Fundamentals of Molecular Dynamics (MD) Simulations and Tools for Examining Nanostructured Materials

In chemistry, physics, biochemistry, and materials sciences, computer simulations are useful methods to examine the nanostructures and dynamics in nanoscopic levels. Molecular dynamics simulations (MD) are one of the principal methods of computational science. In this method, positions and trajectories of particles (atoms, molecules) are determined by solving the equation of motion within a computer. In this book, our discussion is mainly focused on classical MD [1-3] using the potential parameters based on the ab initio calculations. Nowadays, ab initio MD simulations such as the Car-Parrinello method [4, 5] using density functional theory have become important. However, the application of them for complex materials with covering the suitable length and time scales is not necessarily easy, especially in the ab initio method, which requires more resources and times for calculations. Common problems for these methods will be discussed.

In this chapter, after a short description of the fundamentals of MD simulations, several functions and tools useful for the

Molecular Dynamics of Nanostructures and Nanoionics: Simulations in Complex Systems Junko Habasaki

Copyright © 2021 Jenny Stanford Publishing Pte. Ltd.

ISBN 978-981-4800-77-8 (Hardcover), 978-1-003-04490-1 (eBook) www.jennystanford.com characterization of the ionic system as well as nanostructured materials are introduced with examples of a molten NaCl system. From these functions, one can determine several length scales relevant to ionic systems.

Fractal dimension analyses are useful tools to examine the complexity of structures and dynamics. Then results of fractal dimension analyses of density profiles used for characterization of structures in lithium silicates and ionic liquid (IL), (1-ethyl 3-methyl imidazolium nitrate, EMIM-N03) will be shown. Dynamics of these systems are explained by the multifractal nature of the profile and the existence of corresponding two-length scale regions of trajectories of walks. Namely, through multifractal analyses of density profiles and walks, structures can be connected to dynamics. This kind of analysis provides a common framework for the characterization of more complex systems.

Nanostructured systems often consist of networks of constituents and hence, other approaches introduced here are analyses of network structures found in silicates and related systems. Several tools to characterize networks will be explained.

Of course, some of these methods are applicable to simulations by other methods as well as experimental results.

Purpose of MD Simulations

Comparison of results of experiments and MD is an important task; however, the purposes of the MD simulations are not necessarily just reproducing systems. Some of the possible purposes of MD simulations (or other simulations) are classified as follows:

  • 1. They can be used to reproduce structures and properties to mimic a realistic system for comparison with experiments and further examination of details of structures and dynamics. It is also useful to examine the morphology of nanostructures and mechanisms underlying them. Of course, careful judgment is required if it can be comparable or substitute for other experimental methods.
  • 2. They can be used to examine essential physics or chemistry underlying the behaviors of the system both at microscopic and macroscopic levels. Transport properties, structures, and mechanical properties under several situations with modified shapes and/or sizes in different states can be examined. One can examine what happens if the potential models are modified or coarse-grained. Adequate modeling of the system by MD simulations itself is useful to understand the characteristics of the systems.
  • 3. It may be worth mentioning that simulations are highly safe and have a low environmental burden. They can be used to examine the system, which is difficult to treat in experimental methods due to its toxicity, explosive nature, deliquescence, etc.
  • 4. They can be used to examine the system under extreme conditions, such as high pressure and high temperature, which is difficult to treat in experiments.
  • 5. They can be used to design new materials with modifying components, mass, size of particles, etc., or considering new combinations.
  • 6. They can be used for the screening of a suitable system and/or material to fit the usage of them. For example, they are used for a survey of candidates for pharmaceuticals.
  • 7. If the quality of the potential model (for both parameters and functional forms) used is good enough, the model has a power of prediction. Therefore, simulations can be used for the predictions of structures and properties of materials including new materials.
  • 8. They can be used to examine the effects of modification and/or of introducing the complexity of the systems, such as the mixing of components.
  • 9. Simulations are also used to examine the validity of concepts and/or theories as well. If the existent theory or model is not adequate for each purpose, simulations can add useful knowledge, suggestions, answers, and/or new questions.

These purposes are not necessarily separable. For example, a modification of the transport properties of ions by porosity treated in this book is related to 1, 2, 7, and 8. Also, they are not limited to the list mentioned above.

Thus, MD simulations are useful for both applications and more fundamental understanding of physical and/or chemical concepts.

One of the systems covered in this book is the nanocolloidal silica-water-salt system in fully atomistic simulations, although only the coarse-grained level ones tend to be used in colloidal science. The latter treatment is probably coming from the large size difference between colloids and solvent molecule; however, such coarse-gaining is not necessarily suitable for the treatment of nanostructures and dynamics related to them. Since both system size and time scale required to simulate such systems are quite large, it is challenging to do atomistic type simulations.

Once details of atomistic or molecular level understandings are obtained enough, some coarse-grained approaches are also useful. Sometimes simulations of different fining levels are connected to form more macroscopic systems.

Treatment of Complex Structures

In many applications, systems are mixtures of several components and/or the part of more complicated systems. Further treatment of the system having hierarchy including several materials will be necessary.

There are different approaches to treat complex structures. Here these situations are classified as follows for typical situations:

  • 1. Direct simulations, including all components and substructures of the system in the simulations. If it is possible, it includes the interaction among components and hierarchy structures without assumptions for the rules of the formation of structures.
  • 2. The situation is like 1 but each component is substituted by more coarse-grained level ones.
  • 3. Each component is formed in the atomistic-level simulations (in both classical and ab initio methods can be used here). These components are combined with some rules. If each structure has a simple role as a module of electrical circuits such as resistance, condenser, etc., this kind of approach is possible.
  • 4. Several components form higher levels of substructures.

For applications, simulations of more coarse-grained levels might be necessary in several cases. Combinations of methods with several different levels of coarse-graining can be used.

The selection of the methods depends on the purpose of the simulations and may be different case by case. The following consideration appears to be useful for choosing a suitable method.

The coarse-grained systems are useful in the following situations. If feedback from other components is correctly included, the coarse-grained level approach will be successful. When the time scale of the event within a component is considerably different from the event among components, it can avoid the undesired coupling among components. In these cases, key features to select the suitable approaches depend on the magnitude of the coupling or interaction among substructures or domains.

Let's consider the following examples to determine what levels of simulations are suitable. First, the situation to treat ionic motion is considered. When we consider fast ionic conducting systems, the motion of fast ions is known to be de-coupled with the motion of networks forming the ion channels. However, cages of the ions must be flexible for higher ionic conductive systems, and therefore it is difficult to separate or coarse-grained the network part and ions to represent the behavior of ions.

That is, for ionic motions, atomistic-level simulations seem to be required to treat the different kinds of couplings between ions and the matrix.

The treatment with different levels of coarse-graining seems to be useful for some cases to treat ILs [6], which have a more complex inner structure of ions. Ions can be treated as large ions without structures or ions with simplified inner structures.

Another example is the gelation of colloidal systems discussed in Chapters 8 and 9. During atomistic simulations, structures of water are found to be changed. This means that approximation by continuum solvents is not good enough to represent such situations.

If there are no interactions among different levels of hierarchy structures, simulation systems with switching the different levels can be used for complex systems.

Molecular Dynamics Methods Used for Material Designs

In this book, we focus on the classical molecular dynamics simulations using potential parameters based on the ab initio calculations, although sometimes Monte Carlo simulations and ab initio MD simulations such as Car-Parrinello methods and combinations of these methods are referred to. The merit of the first approach is the applicability of relatively larger systems, long time scales with keeping the characteristics of essential properties obtained by ab initio methods. Due to these characteristics, methods can be used for the designing of materials for more complex systems with hierarchy and with more components. One major problem of this approach is that one may encounter the situation of a missing parameter, with an increasing number of components and their combinations. It may be necessary to develop new parameter sets suitable for each purpose. Some parameter sets with considering transferability and/or consistency might be found in the literature. Even in this case, it is desirable to check the applicability and suitability in light of the purpose.

 
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