SIMULATIONS AND MODELING FOR THE NANOSCALE

Uzi Landman
School of Physics
Georgia Institute of Technology
Atlanta, GA 30332-0430

Scientific Drivers

The everlasting desire to probe and understand natural phenomena with increasing spatial and temporal resolution, coupled with the trend toward device miniaturization and the technological and economical potentials of molecularly designed and nanoscale engineered and fabricated materials structures, motivate increasing research efforts pertaining to these issues.

The properties of materials depend on their chemical composition and on the degree (size) and state, form, dimensionality, and phase (structural, morphological, and thermodynamical) of aggregation. While materials properties are normally listed without reference to their size, it is expected, and indeed found, that their physical and chemical properties exhibit size-dependent evolutionary patterns (SEPs), ranging and bridging the molecular and condensed phase (bulk) regimes. The nature and origins of such SEPs of materials properties, which include structural, electronic, spectral, transport, magnetic, chemical, mechanical, and thermodynamical characteristics, are varied, depending on the cluster or nanostructure size and the pertinent length (or time) scale. Such property-dependent materials characteristics include the following:

We reiterate that the relevant operative length scales are materials- and property (functionality)-dependent and should be considered and examined in such context. Thus, for example, novel phenomena are exhibited in semiconductor structures at carrier lengths of tens of nanometers. On the other hand, electron exchange lengths governing cooperative magnetic response are in most magnetic materials on the order of a few lattice spacings requiring structural control of the material on this small scale.

Quantum size effects and consequently dependencies on size and shape occur when the size of a system becomes comparable to the characteristic length scale determining the coherence of the wave functions. Simple considerations show that qualitatively new size-dependent behavior and functionality of metallic systems (such as quantized electronic conductance) are expected to occur mostly for systems where at least one of the spatial dimensions is reduced to a scale of only up to several nanometers, while for semiconductors they may occur for larger systems (10 nm and above, due to small effective masses and large dielectric constants). Interestingly, theoretical studies in our laboratory have predicted, and recent experiments on nanowires have confirmed, that not only the electronic properties (room temperature conductance quantization, magnetotransport, and thermopower), but also the mechanical properties of such systems of reduced dimensions, are modified significantly -- that is, plastic deformations of metallic nanowires are characterized by order-of-magnitude larger yield stresses over bulk values.

Naturally, nanoclusters and nanostructures in this size range, and the physical and chemical functional specificity and selectivity that they possess, suggest they are ideal building blocks for two- and three-dimensional assembled superlattice structures. To maintain and utilize the basic and technological advantages offered by the size specificity and selectivity of nanoclusters, it is imperative that theoretical and experimental understanding be gained and implemented of the principles and methodologies of preparation and processing of cluster assembled materials, in macroscopic quantities and with high standards of size, structural, morphological, and shape uniformity.

In the above, new physical and chemical properties and selectivities originating from the size, dimensionality, and degree of aggregation of materials have been outlined. The ability to fabricate such nanostructures, coupled with the emergence and proliferation of proximal probes and atomic-scale simulation techniques, provide the impetus and means for theoretical and experimental investigations of nanometer-scale modifications, manipulations, and assembly of materials structures as components of devices and machine elements.

In particular, understanding the atomic and molecular processes occurring at the interface of two materials when they are brought together, separated, or moved with respect to each other, is central to many technological problems, including adhesion, contact formation, friction, wear, lubrication, nanoindentation, and machining. For example, molecular dynamics computer simulations have predicted the occurrence of an interfacial "jump-to-contact" instability when two materials surfaces are brought to close proximity (about 0.5 nm) leading to formation of nanoscale adhesive junctions whose resistance to shear is the cause of energy dissipation, that is, nanoscale friction and wear. Furthermore, preventing the formation of such junctions requires that the narrow spacing between the approaching surfaces be lubricated (as, for example, in the case of a read/write head and the surface of an ultrahigh-density information storage device) by a very thin lubricating film. It has been found through both theoretical simulations and experiments that the energetic, structural, dynamic, thermodynamic, and rheological properties of molecular lubricating liquids differ greatly under nanoscale confinements from their bulk behavior. For example, such highly confined liquids (globular or chains) organize into layered structures, forming strata parallel to the confining solid surfaces; are capable of supporting load; may undergo dynamic phase changes; and show rheological, and in particular, visco-elastohydrodynamic response characteristics that depend on the degree of confinement, the nature of the interfaces, the strength of bonding to the surfaces, the molecular architecture of the lubricant (straight vs. branched chains), and the shear velocities.

Methodologies and Perspectives

Investigations of nanoscale materials structures present an immense theoretical challenge. Underlying the theoretical difficulties is the reduced (finite) size of the nanostructural components, which is intermediate between the condensed-phase and molecular regimes. This renders inadequate the well-established solid state approaches and methodologies constructed for extended (often translationally invariant) systems. At the same time, such systems are too large for applications of techniques that are most useful in studies of molecular size systems. The atomistic nature of nanoscale materials systems and methods for their manipulation require development of atomistic theoretical approaches for studies pertaining to energetics, structure, stability, thermodynamics, physical properties (optical, phononic, magnetic, and transport), chemical reactivity, and mechanical characteristics (response, deformations, and rheology), as well as for investigations of mechanisms of nanostructure formation (including self-organization and self-assembly) and the response of such materials to external fields (electric, magnetic, optical, and mechanical).

These considerations have led to development of theoretical atomistic simulations and modeling methodologies that allow investigations of the issues mentioned above with refined spatial and temporal resolution. Among the methodologies we note particularly those based on classical and quantum molecular dynamics (MD) simulations, where the appropriate (atomistic) equations of motion for a system of interacting particles are integrated, and the resulting phase-space trajectories are analyzed (numerically as well as in animated form). In classical MD simulations the interatomic interaction potentials are constructed using semi-empirical data and/or fitting to quantum-chemical calculations. More recently first-principles molecular dynamics (FPMD) methods have been implemented, where the interactions are evaluated concurrently with the atomic motions through self-consistent solution of the many-electron Schrödinger equation. Such FPMD techniques extend our capabilities to investigate systems and phenomena involving electronic rearrangements and chemical transformations, as well as allowing studies of electronic spectral and transport properties. Other simulation methodologies include classical and quantum Monte Carlo techniques and methods for structural optimization (simulated annealing and genetic algorithms).

The emergence of atomistic simulations as a principal theoretical methodology in nanoscience (as well as in other disciplines) is correlated with progress in understanding the nature of bonding and cohesion in complex materials, algorithmic advances, and a symbiosis with novel computer architectures that allow simulations of ever larger systems (up to several million atoms) and for longer time periods.

Current methodologies have demonstrated interpretive and predictive capabilities in several areas: atomic and molecular clusters, nanocrystals and their assemblies, nanowires, surface-supported structures, atomic-scale contacts and switches, atomic-scale surface manipulations, thin film growth, transport in reduced dimensions, interfacial systems, nanotribology, lubrication and molecular scale thin film rheology.

It is imperative, however, that future efforts be focused on development of simulation methodologies and algorithms that will allow extension of such studies to longer time scales. Such approaches may include embedding schemes, renormalization techniques, and methods based on variable/adaptable spatial and temporal resolutions. Progress on these issues, which form "grand challenges" in computational materials science, requires focused timely initiative on a national scale. Indeed, several countries have recognized the critical importance of this challenge and have established major initiatives targeted at its resolution. Already, large-scale programs have been established in Japan and in Europe through creation of institutional and multi-institutional focused programs and consortia.

Selected Literature

Barnett, R.N., and U. Landman. 1997. Cluster-derived structures and conductance fluctuations in nanowires. Nature. In press.

Bhushan, B., J.N. Israelashvili, and U. Landman. 1995. Nanotribology: Friction, wear and lubrication at the atomic scale. Nature 374: 607.

Blöchl, P.E., C. Joachim, and A.J. Fisher, eds. 1993. Computations for the nano-scale. Dordrecht: Kluwer.

Landman, U., and W.D. Luedtke. 1996. Atomistic dynamics of interfacial prosesses: Films, junctions and nanostructures. Appl. Surf. Sci. 92: 237.

Landman, U., W.D. Luedtke, N.A. Burnham, and R.J. Colton. 1990. Atomistic mechanics and dynamics of adhesion, nanoindentation, and fracture. Science 248: 454.

Landman, U., W.D. Luedtke, and J. Gao. 1996. Atomic-scale issues in tribology: Interfacial junctions and nano-elastohydrodynamics. Langmuir 12: 4514.

Landman, U., W.D. Luedtke, J. Ouyang, and T.K. Xia. 1993. Nanotribology and the stability of nanostructures. Jpn. J. Appl. Phys. 32: 1444.

Landman, U., W.D. Luedtke, B.E. Salisbury, and A.L. Whetten. 1996. Reversible manipulations of room temperature mechanical and quantum transport properties in nanowire junctions. Phys. Rev. Lett. 77: 1362.

Luedtke, W.D., and U. Landman. 1996. Structure, dynamics, and thermodynamics of passivated gold nanocrystallites and their assemblies. J. Phys. Chem. 100: 13323.

Martin, T.P., ed. 1996. Large clusters of atoms and molecules. Dordrecht: Kluwer.

Serena, P., ed. 1997. Nanowires. Dordrecht: Kluwer.

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Published: January 1998; WTEC Hyper-Librarian