Bacillus spores as building blocks for stimuliresponsive materials and nanogenerators

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1 Bacillus spores as building blocks for stimuliresponsive materials and nanogenerators Xi Chen, L Mahadevan, Adam Driks & Ozgur Sahin 1- Estimation of energy densities from the AFM based measurements Supplementary Figure S1. Estimation of energy density from indentation force measurements. (a) Illustration of the contact between an AFM tip and a bacterial spore. (b) A simple geometric model of the experiment in (a). Energy density is determined for the case where the spore is uniformly indented along the cylindrical axis (c). Energy density is defined as the amount of work that a unit volume of spores can do in one hydrationdehydration cycle. This value can be determined by measuring the work done in a cycle and dividing it to the volume contributing to the work. Due to the finite size of the tip, the AFM based experiment does not allow uniform compression of the spores even with the large tip radii (~ 850 nm) employed in our experiments (a). The stresses and strains distribute non-uniformly along the long axis of the spore and the maximum pressure appears at the center of the contact region. To account for this non-uniformity, we approximate the spore with a cylinder that is being indented by a rigid sphere (b). We then compare this configuration with the case where the cylinder is uniformly compressed as illustrated in (c) for the same depth of indentation. Material properties are kept constant in (b) and (c). The energy density is determined by first applying the spherical-tip model in (b) to the experimental data to determine an effective elastic modulus value for the hydrated spore and then using this value to calculate the amount of work for the case in (c) when the spore is compressed uniformly with a flat tip. We relied on the experimentally determined values of indentation depths, spore diameters, and work done in a single hydration-dehydration cycle for each individual spore. Supplementary Figure S2. (a) Illustration of the sphere-cylinderplane contact and (b) the planecylinder-plane contact showing variables used in calculations. Figure S2 introduces the parameters used in our calculations. We denote the forces acting on the cylinder in (a) and (b) as and, respectively. Due to symmetry can be written as, where is force at a unit length along the cylinder. The displacements and NATURE NANOTECHNOLOGY 1

2 correspond to the total deformation of the cylindrical sample in (a) and (b), which include deformations at the top and bottom. With these definitions the energy density will be given by the equation: S1.1 The force-distance relationship can be approximated by treating the contacts at the top and bottom sides of the cylinder with the Hertz model for plane-cylinder contact 1 : S1.. Here is the indentation modulus and is the indentation depth at the top side of the cylinder. Because we keep the indentation depths in (a) and (b) the same:. Substituting and into (S1), we get 4 S1. To evaluate this equation, we determine the values of and from the experimentally measured work and deformation. Separating the work done by the deformations at the top and bottom sides of the cylinder in (a) simplifies calculations: S1.4 The work due to deformations at the top side can be estimated using the Hertz model for spherecylinder contact 1-3, which gives force-distance relationship of the form: S1.5 Here is a geometric constant that depends on and. The value of is determined numerically and it is approximately 1.0 for 5 and 5. (Note that goes to infinity, Eq. (S1.5) converges the expression for the contact between sphere and plane 4). The force-distance relationship of the deformations at the bottom side of the cylinder in (a) is more difficult to represent analytically, because stresses are not distributed uniformly as in (b). However, considering that the diameter of the cylinder (~700 nm) is larger than the contact length at the spherecylinder interface (~400 nm), the impact of assuming a uniform stress profile within an interaction region of (See Supp. Fig. S2(a)) to the overall energy density is likely to be small. (To ensure the safety of this assumption, we repeated the calculations for the two extremes where is equal to the contact length and to the length of the spore 1.5 µm. The resulting estimates of energy density were within 10%). With this assumption, the force-distance relationship for the bottom contact is given by (S1.2) evaluated for a total length of L: 4. S1.6 Note that equating (S1.5) and (S1.6) and using the definition allow relating bot and to the experimentally determined using only geometrical parameters, and L. With these substitutions, the work in (S1.4) can be determined by integrating (S1.5) and (S1.6). Equating W to the experimentally determined values gives. (Measurements from all three spore types ranged from 6.0 to 8.0 GPa). Substituting the value of in (S1.3) gives the estimated energy density for uniformly compressed spores (Fig. 1f). 2 NATURE NANOTECHNOLOGY

3 We note that our calculations assumed uniform material properties for spores. Although spores consist of layers, the elastic moduli of these layers are largely similar. For example, previously reported AFM based elastic modulus measurements of the coat and cortex layers provided similar values (13.6 GPa vs. 6.9 GPa) 4. Note that our estimates based on total work in a hydration-dehydration cycle gave similar results (~ 7GPa). Furthermore, measurements with the mutant spore that lacks most of its coat still resulted in similar estimates for elastic modulus, suggesting that the layers have little influence over our estimates of energy density. Other potential sources of uncertainty in energy density estimates are wrinkled coat morphology of spores and measurement uncertainties in spore heights and indentation depths. Standard deviations in the energy densities obtained from 5 spores for each spore type (Fig. 1f) suggest that the effects are relatively small. 2- Design principles for maximum energy transfer to an elastic substrate The contracting spore layer exerts a plane stress at the interface between spores and the substrate. As a result, the substrate shape deforms into a curved surface (Supp. Fig. S3). The relationship between the radius of curvature r and plane stress σ is given with the following formula 5 : (S2.1) Here E is the Young s modulus, ν is the Poisson s coefficient, and t is the thickness of the elastic substrate. In the resulting curved geometry, the strain within the elastic substrate varies linearly with distance. The neutral plane with zero strain is located 2t/3 away from the spore-substrate interface 5. Therefore, the strain s at the interface is given by (S2.2) Supplementary Figure S3. Schematic of an elastic substrate coated with a layer of bacterial spores deformed by the stress generated by the spores. Using s, we can rewrite Eq. (S2.1) as: (S2.3) Eq. S2.3 provides the plain stress-strain relationship dictated by the elastic substrate. Strain within the spore layer provides a second relationship. Precise modeling of this relationship is complicated by the complex geometries of spores and their arrangements on the surface. For simplicity, we assume the following linear relationship: (S2.4) Here M is the modulus of stretching, s dry is the strain induced in unconstrained spores upon drying, and s is given by Eq. (S2.2). Note that s dry has a negative value and for s dry < s < 0, plane stress σ is also negative. Solving (S2.3) and (S2.4) for equilibriumσ and s, and maximizing the work done by the spore layer give. Substituting, where h is the effective thickness and E h is the effective elastic modulus of spore layer, we obtain the condition of maximum energy transfer as: NATURE NANOTECHNOLOGY 3

4 (S2.5) To estimate the value of the left hand side of Eq. (S2.5), we use E h ~ 7 GPa, as estimated from AFM experiments on individual spores. The bacterial spore layer has an approximate thickness of 700 nm. However due to their round shaped cross sections, spores do not make physical contact in the entirety of the 700 nm. To account for this geometrical effect, we assumed h ~ 350 nm. According to Eq. (S2.5), for a given substrate material with elastic modulus E s, maximal energy transfer to the substrate takes place at some specific thickness. In this work we used natural latex rubber sheets, which have E s ~ 1.3 GPa and v ~ 0.5. Then, the thickness of the rubber sheet should be 3.15 mm. We observed cracks in spore layers, likely because of insufficiently strong spore-spore adhesion. Therefore, we reduced the thickness of the rubber sheet to 0.5 mm (Fig. 2) and 0.75 mm (Fig. 3). 3- Typical values reported for materials frequently used or studied in the context of actuators, and stimuli responsive materials Table S1. Typical or demonstrated values of strain and energy density of various actuator materials and water-responsive materials (Values are plotted in Fig. 1g) Materials Strain (%) Energy density (kj/m 3 ) Mammalian skeletal muscle 20 8 Bio-inspired polymer composite (water responsive) Carbon nanotube actuators Piezoceramics Magnetostrictors Dielectric elastomers Thermal expansion (Al, dt = 500 K) Spider silk (water responsive) Shape memory alloys (TiNi) Ref , , References 1 Johnson, K. L. Contact mechanics. (Cambridge University Press, 1985). 2 Puttock, M. J. & Thwaite, E. G. Elastic compression of spheres and cylinders at point and line contact. (Commonwealth Scientific and Industrial Research Organization, 1969). 3 Hrouz, J., Vojta, V. & Ilavsky, M. Penetration Behavior of the System Sphere-Cylinder. Polym Eng Sci 20, , doi:doi /pen (1980). 4 Sahin, O., Yong, E. H., Driks, A. & Mahadevan, L. Physical basis for the adaptive flexibility of Bacillus spore coats. J. R. Soc. Interface 9, , doi: /rsif (2012). 4 NATURE NANOTECHNOLOGY

5 5 Stoney, G. G. The tension of metallic films deposited by electrolysis. Proc. R. Soc. London, Ser. A 82, (1909). 6 Madden, J. D. W. et al. Artificial muscle technology: Physical principles and naval prospects. IEEE J. Ocean. Eng. 29, , doi: /joe (2004). 7 Ma, M., Guo, L., Anderson, D. G. & Langer, R. Bio-inspired polymer composite actuator and generator driven by water gradients. Science 339, , doi: /science (2013). 8 Aliev, A. E. et al. Giant-Stroke, Superelastic Carbon Nanotube Aerogel Muscles. Science 323, , doi:doi /science (2009). 9 Zhang, Q. M., Bharti, V. V. & Zhao, X. Giant electrostriction and relaxor ferroelectric behavior in electron-irradiated poly(vinylidene fluoride-trifluoroethylene) copolymer. Science 280, (1998). 10 Madden, J. D. Mobile robots: Motor challenges and materials solutions. Science 318, , doi:doi /science (2007). 11 Brochu, P. & Pei, Q. B. Advances in Dielectric Elastomers for Actuators and Artificial Muscles. Macromol Rapid Comm 31, 10-36, doi:doi /marc (2010). 12 Agnarsson, I., Dhinojwala, A., Sahni, V. & Blackledge, T. A. Spider silk as a novel high performance biomimetic muscle driven by humidity. Journal of Experimental Biology 212, (2009). NATURE NANOTECHNOLOGY 5

Supplementary Material

Mangili et al. Supplementary Material 2 A. Evaluation of substrate Young modulus from AFM measurements 3 4 5 6 7 8 Using the experimental correlations between force and deformation from AFM measurements,