Accurate modeling of nanohelical structures is important for predictive simulation studies leading to novel nanotechnology applications. Currently, software packages and codes are limited in creating atomistic helical models. We present two procedures designed to create atomistic nanohelical models for simulations, and a graphical interface to enhance research through visualization.
Spring-like materials are ubiquitous in nature and of interest in nanotechnology for energy harvesting, hydrogen storage, and biological sensing applications. For predictive simulations, it has become increasingly important to be able to model the structure of nanohelices accurately. To study the effect of local structure on the properties of these complex geometries one must develop realistic models. To date, software packages are rather limited in creating atomistic helical models. This work focuses on producing atomistic models of silica glass (SiO2) nanoribbons and nanosprings for molecular dynamics (MD) simulations. Using an MD model of “bulk” silica glass, two computational procedures to precisely create the shape of nanoribbons and nanosprings are presented. The first method employs the AWK programming language and open-source software to effectively carve various shapes of silica nanoribbons from the initial bulk model, using desired dimensions and parametric equations to define a helix. With this method, accurate atomistic silica nanoribbons can be generated for a range of pitch values and dimensions. The second method involves a more robust code which allows flexibility in modeling nanohelical structures. This approach utilizes a C++ code particularly written to implement pre-screening methods as well as the mathematical equations for a helix, resulting in greater precision and efficiency when creating nanospring models. Using these codes, well-defined and scalable nanoribbons and nanosprings suited for atomistic simulations can be effectively created. An added value in both open-source codes is that they can be adapted to reproduce different helical structures, independent of material. In addition, a MATLAB graphical user interface (GUI) is used to enhance learning through visualization and interaction for a general user with the atomistic helical structures. One application of these methods is the recent study of nanohelices via MD simulations for mechanical energy harvesting purposes.
Helical nanostructures are typically produced in the laboratory using chemical vapor deposition techniques1-2, while new approaches have been reported in the literature3. In particular nanosprings and nanoribbons have been studied because of their distinct properties and promising applications in sensors, optics, and electromechanical and fluidic devices4-7. Synthesis methods have been reported to produce silica (SiO2) nanoribbons, making these structures potential building block units for hierarchical systems. Novel synthesis of 3D silica nanosprings has expanded their applications to chemiresistors when coated with ZnO8 or nanoparticles for diagnostic applications9-10.
Experimental studies on the mechanical properties of silica nanosprings and nanoribbons are scarce, primarily due to current limitations in manipulation and testing methods and equipment. Investigations into the nanomechanics of nanostructures and nanosprings have been reported using theory and simulations11-14. Some simulations13 have focused on nanomechanical behavior of amorphous nanosprings because they can explore regimes not fully accessible through experimentation. Atomistic studies of metallic nanosprings have been reported in literature to investigate the size dependence of elastic properties15, and more recently the nanomechanics of helical crystalline silica nanostructures14. Experimental testing of nanospring structures has also been performed in different materials such as helical carbon nanostructures and carbon nanocoils16-17. Despite the knowledge gathered thus far, a more complete understanding of the mechanical properties of these novel nanostructures is needed for future nanodevice fabrication efforts.
As MD studies of silica glass (non-crystalline silica) nanohelices are still quite limited, the atomistic modeling of such structures requires the creation of customized codes. No other alternative methods of creating silica glass helical MD models have been identified thus far upon recent literature search. In this work, a bottom-up approach to the atomistic modeling of helical silica glass nanostructures including nanosprings and nanoribbons is pursued for future large-scale MD nanomechanical simulations. The general approach involves the creation of an MD “bulk” silica glass model as reported previously18, and carving out various helical nanostructures from this “bulk” sample via two robust and adaptable computer codes developed for this purpose. Both computational procedures offer a distinct way to create nanoribbon and nanospring models with great efficiency and atomistic detail; these structures are suitable for large-scale atomistic simulations. In addition, a customized graphical user interface is used to facilitate creation and visualization of the helical structures.
The structure of the “bulk” silica glass model is initially created at room temperature. Large-scale MD simulations are conducted for this purpose using the Garofalini interatomic potential similar to prior studies18, which is relatively efficient computationally and appropriate for large systems. The initial “bulk” silica glass structure consists of a cubical model (14.3 x 14.3 x 14.3 nm3) which contains 192,000 atoms. The “bulk” silica glass model is equilibrated at 300 K for 0.5 nsec to obtain the initial state using periodic boundary conditions.
Two computational procedures are designed and utilized to create atomistic silica nanoribbon and nanospring models. The first method involves carving out silica nanoribbons from the “bulk” structure using the parametric equations that define a helix, and its geometry (pitch, radius of helix, and wire radius). This procedure includes using the AWK programming language, the LINUX operating system, and open-source visualization software19. The general iterative procedure to create atomistic models of nanoribbons involves: (1) selecting an atom in the “bulk” silica glass model, (2) calculating the distance from the selected atom to a point in space on a pre-defined helical function, (3) comparing this distance to the radius of the desired nanoribbon, and (4) discarding or keeping the atom in an output data model. A detailed step-by-step description for this method is included in the Scalable Open-Source Codes Supplemental Material. With this method, several silica nanoribbons were created using different pitch, radius of helix and nanoribbon radius values, which were measured subsequently for accuracy against the desired dimensional values with molecular analysis and visualization software19-20. Atomistic models of silica nanoribbons were generated with functional geometries (high values of pitch and low values of nanoribbon radius). Some artifacts, consisting of atoms excluded in error, leading to a less smooth nanoribbon surface, were observed at exceedingly high nanoribbon radius values and extremely low pitch values. Similar methods have been used in the process of creating silica nanowires21-23.
The second method presented here includes carving out silica nanosprings from the “bulk” silica structure by implementing pre-screening methods to increase efficiency in addition to the mathematical equations for a helix. This procedure required creating a more robust C++ code to allow greater flexibility in modeling these helical nanostructures. The iterative method to create atomistic models of nanosprings includes: (1) discarding all atoms guaranteed to fall outside the helical path, (2) deterministically selecting a point on the helical path, (3) comparing all atoms within a specific distance to this selected point, and (4) discarding or storing each atom in an output data model. A step-by-step description for this method is also included in the Scalable Open-Source Codes Supplemental Material. With this method, several silica nanospring models were obtained with varied dimensions (wire radius, radius of helix, and pitch of nanospring) as shown in Figure 1. Highly precise silica nanospring models were obtained efficiently with this method, with no evidence of artifacts found at extreme (low and high) pitch values for the nanospring. The creation and use of the graphical user interface for this method is described in the Protocol section.
Figure 1: A general helical structure showing characteristic dimensions, where r, R and p represent the wire radius, radius of helix, and pitch respectively. H denotes the total height of the helical structure23.
This protocol describes how to prepare the NanospringCarver files, running MATLAB24 on a LINUX25 PC, and use a graphical user interface to prepare atomistic nanospring models. These previously unavailable models serve as the basis for novel molecular dynamics (MD) simulations23 toward materials innovation research.
The general step-by-step procedure to create atomistic nanospring models involves using the following elements: (a) NanospringCarver (v. 0.5 beta) code (open-source in C++ language), (b) bulk silica glass model (input file), (c) MATLAB GUI interface and related files, and (d) MATLAB software (version 7) using a local license on a LINUX PC. Items (a)-(c) above (NanospringCarver code, silica glass model, MATLAB GUI files) are free to download online26. MATLAB (Matrix Laboratory) is a high-level language for numerical computation, visualization, and application development from MathWorks24, which is mostly used for data visualization and analysis, image processing, and computational biology.
1. Preparing NanospringCarver Files and Starting MATLAB on a LINUX PC
The following steps are designed for a general user to make use of the files provided online26.
2. Modifying and Using a Graphical User Interface (GUI) to the NanospringCarver Program
Follow the steps below using the files provided online26.
Figure 2: MATLAB user interface showing how to open MATLAB GUIDE.
Figure 3: MATLAB GUIDE interface initializing.
Figure 4: MATLAB GUIDE interface showing how to open an existing GUI figure file.
Figure 5: MATLAB GUIDE interface showing tools for modifying an existing GUI figure.
Figure 6: Screenshot of using GUI to create an example silica nanospring model.
Figure 7: MATLAB Command window feedback from GUI-based Nanosprings run.
Note: In the above example, the file “model” contains 5,176 atoms comprising the desired spring, one per line, with the first line giving the total number of atoms in the file. Each line defining an atom includes the atom ID, atom type, and x, y, z coordinates of that atom.
3. Verifying NanospringCarver Results in an Open-source Visualizer19
The following steps are designed for a general user to visualize and verify the output spring models created by NanospringCarver.
4. Using NanospringCarver Results in MD Tensile Simulations of Nanosprings
The following steps are summarized for a general user to use the spring models created by NanospringCarver as input to a conventional open-source MD code32.
Figure 8: Screenshot of a silica nanospring during tensile simulation (see also Animated Figure 1).
The atomistic nanoribbon models created with the first computational procedure (nanoribbons code) and their associated dimensions are shown in Figure 9. The resulting nanospring models using the second computational procedure (nanosprings code) and associated dimensions are shown in Figure 10.
Figure 9. Atomistic model of a silica nanoribbon with desired dimensions: r (nanoribbon radius) = 1.07 nm, R (radius of helix) = 5.37 nm, and p (pitch) = 7.16 nm. Snapshots illustrate distinct views of the nanostructure: (a) top view, (b) lateral view, (c) lateral view with additional rotation, and (d)-(f) diagonal views. The SiO2 nanoribbon model contains 3,354 atoms. The total ribbon height H is 14.1 nm23.
Figure 10. Atomistic model of a silica nanospring with specified dimensions: r (wire radius) = 1.07 nm, R (radius of helix) = 4.29 nm, and p (pitch) = 4.29 nm. Snapshots show different views of the nanospring model: (a) top view, (b) lateral view, (c) lateral view with additional forward rotation, and (d)-(f) diagonal views. The SiO2 nanospring model consists of 21,246 atoms. The total spring height H is 14.32 nm 23.
The range of nanoribbon and nanospring dimensions generated with both codes was ample (r < 3.75 nm, R < 9 nm, and p < 12.57 nm). Each of the above methods offers a unique way to create silica nanosprings and nanoribbons suitable for atomistic simulations. Both methods are flexible and can be adapted to produce different helical structures independent of the material, which makes them highly useful and versatile.
Animated Figure 1. Silica nanospring during tensile simulation.
Modification of the original approach to create nanohelical structures led to the development of two distinct codes to allow creation of both nanoribbons and nanosprings from an initial bulk silica glass MD model. The verification of the silica nanoribbon and nanospring models was pursued using different software packages19-20, which confirmed their dimensional accuracy within the measurement capability of the programs. Comparison between nanosprings and nanoribbons was also performed by overlaying the models from different sides and angles, which resulted in additional geometry verification. Both computational methods developed in this project created helical nanostructures in a distinct way, with added value due to their scalability for use with any bulk material model size and potential use in modeling nanohelical structures from other materials. The resultant models presented here showed there are no detectable artifacts (atoms missing from the desired nanohelical structure) generated using either method. In addition, the computational methods developed in this work are flexible for creating right-handed or left-handed helical nanostructures, simply by inverting the order of the sine and cosine functions defining the helix. Future applications of this method will include scaling to larger helical structures allowing extended parameter variation, and exploration of use with different initial materials.
Limitations of this method include dimensional restrictions on the created nanohelices depending on the initial bulk silica model used, which can involve significant computing resources as the model size increases. As currently implemented, the nanoribbon or nanospring height will extend to the size of the original bulk model. The first computational method generates accurate nanoribbon models for a range of parameters when the pitch value is greater than 7.16 nm and the radius of the helical wire is greater than 10% of the shortest dimension of the “bulk” silica glass structure. The second computational method generates accurate nanospring models without parameter limitation. This is particularly important for conducting MD simulations where readily available atomistic nanostructural models are needed to investigate different size conditions.
A critical step in the protocol would be to verify on first use of a particular initial MD bulk material model that the minimum distance between the closest two atoms in the model has been determined and input correctly with the dimensional parameters. Additionally, care should be taken to ensure that requested helical dimensions do not exceed the bulk material model dimensions.
Technological advances have facilitated the creation and characterization of complex helical nanostructures such as oxide nanoribbons and nanosprings in the laboratory. These nanoscale structures have unique properties that require thorough investigation in order to realize their full potential for various applications. MD studies of the mechanical behavior of these helical structures require flexible codes which can easily and precisely create helical nanostructures, and subsequently make use of appropriate interatomic potentials and methods for predictive simulations. To fulfill this first requirement, accurate structural modeling codes were developed which will be used for large-scale MD compression simulations and experimental validation.
This method of creating MD silica glass (non-crystalline) nanohelical models is significant, as similar codes not readily available and other alternative approaches have been focused on crystalline nanostructures. This modeling effort has been expanded, with the resultant nanostructures used in MD simulation studies, which have led to a thesis focused on the elastic response of silica glass nanohelices under tensile loads23. Time-efficient simulation of nanostructures is a challenging problem, however new programming techniques and atomistic models are especially becoming important for predictive studies. This modeling technique is rapidly gaining interest and quickly becoming an efficient method for models which require high performance computing. Future academic efforts will likely include the adaptation of these codes for training computational researchers and in classroom exercises. Performing MD simulations to study the response of helical structures to different loading conditions is certainly feasible with these robust atomistic models. The success of future manufacturing using these nanostructures as building blocks will depend on understanding of their structure and properties, with implications on nanomanipulation and self-assembly processes. This work is a step toward understanding the mechanical behavior of such nanostructures using large-scale MD simulations, which can be potentially useful for designing nanodevices for a large number of applications.
The authors have nothing to disclose.
The authors want to thank Tim Allis at UC Merced for his assistance in this project. The NSF-COINS program at UCM supported (KAM) in an early part of this work. An NSF-BRIGE award supported co-authors (BND and KAM), providing funds for this work and travel expenses to conferences.
The research group wishes to acknowledge primarily the National Science Foundation for funding this work via a BRIGE award. This material is based upon work supported by the National Science Foundation under Grant No. 1032653.
MATLAB numerical computing software | Mathworks | http://www.mathworks.com/products/matlab/description1.html | See Protocol Introduction and Reference [24] |
NanospringCarver program code and files | UC Merced – open source | http://tinyurl.com/qame8dj | See Protocol Section 1 (Step 1.2) and Reference [26] |
MATLAB GUI files | UC Merced – open source | http://tinyurl.com/qame8dj | See Protocol Section 1 (Step 1.2) and Reference [26] |
Atomistic bulk glass input file | UC Merced – open source | http://tinyurl.com/qame8dj | See Protocol Section 1 (Step 1.2) and Reference [26] |
IFrIT visualization software | Open source software | http://sites.google.com/site/ifrithome/ | See Protocol Section 3 and Reference [19] |
LAMMPS molecular dynamics software | Open source software | http://www.lammps.sandia.gov/ | See Protocol Section 4 and Reference [32] |