Interfacial Adhesion Energy Research Articles

Quantitative characterization of interface stress using a nanoindentation technique for high performance flexible electronics

A simple method was introduced to precisely characterize the interface stress of flexible OFETs using nanoindentation. The interface stress could be tuned by controlling the interface adhesion energy between layers, via controlling the film formation process.

Interfacial adhesion of ZnO nanowires on a Si substrate in air.

It is imperative to understand the interfacial adhesive behaviour of nanowires (NW) integrated into a nanoelectromechanical system in order to design commercialisable nanogenerators as well as ultrasensitive sensors. Currently available interfacial adhesion characterisation techniques that utilise in situ electron microscopy subject nanoscale systems to a high-vacuum, electron-irradiated environment, potentially altering their interfacial interactions. Alternatively, force-sensing techniques conducted in air do not provide visual feedback of the interface, and therefore can only indirectly deduce adhesive properties. Here, we present an interface characterisation technique that enforces ZnO NWs to remain partially delaminated on a Si substrate, and permits optical observation of their deformed condition in air. NWs are draped over a wedge and are allowed to conform to their minimum energy state. We evaluate the strain energy stored in the suspended segment of each NW by determining their deflected shape from interferometry. We show that utilising a tailored Euler-Bernoulli beam model which accounts for the tapering and irregularity of a NW is crucial for accurately evaluating their interfacial adhesion energy. A nominal energy per unit interface area value of [capital Gamma, Greek, macron]F-B,irr,taper = 51.1 ± 31.9 mJ m-2 is obtained for the ZnO NW-Si substrate interface; a magnitude lower than that found using electron microscopy, and higher than the upper-bound of the theoretically predicted van der Waals interaction energy of γvdW = 7.2 mJ m-2. This apparent discrepancy has significant implications for any nanotribological study conducted inside an electron microscope. The results also implicate electrostatic and capillary interactions as significant contributors towards a NW's adhesive behaviour during device operation.

Flattening van der Waals heterostructure interfaces by local thermal treatment

Fabrication of custom-built heterostructures based on stacked 2D materials provides an effective method to controllably tune electronic and optical properties. To that end, optimizing fabrication techniques for building these heterostructures is imperative. A common challenge in layer-by-layer assembly of 2D materials is the formation of bubbles at atomically thin interfaces. We propose a technique for addressing this issue by removing the bubbles formed at the heterostructure interface in a custom-defined area using the heat generated by a laser equipped with raster scanning capabilities. We demonstrate that the density of bubbles formed at graphene-ReS2 interfaces can be controllably reduced using this method. We discuss an understanding of the flattening mechanism by considering the interplay of interface thermal conductivities and adhesion energies between two atomically thin 2D materials.

Analysis of interfacial nanostructure and interaction mechanisms between cellulose fibres and calcium silicate hydrates using experimental and molecular dynamics simulation data

Understanding the effects of cellulose fibre on the nanostructure of and adhesion energy at the cellulose fibre-calcium silicate hydrate (C-S-H) interface is essential for designing high-performance cement-based composites (CBCs). Therefore, the chemical structure of cellulose fibre surface and microstructure of the fibre-cement matrix interface were investigated using X-ray photoelectron spectroscopy, Fourier transform infrared spectroscopy, X-ray powder diffraction, scanning electron microscopy, and energy-dispersive X-ray spectroscopy. Molecular dynamics (MD) simulations were used to study the adhesion energy and nanostructure at the cellulose fibre-(C-S-H) interface by comparing crystalline Iβ and amorphous celluloses (AC). The results revealed that the adhesion energy at the AC-(C-S-H) interface was approximately 35% greater than that at Iβ-(C-S-H) interface. Given that the AC configuration was disordered and presented greater deformation than Iβ, the AC-(C-S-H) interface was denser than the Iβ-(C-S-H) interface. Electrostatic interactions between OH groups and Ca2+ ions caused the Ca2+ in C-S-H to migrate towards the interface; the Ca2+ ions exhibit a bridging effect at the interface. Additionally, the OH groups in the cellulose fibre and C-S-H could also interact with each other via hydrogen bonding. The electrostatic and hydrogen bonds increased the interfacial adhesion energy, which was beneficial for improving the performance of cellulose fibre-reinforced CBCs.

Surface Energetics Effects on Mechanical Strength of Fibre Reinforced Polymer Matrix

Surface energetics effects on the mechanical strength of fibre reinforced polymer matrix been studied employed the manual scraper mechanism in extracting fibre from plantain pseudo-stem and was treated with nine different treatments. Cylindrical shape mould was prepared for mechanical test samples with continuous and unidirectional aligned fibres. Two probe liquids; water and glycerol were used in contact angle measurement for all the treated and untreated samples. The contact angle data was used for the interfacial energetics computations using Neumann and Fowkes models and the mathematical analysis were carried out using Matlab software tools. van der Waals notion of particle-particle interaction was employed to explain the physiochemical properties such as the surface interfacial energies. The average value for the interfacial free energy of adhesion for fibre-water and fibre-glycerol are -10mJ/m2 and -16MJ/m2 respectively signifying attractive van der Waal forces. The tensile test results unveil that the average value for treated fibres is greater than the average value of 171.29N/mm2 for untreated fibre except for potassium permanganate and phosphoric acid. These results reveal that an increase in tensile strength leads to an increase in the interfacial surface energy of adhesion. The treated fibres show a significant increase in interfacial surface energy and change in free energy of adhesion which suggests a better bonding mechanism of interaction between the fibre and matrix except for phosphoric acid which reveals otherwise, it may be as a result of the chemical chopped off the fibre during the treatment. The average strain rate of about 0.003 per seconds, 0.002 per seconds and 0.005 per seconds were deduced from the treated Mercerization, Acetone and MEKP respectively which reveals the lower strain rate as compared to the untreated fibre of 0.008 per seconds. The negative strain rate for the potassium permanganate and phosphoric acid was found to be -0.002 and -0.001 respectively reveals that the treatments will debond faster than other treated fibres..

Interfacial mechanics and viscoelastic properties of patchy graphene oxide reinforced nanocomposites

Abstract Graphene oxide (GO) is a promising building block for nanocomposites due to its excellent mechanical properties and tunable interfacial interactions with polymers. While experiments have shown that GO sheets consist of graphitic regions clustering into patches and oxidized regions constituting the remaining areas, the role that these heterogeneous patches play on interfacial and mechanical properties of GO reinforced nanocomposites have not yet been investigated. To address this issue at spatiotemporal scales beyond atomistic simulations, we employ recently developed coarse-grained models of GO sheet and polybutadiene to model patchy GO sheets and a representative GO/polybutadiene nanocomposite with GO sheets serving as fillers. We quantify how interfacial adhesion energy and polymer conformations depend on the size of patches and corroborate these findings with the viscoelastic behaviors of the nanocomposite determined via oscillatory shear simulations conducted at multiple temperatures. We find that heterogeneous patchy structures on GO sheets are responsible for variations in interfacial and viscoelastic properties. Specifically, larger patches result in stronger filler-matrix adhesion or enhanced material stiffness with strong or weak oxidized region-polymer interactions, respectively. Our study provides fundamental insights into the interfacial mechanisms of GO-polymer nanocomposites and the influence of heterogeneous functionalized surfaces on the mechanical properties of polymer nanocomposites.

Compatibilization Behavior of Double Spherical TETA-SiO2@PDVB Janus Particles Anchored at the Phase Interface of Acrylic Resin/Epoxy Resin (AR/EP) Polymer Blends.

The inorganic particles used as a compatibilizer play a role in crack termination and heat resistance. However, the poor compatibility of inorganic particles and polymer hinders their application. Herein, the double spherical SiO2@PDVB Janus particles (JPs) were modified with triethylenetetramine (TETA), and the obtained anisotropic TETA–SiO2@PDVB JPs were used as the compatibilizer of acrylic resin/epoxy resin (AR/EP) composites. The modification and the compatibilization of TETA–SiO2@PDVB JPs were studied by scanning electron microscopy, X-ray photoelectron spectroscopy, differential scanning calorimetry, and dynamic mechanical analyzer, impact test, tensile test, and so forth. Results show that amino groups grafted onto the SiO2 lobe can react with epoxy groups of EP, which results in the TETA–SiO2 lobe being embedded in the EP phase and the PDVB lobe being pushed toward the AR phase. The TETA–SiO2@PDVB JPs anchored at the interface of AR and EP increase their interfacial adhesion, decrease the domain phase size and distribution of dispersed AR, and improve the compatibility of AR/EP composites. The compatibilization of nanoparticles (NPs) is realized by the cavitation and blunting of different scaled AR phase domain distributions and that of JPs is realized by the strong interfacial force originated by JPs. Moreover, the desorption energy of TETA–SiO2@PDVB JPs is higher than that of SiO2–TETA; so the glass transition temperature (Tg) of AR/EP/JP composites is higher than that of AR/EP/NP composites. The strong interfacial adhesion and high desorption energy endow TETA–SiO2@PDVB JPs with a toughening effect and enhancing effect. The impact strength and the tensile strength of AR/EP/TETA–SiO2@PDVB composites are 16.03 kJ/m2 and 63.12 MPa, which are 9.91 kJ/m2 and 16.32 MPa higher than those of AR/EP composites, respectively. JPs used in the thermosetting EP is benefit to its toughening study and the new anisotropic Janus compatibilizer.

Comparison of thermal conductance of graphene/SiO2 and graphene/Au interfaces based on Raman optothermal method

Due to the atom-scale thickness and the large surface area to volume ratio, the interfacial thermal conductance between graphene (Gr) and substrates is a critical property for thermal management application of graphene into micro/nano scale electronic devices. It has been widely proved to be dependent on the interfacial phonons transport, material morphology, and interfacial force. The material category of the substrate is related to the interfacial thermal conductance, but, the experimental studies of which are lacking. In this work, the thermal conductance (G) of Gr on SiO2 and Au substrates is measured using Raman optothermal approach combined with finite element simulations. GGr/SiO2 is determined to be ×103 W · m−2 · K−1, while GGr/Au is (1.7 ± 0.2) × 104 W · m−2 · K−1. They are in the same order of magnitude, but GGr/Au is a little larger than twice of GGr/SiO2. Compared with the elastic-phonon-scattering-dominated heat transfer across the Gr/SiO2 interface, the interfacial thermal conductance of Gr/Au is enhanced by the increased probability of multi-phonons inelastic scatterings due to the lower Debye temperature of Au than the ambient temperature and the additional contribution from electron scatterings. Besides, the interfacial adhesion energy of Gr/Au is higher than that of Gr/SiO2 which contributes to GGr/Au larger than GGr/SiO2. The metallic substrate like Au will benefit the heat transfer across graphene interfaces, with respect to the nonmetallic substrate like SiO2. Our results offer new insights into the interfacial heat transfer mechanisms between graphene and nonmetallic (or metallic) substrates. They also provide guidance for tuning the interfacial heat transfer in applications of 2D materials in thermal management of compact devices by switching the material category of substrates.

Molecular Dynamics Simulation on the Influences of Nanostructure Shape, Interfacial Adhesion Energy, and Mold Insert Material on the Demolding Process of Micro-Injection Molding

In micro-injection molding, the interaction between the polymer and the mold insert has an important effect on demolding quality of nanostructure. An all-atom molecular dynamics simulation method was performed to study the effect of nanostructure shape, interfacial adhesion energy, and mold insert material on demolding quality of nanostructures. The deformation behaviors of nanostructures were analyzed by calculating the non-bonded interaction energies, the density distributions, the radii of gyration, the potential energies, and the snapshots of the demolding stage. The nanostructure shape had a direct impact on demolding quality. When the contact areas were the same, the nanostructure shape did not affect the non-bonded interaction energy at PP-Ni interface. During the demolding process, the radii of gyration of molecular chains were greatly increased, and the overall density was decreased significantly. After assuming that the mold insert surface was coated with an anti-stick coating, the surface burrs, the necking, and the stretching of nanostructures were significantly reduced after demolding. The deformation of nanostructures in the Ni and Cu mold inserts were more serious than that of the Al2O3 and Si mold inserts. In general, this study would provide theoretical guidance for the design of nanostructure shape and the selection of mold insert material.

The influence of the resistance layer dimension and interface doping on the electrical properties of aGNR/NiO/aGNR-structured resistive random access memory

A first-principles method based on density functional theory is used to study the effects of the resistance layer dimension and interface doping on the electrical properties of aGNR/NiO/aGNR-structured resistive random access memory. First, calculations of the interface adhesion energy and Mulliken mean populations show that the aGNR/unilaminar NiO interface has good interface stability. Second, the current–voltage characteristics and the micro formation process of conducting filaments of graphene/NiO/graphene resistive random access memory with resistance layers of different widths are studied. The comprehensive performance of the device is fully exploited, and its storage window can satisfy the requirement of data storage when the width of the resistance layer is 17.6 Å. Finally, an increase in the concentration of excess oxygen causes an increase in power consumption and a decline in the current drive capacity, while the stability of the device is improved; moreover, the size of the storage window decreases but still meets the requirement of data storage. In summary, the storage performance is effectively improved by excess oxygen concentration of 3.82%. These results may provide a theoretical basis for rational design and device optimization regarding the resistance layer dimension and excess oxygen.

Hydrogel/Elastomer Laminates Bonded via Fabric Interphases for Stimuli-Responsive Actuators

Summary The human body is composed of composite structures made of water-rich hydrophilic domains and hydrophobic barriers. Combining hydrogels with elastomers results in similar synthetic biomaterials applicable to fields ranging from stretchable electronics to actuators. Here, we report a method to combine hydrogels with elastomers via a glass fiber fabric interphase. The interphase plays two roles: it enables chemically different materials to be robustly bound without chemical treatment while also dramatically improving the mechanical properties of the composite. Maximum interfacial adhesion energies of ∼1,000 N m−1 between the hydrogel and fabric and ∼360 N m−1 between the elastomer and fabric approach adhesion values of chemically bound soft materials. The composite tearing toughness (143 kJ m−2) vastly exceeds that of all neat components. In these materials, Young's modulus is high (∼1.2 GPa), while bending modulus is low (∼7 MPa), resulting in structures that can serve as actuators through controlled solvent exposure.

Shear properties of the liquid bridge between two graphene films using a refined molecular kinetics theory and molecular dynamics simulations

At the micro/nano-scale, the friction arising from capillary-condensed liquid bridges has a large effect on the friction performance between two sliding surfaces, where the shear field in the vicinity of the moving contact line (MCL) is sufficiently intense. In this study, we develop a refined molecular-kinetic theory (MKT) of dynamic wetting by considering the effect of both the liquid-solid and liquid-solid-vapour interfaces on the shear stress. The capillary shearing process of liquid bridges between two graphene films is studied using large-scale molecular dynamics (MD) simulations. Our MD results show that the shear stress at the liquid-solid-vapour interface is of the same order of magnitude as that at the liquid-solid interface. The stronger depth of the Lennard-Jones (LJ) potential between the liquid and solid molecules results in smaller static/dynamic contact angles and larger friction coefficients and interfacial adhesion energies. The total shear stress of three-dimensional (3D) liquid bridges increases as the velocity of the graphene film increases within a certain range. The sizes of liquid bridges strongly affect the shear stress of the liquid bridges, but hardly affect the static/dynamic contact angles. The present refined MKT has higher accuracy than the other available theoretical models as the velocity of graphene films increases, in comparison with that of the MD simulations. Our results will be of great help for understanding the dynamic wetting at the molecular level and the friction in micro/nano-fluidics and micro/nano-electromechanical systems (M/NEMS).

Numerical and Experimental Investigation of Ice Adhesion Using the Blister Test

<div class="section abstract"><div class="htmlview paragraph">Structures in cold weather environments are susceptible to atmospheric ice formation. A fracture mechanics based approach is proposed for in situ characterization of the interfacial fracture energy of ice on different substrates. This paper summarizes the development of the experimental and analytical framework to measure the ice adhesion energy, calibrated on static ice. The testing configuration utilizes a shaft-loaded blister test to produce stable crack propagation, from a well-defined pre-crack at the interface of the ice layer and the substrate. Measurements of the fracture energy are taken over a range of ice thicknesses and surface roughnesses. The developed analytical framework to estimate adhesion energy are verified and calibrated via finite element numerical simulation of the proposed geometric configuration and employing cohesive surfaces along the interface to simulate the crack nucleation and propagation process. Several different phenomena were observed include the transition from adhesive to cohesive fracture. The measured interfacial adhesion energy was almost independent of the surface roughness in the range of examined roughness. The measured interfacial R-curve showed a steady state plateau for range of interfacial crack propagation. The proposed experimental framework enables precise measurement of the interfacial fracture toughness over a range of surface finishes and ice layer thickness.</div></div>

All-Dry Transfer of Graphene Film by van der Waals Interactions.

We report a method that uses van der Waals interactions to transfer continuous, high-quality graphene films from Ge(110) to a different substrate held by hexagonal boron nitride carriers in a clean, dry environment. The transferred films are uniform and continuous with low defect density and few charge puddles. The transfer is effective because of the weak interfacial adhesion energy between graphene and Ge. Based on the minimum strain energy required for the isolation of film, the upper limit of the interfacial adhesion energy is estimated to be 23 meV per carbon atom, which makes graphene/Ge(110) the first as-grown graphene film that has a substrate adhesion energy lower than that of typical van der Waals interactions between layered materials. Our results suggest that graphene on Ge can serve as an ideal material platform to be integrated with other material systems by a clean assembly process.

Application of peroxymonosulfate-based advanced oxidation process as a novel pretreatment for nanofiltration: Comparison with conventional coagulation

As a practical advanced oxidation process with high-efficiency, ferrous-activated peroxymonosulfate (PMS) technology has been extensively investigated and employed for the degradation of organic substances in water treatment process. However, to our best of knowledge, few studies in applying ferrous-activated PMS as the pretreatment for nanofiltration process have been conducted and the mechanisms of membrane fouling alleviation due to ferrous-activated PMS was still unclear. Consequently, ferrous-activated PMS approach was innovatively adopted as pretreatment for nanofiltration in present study, compared with the conventional pretreatment process (coagulation). The results indicated that both strategies could significantly mitigate organic fouling at membrane surface, but the gypsum scaling was enhanced when Fe(II)/PMS was adopted prior to nanofiltration process at the dose of 80/80 μM, because of the assistance of ferric ions and sulfate anions. ATR-FTIR spectra indicated that the greater alleviation of flux decline caused by Fe(II)/PMS oxidation was attributed to the less accumulation of organic substances on membrane surface, relative to the conventional Fe(III) coagulation. Furthermore, Xtended Derjaguin-Landau-Verwey-Overbeek (XDLVO) theory was utilized to explain the greater interfacial free energy of adhesion (equal to decreased repulsion or increased attraction) between foulants and nanofiltration membranes in ferrous-activated PMS strategies joined nanofiltration process. Interestingly, Fe(II)/PMS oxidation could efficiently improve the quality of effluent in nanofiltration process, and three-dimension excitation emission matrix fluorescence spectroscopy (3D-EEM) spectra demonstrated that Fe(II)/PMS conferred higher removals of organic substances. The removal efficiency of Bisphenol A in Fe(II)/PMS assisted nanofiltration process varied from 53% to 78%, while only 5–12% Bisphenol A was removed in Fe(III) coagulation joined system. Besides, the potential mechanisms of flux decline caused by individual and combined organic substances were also investigated. Therefore, the findings in present study would contribute to the deep understanding of membrane fouling mechanism and promote the practical application of nanofiltration technologies.

Strong Wet Adhesion of Tough Transparent Nanocomposite Hydrogels for Fast Tunable Focus Lenses.

Tough hydrogel adhesives that can bond strongly to wet surfaces have shown great potential in various applications. However, it still remains a challenge to develop the adhered hydrogels integrated with strong wet adhesion, high transparency, exceptional mechanical properties, and fast self-recovery. Herein, tough nanocomposite hydrogels demonstrating high tensile strength, high transparency, and fast self-recovery are reported. The strong wet adhesion between two tough hydrogel films can be realized by introducing chemical bridging across the hydrogel-hydrogel interface, while the interfacial adhesion energy and shearing adhesion strength are up to 2216 J m-2 and 385 N m-1, respectively. The strong adhesion and superior toughness of our hydrogels enable their reassembly capability to produce stretchable sealed balloons that can endure high air pressure without leakage. Most interestingly, the combination of excellent sealability and high transparency also allows our hydrogel balloons to turn into hydraulically driven fast tunable focus convex lenses, which is first reported here for hydrogel lenses. The hydrogel adhesives may open up the door to develop soft sealed containers and intelligent optical devices.

Metal-support interaction controlled migration and coalescence of supported particles

The particle migration and coalescence (PMC) kinetics of a supported metal are the main deactivation mechanisms restricting the successful industrialization of nanoparticles, but the theoretical insights regarding these kinetics are lacking. One key issue is the lack of a physical model to predict the effects of metal-support interaction (MSI) on PMC kinetics. In this paper, we report a theoretical study of PMC kinetics and their dependence on MSI. A new particle diffusion model is proposed based on the surface premelting hypothesis that considers the contact angle of a hemispherical particle on the support. Enhanced MSI suppresses PMC by increasing the radius of curvature and the interfacial adhesion energy, even though the accompanying reduction in the geometry factor partially promotes PMC kinetics. The increased surface energy increases the chemical potential of the atoms in the particle, which is conducive to PMC; an increased surface energy also results in enhanced MSI, which suppresses PMC. The competition between these two contradictory effects leads to a critical contact angle where the surface energy has no influence on the diffusion and resulting PMC kinetics. The proposed diffusion theory mode lincluding the effects of the support and the corresponding kinetic simulations, shed light onto the support-dependence of PMC kinetics and provide a foundation for further optimization and design of supported particles with better stability.

Strain-Tunable Visible-Light-Responsive Photocatalytic Properties of Two-Dimensional CdS/g-C₃N₄: A Hybrid Density Functional Study.

By means of a hybrid density functional, we comprehensively investigate the energetic, electronic, optical properties, and band edge alignments of two-dimensional (2D) CdS/g-CN heterostructures by considering the effect of biaxial strain and pH value, so as to improve the photocatalytic activity. The results reveal that a CdS monolayer weakly contacts with g-CN, forming a type II van der Waals (vdW) heterostructure. The narrow bandgap makes CdS/g-CN suitable for absorbing visible light and the induced built-in electric field between the interface promotes the effective separation of photogenerated carriers. Through applying the biaxial strain, the interface adhesion energy, bandgap, and band edge positions, in contrast with water, redox levels of CdS/g-CN can be obviously adjusted. Especially, the pH of electrolyte also significantly influences the photocatalytic performance of CdS/g-CN. When pH is smaller than 6.5, the band edge alignments of CdS/g-CN are thermodynamically beneficial for oxygen and hydrogen generation. Our findings offer a theoretical basis to develop g-CN-based water-splitting photocatalysts.

Evaluation of failure properties of a DLC/steel system using combined nanoindentation and finite element approach

In the current work, the failure properties of a DLC/steel system are quantitatively characterized by nanoindentation using a conical indenter. The DLC coating with thickness of ~1.7 μm is obtained by physical vapor deposition on a 20CrMnMo gear steel substrate. During the nanoindentation, it is noticed that the circumferential cracking and delamination occur in the coating and interface, respectively. In terms of the energy release theory, the coating fracture toughness and interfacial bonding energy are calculated from the steps in the loading curves. The results show that the interfacial adhesion energy and the fracture toughness are individually <137.113–548.454 J/m2 and ~1.579 MPa·m1/2 for the DLC coating on steel substrate, which accords well with the published data. Furthermore, based on the mechanical properties and cohesive energies of materials obtained above, finite element simulations under the ideal situation (defect-free and residual stress-free) including cohesive zone model are carried out to acquire coating fracture and interfacial bonding strengths as well as evolutions of failures in the coating-substrate system. The present model may find useful application not only for DLC but also for other coatings.

Mechanics of buckled serpentine structures formed via mechanics-guided, deterministic three-dimensional assembly

Many forms of stretchable electronic systems incorporate planar, filamentary serpentine structures to realize high levels of stretchability in ways that allow the use of high performance of inorganic functional materials. Recent advances in mechanics-guided, deterministic three-dimensional (3D) assembly provide routes to transform these traditional, two-dimensional (2D) serpentine layouts into 3D architectures, with significantly improved mechanics and potential for applications in energy harvesters, pressure sensors, soft robotics, biomedical devices and other classes of technologies. One challenge is that, by comparison to other geometries, the relatively low bending stiffnesses of the serpentine structures create difficulties in overcoming the interfacial adhesion energy to allow delamination from the underlying elastomeric substrate, as an essential aspect of the assembly process. An additional complication is that many of the functional materials widely used in stretchable electronics have a low strain threshold for failure such that damage can occur during buckling-induced assembly. Therefore, a clear understanding of the mechanics of buckled serpentine structures is essential to their design, fabrication and application. Through theoretical modeling and finite element analysis, we present models for the phase diagram of buckled states and the maximum strain in the globally-buckled serpentine structures. The analysis yield formulae in concise and explicit forms, clearly showing the effect of geometry/material parameters and the prestrain. The results can be used in designing buckled serpentine structures to ensure their compatibility with the mechanics-guided, deterministic 3D assembly and facilitate their applications in stretchable electronics.