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1.4.2. Levels of abstraction and approximation

In an ideal world, chemists would be able to predict the behavior of molecules by applying quantum electrodynamics (QED) to suitably defined assemblages of nuclei and electrons, and engineers would be able to predict automotive performance in the same manner. In this regard, the world is far from ideal. Although no experiment has yet shown an imperfection in QED as a description of the properties of ordinary matter (setting nuclear and gravitational interactions aside), it is computationally intractable as a description even of small molecules. In the real world, chemists and engineers describe systems using a hierarchy of levels of abstraction and approximation (Table 1.4). It is worth surveying this hierarchy because it provides a framework for practical analysis.

Table 1.4. Levels of abstraction and approximation in molecular systems engineering.

As discussed in Chapter 3, the most rigorous models ordinarily used by chemists apply ab initio molecular orbital methods; these approximate the Schrödinger equation, which approximates the Dirac equation, which approximates QED, which approximates the unknown exact, universal laws of physics. In describing the mechanical properties of large molecular structures, however, chemists abandon molecular orbital methods in favor of molecular mechanics methods of more limited applicability but lower computational cost; these too are discussed in Chapter 3.

At the upper levels of the hierarchy, engineers set objectives in terms of system behavior and use these objectives to determine requirements for subsystem behavior (this can proceed through several layers of subsystems). Systems are commonly analyzed in terms of subsystem capabilities, which are analyzed in terms of lumped-component models, which in turn are analyzed in terms of continuum models. For example, a modern computer is described by its subsystems — processor, memory, disk, bus, cooling, power supply, and so forth. A processor (give or take some intermediate levels) is described as an interconnected network of discrete transistors and other lumped components. Transistors are described by continuum models that consider gate geometries, dopant distributions, electron transport, and so forth. Individual atoms and electrons are neglected in describing transistors, and one never describes a computer by describing electron transport within transistors.

Nanomechanical systems are subject to a similar analysis, describing system-level objectives served by subsystem capabilities implemented using lumped components. Continuum models, however, become problematic on the nanometer scale. Chapter 9 develops bounded continuum models that take sufficient account of surface effects to enable the analysis of a broad range of nanomechanical designs in less than atomic detail. To design the smallest devices, however, detailed molecular mechanics models are necessary, and to provide a first-principles analysis of a mechanochemical process, there is no substitute for molecular orbital methods.

1.4.3. Scope and assumptions

The present volume adheres to design constraints that may not limit future engineering practice. Each constraint excludes possibilities that are presently difficult to analyze, but that may prove both feasible and desirable. The following assumptions and limitations are thus ° conservative, resulting in what are likely to be underestimates of future capabilities:

Figure 1.3. Diamondoid structures are a subset of covalently bonded structures, which are a subset of the broad range of solid structures

a.A narrow range of structures. From the broad range of materials (metals, ionic crystals, molecular crystals, polymers, etc.), the present work selects the class of diamondoid ° covalent solids as its focus (Section 9.3.1f). These structures form a small subset of those that are possible (Figure 1.3), and contain atoms drawn chiefly from the shaded region of Figure 1.4. Diamond itself is the strongest and stiffest structure presently known at ordinary pressures (Kelly, 1973), making it and similar materials attractive on engineering grounds. Since many components can be regarded as polycyclic organic molecules, much of the vast base of knowledge developed by organic chemists is immediately applicable. Small components are subject to large surface effects, but typical organic molecules are, in effect, all surface; accordingly, surface effects are an integral part of molecular models.

Figure 1.4. Periodic table of the atoms, with cells shaded to indicate those of greatest importance to nanomechanical design: hydrogen (H), carbon (C), nitrogen (N), oxygen (O), fluorine (F), silicon (Si), phosphorus (P), sulfur (S), and chlorine (Cl). Other elements have applications, but few of the structures discussed in the following chapters contain them. [H is more often placed above lithium (Li) than above F, but hydrocarbons resemble the stable fluorocarbons far more than they do the reactive lithiocarbons. Like F, H is only one electron short of a closed-shell configuration.]

b. No nanoelectronic devices. On a macroscale, mechanical systems are quite distinct from electronic systems: they involve the motion of materials, rather than of electrons and electromagnetic fields. On a nanoscale, mechanical motions are identified with the displacements of nuclei, but electronic activity can cause such motions. Nevertheless, many systems (e.g., the bearing in Figure 1.1) can be described by molecular mechanics models that take no explicit account of electronic degrees of freedom, instead subsuming them into a potential energy function (Chapter 3) defined in terms of the positions of nuclei. This volume focuses on mechanical systems of this sort.

Some systems are strongly electronic in character, relying on changes of electronic state to change other electronic states, with the associated nuclear motions being of small amplitude. Molecular nanotechnologies will surely include nanometer-scale electronic devices exploiting quantum phenomena to achieve (for example) switching and computation. Research relevant to this class of devices is already in progress.

Although nanoelectronic devices are likely to be important products of molecular manufacturing, they fall beyond the scope of the present work. There are several reasons for this. First, the analytical methods required for quantum electronics differ from those required for molecular machinery; including them would have made this volume larger and later. Second, these analytical methods require approximations that frequently render the results dubious, reducing their value as a premise for further reasoning (the existence in 1992 of at least three competing classes of theories to explain high-temperature superconductivity, observed and studied in cuprates since 1987, suggests the magnitude of the difficulties). Finally, while nanomechanical devices can build nanoelectronic devices, the latter cannot return the favor; thus, nanomechanical devices are in a technological sense more fundamental. Accordingly, the nanocomputers discussed in Chapter 12 are based on mechanical devices, although electronic devices will surely permit greater speed.

Chapter 11 briefly discusses nanoscale electromechanical systems. These use conductors, insulators, and tunneling junctions as components of motors, actuators, and switches. Quantum phenomena are important in nanoscale electromechanical systems, but the gross results (switching, interconversion of electrical and mechanical energy) do not rely on subtle quantum effects. Finally, despite their likely utility, machine-phase electrochemical processes are mentioned only in passing.

c. Machine-phase chemistry. Because it can guide reactions (and can avoid most competing reactions) by tightly constraining molecular motions, machine-phase chemistry can be simpler, in some respects, than is solution-phase chemistry. Mechanosynthesis and other operations can be conducted by systems of molecular machines immersed in a solution environment, and there are sometimes advantages to doing so. These less controlled, more complex chemical systems fall beyond the scope of the present work, save for the discussion of implementation strategies in Part III.

d. Room temperature processes. Reduced temperatures decrease thermally excited displacements (Chapter 5), thermal damage rates (Chapter 6), and phonon-mediated drag (Chapter 7). The opportunities and problems presented by low-temperature systems are nonetheless not explored in the present work. Operation at high temperatures is desirable in some circumstances, and can facilitate both desired and undesired chemical reactions, but discussions of the associated technological opportunities and problems are likewise omitted.

e. No photochemistry. Photochemical damage mechanisms are discussed in Section 6.5. Design of molecular machines for photochemical damage resistance is an important challenge, but for simplicity the following will instead assume that devices operate in optically shielded environments. Deliberate use of photochemistry is mentioned only in passing.

f. The single-point failure assumption. The design of small components that can tolerate atomic-scale damage and defects is worthy of attention, but the following will instead assume that any such flaw causes component-level (and usually subsystem-level) failure, unless the components are relatively large. The use of redundant systems to achieve damage tolerance is proposed and analyzed only at higher levels of system organization. Diverse damage mechanisms are reviewed and modeled in Chapter 6.


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