Use of Factorial-Based Response Surfaces With Confidence Intervals in Method Optimization: Application to Thermal-Optical Analysis for Atmospheric Black Carbon
Joseph M. Conny, G A. Norris, T R. Gould
The use of response surface models involving full second-order polynomials with confidence intervals is presented here for optimizing the measurement of atmospheric black carbon (BC) by thermal-optical transmission (TOT) analysis. By pyrolyzing organic carbon (OC) in particulate matter (PM), TOT distinguishes the mass of OC from native BC, but does not physically separate the two. As a result, OC pyrolysis must be sufficient so that unpyrolyzed OC is not measured as native BC. Moreover, the specific absorption cross section of pyrolyzed OC must be equivalent to that of native BC as determined by the instrument. Modeling was based on a central composite factorial experimental design for assessing the effect of temperature and duration of the critical pyrolysis step (step 4) in the helium phase (Factors 1 and 2) and the extent of heating in the oxidizing phase (Factor 3). The large number of measurements for each sample required a lengthy analysis time and quality controls revealed within-day measurement drift. However, critical randomization and replication features of the design provided a means to detect bias and avoid confounding of the models. Two PM samples collected from Seattle, WA were modeled. The effect from varying the heating step ramp in TOT s oxidizing phase was inconclusive. However, the response surface for the apparent specific absorption cross section of native BC (sBC) revealed a ridge that indicated the temperature and duration of step 4 in helium where OC was sufficiently pyrolyzed. In addition, the intersection of sBC and the apparent specific absorption cross section for pyrolyzed OC (sChar) indicated the step-4 conditions where the cross sections were equivalent. The intersection of the 95 % confidence intervals for the sChar surface with t
, Norris, G.
and Gould, T.
Use of Factorial-Based Response Surfaces With Confidence Intervals in Method Optimization: Application to Thermal-Optical Analysis for Atmospheric Black Carbon, Analytical Chemistry, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=831453
(Accessed June 6, 2023)