Universality in Nonlinear Elasticity of Biological and Polymeric Networks and Gels

Network design for soft materials: addressing elasticity and fracture resistance challenges

Soft materials, such as elastomers and gels, feature crosslinked polymer chains that provide stretchable and elastic mechanical properties. These properties are derived from entropic elasticity, which limits energy dissipation and makes the material susceptible to fracture. To address this issue, network designs that dissipate energy through the plastic zone have been introduced to enhance toughness; however, this approach compromises elasticity, preventing the material from fully recovering its original shape after deformation. In this review, we describe the trade-off between fracture resistance and elasticity, exploring network designs that overcome this limitation to achieve both high toughness and low hysteresis. The development of soft materials that are both elastic and fracture-resistant holds significant promise for applications in stretchable electronics, soft robotics, and biomedical devices. By analyzing successful network designs, we identify strategies to further improve these materials and discuss potential enhancements based on existing limitations.

Revealing Long-Range Order in Brush-like Graft Copolymers Through In Situ Measurements of X-Ray Scattering During Deformation

Brush-like graft copolymers (A-g-B), in which linear A-blocks are randomly grafted onto the backbone of a brush-like B-block, exhibit intense strain-stiffening and high mechanical strength on par with load-bearing biological tissues such as skin and blood vessels. To elucidate molecular mechanisms underlying this tissue-mimetic behavior, in situ synchrotron X-ray scattering was measured during uniaxial stretching of bottlebrush- and comb-like graft copolymers with varying densities of poly(dimethyl siloxane) and poly(isobutylene) side chains. In an undeformed state, these copolymers revealed a single interference peak corresponding to the average spacing between the domains of linear A-blocks arranged in a disordered, liquid-like configuration. Under uniaxial stretching, the emergence of a distinct four-spot pattern in the small-angle region indicated the development of long-range order within the material. According to the affine deformation of a cubic lattice, the four-spot pattern's interference maxima correspond to 110 reflections upon stretching along the [111] axis of the body-centered unit cell. The experimental findings were corroborated by computer simulations of dissipative particle dynamics that confirmed the formation of a bcc domain structure.

Boronate Ester Hydrogels for Biomedical Applications: Challenges and Opportunities

Boronate ester (BE) hydrogels are increasingly used for biomedical applications. The dynamic nature of these molecular networks enables bond rearrangement, which is associated with viscoelasticity, injectability, printability, and self-healing, among other properties. BEs are also sensitive to pH, redox reactions, and the presence of sugars, which is useful for the design of stimuli-responsive materials. Together, BE hydrogels are interesting scaffolds for use in drug delivery, 3D cell culture, and biofabrication. However, designing stable BE hydrogels at physiological pH (≈7.4) remains a challenge, which is hindering their development and biomedical application. In this context, advanced chemical insights into BE chemistry are being used to design new molecular solutions for material fabrication. This review article summarizes the state of the art in BE hydrogel design for biomedical applications with a focus on the materials chemistry of this class of materials. First, we discuss updated knowledge in BE chemistry including details on the molecular mechanisms associated with BE formation and breakage. Then, we discuss BE hydrogel formation at physiological pH, with an overview of the main systems reported to date along with new perspectives. A last section covers several prominent biomedical applications of BE hydrogels, including drug delivery, 3D cell culture, and bioprinting, with critical insights on the design relevance, limitations and potential.

When the Poisson Ratio of Polymer Networks and Gels Is Larger Than 0.5?

We use coarse-grained molecular dynamics simulations to study deformation of networks and gels of linear and brush strands in both linear and nonlinear deformation regimes under constant pressure conditions. The simulations show that the Poisson ratio of networks and gels could exceed 0.5 in the nonlinear deformation regime. This behavior is due to the ability of the network and gel strands to sustain large reversible deformation, which, in combination with the finite strand extensibility results in strand alignment and monomer density, increases with increasing strand elongation. We developed a nonlinear network and gel deformation model which defines conditions for the Poisson ratio to exceed 0.5. The model predictions are in good agreement with the simulation results.

Nonlinear Elastic Bottlebrush Polymer Hydrogels Modulate Actomyosin Mediated Protrusion Formation in Mesenchymal Stromal Cells

The nonlinear elasticity of many tissue-specific extracellular matrices is difficult to recapitulate without the use of fibrous architectures, which couple strain-stiffening with stress relaxation. Herein, bottlebrush polymers are synthesized and crosslinked to form poly(ethylene glycol)-based hydrogels and used to study how strain-stiffening behavior affects human mesenchymal stromal cells (hMSCs). By tailoring the bottlebrush polymer length, the critical stress associated with the onset of network stiffening is systematically varied, and a unique protrusion-rich hMSC morphology emerges only at critical stresses within a biologically accessible stress regime. Local cell-matrix interactions are quantified using 3D traction force microscopy and small molecule inhibitors are used to identify cellular machinery that plays a critical role in hMSC mechanosensing of the engineered, strain-stiffening microenvironment. Collectively, this study demonstrates how covalently crosslinked bottlebrush polymer hydrogels can recapitulate strain-stiffening biomechanical cues at biologically relevant stresses and be used to probe how nonlinear elastic matrix properties regulate cellular processes.

Deformation induced evolution of plasmonic responses in polymer grafted nanoparticle thin films

Multi-functional nanoparticle thin films are being used in various applications ranging from biosensing to photo-voltaics. In this study, we integrate two different numerical approaches to understand the interplay between the mechanical deformation and optical response of polymer grafted plasmonic nanoparticle (PGPN) arrays. Using numerical simulations we examine the deformation of thin films formed by end-functionalised polymer grafted nanoparticles subject to uniaxial elongation. The induced deformation causes the particles in the thin film network to rearrange their positions by two different mechanisms viz. sliding and packing. In sliding, the particles move in the direction of induced deformation. On the other hand, in packing, the particles move in a direction normal to that of the induced deformation. By employing a Green's tensor formulation in polarizable backgrounds for evaluating the optical response of the nanoparticle network, we calculate the evolution of the plasmonic response of the structure as a function of strain. The results indicate that the evolution of plasmonic response closely follows the deformation. In particular, we show that the onset of relative electric field enhancement of the optical response occurs when there is significant rearrangement of the constituent PGPNs in the array. Furthermore, we show that depending on the local packing/sliding and the polarization of the incident light there can be both enhancement and suppression of the SERS response.

Influence of swelling on the elasticity of polymer networks cross-linked in the melt state: Test of the localization model of rubber elasticity

The elasticity of polymer networks, formed by cross-linking high molecular mass polymers in the melt state and then swollen by a solvent, involves contributions from both the presence of cross-link network junctions and the interchain interactions associated with the combined effect of excluded volume interactions and topological constraints that become modified when the network is swollen. We test the capacity of the previously developed localization model of rubber elasticity, a mean field "tube model," to describe changes in elasticity observed in classical experimental studies of the mechanical properties of this type of network. In order to obtain a satisfactory comparison to the experiments, it was found to be necessary to account for the independently observed tendency of the network junctions to become localized in the network with appreciable swelling, as well as the interchain interactions emphasized in previous discussions of the localization model.

Effect of Cross-Link Homogeneity on the High-Strain Behavior of Elastic Polymer Networks

Cross-link heterogeneity and topological defects have been shown to affect the moduli of polymer networks in the low-strain regime. Probing their role in the high-strain regime, however, has been difficult because of premature network fracture. Here, we address this problem by using a double-network approach to investigate the high-strain behavior of both randomly and regularly cross-linked networks with the same backbone chemistry. Randomly cross-linked poly(n-butyl acrylate) networks with target molecular weights between cross-links of 5-30 kg/mol were synthesized via free-radical polymerization, while regularly cross-linked poly(n-butyl acrylate) networks with molecular weights between cross-links of 7-38 kg/mol were synthesized via cross-linking of tetrafunctional star polymers. Both types of networks were then swollen in a monomer/cross-linker mixture, polymerized to form double networks, and characterized via uniaxial tensile testing. The onset of strain stiffening was found to occur later in regular networks than in random networks with the same modulus but was well-predicted by the target molecular weight between cross-links of each sample. These results indicate that the low- and high-strain behavior of polymer networks result from different molecular-scale features of the material and suggest that controlling network architecture offers new opportunities to both further fundamental understanding of architecture-property relationships and design materials with independently controlled moduli and strain stiffening responses.

Coarse-Grained Artificial Intelligence for Design of Brush Networks

The ability to synthesize elastomeric materials with programmable mechanical properties is vital for advanced soft matter applications. Due to the inherent complexity of hierarchical structure-property correlations in brush-like polymer networks, the application of conventional theory-based, so-called Human Intelligence (HI) approaches becomes increasingly difficult. Herein we developed a design strategy based on synergistic combination of HI and AI tools which allows precise encoding of mechanical properties with three architectural parameters: degrees of polymerization (DP) of network strands, nx, side chains, nsc, backbone spacers between side chains, ng. Implementing a multilayer feedforward artificial neural network (ANN), we took advantage of model-predicted structure-property cross-correlations between coarse-grained system code including chemistry specific characteristics S = [l, v, b] defined by monomer projection length l and excluded volume v, Kuhn length b of bare backbone and side chains, and architecture A = [nsc, ng, nx] of polymer networks and their equilibrium mechanical properties P = [G, β] including the structural shear modulus G and firmness parameter β. The ANN was trained by minimizing the mean-square error with Bayesian regularization to avoid overfitting using a data set of experimental stress-deformation curves of networks with brush-like strands of poly(n-butyl acrylate), poly(isobutylene), and poly(dimethylsiloxane) having structural modulus G < 50 kPa and 0.01 ≤ β ≤ 0.3. The trained ANN predicts network mechanical properties with 95% confidence. The developed ANN was implemented for synthesis of model networks with identical mechanical properties but different chemistries of network strands.

Forensics of polymer networks

Our lives cannot be imagined without polymer networks, which range widely, from synthetic rubber to biological tissues. Their properties-elasticity, strain-stiffening and stretchability-are controlled by a convolution of chemical composition, strand conformation and network topology. Yet, since the discovery of rubber vulcanization by Charles Goodyear in 1839, the internal organization of networks has remained a sealed 'black box'. While many studies show how network properties respond to topology variation, no method currently exists that would allow the decoding of the network structure from its properties. We address this problem by analysing networks' nonlinear responses to deformation to quantify their crosslink density, strand flexibility and fraction of stress-supporting strands. The decoded structural information enables the quality control of network synthesis, comparison of targeted to actual architecture and network classification according to the effectiveness of stress distribution. The developed forensic approach is a vital step in future implementation of artificial intelligence principles for soft matter design.

Composite elastomers with on-demand convertible phase separations achieve large and healable electro-actuation

Phase separation has been widely exploited for fabricating structured functional materials. Generally, after being fabricated, the phase structure in a hybrid material system has been set at a specific length scale and remains unchanged during the lifespan of the material. Herein, we report a strategy to construct on-demand and reversible phase switches among homogenous, nano- and macro-phase separation states in a composite elastomer during its lifespan. We trigger the nanophase separation by super-saturating an elastomer matrix with a carefully selected small-molecule organic compound (SMOC). The nanoparticles of SMOC that precipitate out upon quenching will stretch the elastomer network, yet remain stably arrested in the elastomer matrix at low temperatures for a long time. However, at elevated temperatures, the nano-phase separation will transform into the macro-one. The elastic recovery will drive the SMOC onto the elastomer surface. The phase-separated structures can be reconfigured through the homogeneous solution state at a further elevated temperature. Taking advantage of the reversible phase switches leads to a novel strategy for designing high-performance dielectric elastomers. The in situ formed nanoparticles can boost the electro-actuation performance by eliminating electro-mechanical instability and lead to a very large actuation strain (∼146%). Once the actuator broke down, SMOC could on-demand be driven to the breakdown holes and heal the actuator.

Bottlebrush Thermoplastic Elastomers as Hot-Melt Pressure-Sensitive Adhesives

Hot-melt pressure-sensitive adhesives (HMPSAs) are used in applications from office supplies to biomedical adhesives. The major component in HMPSA formulations is thermoplastic elastomers, such as styrene-based block copolymers, that provide both mechanical integrity and moldability. Since neat polymer networks are unable to establish an adhesive bond, large quantities of plasticizers and tackifiers are added. These additives enhance the adhesive performance but complicate the phase behavior and property stability of the pressure-sensitive adhesive. Herein, we introduce an alternative additive-free approach to HMPSA design based on self-assembly of bottlebrush graft-copolymers, where side chains behave as softness, strength, and viscoelasticity mediators. These systems maintain moldability of conventional thermoplastic elastomers, while architecturally disentangled bottlebrush network strands empower several benefits such as extreme softness for substrate wetting, low melt viscosity for molding and 3D-printing, and a broad frequency range of viscoelastic responses for adhesion regulation within almost four orders of magnitude. The brush graft-copolymers implement five independently controlled architectural parameters to regulate the Rouse time, work of adhesion, and debonding mechanisms.

Unveiling the Role of Capping Groups in Naphthalene N-Capped Dehydrodipeptide Hydrogels

Self-assembled peptide-based hydrogels are archetypical nanostructured materials with a plethora of foreseeable applications in nanomedicine and as biomaterials. N-protected di- and tri-peptides are effective minimalist (molecular) hydrogelators. Independent variation of the capping group, peptide sequence and side chain modifications allows a wide chemical space to be explored and hydrogel properties to be tuned. In this work, we report the synthesis of a focused library of dehydrodipeptides N-protected with 1-naphthoyl and 2-naphthylacetyl groups. The 2-naphthylacetyl group was extensively reported for preparation of peptide-based self-assembled hydrogels, whereas the 1-naphthaloyl group was largely overlooked, owing presumably to the lack of a methylene linker between the naphthalene aromatic ring and the peptide backbone. Interestingly, dehydrodipeptides N-capped with the 1-naphthyl moiety afford stronger gels, at lower concentrations, than the 2-naphthylacetyl-capped dehydrodipeptides. Fluorescence and circular dichroism spectroscopy showed that the self-assembly of the dehydrodipeptides is driven by intermolecular aromatic π-π stacking interactions. Molecular dynamics simulations revealed that the 1-naphthoyl group allows higher order aromatic π-π stacking of the peptide molecules than the 2-naphthylacetyl group, together with hydrogen bonding of the peptide scaffold. The nanostructure of the gel networks was studied by TEM and STEM microscopy and was found to correlate well with the elasticity of the gels. This study contributes to understanding the interplay between peptide and capping group structure on the formation of self-assembled low-molecular-weight peptide hydrogels. Moreover, the results presented here add the 1-naphthoyl group to the palette of capping groups available for the preparation of efficacious low-molecular-weight peptide-based hydrogels.

Biomimetic strain-stiffening in fully synthetic dynamic-covalent hydrogel networks

Mechanoresponsiveness is a ubiquitous feature of soft materials in nature; biological tissues exhibit both strain-stiffening and self-healing in order to prevent and repair deformation-induced damage. These features remain challenging to replicate in synthetic and flexible polymeric materials. In recreating both the mechanical and structural features of soft biological tissues, hydrogels have been often explored for a number of biological and biomedical applications. However, synthetic polymeric hydrogels rarely replicate the mechanoresponsive character of natural biological materials, failing to match both strain-stiffening and self-healing functionality. Here, strain-stiffening behavior is realized in fully synthetic ideal network hydrogels prepared from flexible 4-arm polyethylene glycol macromers via dynamic-covalent boronate ester crosslinks. Shear rheology reveals the strain-stiffening response in these networks as a function of polymer concentration, pH, and temperature. Across all three of these variables, hydrogels of lower stiffness exhibit higher degrees of stiffening, as quantified by the stiffening index. The reversibility and self-healing nature of this strain-stiffening response is also evident upon strain-cycling. The mechanism underlying this unusual stiffening response is attributed to a combination of entropic and enthalpic elasticity in these crosslink-dominant networks, contrasting with natural biopolymers that primarily strain-stiffen due to a strain-induced reduction in conformational entropy of entangled fibrillar structures. This work thus offers key insights into crosslink-driven strain-stiffening in dynamic-covalent phenylboronic acid-diol hydrogels as a function of experimental and environmental parameters. Moreover, the biomimetic mechano- and chemoresponsive nature of this simple ideal-network hydrogel offers a promising platform for future applications.

Structural Features and Nonlinear Rheology of Self-Assembled Networks of Cross-Linked Semiflexible Polymers

Disordered networks of semiflexible filaments are common support structures in biology. Familiar examples include fibrous matrices in blood clots, bacterial biofilms, and essential components of cells and tissues of plants, animals, and fungi. Despite the ubiquity of these networks in biomaterials, we have only a limited understanding of the relationship between their structural features and their highly strain-sensitive mechanical properties. In this work, we perform simulations of three-dimensional networks produced by the irreversible formation of cross-links between linker-decorated semiflexible filaments. We characterize the structure of networks formed by a simple diffusion-dependent assembly process and measure their associated steady-state rheological features at finite temperature over a range of applied prestrains that encompass the strain-stiffening transition. We quantify the dependence of network connectivity on cross-linker availability and detail the associated connectivity dependence of both linear elasticity and nonlinear strain-stiffening behavior, drawing comparisons with prior experimental measurements of the cross-linker concentration-dependent elasticity of actin gels.

Super-soft, firm, and strong elastomers toward replication of tissue viscoelastic response

Polymeric networks are commonly used for various biomedical applications, from reconstructive surgery to wearable electronics. Some materials may be soft, firm, strong, or damping however, implementing all four properties into a single material to replicate the mechanical properties of tissue has been inaccessible. Herein, we present the A-g-B brush-like graft copolymer platform as a framework for fabrication of materials with independently tunable softness and firmness, capable of reaching a strength of ∼10 MPa on par with stress-supporting tissues such as blood vessel, muscle, and skin. These properties are maintained by architectural control, therefore diverse mechanical phenotypes are attainable for a variety of different chemistries. Utilizing this attribute, we demonstrate the capability of the A-g-B platform to enhance specific characteristics such as tackiness, damping, and moldability.

Mechanical response of networks formed by end-functionalised spherical polymer grafted nanoparticles

Via computer simulations we examine the mechanical response of hybrid polymer-particle networks composed of rigid spherical nanoparticles with long flexible polymer chains grafted onto their surface. The canopy of grafted polymer arms are end-functionalised such that interacting polymer-grafted nanoparticles (PGNs) form labile bonds when their coronas overlap. In the present study, the number of grafted arms, f, are such that the PGN brushes are in the small (f = 600) and intermediate curvature (f = 900 and 1200) regime with stable bonded interactions. To investigate the mechanical response of networks formed by these PGNs, controlled uniaxial elongation at a specified pulling rate is imposed on a 2-D network of PGNs placed on a hexagonal lattice. In the simulations, the force required to deform the network is measured as a function of the elongation and pulling rate imposed on the network until the network fails. By analysis of the force-strain curves and the rearrangement of the PGNs in the network we show that an increase in the number of grafted arms, pulling velocity and energy of the bonded interactions alters both the toughness and the mode of failure of the networks. In particular, we show that an increase in the number of grafted arms results in a reduction of toughness. Furthermore, analysis of the simulations of force relaxation after rapid extension indicates that the relaxation in deformed networks can be characterised by one or two time scales that depend on the number of grafted arms. The analysis of force-strain curves and force relaxation demonstrate the role of Deborah number, De, and the limitations in the use of a unique De in understanding the mechanical response of the networks respectively.

Effect of functional anisotropy on the local dynamics of polymer grafted nanoparticles

End-functionalised polymer grafted nanoparticles (PGNs) form bonds when their coronas overlap. The bonded interactions between the overlapping PGNs depend on the energy of the bonds (U). In the present study, oscillatory deformation imposed on a simple system with interacting PGNs placed on the vertices of a triangle is employed to examine the local dynamics as a function of energy of the bonds and the frequency of oscillation relative to the characteristic rupture frequency, ω₀ = 2πν exp(-U/k_BT), of the bonds. In particular, the effect of functional anisotropy is studied by introducing bonds of two different energies between adjacent PGNs. A multicomponent model developed by Kadre and Iyer, Macromol. Theory Simul., 2021, 30, 2100005, that combines the features of effective interactions between PGNs, self-consistent field theory and master equation approach to study bond kinetics is employed to obtain the local dynamics. The resulting force-strain curves are found to exhibit a simple broken symmetry where F_x (γ,) ≠ -F_x (-γ,-) and F_y (γ,) ≠ F_y (-γ,-) in systems with functional anisotropy. Fourier analysis of the dynamic response reveals that functional anisotropy leads to finite even harmonic terms and systematic variation of both the elastic and dissipative response from that of the isotropic systems. Furthermore, the intra-cycle variations in the strain stiffening and shear thickening ratios obtained from the analysis indicate that functional anisotropy leads to anisotropic nonlinear response.

Mechanically Diverse Gels with Equal Solvent Content

Mechanically diverse polymer gels are commonly integrated into biomedical devices, soft robots, and tissue engineering scaffolds to perform distinct yet coordinated functions in wet environments. Such multigel systems are prone to volume fluctuations and shape distortions due to differential swelling driven by osmotic solvent redistribution. Living systems evade these issues by varying proximal tissue stiffness at nearly equal water concentration. However, this feature is challenging to replicate with synthetic gels: any alteration of cross-link density affects both the gel's swellability and mechanical properties. In contrast to the conventional coupling of physical properties, we report a strategy to tune the gel modulus independent of swelling ratio by regulating network strand flexibility with brushlike polymers. Chemically identical gels were constructed with a broad elastic modulus range at a constant solvent fraction by utilizing multidimensional network architectures. The general design-by-architecture framework is universally applicable to both organogels and hydrogels and can be further adapted to different practical applications.

Pectin self-assembly and its disruption by water: Insights into plant cell wall mechanics

Plant cell walls undergo multiple cycles of dehydration and rehydration during their life. Cal- cium crosslinked low methoxy pectin is a major constituent of plant cell walls. Understanding the dehydration-rehydration...

Nonequilibrium Processes in Polymer Membrane Formation: Theory and Experiment

Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes─evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest─that dictates the complex structure of the membrane on different scales.

ENTIRE-REGION CONSTITUTIVE RELATION FOR TRELOAR'S DATA

Hyperelastic materials can experience a large deformation process. A constitutive relation suitable for an entire region from small, moderate, to large deformations is of great importance for practical applications such as fracture problems. Treloar's data are first investigated, and the tension curve is divided into three regimes: small-to-moderate regime, strain-hardening regime, and limiting-chain regime. Next, the modeling theory of hyperelastic materials is introduced, and the tensile behaviors of basic energy functions are analyzed for different deformation regimes. Finally, a successive procedure is suggested to establish an entire-region constitutive relation and then applied to Treloar's data. The present constitutive relation can maintain the initial shear modulus while the experimental data are satisfactorily predicted. The present procedure is simple and feasible and hence applicable to other hyperelastic materials when their entire-region constitutive relations are studied based on experimental data.

Adaptively reconstructing network of soft elastomers to increase strand rigidity: towards free-standing electro-actuation strain over 100

Soft biological tissues and muscles composed of semiflexible networks exhibit rapid strain-hardening behaviors to protect them from accidental rupture. In contrast, synthetic soft elastomers, usually featuring flexible networks, lack such behaviors, leading to a notorious issue when applying them to a promising artificial muscle technology (dielectric elastomer, DE), that is electromechanical instability (EMI) induced premature breakdown. We report that a facile thermomechanical training method can adaptively reconstruct the network of a soft triblock copolymer elastomer to transform its flexible network strands into semiflexible ones without extra chemical modifications and additives so that the electro-actuation performance is significantly enhanced by avoiding EMI. The free-standing actuators of trained elastomers exhibit a large stable electro-actuation strain and a high theoretical energy density (133%, 307 kJ m^-3 at 158.1 V μm^-1), and the capacity of actuating at low-temperature environments (-15 °C).

Contact probing of prestressed adhesive membranes of living cells

Atomic force microscopy (AFM) studies of living biological cells is one of main experimental tools that enable quantitative measurements of deformation of the cells and extraction of information about their structural and mechanical properties. However, proper modelling of AFM probing and related adhesive contact problems are of crucial importance for interpretation of experimental data. The Johnson-Kendall-Roberts (JKR) theory of adhesive contact has often been used as a basis for modelling of various phenomena including cell-cell interactions. However, strictly speaking the original JKR theory is valid only for contact of isotropic linearly elastic spheres, while the cell membranes are often prestressed. For the first time, effects caused by molecular adhesion for living cells are analytically studied taking into account the mechanical properties of cell membranes whose stiffness depends on the level of the tensile prestress. Another important question is how one can extract the work of adhesion between the probe and the cell. An extended version of the Borodich-Galanov method for non-direct extraction of elastic and adhesive properties of contacted materials is proposed to apply to experiments of cell probing. Evidently, the proposed models of adhesive contact for cells with prestressed membranes do not cover all types of biological cells because the structure and properties of the cells may vary considerably. However, the obtained results can be applied to many types of smooth cells and can be used to describe initial stages of contact and various other processes when effects of adhesion are of crucial importance. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Anchoring-mediated topology signature of self-assembled elastomers undergoing mechanochromic coupling/decoupling

Soft elastomers with their ability to integrate strain-adaptive stiffening and coloration have recently received significant research attention for application in artificial muscle and active camouflage. However, there is a lack of theoretical understanding of their complex molecular dynamics and mechanochromic coupling/decoupling. In this study, a topological dynamics model is proposed to understand the anchoring-mediated topology signature of self-assembled elastomers. Based on the constrained molecular junction model, a free-energy function is firstly formulated to describe the working principles of strain-adaptive stiffening and coloration in the self-assembled elastomer. A coupled ternary "rock-paper-scissors" model is proposed to describe the topological dynamics of self-assembly, mechanochromic coupling and mechanoresponsive stiffening of the self-assembled elastomers, in which there are three fractal geometry components in the topology network. Finally, the proposed models are verified using the experimental results reported in the literature. This study provides a fundamental approach to understand the working mechanism and topological dynamics in the self-assembled elastomers, with molecularly encoded stiffening and coloration.

Injectable non-leaching tissue-mimetic bottlebrush elastomers as an advanced platform for reconstructive surgery

Current materials used in biomedical devices do not match tissue's mechanical properties and leach various chemicals into the body. These deficiencies pose significant health risks that are further exacerbated by invasive implantation procedures. Herein, we leverage the brush-like polymer architecture to design and administer minimally invasive injectable elastomers that cure in vivo into leachable-free implants with mechanical properties matching the surrounding tissue. This strategy allows tuning curing time from minutes to hours, which empowers a broad range of biomedical applications from rapid wound sealing to time-intensive reconstructive surgery. These injectable elastomers support in vitro cell proliferation, while also demonstrating in vivo implant integrity with a mild inflammatory response and minimal fibrotic encapsulation.

Thermoresponsive and Injectable Composite Hydrogels of Cellulose Nanocrystals and Pluronic F127

Thermoresponsive amphiphilic Pluronic F127 triblock copolymer solutions have been widely investigated in smart biomaterial applications due to the proximity of its critical gel temperature to human body temperature. Meanwhile, cellulose nanocrystals (CNCs) have quickly become the focus of many drug delivery and tissue engineering applications due to their biocompatibility, abundance, ability to conjugate with drug molecules, and superior rheological properties. Herein, we investigate the phase behavior and thermo-rheological properties of the composite hydrogels containing cellulose nanocrystals (up to 5% by weight) and the temperature responsive Pluronic F127. Our results revealed an unprecedented role of CNC network formation on micellization and gelation behavior of the triblock copolymer. Linear and nonlinear rheological analysis suggest that at low and moderate nanocrystal loadings (1-3% by weight), the composite gel remarkably becomes softer and deformable compared to the neat Pluronic F127 gels. The softening effect results from the disruption of the close packed micelles by the rodlike CNCs. At high concentrations, however, the nanocrystals form their own network and the micelles are trapped within the CNC meshes. As a result, the original (neat F127) hard-gel modulus is recovered at 4 to 5% nanocrystal loading, yet the composite gel is much more deformable (and tougher) in the presence of the CNC network. Our temperature sweep experiments show that the CNC addition up to 3% does not change the rapid thermal gelation of the F127 solutions; therefore, these composites are suitable for smart drug delivery systems. On the other hand, at higher CNC concentrations, abrupt viscosity transition is not observed, rather the composite gels smoothly thicken with temperature in contrast to thermal thinning of the aqueous neat CNC. Thus, they can be used as smartly adaptive biolubricants and bioviscostatic materials.

To Mimic Mechanical Properties of the Skin by Inducing Oriented Nanofiber Microstructures in Bottlebrush Cellulose-graft-diblock Copolymer Elastomers

Skin is a vital biological defense system that protects the body from physical harm with its unique mechanical properties attributed to the hierarchical organization of the protein scaffold. Developing a synthetic skinlike material has aroused great interest; however, replication of the skin's mechanical response, including anisotropic softness and strain-stiffening, is difficult to achieve. Here, to mimic the mechanical behaviors of skin, a reprocessable bottlebrush copolymer elastomer was designed with renewable and rigid cellulose as backbones; meanwhile, poly(n-butyl acrylate)-b-poly(methyl methacrylate) (PBA-b-PMMA) diblocks were designed as the grafted side chains. The so-made elastomers were subjected to a step-cyclic tensile deformation, by which the internal structures became oriented nanofibers and endowed stress-strain behaviors pretty much similar to those of the real skin. Overall, our research work currently undertaken would be of great importance in the development of a series of biomimetic skinlike polymer materials.

Double membrane formation in heterogeneous vesicles

Lipids are capable of forming a variety of structures, including multi-lamellar vesicles. Layered lipid membranes are found in cell organelles, such as autophagosomes and mitochondria. Here, we present a mechanism for the formation of a double-walled vesicle (i.e., two lipid bilayers) from a unilamellar vesicle through the partitioning and phase separation of a small molecule. Using molecular dynamics simulations, we show that double membrane formation proceeds via a nucleation and growth process - i.e., after a critical concentration of the small molecules, a patch of double membrane nucleates and grows to cover the entire vesicle. We discuss the implications of this mechanism and theoretical approaches for understanding the evolution and formation of double membranes.

Surfactant Driven Liquid to Soft Solid Transition of Cellulose Nanocrystal Suspensions

Cellulose nanocrystals (CNCs) have recently attracted wide interest due to their abundance, biocompatibility, and extraordinary physical properties. In particular, easy manipulation of their surface properties, hydrophilicity, and high aspect ratio make them ideal rheology modifiers; yet, the gelation mechanisms and microscopic origin of the complex rheological behavior in the presence of secondary components, such as polymers and surfactants, are far from well understood. In this work, we used light scattering, small-angle neutron scattering, and bulk rheology to study the phase behavior and mechanical behavior of aqueous CNC solutions in the presence of cationic 1-decyl trimethyl imidazolium chloride and 1-decyl trimethyl imidazolium ferric tetrachloride. The micelles of these surfactants form at similar cmc's (about 50 mM) and adopt identical hydrodynamic sizes (on the order of a few nanometers) and prolate-shaped ellipsoids but vary in their intermicelle interactions (charged vs neutral), thus allowing us to clarify the unprecedented effect of the surfactant micelle charge on the gel behavior of the aqueous CNC-surfactant complexes. Our results show that the positively charged micelles greatly strengthen the gel network while excessive free micelles weaken the gels due to repulsive micelle-micelle interaction. In the meantime, analysis of the transition from linear to nonlinear deformation regimes suggests that the gels gradually become more fragile with surfactant concentrations due to electrostatic repulsion of the charged micelles. Such a surfactant concentration-dependent gel fragility was not observed in the presence of the neutral micelles. These results provide a great step further in our understanding of the phase behavior and rheology of complex CNC-surfactant mixtures and obtaining biocompatible hydrogels with tunable mechanical properties.

Tug of war in a double-nanopore system

We simulate a tug-of-war (TOW) scenario for a model double-stranded DNA threading through a double nanopore (DNP) system. The DNA, simultaneously captured at both pores, is subject to two equal and opposite forces -f[over ⃗]_{L}=f[over ⃗]_{R} (TOW), where f[over ⃗]_{L} and f[over ⃗]_{R} are the forces applied to the left and the right pore, respectively. Even though the net force on the DNA polymer Δf[over ⃗]_{LR}=f[over ⃗]_{L}+f[over ⃗]_{R}=0, the mean first passage time (MFPT) 〈τ〉 depends on the magnitude of the TOW forces |f_{L}|=|f_{R}|=f_{LR}. We qualitatively explain this dependence of 〈τ〉 on f_{LR} from the known results for the single-pore translocation of a triblock copolymer A-B-A with ℓ_{pB}>ℓ_{pA}, where ℓ_{pA} and ℓ_{pB} are the persistence length of the A and B segments, respectively. We demonstrate that the time of flight of a monomer with index m [〈τ_{LR}(m)〉] from one pore to the other exhibits quasiperiodic structure commensurate with the distance between the pores d_{LR}. Finally, we study the situation where we offset the TOW biases so that Δf[over ⃗]_{LR}=f[over ⃗]_{L}+f[over ⃗]_{R}≠0, and qualitatively reproduce the experimental result of the dependence of the MFPT on Δf[over ⃗]_{LR}. We demonstrate that, for a moderate bias, the MFPT for the DNP system for a chain length N follows the same scaling ansatz as that for the single nanopore, 〈τ〉=(AN^{1+ν}+η_{pore}N)(Δf_{LR})^{-1}, where η_{pore} is the pore friction, which enables us to estimate 〈τ〉 for a long chain. Our Brownian dynamics simulation studies provide fundamental insights and valuable information about the details of the translocation speed obtained from 〈τ_{LR}(m)〉, and accuracy of the translation of the data obtained in the time domain to units of genomic distances.

Bottlebrush Bridge between Soft Gels and Firm Tissues

Softness and firmness are seemingly incompatible traits that synergize to create the unique soft-yet-firm tactility of living tissues pursued in soft robotics, wearable electronics, and plastic surgery. This dichotomy is particularly pronounced in tissues such as fat that are known to be both ultrasoft and ultrafirm. However, synthetically replicating this mechanical response remains elusive since ubiquitously employed soft gels are unable to concurrently reproduce tissue firmness. We have addressed the tissue challenge through the self-assembly of linear-bottlebrush-linear (LBL) block copolymers into thermoplastic elastomers. This hybrid molecular architecture delivers a hierarchical network organization with a cascade of deformation mechanisms responsible for initially low moduli followed by intense strain-stiffening. By bridging the firmness gap between gels and tissues, we have replicated the mechanics of fat, fetal membrane, spinal cord, and brain tissues. These solvent-free, nonleachable, and tissue-mimetic elastomers also show enhanced biocompatibility as demonstrated by cell proliferation studies, all of which are vital for the safety and longevity of future biomedical devices.

Deformation of Chemically Heterogeneous Interfacial Layers of Polymer Nanocomposites

Dynamics of entangled interfacial polymer layers around nanoparticles determine the linear rheological properties of polymer nanocomposites. In this study, the nonlinear elastic properties of nanocomposites are examined under large-amplitude oscillatory shear (LAOS) flow to reveal the effect of interfacial chemical heterogeneity on the deformation mechanism of polymer-grafted and polymer-adsorbed nanoparticle composites. Adsorbed-poly(methyl methacrylate) (PMMA) layers presented stronger interfacial stiffening and reinforcement than PMMA-grafted layers. Chemical heterogeneities of interfacial layers, provided by polymer-adsorbed and low graft density particles, deformed at smaller strains than the poly(ethylene oxide) (PEO) matrix. Interfaces of loosely bound PMMA and PEO exhibited stiffening at low strains due to the enhanced chain mixing and entanglements. These results demonstrate that chemical and dynamic heterogeneities in interfacial layers have significant importance in designing adaptive polymer nanocomposites for large shear deformation.

The elastic Rayleigh drop

Bioprinting technologies rely on the formation of soft gel drops for printing tissue scaffolds and the dynamics of these drops can affect the process. A model is developed to describe the oscillations of a spherical gel drop with finite shear modulus, whose interface is held by surface tension. The governing elastodynamic equations are derived and a solution is constructed using displacement potentials decomposed into a spherical harmonic basis. The resulting nonlinear characteristic equation depends upon two dimensionless numbers, elastocapillary and compressibility, and admits two types of solutions, (i) spheroidal (or shape change) modes and (ii) torsional (rotational) modes. The torsional modes are unaffected by capillarity, whereas the frequency of shape oscillations depend upon both the elastocapillary and compressibility numbers. Two asymptotic dispersion relationships are derived and the limiting cases of the inviscid Rayleigh drop and elastic globe are recovered. For a fixed polar wavenumber, there exists an infinity of radial modes that each transition from an elasticity wave to a capillary wave upon increasing the elastocapillary number. At the transition, there is a qualitative change in the deformation field and a set of recirculation vortices develop at the free surface. Two special modes that concern volume oscillations and translational motion are characterized. A new instability is documented that reflects the balance between surface tension and compressibility effects due to the elasticity of the drop.

Analyzing acoustoelastic effect of shear wave elastography data for perfused and hydrated soft tissues using a macromolecular network inspired model

Shear wave elastography (SWE) has enhanced our ability to non-invasively make in vivo measurements of tissue elastic properties of animal and human tissues. Recently, researchers have taken advantages of acoustoelasticity in SWE to extract nonlinear elastic properties from soft biological tissues. However, most investigations of the acoustoelastic effects of SWE data (AE-SWE) rely on classic hyperelastic models for rubber-like (dry) materials. In this paper, we focus solely on understanding acoustoelasticity in soft hydrated tissues using SWE data and propose a straightforward approach to modeling the constitutive behavior of soft tissue that has a direct microstructural/macromolecular interpretation. Our approach incorporates two constitutive features relevant to biological tissues into AE-SWE: static dilation of the medium associated with nonstructural components (e.g. tissue hydration and perfusion) and finite extensibility derived from an ideal network of biological filaments. We evaluated the proposed method using data from an in-house tissue-mimicking phantom experiment, and ex vivo and in vivo AE-SWE data available in the SWE literature. In conclusion, predictions made by our approach agreed well with measurements obtained from phantom, ex vivo and in vivo tissue experiments.

Dehydropeptide-based plasmonic magnetogels: a supramolecular composite nanosystem for multimodal cancer therapy

Supramolecular hydrogels are highly promising candidates as biomedical materials owing to their wide array of properties, which can be tailored and modulated. Additionally, their combination with plasmonic/magnetic nanoparticles to form plasmonic magnetogels further improves their potential in biomedical applications through the combination of complementary strategies, such as photothermia, magnetic hyperthermia, photodynamic therapy and magnetic-guided drug delivery. Here, a new dehydropeptide hydrogelator, Npx-l-Met-Z-ΔPhe-OH, was developed and combined with two different plasmonic/magnetic nanoparticle architectures, i.e., core/shell manganese ferrite/gold nanoparticles and gold-decorated manganese ferrite nanoparticles with ca. 55 nm and 45 nm sizes, respectively. The magnetogels were characterized via HR-TEM, FTIR spectroscopy, circular dichroism and rheological assays. The gels were tested as nanocarriers for a model antitumor drug, the natural compound curcumin. The incorporation of the drug in the magnetogel matrices was confirmed through fluorescence-based techniques (FRET, fluorescence anisotropy and quenching). The curcumin release profiles were studied with and without the excitation of the gold plasmon band. The transport of curcumin from the magnetogels towards biomembrane models (small unilamellar vesicles) was assessed via FRET between the fluorescent drug and the lipid probe Nile Red. The developed magnetogels showed promising results for photothermia and photo-triggered drug release. The magnetogels bearing gold-decorated nanoparticles showed the best photothermia properties, while the ones containing core/shell nanoparticles had the best photoinduced curcumin release.