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

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

4.6.3 Thermal-Expansion Temperature Sensors

Consider a thin rod of length x and width w, constructed as a sandwich of two dissimilar materials each of thickness h, having coefficients of linear expansion a₁ and a₂, respectively (Fig. 4.8). When heated, the two materials expand differentially to lengths of x (1 + a_i DT) (neglecting the quadratic and higher-order terms in a_i), producing a cantilever deflection of q_t = (x/h) (a₁ - a₂) (radians) from simple geometry. The minimum detectable temperature change DT_min = 2 p Dx_min / x q_t or

{Eqn. 4.37}

where volume of the sandwich rod V_rod = 2 h w x. Taking Dx_min = 10 pm, a₁ = 2.38 x 10^-5 /K for aluminum,⁴⁶⁰ a₂ = 8 x 10^-7 /K for diamond at 310 K,⁴⁶⁰ h = w = 5 nm, and assuming sensor volume V_sensor ~ 2 V_rod in a tightly packed three-dimensional coil configuration, DT_min = 1 microkelvin for an L³ ~ (227 nm)³ sensor ~ 1% of the volume of a 1-micron nanorobot. Use of a suitable negative-coefficient material for a₂, such as the ceramics zirconium tungstate¹⁰²⁵ and cordierite, can further reduce L by 5%-10%.

Measuring the volume of the sensor is essentially like taking an inventory of total stored thermal energy, which has a kT N^1/2 fluctuation term from adding the N uncorrelated kT fluctuations; hence

{Eqn. 4.38}

Hence, to achieve DT ~ 1 microkelvin at T₀ = 310 K with this sensor may require N_meas ~ 47 million independent measurements of Dt_min = 1 nanosec each, or t_meas ~ 47 millisec.

Micromechanical silicon cantilever heat sensors (microcalorimeters) of ~20,000 micron³ volume have already achieved DT_min = 10 microkelvins at room temperature (DT_min / T ~ 3 x 10^-8), responding to ~1 pJ of heat in a measurement time t_meas ~ 1 millisec.⁴⁶¹ Thermal-expansion nanosensors might also exploit the temperature sensitivity of viscoelastic materials (e.g., modulus of relaxation).

Last updated on 17 February 2003