Abstract Polyphilic three-arm star-shaped molecules self-assemble in a wide variety of morphologies. We present an analysis of the geometry of the possible mesophases formed by three-star molecules with mutually immiscible arms. The structures resulting from such molecular self-assembly can be interpreted as partitions of space into three-coloured domains obeying geometrical principles that will be summarized here. The design of morphological templates often involves structural adjustments. This paper investigates elementary topological transformations, how they contribute to relaxing unstable local configurations and the physical reason for this instability. In particular, a vertex can relax in various ways that are explored systematically. It is conjectured that similar dissipative morphological changes may be involved in the rheology and visco-plastic response of these heterogeneous fluids. In analogy with T1 topological changes in soap froths, a cT1 move is introduced, providing elementary conservative topological transformations in three-coloured partitions. This article is part of the theme issue ‘Geometry, materials and the imagination’.
Abstract Green structural colour associated with bicontinuous photonic nano structures occurs in both butterflies (Lycaenidae, Papilionidae) and birds (Chloropseidae leafbirds, Psittaculidae parrots). In butterflies and leafbirds, porous chitin or keratin single gyroids reflect green; in parrots, porous keratin disordered sponges reflect blue that combines with yellow pigment to produce green. We develop an angular–spectral framework to compute responses under biologically relevant viewing conditions. For gyroids, a spectral kernel constructed using experimentally constrained parameters and orientation statistics from Callophrys rubi serves as a generic representation across gyroid-bearing taxa, enabling computation of stereographic reflectance maps and numerical-aperture-dependent spectra as functions of crystallographic orientation distributions in polycrystalline assemblies. For disordered architectures, we introduce a random Gaussian field framework that provides a natural analytical description of bird sponges, enabling forward spectral modelling and quantitative structural characterization. Both ordered gyroids and disordered sponges represent parallel photonic strat egies converging on green through similar length scales and porosities and filtering. Gyroid-bearing species vary through orientation distributions yet maintain similar structural parameters across distantly related taxa. The analytical frameworks enable direct comparison of ordered and disordered bicontinuous structures across butterflies and birds. This article is part of the theme issue ‘Geometry, materials and the imagination’.
Abstract The wings of select Papilionid and Lycaenid butterflies contain a three-dimensional gyroid network of a solid cuticle phase in air. In butterfly scales, gyroid networks are optically interesting, as they create the green colour observed in the wings of these butterflies. Here, we used position-resolved synchrotron small-angle X-ray scattering (SAXS) to map the spatial heterogeneity of these three-dimensional biophotonic networks. An automated analysis procedure extracted crystallographic parameters from >10 000 individual SAXS spectra, which were then mapped onto butterfly photographs. Analysis of Bragg peak positions and shapes across four butterfly species revealed spatial variation in the structural parameters of the single-gyroid network space group (I4132), within individual wings, between individuals and between species. Our approach enables a statistical comparison of lattice parameters between species and of local variations within a species. Intraspecies variation within the wings of a single individual of Callophrys rubi was identified. A larger difference in the unit cell size was identified among individuals of the species Callophrys gryneous, Parides sesostris and Callophrys rubi. Among the four species, a single specimen of Teinopalpus imperialis exhibited the greatest variability in unit cell size, largest crystalline domain size and distribution of the cubic phase within the wing. This article is part of the theme issue ‘Geometry, materials and the imagination’.
Abstract Triply periodic hyperbolic surfaces have been extensively investigated in various natural and artificial self-assembled systems and have attracted great attention because of their complexity and geometrical beauty. However, understanding their formation during bottom-up processes remains challenging because of the short lifetimes of structural intermediates and the soft nature of amphiphilic systems. Herein, we introduce UV light curing technology, which rapidly solidifies reaction intermediates without interfering with the final structure. The synthesis involves a miktoarm block copolymer, poly(ethylene oxide)-s-(polystyrene)2, with tetraethyl orthosilicate in a mixture of tetrahydrofuran and an aqueous HCl solution to form a silica scaffold with a shifted double diamond structure. By capturing intermediate phases at different reaction stages, we disclosed the following sequence of structural transformations: lamellar → perforated lamellar → single network → double diamond network → shifted double diamond after calcination. Our findings underscore the pivotal role of perforated lamellar structures and single networks as key intermediates, which exhibit instability conducive to transitioning into more stable double network configurations. This transformation also explains the coexistence of single and double networks observed in previous experiments and their unit cell parameter discrepancies. This research provides new insights into the formation of hyperbolic structures and the design of future self-assembly processes. This article is part of the theme issue ‘Geometry, materials and the imagination’.
Abstract We investigate the self-assembly of compositionally asymmetric AB diblock co-polymers confined to thin hyperbolic films on the three cubic minimal surfaces: the primitive, the diamond and the gyroid. To analyse and quantify the assemblies, we use a computational pipeline where decorations of the curved surfaces from (flat) three-dimensional space are visualized in curved two-dimensional space using the Poincaré disc model of the hyperbolic plane. This allows us to pinpoint the role of the intrinsic geometry and probe the role of the Gaussian curvature of the film on the resulting assemblies. We find three distinct symmetric arrays of discs favoured for specific values of the average Gaussian curvature of the film, whose relative appearance as a function of the average film curvature is common to all three minimal surfaces, which strongly suggests these assemblies are not influenced by the extrinsic embedding of the film. In general, the assembled discs are located in regions with minimal (absolute) Gaussian curvature, likely in order to minimize the effective line tension within the system corresponding to the enthalpic cost of co-polymer assembly along the perimeters of the discs. This article is part of the theme issue ‘Geometry, materials and the imagination’.
Abstract The regular arrangements of identical spheres on the gyroid surface have been investigated using Monte Carlo simulations of hard spheres undergoing the Alder transition. In our preceding study, we showed that these regular structures on saddle-shaped triply periodic minimal surfaces are systematically classified by the hexagulation number H, analogous to the Caspar–Klug triangulation number for icosahedral viruses. In this paper, we focus on the non-centrosymmetric regular structures that emerge when H is a multiple of three on the gyroid surface. In these cases, the space group Ia3¯d of the gyroid is reduced to its non-centrosymmetric subgroup I4¯3d. By considering both inversion structures, we construct an efficient bilayer configuration that forms a truss-like structure. These physically efficient designs may provide inspiration for future applications in soft-matter science, DNA-origami nanotechnology, metamaterials, and even architectural design. This article is part of the theme issue ‘Geometry, materials and the imagination’.
Abstract This article is an introduction to a special issue of the journal ‘Interface Focus’ dedicated to Professor Stephen T. Hyde on the occasion of his retirement. Professor Hyde’s scientific career has revolved around using the geometric study of structures with negative Euler index χ—bicontinuous and other negatively curved surfaces, spatial nets, tangles and knots—to understand the emergence of shape and form in chemical and biological systems, including in lipid polymorphism, biological membranes and nanostructures, and atomic networks such as metal-organic frameworks and zeolites. Professor Hyde’s publications include articles from multiple disparate fields, including e.g. the mathematical enumeration of tillings of hyperbolic spaces and the physical chemistry of lyotropic liquid crystal polymorphism. The bulk of his work, however, comprises remarkable interdisciplinary studies that bring together fundamental geometry and applied, often experimental, science in a way where the whole truly is more than the sum of its parts. This introduction does not provide a comprehensive biography of Professor Hyde. Rather, it celebrates some of his many contributions in chronological order, together with a few anecdotes and photos, and within their historical and current context. This article includes as an appendix an unpublished manuscript entitled ‘Desperately seeking life’ by Hyde & García-Ruiz in regard to ‘biomorphs’, with shapes reminiscent of biological forms but of purely inorganic origins. This article is part of the theme issue ‘Geometry, Materials and the Imagination’.
Abstract The EPINET project (Euclidean Patterns In Non-Euclidean Tilings) catalogues crystalline frameworks (three-periodic nets) generated from tilings of triply periodic minimal surfaces. These nets have a broad distribution of structural motifs that are of potential interest to chemists and materials scientists working at arbitrary length scales. The catalogue has been available as a searchable online database at https://epinet.anu.edu.au/ since 2006; this paper reviews the history and context of EPINET and announces a major update of the website functionality. As a set of examples found using recently computed additional information about the nets, we describe the s-nets that have rings of exactly one size. This article is part of the theme issue ‘Geometry, materials and the imagination’.
Abstract Advances in soft and wearable robotics, surgery, biomaterials and biomimetics suggest that implantable artificial muscles are becoming a reality. If successful, these implants promise to help alleviate muscular conditions, like sarcopenia, by complementing natural muscles. Artificial muscles therefore promise to empower and benefit their recipients—but they also risk them (and others) being disempowered or otherwise harmed. We adopted a future-focused, anticipatory ethics approach to explore the ethical dimensions of the design, development and deployment of artificial muscles. A narrative review of pertinent literature was conducted to explore ethical questions associated with the overarching obligations to respect autonomy, balance benefits and burdens, and serve the public interest. Our analysis suggests that careful consideration should be given to: the selection of materials and methods; participants and patients; ensuring that recipients provide voluntary and informed consent; mechanisms of review and redress; arrangements for sharing and protecting data; managing access and distribution; and ensuring the inclusion of, and engagement with, diverse stakeholders. We conclude that further such engagement is now needed, including in the co-production of standards—such as an ethical framework—to guide developments going forward.
Decoding the activity of the nervous system is a critical challenge in neuroscience and neural interfacing. In this study, we present a neuromuscular recording system that enables large-scale sampling of muscle activity using microelectrode arrays with over 100 channels embedded in forearm muscles. These arrays captured intramuscular high-density signals that were decoded into patterns of activation of spinal motoneurons. In two healthy participants, we recorded high-density intramuscular activity during single- and multi-digit contractions, revealing distinct motoneuron recruitment patterns specific to each task. Based on these patterns, we achieved perfect classification accuracy (100%) for 12 single- and multi-digit tasks and over approximately 96% accuracy for up to 16 tasks, significantly outperforming state-of-the-art electromyogram classification methods. This intramuscular high-density system and classification method represent an advancement in neural interfacing, with the potential to improve human-computer interaction and the control of assistive technologies, particularly for replacing or restoring impaired motor function.
Abstract Muscle-driven biohybrid robotics has gained substantial attention for its potential to enable advanced mechanical systems with flexibility, high energy efficiency, self-healing capability and adaptability. Autonomous or stimulated muscle contractions have been used as driving forces of mechanical functions and have successfully demonstrated walking, swimming and crawling behaviours of biohybrid robots. Despite these advances, many opportunities exist to achieve greater actuation, precise control, longer-term viability, and programmability. This review provides insights into the next generation of biohybrid systems by examining prior studies on locomotive biohybrid robots specifically designed for walking and crawling locomotion. We introduce diverse biohybrid walker and crawler models and describe their design principles and operating mechanisms, and discuss key factors for optimal engineering strategies. Furthermore, we classify these models according to three primary muscle-stimulation techniques, i.e. electrical field, optical, and neuromuscular junction, and discuss their unique characteristics, including their advantages and limitations. We also highlight approaches for multi-directional locomotion and wireless control, which can contribute to achieving higher dynamic control of biohybrid robots.
Abstract Volumetric muscle loss (VML) refers to the loss of skeletal muscle that exceeds intrinsic repair and heals with fibrosis, poor perfusion and denervation. Conventional treatments such as muscle grafts and decellularized matrices improve structure but rarely restore normal strength or limb use. Hydrogels have emerged as injectable scaffolds that fill irregular defects, deliver cells and cues and better match muscle-like mechanics. This review summarizes hydrogels for VML repair, including natural and semi-synthetic systems (gelatin, collagen, hyaluronan, fibrin, alginate, muscle-derived decellularized extracellular matrix (ECM)), synthetic networks and peptide-based hydrogels. Natural matrices provide tissue-derived signals but offer limited control over stiffness and degradation. Synthetic hydrogels allow precise tuning of mechanics and porosity but require additional ligands and growth factors to effectively support VML repair. Peptide hydrogels self-assemble into ECM-like nanofibres and can display multiple motifs for adhesion, immunomodulation, angiogenesis and neurotrophic support, although direct VML data remain sparse. Across these material classes, we highlight shared design principles: aligned architectures and hierarchical porosity, graded properties at muscle–tendon and muscle–nerve interfaces and degradation and cue delivery matched to overlapping healing phases, combined with appropriate cell strategies. Together, these concepts support a shift from passive defect filling towards reconstruction of a regenerative niche with hybrid hydrogel constructs for VML repair.
Dielectric elastomer actuators (DEAs) stand out as versatile devices with promising applications. Their use has been proposed as artificial muscle implants, aiming to replace paralyzed facial muscles and restore the corresponding movements. By reinforcing DEAs with unidirectional fibres, substantial uniaxial deformations can be induced, resulting in previously reported strains up to 75% higher than isotropic DEAs. In this work, the control of the actuator is explored by investigating the dynamic electro-viscoelastic response of a dielectric elastomer with transversally isotropic properties. A model for anisotropic viscoelastic dielectric elastomers is proposed, which is employed to describe the actuator’s dynamic response and design a closed-loop controller in order to achieve a precise actuation of the facial prosthesis. The model is validated with two types of input signals. The control system demonstrated its efficacy in minimizing error and improving actuation performance. The designed prosthesis showed a root mean square error of 2.06% in response to electromyography signals recording movement on the zygomaticus major muscle responsible for smiling.
Design of a medical implant needs to ensure the device can be positioned accurately and removed subsequently if needed. This necessitates specific design considerations for implantation. This review is an opinion paper considering how an operation to introduce an implant into a patient may affect design, focusing on development of implantable artificial muscles (IAMs). Compatibility with endoscopic ports or the Seldinger technique will help deliver treatment with shorter hospital stay and quicker recovery. This means an IAM device has to have configurations to suit both deployment and use. Replacement of the device or removal as an emergency means it must be easy to extract without damage to the patient’s tissues, using standard surgical equipment. The implant has to be compatible with processes for sterilizing medical devices. But design of the packaging of the implant is equally important, since transfer of the device from its sterile-packaged storage state to the operating table for deployment into a patient is a vulnerable process in which contamination can occur. Implant surgery is a high-risk healthcare intervention. Those developing IAMs should consider aspects relating to surgical approach, deployment, wear, fixation, avoidance of perioperative complications and subsequent removal.
Soft actuators have been extensively developed over the past two decades, yet their control strategies remain rudimentary and do not exploit well their unique viscoelastic properties. To develop skilful control of soft actuators, we take inspiration from human sensorimotor control, which achieves dynamic and accurate movements despite relying on noisy and slow muscles. We first examine how the human nervous system (HNS) optimally controls muscles to exchange energy with the environment and extract maximal information from it. Critically, the HNS prepares interactions by learning specific patterns of reciprocal activation and co-activation, thereby regulating force and impedance, storing elastic energy and embodying uncertainty. We then show that soft actuators share key mechanical characteristics with human muscles and could thus benefit from recently identified computational mechanisms of the HNS, yielding efficient nonlinear adaptive impedance and stochastic nonlinear optimal control algorithms.
Recently, ionic diodes have garnered significant attention due to their potential applications in flexible electronics and implantable bioelectronics, where conventional semiconductor-based devices face inherent limitations. Here, we report a dual-network hydrogel-based ionic diode composed of polyvinyl alcohol and polyacrylamide matrices incorporating cationic polydiallyldimethylammonium and anionic poly(sodium 4-styrenesulfonate) polyelectrolytes. The system is fabricated via chemical and freeze-thaw crosslinking, achieving a synergistic balance of mechanical integrity and ionic mobility. The optimized device exhibits a very high current rectification ratio of 53.9, attributed to enhanced interfacial ion transport. This strategy enables scalable fabrication of robust ionic diodes, offering a versatile platform for next-generation ionic devices and flexible bioelectronic systems.
Conductive hydrogels are promising materials for soft strain sensing because they combine tissue-like mechanics with electrical functionality. However, many existing systems emphasize conductivity or sensitivity at the cost of mechanical reversibility, leading to pronounced hysteresis and limited cyclic stability. Here, we report a two-step fabrication strategy that decouples mechanical and electrical optimization. A highly entangled polyacrylamide (PAAm) hydrogel is first prepared as a mechanically reversible scaffold, followed by in situ polymerization of polypyrrole (PPy) to introduce conductivity, yielding a composite hydrogel (PAAm@PPy). The material exhibits soft-tissue-level stiffness (Young's modulus of 75 kPa), high stretchability (strain at break of 246%) and low mechanical hysteresis (5.7% at 50% strain). The as-synthesized PAAm@PPy shows an apparent bulk conductivity of 0.094 S cm(-)& sup1; and a linear positive piezoresistive response with a gauge factor of 2.04 over 0-50% strain, together with stable cyclic sensing (500 cycles at 30% strain). A proof-of-concept finger-bending demonstration confirms its fast response and signal stability. This work establishes a conductive hydrogel design paradigm that prioritizes low hysteresis and cyclic stability through a decoupled two-step co-synthesis of highly entangled hydrogels and conductive polymer, enabling reliable strain sensing for soft electronic applications.
Surgical implants, such as joint replacements, are used for many serious conditions. Innovation continues to supply new implants, including outputs of the soft robotics revolution. However, they carry risk of complications with potentially devastating consequences. We present an opinion paper providing the reflections of two surgical technologists on present challenges to safety, efficacy and broad implementation of medical implants. We highlight lack of familiarity with implant surgery in healthcare services, with concomitant risk. First-in-human application of new implants is not sufficiently standardized and regulated. IDEAL-D is a structured framework for medical devices (Idea, Development, Exploration, Assessment, Long-term study). Once CE-marked and approved for mainstream use, there are problems with the implementation. ‘Early adopter’ surgeons and centres face cultural inertia, lack of funding support and issues around training, especially learning curves. Patient selection may not be well-defined, and complications inaccurately reported, affecting implant dissemination detrimentally. The Cumberlege report showed how harmful this can be. There is need to standardize early clinical studies. Implementation of implantable devices requires changes to whole-team training, funding and post-implementation reporting. The IDEAL-D framework represents an important step, but other system-wide changes are required if implants are to achieve their intended clinical impact.
Light-responsive polymers hold great promise for remote or battery-free actuation in soft robotics. Yet, current systems often suffer from limited responsiveness, processability and biocompatibility-challenges that are particularly critical for muscle restoration applications. Here, we introduce MyoHybrid, a 'dual-photoresponsive' skeletal muscle actuator combining optogenetic myofibres with a scalable, unidirectionally aligned polyurethane-azobenzene (PAzo) nanofibre scaffold. The term 'dual-photoresponsive' refers to the synergy between intrinsic PAzo photoactuation-driven by coupled photochemical and photothermal effects-and optogenetically induced myofibre contractions. This anisotropic integration enables cooperative light-driven actuation of both nanofibres and myotubes. Compared with PAzo flat solid substrate, aligned PAzo nanofibres improved unidirectional myotube fusion by 25.3% and enhanced maturation by 37.7%. Furthermore, optogenetic stimulation of the resulting myofibres led to a 60% increase in contraction velocity and force relative to glass controls. MyoHybrid established a seamless interface between synthetic nanofibres and biological myofibres, offering a programmable platform for muscle-on-chip models, biohybrid actuators and light-driven soft tissue systems. This work bridges mechanical bionics and cellular actuation, advancing next-generation soft robotics and regenerative technologies.
