  Recent analyses of thermoelectric amplification of acoustic phonons in
Free-Standing Graphene (FSG) $\Gamma_q^{grap}$ have prompted the theoretical
study of the influence of external temperature gradient ($\nabla T$) on the
acoustoelectric current $j_T^{(grap)}$ in FSG. Here, we calculated thermal
field on open circuit ($j_T^{(grap)} = 0$) to be $(\nabla T)^g = 746.8Km^{-1}$.
We then calculated acoustoelectric current ($j_T^{(grap)}$)to be $1.1mA\mu
m^{-2}$ for $\nabla T = 750.0 Km^{-1}$, which is comparable to that obtained in
semiconductors ($1.0mA\mu m^{-2}$), the thermal-voltage $(V_T)_0^g$ to be
$6.6\mu V$ and the Seebeck coefficient $S$ as $8.8\mu V/K$. Graphs of the
normalized $j_T^{(grap)}/j_0$ versus $\omega_q$, $T$ and $\nabla T/T$ were
sketched. For $j_T^{(grap)}$ on $T$ for varying $\omega_q$, Negative Difference
Conductivity (NDC) ($| \frac{\partial j}{\partial T}| < 0$) was observed in the
material. This indicates graphene is a suitable material for developing thermal
amplifiers and logic gates.
