Self-folding thermo-magnetically responsive soft- microgrippers
Supporting Information
Self-folding thermo-magnetically responsive softmicrogrippers Joyce C. Breger,†, ¥ ChangKyu Yoon,‡ Rui Xiao,§ Hye Rin Kwag,† Martha O. Wang,# John P. Fisher,# Thao D. Nguyen,‡,§ and David H. Gracias*,†,‡ †
Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore MD, 21218, USA ‡ Department of Materials Science and Engineering, The Johns Hopkins University, Baltimore MD, 21218, USA § Department of Mechanical Engineering, The Johns Hopkins University, Baltimore MD, 21218, USA # Fischell Department of Bioengineering, University of Maryland, College Park, College Park MD, 20742, USA
Photolithographic process flow of PPF/pNIPAM-AAc microgrippers Metallic alignment markers composed of 50/100 nm thermally evaporated Cr/Cu and a transparent, water soluble sacrificial layer of PVA were first added to a silicon (Si) substrate. By evaporating the alignment markers onto the Si wafer before patterning PPF or pNIPAM-AAc, excellent alignment of the two transparent layers could be obtained. A PPF/DEF solution was spin coated on top of the wafer (Figure 2A), placed under a photomask and exposed to UV light to initiate crosslinking of the exposed areas of PPF (Figure 2B). A prepolymer solution of pNIPAM-AAc was spread by hand over top of the PPF layer (Figure 2C). A second dark field mask that is the outline of the structure was used (Figure 2D) with UV light crosslinking the exposed pNIPAM-AAc areas. The unreacted DEF/PPF and pNIPAM-AAc components were washed away with EtOH, MeOH, and DI H2O, leaving behind the grippers on the wafer (Figure 2E). The grippers were released from the substrate by soaking the wafer in DI H2O for at least 30 mins to dissolve the PVA sacrificial layer (Figure 2F). Optimization of PPF segment spacing and thickness PPF is traditionally used in relatively large quantities for filling bone defects. To determine the optimal thickness and spacing that could be achieved by photopatterning thin films of PPF, we varied the spin coat speed, UV intensity (Supplemental Figure 1A), and the spacing between PPF patterns (Supplemental Figure 1B). At a 3000 rpm spin speed, we observed no measurable difference in PPF thickness as a function of UV exposure. Therefore, an exposure of 650 mJ/cm2 was chosen for microgripper patterning. We photopatterned squares of various lateral dimensions (1000 to 100 µm in length) and spacing (780 to 10 µm apart) to optimize the lateral resolution. Based on these results, we fabricated grippers with PPF segments that were 225 µm apart and 10 μm thick (Supplemental Figure 1C). The tip-to-tip diameter of a polymeric gripper on a Si S1
wafer was 4.5 mm and up to 70 polymeric grippers could be patterned on a single 3 inch diameter Si wafer. Photopatterning of grippers on wafers illustrates how large quantities of grippers could be mass produced with excellent alignment between the two layers.
Supplemental Figure 1. Optimization of the photopatterning of the microgrippers. (A) Films of different PPF thickness ranging from 10 to 100 µm were created by controlling the spin coat speed and the UV exposure intensity. Each point in the plot represents the average of four measurements along with the standard deviation. (B) Optical images showing the resolution of photopatterning. The smallest squares that could be reproducibly patterned were 100 x 100 μm squares (the smallest size on the dark field mask) spaced approximately 130 μm apart. (C) Optical images of developed PPF/pNIPAM-AAc microgrippers on the substrate prior to release from the wafer. The image highlights the parallel and mass-producible features of the microgripper photopatterning process.
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Finite Element Analysis of Gripper Folding The deformation gradient, defined as F = ∂(X)/∂X, describes the mapping of material lines from the reference dry and stress free configuration to the swollen and stressed configuration. We assume that the deformation gradient can be decomposed into a mechanical part Fe and a swelling part Fs as: F = (φ)−1/3 Fe = (φ0)−1/3 f
(1)
where φ and φ0 are the polymer volume fraction defined from the dry and initially swollen-stress free state respectively, and f is the deformation gradient mapping between the initially swollen and existing configuration. The polymer volume fraction is represented as φ = 1/(1 + vc) where v is the volume per solute molecule and c is the number of solute molecules per volume. We first define the left and right Cauchy-Green tensor as b = FFT and C = FTF and the first invariant as I1 = trace(b) = trace(C). We also define Θ = det [F] and Θe = det [Fe] as the total volume change ratio and the component caused by the elastic deformation. The corresponding deformation tensors relative to the initially swollen intermediate configuration are defined as b* = ffT and Θ* = det [f]. The free energy of the system is assumed to be a combination of the mixing and the entropic change of stretching polymer chains by swelling and mechanical deformation as: mixing () mechanical(F, e ) (2) The Flory-Huggins model1 is adopted to represent the free energy change from the mixing of polymers and solvents:
mixing ()
RT ((1 ) ln(1 ) (1 )) v
(3)
where R is gas constant and χ is Flory-Huggins interaction parameter. We assumed a Gaussian distribution for the polymer chains and a volumetric quasi-incompressible model for mechanical deformation. Thus, the free energy change associated with the stretching polymer chains2 is:
G mecahnical h I1 3 2 ln h e2 2 ln e 1 2 4
(4)
where Gh is shear modulus and h is bulk modulus. We assumed that the bulk modulus is 1000 times that of the shear modulus to achieve the volumetric incompressible of mechanical deformation. The Cauchy-Green stress is calculated as σ= (1/Θ) F (∂Ψ/∂C) FT and the chemical potential is obtained as µ =∂Ψ/∂c.3 Substituting equations (2)-(4) into the previous two equations yields:
Gh κ b I h e2 1 I 2
(5)
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RT ln 1 2
κ h ν 2 e 1 2
(6)
Applying the decomposition in equation 1 of F into f and φ0 as the stress response can be expressed as,
2 3 b * I κ h 2 1 I 0 0 2 * 0 e *
Gh
(7)
To model thermo-responsive effect, we assumed the following temperature-dependent function for the Flory-Huggins interaction parameter χ,4
1 L H 1 H L tanh T Ttran 2 2 ΔT
(8)
where χL and χH is the Flory-Huggins interaction parameters at low temperature and high temperature, Ttran is the transition temperature and ΔT is the width of the transition region. We adopted a generalized Neo-Hookean model for PPF. The Cauchy stress is represented as a combination of the deviatoric part and volumetric part,
Gp 1 κp 2 1I b I 1 b 3 2
(9)
̅ is the deviatoric part of left Cauchy-Green tensor, defined as –𝒃 ̅ = Θ-2/3𝒃, and I1(–𝒃 ̅) is where 𝒃 ̅ trace of 𝒃. The material parameters for the two materials listed in Table 1 are obtained from the swelling test and mechanical test described in the experimental section and the detailed information about the procedures can be found.5 Supplemental Table 1. Parameters of the constitutive model for pNIPAM-AAc and PPF Parameters Values
Gh
χL
χH
Ttran
ΔT
162 KPa
0.556
0.710
36 oC
4 oC
(pNIPAM-AAc)
Gp
(PPF)
16 MPa
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The constitutive model was implemented in an open-source finite element code TAHOE (Sandia National Laboratories). Supplemental Figure 2 shows the finite element model of gripper specimen. The mesh was discretized by trilinear hexahedral elements. The displacement boundary condition were set as follows, ux (x = 0, y, z) = 0, uy (x = 0, y = 0, z) = 0,
(10)
uz (x = 0, y = 0, z = 0) = 0.
Supplemental Figure 2. Finite element model of gripper specimen The simulation starts from the intermediate swollen, stress free state at temperature T = 35 oC. The equilibrium polymer fraction φ0 is obtained by solving equations (5) and (6) with condition σ = 0 and µ = 0. During every time step, the temperature is changed and the deformation gradient f and polymer concentration φ are updated to satisfy the force balance and chemical potential equilibrium.
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Supplemental Movie 1. Polymeric grippers opening and closing in response to increasing temperature (8X speed). Supplemental Movie 2. Simulation results of polymeric gripper deswelling. The snap shots are in Figure 3B. Supplemental Movie 3. Simulation results of polymeric gripper swelling. The snap shots are in Figure 3B.
Supplemental Movie 4. Fe2O3 doped polymeric grippers opening in unison in response to increasing temperature (8X speed). Supplemental Movie 5. Magnetic gripper opening in warm water and moving in response to an external magnet (8X speed). The snap shots are in Figure 5A. Supplemental Movie 6. Polymeric gripper opening and closing around a L929 clump of cells stained with Calcein AM (8X speed). The snap shots are in Figure 5B.
References (1) (2) (3) (4)
(5)
Flory, P. J.; Rehner, J. Statistical Mechanics of CrossLinked Polymer Networks II. Swelling. The J.Chem.Phys. 1943, 11, 521-526. Flory, P. J. Principles of Polymer Chemistry. Cornell University Press. 1953. Hong, W.; Zhao, X.; Zhou, J.; Suo, Z. A Theory of Coupled Diffusion and Large Deformation in Polymeric Gels. J. Mech. Phys. Solids 2008, 56, 1779-1793. Chester, S. A.; Anand, L. A Thermo-Mechanically Coupled Theory for Fluid Permeation in Elastomeric Materials: Application to Thermally Responsive Gels. J. Mech. Phys. Solids 2011, 59, 1978-2006. Jamal, M.; Kadam, S. S.; Xiao, R.; Jivan, F.; Onn, T.-M.; Fernandes, R.; Nguyen, T. D.; Gracias, D. H. Bio-Origami Hydrogel Scaffolds Composed of Photocrosslinked PEG Bilayers. Adv. Healthcare Mater. 2013, 2, 1142-1150.
S6
Self-folding thermo-magnetically responsive softmicrogrippers Joyce C. Breger,†, ¥ ChangKyu Yoon,‡ Rui Xiao,§ Hye Rin Kwag,† Martha O. Wang,# John P. Fisher,# Thao D. Nguyen,‡,§ and David H. Gracias*,†,‡ †
Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore MD, 21218, USA ‡ Department of Materials Science and Engineering, The Johns Hopkins University, Baltimore MD, 21218, USA § Department of Mechanical Engineering, The Johns Hopkins University, Baltimore MD, 21218, USA # Fischell Department of Bioengineering, University of Maryland, College Park, College Park MD, 20742, USA
Photolithographic process flow of PPF/pNIPAM-AAc microgrippers Metallic alignment markers composed of 50/100 nm thermally evaporated Cr/Cu and a transparent, water soluble sacrificial layer of PVA were first added to a silicon (Si) substrate. By evaporating the alignment markers onto the Si wafer before patterning PPF or pNIPAM-AAc, excellent alignment of the two transparent layers could be obtained. A PPF/DEF solution was spin coated on top of the wafer (Figure 2A), placed under a photomask and exposed to UV light to initiate crosslinking of the exposed areas of PPF (Figure 2B). A prepolymer solution of pNIPAM-AAc was spread by hand over top of the PPF layer (Figure 2C). A second dark field mask that is the outline of the structure was used (Figure 2D) with UV light crosslinking the exposed pNIPAM-AAc areas. The unreacted DEF/PPF and pNIPAM-AAc components were washed away with EtOH, MeOH, and DI H2O, leaving behind the grippers on the wafer (Figure 2E). The grippers were released from the substrate by soaking the wafer in DI H2O for at least 30 mins to dissolve the PVA sacrificial layer (Figure 2F). Optimization of PPF segment spacing and thickness PPF is traditionally used in relatively large quantities for filling bone defects. To determine the optimal thickness and spacing that could be achieved by photopatterning thin films of PPF, we varied the spin coat speed, UV intensity (Supplemental Figure 1A), and the spacing between PPF patterns (Supplemental Figure 1B). At a 3000 rpm spin speed, we observed no measurable difference in PPF thickness as a function of UV exposure. Therefore, an exposure of 650 mJ/cm2 was chosen for microgripper patterning. We photopatterned squares of various lateral dimensions (1000 to 100 µm in length) and spacing (780 to 10 µm apart) to optimize the lateral resolution. Based on these results, we fabricated grippers with PPF segments that were 225 µm apart and 10 μm thick (Supplemental Figure 1C). The tip-to-tip diameter of a polymeric gripper on a Si S1
wafer was 4.5 mm and up to 70 polymeric grippers could be patterned on a single 3 inch diameter Si wafer. Photopatterning of grippers on wafers illustrates how large quantities of grippers could be mass produced with excellent alignment between the two layers.
Supplemental Figure 1. Optimization of the photopatterning of the microgrippers. (A) Films of different PPF thickness ranging from 10 to 100 µm were created by controlling the spin coat speed and the UV exposure intensity. Each point in the plot represents the average of four measurements along with the standard deviation. (B) Optical images showing the resolution of photopatterning. The smallest squares that could be reproducibly patterned were 100 x 100 μm squares (the smallest size on the dark field mask) spaced approximately 130 μm apart. (C) Optical images of developed PPF/pNIPAM-AAc microgrippers on the substrate prior to release from the wafer. The image highlights the parallel and mass-producible features of the microgripper photopatterning process.
S2
Finite Element Analysis of Gripper Folding The deformation gradient, defined as F = ∂(X)/∂X, describes the mapping of material lines from the reference dry and stress free configuration to the swollen and stressed configuration. We assume that the deformation gradient can be decomposed into a mechanical part Fe and a swelling part Fs as: F = (φ)−1/3 Fe = (φ0)−1/3 f
(1)
where φ and φ0 are the polymer volume fraction defined from the dry and initially swollen-stress free state respectively, and f is the deformation gradient mapping between the initially swollen and existing configuration. The polymer volume fraction is represented as φ = 1/(1 + vc) where v is the volume per solute molecule and c is the number of solute molecules per volume. We first define the left and right Cauchy-Green tensor as b = FFT and C = FTF and the first invariant as I1 = trace(b) = trace(C). We also define Θ = det [F] and Θe = det [Fe] as the total volume change ratio and the component caused by the elastic deformation. The corresponding deformation tensors relative to the initially swollen intermediate configuration are defined as b* = ffT and Θ* = det [f]. The free energy of the system is assumed to be a combination of the mixing and the entropic change of stretching polymer chains by swelling and mechanical deformation as: mixing () mechanical(F, e ) (2) The Flory-Huggins model1 is adopted to represent the free energy change from the mixing of polymers and solvents:
mixing ()
RT ((1 ) ln(1 ) (1 )) v
(3)
where R is gas constant and χ is Flory-Huggins interaction parameter. We assumed a Gaussian distribution for the polymer chains and a volumetric quasi-incompressible model for mechanical deformation. Thus, the free energy change associated with the stretching polymer chains2 is:
G mecahnical h I1 3 2 ln h e2 2 ln e 1 2 4
(4)
where Gh is shear modulus and h is bulk modulus. We assumed that the bulk modulus is 1000 times that of the shear modulus to achieve the volumetric incompressible of mechanical deformation. The Cauchy-Green stress is calculated as σ= (1/Θ) F (∂Ψ/∂C) FT and the chemical potential is obtained as µ =∂Ψ/∂c.3 Substituting equations (2)-(4) into the previous two equations yields:
Gh κ b I h e2 1 I 2
(5)
S3
RT ln 1 2
κ h ν 2 e 1 2
(6)
Applying the decomposition in equation 1 of F into f and φ0 as the stress response can be expressed as,
2 3 b * I κ h 2 1 I 0 0 2 * 0 e *
Gh
(7)
To model thermo-responsive effect, we assumed the following temperature-dependent function for the Flory-Huggins interaction parameter χ,4
1 L H 1 H L tanh T Ttran 2 2 ΔT
(8)
where χL and χH is the Flory-Huggins interaction parameters at low temperature and high temperature, Ttran is the transition temperature and ΔT is the width of the transition region. We adopted a generalized Neo-Hookean model for PPF. The Cauchy stress is represented as a combination of the deviatoric part and volumetric part,
Gp 1 κp 2 1I b I 1 b 3 2
(9)
̅ is the deviatoric part of left Cauchy-Green tensor, defined as –𝒃 ̅ = Θ-2/3𝒃, and I1(–𝒃 ̅) is where 𝒃 ̅ trace of 𝒃. The material parameters for the two materials listed in Table 1 are obtained from the swelling test and mechanical test described in the experimental section and the detailed information about the procedures can be found.5 Supplemental Table 1. Parameters of the constitutive model for pNIPAM-AAc and PPF Parameters Values
Gh
χL
χH
Ttran
ΔT
162 KPa
0.556
0.710
36 oC
4 oC
(pNIPAM-AAc)
Gp
(PPF)
16 MPa
S4
The constitutive model was implemented in an open-source finite element code TAHOE (Sandia National Laboratories). Supplemental Figure 2 shows the finite element model of gripper specimen. The mesh was discretized by trilinear hexahedral elements. The displacement boundary condition were set as follows, ux (x = 0, y, z) = 0, uy (x = 0, y = 0, z) = 0,
(10)
uz (x = 0, y = 0, z = 0) = 0.
Supplemental Figure 2. Finite element model of gripper specimen The simulation starts from the intermediate swollen, stress free state at temperature T = 35 oC. The equilibrium polymer fraction φ0 is obtained by solving equations (5) and (6) with condition σ = 0 and µ = 0. During every time step, the temperature is changed and the deformation gradient f and polymer concentration φ are updated to satisfy the force balance and chemical potential equilibrium.
S5
Supplemental Movie 1. Polymeric grippers opening and closing in response to increasing temperature (8X speed). Supplemental Movie 2. Simulation results of polymeric gripper deswelling. The snap shots are in Figure 3B. Supplemental Movie 3. Simulation results of polymeric gripper swelling. The snap shots are in Figure 3B.
Supplemental Movie 4. Fe2O3 doped polymeric grippers opening in unison in response to increasing temperature (8X speed). Supplemental Movie 5. Magnetic gripper opening in warm water and moving in response to an external magnet (8X speed). The snap shots are in Figure 5A. Supplemental Movie 6. Polymeric gripper opening and closing around a L929 clump of cells stained with Calcein AM (8X speed). The snap shots are in Figure 5B.
References (1) (2) (3) (4)
(5)
Flory, P. J.; Rehner, J. Statistical Mechanics of CrossLinked Polymer Networks II. Swelling. The J.Chem.Phys. 1943, 11, 521-526. Flory, P. J. Principles of Polymer Chemistry. Cornell University Press. 1953. Hong, W.; Zhao, X.; Zhou, J.; Suo, Z. A Theory of Coupled Diffusion and Large Deformation in Polymeric Gels. J. Mech. Phys. Solids 2008, 56, 1779-1793. Chester, S. A.; Anand, L. A Thermo-Mechanically Coupled Theory for Fluid Permeation in Elastomeric Materials: Application to Thermally Responsive Gels. J. Mech. Phys. Solids 2011, 59, 1978-2006. Jamal, M.; Kadam, S. S.; Xiao, R.; Jivan, F.; Onn, T.-M.; Fernandes, R.; Nguyen, T. D.; Gracias, D. H. Bio-Origami Hydrogel Scaffolds Composed of Photocrosslinked PEG Bilayers. Adv. Healthcare Mater. 2013, 2, 1142-1150.
S6
