Nanomedicine, Volume I: Basic Capabilities

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

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

 

6.3.1 Thermal Energy Conversion Processes

The second law of thermodynamics says that it is impossible to to convert heat into useful work if the heat reservoir and the device are both at the same temperature, as demonstrated by Feynman's classical example of the Brownian motor using an isothermal ratchet and pawl machine,2611 although nonequilibrium fluctuations, whether generated by macroscale electric fields or chemical reactions far from equilibrium, can drive a Brownian motor.696 It has also been suggested that reversible-energy-fluctuation converters can obtain useful electrical work from thermal Nyquist noise, up to power densities of 1015-1016 watts/m3 at ~300 K.1606,1607

Of course, a reversible Carnot-cycle heat engine can extract useful work from even a small temperature differential with a Carnot efficiency of e% = DT / T. For example, a nanorobot circulating with the blood between core and peripheral tissues may experience a temperature variation up to several kelvins during each vascular circuit of duration tcirc ~ 60 sec (Section 8.4.1). From this small temperature differential an ideal biothermal thermomechanical engine may extract a maximum power:

{Eqn. 6.10}

where nanorobot thermal storage volume is Vn = 1 micron3, heat capacity CV = 4.19 x 106 joules/m3-K for a device filled with water, T2 = 310 K at the human body core and T1 = 307 K at the periphery. The thermal store, vacuum-isolated to prevent heat loss (see below), is equilibrated in the hotter core environment to T2, which heat is then stored until the device reaches the cooler peripheral environment at T1. From Eqn. 6.10, this temperature differential yields at most Pn ~ 0.002 pW with efficiency e% = (T2 - T1) / T2 ~ 0.01(1%) and a peak (accessible) energy density of Pn tcirc / Vn ~ 105 joules/m3. The change in temperature can be made to cause gas in a three-dimensional coiled piston to slowly expand or contract, driving a rod back and forth thus providing a cyclical linear mechanical output, a Stirling engine configuration. The gas expansion is isobaric and reversible because thermal equilibration time tEQ ~ Vn CV / h Kt = 105 sec for a conduction layer of thickness h ~ 0.5 micron and thermal conductivity Kt = 0.623 watt/m-K for water at 310 K, so tEQ << tcirc. (Exploiting the diurnal variation in mean body temperature, typically ranging from 309.3 K in early morning to 310.4 K in the evening, produces at most ~2 x 107 pW of power.) A nanorobot resting on the epidermal surface may exploit the temperature differential between skin and air, up to 8-13 K (Section 8.4.1.1) giving a maximum Carnot efficiency e% ~ 0.04 (4%); for classical radiative transfer (see below), the nanorobot develops a net power through an L2 = 10 micron2 epidermal contact surface of Pn ~ s (T24 - T14) L2 e% = 0.04 pW.

Nakajima541 has built and operated a 50 mm3 Stirling engine working at 10 Hz between 273-373 K producing 102 watts (power density 2 x 105 watts/m3), and has demonstrated the theoretical engineering feasibility of microscale Stirling engines. In 1993 Jeff Sniedowski of Sandia National Laboratories constructed a 50-micron steam engine on a silicon chip producing forces ~100 times higher than those of electrostatic motors of similar size.3486 (The steam was produced electrically.) Computer simulations of a molecular-scale steam engine have been performed by Donald W. Noid at Oak Ridge National Laboratory.3488 A conservative and practical upper limit to nanorobot Carnot efficiency is probably ~50% (T2 = 620 K).

A heat engine may exploit the temperature difference between the largely isothermal human body acting as a sink and a hot, high-capacity source of stored heat energy. Because the rate of conductive heat loss is scale-dependent, such exploitation is not feasible in nanodevices relying on stored heat sources unless a vacuum isolation suspension is employed (Section 6.3.4.4). As a simple demonstration, consider a vacuum-isolated spherical thermos bottle of inside radius r, coated with a material of total emissivity er and filled with a hot working fluid of heat capacity CV at initial temperature T2. Conduction and convection are eliminated; heat loss in vacuo occurs only by radiative transfer. In the classical macro-scopic formulation, radiated power Pr = 4 p r2 er s (T24 - T14) (watts), where s = 5.67 x 10-8 watts/m2-K4 (Stefan-Boltzmann constant). The thermal energy contained in the hot material is Hr = (4/3) p r3 CV (T2-T1) (joules); hence the time required for half of the energy to radiate away is:

{Eqn. 6.11}

For r = 1 micron, CV = 4.2 x 106 joules/m3-K for water, er = 0.02 for polished silver, T1 = 310 K inside the human body, and T2 = 350 K up to 647 K (~critical temperature of water at 218 atm pressure), t1/2 <~ 6 sec (at T2 > 350 K) starting from an initial (accessible) energy density of ~108 joules/m3; Hr = 1.5 nanojoule for a 1-micron core at 647 K. Almost the entire thermal energy store (~99%) leaks away in just 40 sec (at T2 = 350 K). Smaller thermos bottles leak even faster, due to the ~r dependence of t1/2.

Radiators lying within <1 micron of a lower-temperature material surface exhibit near-field anomalous radiative transfer (Section 6.3.4.4 (E)) and thus exhibit different cooling characteristics than Eqn. 6.11 predicts. Taking Pr = Panomalous from Eqn. 6.21 for spherical surfaces <200 nm apart, then t1/2 ~ 0.01 (h2 c2 / k3) (r CV / scond T22) (seconds); for T2 = 647 K and r = 1 micron, t1/2 ~ 10 sec using a germanium shell but ~105 sec using a boron shell.

Other thermomechanical transducers include sandwich cantilevers (Section 4.6.3) made of composite materials with high coefficients of linear expansion (e.g., heated metal bimorphs547), Nitinol or other temperature-sensitive shape-memory alloys,548 thermally-driven phase-change microactuators,545 thermally-powered contraction turbines,597 and thermally-driven contractile proteins.1261 Thermochemical transducers that make use of thermal energy stored as a phase change of a refrigerant can display energy densities of ~108 joules/m3,1197 and a thermoacoustic Stirling engine with no moving parts has been demonstrated.3267

A thermoelectric transducer may be constructed from a crystal with piezoelectric properties. When such a crystal is heated or cooled, charges are produced on its surfaces (called pyroelectricity553 or heat electricity) setting up mechanical strains in the crystal that produce the same electrical effect as the application of external forces in piezoelectricity.551 Both bone and tendon exhibit the pyroelectric effect;3088 all pyroelectric materials are piezoelectric, though the converse is not true.3089 Thermocouples are another example of direct thermoelectric energy transduction, and thermophotovoltaic generators are well-known.1983

A high emissivity blackbody radiator provides thermooptical transduction at temperatures >650 K, increasing in efficiency up to ~6000 K.

 

Last updated on 18 February 2003