Harnessing the interface mechanics of hard films and soft substrates for 3D assembly by controlled buckling.

Techniques for forming sophisticated, 3D mesostructures in advanced, functional materials are of rapidly growing interest, owing to their potential uses across a broad range of fundamental and applied areas of application. Recently developed approaches to 3D assembly that rely on controlled buckling mechanics serve as versatile routes to 3D mesostructures in a diverse range of high-quality materials and length scales of relevance for 3D microsystems with unusual function and/or enhanced performance. Nonlinear buckling and delamination behaviors in materials that combine both weak and strong interfaces are foundational to the assembly process, but they can be difficult to control, especially for complex geometries. This paper presents theoretical and experimental studies of the fundamental aspects of adhesion and delamination in this context. By quantifying the effects of various essential parameters on these processes, we establish general design diagrams for different material systems, taking into account 4 dominant delamination states (wrinkling, partial delamination of the weak interface, full delamination of the weak interface, and partial delamination of the strong interface). These diagrams provide guidelines for the selection of engineering parameters that avoid interface-related failure, as demonstrated by a series of examples in 3D helical mesostructures and mesostructures that are reconfigurable based on the control of loading-path trajectories. Three-dimensional micromechanical resonators with frequencies that can be selected between 2 distinct values serve as demonstrative examples.

Guided Formation of 3D Helical Mesostructures by Mechanical Buckling: Analytical Modeling and Experimental Validation.

Three-dimensional (3D) helical mesostructures are attractive for applications in a broad range of microsystem technologies, due to their mechanical and electromagnetic properties as stretchable interconnects, radio frequency antennas and others. Controlled compressive buckling of 2D serpentine-shaped ribbons provides a strategy to formation of such structures in wide ranging classes of materials (from soft polymers to brittle inorganic semiconductors) and length scales (from nanometer to centimeter), with an ability for automated, parallel assembly over large areas. The underlying relations between the helical configurations and fabrication parameters require a relevant theory as the basis of design for practical applications. Here, we present an analytic model of compressive buckling in serpentine microstructures, based on the minimization of total strain energy that results from various forms of spatially dependent deformations. Experiments at micro- and millimeter-scales, together with finite element analyses (FEA), were exploited to examine the validity of developed model. The theoretical analyses shed light on general scaling laws in terms of three groups of fabrication parameters (related to loading, material and 2D geometry), including a negligible effect of material parameters and a square root dependence of primary displacements on the compressive strain. Furthermore, analytic solutions were obtained for the key physical quantities (e.g., displacement, curvature and maximum strain). A demonstrative example illustrates how to leverage the analytic solutions in choosing the various design parameters, such that brittle fracture or plastic yield can be avoided in the assembly process.

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures.

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

A finite deformation model of planar serpentine interconnects for stretchable electronics.

Lithographically defined interconnects with filamentary, serpentine configurations have been widely used in various forms of stretchable electronic devices, owing to the ultra-high stretchability that can be achieved and the relative simple geometry that facilitates the design and fabrication. Theoretical models of serpentine interconnects developed previously for predicting the performance of stretchability were mainly based on the theory of infinitesimal deformation. This assumption, however, does not hold for the interconnects that undergo large levels of deformations before the structural failure. Here, an analytic model of serpentine interconnects is developed starting from the finite deformation theory of planar, curved beams. Finite element analyses (FEA) of the serpentine interconnects with a wide range of geometric parameters were performed to validate the developed model. Comparisons of the predicted stretchability to the estimations of linear models provide quantitative insights into the effect of finite deformation. Both the theoretical and numerical results indicate that a considerable overestimation (e.g., > 50% relatively) of the stretchability can be induced by the linear model for many representative shapes of serpentine interconnects. Furthermore, a simplified analytic solution of the stretchability is obtained by using an approximate model to characterize the nonlinear effect. The developed models can be used to facilitate the designs of serpentine interconnects in future applications.

Full-field measurement of surface topographies and thin film stresses at elevated temperatures by digital gradient sensing method.

Thin film stresses in thin film/substrate systems at elevated temperatures affect the reliability and safety of such structures in microelectronic devices. The stresses result from the thermal mismatch strain between the film and substrate. The reflection mode digital gradient sensing (DGS) method, a real-time, full-field optical technique, measures deformations of reflective surface topographies. In this paper, we developed this method to measure topographies and thin film stresses of thin film/substrate systems at elevated temperatures. We calibrated and compensated for the air convection at elevated temperatures, which is a serious problem for optical techniques. We covered the principles for surface topography measurements by the reflection mode DGS method at elevated temperatures and the governing equations to remove the air convection effects. The proposed method is applied to successfully measure the full-field topography and deformation of a NiTi thin film on a silicon substrate at elevated temperatures. The evolution of thin film stresses obtained by extending Stoney's formula implies the "nonuniform" effect the experimental results have shown.

Multiwavelength shearing interferometry for measuring the slopes, curvatures, and shapes of thin films/substrate systems.

Multiwavelength shearing interferometry, a full-field, real-time, and vibration-insensitive method with enhanced accuracy, is proposed. Theoretically, the more wavelengths that are used for shearing interferometers, the higher the precision that can be achieved in the measurement of slopes, curvatures, and the shapes of reflective surfaces. A spherical mirror with specified curvature radius is used to calibrate this method, and then the nonuniform deformation and shape of the TiNi film/Si substrate system are obtained experimentally.

Buckling in serpentine microstructures and applications in elastomer-supported ultra-stretchable electronics with high areal coverage.

Lithographically defined electrical interconnects with thin, filamentary serpentine layouts have been widely explored for use in stretchable electronics supported by elastomeric substrates. We present a systematic and thorough study of buckling physics in such stretchable serpentine microstructures, and a strategic design of serpentine layout for ultra-stretchable electrode, via analytical models, finite element method (FEM) computations, and quantitative experiments. Both the onset of buckling and the postbuckling behaviors are examined, to determine scaling laws for the critical buckling strain and the limits of elastic behavior. Two buckling modes, namely the symmetric and anti-symmetric modes, are identified and analyzed, with experimental images and numerical results that show remarkable levels of agreement for the associated postbuckling processes. Based on these studies and an optimization in design layout, we demonstrate routes for application of serpentine interconnects in an ultra-stretchable electrode that offer, simultaneously, an areal coverage as high as 81%, and a biaxial stretchability as large as ~170%.

Accuracy of individual trabecula segmentation based plate and rod finite element models in idealized trabecular bone microstructure.

Currently, specimen-specific micro finite element (µFE) analysis based micro computed tomography (µCT) images have become a major computational tool for the assessment of the mechanical properties of human trabecular bone. Despite the fine characterization of the three-dimensional (3D) trabecular microstructure based on high-resolution µCT images, conventional µFE models with each voxel converted to an element are not efficient in predicting the nonlinear failure behavior of bone due to a prohibitive computational cost. Recently, a highly efficient individual trabecula segmentation (ITS)-based plate and rod (PR) modeling technique has been developed by substituting individual plates and rods with shell and beam elements, respectively. In this technical brief, the accuracy of novel PR µFE models was examined in idealized microstructure models over a broad range of trabecular thicknesses. The Young's modulus and yield strength predicted by simplified PR models strongly correlated with those of voxel models at various voxel sizes. The conversion from voxel models to PR models resulted in an ∼762-fold reduction in the largest model size and significantly accelerated the nonlinear FE analysis. The excellent predictive power of the PR µFE models, demonstrated in an idealized trabecular microstructure, provided a quantitative mechanical basis for this promising tool for an accurate and efficient assessment of trabecular bone mechanics and fracture risk.

Dissolvable films of silk fibroin for ultrathin conformal bio-integrated electronics.

Electronics that are capable of intimate, non-invasive integration with the soft, curvilinear surfaces of biological tissues offer important opportunities for diagnosing and treating disease and for improving brain/machine interfaces. This article describes a material strategy for a type of bio-interfaced system that relies on ultrathin electronics supported by bioresorbable substrates of silk fibroin. Mounting such devices on tissue and then allowing the silk to dissolve and resorb initiates a spontaneous, conformal wrapping process driven by capillary forces at the biotic/abiotic interface. Specialized mesh designs and ultrathin forms for the electronics ensure minimal stresses on the tissue and highly conformal coverage, even for complex curvilinear surfaces, as confirmed by experimental and theoretical studies. In vivo, neural mapping experiments on feline animal models illustrate one mode of use for this class of technology. These concepts provide new capabilities for implantable and surgical devices.

Full-field measurement of nonuniform stresses of thin films at high temperature.

Coherent gradient sensing (CGS), a shear interferometry method, is developed to measure the full-field curvatures of a film/substrate system at high temperature. We obtain the relationship between an interferogram phase and specimen topography, accounting for temperature effect. The self-interference of CGS combined with designed setup can reduce the air effect. The full-field phases can be extracted by fast Fourier transform. Both nonuniform thin-film stresses and interfacial stresses are obtained by the extended Stoney's formula. The evolution of thermo-stresses verifies the feasibility of the proposed interferometry method and implies the "nonlocal" effect featured by the experimental results.

Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations.

Electronic systems that offer elastic mechanical responses to high-strain deformations are of growing interest because of their ability to enable new biomedical devices and other applications whose requirements are impossible to satisfy with conventional wafer-based technologies or even with those that offer simple bendability. This article introduces materials and mechanical design strategies for classes of electronic circuits that offer extremely high stretchability, enabling them to accommodate even demanding configurations such as corkscrew twists with tight pitch (e.g., 90 degrees in approximately 1 cm) and linear stretching to "rubber-band" levels of strain (e.g., up to approximately 140%). The use of single crystalline silicon nanomaterials for the semiconductor provides performance in stretchable complementary metal-oxide-semiconductor (CMOS) integrated circuits approaching that of conventional devices with comparable feature sizes formed on silicon wafers. Comprehensive theoretical studies of the mechanics reveal the way in which the structural designs enable these extreme mechanical properties without fracturing the intrinsically brittle active materials or even inducing significant changes in their electrical properties. The results, as demonstrated through electrical measurements of arrays of transistors, CMOS inverters, ring oscillators, and differential amplifiers, suggest a valuable route to high-performance stretchable electronics.

Arrays of sealed silicon nanotubes as anodes for lithium ion batteries.

Silicon is a promising candidate for electrodes in lithium ion batteries due to its large theoretical energy density. Poor capacity retention, caused by pulverization of Si during cycling, frustrates its practical application. We have developed a nanostructured form of silicon, consisting of arrays of sealed, tubular geometries that is capable of accommodating large volume changes associated with lithiation in battery applications. Such electrodes exhibit high initial Coulombic efficiencies (i.e., >85%) and stable capacity-retention (>80% after 50 cycles), due to an unusual, underlying mechanics that is dominated by free surfaces. This physics is manifested by a strongly anisotropic expansion in which 400% volumetric increases are accomplished with only relatively small (<35%) changes in the axial dimension. These experimental results and associated theoretical mechanics models demonstrate the extent to which nanoscale engineering of electrode geometry can be used to advantage in the design of rechargeable batteries with highly reversible capacity and long-term cycle stability.

Nature's design of hierarchical superhydrophobic surfaces of a water strider for low adhesion and low-energy dissipation.

The mechanics of wet adhesion between a water strider's legs and a water surface was studied. First, we showed that the nanoscale to microscale hierarchical surface structure on striders' legs is crucial to the stable water-repellent properties of the legs. The smallest structure is made for the sake of a stable Cassie state even under harsh environment conditions, which sets an upper limit for the dimension of the smallest structure. The maximum stress and the maximum deformation of the surface structures at the contact line are size-dependent because of the asymmetric surface tension, which sets a lower limit for the dimension of the smallest structure. The surface hierarchy can largely reduce the adhesion between the water and the legs by stabilizing the Cassie state, increasing the apparent contact angle, and reducing the contact area and the length of the contact line. Second, the processes of the legs pressing on and detaching from the water surface were analyzed with a 2D model. We found that the superhydrophobicity of the legs' surface is critically important to reducing the detaching force and detaching energy. Finally, the dynamic process of the legs striking the water surface, mimicking the maneuvering of water striders, was analyzed. We found that the large length of the legs not only reduces the energy dissipation in the quasi-static pressing and pulling processes but also enhances the efficiency of energy transfer from bioenergy to kinetic energy in the dynamic process during the maneuvering of the water striders. The mechanical principles found in this study may provide useful guidelines for the design of superior water-repellent surfaces and novel aquatic robots.

Alignment controlled growth of single-walled carbon nanotubes on quartz substrates.

Single-walled carbon nanotubes (SWNTs) possess extraordinary electrical properties, with many possible applications in electronics. Dense, horizontally aligned arrays of linearly configured SWNTs represent perhaps the most attractive and scalable way to implement this class of nanomaterial in practical systems. Recent work shows that templated growth of tubes on certain crystalline substrates yields arrays with the necessary levels of perfection, as demonstrated by the formation of devices and full systems on quartz. This paper examines advanced implementations of this process on crystalline quartz substrates with different orientations, to yield strategies for forming diverse, but well-defined horizontal configurations of SWNTs. Combined experimental and theoretical studies indicate that angle-dependent van der Waals interactions can account for nearly all aspects of alignment on quartz with X, Y, Z, and ST cuts, as well as quartz with disordered surface layers. These findings provide important insights into methods for guided growth of SWNTs, and possibly other classes of nanomaterials, for applications in electronics, sensing, photodetection, light emission, and other areas.

Optimized structural designs for stretchable silicon integrated circuits.

Materials and design strategies for stretchable silicon integrated circuits that use non-coplanar mesh layouts and elastomeric substrates are presented. Detailed experimental and theoretical studies reveal many of the key underlying aspects of these systems. The results shpw, as an example, optimized mechanics and materials for circuits that exhibit maximum principal strains less than 0.2% even for applied strains of up to approximately 90%. Simple circuits, including complementary metal-oxide-semiconductor inverters and n-type metal-oxide-semiconductor differential amplifiers, validate these designs. The results suggest practical routes to high-performance electronics with linear elastic responses to large strain deformations, suitable for diverse applications that are not readily addressed with conventional wafer-based technologies.

Curvilinear electronics formed using silicon membrane circuits and elastomeric transfer elements.

Materials and methods to achieve electronics intimately integrated on the surfaces of substrates with complex, curvilinear shapes are described. The approach exploits silicon membranes in circuit mesh structures that can be deformed in controlled ways using thin, elastomeric films. Experimental and theoretical studies of the micromechanics of such curvilinear electronics demonstrate the underlying concepts. Electrical measurements illustrate the high yields that can be obtained. The results represent significant experimental and theoretical advances over recently reported concepts for creating hemispherical photodetectors in electronic eye cameras and for using printable silicon nanoribbons/membranes in flexible electronics. The results might provide practical routes to the integration of high performance electronics with biological tissues and other systems of interest for new applications.

Mechanical assembly of complex, 3D mesostructures from releasable multilayers of advanced materials.

Capabilities for assembly of three-dimensional (3D) micro/nanostructures in advanced materials have important implications across a broad range of application areas, reaching nearly every class of microsystem technology. Approaches that rely on the controlled, compressive buckling of 2D precursors are promising because of their demonstrated compatibility with the most sophisticated planar technologies, where materials include inorganic semiconductors, polymers, metals, and various heterogeneous combinations, spanning length scales from submicrometer to centimeter dimensions. We introduce a set of fabrication techniques and design concepts that bypass certain constraints set by the underlying physics and geometrical properties of the assembly processes associated with the original versions of these methods. In particular, the use of releasable, multilayer 2D precursors provides access to complex 3D topologies, including dense architectures with nested layouts, controlled points of entanglement, and other previously unobtainable layouts. Furthermore, the simultaneous, coordinated assembly of additional structures can enhance the structural stability and drive the motion of extended features in these systems. The resulting 3D mesostructures, demonstrated in a diverse set of more than 40 different examples with feature sizes from micrometers to centimeters, offer unique possibilities in device design. A 3D spiral inductor for near-field communication represents an example where these ideas enable enhanced quality (Q) factors and broader working angles compared to those of conventional 2D counterparts.

Osteocyte-viability-based simulations of trabecular bone loss and recovery in disuse and reloading.

Osteocyte apoptosis is known to trigger targeted bone resorption. In the present study, we developed an osteocyte-viability-based trabecular bone remodeling (OVBR) model. This novel remodeling model, combined with recent advanced simulation methods and analysis techniques, such as the element-by-element 3D finite element method and the ITS technique, was used to quantitatively study the dynamic evolution of bone mass and trabecular microstructure in response to various loading and unloading conditions. Different levels of unloading simulated the disuse condition of bed rest or microgravity in space. The amount of bone loss and microstructural deterioration correlated with the magnitude of unloading. The restoration of bone mass upon the reloading condition was achieved by thickening the remaining trabecular architecture, while the lost trabecular plates and rods could not be recovered by reloading. Compared to previous models, the predictions of bone resorption of the OVBR model are more consistent with physiological values reported from previous experiments. Whereas osteocytes suffer a lack of loading during disuse, they may suffer overloading during the reloading phase, which hampers recovery. The OVBR model is promising for quantitative studies of trabecular bone loss and microstructural deterioration of patients or astronauts during long-term bed rest or space flight and thereafter bone recovery.

Mechanics of finger-tip electronics.

Tactile sensors and electrotactile stimulators can provide important links between humans and virtual environments, through the sensation of touch. Soft materials, such as low modulus silicones, are attractive as platforms and support matrices for arrays sensors and actuators that laminate directly onto the fingertips. Analytic models for the mechanics of three dimensional, form-fitting finger cuffs based on such designs are presented here, along with quantitative validation using the finite element method. The results indicate that the maximum strains in the silicone and the embedded devices are inversely proportional to the square root of radius of curvature of the cuff. These and other findings can be useful in formulating designs for these and related classes of body-worn, three dimensional devices.

Identifying the molecular mechanics and binding dynamics characteristics of potent inhibitors to HIV-1 protease.

Human immunodeficiency virus type 1 protease (HIV-1 PR) is one of the primary inhibition targets for chemotherapy of AIDS because of its critical role in the replication cycle of the HIV. In this work, a combinatory coarse-grained and atomistic simulation method was developed for dissecting molecular mechanisms and binding process of inhibitors to the active site of HIV-1 PR, in which 35 typical inhibitors were trialed. We found that the molecular size and stiffness of the inhibitors and the binding energy between the inhibitors and PR play important roles in regulating the binding process. Comparatively, the smaller and more flexible inhibitors have larger binding energy and higher binding rates; they even bind into PR without opening the flaps. In contrast, the larger and stiffer inhibitors have lower binding energy and lower binding rate, and their binding is subjected to the opening and gating of the PR flaps. Furthermore, the components of binding free energy were quantified and analyzed by their dependence on the molecular size, structures, and hydrogen bond networks of inhibitors. Our results also deduce significant dynamics descriptors for determining the quantitative structure and property relationship in potent drug ligands for HIV-1 PR inhibition.