Miniaturization of electronic devices carries them to the quantum limits which mean quantum effect will be dominant in nano-size device characterization. A first band analytical model of the quantum capacitance for (16, 0) zig-zag graphene nanoscroll (ZGNS) is presented. The behavior of the quantum capacitance within the degeneracy limits is approximated using the Maxwell–Boltzmann approximation within a range of E - EF > 3KBT. The quantum capacitance is subsequently derived from the carrier density of the ZGNS due to its significance within one-dimensional (1D) devices by employing the Taylor's series expansion for parabolic energy band structure approximation. Additionally, the quantum capacitance analytical derivation in term of ZGNS physical form considering the Archimedean spiral-type structure is modeled. Because of its unique geometry structure which provides high area for intercalation, it is expected that ZGNS structure (length and interlayer distances) will alter the quantum capacitance. We also report that at first sub-band of (16, 0) ZGNS the quantum capacitance reach degenerate limit at approximately of ≅ 0.49 × 10-10 F/m @ 49 pF/m .
