The biomimetic approach and research methodology
For the present study the centric diatom Coscinodiscus oculus-iridis was chosen as a representative sample with the most interesting variations in structural elements that can affect their mechanical and photonic properties. We investigated cleaned frustules consisting of two halves with different outer and inner surfaces, as well as wet and dried diatom cells containing organic components (Fig. 1a). The state of the sample interrogated is indicated by the small cartoons shown in the upper right corner to aid understanding. The striking similarity between diatom valves and the membranes used in modern MEMS microphones12 (Fig. 1b) is shown in Fig. 1c. Two different AFM modes used in this study are schematically illustrated in Fig. 1d, whilst in situ nanoindentation in the SEM column is shown in Fig. 1e. The details of these experimental approaches are explained in the Materials and Methods section. The mechanical contact between a sharp indenter and diatom frustule is a frequent occurrence in nature in the course of interaction with marine zooplankton. For example, several species of copepods use the force of their mandibles to crush diatoms using silica-tipped parts called opal teeth45, as illustrated in Fig. 1f.
Morphology And Topography Study: From Micro To Nanoscale
Figure 2 shows morphology and topography of Coscinodiscus oculus-iridis first identified by Ehrenberg in 1839.
The frustule shown in Fig. 2a consists of two valves: the upper epitheca and the lower hypotheca, connected by a series of siliceous rings called girdle bands46. The diameter of valves ranges from 30 to 70 µm, while their height varies from 10 to 15 µm, although much larger size ranges can be found in literature. The cross-sectional view of a diatom frustule after FIB (Fig. 2b, c) demonstrates the multi-layered hierarchical structure of the cell wall, formed by orthosilicic acid in silica deposition vesicle36,47. The wall thickness is in the 0.3–1.5 µm range. The disk-shaped valve faces are slightly depressed in the central area, which is frequently less silicified than the peripheral region48. The outer thin perforated silica layer called cribrum (Fig. 2d, e, j) consists of a regularly spaced array of 40–70 nm pores (cribellum)49 (Fig. 2f, m). The pore-to-pore distance in one array is around 100 nm. The honeycomb-like chambers called areolae are open to the cell interior via rimmed circular openings (Fig. 2g) – foramen with a diameter of around 0.2–0.5 µm (Fig. 2h, i). The porous pattern of the cribrum layer is located exactly above the foramen. The rimoportula openings having the shape of a pair of lips are distributed along the perimeter of the internal valve (Fig. 2h). On the external valve face, the rimoportula opening is a simple, round aperture, through which they extrude polysaccharides and other carbon compounds. AFM topography images (Fig. 2j-m) show that the surface of the air-dried live diatom cell containing organic material is not flat and monotonously "smoothed", but form a hilly terrain (Fig. 2l, m). Organic components of diatoms can be classified in the following way: 1) an organic casing represented by a thin layer surrounding silica wall, 2) the diatotepum or diatotepic layer located between the plasmalemma and the silica, 3) molecules or organic complexes trapped within the silica, 4) mucilage associated with the cell surface or secreted by diatoms which can be used for motility, adhesion or protection50. On the cleaned frustule the perforations on the outermost surface are simple openings (Fig. 2j), while on the inner surface they have thickened rims (Fig. 2k).
AFM and AMFM studies of mechanical properties of cleaned frustules and wet diatom cells in static mode
Figure 3 shows AFM topography and corresponding maps of Young’s modulus measured on the inner (Fig. 3a, d) and the outer (Fig. 3b, e) surfaces of cleaned diatom frustules and on the wet cell containing organic material (Fig. 3c, f). The Young’s modulus data were obtained by collecting force-distance curves in the elastic regime.
The results show that Young’s modulus of the thick space between pores is E = 15 ± 2 GPa and E = 10 ± 4 GPa for the inner and the outer surfaces of cleaned frustules, respectively, while for the wet diatom cell E = 25 ± 5 GPa, which was expected considering the support from the organic material trapped inside the frustule. According to study51, the introduction of molecular water into the silica network leads to an increase of Young's modulus of silica glass at low water content. On the other hand, due to excessive boiling in concentrated nitric acid, the frustule material can become friable and fine structures in some cases may be lost which leads to the lower mechanical performance. Conversely, if the oxidation was weak and the samples were poorly washed, the organic matter lays down on the surface of the frustule in a thin layer, covering and masking fine structures. The stronger mechanical structure of the internal plate is expected as this layer is the basic framework for building the other porous layers – cribrum and cribellum. Note, however, that the values fall within the error margins (Supplementary Fig. 1). Finite element simulation of an isolated pleura of T. punctigera42 showed that the Young's modulus of diatom silica is 22.4 GPa, which is comparable to cortical bone (20 GPa) and in good agreement with our study. Young’s modulus of the rims around pores is lower probably because the material of the rims is not clamped in in-plane direction, as shown in Supplementary Fig. 2.
We also performed indentation at specific points on the inner surface of the cleaned frustule by applying different indentation force, as indicated in Fig. 4a.
Young’s modulus calculated from these data using the DMT model (Fig. 4b) show the same trend as for the reference fused silica sample (Supplementary Fig. 1), i.e., correct values are at the applied force below 20 µN where the tip-surface contact geometry may be approximated by a sphere and interaction is mainly elastic. At higher forces the model does not fit well because the contact geometry deviates from the spherical one, while at 75 µN the valve breaks. Hardness calculated as a ratio of the maximum indentation force to the indent area is between 4.0 and 4.5 GPa and slightly decreases with increasing loading force, which is typical for nanohardness measurements (Fig. 4c).52 Similar behaviour was observed on the reference fused silica sample (Supplementary Fig. 1). The hardness of the measured cleaned inner valve was significantly higher compared to the outer porous layers ((0.033–0.116 GPa) – at the center, (0.076–0.120 GPa) – at the edge), according to the study39. The Young’s modulus values obtained in our study were higher than in the study by Losic et al.39, where they varied from 0.591 to 2.768 GPa at the center of the frustule and from 0.347 to 2.446 GPa closer to the edge.
Young’s modulus on the cribrum in Fig. 3 appears smaller than on the thicker parts of the sample. It can be explained by the fact that the cribrum is so thin that during force-distance curve acquisition it bends as a membrane even at low applied force (100 nN). In this case the obtained values of Young’s modulus do not correctly reflect properties of the material. In order to obtain more accurate results for the cribrum, we used a gentler AMFM viscoelastic mapping method53, in which the AFM cantilever scans the sample’s surface in the tapping mode in the repulsive regime54 being excited simultaneously at two resonance frequencies. The results are shown in Fig. 5.
The AMFM Young’s modulus is up to two times higher than the modulus calculated from the force-distance curves. On the outer surface of the cleaned frustule Young’s modulus of the cribrum is about 3 times lower than of the thicker space in between, while on the wet diatom cell, where the inorganic frustule is supported by the organic interior, the difference almost vanishes. This result implies that Young’s modulus calculated on the cribrum from the force-distance curves is indeed affected by the membrane effect and is lower than the real one.
To get deeper insight into mechanical properties of the cleaned valve we acquired force-distance curves from the edge towards the center of the outer surface along green lines shown in Fig. 6a using the stiff diamond probe. The maximum loading force of 7.7 µN falls into the elastic regime (without indentation) and the frustule’s outer surface bends as a membrane under the load. The results showed that the bending increases from the side towards the center of the valve. Young’s modulus calculated using the Hertz fitting model decreases as the distance from the edge towards the center of the valve increases.
Compliance Of Cleaned Frustules: Static Vs. Dynamic Approach
The data obtained was used in combination with the analytical model for circular membrane deformation given by Melnikov55. The Green’s function of a point force \(G(z, \zeta )\) for Kirchhoff plates satisfies the equation:
$$\begin{array}{c}D{\nabla }^{4}G\left(z,\zeta \right)=\delta \left(z-\zeta \right) \#\left(1\right)\end{array}$$
where \(D=E{h}^{3}/12\left(1-{\nu }^{2}\right)\) is the flexural rigidity of the diatom valve given in terms of Young’s modulus \(E\), thickness \(h\) and \(\nu\) is Poisson’s ratio, while \(z = r(\text{c}\text{o}\text{s}\phi + i \text{s}\text{i}\text{n}\phi )\) and \(\zeta = \rho (\text{c}\text{o}\text{s} \psi + i \text{s}\text{i}\text{n} \psi )\) represent the observation point and the force application point, respectively. The solution is given by:
$$\begin{array}{c}G\left(z,\zeta \right)=\frac{1}{8\pi D}\left[\frac{1}{2{a}^{2}}\left({a}^{2}-{\left|z\right|}^{2}\right)\left({a}^{2}-{\left|\zeta \right|}^{2}\right)-{\left|z-\zeta \right|}^{2}\text{l}\text{n} \frac{\left|{a}^{2}-z\underset{\_}{\zeta }\right|}{a\left|z-\zeta \right|} \right] \#\left(2\right)\end{array}$$
where a is the radius of the diatom. By fitting the model to experimental observations, the membrane flexural rigidity can be used to determine the overall apparent Young’s modulus of the diatom valve as a circular membrane. The compliance defined as the measure of the structure deformation under the action of external forces was calculated as the reciprocal of rigidity. The dependence of compliance on the relative radial position calculated using influence function of a point force is shown in Fig. 6b. Maximum similarity with the experimental values was achieved at h = 477 nm and E = 9.35 GPa.
The results of cyclic loading (amplitude 1 µm, period 1 s) performed on cleaned diatom frustule in the SEM column are shown in Fig. 6c, Supplementary Fig. 3, and Supplementary Video 1, 2. Based on the dependence of the displacement on time, considering sinusoidal motion represented as A·sin(ωt), we found the stiffness and subsequently compliance as a function of cycle number, as presented in Fig. 6d. Compliance increases with increasing number of cycles. The average compliance was found to be 0.019. The frustule begins to break along one edge after ca. 300 s, but continues to oscillate during cyclic loading without complete rupture.
Mechanical Response From Cleaned Frustules Vs. Dried Diatom Cells
We also performed static in situ nanoindentation inside SEM on dried cells with cellular material (Fig. 7a) as well as cleaned diatom frustules (Fig. 7b) and based on the force- displacement curves we analysed their mechanical performance. Static studies lead us to a more precise definition of the module of a material as a whole. Figure 7c shows the force-displacement curves of dried cells, which vary depending on the orientation and size. As can be seen, dried cells 1–4 (diameter, 37–40 µm; height, 11–13 µm) have a similar size and mechanical behaviour, which is different from the dried cell 5, whose diameter/height ratio is smaller (diameter, 41 µm; height, 18 µm). On the other hand, we observed a difference in mechanical performance when indenting a dried cell 6 from the girdle band point.
The nature of the curves of cleaned frustules and dried cell with organic material is different (Supplementary Fig. 4). Also, the forces are significantly lower in the case of cleaned frustules, as well as the area under the curves, which is equal to work done on the object (Fig. 7d). With the help of AFM, we made local indentations which gives us more information about material, however we did not completely deform the structure, as in the case of nanoindentation in SEM column performed with the blunt tip indenter. The differences between the values can also be attributed to the layered “burger” structure within the frustule of some diatoms, as demonstrated in Fig. 7e. This situation can occur in old cultures when the process of cell division is corrupted and formation of the valves is not accompanied by cytokinesis.