During the initial stages of the growth of the nanowire of

Chapter , Problem 3.138

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During the initial stages of the growth of the nanowire of 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 nonuniform 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 nano spring 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. Hint: Assume the spring radius does not change when the spring is heated. The overall spring length may be approximated by the formula