Transcribed Text
3. Coulomb blockade in gold nanoparticles. The capacitance of a nanoparticle is given as πΆ =
πππ0
π
π (π + π). where π is the dielectric constant of the ligand shell of thickness d, and r is the core
radius.
(a) For a single-nanoparticle STM experiment, the charging energy, π = π2
2πΆ
. In order to observe the
Coulomb blockade, thermally-driven electron tunneling must be prevented, which is the requirement
ππ΅π βͺ π. Practically, this requirement meansππ΅ππππ β π/25, where ππππ is the maximum
temperature at which the Coulomb blockade is observable. Find an expression for ππππ in terms of π, π
and π.
(b) Consider octanethiolate-stabilized Au nanoparticles, for which π = 0.8 and π = 1.0 inn. Plot ππππ vs
π for radii from 1 nm to 10 nm.
(c) For which radius is ππππ room temperature (293 K)? (An estimate from your graph is OK.)
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