Black-body Thermal Radiative and Thermodynamic Functions of 1-Dimensional Self-Assembly Nanotubes

TL;DR

This paper derives analytical expressions for the thermal radiative and thermodynamic functions of 1D nanotubes modeled as black-body radiators, within a specific frequency range, to understand their thermal behavior.

Contribution

It introduces a model representing 1D nanotubes as black-body radiators and provides analytical formulas for their thermodynamic functions in a finite spectral range.

Findings

Expressions for energy density, Stefan-Boltzmann law, and other thermodynamic functions derived.

Functions expressed in terms of polylogarithm functions for specific frequency range.

Validation requires experimental measurement of energy density in the specified spectral range.

Abstract

Assuming that 1-dimensional self-assembly nanotubes can be represented as a 1-dimensional cavity-type black-body radiator of length L and radius r in thermal equilibrium at a temperature T, analytical expressions for the thermal radiative and thermodynamic functions of the emitted black-body radiation are obtained in the finite spectral range of the electromagnetic spectrum. The total energy density, the Stefan-Boltzmann law, the number density of the photons, the Helmholtz free energy density, the entropy density, the heat capacity at constant volume, and the pressure are expressed in terms of the polylogarithm functions. In the frequency range 0.05-0.19 PHz, the thermal radiative and thermodynamic functions of the 1-dimensional black-body radiation at different temperatures are calculated. To confirm our assumption, it is necessary to measure the total energy density in the direction L in the finite frequency range 0.05-0.19 PHz, using a single nanoparticle mass spectrometer or other optical devices.