Slanted Functional Gradient Micropillars for Optimal Bioinspired Dry
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1 Supporting Information for Slanted Functional Gradient Micropillars for Optimal Bioinspired Dry Adhesion Zhengzhi Wang * Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei , China zhengzhi.wang@whu.edu.cn Figure S1. Morphology characterizations of v-fgps with a high AR of ~ 12. SEM image from (a) top view and (b) side view, and (c) transmission optical micrograph of the FGPs showing the gradient material distribution. The FGPs kept well-aligned structures with only slightly bent tips. Scale bar: 10 µm in a) and 5 µm in b) and c). 1
2 Figure S2. Transmission electron microscope (TEM) images of different positions along individual SP and FGP (AR 8), showing a uniform nanoparticle distribution of the former and a smoothly-gradient distribution from the tip to the base of the latter. Insets showing high-resolution TEM images of the PUA-based nanocomposite and the core-shell structure of single Fe 3 O 2 nanoparticle. 2
3 Figure S3. Isotropic adhesion of the vertical micropillars measured by non-conformal sliding tests. (a) Illustration of the loading process and pillars deformation for v-cps, v-sps and v-fgps when sliding in two opposite directions. (b) Shear and normal forces during shear displacements after a preload of 4 mn. The maximum shear forces are extracted and compared with those of slanted pillars as shown in Figure 3c. 3
4 Figure S4. Pull-off forces measured in the load-drag-pull tests for the various micropillar samples (after dragging along either the gripping or the releasing direction) in comparison with the unpatterned PUA film. Dashed line is provided for visual assistance of the comparison, where the differences of the pull-off force between samples become much less significant compared to those of the shear force shown in Figure 3c in the article. 4
5 Figure S5. Demonstration of the micropillars bending controlled by external magnetic field. (a) Schematic diagram of the experimental setup showing the configuration of magnetic field (H) with respect to the vertical pillars made of homogeneous PUA/Fe 3 O 2 nanocomposite (i.e. v-sps). SEM image of the pillars upon applying magnetic field with intensity of around (b) 100 mt, (c) 400 mt and (d) 800 mt. The images were captured by applying the magnetic field in situ using a permanent NdFeB magnet inside the sample chamber of SEM. The magnetic field intensity was adjusted by controlling the magnet-sample space as detailed in our previous study. S1 The pillars bending deformation increases with the increase of magnetic field intensity. Scale bars: 10 µm. 5
6 Text S1. Magnetically-actuated functional gradient nanocomposites As detailed in our previous study, S1 we realized precise controls over the spatial distribution of magnetic-responsive nano-reinforcements pre-dispersed in a monomeric fluid (the uncured PUA in this study) by applying a magnetic field gradient using a disk-shaped permanent magnet. The magnetophoresis-induced drift-diffusion led to migration of the reinforcements towards desired direction until a steady-state concentration gradient was formed. Upon curing the redistributed mixture system, functional gradient nanocomposites with tunable mechanical properties were obtained. To facilitate the magnetophoresis process, the superparamagnetic Fe 3 O 4 nanoparticles were coated with silica shells to improve the dispersibility and the core-shell Fe 3 O 2 particles were silanized to build strong covalent bonds with the matrix upon curing. S2 For the PUA matrix adopted in this study (viscosity of ~ 0.16 Pa.s), the prepared core-shell reinforcements could be well dispersed at a maximum volume fraction of ~ 30 vol.% without precluding the photo-curability of the resins. During the magnetophoresis process, additional mechanical stimuli (vibration) was applied to the monomer/filler mixture to enhance the mobility and promote the steric occupations of the nanoparticles. S3 Using the effective dipole moment method, S4 we previously calculated the one-dimensional (1D) magnetic field and force (F m ) as a function of the particle-magnet distance and showed that the driving force for the particle migration could be precisely controlled by simply adjusting the specimen-magnet distance within a certain range. S1 By assuming the nanoparticle migration in viscous media as 6
7 a drift-diffusion transport process, S5 we also derived a theoretical model to predict the relationship between the evolving particle concentration (c (z, t)) and the applied magnetic field: S1 (, ) c z t t (, ) ( ) (, ) = µ µ 2 kbt c z t Fm d0 c z t (S1) where µ = 1 / (6 πη R p ) is the mobility of a particle with radius of R p in a fluid of viscosity η, k B is the Boltzmann s constant, T is the absolute temperature, F ( ) m d 0 is the magnetic force at a specimen-magnet distance of d 0, z is the distance from the magnet within the specimen domain and t is the time. Equation (S1) can be solved using the finite volume method (FVM) as detailed elsewhere S5 to obtain the position- and time-dependent concentration c (z, t), considering a zero-flux boundary condition. According to our previous study, S1 such a simplified theory could well predict the final concentration gradient of the nanoparticles if the applied magnetic field intensity was not too high (lower than ~ 300 mt). Validated by the experiments, the theory also predicted that a near-optimized intensity of ~ 150 mt and a ~ 20 min processing duration could generate a smoothly-gradient distribution of the nanoparticles (transitioning from pure resin to highly-filled composite) within a distance of tens of microns in the resin matrix. We therefore continued adopting these experimental parameters in the present study. Text S2. Critical aspect ratio of micropillars Based on a balance between stored elastic energy and surface energy, Glassmaker 7
8 et al. S6 derived a theoretical model to predict the maximum height (h max ) of fibrillar structures that can maintain lateral stability (i.e. not subjected to lateral collapse). For round cross-section pillars, the model gives: h max 4 1 / / 4 π Er 12 Er ( d / 2) (1 ) = γ ν γ (S2) where E, r, γ, ν, and d are respectively the elastic modulus, radius, surface energy, Poisson s ratio, and center-to-center distance of the pillars. Considering the experimental parameters of our PUA micropillars (i.e. CPs), E = 20 MPa, r = 1.25 µm, γ = 40 mj/m 2, ν = 0.48, and d = 6 µm, Equation (S2) gives h max = 24.5 µm. That is to say, the maximum AR of the micropillars that pure PUA can achieve is ~ 24.5/2.5 = 9.8, which is slightly higher than the experimentally observed AR of 8 for the CPs but lower than the AR of 12 that the FGPs achieved. Therefore, the gradient design in material well circumvents the theoretical limit of the maximum AR for simultaneously structurally-stable and mechanically-flexible fibrillar structures. Text S3. Effective elastic modulus of functional gradient pillars array By treating the micropillars as cantilever beams and using Euler-Bernoulli beam theory, S7 we previously derived the deflection (δ) of a FGP subjected to a concentrated force (F) loaded perpendicular to the pillar at the free end: S1 FE1 F 2 FE1 (1+ ln( E2)) FE1E 2 ln( E2) δ ( x) = ( E 3 2 sx)ln( E2 sx) x + x (S3) 2 3 Is 2Is Is Is where the simplest linear transition of the elastic modulus from pillar tip to base (close to the case in our experiments) was assumed and s= ( E2 E1 ) / L is the slope 8
9 of the transition with E 1 and E 2 being respectively the elastic modulus of the tip and base end of the FGP and L the length of the pillar. In Equation (S3), I = π r 4 / 4 is the moment of inertia of the pillar and x is the distance from the fixed end of the pillar. For x = L (i.e. at the free end), Equation (S3) becomes: (S4) 2 2 E1 ln( E1 ) + E1E 2 ln( E2) E1L(1+ ln( E2)) L δ = + F C F 3 2 = Is Is 2Is where C is a material- and geometry-dependent coefficient, representing the effective compliance of the FGP. For calculation of the effective elastic modulus (E eff ) of slanted FGPs array, we consider a single FGP subjected to a normal compressive force F and a tangential friction force T due to shear sliding (T = µ F for sliding with the pillar, T = µ F for sliding against the pillar and T = 0 for no sliding, where µ is the frictional coefficient), S8 shown schematically in Figure S5. The normal component of the tip deflection (i.e. pillar deformation in the normal direction) can be calculated as: 2 ( cos γ sinγ cosγ) = C F + T (S5) Figure S5. Schematic diagram of a FGP subjected to a normal compressive force F and a tangential friction force T for derivation of the effective elastic modulus of FGPs array. 9
10 According to Hooke s law, the stress applied to the FGPs array can be calculated as: σ = ε (S6) E eff where ε is the resulting strain in the normal direction and can be approximated as ( L γ) ε = / sin. Substituting Equation (S5) and considering σ = FD for an array with pillar density D, one can obtain: E eff = C DLsin( γ ) γ µ γ 2 cos ( )[1± tan( )] (S7) For the micropillars in our study, adapting relevant parameters (E 1 = 20 MPa, E 2 = 110 MPa, r = 1.25 µm, D mm -2, γ = 70, L = 20 µm, and µ = 0.25) into Equation (S7) yield the different effective elastic modulus as listed in Table 1. Supplementary References (S1) Wang, Z.; Shi, X.; Huang, H.; Yao, C.; Xie, W.; Huang, C.; Gu, P.; Ma, X.; Zhang, Z.; Chen L.Q. Magnetically Actuated Functional Gradient Nanocomposites for Strong and Ultra-Durable Biomimetic Interfaces/Surfaces. Mater. Horiz. 2017, 4, (S2) Rho, W.-Y.; Kim, H. M.; Kyeong, S.; Kang, Y. L.; Kim, D. H.; Kang, H.; Jeong, C.; Kim, D. E.; Lee, Y. S.; Jun, B. H. Facile Synthesis of Monodispersed Silica-Coated Magnetic Nanoparticles. J. Ind. Eng. Chem. 2014, 20, (S3) Libanori, R.; Erb R. M.; Studart, A. R. Mechanics of Platelet-Reinforced Composites Assembled Using Mechanical and Magnetic Stimuli. ACS Appl. Mater. Inter. 2013, 5, (S4) Furlani, E. P.; Ng, K. C. Analytical Model of Magnetic Nanoparticle Transport and Capture in the Mictovasculature. Phys. Rev. E 2006, 73, (S5) Furlani, E. P.; Ng, K. C. Nanoscale Magnetic Biotransport with Application to Magnetofection. Phys. Rev. E 2008, 77, (S6) Glassmaker, N. J.; Jagota, A.; Hui, C.-Y.; Kim, J. Design of Biomimetic 10
11 Fibrillary Interfaces: 1. Making Contact. J. R. Soc. Interface 2004, 1, (S7) Timoshenko, S. P.; Goodier, J. N. Theory of Elasticity. 3rd ed. New York: McGraw-Hill Book Company.; 1970, pp (S8) Autumn, K.; Majidi, C.; Groff, R. E.; Dittmore, A.; Fearing R. Effective Elastic Modulus of Isolated Gecko Setal Arrays. J. Exp. Biol. 2006, 209,
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