ ions in the aqueous solution of sodium alginate, and the covalently crosslinked alginate gels or chemical alginate hydrogels are obtained via amidation reactions. Because of their structural differences, ionic and chemical alginate hydrogels display different scattering profiles captured by using small angle X-ray scattering (SAXS) technique. Both ionic and chemical alginate hydrogels exhibit strain stiffening behavior when subjected to large amplitude oscillatory shear (LAOS) and the strain-stiffening behavior is accompanied by negative normal stress. A custom-built cavitation rheometer has been utilized to probe the local failure behavior of these gels. The cavitation rheometry captures different defect growth or fracture mechanism in ionic versus chemical alginate hydrogels, even if these two types of gels have a similar linear elastic modulus. Based on the critical pressure for gel fracture, we have provided an estimate of the critical energy release rate.

Residual strain effects in needle-induced cavitation

Needle-induced cavitation (NIC) locally probes the elastic and fracture properties of soft materials, such as gels and biological tissues. Current NIC protocols tend to overestimate properties when compared to traditional techniques. New NIC methods are needed in order to address this issue. NIC measurements consist of two distinct processes, namely (1) the needle insertion process and (2) the cavitation process. The cavitation process is hypothesized to be highly dependent on the initial needle insertion process due to the influence of residual strain below the needle. Retracting the needle before pressurization to a state in which a cylindrical, tube-like fracture is left below the needle tip is experimentally demonstrated to reduce the impact of residual strain on NIC. Verification of the critical cavitation pressure equation in this new geometry is necessary before implementing this retraction NIC protocol. Complementary modeling shows that the change in initial geometry has little effect on the critical cavitation pressure. Together, these measurements demonstrate that needle retraction is a viable experimental protocol for reducing the influence of residual strain, thus enabling the confident measurement of local elastic and fracture properties in soft gels and tissues.

Using cavitation rheology to understand dipeptide-based low molecular weight gels

The study of dipeptide-based hydrogels has been the focus of significant effort recently due to their potential for use in a variety of biomedical and biotechnological applications. It is essential to study the mechanical properties in order to fully characterise and understand this type of soft materials. In terms of mechanical properties, the linear elastic modulus is normally measured using traditional shear rheometry. This technique requires millilitre sample volumes, which can be difficult when only small amounts of gel are available, and can present difficulties when loading the sample into the machine. Here, we describe the use of cavitation rheology, an easy and efficient technique, to characterise the linear elastic modulus of a range of hydrogels. Unlike traditional shear rheometry, this technique can be used on hydrogels in their native environment, and small sample volumes are required. We describe our set-up and show how it can be used to probe and understand different types of gels. Gels can be formed by different triggers from the same gelator and this leads to different microstructures. We show that the data from the cavitational rheometer correlates with the underlying microstructure in the gels, which allows a greater degree of understanding of the gels than can be obtained from the bulk measurements.

Volume-controlled cavity expansion for probing of local elastic properties in soft materials

Cavity expansion can be used to measure the local nonlinear elastic properties in soft materials, regardless of the specific damage or instability mechanism that it may ultimately induce. To that end, we introduce a volume-controlled cavity expansion procedure and an accompanying method that builds on the Cavitation Rheology technique [J. A. Zimberlin et al., Soft Matter, 2007, 3, 763-767], but without relying on the maximum recorded pressure. This is achieved by determining an effective radius of the cavity that is based on the volume measurements, and is further supported by numerical simulations. Applying this method to PDMS samples, we show that it consistently collapses the experimental curves to the theoretical prediction of cavity expansion prior to the occurrence of fracture or cavitation, thus resulting in high precision measurement with less than 5% of scatter and good agreement with results obtained via conventional techniques. Moreover, since it does not require visual tracking of the cavity, this technique can be applied to measure the nonlinear elastic response in opaque samples.

Quantitative relationship between cavitation and shear rheology

Cavitation rheology is a powerful, simple, and inexpensive technique to study the moduli of polymer gels, however its use has not yet become widespread because few studies to date have directly compared this technique to traditional oscillatory shear rheology. Herein, we report a quantitative relationship between the gel modulus determined using cavitation and shear rheology for three series of model gels whose networks are composed of (1) permanently covalent, (2) dynamic-covalent, and (3) physical hydrogen-bond crosslinks. We determine a simple proportionality constant that allows for conversion of the moduli obtained from both types of experiments and is highly dependent on the bond energy responsible for gelation. This study provides a framework for researchers in a broad range of disciplines who can exploit the ease of cavitation rheology and place their results in the context of traditional oscillatory shear rheology.

Cavitation in inhomogeneous soft solids

A tiny spherical cavity expands in a homogenous neo-Hookean solid when subjected to an externally applied hydrostatic tension. If the applied tension reaches 2.5 times the shear modulus of the solid, the cavity expands unboundedly. Such a phenomenon is usually referred to as cavitation in soft solids. In previous studies, the soft solid is often assumed to have homogeneous mechanical properties. In this article, we study cavity expansion in inhomogeneous soft solids through analytical formulation and finite element simulations. We find that cavitation in an inhomogeneous soft solid can be greatly different from that in a homogenous one. In particular, we show that the relationship between the applied hydrostatic tension and the cavity size can be either monotonic or non-monotonic, depending on the geometry and material properties of the soft solid. We hope the results obtained in this article will be helpful in understanding the cavitation phenomenon in complex soft materials.

Investigation of failure behavior of a thermoplastic elastomer gel

Gels are increasingly being used in many applications, and it is important to understand how these gels fail subjected to mechanical deformation. Here, we investigate the failure behavior of a thermoplastic elastomer gel (TPEG) consisting of poly(styrene)-poly(isoprene)-poly(styrene) in mineral oil, in tensile mode, under constant stress, and in fracture tests, where the fracture initiates from a predefined crack. In these gels, the poly(styrene) endblocks associate to form spherical aggregates, as captured using SAXS. Shear-rheology experiments indicate that the poly(isoprene) midblocks connecting these aggregates are loosely entangled. The relaxation behavior of these gels has been captured by time-temperature superposition of frequency sweep data and stress-relaxation experiments. The relaxation process in these gels involves endblock pullout from the aggregates and subsequent relaxation of the chains. An unfavorable enthalpic interaction between the endblock and mineral oil results in a significantly large relaxation time. These gels display rate dependent mechanical properties, likely due to the midblock entanglements. Fracture and creep failure tests provide insights into the gel failure mechanism. Creep experiments indicate that these gels fail by a thermally activated process. Fracture experiments capture the energy release rate as a function of crack-tip velocity. The critical energy release rate is estimated by incorporating the friction force the polystyrene chains are subjected to, as those are pulled out of aggregates, and the enthalpic cost to overcome unfavorable interaction between poly(styrene) and mineral oil. Our results provide further insights to the failure behavior of the self-assembled TPEGs.

Viscoplastic fracture transition of a biopolymer gel

Physical gels are swollen polymer networks consisting of transient crosslink junctions associated with hydrogen or ionic bonds. Unlike covalently crosslinked gels, these physical crosslinks are reversible thus enabling these materials to display highly tunable and dynamic mechanical properties. In this work, we study the polymer composition effects on the fracture behavior of a gelatin gel, which is a thermoreversible biopolymer gel consisting of denatured collagen chains bridging physical network junctions formed from triple helices. Below the critical volume fraction for chain entanglement, which we confirm via neutron scattering measurements, we find that the fracture behavior is consistent with a viscoplastic type process characterized by hydrodynamic friction of individual polymer chains through the polymer mesh to show that the enhancement in fracture scales inversely with the squared of the mesh size of the gelatin gel network. Above this critical volume fraction, the fracture process can be described by the Lake-Thomas theory that considers fracture as a chain scission process due to chain entanglements.

Probing Gelation and Rheological Behavior of a Self-Assembled Molecular Gel

Molecular gels have been investigated over the last few decades; however, mechanical behavior of these self-assembled gels is not well understood, particularly how these materials fail at large strain. Here, we report the gelation and rheological behavior of a molecular gel formed by self-assembly of a low molecular weight gelator (LMWG), di-Fmoc-l-lysine, in 1-propanol/water mixture. Gels were prepared by solvent-triggered technique, and gelation was tracked using Fourier transform infrared (FTIR) spectroscopy and shear rheology. FTIR spectroscopy captures the formation of hydrogen bonding between the gelator molecules, and the change in IR spectra during the gelation process correlates with the gelation kinetics results captured by rheology. Self-assembly of gelator molecules leads to a fiber-like structure, and these long fibers topologically interact to form a gel-like material. Stretched-exponential function can capture the stress-relaxation data. Stress-relaxation time for these gels have been found to be long owing to long fiber dimensions, and the stretching exponent value of 1/3 indicates polydispersity in fiber dimensions. Cavitation rheology captures fracture-like behavior of these gels, and critical energy release rate has been estimated to be of the order 0.1 J/m². Our results provide new understanding of the rheological behavior of molecular gels and their structural origin.

Molecular Insights into Gelation of Di-Fmoc-l-Lysine in Organic Solvent-Water Mixtures

Despite significant interest in molecular gels due to their intriguing structure formation through self-assembly and their stimuli-responsive behavior, our understanding of the gel formation mechanism of a low-molecular-weight gelator (LMWG) is incomplete. Here, we report a combined experimental and computational study on a LMWG, di-Fmoc-l-lysine, that has two aromatic moieties and multiple hydrogen bond donors and acceptors. Gelation in various organic solvent-water mixtures was obtained through the solvent-triggered technique. We show that an approach based on approximate cohesive energy density derived from density functional theory (DFT) calculations can capture the experimental solubility trend of LMWGs in different organic solvents. Furthermore, DFT calculations indicate parallel and helical structures to be the preferred structural motifs for gelator dimers. We believe that these motifs can potentially lead to fiber formation as observed with microscopy. Our work provides a relatively simple yet effective approach to quantify interactions between solvents and complex gelators that can help rationalize solubility and gelation behavior.

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.

Solvent effects on modulus of poly(propylene oxide)-based organogels as measured by cavitation rheology

A series of novel organogels were synthesized from poly(propylene oxide) (PPO) functionalized with main chain urea moieties which provided rapid gelation and high moduli in a variety of solvents. Three different molecular weight PPOs were used in this study: 430, 2000, and 4000 g mol(-1), each with α,ω-amino-end groups. Four urea groups were introduced into the main chain by reaction with hexamethylene diisocyanate followed by subsequent reaction with a monofunctional alkyl or aromatic amine. This PPO/urea gelator was found to form gels in carbon tetrachloride, chloroform, dichloromethane, toluene, ethyl acetate, and tetrahydrofuran. Among these, carbon tetrachloride and toluene were found to be the best solvents for this system, resulting in perfectly clear gels with high moduli at low mass fraction for PPO-2000 systems. Flory-Huggins polymer-solvent interaction parameter, χ, was found to be a useful indicator of gel quality for these systems, with χCCl4/PPO-2000 < 0.5 and χtoluene/PPO-2000≈ 0.5. Systems with χ parameters >0.5 were found to form low moduli gels, indicating that for these systems, polymer-solvent interaction parameters can be a useful predictor of gel quality in different solvent systems.

Elastic cavitation and fracture via injection

The cavitation rheology technique extracts soft materials mechanical properties through pressure-monitored fluid injection. Properties are calculated from the system's response at a critical pressure that is governed by either elasticity or fracture (or both); however previous elementary analysis has not been capable of accurately determining which mechanism is dominant. We combine analyses of both mechanisms in order to determine how the full system thermodynamics, including far-field compliance, dictate whether a bubble in an elastomeric solid will grow through either reversible or irreversible deformations. Applying these analyses to experimental data, we demonstrate the sensitivity of cavitation rheology to microstructural variation via a co-dependence between modulus and fracture energy.

Weak Hydrogen Bonding Enables Hard, Strong, Tough, and Elastic Hydrogels

A new type of "rigid and tough" hydrogel with excellent elasticity is designed by dense clustering of hydrogen bonds within a loose chemical network. The resultant hydrogel exhibits a good combination of high modulus (28 MPa), toughness (9300 J m(-3) ), extensibility (800%), and tensile stress (2 MPa). Furthermore, the gel displays good fatigue-resistance and complete and extremely fast recovery of shape and mechanical properties (3 min at 37°C).

Effect of graphene on the self-assembly and rheological behavior of a triblock copolymer gel

Self-assembly and the mechanical properties of graphene containing physical gels are reported in this work.