During the initial stages of the growth of the nanowire of Problem 3.109, a slight perturbation of the liquid catalyst droplet can cause it to be suspended on the top of the nanowire in an off-center position. The resulting non-uniform deposition of solid at the solid-liquid interface can be manipulated to form engineered shapes such as a nanospring, that is characterized by a spring radius, r, spring pitch, s, overall chord length, Lc (length running along the spring), and end-to-end length, L, as shown in the sketch. Consider a silicon carbide nanospring of diameter D = 15 nm, r = 30 nm, s = 25 nm, and Lc = 425 nm. From experiments, it is known that the average spring pitch s varies with average temperature T by the relation ds/dT = 0.1 nm/K. Using this information, a student suggests that a nanoactuator can be constructed by connecting one end of the nanospring to a small heater and raising the temperature of that end of the nanospring above its initial value. Calculate the actuation distance, ∆L, for conditions where h = 106 W/m2 ∙ K, T∞ = Ti = 25°C, with a base temperature of Tb = 50°C. If the base temperature can be controlled to within 1°C, calculate the accuracy to which the actuation distance can be controlled.

Transcribed Image Text:

Le 27 Vr + (5/2) Ть T, h oot