Mat Res Innovat (2001) 5:12–14

© Springer-Verlag 2001

ORIGINAL ARTICLE

John J. Gilman

Nanotechnology

Received: 16 October 2000 / Reviewed and accepted: 23 January 2001

Nanotechnology. What a great word with such an impressive idea underlying it! If things are made smaller, they get better! It is reminiscent of the golden age of chemical engineering when “economy of scale’’ was discovered. The idea then was that the larger the chemical plant, the smaller the cost of manufacturing a product. Imagine the leverage! By using a sufficiently large plant, a product could be made for no cost. Such a plant would be better than a monopoly. Now the idea is that materials and operations will be better if done on a small scale; such as a nanometer scale which is 0.001 as large as a micrometer, or about five atomic diameters. Thus a nanoscale particle consists of about 125 atoms; and if made of gold, would cost only about 6×10–19 dollars at the present market price of gold. Quite inexpensive! In the nanotechnology literature it is stated by several authors that carbon “nanotubes’’ have elastic stiffnesses (Y = Young’s modulus) of 1.25 TPa, or 1250 GPa = 12.5 Mbar. This may be compared with steel of modulus = 2 Mbar. Six times as stiff as steel! Impressive! However, compared with diamond (maximum stiffness = 1.08 TPa) it is not so impressive; especially when the approximate isotropy of diamond is taken into account together with the fact that specimens about 105 times larger are available. Also, claiming superiority over steel is specious in the light of the cost difference; roughly 1024 $ / # for strong tubes compared with about 5 cents / # for semi-finished steel (a factor of 2×1025). If nano- is good imagine how much better picowould be. Perhaps neutrons can be crystallized to form a new class of materials. A smaller step, but probably easier to achieve, would be to crystallize hydrogen atoms to form metastable metallic hydrogen. Since bond energies scale approximately with volume, and hydrogen atoms are about half as large as carbon atoms, metallic hydroJ.J. Gilman (✉) Materials Science and Engineering, University of California at Los Angeles, Los Angeles, California 90095, USA

gen might be 50 times as strong as steel! And, if destabilized, what a terrific explosive it would make! Strength properties of polycrystalline materials (both metals and ceramics) are known to depend on the average crystallite size in a characteristic way. That is, yield stresses and fracture stresses tend to increase inversely with the square root of the crystallite size. Therefore, by decreasing the crystallite size of any particular material from a millimeter to a nanometer should increase its strength by a factor of 1000. Since the feasible size of aerospace structures scale approximately with the maximum allowable stress, perhaps airplanes capable of carrying 1000, or more, passengers could be built with such materials. A most exciting prospect of nanotechnology is nanocomputers. Computers based on micrometer circuit elements weigh about five pounds and occupy about 100 cubic inches of space (this includes the power supply, and the display). By using superconducting circuit elements, solar drives, and direct output to the nerves of the user’s brain, the soon to come (ten years or so) nanocomputers will occupy 0.1 cubic inches, and weigh only 0.2 pounds (3 ounces). The times are surely changing. So far this essay has consisted of science fiction. Now it will touch some facts.

The utility of nanotechnology The number of substances in the Universe is essentially limitless. By comparison, the number of useful materials is quite small. And the number of useful materials systems with nanometer dimensions is vanishingly small. The enthusiasts for nanotechnology often use MEMS technology as an example of usefulness, but this is not valid since the dimensions of MEMS devices are in the micron range, and therefore belong to the microtechnology category (a factor of 1000× larger). The only valid measure of utility in this case is an economic one. That is, the marketplace. The reason is

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that taxes are paying for the development of the technology, and they are part of the economic system. Therefore, a new material, process, or device, must offer a net increase in economic utility if it is to be considered successful. Ideally this can be expressed in monetary terms, but this is sometimes inadequate; or fallacious. For entities that relate to the basic needs of everyday living, utility closely parallels prices. Thus the utility of a five pound bag of potatoes is determined by its price. Its demand curve (price/pound vs. pounds consumed per unit time) is elastic (the lower the price, the greater the rate of consumption). For a product like luxury automobiles, one of many „vanity“ markets, Lexus cars have nearly the same utility (ability to provide transportation) as Camrys yet they cost more than twice as much. Such a market is relatively inelastic. For critical products such as prescription medicines, markets are quite inelastic. Thus, in the presence of an attack of gout, I will pay almost any price for a tablet of anti-inflamatory Indomethacin. Clearly utility has both objective and subjective aspects. Nevertheless, it can usually be identified as a real contribution to some aspect of well-being. Absolute utility is not a particularly useful quantity because, for instance, the utility of a very large project such as a new bridge cannot be sensibly compared with the utility of a small project such as a new house. Therefore, the quantity called marginal utility is used; usually in the form of “Bernoulli’s hypothesis’’. That is, the marginal utility, dU(x), equals the logarithmic derivative of x. Thus: dU = dx / x. In other words, an incremental change in utility (as measured in terms of some parameter, x; say dollars) is equal to the fractional change in the parameter. It is easy to see that this is more useful than U itself. Firstly, the marginal utility of a quantity of value now depends on the context. As it should. For example, the marginal utility of one dollar is vastly smaller in the bank account of Warren Buffet than it is in mine. A factor of ten thousand or so smaller. The marginal utility of one large bridge is greater than that of one automobile, and so on. Furthermore, marginal utilities can be compared, and ranked, whereas absolute ones cannot. Comparison of them suggests that equilibrium is achieved between two products, or processes, when the marginal utility of one (dU1) equals that of the other (dU2). If dU2 is larger than dU1, then the product (or process) that it represents will grow at the expense of the one represented by dU1. In other words, product 2 will substitute for product 1. Furthermore, the driving force will be proportional to the difference between dU2 and dU1. This is a problem for electric automobiles, for example. Their marginal utility is not significantly greater than that of gasoline powered automobiles, but manufacturing and operating costs are much greater. It was also a problem for nuclear electric power. The difference in marginal utility between nuclear boilers and coal-fired boilers was only slightly greater than zero (this may change with time, of course). Therefore, a relatively small increase in the environmental expenses of nuclear boilers (a decrease in their marginal

utilities) stopped further construction of them (in the USA). It is also of interest to keep in mind the way in which utility develops with time. This is the integral of the marginal utility, and is proportional to the logarithm of x. Thus for constant increments, dx per year, the integral increases logarithmically with time, but the marginal utility decreases because x itself keeps getting larger. Therefore, the utility for a given material may remain larger than those of its its competitors, but the difference may be declining. All in all, the Bernoulli definition offers several useful properties. So what does marginal utility have to do with nanotechnology? The answer is everything if the research is put in the context of economic competitiveness; or if one wishes to understand the difference between materials and substances; or the difference between processes and techniques. This does not apply, of course, if the research context is that of the expansion of cultural knowledge. Although culture and economic competition are not completely independent, they are sufficiently different to warrant separate discussions, separate funding philosophies, and so on. In part, the use of different categories, is simply to avoid the difficulty of defining the marginal utility of culture. I find it discouraging, and sometimes annoying, that the concept of marginal utility is rarely applied in the field of materials research. Neither researchers themselves, nor the distributors of the supporting funds derived from various forms of taxes apply the utility concept. This has the effect of putting much of the research, and many of the researchers at odds with society at large since capitalism is largely based on the concept of marginal utility. When marginal utility is ignored the belief tends to develop in the general society that research has little, or no, utility. For every 100 projects that have technical merit, there are only about 10 that have marginal utility, and only about one that has substantial marginal utility. In order for a substance to qualify as a material, it seems to me that it should have sufficient marginal utility to be used in commercial artifacts. Thus, the number of substances that exist is very large compared with the number of materials. In order for this definition to be sensible, there must be “probationary materials’’, of course. That is, substances in the process of becoming materials. Also, with time it is to be expected that there will be a flux of substances becoming materials, and an inverse flux of materials becoming substances. Although there is no time independent definition of a material, its definition in terms of marginal utility should be reasonably clear. Furthermore, it is clear that not every substance in the universe is a material. A corollary is that not all studies of substances qualify as materials research. To be a legitimate materials research project, a study should be aimed at finding a substance with positive marginal utility. Other studies belong to dilettantism. Currently, all too many studies are passed off as “science’’,

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when they do not meet the utility criterion. However, to qualify as science they need to be part of a search for an invariant of some kind; not a completely arbitrary choice. Parallel to materials research, work on processes is often done. Here again, there are two categories of activities: those with super-critical marginal utilities (real processes); and those with sub-critical marginal utilities (techniques). In the technique category are activities that are too expensive to be practiced commercially. In some cases a technique may be a potential process, but needs further development. Getting from a technique to a process with substantial marginal utility can be a difficult and costly task. Therefore, invention of a technique is only the very beginning of the effort needed to convert the technique into a process with appreciable marginal utility. This being true, the size of the investment made to create a new sub-

stance, or technique, should be relatively small because the cost of converting the new substance into a real material, or a technique into a real process, can be expected to be very much larger (about a factor of ten). Current research policy does not follow the simple principles just outlined. The plan is to spend large amounts of money at the beginning of the innovation process rather than at the end. This money is unlikely to ever be recovered. Why is this the policy? Because the policy is set by politics rather than economic logic. The dangers of doing this have been discussed in detail in the book by Terence Kealey (The Economic Laws of Scientific Research, St. Martin’s Press, New York, 1996). The astute reader will also recognize the danger from the exaggerations of the first several paragraphs of this essay. These are similar to the statements to be found in the science news (fiction) literature.