Tangible Nanomoney

This paper was written in December 1999 and was originally published in the July 2000 issue of Nanotechnology Industries Newsletter. The correct literature citation and URL for this document are:

Robert A. Freitas Jr., "Tangible Nanomoney," Nanotechnology Industries Newsletter, Issue II, July 2000, pp. 2-11.

http://www.rfreitas.com/Nano/TangibleNanomoney.htm http://www.zyvex.com/Publications/papers/nanomoney (alternate)

Robert Freitas, author of the recently-published groundbreaking technical book Nanomedicine, reflects on how we might pay for very advanced medicine -- or indeed, pay for anything at all -- in a world where artificial molecular machine systems are commonplace. Hint: Perhaps we'll be using coins made of tantalum or ununquadium!

I'm sometimes asked how we're going to pay for nanomedicine [1], once medical nanorobotic treatments become available. Surely all this advanced technology will be so expensive that only the rich will be able to afford it? I usually reply that it is a rational and defensible expectation that nanomedicine may actually cost far less, per treatment, than today's traditional medical interventions. But these questions about costs have gotten me thinking. How will we pay for anything in a future world of ubiquitous artificial molecular machine systems?

I won't try to pass judgment on whether electronic money or some other intangible form of currency might be sufficient for all necessary economic purposes. I'll simply note that tangible money has always played a role in human commerce, so for now the safest assumption is that tangibles will probably continue to do so, though perhaps with somewhat lesser importance in the overall economy.

What Is Money?

1. Money should be an efficient store of value, having high value per unit volume or per unit mass.
2. Money should be available in small enough physical sizes to be readily portable, even in the largest denominations, by human users, thus facilitating exchange transactions and specie warehousing.
3. Money should be physically stable for a duration of time spanning at least the maximum intended period of transactions and/or the maximum value storage horizon.
4. Money should not be inherently physically dangerous to its owner (e.g. radioactive, poisonous, explosive, etc.).

5. Money should be difficult to counterfeit.
6. Money should be difficult or impossible to replicate at a cost less than its cost of manufacture even by the most efficient means possible. That is, production costs (aka "intrinsic value") should approximate face value; seigniorage should be minimal to nil.
7. Money should be immediately recognizable as the intended denomination of the intended specie. Once revealed, the intrinsic value of the specie should be difficult to disguise. If unrevealed, the specie should still be compact enough to hide (from thieves or tax authorities) on one's person or elsewhere; see (2) above.
8. Money should be self-validating by its own physical form, and not rely upon any legalistic governmental imprimatur, easily-altered surface stamping, or monopoly minting authority to partake of value (e.g., no "fiat" specie).

The same objection applies to any specimen of complexly structured ordinary matter, such as sculpted gemstones [5] or other 3-dimensional art pieces constructed with nanoscale features, or atomically-encoded data storage blocks. With a mature nanotechnology, many if not most physically stable 3-D atomic structures should become accessible to cheap fabrication, and pure information has different values in different contexts. If we someday conceive of exotic molecular structures that cannot be manufactured by any known molecular assembler technology, then by definition these structures also cannot be manufactured by biological or other natural (e.g. geological) self-assembly processes -- as these processes may be regarded as subsets of the nanotechnology toolchest. Hence such exotic structures would not exist in nature and are impossible to fabricate as specie, and so cannot be used as money.

Gold

Perhaps you are thinking that it might make more sense to do a little environmental remediation while reworking the mining industry tailings, which are typically ~1,000 ppb gold [6], and extracting all of the remaining precious metal. Working on the richer tailings rather than raw crustal rock, our nanotech desktop refinery could produce ~300 troy ounces of pure gold per year, worth $100,000/yr at current market prices. Unfortunately, the energy cost is still $900,000/yr at today's $0.10/Kw-hr electric rates. If future energy rates are a lot cheaper than today's rates, well and good. But note that only ~10⁸ tons of new mine tailings are piled up annually, with each year's leavings containing ~100 tons of unextracted gold. Even if completely extracted, all of the gold in these tailings would still be far less than the total aboveground worldwide stockpile of the metal. What about seawater extraction [8]? Gold is ~100 times less plentiful in seawater than in the crust, though gross filtration and bulk preprocessing might improve throughput. Other potentially inflationary imports into the world economy from future extraterrestrial sources of monetary gold -- such as metal-rich asteroids -- may be largely offset by relatively high prospecting and shipping/insurance costs, and by a fast-growing economy able to fully absorb a rapidly expanding money supply.

The bottom line is that at ~$200/cm³, gold at least minimally satisfies our eight criteria for an ideal tangible nanomoney. Its rareness will not be decisively altered by nanotechnology. But the "precious yellow" owes its historical preeminence to the fact that gold is the most easily extractible inert rare element in the Earth's crust. In the nanotech era, other alternatives may exist.

Antimatter

To be practical as currency, however, the antimatter would have to be passively stable, else it would be too dangerous for common use. (Antimatter in contact with ordinary matter, such as container walls or pants pockets, decomposes explosively into a shower of nuclear particles and high-energy photons.) Matter-friendly stabilized antimatter has been proposed theoretically [10], and it has been suggested [1] that a two-component hypergolic antimatter fuel could permit controlled energy recovery up to a theoretical maximum energy storage density of ~2 ×10²¹ J/m³. At today's $0.10/Kw-hr electric rates, this maximum energy density would correspond to a recoverable energy value of $56 million/cm³. However, stabilized antimatter remains a purely speculative possibility.

Ordinary Matter

NOTES:

1. moderately radioactive, decays by gamma emission and electron capture to Mo⁹⁷, t_1/2 = 2.6 ×10⁶ yr;
2. moderately radioactive, decays by gamma and beta emission to Ru⁹⁸, t_1/2 = 4.2 ×10⁶ yr;
3. only 51% enrichment;
4. only 4.19% enrichment of this slightly radioactive alpha emitter, t_1/2 = 7 ×10¹¹ yr;
5. only 79.48% enrichment;
6. only 70.43% enrichment;
7. only 78.18% enrichment;
8. only 31%-48% enrichment;
9. only 5.70% enrichment, as oxide;
10. moderately radioactive alpha emitter, t_1/2 = 2.48 ×10⁵ yr;
11. only 41.63% enrichment of this slightly radioactive alpha emitter, t₁/2 ~ 10¹⁵ yr;
12. 77.71% enrichment;
13. investment grade D flawless, cut gemstones, 1-carat size (1997 JCK market quotes).




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Technetium

Helium and Xenon

Noble gas atoms may be encapsulated in fullerene cages such as C₆₀ [18, 19]. One present-day encapsulation technique involves heating bulk fullerenes to 650°C at 3000 atm gas pressure, a procedure which entrains 1 of every 1000 fullerene molecules with a single noble gas atom [19]. With proper chemical treatment, a C₆₀ molecule can also have a stable orifice of fixed diameter opened up in its side, only allowing atoms smaller than a certain size to enter [90, 91]; radioactive holmium atoms trapped in C₈₂ cages are already used in biodistribution experiments [92]. If we can find a low-cost method of purifying the gas-entrained cage molecules, or can devise a more efficient production method that achieves closer to ~100% entrainment, then closely-packed roughly spherical C₆₀ molecules each of volume ~0.70 nm³ with a volumetric packing factor of 68% would allow ~0.95 ×10²¹ noble gas atoms/cm³ to be stably stored, equivalent to a net storage pressure of 30-40 atm. This gives an effective storage density of 0.005 gm/cm³ for He³ (specie value $3/cm³ [20]) but 0.20 gm/cm³ for Xe¹²⁶ (specie value $5,800/cm³ [21]). Although very rare, He³ is paradoxically a relatively cheap isotope because of the vast supply of helium produced by the petroleum industry -- gas-well helium averages 1.5 ×10^-5 % He³ [22].

If we could raise the storage pressure to 1000 atm (12.3 ×10²¹ He³ atoms/cm³ or 9.48 ×10²¹ Xe atoms/cm³) and pack these gas atoms into sturdy single-walled carbon nanotubes (SWCTs), then storage density rises to ~0.061 gm/cm³ for He³ (specie value $39/cm³) and ~2.0 gm/cm³ for Xe¹²⁶ (specie value $58,000/cm³). Note that the Van der Waals gas equation governs at such high pressures [1], not the ideal gas law, so still greater compression permits little improvement in packing density.

For comparison, the volumetric values of more traditional specie are $2/cm³ for silver, $200/cm³ for gold, $260/cm³ for platinum, and $100,000/cm³ for late-20th-century investment-grade diamonds.

NMR (nuclear magnetic resonance) could be used to noninvasively measure the quantity of fullerene-entrained He³ present inside the cladding because He³ is an excellent spin-1/2 NMR nucleus with a high gyromagnetic ratio [19] at a resonance frequency of ~7618 MHz. Xe¹²⁹ (spin 1/2, ~2781 MHz) and Xe¹³¹ (spin 3/2, ~824 MHz) are also known to be NMR active [12]. Gold cladding would be NMR active at ~175 MHz (Au¹⁹⁷, nuclear spin 3/2), the only natural isotope [12]. The most abundant platinum isotope (Pt¹⁹⁵, 33.832%) is also NMR active with a nuclear spin of 1/2 and a resonance at ~2141 MHz, but the other two most common natural platinum isotopes (Pt¹⁹⁴ at 32.967% and Pt¹⁹⁶ at 25.242%) would provide a completely NMR-inactive cladding [12]. Diamond cladding with pure C¹² crystal would also be NMR-inactive, but may be too brittle for practical use in circulating coinage.

Helium is not known to form covalent compounds, but by 1999 ~80 covalent compounds had been produced with xenon bonded to fluorine and oxygen [23], one of which possibly might provide a slightly higher effective storage density of rare-isotope atoms than the compressed gas. Unfortunately, xenon compounds tend to be highly toxic because of their strong oxidizing character [23], hence represent a health threat to users in the event of breach of the cladding material. Pure He and Xe are biologically harmless in trace quantities, though in larger quantities xenon gas has been used as an experimental surgical anesthetic in humans for several decades [11, 24].

Osmium

Os¹⁸⁴ is so rare that its price is not conveniently available, but a linear extrapolation of a log-log plot of price vs. abundance for six other natural osmium isotopes whose prices are readily available (ranging from $10,400/gm for Os¹⁹² up to $600,500/gm for Os¹⁸⁶ [26] would imply a price for Os¹⁸⁴ (~100 times rarer than Os¹⁸⁶) of ~$30 million/gm, or ~$700 million/cm³. Natural mixed-isotope osmium is several times rarer than gold in Earth's crust, so a nanotech desktop refinery won't make this metal cheap.

Tantalum

Interestingly, the naturally-occurring isotope is not in the ground state but is a nuclear isomer at an excitation energy of 73 KeV with a spin parity of J^p = 9^- [28]. In the ground state, Ta¹⁸⁰ decays in 8.15 hours by electron-capture (EC) to Hf¹⁸⁰ and by beta-decay to W¹⁸⁰. It was originally predicted that Ta^180m would exhibit similar decay routes, but the most recent experimental search [28] has found no evidence of radioactive decay products distinguishable from background levels, establishing a lower limit on the Ta^180m half-life of > 3.0 ×10¹⁵ yr for EC and > 1.9 ×10¹⁵ yr for beta-decay and raising the possibility that these atoms are completely stable.

Tantalum is a hard, greyish-silver, heavy (16.6 gm/cm³) metal that can be drawn into a very fine wire (high ductility), and has a high melting point (3017°C) exceeded only by osmium, rhenium, and tungsten. The metal is completely immune to chemical attack at temperatures below 150°C and above this temperature is attacked only by hydrofluoric acid, acidic solutions containing the fluoride ion, and free sulfur trioxide, and only very slowly by alkalis. Coins minted of pure Ta^180m extracted using current bulk separation methods would have a value of at least $284 million/cm³, or even more because the value given in Table 2 is for 5.7%-enriched metal only. Natural tantalum metal and its stable pentoxide are biologically inert [31-34], so the metal is widely used in medical implants such as sutures, cranial repair plates, and other prostheses. But Ta^180m coins might still be cladded with gold or platinum to forestall a decline in their value due to wear abrasion. Coin purity can be determined by bremsstrahlung irradiation photoactivation analysis [30] or by other means; a cheap cladding made of Ta¹⁸¹, the most abundant natural isotope, would be NMR-active (spin 7/2, ~1199 MHz).

Couldn't we just buy some natural bulk pure tantalum (mostly Ta¹⁸¹), currently costing $1.20/gm [89], then use nanotech concentrators to perform an isotopic separation to extract the 1 atom in every 81,300 that is a Ta^180m atom? We could indeed! Neglecting chemical pre- and post-processing expenses, a 0.02 M aqueous solution of TaF₅ fed into a 32-stage teragravity nanocentrifuge cascade [1] could have its Ta^180m content enriched from 0.0123% to 5.7% for an energy cost of ~$1,000/gm ($16,600/cm³), assuming $0.10/Kw-hr.

But keep in mind that today's relatively cheap natural tantalum is derived from concentrated tantalite ores, not from random crustal rocks. The total quantity of Ta^180m available in the entire 1996 world reserve base of tantalum (including all known economic, marginal, and even subeconomic reserves still in the ground) was a mere 4,200 kg [93]. At $1,000/gm, our 4,200 kg of metal is only worth $4.2 billion -- a spit in the bucket against today's $20 trillion world money supply. Once the whole 4,200 kg has been extracted and there is still demand, the metal price must rise sharply or else new (but presumably poorer, harder to find) ore deposits must be discovered. How high could the price go? Who knows? But we do know that the world reserve base for gold in 1996 was 61,000,000 kg [93], and at ~$350/oz the market was valuing this reserve base of monetary metal at ~$0.7 trillion. If the world reserve base of Ta^180m is assigned gold's monetary function and is similarly valued at $0.7 trillion, and if vast new tantalum ore deposits prove difficult to find, then the price of Ta^180m could rise to ~$170,000/gm ($2.8 million/cm³). Note also that tantalum is more than 1000 times rarer than gold, in seawater [12].

Ta¹⁸¹ would be a convenient "base" substance with which to dilute the Ta^180m down to minute concentrations, in order to make lower-denomination coins. Nanotech coin-verifying machines could quickly clean and map the worn, scratched exterior surface of a specimen coin to atomic resolution, then weigh the specimen coin to single-proton mass accuracy [1], allowing the computation of the precise number of Ta^180m atoms present within the cladding on the assumption that Ta^180m is the only impurity in the Ta¹⁸¹ base metal. In theory, a more detailed assay could be done, with the coin completely deconstructed, counted and verified atom by atom, then reconstructed back into the original form in a few minutes, perhaps using a verification machine similar in size and speed to the desktop manufacturing appliance mentioned earlier.

Can we breed new Ta^180m atoms more cheaply by artificial means, avoiding the costly enrichment process from limited and dilute natural sources? Maybe, maybe not. Five nucleosynthetic techniques have been proposed for making Ta^180m [29, 30]. Two seem to require Type II supernova conditions, and another is now believed not to work. The other two methods involve a rare s-process neutron capture synthesis. One of these is at most ~0.01% efficient [29]. The other method requires nuclear precursors to be held near 300,000,000 degrees K to induce transformation, but at this temperature the normally stable Ta^180m has a half-life of only 130,000 sec [30]. Additionally, the high-nuclear-energy Ta^180m isomer thus produced then decays into the stable Ta^180m isomer with only 3.8% probability, so this method also appears very inefficient. A 0.01% production efficiency, requiring ~10,000 26-KeV neutrons per atom of Ta^180m synthesized, would imply a minimum energy cost of $40,000/gm (~$600,000/cm³) to manufacture stable Ta^180m, assuming the current $0.10/Kw-hr electric rate. The apparent difficulty of making this isotope may be a fundamental physical limitation which the future advent of nanotechnology is not likely to substantially alter.

Superheavy Elements

The number of elements is limited because nuclei become increasingly unstable against spontaneous fission and alpha-decay as proton number increases. For example, between thorium and the heavy fermium isotopes, the spontaneous fission half-life plunges by 30 orders of magnitude [76]. But in 1948, Goeppert-Mayer [35] pointed out that nuclear shell closure effects would substantially increase nuclear stability, and Wheeler [36] in 1955 and Scharff-Goldhaber in 1957 [37] postulated the existence of transactinide elements with atomic numbers above 103, the SHEs. By equating Coulombic and surface energy of the nucleus, Huizenga [38] had argued that the maximum number of chemical elements should be ~125, but in 1990 Seaborg estimated that more than 500 undiscovered transuranic isotopes might exist [73], and in 1996 Seaborg reproduced a "Futuristic Periodic Table" with atomic numbers running as high as hypothetical element 168 [39] similar to other hypothetical tables published decades earlier [40, 62]. There have been speculations on the possible chemical properties of elements with atomic numbers up to 184 [61, 64] and on the nuclear stability of elements with atomic numbers up to 274 [41].

Starting in the 1960s and 1970s, theoretical research on the SHEs largely centered on a hypothesized nuclear "island of stability" centered on element 114²⁹⁸ [42-48], with half-life predictions ranging from a few months [49] for 114³¹⁰, 5 years [74] for 118³⁰², 1000 years [41] for 112²⁹⁶, and 1079 years [74] for 116³⁰⁰, up to as high as 0.1 million years [41, 50], 20 million years [51], 1 billion years [41], or 2.5 billion years [52] for 110²⁹⁴. The stabilization near 114²⁹⁸ is due to the complete filling of nuclear proton and neutron shells, analogous to the complete filling of electronic shells in the noble gases in chemistry. Another "island of stability" was predicted to exist around element 164⁴⁷² by Sobiczewski et al [53], with half-lives ranging from 10⁵-10⁷ years. Taking spontaneous fission, alpha and beta decay, proton emission and electron-capture decay modes simultaneously into account, others have estimated more pessimistic half-lives [74-78]. On the other hand, if certain unconventional assumptions are made about nuclear shapes and deformations [54], some elements with atomic numbers above 134 might be stable.

The possibility of very long-lived SHEs triggered a major hunt for these atoms in nature. Searches of various ores and minerals, meteorites and hot brines, leaded glass, cosmic rays, and even lunar samples for evidence of SHEs came up empty [45, 74]. Flerov and Ter-Akopian [45] report negative detection limits as low as 10^-14 - 10^-17 gm/gm. Thus any natural SHEs that might be present must be 1-1000 times rarer than He³ atoms and 0.01-10 million times rarer than Ta^180m atoms. Current thinking is that it is unlikely that the r-process (rapid neutron capture in supernovae, >~10²⁷ neutrons/cm²-sec for 1-100 sec [55]) of heavy element nucleosynthesis will lead to the production of SHE nuclei [56, 73]. (Nuclear explosions typically produce neutron fluxes of >~10³¹ neutrons/cm²-sec for ~10^-6 sec [55, 57]; light-water nuclear reactors generate 2-5 ×10¹⁵ neutrons/cm²-sec for > 10⁷ sec [73].) However unlikely, the possible existence of SHEs in nature cannot yet be positively excluded [58]. For instance, a black hole/neutron star binary system might provide an appropriate mechanism [59].

The chemical nature of hypothetical SHEs has been extensively investigated [60-70] although the theory is complicated by the need to include relativistic effects [70] -- e.g., for atomic numbers greater than 90, orbital electron velocities exceed 50% of the speed of light [73]. Pitzer [63] concluded that elements 112 ("eka-mercury") and 114 ("eka-lead") might be slightly metallic gases or volatile liquids near room temperature, and element 118 ("eka-radon") should also be a gas or volatile liquid. Fricke [64] agreed that element 112 should be "a distinctly noble metal" in macroscopic quantities with a density of 16.8 gm/cm³, but "the interatomic attraction in the metallic state will be small, possibly leading to high volatility as in the noble gases." Hulet [79] predicted that element 112 will boil at or below room temperature. Keller et al [60] estimated a melting point for element 113 ("eka-thallium") of 430°C and a density of 16 gm/cm³. For element 114, Keller et al [60] estimated a melting point of 67°C, a boiling point of 147°C, and a density of 14 gm/cm³. Element 114 is likely to be very chemically inert [64, 69]. (Note again that gaseous or liquid atoms can be entrained in fullerene cages, and thereby embodied in useful specie.) Fricke [64] estimated a density of 13.5 gm/cm³ and a melting point of 400°C for element 115. Stable element 164, if it exists, might have the highest density of any element, ~46 gm/cm³ [64].

During the 1970s and 1980s, SHE element 106 was produced from O¹⁸ + Cf²⁴⁹ with a cross section of 0.3 nanobarns [81] and element 108 was made from the Fe⁵⁸ + Pb²⁰⁸ reaction at 0.02 nanobarns [82]. In the 1990s, efforts to create SHEs met with increasing success. For example, by 1999 four isotopes of the famed element 114 (eka-lead or "ununquadium" (symbol "UUQ"), the provisional IUPAC designation) had been created artificially [83-86], including 114²⁸⁵ (t_1/2 = 0.6 millisec), 114²⁸⁷ (t_1/2 ~ 5 sec), 114²⁸⁸ (t_1/2 < 0.03 sec), and 114²⁸⁹ (t_1/2 = 30.4 sec). In Oganessian's group [85], 114²⁸⁹ was produced by bombarding a Pu²⁴⁴ target with a 236-MeV Ca⁴⁸ beam of intensity 4 ×10¹² ions/sec, making just one atom of the SHE with a cross-section of ~1 picobarn -- out of 5.2 x 10¹⁸ incident calcium ions over a 34-day period, only one fusion event corresponded to a compound nucleus that survived to give a Z = 114 nucleus [48]. By late 1999, elements 110²⁷⁷, 112²⁸¹, 116²⁸⁹, and 118²⁹³ had also been synthesized [84].

Even if stable, long-lived SHEs can be artificially manufactured, they are likely to remain extremely rare. There is a rapid decrease in the production cross section, with increasing nuclear charge, typically <~1 nanobarn for elements above 105 [79, 80]. For example, Wolf et al [87] predicted the peak cross-section for making element 106 from the Es²⁵³ + Xe¹³⁶ deep inelastic transfer reaction to be 10 nanobarns, but only ~1 picobarn for producing element 110 and ~0.1 picobarn for making 114²⁹⁰ in the same reaction. Nitschke [88] estimated the cross-section to produce element 114 from the U²³⁸ + U²³⁸ reaction as ~0.1 nanobarns, and from a variety of other reactions as from 0.00002-20,000 picobarns. Production rates of SHEs are on the order 1 atom/hour or less [70] and Coulomb barrier energies are on the order of 200-300 MeV [79]. Seaborg and Loveland [73] note that the predicted cross-sections for heaviest element formation by heavy ion bombardment are less than 10^-8 of the total reaction cross section, "corresponding to the production of less than 1 atom per day of irradiation" using incident beam particle fluxes of 10¹³-10¹⁵ ions/sec from modern accelerators.

We see that stable superheavy atoms could be perhaps a trillion times more costly to manufacture than artificial Ta^180m, suggesting a very speculative value of ~$0.001/atom (~$2 ×10¹⁸/gm) using our customary electric rate assumptions. Even if the material was slightly radioactive, very few SHE atoms would be required to impart great value to the specie, substantially eliminating the radiation risk. For example, a coin with $1 million face value need contain only 10⁹ SHE atoms worth $0.001/atom. Assuming a 10⁶-year half life, there are only ~2 disintegrations per day, well below the background count from today's circulating base-metal coins (~3-30 counts/day, per gram). Our million-dollar coin would lose only ~$0.50/yr (~$500/millennium) of intrinsic value due to radioactive decay.

Aside from the radioactivity, any biotoxicity of SHEs is unlikely to be of much importance since the concentration of SHE would be so low and because the bulk of the coin would consist primarily of "cheap" bioinert material such as gold, platinum (failure strength ~100 times greater than gold), or diamond. Such coins, perhaps containing trace amounts of ununquadium or some other relatively stable SHE, might prove to be the ultimate tangible nanomoney.

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Original hypertext version of this document prepared by Robert J. Bradbury, February 2001.

Last updated by the author on 18 May 2003.