Representative
tree structures of PE trees and PPP trees from level
1 to 5 are shown in (a) and (b), respectively. When a AuNP is located
deeper into the plane, it is shown in a lighter color, The underlying
scheme for the heat conductance calculation up is shown in (c). Using
the level 3 PE tree as an example, the 8 AuNP leaves on top are heat
sources at 340 K and the 1 AuNP root at the bottom is the heat sink
at 295 K. The tree branch lengths are all the same. PE branches are
50 carbons, and PPP branches are 48 carbons (12 rings). (d) The accumulative
heat additions at the 8 different AuNP leaves are shown in 8 different
colored dotted lines, and the energy subtraction at the 1 AuNP root
is shown in blue. As noted in the text, the sum of the accumulated
heat across all 8 leaves exceeds the energy subtraction by the initial
transient energy addition needed to compensate the mismatch in heat
capacities between the leaves and the root. The red curve thus displays
the sum of the 8 leaves subtracted by this transient energy. (All
colors are in grayscale in colorless prints and indicated by the legend.).