© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

6.3.7.1 Radionuclides

The most common mode of fissile energy release occurs when an unstable radioactive atomic nucleus emits a small particle such as an electron (b decay), a positron (b⁺ decay), a helium nucleus (alpha decay), or a high-energy photon (gamma decay), often transforming the nucleus into another element. Selection of an optimum radioactive fuel is guided primarily by safety criteria:

A. Penetration Range -- The mass of the a-particle is ~7000 times greater than that of an electron, so the velocity and hence the range of a-particles in matter is considerably less than for b-particles of equal energy. Consequently the optimum radionuclide for medical nanorobots is predominantly an a emitter. A simple "stopping power" approximation⁵⁶⁷ for the range of 1-10 MeV a-particles is:

{Eqn. 6.25}

where E_MeV = energy per a decay (MeV) and r_absorb = absorber density (21,450 kg/m³ for Pt). Thus a 3 MeV a-particle (initially traveling at ~0.04c) has a range of ~2 cm in air, ~30 microns in water, ~10 microns in germanium, and ~5 microns in platinum, with a fairly sharp cutoff and only ~1% straggling (fluctuation of particle range around mean range). By contrast, as a crude approximation the range of b-particles of equal energy (initially traveling at ~0.99c) is ~10² R_a and the range of g photons and fast neutrons of equal energy is ~10⁴ R_a, although "range" for these particles is imprecisely defined because beam intensity is never truly reduced to zero but rather decays exponentially with increased shielding. Partly because of the heavy shielding required, ₆₁Pm¹⁴⁷-powered betavoltaic batteries developed in the 1970s achieved only ~30 watts/m³,⁶⁰³ while ₉₄Pu²³⁸-powered thermoelectric batteries produced up to ~58 watts/m³;⁶³¹ over 2300 nuclear-powered cardiac pacemakers were implanted without mishap during 1970-76,⁶³³ but new implantations apparently ceased in 1983.³⁴⁹²

The absorption of a-particles in matter results almost entirely from collisions with electrons, or ionization reactions, which create 10⁵-10⁶ ion pairs per ~MeV aparticle (depending upon absorber material), slowing the particle almost to a halt. For some light-nucleus absorbers, there may also be an extremely small contribution from direct interactions with the nucleus. Alpha particles with energies as low as 4.8 MeV (e.g., from ₈₈Ra²²⁶) were observed to transmute atoms of all elements from ₅B up to ₁₉K (except for ₆C and ₈O) with the emission of protons.¹⁰⁰⁷ Low-energy a-particles can also occasionally transmute light-atom nuclei to produce neutrons -- one of the strongest such reactions involves 4.6 MeV a-particles emanating from ₈₆Rn²²² striking a ₄Be⁹ absorber, wherein one a-particle out of every 5000 enters the beryllium nucleus and sends out a neutron (with a much longer range than an a-particle of equal energy), a 0.02% reaction probability.¹⁰⁰⁸ Thus the worst case (e.g., shield materials are poorly chosen) is one low-energy proton or neutron emitted per 10⁹ - 10¹⁰ ion pairs generated (e.g., ~1 every 2000 sec at an a-particle current of 1 picoamp), though most such secondary reactions have far lower probabilities.

However, naturally emitted a-particles generally cannot penetrate the nuclei of heavier elements and therefore generally cannot create significant secondary radiation in heavy-nucleus absorbers, hence shielding should be made from heavier elements. To first order, overcoming Coulomb repulsion and entering the nucleus requires an a-particle energy E_repulse > 2 Z e² / 4 p e₀ r_nucl (joules),¹⁰⁰⁵ where Z is atomic number (nuclear charge number), e = 1.60 x 10^-19 coul (elementary charge), e₀ = 8.85 x 10^-12 farad/m (permittivity constant), and Rutherford's classical formula for nuclear radius r_nucl ~ r_nucl Z^1/3,¹⁰⁰⁶ where r_nucl ~ 1.6 x 10^-15 m.* Thus for example, using a ₇₈Pt absorber, r_nucl ~ 7 x 10^-15 m and E_repulse > 33 MeV; with a ₃₂Ge absorber, r_nucl ~ 5 x 10^-15 m and E_repulse > 18 MeV. In either case, the 24 MeV low-energy natural-emission alpha particles likely to be employed in nanomedical nucleoelectric systems (Table 6.5) have energies about an order of magnitude smaller than E_repulse.

* Some exotic artificial nuclei such as Li¹¹ do not obey the classical Z^1/3 rule.¹¹²⁸

B. Gamma Rays -- Gamma rays are toxic to most biomaterials, have the greatest penetrating power, dissipate useful fissile energy, and may foster erosion of shielding due to electron-positron pair creation. Thus the ideal medical nanorobot radionuclide fuel emits no g-rays during disintegration.

C. Decay Chain -- Radioactive elements typically decay to progressively lighter elements which may also be radioactive. Ideally, each of the daughter products of the ideal radionuclide should meet the above criteria for the entire decay chain down to stable nuclei.

Since each decay event produces a fixed amount of energy, power density P_rad of a radionuclide of density r is proportional to the number of disintegrations per second, or inversely proportional to half-life, as:

{Eqn. 6.26}

where AW = atomic weight (gm/mole), t_1/2 = half-life (sec), and k_rad = 10⁹ ln(2) N_A E_eV where N_A = 6.023 x 10²³ atoms/mole (Avogadro's number) and E_eV = 160 zJ/eV. To be useful in medical nanorobots, t_1/2 should be at least 10 days (~10⁶ sec) or longer for convenience of storage and use -- ideally, commensurate with the anticipated mission duration to preclude the need for potentially hazardous refueling operations in vivo. Table 6.5 gives power densities P_rad for several candidates and data for a few other benchmark radionuclides.^763,764

Among all gamma-free alpha-only emitters with t_1/2 > 10⁶ sec, the highest volumetric power density is available using Gd¹⁴⁸ (gadolinium) which a-decays directly to Sm¹⁴⁴ (samarium), a stable rare-earth isotope. A solid sphere of pure Gd¹⁴⁸ (~7900 kg/m³) of radius r = 95 microns surrounded by a 5-micron thick platinum shield (total device radius R = 100 microns) and a thin polished silver coating of emissivity e_r = 0.02 suspended in vacuo would initially maintain a constant temperature T₂ (far from a surface held at T₁ = 310 K) of:

{Eqn. 6.27}

with a 75-year half-life, initially generating 17 microwatts of thermal power which can be converted to 8 microwatts of mechanical power by a Stirling engine operating at ~50% efficiency. (Smaller spheres of Gd¹⁴⁸ run cooler.) While probably too large for most individual nanorobot designs, such spheres could be an ideal long-term energy source for a swallowable or implantable "power pill" (Chapter 26) or dedicated energy organ (Section 6.4.4). A ~0.2 kg block of pure Gd¹⁴⁸ (~1 inch³) initially yields ~120 watts, sufficient in theory to meet the complete basal power needs of an entire human body for ~1 century (given suitable nucleochemical energy conversion and load buffering mechanisms, and a sufficiently well-divided structure). Nuclear powered energy organs are discussed further in Section 6.4.4.

A 1 micron³ block of radioactive gadolinium yields a useful ~3 pW of thermal power. However, a minimum of 5 microns of Pt shielding is still required, so the minimum possible diameter of a zero-emissions Gd¹⁴⁸powered nanorobot is ~11 microns,* reducing power density to ~10⁴ watts/m³.** The low energy density would produce a surface temperature of 320 K, allowing only ~3% thermal conversion efficiency.** Higher efficiencies may be achieved using semiconductor junction a-particle nucleoelectric transducers that convert the linear ionization trail of electron-hole pairs directly into electrical current in ~10^-9 sec (Fig. 6.7). Such ionization in silicon and germanium is well-studied: the average energy loss per ion pair produced by a passing a-particle is 3.6 eV (580 zJ) for Si, 3.0 eV (480 zJ) for Ge;⁵⁶⁷ an 11-micron thick Ge wall is required to stop the 3.18 MeV a-particles. A (1 micron)³ cube of Gd¹⁴⁸ produces ~5 a-particles/sec, yielding an output current of ~1 picoampere at ~3 volts (e.g., ~3 pW). Unlike most nanomachinery for which a single-point failure would ordinarily be fatal to machine function¹⁰ (Chapter 13), the design presented here should be extremely resistant to such failures. The C-C bond energy is also ~3.4 eV, so direct nucleochemical transduction of a-particle energy into chemical form is theoretically possible -- conversion of carbonaceous material to diamond crystal by fission fragment irradiation has been reported.¹⁰²⁹

* The orbit radius r_orbit of an alpha particle of mass m = 6.68 x 10^-27 kg, charge q = 2 x (1.6 x 10^-19) coul and energy E_MeV = 3.18 MeV circling in a uniform magnetic field B = 1 tesla in vacuo is r_orbit = (k_a E_MeV m / q² B²)^1/2 = 0.3 meter (k_a = 3.2 x 10^-13), about as wide as a human body, so more compact in vivo nanocyclotronic storage of alpha particle emissions to allow a controlled energy release is not feasible.

** Plutonium dioxide radioactive thermal generator (RTG) systems developed by NASA and DOE in the 1980s produced thermal power of ~10⁵ watts/m³ and electrical power of ~10⁴ watts/m³, a ~10% conversion efficiency. Conventional large nuclear power plants average ~32% conversion efficiency, according to U.S. Federal Energy Information Agency statistics.

Are Gd¹⁴⁸powered nanorobots safe? Yes, if their shielding remains intact. There are no b or g emissions, and given adequate shielding, no a-particles can escape. Significant shield erosion is unlikely because:

1. almost all a-particle interactions are with orbital electrons, not nuclei, of shield atoms;

2. a-particle emission rates are low (e.g., ~5/sec);

3. radioactive impurities need not be present in nanomanufactured structures; and

4. background radiation is not a major reliability issue for homogeneous components larger than ~10 nm (Chapter 13).¹⁰

In the extremely unlikely event of complete shield removal, maximum range of a-particles in water or soft tissues is ~30 microns or ~one cell width. The radiation from the radioactive cores of ~1 billion Gd¹⁴⁸-powered nanorobots, if all their shielding was destroyed, would deliver a ~500 rad lifetime lethal radiation dose in ~1 day; an unshielded ~0.2 kg block of Gd¹⁴⁸ (~100 watt output) delivers an LD50 (see below) dose in ~10 seconds. Gd¹⁴⁸ is a nonfissionable material, hence fissile chain reactions or explosions are not possible. Indeed, gadolinium has the highest neutron absorption cross-section of any known element and is more useful in control rods or as a nuclear shield. As for chemical toxicity in the event of a breach, ionic Gd is rapidly converted to colloidal hydroxide and phosphates in the blood, which is then rapidly taken up by the reticuloendothelial system mostly in the liver and spleen;⁵⁹⁸ half-time in the lung is ~2 hours.⁶⁰⁰ In macrophages, the rare earths localize in lysosomes as insoluble phosphates.⁵⁹⁹ Rare earths such as Gd or Sm are not particularly toxic -- LD50 is typically 0.55 grams/kg body weight,⁶⁰¹ or 35-350 gm for a 70 kg human adult. No chemical carcinogenicity or mutagenicity has been found.⁶⁰¹ In 1998, Gd¹⁴⁸ could be purchased from Los Alamos National Laboratory for $0.50/micron³.²³¹⁵ This cost must be significantly reduced for Gd¹⁴⁸powered nanorobots to become economically feasible.

If greater operating power densities are required, radionuclide-powered nanorobots with power cores that are hotter or are smaller than ~1 micron³ (but with shielded diameters still >11 microns) will require switching to a less-safe material of higher energy density, such as Po²¹⁰, which decays to stable Pb²⁰⁶ with a 5-month half-life. For example, a Po²¹⁰ spherical power core of radius 100 nm has a surface temperature of ~600 K and produces ~6 pW which may be tapped via heat engine as described earlier. However, such a heat source also produces one 0.79 MeV gamma photon every ~10⁴ sec; unshielded, ~300 such photons represent a lethal dose (~500 rad or ~5 joules/kg soft tissue) to a single mammalian cell, giving a dose rate of ~10 millirad/hour vs. ~5 millirad/hour for the early implantable Pu²³⁸ nuclear thermoelectric batteries.⁷²⁴ Thus the lifetime exposure* of any cell visited by Po²¹⁰powered nanorobots is restricted for safety to at most ~1 nanorobot-month, which may be acceptable in many short-duration applications. No such restriction would apply to the Gd¹⁴⁸ device, discussed earlier.

* The rad is the standard unit of absorbed dose, defined as 1 rad = 0.01 joule/kg. LD50 is the absorbed dose that produces lethality in 50% of all exposures, typically 400-500 rads for human tissue. The traditional LD50 for a 70-kg human body (~500 rads) thus requires the absorption of ~350 joules. For a single ~10 nanogram human liver cell, assuming the traditional LD50 (~500 rads) would require the absorption of ~50 pJ of ionizing radiation energy. To rigorously assess the safety of radiation emitted from nanorobots, the effects of the particular radiation on specific cells or organs must be evaluated.^3075-3078 There are large differences in organ sensitivity, ion-mass sensitivity, and environmental sensitivities such as variations in iron, Vitamin C, or melatonin levels. Lethality of cells is at one end of a continuum which also includes lower-dose effects (e.g., cancer transformation rates) that disturb the cell's function without killing it, thus harming the body the cell is serving. The availability of cellular repair devices vastly increases both LD50 and traditional "lifetime exposure" radiation limits that may be tolerated by humans (Chapter 24). Substantial genomic, biotechnological, and nanotechnological engineering to increase the radiation tolerance of cells (Chapter 24) also could help to minimize cancer risks and birth defects, and to allow human beings to more easily live and work in space. Nevertheless, a fundamental nanomedical design principle is to avoid using devices whose normal behavior causes additional damage to the body (Chapter 11).

Larger amounts of energy (up to ~0.1% of rest mass) may be released by the fission of a heavy atomic nucleus into nuclei of two lighter elements of roughly equal mass, followed by any of ~50 distinct decay chains down to stable nuclei for the unstable fission fragments, as for example:

{Eqn. 6.28}

which achieves ~0.091% mass conversion to energy. During fission, typically one neutron is absorbed by a nucleus but 1-3 neutrons are emitted, making possible a chain reaction. In effect, neutrons act as fission catalysts. Nuclear species which may support a net-energy-producing fissile chain reaction include U²³², U²³³, U²³⁵ (critical mass ~ 3.6 kg), Pu²³⁹, Am²⁴¹ and Am²⁴² (thermal or fast neutrons) and Th²³², Pa²³¹ and U²³⁸ (fast neutrons only). From a nanomedical perspective, the minimum size of a neutron-mediated fission power plant is restricted primarily by the shielding requirement for g-rays totalling ~5 MeV per reaction, which apparently precludes microscale in vivo medical fission reactors. For instance, ~8 cm of solid Pt shielding (e.g., a cantaloupe-sized ball, weighing ~46 kg) only reduces g-ray intensity to 1% of its incident value. High g fluxes are also very damaging to nanomachinery.

Last updated on 18 February 2003