Excess Specific Heat of Ptfe and Pctfe at Low Temperatures: Approximation Details

TL;DR

This paper presents an improved approximation method for the excess specific heat of PTFE and PCTFE at low temperatures using an orthonormal polynomial expansion that incorporates experimental errors, providing detailed numerical results and sensitivities.

Contribution

It introduces a novel weighting function in the OPEM that accounts for experimental errors, enhancing the accuracy of specific heat approximations for fluoropolymers at low temperatures.

Findings

Accurate polynomial approximations of C^{excess}/T^{5} over specified temperature ranges.

Quantitative deviations and sensitivities of the approximations are provided.

The method improves the modeling of low-temperature thermal characteristics.

Abstract

Approximation of the previously estimated excess specific heat C^{excess}/T^{5} of two fluoropolymers, PTFE and PCTFE, is presented using Orthonormal Polynomial Expansion Method (OPEM). The new type of weighting functions in OPEM involves the experimental errors in every point of the studied thermal characteristic. The investigated temperature dependence of the function C^{excess}/T^{5} is described in the whole temperature ranges 0.4\div8 K and 2.5\div7 K respectively for PTFE and PCTFE as well as in two subintervals (0.4\div2) K, (2.5\div8) K for PTFE. Numerical results of the deviations between the given C^{excess}/T^{5} data and their approximating values are given. The usual polynomial coefficients obtained by orthonormal ones in our OPEM approach and the calculated in every point absolute, relative and specific sensitivities of the studied thermal characteristic are proposed too. The approximation parameters of this type thermal characteristic are shown in Figures and Tables.