Surface tension and the mechanics of liquid inclusions in compliant solids

Interaction between an edge dislocation and a circular incompressible liquid inclusion

We use Muskhelishvili's complex variable formulation to study the interaction problem associated with a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation at an arbitrary position. A closed-form solution to the problem is derived largely with the aid of analytic continuation. We obtain, in explicit form, expressions for the internal uniform hydrostatic stresses, nonuniform strains and nonuniform rigid body rotation within the liquid inclusion; the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. We observe that (1) the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix; (2) the internal hydrostatic stress field within the liquid inclusion is unaffected by Poisson's ratio of the matrix and is proportional to the shear modulus of the matrix; and (3) an unstable equilibrium position always exists for a climbing dislocation.

Wrinkling composite sheets

We examine the buckling shape and critical compression of confined inhomogeneous composite sheets lying on a liquid foundation. The buckling modes are controlled by the bending stiffness of the sheet, the density of the substrate, and the size and the spatially dependent elastic coefficients of the sheet. We solve the beam equation describing the mechanical equilibrium of a sheet when its bending stiffness varies parallel to the direction of confinement. The case of a homogeneous bending stiffness exhibits a degeneracy of wrinkled states for certain lengths of the confined sheet; we explain this degeneracy using an asymptotic analysis valid for long sheets, and show that it corresponds to the switching of the sheet between symmetric and antisymmetric buckling modes. This degeneracy disappears for spatially dependent elastic coefficients. Medium length sheets buckle similarly to their homogeneous counterparts, whereas the wrinkled states in large length sheets concentrate the bending energy towards the soft regions of the sheet.

High-Performance Supramolecular Organogel Adhesives for Antimicrobial Applications in Diverse Conditions

Supramolecular organogel coatings that can disinfect the deposited microbial pathogens are emerging as an effective vehicle to prevent pathogen transmission. However, the development of anti-pathogen supramolecular adhesives with mechanical robustness and controlled oil inclusion is technically challenging. Here, we report supramolecular adhesives with mechanical integrity and robust interfacial adhesion over a wide range of biogenic antimicrobial oil. Bifunctional monomers are synthesized and assembled into linear polymers with semicrystalline stackings through hierarchical hydrogen bonds, where incorporated bioactive oil could regulate the semicrystalline stackings into nanosized crystalline domains through intermolecular hydrogen bonds. The abundant bonding motifs provided by the supramolecular cross-linked networks could accommodate oil molecules with high inclusion capability and provide more interfacial binding sites with high adhesion strength, and the nanosized crystalline domains could stabilize the organogel network and compensate for the interactions with oil molecules to enhance structural and mechanical stability. In addition, rapid healing, robust adhesion, and antimicrobial and antiviral properties of the resultant organogel coatings are demonstrated. This study paves the way for the development of high-performance antimicrobial supramolecular adhesives with controlled oil inclusion, showing potential applications in soft robotics, tissue engineering, and biomedical devices.

Bio-enabled Engineering of Multifunctional "Living" Surfaces

Through the magic of "active matter"─matter that converts chemical energy into mechanical work to drive emergent properties─biology solves a myriad of seemingly enormous physical challenges. Using active matter surfaces, for example, our lungs clear an astronomically large number of particulate contaminants that accompany each of the 10,000 L of air we respire per day, thus ensuring that the lungs' gas exchange surfaces remain functional. In this Perspective, we describe our efforts to engineer artificial active surfaces that mimic active matter surfaces in biology. Specifically, we seek to assemble the basic active matter components─mechanical motor, driven constituent, and energy source─to design surfaces that support the continuous operation of molecular sensing, recognition, and exchange. The successful realization of this technology would generate multifunctional, "living" surfaces that combine the dynamic programmability of active matter and the molecular specificity of biological surfaces and apply them to applications in biosensors, chemical diagnostics, and other surface transport and catalytic processes. We describe our recent efforts in bio-enabled engineering of living surfaces through the design of molecular probes to understand and integrate native biological membranes into synthetic materials.

Highly Stable Liquid Metal Conductors with Superior Electrical Stability and Tough Interface Bonding for Stretchable Electronics

Ga-based liquid metal stretchable conductors have recently gained interest in flexible electronic devices such as electrodes, antennas, and sensors. It is essential to maintain electrical stability under strain or cyclic strain for reliable data acquisition and exhibit tough interfacial bonding between liquid metal and polymers to prevent performance loss and device failure. Herein, a highly stable conductor with superior electrical stability and tough interface bonding is introduced by casting curable polymers and a peeling-activated process from liquid metal particles. Based on the compensating effect of liquid metal, similar to the recharge relationship of water between rivers and lakes in nature, the conductor is not only strain-insensitive (ΔR/R₀ < 10% for 100% strain) but also immune to cyclic deformation (ΔR/R₀ < 7% with 5000 stretching cycles at 50% strain). Embedding liquid metal within the elastomer to create stretchable conductors effectively improves interfacial adhesion properties (the fluid-solid interfacial adhesion force increases from 0.48 to 0.62 mN/mm²). The constructed tough interface could even withstand sonication treatment. Finally, by combining strategies in material design and fabrication, an integrated array composed of vertical interconnect access and robust electrodes is fabricated, which simultaneously holds tough interfacial bonding with the upper and lower layers.

The effective shear modulus of a random isotropic suspension of monodisperse liquid n-spheres: from the dilute limit to the percolation threshold

A numerical and analytical study is made of the macroscopic or homogenized mechanical response of a random isotropic suspension of liquid n-spherical inclusions (n = 2, 3), each having identical initial radius A, in an elastomer subjected to small quasistatic deformations. Attention is restricted to the basic case when the elastomer is an isotropic incompressible linear elastic solid, the liquid making up the inclusions is an incompressible linear elastic fluid, and the interfaces separating the solid elastomer from the liquid inclusions feature a constant initial surface tension γ. For such a class of suspensions, it has been recently established that the homogenized mechanical response is that of a standard linear elastic solid and hence, for the specific type of isotropic incompressible suspension of interest here, one that can be characterized solely by an effective shear modulus _n in terms of the shear modulus μ of the elastomer, the initial elasto-capillary number eCa = γ/2μA, the volume fraction c of inclusions, and the space dimension n. This paper presents numerical solutions-generated by means of a recently introduced finite-element scheme-for _n over a wide range of elasto-capillary numbers eCa and volume fractions of inclusions c. Complementary to these, a formula is also introduced for _n that is in quantitative agreement with all the numerical solutions, as well as with the asymptotic results for _n in the limit of dilute volume fraction of inclusions and at percolation . The proposed formula has the added theoretical merit of being an iterated-homogenization solution.

Influence of microstructural alterations of liquid metal and its interfacial interactions with rubber on multifunctional properties of soft composite materials

Liquid metal (LM)-based polymer composites are currently new breakthrough and emerging classes of soft multifunctional materials (SMMs) having immense transformative potential for soft technological applications. Currently, room-temperature LMs, mostly eutectic gallium‑indium and Galinstan alloys are used to integrate with soft polymer due to their outstanding properties such as high conductivity, fluidity, low adhesion, high surface tension, low cytotoxicity, etc. The microstructural alterations and interfacial interactions controlling the efficient integration of LMs with rubber are the most critical aspects for successful implementation of multifunctionality in the resulting material. In this review article, a fundamental understanding of microstructural alterations of LMs to the formation of well-defined percolating networks inside an insulating rubber matrix has been established by exploiting several existing theoretical and experimental studies. Furthermore, effects of the chemical modifications of an LM surface and its interfacial interactions on the compatibility between solid rubber and fluid filler phase have been discussed. The presence of thin oxide layer on the LM surface and the effects and challenges it poses to the adequate functionalization of these materials have been discussed. Plausible applications of SMMs in different soft matter technologies, like soft robotics, flexible electronics, soft actuators, sensors, etc. have been provided. Finally, the current technical challenges and further prospective to the development of SMMs using non‑silicone rubbers have been critically discussed. This review is anticipated to infuse a new impetus to the associated research communities for the development of next generation SMMs.

A micromechanical model for phase-change composites

Phase-change composites have a wide range of tunable mechanical properties caused by temperature-driven phase transition, and have been widely applied in many cutting-edge fields like soft robotics. Previous studies on the effective mechanical properties of phase-change composites mostly use experimental methods, and there have been few theoretical approaches. In this work, we develop a micromechanical framework capable of tracking the effective mechanical properties of phase-change composites throughout the entire phase transition. The phase-change materials embedded in the composites are modelled as inclusions, and the non-phase-change materials are modelled as the matrix. This allows us to determine the effective mechanical properties of phase-change composites via the energy equivalency approach. Moreover, since the new phase will be generated inside the phase-change inclusions in the form of sub-inclusions during the phase transition, the inclusions are modelled as two-phase composites, and their effective mechanical properties are then determined using the Mori–Tanaka method. Finally, by comparing theoretical predictions with experimental data, the accuracy and reliability of the present model are verified. We believe that the proposed model can serve as a powerful tool for evaluating the effective mechanical properties of phase-change composites and provide theoretical guidelines for the design of advanced devices with tunable mechanical performance.

Active elastocapillarity in soft solids with negative surface tension

Active solids consume energy to allow for actuation, shape change, and wave propagation not possible in equilibrium. Whereas active interfaces have been realized across many experimental systems, control of three-dimensional (3D) bulk materials remains a challenge. Here, we develop continuum theory and microscopic simulations that describe a 3D soft solid whose boundary experiences active surface stresses. The competition between active boundary and elastic bulk yields a broad range of previously unexplored phenomena, which are demonstrations of so-called active elastocapillarity. In contrast to thin shells and vesicles, we discover that bulk 3D elasticity controls snap-through transitions between different anisotropic shapes. These transitions meet at a critical point, allowing a universal classification via Landau theory. In addition, the active surface modifies elastic wave propagation to allow zero, or even negative, group velocities. These phenomena offer robust principles for programming shape change and functionality into active solids, from robotic metamaterials down to shape-shifting nanoparticles.

A skin-inspired soft material with directional mechanosensation

Lessons about artificial sensor design may be taken from evolutionarily perfected physiological systems. Mechanosensory cells in human skin are exquisitely sensitive to gentle touch and enable us to distinguish objects of different stiffnesses and textures. These cells are embedded in soft epidermal layers of gel-like consistency. Reproducing these mechanosensing capabilities in new soft materials may lead to the development of adaptive mechanosensors which will further enhance the abilities of engineered membrane-based structures with bioinspired sensing strategies. This strategy is explored here using droplet interface bilayers embedded within a thermoreversible organogel. The interface between two lipid-coated aqueous inclusions contained within a soft polymeric matrix forms a lipid bilayer resembling the lipid matrix of cell membranes. These interfaces are functionalized with bacterial mechanosensitive channels (V23T MscL) which convert membrane tension into changes in membrane conductance, mimicking mechanosensitive channel activation in mammalian mechanosensory cells. The distortion of encapsulated adhered droplets by cyclical external forces are first explored using a finite element composite model illustrating the directional propagation of mechanical disturbances imposed by a piston. The model predicts that the orientation of the droplet pair forming the membrane relative to the direction of the compression plays a role in the membrane response. The directional dependence of mechanosensitive channel activation in response to gel compression is confirmed experimentally and shows that purely compressive perturbations normal to the interface invoke different channel activities as compared to shearing displacement along a plane of the membrane. The developed system containing specially positioned pairs of droplets functionalized with bacterial mechanosensitive channels and embedded in a gel creates a skin-inspired soft material with a directional response to mechanical perturbation.

Contact lines on stretched soft solids: modelling anisotropic surface stresses

We present fully analytical solutions for the deformation of a stretched soft substrate due to the static wetting of a large liquid droplet, and compare our solutions to recently published experiments (Xu et al. 2018 Soft Matter 14, 916–920 (doi:10.1039/C7SM02431B)). Following a Green’s function approach, we extend the surface-stress regularized Flamant–Cerruti problem to account for uniaxial pre-strains of the substrate. Surface profiles, including the heights and opening angles of wetting ridges, are provided for linearized and finite kinematics. We fit experimental wetting ridge shapes as a function of applied strain using two free parameters, the surface Lamé coefficients. In comparison with experiments, we find that observed opening angles are more accurately captured using finite kinematics, especially with increasing levels of applied pre-strain. These fits qualitatively agree with the results of Xu et al ., but revise values of the surface elastic constants.

Splashing on Soft Elastic Substrates

Drop impact onto soft substrates is important in applications such as bioprinting, spray coating, and aerosol drug delivery. Experiments are conducted to determine the effect of elasticity on the splash morphology, as defined by the splashing threshold, spine number, spreading factor, and retraction factor. PDMS silicone gel and gelatin hydrogel are used as the substrates because they have different wetting properties and a large range of elasticities. The splash threshold, as defined by the Weber number We, increases as the substrate elasticity decreases indicating that it is harder to splash on soft substrates. After impact, the drop spreads to a maximum diameter that decreases for soft substrates, irrespective of wetting properties, illustrating the role of substrate deformation in the energy balance during splashing. The number of spines that form at the leading edge of the drop depends upon the elasticity and the wetting properties of the liquid/substrate system. Following spreading, the drop retracts to an equilibrium diameter which does not show a strong correlation with any material properties. The reported results agree well with the existing literature for most cases and also provide new insights into gels with small elasticity.

Mechanically Cloaked Multiphase Magnetic Elastomer Soft Composites for Wearable Wireless Power Transfer

Wearable electronics allow for new and immersive experiences between technology and the human body, but conventional devices are made from rigid functional components that lack the necessary compliance to safely interact with human tissue. Recently, liquid inclusions have been incorporated into elastomer composites to produce functional materials with high extensibility and ultrasoft mechanical responses. While these materials have shown high thermal and electrical conductivity, there has been an absence of research into compliant magnetic materials through the incorporation of magnetic fluids. Compliant magnetic materials are important for applications in soft matter engineering including sensing, actuation, and power transfer for soft electronics and robotics. In this work, we establish a new class of highly functional soft materials with advanced magnetic and mechanical properties by dispersing magnetic colloidal suspensions as compliant fluid inclusions into soft elastomers. Significantly, the rigid magnetic particles are encapsulated by the fluid. This mechanically cloaks the solid particles and enables a fluid-like mechanical response while imparting high magnetic permeability to the composite. This microstructure reduces the modulus of the composite below that of the initial elastomer to <40 kPa while increasing the permeability by over 100% to greater than 2. We demonstrate the functionality of these materials through conformable magnetic backplanes, which enables a completely soft, coupled inductor system capable of transferring power up to 100% strain and wearable devices for wireless power transfer.

Network topologies dictate electromechanical coupling in liquid metal-elastomer composites

Elastomers embedded with micro- and nanoscale droplets of liquid metal (LM) alloys like eutectic gallium-indium (EGaIn) can exhibit unique combinations of elastic, thermal, and electrical properties that are difficult to achieve using rigid filler. For composites with sufficient concentrations of liquid metal, the LM droplets can form percolating networks that conduct electricity and deform with the surrounding elastomer as the composite is stretched. Surprisingly, experimental measurements performed on LM-embedded elastomers (LMEEs) show that the total electrical resistance of the composite increases only slightly even as the elastomer is stretched to several times its natural length. In contrast, Pouillet's law would predict an exponential increase in resistance (Ω) with stretch (λ) due to the incompressibility of liquid metal and elastomer. In this manuscript, we perform a computational analysis to examine the unique electromechanical properties of conductive LMEE composites. Our analysis suggests that the gauge factor that quantifies electromechanical coupling (i.e. G = {ΔΩ/Ω0}/λ) decreases with increasing tortuosity of the conductive pathways formed by the connected LM droplets. A dimensionless parameter for path tortuosity can be used to estimate G for statistically homogeneous LMEE composites. These results rationalize experimental observations and provide insight into the influence of liquid metal droplet assembly on the functionality of the composite.

Investigation of thermal conductivity for liquid metal composites using the micromechanics-based mean-field homogenization theory

For the facile use of liquid metal composites (LMCs) for soft, stretchable and thermal systems, it is crucial to understand and predict the thermal conductivity of the composites as a function of liquid metal (LM) volume fraction and applied strain. In this study, we investigated the effective thermal conductivity of LMCs based on various mean-field homogenization frameworks including Eshelby, Mori-Tanaka, differential and double inclusion methods. The double inclusion model turned out to make the prediction closest to the experimental results in a wide range of LM volume fractions. Interestingly, we found that the theoretical models based on the assumption of ideal LM dispersion and zero interfacial resistance underestimated the thermal conductivity compared to the experimental results in a low volume fraction regime. By considering the accompanied variations in the LM inclusion's aspect ratios under a typical size distribution of inclusions (∼μm), the change of effective thermal conductivity was predicted under a uniaxial 300% tensile strain. Our study will deepen the understanding of the thermal properties of LMCs and support the designs of stretchable thermal interfaces and packaging with LMCs in the future.

Nonlinear theory of wetting on deformable substrates

The spreading of a liquid over a solid material is a key process in a wide range of applications. While this phenomenon is well understood when the solid is undeformable, its "soft" counterpart is still misunderstood and no consensus has been reached with regard to the physical mechanisms ruling the spreading of liquid drops over soft deformable materials. In this work we provide a theoretical framework, based on the nonlinear theory of discontinuities, to describe the behavior of a triple line on a soft material. We show that the contact line motion is opposed both by nonlinear localized capillary and visco-elastic forces. We give an explicit analytic formula relating the dynamic contact angle of a moving drop to its velocity for arbitrary rheology. We then specialize this formula to the experimentally relevant case of elastomers with the Chasset-Thirion (power-law) type of rheologies. The theoretical prediction is in very good agreement with experimental data, without any adjustable parameters. We then show that the nonlinear force balance presented in this work can also be used to recover classical models of wetting. Finally we provide predictions for the dynamic behavior of the yet largely unexplored case of a viscous drop spreading over a soft visco-elastic material and predict the emergence of a new form of apparent hysteresis.

Surface phase transitions in ice: from fundamental interactions to applications

Interfaces divide all phases of matter and yet in most practical settings it is tempting to ignore their energies and the associated implications. There are many reasons for this, not the least of which is the introduction of a new pair of canonically conjugate variables-interfacial energy and its counterpart the surface area. A key set of questions surrounding the treatment of multiphase flows concerns how and when we must account for such effects. I begin this discussion with an abbreviated review of the basic theory of lower-dimensional phase transitions and describe a range of situations in which the bulk behaviour of a two-phase (and in some cases two-component) system is dominated by surface effects. Then I discuss a number of settings in which the bulk and surface behaviour can interact on equal footing. These can include the dynamic and thermodynamic behaviour of floating sea ice, the freezing and drying of colloidal suspensions (such as soil) and the mechanisms of protoplanetesimal formation by inter-particle collisions in accretion discs. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

Liquid Metal-Elastomer Soft Composites with Independently Controllable and Highly Tunable Droplet Size and Volume Loading

Soft composites are critical for soft and flexible materials in energy harvesting, actuators, and multifunctional devices. One emerging approach to create multifunctional composites is through the incorporation of liquid metal (LM) droplets such as eutectic gallium indium (EGaIn) in highly deformable elastomers. The microstructure of such systems is critical to their performance; however, current materials lack control of particle size at diverse volume loadings. Here, we present a fabrication approach to create liquid metal-elastomer composites with independently controllable and highly tunable droplet size (100 nm ≤ D ≤ 80 μm) and volume loading (0 ≤ ϕ ≤ 80%). This is achieved through a combination of shear mixing and sonication of concentrated LM/elastomer emulsions to control droplet size and subsequent dilution and homogenization to tune LM volume loading. These materials are characterized utilizing dielectric spectroscopy supported by analytical modeling, which shows a high relative permittivity of 60 (16× the unfilled elastomer) in a composite with ϕ = 80%, a low tan δ of 0.02, and a significant dependence on ϕ and minor dependence on droplet size. Temperature response and stability are determined using dielectric spectroscopy through temperature and frequency sweeps with DSC. These results demonstrate a wide temperature stability of the liquid metal phase (crystallizing at <-85 °C for D < 20 μm). Additionally, all composites are electrically insulating across wide frequency (0.1 Hz-10 MHz) and temperature (-70 to 100 °C) ranges even up to ϕ = 80%. We highlight the benefit of LM microstructure control by creating all-soft-matter stretchable capacitive sensors with tunable sensitivity. These sensors are further integrated into a wearable sensing glove where we identify different objects during grasping motions. This work enables programmable LM composites for soft robotics and stretchable electronics where flexibility and tunable functional response are critical.

A mesoscale study of creep in a microgel using the acoustic radiation force

We study the motion of a sphere of diameter 330 μm embedded in a Carbopol microgel under the effect of the acoustic radiation pressure exerted by a focused ultrasonic field. The sphere motion within the microgel is tracked using videomicroscopy and compared to conventional creep and recovery measurements performed with a rheometer. We find that under moderate ultrasonic intensities, the sphere creeps as a power law of time with an exponent α ≃ 0.2 that is significantly smaller than the one inferred from global creep measurements below the yield stress of the microgel (α ≃ 0.4). Moreover, the sphere relaxation motion after creep and the global recovery are respectively consistent with these two different exponents. By allowing a rheological characterization at the scale of the sphere with forces of the order of micronewtons, the present experiments pave the way for acoustic "mesorheology" which probes volumes and forces an intermediate between standard macroscopic rheology and classical microrheology. They also open new questions about the effects of the geometry of the deformation field and of the sphere size and surface properties on the creep behaviour of soft materials.

Hierarchically Patterned Elastomeric and Thermoplastic Polymer Films through Nanoimprinting and Ultraviolet Light Exposure

The surface relief structure of polymer films over large areas can be controlled by combining nanoscale imprinting and microscale ultraviolet-ozone (UVO) radiation, resulting in hierarchical structured surfaces. First, nanoscale patterns were formed by nanoimprinting elastomer [poly(dimethylsiloxane) (PDMS)] films with a pattern on a digital video disk. Micron-scale patterns were then superimposed on the nanoimprinted PDMS films by exposing them to ultraviolet radiation in oxygen (UVO) through a transmission electron microscopy grid mask having variable microscale patterning. UVO exposure leads to conversion and densification of PDMS to SiO x , leading to micron height relief features that follow a linear scaling relation with pattern dimension. Further, the pattern scopes are shown to collapse into a master curve by normalized feature values. Interestingly, these relief structures preserve the nanoscale features. In this paper, the influence of the self-limiting PDMS densification, wall stress at the boundary of micro-depression, and UVO exposure energy is studied in control of the micro-depression scale. This simple two-step imprinting process involving both nanoimprinting and UV radiation allows for facile fabrication of the dimension adjustable micro-nano hierarchically structures not only on elastomer films but also on thermoplastic polymer films. Coarse-grained molecular dynamics simulations were performed to correlate the surface tension and elastic properties of polymeric materials to the deformation of the pattern structure.

A Translucent Nanocomposite with Liquid Inclusions of a Responsive Nanoparticle Dispersion

Active nanocomposites are created with liquid inclusions that contain plasmonic gold nanoparticles inside a polymeric matrix. The alkylthiol-coated gold particles are designed to reversible agglomerate at certain temperatures, which changes the plasmonic coupling and thus optical properties. It is found that particles confined to the liquid inclusions inside the active composite retain this capability and cause macroscopic, temperature-dependent color change of the solid. The transition is fully reversible for at least 100 times and tunable in temperature via particle size and ligand. This method is suitable to "package" responsive dispersion in solid composites to exploit their dynamic properties in materials.

An elliptical liquid inclusion in an infinite elastic plane

Beyond recent related literature, which focused on spherical incompressible liquid inclusions, the present work studies an elliptical compressible liquid inclusion in an infinite elastic plane under static remote mechanical loading. Here, it is assumed that the change of pressure inside the liquid inclusion is linearly related to the change of inclusion volume with the bulk modulus of the liquid as the proportionality coefficient. Also, the role of the liquid surface tension on the solid–liquid interface is examined especially when the size of the liquid inclusion is comparable to or smaller than the elastocapillary length. Our results show that both the surface tension and the change of liquid pressure have a significant effect on reducing the stress concentration factor at the endpoints of an elliptical liquid inclusion. In addition, the pressure change inside the liquid inclusion is studied when a uniaxial remote stress is applied perpendicular or parallel to the major axis of the elliptical liquid inclusion. In particular, the effective plane-strain Young's modulus of a solid–liquid composite containing circular liquid inclusions predicted by the present model is linearly related to the volume fraction of the liquid inclusions, in reasonable agreement with existing experimental data.

Encapsulating Networks of Droplet Interface Bilayers in a Thermoreversible Organogel

The development of membrane-based materials that exhibit the range and robustness of autonomic functions found in biological systems remains elusive. Droplet interface bilayers (DIBs) have been proposed as building blocks for such materials, owing to their simplicity, geometry, and capability for replicating cellular phenomena. Similar to how individual cells operate together to perform complex tasks and functions in tissues, networks of functionalized DIBs have been assembled in modular/scalable networks. Here we present the printing of different configurations of picoliter aqueous droplets in a bath of thermoreversible organogel consisting of hexadecane and SEBS triblock copolymers. The droplets are connected by means of lipid bilayers, creating a network of aqueous subcompartments capable of communicating and hosting various types of chemicals and biomolecules. Upon cooling, the encapsulating organogel solidifies to form self-supported liquid-in-gel, tissue-like materials that are robust and durable. To test the biomolecular networks, we functionalized the network with alamethicin peptides and alpha-hemolysin (αHL) channels. Both channels responded to external voltage inputs, indicating the assembly process does not damage the biomolecules. Moreover, we show that the membrane properties may be regulated through the deformation of the surrounding gel.

Controllable Interface Junction, In-Plane Heterostructures Capable of Mechanically Mediating On-Demand Asymmetry of Thermal Transports

Designing structures with thermal rectification performance that can be regulated by or adapted to mechanical deformation is in great demand in wearable electronics. Herein, using nonequilibrium molecular dynamics simulation, we present an in-plane graphene-boron nitride heterostructure with a controlled interface junction and demonstrate that its thermal transport ability is asymmetric when reversing the direction of heat flow. Such thermal rectification performance can be further regulated by applying an external tensile loading due to the mitigation of stress concentration, phonon resonance, and phonon localization. The analyses on heat flow distribution, vibrational spectra, and phonon participation suggest that the out-of-plane phonon modes dominate thermal rectification at a small tensile strain, while the mechanical stress plays a dominant role in regulation at a large tensile strain due to the weakened localization of out-of-plane phonon modes. The effect of tensile loading on the thermal rectification is demonstrated by selective interface junction-enabled heterostructures, and the results indicate that both asymmetry and direction of thermal transport can be controlled by introducing defects to the interface junction and/or applying mechanical tensile strain. These findings and models are expected to provide an immediate guidance for designing and manufacturing 2D material-based devices with mechanically tunable thermal management capabilities.

Soft Multifunctional Composites and Emulsions with Liquid Metals

Binary mixtures of liquid metal (LM) or low-melting-point alloy (LMPA) in an elastomeric or fluidic carrier medium can exhibit unique combinations of electrical, thermal, and mechanical properties. This emerging class of soft multifunctional composites have potential applications in wearable computing, bio-inspired robotics, and shape-programmable architectures. The dispersion phase can range from dilute droplets to connected networks that support electrical conductivity. In contrast to deterministically patterned LM microfluidics, LMPA- and LM-embedded elastomer (LMEE) composites are statistically homogenous and exhibit effective bulk properties. Eutectic Ga-In (EGaIn) and Ga-In-Sn (Galinstan) alloys are typically used due to their high conductivity, low viscosity, negligible nontoxicity, and ability to wet to nonmetallic materials. Because they are liquid-phase, these alloys can alter the electrical and thermal properties of the composite while preserving the mechanics of the surrounding medium. For composites with LMPA inclusions (e.g., Field's metal, Pb-based solder), mechanical rigidity can be actively tuned with external heating or electrical activation. This progress report, reviews recent experimental and theoretical studies of this emerging class of soft material architectures and identifies current technical challenges and opportunities for further advancement.

Morphological explanation of high tear resistance of EPDM/NR rubber blends

The fatigue properties of cross-linked blends of ethylene propylene diene rubber (EPDM) with low natural rubber (NR) content and reinforced with carbon black (CB) are studied. It is found that such EPDM/NR compounds have superior crack growth resistance and fatigue lifetime. For low NR contents, transmission electron microscopy reveals that the NR phase forms small droplets of 20-50 nm. Remarkably, these droplets are even smaller than the primary CB particles. Atomic force microscopy shows that the the NR phase droplets have a higher loss factor and a smaller elastic modulus than the surrounding EPDM matrix. Rheometer measurements are used to study the effect of the phase morphology on the rubber mechanical properties. These rheological data are compared with the prediction of the Eshelby model describing the effect of elastic inclusions on solids. A complex interplay between the rubber phase morphology and the solubility of both the sulfur cross-linking system and CB is observed, which cannot be predicted theoretically. It is proposed that the soft NR droplets effectively inhibit the crack propagation in the EPDM matrix.

Surface tension and a self-consistent theory of soft composite solids with elastic inclusions

The importance of surface tension effects is being recognized in the context of soft composite solids, where they are found to significantly affect the mechanical properties, such as the elastic response to an external stress. It has recently been discovered that Eshelby's inclusion theory breaks down when the inclusion size approaches the elastocapillary length L≡γ/E, where γ is the inclusion/host surface tension and E is the host Young's modulus. Extending our recent results for liquid inclusions, here we model the elastic behavior of a non-dilute distribution of isotropic elastic spherical inclusions in a soft isotropic elastic matrix, subject to a prescribed infinitesimal far-field loading. Within our framework, the composite stiffness is uniquely determined by the elastocapillary length L, the spherical inclusion radius R, and the stiffness contrast parameter C, which is the ratio of the inclusion to the matrix stiffness. We compare the results with those from the case of liquid inclusions, and we derive an analytical expression for elastic cloaking of the composite by the inclusions. Remarkably, we find that the composite stiffness is influenced significantly by surface tension even for inclusions two orders of magnitude more stiff than the host matrix. Finally, we show how to simultaneously determine the surface tension and the inclusion stiffness using two independent constraints provided by global and local measurements.

Stabilizing electrodeposition in elastic solid electrolytes containing immobilized anions

Ion transport-driven instabilities in electrodeposition of metals that lead to morphological instabilities and dendrites are receiving renewed attention because mitigation strategies are needed for improving rechargeability and safety of lithium batteries. The growth rate of these morphological instabilities can be slowed by immobilizing a fraction of anions within the electrolyte to reduce the electric field at the metal electrode. We analyze the role of elastic deformation of the solid electrolyte with immobilized anions and present theory combining the roles of separator elasticity and modified transport to evaluate the factors affecting the stability of planar deposition over a wide range of current densities. We find that stable electrodeposition can be easily achieved even at relatively high current densities in electrolytes/separators with moderate polymer-like mechanical moduli, provided a small fraction of anions are immobilized in the separator.

Surface stress of graphene layers supported on soft substrate

We obtain the surface stress of a single layer and multilayers of graphene supported on silicone substrates by measuring the deformation of the graphene-covered substrates induced by the surface tension of liquid droplets together with the Neumann’s triangle concept. We find that the surface stress of the graphene-covered substrate is significant larger than that of the bare substrate, and it increases with increasing graphene layers, and finally reaches a constant value of about 120 mN/m on three and more layers of graphene. This work demonstrates that the apparent surface stress of graphene-substrate systems can be tuned by the substrate and the graphene layers. The surface stress and the tuning effect of the substrate on it may have applications in design and characterization of graphene-based ultra-sensitive sensors and other devices. Moreover, the method may also be used to measure the surface stress of other ultrathin films supported on soft substrates.

Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids

Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However, it ignores interfacial stress and only applies to very dilute composites-i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular, we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, R, to an elastocapillary lengthscale, L. Interfacial tension substantially impacts the effective elastic moduli of the composite when [Formula: see text]. When R<3L/2 (R=3L/2) liquid inclusions stiffen (cloak the far-field signature of) the solid.

Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids

In the dilute limit Eshelby's inclusion theory captures the behavior of a wide range of systems and properties. However, because Eshelby's approach neglects interfacial stress, it breaks down in soft materials as the inclusion size approaches the elastocapillarity length L≡γ/E. Here, we use a three-phase generalized self-consistent method to calculate the elastic moduli of composites comprised of an isotropic, linear-elastic compliant solid hosting a spatially random monodisperse distribution of spherical liquid droplets. As opposed to similar approaches, we explicitly capture the liquid-solid interfacial stress when it is treated as an isotropic, strain-independent surface tension. Within this framework, the composite stiffness depends solely on the ratio of the elastocapillarity length L to the inclusion radius R. Independent of inclusion volume fraction, we find that the composite is stiffened by the inclusions whenever R < 3L/2. Over the same range of parameters, we compare our results with alternative approaches (dilute and Mori-Tanaka theories that include surface tension). Our framework can be easily extended to calculate the composite properties of more general soft materials where surface tension plays a role.

Adsorption of soft particles at fluid interfaces

Soft particles can be better emulsifiers than hard particles because they stretch at fluid interfaces. This deformation can increase adsorption energies by orders of magnitude relative to rigid particles. The deformation of a particle at an interface is governed by a competition of bulk elasticity and surface tension. When particles are partially wet by the two liquids, deformation is localized within a material-dependent distance L from the contact line. At the contact line, the particle morphology is given by a balance of surface tensions. When the particle radius R≪L, the particle adopts a lenticular shape identical to that of an adsorbed fluid droplet. Particle deformations can be elastic or plastic, depending on the relative values of the Young modulus, E, and yield stress, σp. When surface tensions favour complete spreading of the particles at the interface, plastic deformation can lead to unusual fried-egg morphologies. When deformable particles have surface properties that are very similar to one liquid phase, adsorption can be extremely sensitive to small changes of their affinity for the other liquid phase. These findings have implications for the adsorption of microgel particles at fluid interfaces and the performance of stimuli-responsive Pickering emulsions.