Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

DOI: 10.1039/C9JA00186G
(Paper)
J. Anal. At. Spectrom., 2019, Advance Article

Lyndsey Hendriks,
Alexander Gundlach-Graham* and
Detlef Günther

Department of Chemistry and Applied Biosciences, ETH Zurich, Zurich, Switzerland. E-mail: graham@inorg.chem.ethz.ch

Received
28th May 2019
, Accepted 25th July 2019

First published on 25th July 2019

Accurate separation of signals from individual nanoparticles (NPs) from background ion signals is decisive to correct sizing and number-concentration determinations in single-particle (sp) ICP-MS analyses. In typical sp-ICP-MS approaches, NP signals are identified via outlier analysis based on the assumption of normally distributed (i.e. Gaussian) or Poisson-distributed background signals. However, for sp-ICP-MS with a Time-of-Flight (TOF) mass spectrometer that digitizes MS signal by fast analog-to-digital conversion (ADC), the background ion signals are neither Gaussian nor Poisson. Instead, steady-state ion signals with ICP-TOFMS follow a compound Poisson distribution that reflects noise contributions from Poisson-distributed arrival of ions and gain statistics of microchannel-plate-based ion detection. Here, we characterize this compound Poisson distribution with Monte Carlo simulations to establish net critical values (L_{C(ADC)}) as detection decision levels for the discrimination of discrete NPs in sp-ICP-TOFMS analyses. We apply L_{C(ADC)} to the analysis of gold-silver core–shell nanoparticles (Au–Ag NPs), and compare these results to conventional sigma-based NP-detection thresholds. Additionally, we investigate how accurate modelling of the compound Poisson TOFMS signal distribution enables separation of overlapping background and NP distributions; we demonstrate accurate size measurement of 20 nm Au NPs that have mean signal intensity of less than four counts.

In sp-ICP-MS, accurate measurement of NP size or particle number concentration (PNC) is only possible if NP signals are distinguishable from background signals,^{6–8} which means that NP-size detection limits can only be improved through increasing the NP-to-dissolved background signal ratio. To accomplish this, either the instrument sensitivity can be increased or the dissolved background can be reduced. For example, dissolved background can be reduced through simple sample dilution, ion-exchange purification,^{9,10} NP extraction,^{11} or separation methods.^{12–14} Despite the effectiveness of the different approaches to remove dissolved analyte species, there will always be a non-zero background and, for the detection of small NPs that produce low ion-count signals, analyte sensitivity becomes the major limitation. Recall that the mass content scales with the cube of the diameter, so a 10 nm diameter Au NP, which is only 5 times smaller in diameter than a 50 nm diameter Au NP, contains little mass (∼10 ag) compared to a 50 nm Au NP (∼1260 ag). To date, the smallest detectable Au NPs are between 4–7 nm in diameter,^{15,16} and in order to measure NPs with half this diameter, one would require 8-times higher sensitivity. Near the size detection limit, particle signals are, by definition, similar in signal intensity to background signals, so data processing algorithms used to discriminate NP and dissolved background signals are critical. Currently, sp-ICP-MS NP identification algorithms are either based on outlier detection^{17–20} or deconvolution^{21} of the dissolved and particulate fractions.

The basic steps of iterative outlier analysis for sp-ICP-MS are: (1) the entire dataset is averaged, (2) all events that are above μ + nσ are recognized as outliers and removed from the dataset, (3) μ and σ of the remaining dataset are recalculated and new outliers are collected, (4) iterations continue until no data are detected above the final μ + nσ threshold. Importantly, the NP-detection limit as defined here is, in fact, a decision level based solely on controlling the number of false positives (i.e. dissolved signals identified as NPs): at the NP-detection limit, by definition (assuming homoscedasticity), 50% of analyte NPs would be recorded as false negatives.^{24} Because we have no a priori information on shape, size, or predicted signal variance from analyte NP populations, identification of NP signals is best achieved with a decision level. In the case of μ + nσ detection decisions, in which background signal is assumed to be normally distributed (i.e. Gaussian), the μ + nσ method should find outliers (i.e. NPs) with false positive rates of 0.135%, 0.0032%, or 0.000028% (280 ppb) for n values of 3, 4, or 5, respectively. At low background ion-count rates, nσ thresholds do not accurately predict false positive rates because counting statistics dominate and the background more closely matches a Poisson distribution for pulse counting MS detectors.^{19}

Throughout the sp-ICP-MS literature, there is no consensus on what integer value of sigma should be used to discriminate NP signals from dissolved signals. Studies independently report that 3σ,^{25} 5σ,^{15,20} or even 7σ^{26} threshold criteria provide best NP-detection accuracy. The range of NP-detection criteria routinely used is evidence of the importance of accurate background noise characterisation. False-positive rates for NP detection thresholds above 5σ do not provide (statistically) more discrimination power for the PNCs typically measured; instead, these more restrictive NP-detection thresholds are used because the background signals cannot be fully described by a normal distribution.

In our treatment of detection criteria for sp-ICP-TOFMS, we follow the definition of detection developed by Currie^{28,29} and adopted by IUPAC,^{30} in which the minimum detectable signal (i.e. the detection decision) is termed the critical value L_{c}. In sp-ICP-MS, the critical value is equivalent to the NP-detection threshold: it is the signal value above which one claims all signals come from NPs.^{19} According to Currie, detection is, in principle, a judgement on whether an observed signal originates from the analysed sample or whether it is caused by blank or background signal. If one understands or can predict the background distribution, then one can set a critical value above which there is only a small probability that a signal comes from the background, i.e. it is a false positive. Currie defines the false positive rate as the term α. For conventional steady-state signals, an α of 0.05 (5%) is custom.^{29} However, in sp-ICP-MS, background events typically greatly outnumber NP events, so more conservative α values of 0.1% or even 0.01% are suggested.^{19,27} For example, in sp-ICP-MS measurements, often less than 10% of the dataset is occupied by NP signals. Assuming a background:NP event ratio of 10000:1000 and NP-detection with α values of 5% and 0.1%, one would expect 500 and 10 signals falsely recognized as NP signals, respectively, which would lead to errors of +50% or +1% in particle number. Consequently, the assignment of robust NP-detection critical values in sp-ICP-MS depends both on the ability to accurately predict and describe background distributions, as well as on the selection of an appropriate α value for the expected ratio of recorded NP events to background.

In the following discussion, we demonstrate how to accurately characterize compound Poisson background distributions in sp-ICP-TOFMS and evaluate the robustness of compound-Poisson-derived net critical values (L_{C(ADC)}), for use as NP-detection thresholds. We specifically explore the use L_{C(ADC)} for the challenging case of detecting of small Au NPs (20 and 30 nm in diameter) that produce low-ion signals of similar magnitude to signals from the dissolved background.

Total diameter (TEM) | 61 ± 6 nm |

Au core diameter (TEM) | 30 ± 3 nm |

Particle concentration | 1.5 × 10^{10} particles per mL |

Mass concentration (Au) | 5 μg mL^{−1} |

Mass concentration (Ag) | 0.016 μg mL^{−1} |

Shell thickness (calculated from total diameter) | 15.5 ± 4 nm |

Mass Au core (calculated from Au-core diameter) | 0.28 ± 0.08 fg |

Mass Ag shell (calculated from volume) | 1.13 ± 0.4 fg |

Mass Ag shell (calculated from mass concentration) | 1.07 fg |

Microdroplets were used for NP mass calibration and calibration solutions were prepared by diluting commercially available single-element standard solutions of Au and Ag (Inorganic Ventures, USA) in 1% sub-boiled HNO_{3} and 1% HCl (VWR Chemicals, USA). 100 μg L^{−1} of Cs was also added to microdroplet solutions; Cs signals were used as a tracer to identify microdroplet signals. All dilutions were performed gravimetrically using a balance (Mettler AE240, Mettler-Toledo, Greifensee, Switzerland).

a In order to increase the sensitivity for Au and Ag, the TOF spectral acquisition rate was adjusted from its standard value of 21.739 kHz to 25.316 kHz, which increased sensitivity of 30%, but introduced a high-m/z cut-off above 200 Th.b Averaged mass spectra are composed of data summed from 44 full mass spectra collected every 39.5 μs. Note that, for continuous liquid sample introduction of Au (see Fig. 1), the averaged spectrum acquisition rate was of 2.024 ms (i.e. 44 mass spectra at 21.739 kHz). | |
---|---|

Microdroplet Introduction | |

Droplet diameter | 42.8 μm |

Droplet frequency | 40 Hz |

Ag concentration in droplets | 105 μg L^{−1} |

Au concentration in droplets | 96 μg L^{−1} |

He gas flow in falling tube | 0.56 L min^{−1} |

Ar gas flow in falling tube | 0.15 L min^{−1} |

Pneumatic nebulizer | |

Nebulizer gas (Ar) | 0.82 L min^{−1} |

Solution uptake rate | ∼600 μL min^{−1} |

ICP conditions | |

Intermediate gas flow (Ar) | 0.8 L min^{−1} |

Outer gas flow (Ar) | 15 L min^{−1} |

Power | 1550 W |

Sampling position | 5 mm above load coil |

Collision/reaction cell (He) | 1 mL min^{−1} |

TOFMS conditions | |

TOF spectral acquisition rate^{a} |
25.316 kHz |

Averaged spectrum acquisition rate^{b} |
575.36 Hz (1.738 ms) |

Monte Carlo simulations were used to fit ICP-TOFMS background signal distributions to a compound Poisson model in the same manner as previously described.^{27} Briefly, ICP-TOFMS data was truncated above the 90%-quantile (or at 3 counts, whichever is larger) in order to minimize the number of NP signals in the dataset. The background data was then iteratively modelled as a compound Poisson distribution in which the TOFMS signal acquisition is considered to be the sum of a Poisson-distributed number of ions that each sample the measured single-ion-signal (SIS) distribution of the ADC-based TOF detection system. Fitting of the background TOFMS data distribution was done with a sum of squared error (SSE) minimization procedure that globally samples a range of background count rates (λ_{bkgd}) and number of acquisitions (N_{acq}) to estimate values that best describe the measured data. Critical values (L_{C(ADC)}) for NP detection were also calculated by Monte Carlo simulation with an in-house written LabVIEW program (available upon request) to approximate the relationship between L_{C(ADC)} and λ_{bkgd} relationship for a given false-positive rate (α).^{27} Because L_{C(ADC)} depends on the shape of the SIS distribution of the TOFMS detection system, we measured the SIS histogram prior to sp-ICP-TOFMS analysis. To assign a value to L_{C(ADC)} for a given analysis, we used λ_{bkgd} determined by Monte Carlo fitting of the data and the derived expression for L_{C(ADC)}. Subtraction of Monte-Carlo simulated background from measured signal distributions was performed in LabVIEW and results were saved as frequency histograms. Processed sp-ICP-TOFMS data were plotted with OriginPro (ver 8.6.0, OriginLab Corp., MA, USA) and final figures were assembled in Adobe Illustrator (ver. 16.2.0, Adobe Systems Inc., USA).

For comparison of conventional NP-detection threshold determination methods (i.e. μ + 3σ and μ + 5σ) with our compound-Poisson-based critical value approach, iterative outlier analysis was performed in Matlab. Due to an abundance of zero-count signals in the TOFMS data, signals with zero counts were removed from the dataset prior to outlier analysis. Alternative to outlier analysis, we found that fitting signal histograms with a Gaussian function provided a better estimation of μ and σ. Gaussian fitting of the background was also performed in Matlab.

NP mass calibration was carried out using analyte sensitivities determined from the microdroplets. The signals from at least 500 microdroplets for each sp-ICP-TOFMS measurement were recorded and averaged to determine the average single-droplet signal. Microdroplets for each measurement were size-calibrated based on imaging dispensed droplets with a camera with known magnification and CMOS sensor pixel size.^{40} Then, as the microdroplet size and content are known, the average sensitivity in counts per unit mass of analyte in each droplet can readily be determined.^{41} NP diameter was calculated assuming spherical geometry of the NPs and bulk density of the NP metal.

Since low-count TOFMS signals are best described with a compound Poisson distribution, the most accurate approach to establish a NP-detection threshold is to calculate net critical values specifically for this given distribution, i.e. L_{C(ADC)}. Unlike Gaussian-distributed background noise, which has well-established z-scores that allow direct calculation of L_{C} based on measurement or estimation of σ,^{24,28} the compound Poisson distribution obtained with TOFMS detection does not follow a known distribution and is dependent on an empirical detector response curve, and thus cannot be simply calculated. For this reason, we estimate the relationship between L_{C(ADC)} and λ_{bkgd} for a given false-positive rate (α) through Monte Carlo simulation of compound Poisson distributed TOF signals for a range of λ_{bkgd} values (from 0.25–25 counts per acq) and a measured SIS histogram.^{27} Importantly, because the compound Poisson distribution changes as a function of shape of the TOF detection system response curve (i.e. SIS histogram), routine measurements and calibration of the SIS are required to define a reliable L_{C(ADC)}. For example, SIS histograms likely vary between instruments or could change due to detector aging.

For measurements reported here, L_{C(ADC)}, is defined in eqn (1), where the α value is set conservatively to 0.0001 (0.01%).

(1) |

To use L_{C(ADC)} as a detection decision to identify NPs, it is more convenient to work with the gross signal critical value (S_{C(ADC)}), which is defined as the net critical value L_{C(ADC)} plus λ_{bkgd} (see eqn (2)). To determine the analyte-mass detection decision (X_{C(ADC)}), the net signal critical value (L_{C(ADC)}) is divided by the net absolute mass sensitivity (A_{i,drop}) obtained from microdroplet standards, as seen in eqn (3).

(2) |

(3) |

For determination of L_{C(ADC)} and S_{C(ADC)}, we set α = 0.01% because our analyses of Au–Ag and Au NPs have relatively few NP events compared to the background. For each sp-ICP-TOFMS analysis, we measure about 90000 data points, so α = 0.01% predicts nine false-NP signal events. Considering an acceptable false-detection rate of 10% of the total NPs, our chosen α should enable quantitative counting of NPs of down to ∼90 measured NP events. To detect lower numbers of NPs quantitatively, α would need to be lowered, which would elevate S_{C(ADC)} and might cause non-detection of analyte NPs. In general, the choice of α for NP detection is somewhat arbitrary, and the analyst must find a useful compromise between selection of acceptable false-positive rates and NP-detection threshold.

In Fig. 2, we plot a portion of the Au–Ag NP time trace, as well as the signal-intensity frequency histograms for ^{107+109}Ag and ^{197}Au, respectively (see Fig. 2b and c). As displayed in Fig. 2b, the Ag NP signal distribution is baseline separated from the dissolved background signals, and a visually set threshold value of 10 counts was used to distinguish NP signals from the background. However, for ^{197}Au^{+} signals, there is no clear separation between the dissolved background and NP distributions. Instead, we find a bimodal, but uninterrupted, distribution that has a very similar shape to the distribution observed in Fig. 1a. Again, most ion signals occupy the zero-count bin and a right-screwed distribution is present at slightly higher count values. To determine the fraction of the Au signal associated with the dissolved background, we fit the Au-signal distribution with our Monte Carlo method to find λ_{bkgd} and N_{acq}. Then, we used this λ_{bkgd} value to calculate S_{C(ADC)}. As shown in Fig. 3, thresholding Au-signals based on S_{C(ADC)} = 2.77 counts provides accurate identification of Au-NP signals (98.3% NP recovery). The detection decision level in terms of Au-mass (X_{C(ADC)}) is 68 ag, or ∼19 nm in diameter. We do not measure 100% of the Au NPs because some of the Au–Au NPs produce ^{197}Au^{+} signals of less than 2.77 counts. Based on concomitance of found Au-NP signals and Ag-NP signals, we determined that 10 of the identified ^{197}Au^{+} signals found above S_{C(ADC)} were false positives, which is slightly less than the 26 predicted based on our assignment of α = 0.01%.

For comparison, we also attempted to identify Au-NP signals based on conventional iterative outlier analysis with outlier thresholds of μ + 3σ and μ + 5σ. In this iterative outlier analysis, we found that data with zero counts had to be removed from the dataset to prevent the threshold-value from converging to zero. However, in our particular case, when zero-count data was removed, the background:NP number ratio was low (∼2:1) and the iterative outlier analysis algorithm failed to accurately distinguish background and NP distributions, which resulted in artificially high NP-detection thresholds and low Au-NP recoveries (see Fig. 3a).

On the other hand, we also determined μ + 3σ and μ + 5σ NP-detection thresholds based on fitting the non-zero background histogram with a Gaussian function. This Gaussian-fitting procedure produced more realistic results than the iterative outlier analysis, with NP recoveries of 103% and 99% for μ + 3σ and μ + 5σ thresholds, respectively. However, it should be noted that if the non-zero-background was truly Gaussian distributed, a μ + 3σ detection threshold should produce 0.135% false positives. Consequently, as our non-zero-background is composed of ∼3000 data points, one would predict only 4 false-positive NP signals. Instead, the μ + 3σ detection decision produces 38 false-positive Au-NP signals. Deletion of zero-count data—which is the major signal level in the background—prior to background variance calculation alters the true shape of the background distribution. This signal truncation causes the calculated detection decisions to be based on fitting of incomplete datasets, and it is difficult to predict how characteristics such as background:NP event ratios or instrument response function could affect the performance of these detection decisions. The use of S_{C(ADC)} instead of σ-based NP-detection criteria takes into account the compound Poisson nature of the ICP-TOFMS data to provide a more complete description of the dissolved background signal, and therefore offers more robust NP detection with predictable false positive rates.

In Fig. 4, we report the quantified mass of Ag and Au in each Au–Ag core–shell NP based on online microdroplet calibration, which was used to establish absolute sensitivities for ^{107+109}Ag and ^{197}Au.^{32,33} Prior to quantification, Au-NP signals were identified based on the S_{C(ADC)} threshold. As seen, the determined element mass for both the Ag shell and the Au core matches expectations (see Table 1). For the Au core, we also plot the diameter frequency distribution—which again matches expectations. An important point to highlight here is that the use of a NP-detection threshold (i.e. S_{C(ADC)}) enables the identification of NPs on a particle-to-particle basis. Hence, for each Au NP detected above S_{C(ADC)}, the corresponding mass of Ag in that NP can be determined, which is an important requirement for studies that classify NPs based on their multi-elemental composition.^{35,36,38}

Sizing results are compared with S(T)EM measurements presented in Fig. 6. From the S(T)EM measurements, it can be observed that not all NPs are as spherical as initially expected. Large non-spherical particles were not accounted for in the S(T)EM data evaluation, which could explain the slightly lower average Au NP diameter found by S(T)EM image analysis compare to sp-ICP-TOFMS results.

In addition to developing NP-detection thresholds for sp-ICP-TOFMS, we also demonstrate that, in cases where NP and the dissolved fractions overlap—such as in the case of 20 nm diameter Au NPs—the subtraction of a Monte Carlo modelled distribution from the measured signal distribution can be used to predict the fraction of NPs present below S_{C(ADC)}. This treatment relies on very accurate Monte Carlo modelling of the background distribution and necessarily eliminates the information on individual particles. While modelled background subtraction is a promising approach, more work on characterizing uncertainty in Monte Carlo modelled distributions is required, especially if the approach is applied to sp-ICP-TOFMS measurement with low NP numbers.

In the presented method, the advantages of microdroplet calibration and the dual sample introduction system are combined with the new insights in TOFMS noise. Online calibration with microdroplets allows for wide flexibility in terms of materials and sizes of NPs, and also automatically compensates for plasma-related matrix effects.^{33} The development of more accurate noise characterization for ICP-TOFMS as demonstrated here, combined with dual sample introduction and online microdroplet calibration, make sp-ICP-TOFMS a promising method for the simultaneous quantification of diverse metal-containing NPs in terms of NP composition and number concentration in complex sample matrices.

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