FEM exploration of the potential of silica diatom frustules for vibrational MEMS applications
Graphical abstract
Introduction
The biological class of diatomic algae is an example of nature’s fascinating collection of intricate hierarchical architectures of exoskeletons (known as frustules) that are optimized for functional and structural performance at multiple length scales, and produced in a cheap and environmentally friendly way in the volume that vastly exceeds that of artificially manufactured nanostructured materials [1,2]. Diatoms, a class of single-cell algae found in aquatic environments have millions of unique species with distinct morphologies of frustules made from amorphous hydrated silica [3]. Depending on symmetry diatoms are usually classified into two groups: centric (often circular) and pennate (elongated) (Fig. 1). Extraordinary mechanical properties, such as high deformability and high specific strength [4], are combined with the ability of biological reproduction even in Antarctic temperatures (below freezing) [5], making diatoms a unique instance of natural nano-fabrication at the global scale. The manipulation and genetic control of diatom frustule nano-structuring could revolutionize the device fabrication routes for energy storage, optoelectronics, solar cells [6], and batteries [7]. Diatoms have intricate intrinsic features: biocompatibility, unique nano-pore arrangement, specific surface area and mechanical strength. In recent decades they have been proposed for use in drug delivery [[6], [7], [8]], microfluids [9,10], batteries [11,12], templates [[13], [14], [15]], biosensors [16,17], for energy conversion and storage [18]. Diatoms used as a platform for nanotechnology hold a crucial advantage over photolithography because they multiply in geometric progression, i.e. at a much faster rate than is possible for any technology of fabrication for MEMS [18] and in which is faster than the manufacturing speed of MEMS. This bioinspired silica can be used directly or in modified form in design for specific properties. Diatoms have rigid surfaces in relative motion, and their tribology has a high potential regarding 3D MEMS [19]. Some studies of the mechanical properties of diatom frustules have been reported in the literature. The mechanical vibration behaviour of diatom frustules is important because their small size, light weight and high stiffness lead to the expectation of them having high natural vibration frequencies with potential applications in MEMS, especially considering the diversity of sizes and shapes that diatoms offer. The Finite Element Method offers a suitable analysis technique for the study of mechanical properties of small biomaterials. The mechanical properties of diatoms are widely studied in the literature [4]. In particular, computer modelling has become an increasingly popular approach to the study of biomaterials with complex structure at the nano- and micro- scales. Hamm et al. performed Finite Element Analysis of Fragilariopsis kerguelensis frustules and showed that diaphragmatic grooves have high rigidity of about 9.8 GPa [4]. The authors considered that diatoms obtained their unique architecture as a result of a long evolutionary process under the influence of environmental factors, in order to optimize such properties as protection from predators. Several studies attempted to analyze diatom frustule structere in the context of hierarchical design by Nature. Moreno et al. studied the relationship between porosity and mechanical properties [21]. Similarly, Gutiérrez et al. investigated the effect of morphological features (such as the diameter of diatoms, pore size and thickness of individual walls) on the deformation response of centric diatoms [22]. It remains extremely challenging, if not impossible to simulate the real structure of diatoms. Several studies have shown the most considerable importance of pore size for the properties of diatom frustules. Yuan Xing proposed the use of Focused Ion Beam - Scanning Electron Microscopy (FIB-SEM) as a powerful tool for the systematic 3D study of the morphological features of diatoms on the basis of a series of high-resolution images [23]. Lu el. reported high precision simulation of Coscinodiscus sp. valve, starting with a unit cell that included three layers of the valve (hole, cribrum and cribellum) and even taking into account the curvature of the pore walls of the hole (areola chambers) [24]. Meza et al. made a significant advance in additive manufacturing complex microarchitectural materials down to the nanometer precision. in situ nanomechanical testing showed high strength and stiffness, and near complete recovery (up to 98 %) after large compression up to ≥50 % [25]. More recently, E. Topal et al. used the combination of X-ray computed tomography (XCT), FEM analysis and micro-scale testing to study the mechanical response to Didymosphenia geminata. They were able to obtain accurate 3D morphological data for model input. The limited XCT resolution of 130 nm meant that SEM was used to define nanopore size and shape. Effective Young’s Modulus of the frustule was determined to be 31.8 GPa, significantly lower than bio-silica (70 GPa) due to porosity, as is the case for many biological materials with hierarchical structure.
In the present study, we focus our attention on the numerical study of the effect of morphology and material properties of diatom frustules on the mechanical vibration behaviour. The type of diatoms was selected based on the ordered arrangement of pores and symmetry. Symmetry alleviates simulation analysis and visualization. Coscinodiscus sp. (centric) and Synedra acus (pennate) diatom species satisfy the criteria above. Their slim nanostructures can be integrated into nanodevices, which is the strategic focus of our study. The main objective of our research is to explore diatom’s potential for MEMS, namely, oscillators or vibrational sensors able to resonate at eigenfrequencies detecting specific external vibration. Our scientific group recently managed to make other steps towards this goal, namely, to achieve guided colonization of Si wafers with diatoms [21] and to reduce natural diatom opal to obtain nanostructured Si objects while retaining neat nanostructure [22]. These steps are being theoretically and conceptually supported by the modelling presented in this manuscript.
Coscinodiscus sp. and Synedra acus diatoms represent the extremes in terms of taxonomy and, as one can see, topology as well. Centric diatoms can be considered as quasi-spherical thin shells (or domes) fundamentally and thoroughly studied in continuous mechanics. The issues of porosity and height-to-diameter aspect become crucial for eigenfrequencies. Pennate diatoms depending on the width-to-length aspect may be treated as close to centric or, like for the considered Synedra, as slender rod or beam, or even as elastic continuous string. Theoretical models for long rods or elastic strings are also well documented in scientific literature and simplest formulae can be applied for fast estimations. Porosity can be accounted for as reduction factors for density and stiffness. Diatom frustules consist of 10–70% amorphous silica with the density not exceeding 2600 kg/m3, and the remaining organic components such as proteins with the density of 1300 kg/m3, and polysaccharides of 1070 kg/m3. Therefore, frustule densities can range from 1400 kg/m3 to 2200 kg/m3, according to literature [24]. The frustules of diatom algae consist of two halves, known as valves. In the case of Coscinodiscus sp. with centric symmetry (Fig. 1a) the shape of each valve is remindful of a Petri dish with the diameter ranging from 50 to 200 μm, and the dome height of 12 μm. A system of holes or pores with the diameters of 0.4 μm–2.6 μm penetrate the frustule from the concave to the convex surface. The valves that are joined by the surrounding circular girdle band of about 3 μm width. The thickness of the silica frustule walls varies from 0.2 to 2 μm [20]. In previous studies, nanoindentation of Coscinodiscus sp. revealed the material stiffness of 22.4 GPa [4], which is comparable to that of the cortical bone (20 GPa) [25], but is significantly lower than that of bulk silica glass (73 GPa) [26] perhaps due to the presence of both organic binder and nanometer size porosity. Synedra acus with the structure illustrated in Fig. 1b is a class Fragilariophyceae that is abundant in ground water. It was chosen as representative of the pennate group of diatoms that display bi-fold symmetry. Pennate diatoms typically have the form of elongated ellipsoids consisting of the upper valve (epitheca) and lower valve (hypotheca) joined by the girdle band. Each half shell consists of ribs (costae) with orifices classified according to their location and size into raphe (central longitudinal ridge), striae and areolae. The cell culture was isolated from the natural population endemic in Lake Baikal and was allowed to grow naturally in a plastic contained placed on a laboratory windowsill.
Section snippets
3D CAD and FEA modelling of hierarchically structured frustules
The numerical simulations carried out in the current project studied the dependence of vibration properties on a range of parameters, namely, the overall frustule geometry, the dimension of characteristic features, and material properties. Additionally, the mesh size effect was considered to ensure the reliability of results. At the start of the simulation, a three-dimensional CAD model was created using SolidWorks software version SP5.0. The model was constructed based on the actual morphology
Analysis of the results
For the purposes of evaluating the suitability of diatom frustules for MEMS applications as vibration elements, the key requirement concerns the ability to predict the eigenfrequency values based on the frustule size, shape, and mechanical characteristics.
Modal shapes
The shapes of first six vibration modes are illustrated in Fig. 3. For Coscinodiscus sp. the displacements mapped correspond to the direction along the symmetry axis of the valve. For Synedra acus the displacements shown are normal to the
Comparison between numerical simulations and analytical solution
To confirm the reliability of our results, we used the analytical results, particularly those of Shang [31,[32], [33], [34], [35], [36], [37], [38], [39], [40]]. Using the Naghdi-Reissner shell theory and Legendre functions, an analytical solution was obtained for vibration frequencies of spherical-cylindrical shells that was expressed in the form:
, where λ is a dimensionless scaling parameter, that can be re-written in our notation as and compared with our result:
Conclusions
The natural vibration frequencies of two different diatom frustule shapes were analysed, centric Coscinodiscus sp. and pennate Synedra acus. For the former centric shape in particular it was revealed how the natural frequencies depend on the frustule morphological features, such as material stiffness and density, valve diameter, wall thickness, and pore diameter. Diatom frustules are expected to have vibration frequencies in the MHz range. Bio-silica low density and high Young’s Modulus make
Author statement
Bakhodur Abdusatorov – simulation, interpretation. PhD student, Skoltech CEST
Alexey I. Salimon – conceptualization, supervision. PhD, Senior Research Engineer, Skoltech CEST
Yekaterina D. Bedoshvili – conceptualization, supervision. PhD, specialization in limno-biology
Yelena V. Likhoshway – conceptualization, supervision. D. Sci., Professor, specialization in limno-biology.
Alexander M. Korsunsky – conceptualization, supervision, intellectual leadership. Professor, specialization in materials
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
AMK wishes to acknowledge funding support from the Royal Society (UK) under project IEC/R2/170223.
References (40)
- et al.
Diatoms embedded, self-assembled carriers for dual delivery of chemotherapeutics in cancer cell lines
Int. J. Pharm.
(2020) - et al.
Characterization and analysis of Coscinodiscus genus frustule based on FIB-SEM et al
Prog. Nat. Sci.
(2017) - et al.
Nature’s hierarchical materials
Prog. Mater. Sci.
(2007) - et al.
A continuous wave technique for the measurement of the elastic properties of cortical bone
J. Biomech.
(1984) - et al.
A continuous wave technique for the measurement of the elastic properties of cortical bone
J. Biomech.
(1984) - et al.
Free vibration analysis of thin plates by using a NURBS-based isogeometric approach
Finite Elem. Anal. Des.
(2012) Exact solution for free vibration of a hermetic capsule
Mech. Res. Com.
(2001)- et al.
Microorganisms for MEMS
J. MEMS
(2007) - et al.
Preparation of biosilica structures from frustules of diatoms and their applications: current state and perspectives
Appl. Microbiol. Biotechnol.
(2013) - et al.
The Diatoms: Biology and Morphology of the Genera
(1990)
Architecture and material properties of diatom shells provide effective mechanical protection
Nature
The diatom of Antarctica and their potential roles in nanotechnology
Targeted drug delivery using genetically engineered diatom biosilica
Nat. Commun.
Natural diatom biosilica as microshuttles in drug delivery systems
Pharmaceutics
Biobased high-performance rotary micromotors for individually reconfigurable micromachine arrays and microfluidic applications
ACS Appl. Mater. Interfaces
Self-powered microfluidic pump using evaporation from diatom biosilica thin films
Microfluid Nanofluid
Carbon-coated, diatomite-derived nanosilicon as a high rate capable li-ion battery anode
Sci. Rep.
Fride Vullum-Bruerc and Ann Mari Svensson, Silica from diatom frustules as anode material for Li-ion batteries
RSC Adv.
Cited by (8)
Submerged membrane photobioreactor for the cultivation of Haslea ostrearia and the continuous extraction of extracellular marennine
2022, Bioresource TechnologyCitation Excerpt :This method could then also be an effective approach to reduce harvest costs as demonstrated by Bilad et al. (2014). Then, the recovered biomass can be exploited for the extraction of intracellular marennine as well as the siliceous exoskeleton called frustule which could change the ways of manufacturing devices for energy storage, optoelectronics, solar cells and batteries (Abdusatorov et al., 2020). In this study and as shown in Fig. 2, the pseudo-stabilization phase depends on the dilution rate applied.