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
10.5.1 Dimensional Stability and Strength
At high applied stress, covalent bonds cleave much more readily at higher temperatures. For example,10 at an applied stress of 8 nN/bond a C=C double bond cleaves in ~1027 sec at 0 K, ~104 sec at 300 K, and ~10-3 sec at 500 K. The positional uncertainty is somewhat less problematic in design -- the mean classical thermal longitudinal displacement of a diamondoid logic rod varies only as ~T1/2.10 The endpoint of such a rod 1 nm wide and 100 nm long displaces ~0.05 nm at 77 K (liquid N2 ), ~0.10 nm at 300 K, and ~0.14 nm at 600 K (liquid lead). Mechanical elements thus become more reliable at lower temperature -- e.g., the probability of error in a force sensor (Section 4.4.1) scales as ~exp(1/T), so a 1% error in a sensor at 310 K increases to a 10% error at 600 K, but falls to just 10-6 % error at 77 K.
Most materials contract when cold and expand when hot (although zirconium tungstate is a well-known exception2938). Thus a 1000-nm long diamondoid rod at 310 K contracts to ~999 nm at 77 K and expands to 1001 nm at 600 K. However, the coefficients of thermal expansion and various other thermophysical parameters are themselves temperature-dependent. The coefficients of volumetric thermal expansion at ~298 K (~25°C) are 3.5 x 10-6 K-1 for diamond, 15.6 x 10-6 K-1 for sapphire, 1.2 x 10-6 K-1 for vitreous silica and 36 x 10-6 K-1 for crystalline silica or quartz.567
Young's modulus (modulus of elasticity) and the other moduli are also temperature-sensitive, especially and most obviously near phase changes -- e.g., sapphire melts at 2310 K but "softens" at 2070 K.1602 At ~1773 K, diamond plastically deforms at just ~1 atm pressure, but >60,000 atm are required to deform diamond at ~1300 K.2041 At the cold extreme, anyone who has seen the hammering of a nail using a piece of banana cooled in liquid N2 has witnessed the temperature sensitivity of materials strength.
Last updated on 24 February 2003