High resolution Varying Field Drift Tube Ion Mobility Spectrometer with diffusion autocorrection

Highlights

• The Varying Field Drift Tube (VFDT), an IMS for the classification of nanoparticles at atmospheric pressure, has been tested.

• A linearly decreasing electric field has been proven to provide diffusion constriction in the axial direction.

• Resolutions of up to 100 have been proven experimentally while higher resolutions are expected from theoretical analysis.

• The VFDT system is fast and has a high resolution which is necessary to study fast changing aerosols.

Abstract

Drift tubes (DT) are prominent tools to classify small ions in the gas phase. This is in contrast with its limited use in the aerosol field at atmospheric pressures where the differential mobility analyzer (DMA) has been the tool of choice. While the DMA has been successful, it does not normally achieve the resolution of a common DT. On the other hand, the size range of the DT is limited as well as its sensitivity. Here we propose a variation of the DT where a varying linearly decreasing field is used instead of the constant field commonly used in DT. The Varying Field Drift Tube (VFDT) has the advantage that it allows for diffusion constriction in the axial direction and thus a larger package of ions can be allowed into the system increasing its sensitivity without hampering its resolution. The VFDT also generally outperforms the DT in resolution and this is demonstrated theoretically and empirically reaching resolutions of over 90 in our data although higher resolutions are expected. The diffusion constriction capabilities are also proven theoretically and experimentally by using a mixture of tetraalkylammonium salts while injecting broad packets of ions into the system. The transformation from the raw variable arrival time distribution to Collision Cross Section or mobility diameter is linear making the transformation as simple as with a DMA.

Introduction

Drift Tubes (DT) have been used prominently to classify ions in the gas phase and its simplicity has made it the Ion Mobility Spectrometer (IMS) of choice for analytical chemists (Cumeras, Figueras, Davis, Baumbach, & Gracia, 2015). This is in juxtaposition to its very limited or negligible use in aerosol science, where the Differential Mobility Analyzer has been the tool of choice even for ions as small as a few nanometers (Knutson & Whitby, 1975). There are obvious reasons for both choices, but there are some inherent advantages to each system that should not be ignored by the other field. The DMA coupled to a Condensation Particle Counter (CPC) (McMurry, 2000), in what has been known to date as a scanning mobility particle sizer (SMPS) (Wang and Flagan, 1989, 1990), has very high transmission and measurement range although many commercially available systems have low resolution (Hagwood, Sivathanu, & Mulholland, 1999), are relatively slow and suffer from diffusion problems for small nanometer sizes (Flagan, 1999). On the other hand, the DT has relatively higher resolution, it is generally faster than a regular scanning DMA but has lower transmission (due to its duty cycle), and its measurement range is, in general, limited to a few nanometers (Koeniger et al., 2006; Merenbloom, Koeniger, Valentine, Plasencia, & Clemmer, 2006).

It is noteworthy to mention that some of the points addressed in the previous paragraph are generalizations. There exist high resolution DMA systems which can reach resolutions in excess of 100 (Amo-Gonzalez and Perez, 2018, Rus et al., 2010) and there are plenty of studies on improving the transmission and reducing diffusion losses for small ions in DMAs (Downard, Dama, & Flagan, 2011; Franchin et al., 2016). Another issue that requires clarification is that pertaining to the characterization speed of the instruments. While a scanning DMA may take several minutes to collect the spectra, one can potentially have response times in a DMA of tens to hundreds of microseconds (the residence time in the DMA). In contrast, not all DTs have poor transmission, there are some that use a Hadamard transform with convoluted pulsing times which increase overall transmission to 50% (Clowers, Siems, Hill, & Massick, 2006; Szumlas, Ray, & Hieftje, 2006).

In all, given the capability of DT systems, their use should be naturally extended to the study of aerosols. In fact, there are plenty of examples of atmospheric pressure drift tubes with high resolution to study small ions (Eiceman, Hill, & Karpas, 2014, pp. 119–153; Eiceman & Stone, 2004; Siems et al., 1994; Wu et al., 2002). Despite this, it has not been until very recently that there has been a major push to bring the technology into the aerosol field (Hollerbach et al., 2017, 2018; Oberreit, McMurry, & Hogan, 2014). The reasons behind its lack of use might have been the necessity for a fast response CPC, the limited size range, or the inability to bring a flow of charged particles into a high voltage DT system. Whatever the reason, new technology is now becoming available to overcome these deficiencies and thus the DT should eventually become a useful tool for sub 100 nm aerosol particles.

The operational principle of a DT system is quite simple. A constant field generated by a series of cylindrical electrodes is used to propagate a swarm of ions of different mobilities into a detector where an arrival time distribution is recorded. In order to correctly quantify this time, the ions are pulsed into the system through a gate at known intervals. In this way, the resolution of an initial point source distribution is given by (Mason & McDaniel, 1988):

$$R_{DT-IMS}=\frac{\bar{x}}{\text{Δ}x}=\frac{t{v}_{drift}}{{\left(16D_{L}tln2\right)}^{1/2}}={\left(\frac{qEL}{16k_{b}Tln2}\right)}^{1/2},$$

where q is the charge, E is the electric field, L is the tube length, $k_b$ is the Boltzmann constant and D_L is the longitudinal diffusion and T is the temperature. It seems evident that the resolution is proportional to the square root of the electric field and the length of the tube. Eq. (1), however, is sometimes misleading as the initial ion package width is not infinitesimal (Kirk, Allers, Cochems, Langejuergen, & Zimmermann, 2013). The initial package width greatly impacts resolution and leads to a maximum possible theoretical resolution which does not occur at the highest field. This initial package diffuses as it travels through the system, worsening resolution-due to longitudinal diffusion-as well as transmission-due to transversal diffusion. It suffices to say that controlling or correcting diffusion would increase the resolution and transmission of the system.

Attempts at diffusion correction have been done previously. In particular, transversal diffusion has been corrected at low pressures by using radio frequency (RF) technology, but the high voltage and frequency needed precludes its use at atmospheric pressure. RF technology can be observed in extremely long drift tubes, either in portions of the system where a funnel centers the ions (Hagwood et al., 1999), or throughout the whole path length such as in Structures for Lossless Ion Manipulation (SLIM) that allows the ions to travel paths that can extend for kilometers (Garimella et al., 2015; Wojcik et al., 2019). Studies aimed at correcting longitudinal diffusion are more scarce. In such systems, a non-constant field in the axial direction is used to constrict axial diffusion. The concept of using a varying field is not new. It was first attempted by Zeleny (Zeleny, 1898) in the 19th century and later on used mostly conceptually for multiple geometries and different pressures. The principle is based on the solenoidal principle of an unperturbed electric field ($\nabla \cdot \overrightarrow{E}=0$) that suggests that a variation of a field can be used to compress the ions in a particular dimension while stretching them in another. At low pressures, a commercially available system that makes use of this principle is the Trapped Ion Mobility Spectrometer (TIMS) which, as the name suggests, traps the ions thanks to varying fields and the use of RF to subsequently release them (Hernandez et al., 2014). At atmospheric pressure, there are a few systems that have taken advantage of nonlinear fields. Interestingly, one of its first appearances was to improve DMA resolution through the reduction of diffusive broadening in what was labeled a Drift Differential Mobility Analyzer (Loscertales, 1998). Ion compression was also observed when studying the three zones of Bradbury-Nielsen type gates where “the enlarged depletion zone, the reduced dispersion zone, and the electrically enhanced compression zone consistently help to produce narrower peaks” (Du, Wang, & Li, 2012). This non-uniform field idea was later explored by the same authors to increase the sensitivity of Ion Mobility Spectrometers (Chen et al., 2019). The principle of the Inverted Drift Tube (IDT) (Larriba-Andaluz, Chen, Nahin, Wu, & Fukushima, 2019; Nahin, Oberreit, Fukushima, & Larriba-Andaluz, 2017) has been recently explored where a gas flow pushes the ions forward while a linearly increasing electric field is used as a means to separate them. The ions cannot be trapped in the IDT system and hence they have to be constantly pushed through the system. Since no RF can be used, the IDT suffers from loss of signal due to an enhanced radial dilation of the ion distribution and the difficulty of aligning the centers of symmetry of field and gas.

In this manuscript, the knowledge gained with the IDT is put to the test to develop a new type of Drift Tube that uses a varying electric field and benefits from diffusion correction. In the Varying Field Drift Tube (VFDT), a linearly decreasing electric field is employed to propagate the ions forward which allows for diffusion constriction to occur axially. An experimental prototype is used to show that resolutions of 90 or more are achievable for singly charged small ions and nanoparticles (1–3 nm), but where there is no particular limitation to achieve high resolution for larger particles as well. The theoretical expression for the resolution is inferred theoretically from the Nernst-Planck ion balance equation revealing that the asymptotic resolution of the VFDT is higher than that of the DT even for an infinitesimal source. It is also shown that when starting with an initially broad distribution in the axial direction, a narrower distribution can be collected at the end of the tube making this system unique. The drawback is that the distribution is constricted axially at the expense of enlarging it radially (Larriba-Andaluz et al., 2019; Nahin et al., 2017). The effect of enhanced radial diffusion can be shown theoretically to be negligible as long as the distribution is kept in the center of the tube. The transformation from arrival time distribution to mobility depends on the slope of the electric field but it is a simple linear transformation for all mobilities. Finally, the transformation from mobility to diameter of Collission Cross Section (CCS) can be done using Stokes-Millikan's or Mason-Schamp's equation and a comparison to models using Molecular Dynamics is performed.