Analysis of temperature-programmed diffusion chromatograms obtained with zeolite–gas systems

Abstract

A complete theoretical solution of the diffusion equation for gas in uniform spherical particles under temperature-programmed conditions is provided. From this solution temperature-programmed diffusion (t.p.di.) curves have been computed for a wide range of heating rates, β, and activation parameters, E and D₀. Although the entire t.p.di. curve differs markedly from the curve based on the first term of the sum in the diffusion equation (from which previous t.p.di. expressions were derived), it is shown that both curves lead to the same value of E, and the difference between the pre-exponential factors, D₀, is very small. Computed maximal-rate temperatures are shown to obey perfectly the pseudo-Arrhenius linear dependence of log (T^M₂/β) on 1/T_M. Simple, easy-to-use peak-shape expressions relating the activation parameters to T_M and the half-height width of the t.p.di. curve, ω, are derived from the diffusion equation and computed quantities, i.e.E=3.6 RT²_M//_ω and D₀=2.5βr²₀//_π²ωexp (3.6 T_M/ω). The peak-shape method is compared with and concluded to be complementary to the graphical method. Experimental t.p.di. curves of hydrogen encapsulated in various forms of zeolite A agree fairly well with computed curves based on activation parameters calculated by either of the above methods from experimental values of T_M and β or ω. Finally, the effect of particle non-uniformity is shown to be substantial and to require a compensation factor in the calculation of E(and D₀). In practice, however, this effect is normally in the range of experimental inaccuracy, and thus can be ignored.