Hansen parameter evaluation for the characterization of titania photocatalysts using particle size distributions and combinatorics

Abstract

Titania photocatalysts have great potential as remidiators of air pollution. While various aspects of photocatalyst synthesis, adsorption and photoactivity have been investigated, thorough understanding of the particle surface behavior has...

Determination of Hansen Parameters of Nanoparticles: A Comparison of Two Methods Using Titania, Carbon Black, and Silicon/Carbon Composite Materials

“…For accurate analysis, it is important to be able to determine HSPs properly. In this work, the HSPs of P25, CB, and Si/C were derived via two different methods-IEA and PSDC-based on the works of Süß et al and Anwar et al [18,21] The results show that the methods chosen lead to similar HSPs. It has been further shown that the steps to end up in a consistent PL categorization, and thus the resulting PL list has a major effect on the observed and remaining differences in the finally derived HSPs.…”

“…In contrast, the PSDC method uses combinatorics which calculates all possible combinations with a good fit, and any bad fit is neglected. [20,21] In addition, the resulting HSP reporting summary, here provided as a best-practice-example, includes all the data needed to form an informed opinion about the data of the material analyzed. A general trend observed was that the PSDC method results in smaller HSP spheres and therefore enables to better differentiate between variations of the same material.…”

“…For the calculation of PSDs, the constant position method was chosen with five nodal positions (122, 123.5, 125, 126.5, 128 mm) of 1.0 mm nodal width. More details on the PSD derivation are discussed by Detloff et al [39] Product ratios are then calculated according to our previous work using Equation 3 below and used for making the PL list in order of increasing product ratios (details available in Anwar et al): [21] Product ratio = Finally, the PLs were categorized into good, uncertain, and poor based on the clustering of their product ratio values. The HSP values for each uncertain PL were then calculated and noted down as described by Bapat et al [20] Combinations of HSPs where the condition of all good PLs in and all poor PLs out (of the HSP sphere) was fulfilled were chosen for providing the range of HSPs for each material, while the ones that did not fulfill the condition were reported as outliers.…”

“…One significant advantage of using PSDs is that, although in our work they were derived from AC, they could equally be derived from other size measurement techniques such as DLS, laser diffraction, or electron microscopy. [21] However, it remains to apply this method to other materials and verify the application of PSDs while simultaneously comparing it with the standardized routine developed by Süß et al [18] In this work, we compare two elaborate methods, namely IEs with step-wise addition (IEA), and PSDs with combinatorics (PSDC) for HSP derivation and show their convergence for three different yet technologically relevant materials. [18,21] We introduce some additional considerations for simplicity in selection of the threshold required for the IEA method.…”

“…[21] However, it remains to apply this method to other materials and verify the application of PSDs while simultaneously comparing it with the standardized routine developed by Süß et al [18] In this work, we compare two elaborate methods, namely IEs with step-wise addition (IEA), and PSDs with combinatorics (PSDC) for HSP derivation and show their convergence for three different yet technologically relevant materials. [18,21] We introduce some additional considerations for simplicity in selection of the threshold required for the IEA method. The derived HSPs will serve as values for comparison in literature since all the information needed for a thorough comparison is provided according to the Hansen reporting framework.…”