  This computational research study will compare the specific charge capacity
(SCC) between lithium ions inserted into crystallize silicon (c-Si) nanowires
versus sodium ions inserted into amorphous silicon (a-Si) nanowires. It will be
demonstrated that the potential energy V(r) within the lithium-silicon nanowire
supports a coherent energy state model with discrete electron particles while
the sodium-silicon nanowire potential energy will be discovered to be
essentially zero and thus the electron current that travels through the
sodiated silicon nanowire will be modeled as free electron with wave-like
characteristics. This is due to the vast differences in the electric fields of
the lithiated and sodiated silicon nanowires where the electric fields are of
the order of 10^(+10)V/m and 10^(-15) V/m respectively. The main reason for the
great disparity in electric fields are due to the present of optical
amplification within lithium ions and the absence of this process within sodium
ions. It will be shown that optical amplification develops coherent optical
interactions which is the primary reason for the surge of specific charge
capacity in the lithiated silicon nanowire. Conversely, the lack of optical
amplification is the reason for the incoherent optical interactions within
sodium ions which is the reason for the low presence of SCC in sodiated silicon
nanowires.
