Letter pubs.acs.org/JPCL
Skewness Analysis in Variance Spectroscopy Measures Nanoparticle Individualization Stephen R. Sanchez,† Sergei M. Bachilo,† Yara Kadria-Vili,† and R. Bruce Weisman*,†,‡ †
Department of Chemistry and the Smalley-Curl Institute, Rice University, 6100 Main Street, Houston, Texas 77005, United States Department of Materials Science and NanoEngineering, Rice University, 6100 Main Street, Houston, Texas 77005, United States
‡
S Supporting Information *
ABSTRACT: An important enabling step in nanoparticle studies is the sorting of heterogeneous mixtures to prepare structurally homogeneous samples. It is also necessary to detect and monitor aggregation of the individual nanoparticles. Although variance spectroscopy provides a simple optical method for finding low concentrations of heteroaggregates in samples such as single-walled carbon nanotube dispersions, it cannot detect the homoaggregates that are relevant for well-sorted samples. Here we demonstrate that variance spectral data can be further analyzed to find third moments of intensity distributions (skewness), which reveal the presence of emissive homoaggregates. Using experimental measurements on variously processed nanotube dispersions, we deduce a simple numerical standard for recognizing aggregation in the highly sorted samples that are increasingly available to nanoscience researchers.
R
measure spectra from different regions of a dilute nanoparticle dispersion, ensuring that the spectra are statistically independent. Recently, we have used variance spectroscopy to deduce absolute absorption cross-sections for the first electronic transition of 11 different SWCNT structural species.11 We have also used variance analysis to expose spectral differences in DGU-sorted SWCNT samples.12 By comparing the mean emission and covariance spectra, we identified inhomogeneous components present in these highly enriched fractions. Covariance analysis also gives insight into the aggregation state of SWCNT dispersions.10 Two-dimensional covariance matrices can reveal off-diagonal features caused by spatial correlations between (n,m) species emitting at different wavelengths, allowing a quantitative measure of emissive aggregates that are hybrids containing those species. However, covariance analysis fails if the sample is highly purified in a single (n,m) species because homoaggregates do not generate off-diagonal features. We therefore present a complementary method, using higher order moment analysis of the same variance data set, to monitor aggregation in highly enriched samples. The method is based on the fact that in loose homoaggregates the nanotubes remain electronically and optically separate. When such an aggregate is probed, it emits more brightly than an individual nanotube and generates an anomalously large positive intensity fluctuation. This asymmetry in the distribution of intensities can be captured through third moment statistical analysis.
esearch and applications of artificial nanomaterials are often hindered by sample heterogeneity. Typical asproduced nanoparticle samples contain a variety of structural forms with distinct physical properties. For quantum dots or metallic nanoparticles, this heterogeneity may be simply a smooth distribution of particle sizes. Single-walled carbon nanotubes show similarly continuous length distributions, but their electronic and optical properties are governed by discrete transverse structure (diameter and roll-up angle), which is labeled by a pair of integers, (n,m).1 Many applications of SWCNTs could benefit from samples containing only a few or even a single (n,m) species. Therefore, several powerful sorting techniques, including density gradient ultracentrifugation (DGU),2−4 aqueous two-phase extraction,5−7 and gel chromatography,8,9 have been developed to selectively sort individual (n,m) species from complex mixtures. The large and growing interest in sorted SWCNT samples demands analytical tools that can characterize their dispersion quality and monitor aggregation. Here we describe a technique to measure the aggregation state of highly enriched or single-species SWCNT dispersions using skewness analysis in variance spectroscopy. This method offers a practical means of characterizing structurally sorted SWCNTs and it may prove useful for spectrally heterogeneous dispersions of other nanoparticles. We have previously described the new method of variance spectroscopy.10 This technique determines several dispersion characteristics, such as structure-specific particle concentrations, emission efficiencies, and aggregation states, by analyzing the spectral intensity fluctuations resulting from statistical variations in concentration. These variations are detectable in fluorescence spectra measured from very small observation volumes. In a typical experiment, we use a sample translator to © XXXX American Chemical Society
Received: May 12, 2017 Accepted: June 12, 2017 Published: June 12, 2017 2924
DOI: 10.1021/acs.jpclett.7b01184 J. Phys. Chem. Lett. 2017, 8, 2924−2929
Letter
The Journal of Physical Chemistry Letters
Figure 1. Variance spectral analysis of a well dispersed (6,5)-enriched sample prepared by NDGU and excited at 785 nm. (A) Mean (first moment) emission spectrum. (B) Histogram of the fluorescence fluctuations at the (6,5) peak position. The value of skewness, s, was calculated from this distribution of fluctuations. (C) Variance (second moment) emission spectrum. (D) Contour plot of the sample’s covariance matrix. Note the limited possibility of observing off-diagonal elements because of the high (n,m) purity.
observation volume in a FCS experiment has been deduced from the photon-count histograms or from higher moment analysis (up to the third moment for a two-component system).14,15 Additionally, high-order autocorrelation functions have permitted studies of aggregation and oligomerization of proteins, lipids, and other biological molecules as an extension to FCS.16,17 Other fluorescence fluctuation methods suitable for tracking aggregation states include fluorescence moment image analysis as well as number and brightness analysis.18−20 Skewness has also been used to quantify actin microfilament clustering in plant cells through an automated microscopic approach.21 We have extended these ideas to study aggregates in nanoparticle suspensions using variance spectroscopy. A test sample highly enriched in (6,5) SWCNTs was prepared by nonlinear density gradient ultracentrifugation (NDGU) and precision fractionation. Such samples are typically very well dispersed. However, to maximize nanotube individualization and prepare a negative control, we further processed the extracted sample with 20 s of 3 W tip sonication. We then measured a sequence of 2000 fluorescence spectra using our recently refined variance spectrometer with 785 nm excitation. From the resulting data set, we calculated the mean emission (Figure 1A) and variance (Figure 1C) spectra. These showed that the sample contained predominately (6,5) SWCNTs, with only a few percent of several other small diameter species: (9,1), (8,3), (7,5), and (10,2). We previously demonstrated that aggregation in a SWCNT dispersion gives off-diagonal features in the 2D covariance matrix when
Variance spectroscopy relies on moment analysis of measured spectral intensities. For most applications, the first two moments (fluorescence mean intensity and variance) are sufficient. After calculating these two values for each spectral channel, we can combine them to deduce the mean number of nanoparticles emitting in the probed sample volume and analyze for correlations between different wavelength channels. Additional useful information is available from the intensity distribution’s third standardized moment, known as skewness.13 The wavelength-dependent skewness of the emission intensity, skewness(I(λ)), is defined as 3⎤ ⎡⎛ I ( λ ) − I ̅ (λ ) ⎞ ⎥ skewness(I(λ)) = E⎢⎜ ⎟ ⎢⎣⎝ σ (λ ) ⎠ ⎥⎦
(1)
Here E is the expectation value operator (a simple average over measurements to get the mean value), I(λ) is the emission intensity from an individual measurement at a specific wavelength, I(̅ λ) is the mean emission intensity at that wavelength, and σ(λ) is the standard deviation of emission intensities at that wavelength. We note that in the regime of interest here, skewness and σ values are not strongly coupled, despite the form of eq 1. Moments and autocorrelations higher than second order have previously been used to assess aggregation levels in microscopic techniques such as fluorescence correlation spectroscopy (FCS) and image correlation spectroscopy. For example, the degree of aggregation of fluorescent molecules diffusing through the 2925
DOI: 10.1021/acs.jpclett.7b01184 J. Phys. Chem. Lett. 2017, 8, 2924−2929
Letter
The Journal of Physical Chemistry Letters aggregates contain different semiconducting (n,m) species.10 Figure 1D shows a contour plot of the covariance matrix measured for this sorted sample. Because of the small relative abundance of heteroaggregation partners in the sample, no offdiagonal cross peaks are possible. This prevents the use of firstand second-moment analysis to assess aggregation state. Extending analysis of our data set, we plot the full (6,5) emission fluctuation distribution as a histogram in Figure 1B and as a box-and-whisker plot in Figure S1. Evaluation of eq 1 gives a skewness value of 0.14 ± 0.11, with the uncertainty representing the 95% confidence interval or twice the skewness standard error. This small skewness value implies a minimal abundance of emissive aggregates, a result that is consistent with the sample’s processing history but could not be deduced from lower order fluctuation analysis. As a positive skewness control, we prepared a sorted (6,5) sample containing aggregates. Following NDGU processing and extraction, an undiluted (6,5) fraction was stored for 1 week in a 0.65 mL Eppendorf tube. We have previously found that such undiluted samples spontaneously aggregate during storage, possibly aided by the high concentration of iodixanol density gradient medium. After the 1 week of incubation, we diluted the sample and divided it into two equal aliquots. One aliquot was promptly measured with the variance spectrometer, and the other was measured following agitation with a vortex mixer and then again after 25 s of tip sonication to promote disaggregation. Very similar skewness values of 0.91 ± 0.11 and 1.15 ± 0.11 were found before and after vortex mixing, respectively (see Figure S2), indicating the presence of aggregates resistant to low-shear mechanical mixing. By contrast, the brief tip sonication lowered the measured skewness by a factor of 2.4, from 1.15 ± 0.11 to 0.48 ± 0.11. This change in the fluorescence distribution asymmetry is represented in Figure 2 with box-and-whisker plots.22 The y
percentile level. Solid squares mark the mean values of the fluctuation distributions. Whisker lengths are 1.5 times the respective interquartile ranges (IQRs). This means that the length of the upper whisker is 1.5 times the spacing between 75th and 50th percentiles, and the lower whisker is 1.5 times the spacing between 25th and 50th percentiles. The circles in the plot show first and 99th percentile levels, and filled triangles mark the minimum and maximum values in the fluctuation distribution. Prior to sonication, the 99th percentile circle was far above the upper whisker, while the first percentile circle remained within the lower IQR. This is a clear graphical signature of a positively skewed distribution, with an overabundance of high-intensity observations compared with lowintensity ones. Sonication caused the 99th percentile circle to drop within the upper whisker, while the first percentile remained nearly unchanged, marking a less skewed, more normal distribution resulting from the breakup of (6,5) aggregates. The maximum and minimum values also moved closer to the box because the fluctuation distribution was narrowed by an increase in particle abundance. (See Figure S3 for the histograms underlying Figure 2.) We interpret the particle abundance increase as disaggregation rather than nanotube cutting, in view of the brief sonication and the relatively short initial mean SWCNT length (ca. 400 nm) in the sample. To judge whether the aggregation state can also be deduced from lower moment fluctuation data, we collected variance spectra on this sample before and after the 25 s sonication. The sonication increased the mean emission values (Figure 3A) and decreased the variance values (Figure 3B). We attribute these changes to an increase in the number of emissive particles, consistent with the breakup of (6,5) aggregates deduced from skewness. Note that the emission spectral parameters (such as peak position and width) are nearly unchanged by sonication. Both covariance matrices for this sample, shown in Figure 3C,D, are equivalent to that for the individualized sample (Figure 1D). We conclude that the sorted sample’s aggregation state, which can be assessed by skewness analysis, is not detectable by single measurements of the mean, variance, or covariance matrix spectra. To further check that our measured skewness reflects nanotube aggregation, we deliberately induced coagulation in a CoMoCAT SWCNT sample containing mostly (8,3), (6,5), and (7,5) SWCNTs by adding 60 mM NaCl. Previous research has shown that the addition of salt to SWCNT suspensions produces emissive aggregates.10 As shown in Figure 4A, the mean emission spectrum decreased in intensity by
