Langmuir, Vol.19, No.19, 7919-7928, 2003
Analysis of uncertainties in manometric gas-adsorption measurements. I: Propagation of uncertainties in BET analyses
A detailed analysis and calculation of the uncertainties associated with manometric gas-adsorption measurements are presented for experimental data for nitrogen adsorption at, approximate to77 K by a traceable standard carbon black material (004-16820-02). Equipment- and measurement-related uncertainty sources derive from the dosing and sampling volumes; temperature control of these volumes; dosing, equilibrium, and barometric-pressure measurements; liquid nitrogen level control; and sample-mass measurements. Data processing errors derive from ignoring thermal transpiration effects and nonideal gas behavior. Departure from ideal gas behavior contributions to the amount adsorbed was accounted for by considering the temperature relationship of the second virial coefficient of the virial equation of state. Variation in the liquid nitrogen level control is shown to have an enormous impact on the pressure-measurement precision and, hence, the amount adsorbed. Variation of the liquid nitrogen level by +/-1 mm results in a variation of the equilibrium pressure from -0.42 to +0.52% and the volume of gaseous nitrogen adsorbed from -8.53 to +5.94% when compared with the results obtained during precise level control (within +/-0.2 mm). In addition to these uncertainty sources, reproducibility in the sample-mass measurement is important; a decrease in the mass resolution from 5 x 10(-5) to 5 x 10(-4) g generates a relative combined standard uncertainty of the volume of nitrogen adsorbed by 10-fold varying from 2.78 to 9.86% over the relative pressure range from 0.0007 to 0.98. For a similar standard mass uncertainty applied to the Brunauer-Emmet-Teller specific surface area analysis, the final area relative combined uncertainty increases from 0.63 to 6.19%. The calculated cumulative relative combined uncertainty in the volume adsorbed increases continuously with each experimental point from 0.28 (for the first experimental point on the adsorption branch of the isotherm) to 9.54% (for the last experimental point on the desorption branch of the isotherm), with subsequent implications for mesopore modeling and analysis accuracy.