A quadrupole ICP-MS instrument (Agilent 7700x ICP-MS; Agilent Technologies, CA, USA) equipped with an ICP torch with an injector tube of diameter 1.5 mm, a conventional MicroMist nebulizer, and Scott double-pass spray chamber cooled at 2 ℃ was used for spICP-MS in combination with an externally assembled high-speed pulse signal processing system [
23]. The ICP-MS instrument was tuned daily using a tuning solution containing 1 ng/mL each of Li, Co, Y, Ce, and Tl in 2 % nitric acid to achieve optimum signal intensity and stability. The typical operating conditions of the ICP-MS instrument are listed in
Table 1. Measurements were conducted in the helium (He) mode and at the dwell time of 100 µs. All samples were measured three times for a 60-s period each to ensure the detection of a sufficient number of particles; this enables the attainment of statistically reliable results. The cleaning time between samples with 2 % nitric acid was 3 min.
Particle size measurements by spICP-MS are based on a conventional calibration approach using an ion standard solution (i.e., the ion standard solution approach) [
24,
25]. This approach uses a mass flux calibration curve from standard ion solutions and determines the particle size from the mass of the target particle, assuming a spherical geometry. Briefly, a calibration curve was constructed by relating the concentration of the ion standard solutions to the signal intensity. The concentration of the ion standard solution was then converted to mass flux using Equation (1):
where
W is the delivered mass per dwell time (ng),
is the mass concentration (ng/g),
is the sample flow rate (g/s),
is the dwell time (s), and
is the transport efficiency (%). The mass concentration, sample flow rate, dwell time, and transport efficiency were determined experimentally. The actual sample flow rate based on the nebulizer pump speed set at 0.10 rps was 0.352 g/min. Transport efficiency is defined as the ratio of the amount of analyte entering the ICP system to the amount of aspirated analyte. In this study, the particle-size method examined by Pace et al. [
23] was applied to determine the transport efficiency. The signal intensity of each particle event was then substituted into the resulting mass–flux calibration curve. The obtained signal intensities were converted to the masses of the corresponding particles using Equation (2),
where
is the mass of the particle,
is the mass fraction (the fraction of the particle mass due to the analyte element),
is the signal intensity of the particle event,
is the background signal intensity, and
is the slope of the mass–flux calibration curve. The resulting
was converted to diameter (
) using Equation (3), assuming a spherical geometry,
where
is the particle density and
is the overall porosity (described below in detail). In the case of the non-porous SiO
2 microsphere, the particle density (simply called
) was assumed to be equal to the density of the bulk material (2.65 g/cm
3 for SiO
2), similar to the assumption made in many previous studies [
23,
24,
25]. In the case of the mesoporous SiO
2 microsphere, the particle density (called
) was measured as the “true density” using the gas pycnometry method following the procedure in the ISO 12154:2014 standard [
26] and using a BELPycno helium pycnometer (MicrotracBEL, Osaka, Japana). The sample cell volume was 1 cm
3, and the measurement temperature was set at 23 ℃. Using the overall porosity (
) and lower size detection limit for the non-porous (solid) particles (i.e.,
), the lower size detection limit for the porous particles (i.e.,
) can be calculated as follows.
The value of
was determined using the method described by Lee et al. [
27].