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

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

6.3.4.4 Glucose Engines

There are many pathways for glucose oxidation in the human body, some which directly involve molecular oxygen. For instance, the glucose-6-phosphate dehydrogenase and the 6-phosphogluconic dehydrogenase enzymes both employ molecular oxygen directly to oxidize a glucose derivative. Although evolution has largely replaced pathways involving direct combination with oxygen, there are still a number of organisms (molds, some bacteria) which have retained these primitive pathways and a few can even be found in mammalian tissues. For example, enzymes in the liver use the reactions:

{Eqn. 6.14}

with

{Eqn. 6.15}

One very crude approach for medical nanorobots is to use mechanochemistry techniques to force an exothermic chemical reaction, making a change in volume or generating heat which is subsequently exploited to produce mechanical motion. Given that glucose may be the preferred chemical fuel for nanomedical systems (Section 6.3.4.1), we concentrate our attention on the high-energy exothermic oxyglucose combustion reaction

{Eqn. 6.16}

The kinetic model for the glucose oxidation reaction has not been extensively studied experimentally at pressures >30 atm, so it has not yet been proven that an oxyglucose mixture can be ignited at high pressure near human body temperature at 310 K (37°C). Such a model could have a complex structure, such as the well-studied stoichiometric H₂/O₂ mixture which shows a minimum ignition temperature of only ~380 K (107°C) at ~2500 atm.⁵⁸²

Pure sugar in air is not ignited by open flame (e.g., bunsen burner, matchstick), but readily burns if a catalyst such as ash is added.³¹²⁰ Exposed to moist air below 323 K (50°C), each molecule of anhydrous glucose hygroscopically absorbs a single molecule of noncovalently-bound water, yielding the monohydrate. Heated above 323 K, anhydrous glucose "caramelizes" when it reaches ~433 K (160°C). Caramelization is not oxidation, but rather is an endothermic decomposition process involving successive dehydration, condensation, and polymerization reactions, that includes the making and breaking of covalent bonds, resulting in brown melanines^3109-3111 and possibly some carbonization.³⁰⁸⁷ At 433 K the total translational kinetic energy of the 7 oxyglucose reactant molecules would be 7(3/2)(kT) ~ 63 zJ.

What is the minimum ignition pressure (P_ignition) of glucose? Pressures of 5,000-15,000 atm deactivate antibodies, enzymes, and proteins (Table 10.3), and ignition temperatures normally fall with rising pressure in combustion reactions.^583,584 In food science, the well-known Maillard reaction ("browning")^3109-3111 between amino acids from protein (mainly lysine) and reducing sugars (glucose and lactose) involves a potpourri of Amadori rearrangements, Schiff's base formations, and Strecker degradations, and occurs during heating (cooking) and pressurization (e.g., the glucose-lysine system at 6000 atm),³¹⁰⁸ and even occurs slowly at body temperature, producing insoluble melanoids and glycosylating proteins during aging (Chapter 29). Initiating the Maillard reaction apparently requires 108-174 zJ/molecule (15.5-25 Kcal/mole),³¹¹⁰ the rate increasing 23 times with each 10 K temperature rise.³¹¹¹ Pressure-induced peroxidation of lipids has been shown,³¹¹³ with browning greatly accelerated by pressurized oxygen.³²¹⁸ It is also well-known that the hydrocarbons found in oils and greases, and many other organic compounds, will "ignite almost spontaneously" in oxygen stored in compressed tanks at ~150 atm.³¹¹⁴ Upon contact with liquid oxygen (LOX), paper, textiles, asphalt, tar, kerosene, wood, stainless steel, teflon, and silicones are combustion hazards, and pulverized organic materials such as sawdust, polystyrene and charcoal,³¹¹⁹ and powdered magnesium, can spontaneously ignite or explode:^3115-3118 "when saturated with LOX these materials have exploded after an impact as slight as a footstep".³¹¹⁶ The density of oxygen molecules trapped in a mechanochemical binding site at 1000 atm is 12.6 molecules/nm³, not much below the ~21.5 molecules/nm³ density in LOX (Table 10.2).

Lacking firm experimental data, we provisionally approximate P_ignition as the minimum ~63 zJ activation energy (required to induce covalent bond modification during caramelization), divided by the total reactant volume at 310 K computed by summing the volumes of one glucose (1.91 x 10^-28 m³/molecule) plus 6 molecular oxygens (8.85 x 10^-29 m³/molecule at 860 atm using van der Waals' equation; Section 10.3.2). The required energy density is 8.7 x 10⁷ joules/m³, which can be supplied to the reactants by applying a mechanical pressure of P_ignition ~ 860 atm. Operating the glucose engine at P_ignition ~ 1000 atm, possibly including durable catalysts to accelerate the reaction, thus would ensure complete and reliable combustion. (Note that biology already achieves full stepwise glucose oxidation at 310 K, constituting a general proof of principle.)

J. Soreff suggests several interesting design alternatives:

1. Convert glucose to a more stable fuel such as methane (which will not caramelize), possibly by biochemical means, incurring some loss in efficiency;

2. precompress the fuel/oxidizer mixture in a single tank to subignition pressures, then trigger the reaction purely thermally or possibly by adding free radical initiators such as benzoyl peroxide to the tank; or

3. nitrate the glucose hydroxyls, producing combustion and evolution of N₂ which must then be recycled back to HNO₃ via nitrogen fixation (Chapter 19) to nitrate the next batch of fuel.

Once oxyglucose combustion has taken place, the energy thus released may be converted to mechanical energy by various means. In the ideal case of an isothermal expansion at constant (P = 1000 atm) pressure, P DV = E_glu would imply a volume change DV ~ 47 nm³, producing a ~5 nm power stroke on a piston of area ~10 nm² and a ~1 nN applied force. Vacuum isolation of the combustion chamber assembly (see below) helps prevent rapid energy dissipation via thermal conduction to the external medium. Burning 10⁶ sec^-1 glucose molecules in a ~500,000 nm³ combustion/engine device (which includes a generous volumetric allowance for support structure) generates ~5 pW with a theoretical power density of ~10¹⁰ watts/m³. Note that while the oxyglucose reaction products occupy 0.047 nm³ more volume than the reactants, relying upon this volume change only allows a highly inefficient (~0.1%) extraction of ~5 zJ per glucose molecule at 1000 atm operating pressure.

A complete design for a working nanoscale glucose engine is beyond the scope of this book. However, as a concept demonstration without regard to maximizing efficiency, one simplistic implementation might employ a combustion chamber at the center of a vacuum-isolated "thermos bottle." A series of combustion events maintains the isolated heat source at a high operating temperature, thus providing a sizable temperature differential against the external medium. This differential can subsequently be used to drive a microscale Stirling engine to produce a mechanical power output,⁵⁴¹ or to stimulate mechanical motion by differential expansion of dissimilar materials (Section 4.6.3), or even to energize an electrical microthermocouple or pyroelectric nanocrystal (Section 6.3.1).

A key component of the glucose engine is a stable heat source, which requires at least five critical design elements:

A. Combustion Mechanism -- (Figure 6.4A) shows a heat-generating mechanism which employs two opposed sorting rotors. These rotors contain binding sites which must be exceptionally robust and damage-resistant. Each rotor is a cylinder 40 nm tall with ten staggered rings of opposed binding sites (Fig. 6.4B). The left rotor has binding sites which accept one glucose molecule at a time from the aqueous fuel solution, simultaneously applying sufficient force to strip off the associated water of hydration. The right rotor has binding sites each of which accepts oxygen molecules, six at a time. During operation, these "crushing rotors" compress paired reactant packets into the activation volume required for the oxyglucose combustion reaction to occur. This reaction volume may change shape during the compression cycle, perhaps employing a judicious series of insertions and retractions of binding pocket rods in order to accommodate intermediate reaction products and multistep reaction events. The end result is to force a complete combustion at the rate of 3 x 10⁶ glucose molecules per second (~7 pW). Effluent molecules are ejected into the outer jacket, transferring their heat to the thermally-conductive structure in <10^-9 sec (Section 4.6.1). The glucose solvation water discharge pathway is not shown in the Figure.

B. Fuel Tanks -- The combustion mechanism has fuel tanks sized to stoichiometric requirements from which combustion reactants are drawn during each 100 millisec discharge cycle. Tanks are refilled once during each discharge cycle with a saturated 70% glucose (aqueous) solution and O₂ at >1000 atm pressure. During refueling, the thermos structure equilibrates to 310 K in ~10^-9 sec by thermal conduction through the refilling mechanism, which physically plugs into the refueling sockets. Refilling requires <10^-7 sec. The refilling mechanism then disconnects and withdraws at least 100 nm, after which the combustion mechanism raises thermos temperature back to the 600 K operating temperature in ~30 millisec. Thermos temperature then remains at 600 K throughout the remainder of the 100 millisec discharge cycle. Presumably this cycle is fast enough to avoid glucose fuel caramelization at 433 K inside the tank; if not, a faster cycle or a lower operating temperature may be used, forcing a somewhat lower efficiency on the entire design. (The boiling point of the water solvent exceeds 433 K at >6.4 atm (Section 10.3.2); at 600 K, well below water's critical temperature T_crit = 647.3 K (Section 10.3.2), water remains liquid at pressures >~140 atm.)

C. Rotor Drive Source -- Stacked above the 40-nm tall fuel/rotor complex is a second O₂ storage tank (~15 nm tall) at >2000 atm pressure (Figure 6.4B). This gas passes through a simple ducted turbine mechanism which is coaxial with the two rotors, driving rotor rotation. Spent drive gas passes into the main O₂ storage tank and is later used as combustion reactant. Drive gas is recharged, and effluent gases are drained off, each process taking ~10^-7 sec, once every 100 millisec discharge cycle.

D. Electrodynamic Suspension -- It is crucial to avoid any thermally conductive physical pathways until the cycling Stirling engine (or other intentional energy transfer mechanism) calls for heat. Even the best thermal insulators such as wood, plastic and glass have conductivities K_t = 0.01-1 watts/m-K (Table 8.12, Appendix A), so a 10-nm cube of such material straddling a DT = 290 K temperature differential conducts away the entire energy store of E_store ~ 1 pJ in ~0.1-10 microsec. Using N_rod = 6 carbyne rod supports, each of cross-sectional area A_rod ~ (0.2 nm)², length L_rod = 100 nm, and K_t = 2000 W/m-K for diamond, the thermal leakaway time is:

{Eqn. 6.17}

still much too fast. (J. Soreff notes that glasslike disorder in molecular chains may be obtained by placing C¹² and C¹³ atoms randomly throughout the carbyne structure, rendering local most of the high spatial and temporal frequency modes and possibly significantly reducing thermal conduction. For somewhat weaker strands, N/CH or O/NH/CH₂ units might be intermixed with similar effect.) Fortunately, vacuum non-contact isolation of the entire combustion assembly also is possible via electric levitation.

Earnshaw's theorem²¹⁷² states that static levitation against gravity is not possible in classical physics using any combination of fixed magnets or electric charges. However, stable levitation may be achieved by using quantum effects (Section 9.2), diamagnetic suspension materials,^2173,2174 rotation of the suspended object as in the levitron,²¹⁷⁵ oscillating magnetic fields,²¹⁷⁶ or dynamic feedback control mechanisms. Three-dimensional electro-dynamic confinement of charged micron-sized aluminum particles was demonstrated experimentally in the late 1950s.⁶⁵⁴ From the formulas given, a 100-nm particle with 10 surface charges (charge/mass ~ 1) can be stably confined to a 200-nm volume in a circular Lissajous pattern using a ~1 volt hyperbolic quadrupole AC field at a ~10 MHz resonance frequency plus a ~10 mV DC field to neutralize gravity. A stiffer confinement field on micron-scale particles has been produced inside a spherical void electrodynamic levitator constructed as two joined hemispheres,⁶⁵⁵ and more complex configurations have been designed.^658,659 Electric suspension bearings for micromotors using a resonant circuit driven by radio frequency AC voltage can achieve stable levitation of charged objects without requiring feedback signals or sensors,^656,657 and stable passive trapping may also be achieved using cylindrically symmetric dielectrophoretic levitation electrode structures.⁶⁶⁰ Translational and rotational motions may be imposed on the suspended object by applying appropriate DC or oscillating fields.

Levitation is particularly effective at the smallest scales. Electrically levitating an object of thickness t, density r, and dielectric strength k e_0, against a gravitational acceleration g requires an electric field:⁶⁵⁶

{Eqn. 6.18}

If r = 1000 kg/m³, g = 9.81 m/sec², t = 100 nm, k = 2.1 (e.g., Teflon), e₀ = 8.85 x 10^-12 farad/m, then E_lev = 20,000 volts/m or 20 mV across a 1 micron gap (~typical in biological cells). Two unit charges separated by 100 nm in vacuo feel a mutual repulsion of ~0.1 pN, sufficient to resist an external acceleration of ~10⁴ g's on a (100 nm)³ block of density r = 1000 kg/m³; 10⁴ g's is the largest natural acceleration imposed on objects of this size inside the human body (Section 4.3.3.2) and is near the maximum safe acceleration for human cells (Chapter 11).

One possible stable open-loop levitation configuration is shown schematically in Figure 6.4C, wherein the combustion assembly is affixed to a simple permanently-polarized dipole electret carrier which is itself electrodynamically levitated by same-sign control electrets positioned at either end. Thermal electrets (electric field applied across heated material^727,2177) may be made of wax, Teflon, or Mylar; several polymer electrets have extrapolated lifetimes of several thousand years at room temperature.⁷²⁷ Homocharge electrets (electron beam-embedded charges²¹⁷⁷) may have longer lifetimes at higher temperatures, or other thermostable electret materials with designed nanoscale charge patterns may be found.³⁰⁹⁹

E. Thermal Insulation -- The combustion assembly shown in Figures 6.4A and 6.4B measures (110 nm)² x 90 nm. For an isolated hot surface in proximity to a cooler surface, both surfaces of area A and separated by vacuum, the rate of heat transfer is given by:

{Eqn. 6.19}

with variables as defined for P_r in Eqn. 6.11; the peak vacuum emission wavelength is given by Wien's relation as:

{Eqn. 6.20}

which, for h = 6.63 x 10^-34 joulesec, c = 3 x 10⁸ m/sec, k = 0.01381 zJ/K, and T₂ = 310 K, gives l_max = 9.3 microns; at T₂ = 540 K, l_max = 5.3 microns.

At planar separations d >~ l_max, radiative power is independent of separation distance. However, at smaller separations d < l_max, radiative heat transfer may be greatly enhanced due to near-field coupling of nonradiative electromagnetic modes in the surfaces.^652,653 In particular, surfaces at temperatures between 300-600 K transfer heat approximately as ~(s_cond d⁴)^-1 for 0.2 micron <~ d <~ 2 microns, where s_cond is electrical conductivity. Surfaces with 10 nm <~ d <~ 200 nm again exchange energy independent of d, but according to:

{Eqn. 6.21}

The basic energy exchange relation for d < 200 nm is simply P_glu = P_anomalous + P_ext, where the combustion power P_glu = n_glu E_glu / t_glu, n_glu = number of glucose molecules oxidized per cycle (e.g., 3 x 10⁵), t_glu = combustion cycle time (e.g., 100 millisec), and P_ext is the working power extracted by the Stirling engine. Assuming d = 100 nm, a highly conductive silver or aluminum surface with s_cond ~4-7x10¹⁸ sec^-1 results in a negligible temperature differential (T₂ - T₁) ~ 0.0001 K. However, a germanium surface (melting point 1211 K) with s_cond ~10¹¹ sec^-1 could allow a useful operating temperature T₂ > 600 K, giving a maximum Carnot efficiency (T₂ - T₁) / T₂ = 0.48(48%) (vs. ~25% for gasoline internal combustion engines). With device volume ~0.02 micron³, power density would be ~10⁹ watts/m³. A boron surface (m.p. 2573 K) with s_cond ~ 10⁷ sec^-1 might provide even better vacuum insulation properties. More research is required on the mechanisms of anomalous radiative heat transfer in order to fully assess the feasibility of this approach.

Last updated on 18 February 2003