Molecular mechanics is powerful tool for developing some of the fundamental bulk properties of nanostructures. It is shown in this chapter how many researchers and engineers have successfully used molecular mechanics, and the results they achieved as well as some of the challenges they faced. The intent of this chapter is not to provide new research findings but to lay out for the reader some of concepts for developing bulk properties of nanostructures using molecular mechanics and molecular dynamics with the cited references providing the details.
The great majority of the models that engineers use are continuum based. For example, concrete is made of particles of various sizes and in addition is often reinforced by steel rods. Yet engineers design concrete structures essentially as continua. Indeed, nearly all structures tend to be treated as a continuum. This makes it possible to use continuum mechanics, beam equations, plate and shell theory, and the finite element method.
The bulk properties of the continuum, such as its constitutive properties and its strength, have been traditionally derived from test, and standard test methods such as ASTM have been developed. Once the bulk properties are derived, they become input to computer codes such as finite element programs. The traditional testing approach has proven satisfactory for many material systems. For example, for many metals, databases of properties established by test have been established. These databases may provide mean test values as well as statistical information concerning their probabilistic scatter derived from the replicas tested. However, in the age of composite materials, the traditional approach of depending solely on test has become cumbersome. This is because composites present an essentially unlimited number of material systems, so databases are limited.
In the case of composites, instead of testing the composite for its properties, one may test the constituents for their properties and then use material laws and assumptions to derive the composite properties. However, even this approach has its difficulties because some of the constituents making up the composite can be challenging to test and these difficulties invariably translate into time and money, each of which are limited resources.
In this chapter, attention is focused on composites containing nanomaterials. The nanomaterials may take the form of carbon nanotubes (CNTs) (Fig. 1.1) or another nanostructure such as nanoplatelets (Fig. 1.2). A CNT may have polymers attached to its surface (Fig. 1.3) to enhance its bonding with a composite’s resin system. The process of enhancing a CNT’s ability to bond with the surrounding resin is called “functionalization” of the CNT. The functionalization may change some of the properties of the CNT for better or for worse.
As Valavala1 points out, nanostructures are very valuable to nanocomposites, particularly if they adhere well to the surrounding medium they are in. Exploring whether this is taking place may be best left to analysis rather than test since many cases will need to be considered and testing of nanostructures can be challenging. Validation would be left to test.
Many researchers, engineers, and others have sought to derive the properties of nanomaterials from molecular mechanics (MM) and there has been a large measure of success in doing so. The purpose of this chapter is to review some of the MM methodologies that have been developed and that can be used to derive the bulk properties of nanomaterials useful to nanocomposite engineering.
The intended reader of this chapter is the practicing engineer. It is not the intent of this chapter to provide derivations of formulas presented or to present detailed explanations of molecular chemistry or any new information that has not already been published. Rather, all equations and results in the chapter have been published previously and appropriate credit is rightfully given to the authors.
1.1.1 Modeling of the Atomistic Domain Using Molecular Mechanics and Dynamics
The molecular nanostructure is composed of many atoms. The most accurate approach, known to date, in modeling the nanostructure atomistic domain would be to do so using quantum mechanics. Quantum mechanics involves modeling electron densities based on Schrodinger’s equation. It would effectively model all the attractive and repelling forces in the nanostructure, including possib...
