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

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

4.3.3.1 Box-Spring Accelerometers

As one member of a class of devices, a simple nanoscale omni-directional accelerometer is conceptualized as a reaction mass suspended by three pairs of reaction springs (one pair per orthogonal directional axis) with each spring connected to the walls of an evacuated box (Fig. 4.4). Acceleration in any direction extends some springs and compresses others, which is measured by force or displacement sensors attached to each spring. The signal/noise ratio for this sensor is

{Eqn. 4.11}

For a sensor mass m = 10^-17 kg (~78 nm-wide platinum* or ~140 nm-wide diamond cube) suspended with k_s = 1 N/m floppy springs at T = 310 K, the minimum detectable acceleration a_min = 1.6 x 10⁶ g's for SNR = 1 and 2.6 x 10⁶ g's for SNR = 2 (undamped resonant acceleration ~ L k_s/m ~ 10⁹ g's for L = 100 nm). Undamped resonance frequency w_res = (k_s/m)^1/2 = 3 x 10⁸ radians/sec, which is measurable (Section 4.3.4.3).

* Platinum is probably the ideal choice for medical nanodevice components requiring maximum density. Depleted uranium, a relatively abundant element, is more common in macroscale nonmedical devices. However, pure U²³⁸ has a density of 19,050 kg/m³, somewhat lower than the density of Pt (21,450 kg/m³) or even gold (19,320 kg/m³). Uranium and its compounds are highly toxic, and finely divided (e.g. micron-scale) uranium metal is pyrophoric (spontaneously combustible) in air. By comparison, Pt metal is almost completely inert in air and in the body, thus is nontoxic, and is mechanically ~50 times stronger than gold (Table 9.3). Only two elements have higher density than Pt: Os (22,480 kg/m³) and Ir (22,420 kg/m³). Osmium is brittle even at high temperatures and the powdered metal oxidizes in air, giving off osmium tetroxide which has a strong smell and is highly toxic (as little as 100 nanograms per m³ of air causes lung congestion, skin and eye damage). Iridium metal is also very brittle and, like osmium, is at least five times less abundant than Pt.^691,763

Sensor mass exchanges reciprocally with acceleration sensitivity in Eqn. 4.11, so the lower limit even for a dedicated micron-scale platinum-core box-spring accelerometer is a_min ~1000 g's at SNR ~ 2 (undamped resonant acceleration ~ 10⁶ g's for L = 2 microns). The maximum detectable acceleration requires m ~ 10^-23 kg (~1.4 nm diamond cube) and k_s ~ 1000 N/m, giving a_max ~5 x 10¹³ g's at SNR = 1.

If the accelerometer depicted in Figure 4.4 is installed near the center of mass of a nanorobot, the sensor may avoid confusing centrifugal and translation forces. Otherwise, information from multiple sensors must be combined to obtain an unambiguous measurement. Multiple measurements can improve the SNR for constant accelerations of long duration.

In 1998, ~100-nm vibrating-beam silicon accelerometers were under development by Analog Devices and Daimler-Benz. Tunneling accelerometers had been fabricated with ~10^­6 g resolution at a 350 Hz bandwidth or ~10^-8 g/Hz^1/2.³⁰⁴¹ Silicon-based capacitive accelerometers (5-1000 g full scale) manufactured by Silicon Designs (Issaquah, WA) were widely used in automotive airbag safety systems; in 1998, Motorola shipped its ten-millionth accelerometer, and the global market for automotive silicon accelerometers was expected to reach $463 million by 2002.

Last updated on 17 February 2003