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DIFFERENTIAL MOBILITY SPECTROMETRY/MASS SPECTROMETRY HISTORY, THEORY, DESIGN OPTIMIZATION, SIMULATIONS, AND APPLICATIONS Bradley B. Schneider,1* Erkinjon G. Nazarov,2 Frank Londry,1 Paul Vouros,3 and Thomas R. Covey1 1

AB SCIEX, Concord, ON, Canada, L4K 4V8 The Charles Stark Draper Laboratory, Tampa, FL 33612-9220 3 Department of Chemistry and Chemical Biology, Barnett Institute, Northeastern University, Boston, MA 02115 2

Received 18 September 2014; accepted 26 November 2014 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/mas.21453

This review of differential mobility spectrometry focuses primarily on mass spectrometry coupling, starting with the history of the development of this technique in the Soviet Union. Fundamental principles of the separation process are covered, in addition to efforts related to design optimization and advancements in computer simulations. The flexibility of differential mobility spectrometry design features is explored in detail, particularly with regards to separation capability, speed, and ion transmission. # 2015 Wiley Periodicals, Inc. Mass Spec Rev XXXX:XX–XX, 2015

The third aspect describes advances in the development of computer simulators of ion motion in a DMS instrument. The primary value of simulators is as tools to be used to further advance and optimize the performance of DMS-MS systems. A new method to calculate the differential ion-mobility function for specific ions, the alpha function, is derived and access to software that will perform the calculation with the appropriate inputs from the interested practitioner of DMS-MS is provided.

Keywords: Differential mobility spectrometry; Mass spectrometry; ion

The concept of using the specific non-linear electric field dependence of an ion’s coefficient of mobility for separation was originally conceived in the Soviet Union in the early 1980s (Gorshkov, 1982), and for a long time was referred to by the simple moniker Gas Analyzer of Ions. This concept is the principle behind the separation process in differential mobility spectrometry (DMS). Development efforts continued in the Soviet Union from laboratories in Siberia, Uzbekistan, and St. Petersburg (Avakov et al., 1987; Rasulev, Nazarov, & Buryakov, 1991; Buryakov, Krylov, & Soldatov, 1991; Buryakov et al., 1991a,b, 1993a,b; Verenchikov et al., 1991). One of the motivations behind these efforts was the development of fielddeployable sensors to detect land mines in the conflict in Afghanistan at that time. During the late 1980s and early 1990s, the development process in Russia diverged with the efforts of two independently operated teams. Gorshkov’s team at the Institute of Thermo physics of the Siberian Academy of Science built cylindrical geometry devices, which were initially called Field Ion Spectrometers. This technology was eventually transferred to Mine Safety Associates in Pittsburgh to further develop and explore commercialization opportunities in this area (Carnahan et al., 1995). A decade later, it would be referred to as High Field Asymmetric Waveform Ion Mobility Spectrometry or FAIMS (Purves & Guevremont, 1999). One motivation for this approach was to try to take advantage of the ion-focusing properties of the inhomogeneous fields created with curved electrodes (Guevremont & Purves, 1999; Guevremont, 2004). The second team, with members located in Siberia (Buryakov, Krylov, & Soldatov, 1991) and Tashkent (Nazarov & Rasulev, 1991), worked on planar designs of sensors. They initially referred to this device as a Drift Spectrometer, which

I. INTRODUCTION This manuscript is organized around five general aspects of differential mobility spectrometry-mass spectrometry instrumentation. The first topic, History, draws upon literature citations and interviews with individuals who partook in the early development of the technique in the Soviet Union. The last topic, Applications, covers only the recent past, when these reports began to proliferate after DMS-MS systems gained commercial traction. The three remaining topics focus on fundamentals and instrumentation. The first topic covers the fundamental physical and chemical principles that underlie DMS instrumentation, analytical models of the separation process, and mechanisms involved in collisions of ions and neutrals, a central tenant of all ion-mobility separations. The second aspect considers efforts in design optimization based on extensive experimental data and information from the literature. Particular focus is placed on the four primary figures of merit; resolving power, peak capacity, speed, and sensitivity and how the design can balance these specifications to meet the needs of specific applications. Contract grant sponsor: National Institutes of Health; Contract grant number: 1RO1 CA069390.  Correspondence to: Dr. Bradley B. Schneider, AB SCIEX, 71 Four Valley Drive, Concord, ON, Canada, L4K 4V8. E-mail: [email protected]

Mass Spectrometry Reviews, 2015, 9999, 1–51 # 2015 by Wiley Periodicals, Inc.

II. HISTORY

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eventually migrated to the more descriptive name Differential Mobility Spectrometer or DMS for devices with this geometry which creates a homogeneous field throughout the length of the cell (Nazarov et al., 2002). The motivations for this approach were to create a device where all ions would be transmitted without discrimination when the separation voltages were turned off, to transmit positive and negative ions simultaneously during filtering, and to optimize performance when polar transport-gas modifiers are used. These characteristics were known absent with the curved geometry cells. Nevertheless, DMS and FAIMS both share the same physical separation principle conceived by Gorshkov, fundamentally based on the difference in the highand low-field mobility of a particular gas-phase ion. They both produce a continuous ion beam from an ion-mobility separation that occurs during each period of the waveform in a radio frequency field. However, it was beginning to be recognized in the early days of this century that the different geometries imparted different analytical properties that warranted one to distinguish them with the separate terms FAIMS and DMS. This review will primarily focus on the design aspects of the planar DMS as distinct from the curved geometry version FAIMS, but will draw comparisons where it serves to illustrate the concepts being discussed. In the early 1980s, the development of electrospray ionization mass spectrometry occurred in Moscow (Alexandrov et al., 1984) in parallel to research in Europe and North America (Thomson & Iribarne, 1978, 1979; Thomson, Iribarne, & Dziedzic, 1982; Yamashita & Fenn, 1984). In 1991, a Soviet mass spectrometry group from St. Petersburg collaborated with the Moscow group and the DMS researchers in Siberia to demonstrate the coupling of DMS to an electrospray ionization mass spectrometer (Verenchikov et al., 1991). The group from Tashkent coupled a DMS to a quadrupole mass spectrometer with atmospheric pressure chemical ionization to measure atmospheric contaminants (Buryakov et al., 1993a). By the close of the 20th Century, efforts to further develop and commercialize DMS and FAIMS technology coupled to mass spectrometry began to take hold in North America. The Mine Safety Appliances cylindrical FAIMS device was utilized by the National Research Council in Ottawa to couple to a mass spectrometer, (Guevremont & Purves, 1999; Guevremont, 2001,2004) and became the basis of the company Ionalytics that was subsequently bought by Thermo Fisher Scientific, Inc. (Waltham, MA) in 2005 to commercialize this as a FAIMS-MS system (Barnett et al., 2007). The planar DMS design entered North America through the laboratory of Gary Eiceman at New Mexico State University (NMSU) around the year 2000, and stimulated a lineage of publications from this group and others (Spangler, 2000; Eiceman, Nazarov, & Miller, 2000; Eiceman et al., 2001, 2002, 2004; Miller et al., 2001; Krylov et al., 2002, 2003; Krylov, 2003; Eiceman & Karpas, 2005). The Charles Stark Draper Laboratory (Cambridge, MA) funded and provided technical support to build a planar DMS sensor at NMSU with University Research and Development (UR&D) funding (Miller et al., 2000a,b, 2001). After the demonstration of the analytical potential of DMS systems, efforts for commercialization of this technique as a stand-alone sensor started at Sionex, Inc. (Bedford, MA). A GC-DMS based system was developed by Sionex and the Charles Stark Draper Laboratory for continuous cabin-air monitoring on the International Space Station, and this 2

device remains operational today (James et al., 2010; Limero et al., 2011, 2012). Other GC-DMS systems were produced with the core Sionex technology that included the Varian CP 4900 microGC to detect mercaptans and sulfur compounds in environmental samples and the Thermo Fisher EGISTM Defender for simultaneous detection of explosives and narcotics in transportation security. Stand-alone DMS air monitors also emerged from these efforts, including the Chemring’s (Derby, UK) handheld JUNOTM for the trace detection and identification of chemical warfare agents and toxic industrial chemicals, Hamilton Sundstrand’s (Windsor Locks, CT) Tandem Mobility Spectrometer for chemical warfare agents and toxic industrial chemical monitoring, and TechnoScan Systems, Inc. (Vaughan, ON, Canada) prototype TSI-3000 to detect threats in cargo. Significant development of DMS-MS technology continued from this time in several laboratories that leveraged the expertise of the original Soviet developers now in North America (Nazarov et al., 2006a,b; Krylov, Nazarov, & Miller, 2007; Borsdorf, Nazarov, & Miller, 2007; Krylov & Nazarov, 2009; Nazarov, 2012a,b). Activities expanded into other groups outside this sphere of influence (Roetering et al., 2010; Borsdorf & Mayer, 2010; Spangler, 2012;). Notable efforts sprung up among new groups at the Pacific Northwest National Laboratories (PNNL) (Richland, WA) (Shvartsburg, Maskevich, & Smith, 2006; Shvartsburg & Smith, 2007, 2011a, 2013b; Shvartsburg, 2008; Shvartsburg, Danielson, & Smith, 2010; Shvartsburg, Tang, & Smith, 2010; Shvartsburg et al., 2010), University of Florida (Rorrer & Yost, 2011; Tsai, Yost, & Garrett, 2012), University of North Carolina (Ferzoco et al., 2009; Ridgeway, Remes, & Glish, 2009; Isenberg, Armistead, & Glish, 2014), and Northeastern University (Levin et al., 2006a,b, 2007; Hall et al., 2012a,b, 2013; Kafle et al., 2013, 2014). Work in the field of nanofabrication at the University of Cambridge led to the development of micro machine-based DMS sensors and the emergence of the company Owlstone (Owlstone Ltd, Cambridge, UK) that has recently launched a DMS for direct coupling to mass spectrometry (Wilks et al., 2012). Groups from Loughborough University and PNNL demonstrated the utility of this coupling (Shvartsburg et al., 2009a,b; Brown et al., 2010, 2012). In 2007, AB SCIEX began a collaboration with Sionex to develop what eventually became the commercial DMS-MS system with the trade name SelexIONTM (Schneider et al., 2010a,b,c, 2012a, 2013; Krylov et al., 2010; Covey, Schneider, & LeBlanc, 2012). Figure 1 summarizes the development and migration of the two different geometries between continents and institutions over the last 35 years. Additional reviews on this topic and ion mobility in general can be found. The use of ion mobility for various applications has been reviewed (Kolakowski & Mester, 2007), and more specific reviews focused on security applications (Eiceman & Stone, 2004; M€akinen, Anttalainen, & Sillanp€a€a, 2010) and mass spectrometrybased proteomics (Swearingen & Moritz, 2012) are available, in addition to commercial technology reviews (Borsdorf et al., 2011; Lapthorn, Pullen, & Chowdry, 2013). A useful monograph on the topic is available on-line (Boyle, 2012). Of particular mention is the latest issue of the classic text “Transport Properties of Ions in Gases” by Mason and McDaniel (1988), which provided Gorshkov the inspiration for the original invention after he read the Russian translation of an earlier version. Mass Spectrometry Reviews DOI 10.1002/mas

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FIGURE 1. A 35-year chronological history of DMS and FAIMS development, including the migration process of these two geometries among institutions (see E.G. Nazarov in Boyle, 2012; Covey, Schneider, & LeBlanc, 2012). This historical information was drawn from the literature and the personal experience of Evgeny Krylov and Erkin Nazarov, both were engaged in much of the early Soviet research and later commercialization activities in North America. Their contributions to this historical perspective are much appreciated. NMSU ¼ New Mexico State University, NEU ¼ Northeastern University, UNC ¼ University of North Carolina, LU ¼ Loughborough University, PNNL ¼ Pacific Northwest Laboratory, MSA ¼ Mine Safety Associates.

III. THEORY A. Principle of Operation DMS separations occur in a gap between two electrically isolated plates that are planar and parallel, as shown in Figure 2. For stand-alone DMS devices such as the one depicted in Figure 2A, the design might include two additional detector electrodes (Faraday plates) floated at different polarities for independent and simultaneous detection of positive- and negative-ion species. An alternative is to use the mass spectrometer as the detector for the DMS, in which case, the DMS operates as a pre-filter for MS, as shown in Figure 2B. Ions drift axially between the electrodes, dragged by a flow of gas, typically at atmospheric pressure. Under the effect of an electric field, a radial motion is imparted to the ions’ trajectories with an average velocity (v) given by Equation (1), vðtÞ ¼ KðtÞEðtÞ

ð1Þ

where K is the ion mobility and E is the electric field. When the electric field is low, the mobility coefficient is a constant value over a broad range of field strengths, typically referred to as the low-field mobility constant (K(0)). In systems that operate at high gas pressure, such as mobility analyzers, field strengths are expressed in Townsends (Td) to account for gas collisions as well as electric field strength (E/N, where N is defined as the gas number density). Low-field mobility forms the basis for separation in conventional drift tube ion-mobility devices, where mobility remains constant under different field strengths up to certain limits. Drift tube ion mobility devices operate by Mass Spectrometry Reviews DOI 10.1002/mas

gating ions into a drift region, where the velocity of individual species is proportional to the mobility coefficient and the strength of the electric field, as shown in Equation (1). For a fixed value of electric field, ions are separated by drift time, according to the absolute value of the ion-mobility coefficient, and the mobility coefficient can be related to the reduced mass and cross sectional area (or size) of individual species through the Mason–Schamp equation (Revercomb & Mason, 1975). Therefore, ion characterization in ion-mobility devices may provide ion structural parameters. When the E/N ratio is high (>10 Td), the mobility characteristics of an ion are altered from the low-field condition. The mobility becomes field-dependent and varies based on the unique physical characteristics of different ions and their response to high fields (Mason & McDaniel, 1988; Shvartsburg, 2008). Ions with the same lowfield mobility can have substantially different high-field mobility due to changes in the nature of the ion–molecule interactions (Revercomb & Mason, 1975; Ellis et al., 1978). This difference forms the basis for differential mobility separations. The differential mobility function, referred to as alpha, can be generally expressed as the normalized difference between the high- and low-field mobilities, and is derived in Section III.B Analytical Model, and two methods to calculate alpha are presented in V.A and V.B of Section V. Simulations. It is referred to as a function, rather than as a constant like K(0), because it varies with field strength. In a differential-mobility cell, ions are exposed to alternating high- and low-field conditions by the application of a radio frequency waveform applied to the parallel electrodes as shown in Figure 2B. Each period of the waveform exposes the ion to a high field for a short period, to force the ion toward one 3

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FIGURE 2. A) Schematic of a stand-alone DMS sensor. The ion-filter region is composed of two planar, parallel electrodes. Faraday plates at the exit serve as the detector for positive and negative ions simultaneously. B) Schematic of a DMS with a mass spectrometer as the ion detector, and depiction of the asymmetric waveform, where the integrated voltage/time areas under the low- and high-field portions within each period are the same (blue areas). The RF waveform is drawn as an idealized square wave, but not all DMS power supplies are designed to deliver square wave functions for practical reasons related to power consumption. The amplitude of the waveform is referred to as the separation voltage (SV). The compensation voltage (CoV) is a DC potential applied to an electrode used to counteract an ion’s migration toward an electrode in response to the SV; its magnitude is proportional to the ion’s differential mobility. It is shown as a voltage ramp here, but can be set to a fixed value to allow targeted ions to pass through the DMS, while excluding non-targeted ions.

electrode, followed by a low field of the opposite polarity for a longer period, which reverses its trajectory with the same net force (the product of the voltage and time for each condition is the same). Thus, the term “asymmetric waveform” as diagrammed in Figure 2B. It should be noted that it makes no difference if the polarities of the high and low fields are switched as long as they are opposite to each other. The ions are displaced radially toward one electrode by the RF field as the gas transports them in the axial direction along the length of the cell. If an ion has the same high- and low-field ion mobility (a ¼ 0), then it would move with a saw-tooth trajectory down the centerline of the cell without striking either electrode, as shown in Figure 2B. However, all ions exhibit some degree of either positive or negative alpha that results in 4

their migration to one or the other electrode, where they are neutralized before detection at the exit. A DC voltage is applied to the electrodes, called compensation voltage (CoV), to steer them onto the center axis for detection at the exit. When the CoV is set to the appropriate value to counteract the unique differential mobility of a particular ion, a continuous ion beam passes to the detector for that species. This mode of operation is similar in concept to setting a quadrupole mass filter to pass an ion of a particular mass. This mode of operation is typical for the analysis of targeted chemical species for which the appropriate CoV has been empirically pre-determined. Alternatively, the CoV can be ramped to sequentially pass ions that have a broad range of CoV values; this mode of operation is typically used for the analysis of unknown chemical species. Mass Spectrometry Reviews DOI 10.1002/mas

DIFFERENTIAL MOBILITY SPECTROMETRY/MASS SPECTROMETRY

The CoV is a direct measurement of an ion’s differential mobility under any particular set of experimental conditions, and is the primary means to control an ion’s trajectory through a cell. However, the amplitude of the RF waveform (separation voltage, SV) will alter an ion’s differential mobility and thus trajectory. When the SV is changed to alter the differential mobility of an ion, for instance to optimize a particular separation, a new CoV will be required to correct its trajectory. Graphs of the dependence of CoV on SV form the basis of alpha plots, and they provide particular insights into the physical mechanism that dominates the differential mobility behavior of an ion. These graphs are used to calculate and verify the alpha function of an ion, and are used extensively to validate computer simulations of an ion’s motion, as will be further discussed in Sections III.C Ion/Molecule Interactions and the Mechanisms of Separations and V. Simulations.

rov, & Miller, 2007; Papanastasiou et al., 2008), and the feasibility of more complex waveforms has been evaluated (Shvartsburg, Maskevich, & Smith, 2006). The majority of commercial DMS devices use bisinusoidal waveforms, or clipped sinusoidal waveforms (Krylov, 1997; Purves & Guevremont, 1999; Eiceman et al., 2004; Barnett et al., 2007; Schneider et al., 2010a; Wilks et al., 2012) due to the relative simplicity coupled with high performance. DMS separations exploit the non-linear electric field dependence of ion mobility K(E). In general, ion velocity increases with field strength and decreases with the volume density of neutral particles. Consequently, the complete expression for mobility is usually written as a function of the ratio E/N. Typically, E/N is expressed in Townsend units, where 1 Td ¼ 1021 Vm2. Following this scheme, mobility can be written as shown in Equation (4) (Buryakov et al., 1991b),      E E ¼ Kð0Þ 1 þ a K N N

B. Analytical Model The SV and CoV potentials give rise to RF and DC electric fields within the DMS analyzer, which will be designated as S and C, respectively. Throughout this manuscript, S and C will be presented as gas-number density-normalized values (E/N) to simplify the discussion (Nazarov et al., 2006b), where N is calculated from the ideal gas law. The RF separation field in a DMS analyzer has the following form: SðtÞ ¼ S0 f ðtÞ

ð2Þ

where S0 is the 0-peak amplitude of the separation field, and f(t) is a function that describes the shape of the waveform. S and C are assumed to be perpendicular to the DMS electrodes. Therefore, in the discussion that follows, fringing effects at the ends of the plates will be ignored. Ion separation in DMS occurs under the periodic effect of a strong asymmetric waveform electric field applied between two electrodes separated by a distance (h). A general requirement for the asymmetric waveform function is that the average value of the electric field over one period of the waveform should be 0 so that it is possible to reference the magnitude of CoV shifts relative to 0 V. 1 hSðtÞi ¼ T

Z

T

SðtÞdt ¼ 0

ð3Þ

t¼0

The ideal shape for a DMS waveform is a square function, in which the waveform alternates between fixed “high-field” and “low-field” values; however, in practice this square function can be difficult to achieve due to excessive power load requirements (Papanastasiou et al., 2008; Krylov et al., 2010). More typically, DMS waveforms are constructed by superimposing two sinusoidal waveforms, with two different frequencies (v and 2v), as has been described in the literature (Krylov, 1997). The superimposed sinusoids might be applied onto either one of the two DMS electrodes, or alternatively a single sinusoid might be applied to each of the electrodes, such that the asymmetric waveform results in the gap between the electrodes (Krylov et al., 2010). A number of papers discuss the optimization of waveforms for different types of DMS separations (Krylov, 1997; Shvartsburg, Maskevich, & Smith, 2006; Krylov, NazaMass Spectrometry Reviews DOI 10.1002/mas

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ð4Þ

where K(0) is the mobility coefficient under low-field conditions and a(E/N)  1 is a normalized function that describes how mobility changes with E/N as shown in Equation (5). a

    K E  Kð0Þ E ¼ N N Kð0Þ

ð5Þ

a(E/N) is the alpha function, that quantifies the differential mobility of an ion at different field strengths. For example, when E/N is very low, a(E/N) is 0 and K(E/N) reduces to K(0). Alternatively, when the amplitude of the separation waveform is high, a is simply the normalized difference between an ion’s high- and low-field mobility as demonstrated by Equation (5).

C. Ion/Molecule Interactions and the Mechanisms of Separations Data-mapping the relationship between CoV and SV can be used to calculate the alpha function and generate so-called alpha curves. The shape of the alpha curve depends upon specific properties of ion–molecule pairs and collision properties to provide insights into the dominant mechanism involved in the collisions between ions and neutral gas molecules that affect separations (Buryakov et al., 1993a; Eiceman, Nazarov, & Miller, 2000). Methods of calculating alpha are described in detail in Section V. Simulations. The alpha curves typically exhibit one of three general shapes, as illustrated in Figure 3. Type A behavior shows high-field mobility increasing relative to low field as the separation field is increased. Type C behavior shows high-field mobility decreasing relative to low field as the separation field is increased. Type B behavior shows high-field mobility initially increasing relative to low-field mobility, as with Type A behavior, then reversing at some inflection point as the field increases to exhibit a negative slope indicative of Type C behavior (Guevremont & Purves, 1999). A physical explanation for such complex behaviour of the alpha function is based upon the underlying ion–molecule interaction processes (Nazarov et al., 2006b). 5

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Type A

Alpha

0.4

0.2

Type B 0.0

Type C -0.2 0

20

40

60

E/N (Td)

80

100

120

FIGURE 3. Three general shapes of alpha curves that indicate the different types of ion–molecule interactions that can occur. The curves portray the change in an ion’s differential mobility as the amplitude of the RF waveform (SV or separation field) is increased. The field strength (E) is normalized to the background gas density (N) and expressed in Townsends.

Type A behavior is generally understood to result from repetitive clustering and declustering of an ion with polar neutral species in the transport gas. During the low-field portion of the waveform, clusters are formed to varying sizes and shapes that depend on the chemistry of a particular ion structure. The mobility of the cluster complex is reduced relative to the naked ion because of its size, largely determined by the unique reactivity of a particular ionic species with gas-phase neutral molecules. As the field is increased during the second half of the waveform period, and collisions take on greater energy, ions are either released from the cluster, or their cluster number is reduced to result in an increase in the mobility of the ionic species. The net result is amplification of the differential ion mobility, and the amplification gets more pronounced at high separation fields, and is reflected in the characteristic rapid increase in the positive slope of the alpha curve. Chemicalclustering processes can provide dramatic improvements in ion separation for this reason (Buryakov et al., 1993a; Eiceman et al., 2004; Levin et al., 2006a; Schneider et al., 2010b,c, 2013; Rorrer & Yost, 2011). Examples of improved separations due to chemical-clustering will be shown in Section Improvement of peak capacity with transport gas chemical modifiers. In some instances with elemental ions, Type A behavior appeared to be occurring in the absence of clustering agents, which suggests polarization may also contribute to Type A behavior (Sinatra et al., 2015). However, it is unclear how pure the transport gases were during these observations as trace levels of moisture can produce significant clustering effects. Type A behavior has also been shown for O ions in CO2, in the absence of additional clustering agents (Ellis et al., 1978). Type C behavior can be explained on the basis of simple physical impacts with little or no polar interactions or clustering of any sort to provide influence. These types of collisions are often referred to as hard-sphere interactions, with analogy drawn to the collisions of billiard balls, and are observed with ions and transport-gas conditions that provide minimal opportunity for clusters to form. They are observed with highly purified inert transport gases and typically with ions with a mass-to-charge ratio above 300. Under this scenario, during the high-field 6

portion of each period of the waveform, the high-energy collisions result in a decrease in the mobility of the rebounding ions because they tend to lose forward momentum and are deflected backward under these conditions. During the low-field portion of the waveform, ion–molecule interactions are less energetic, so backward deflection happens to a much lesser extent, if at all. This situation creates a differential mobility that imparts a negative slope to the alpha curve. Type B can be viewed as a combination of Types A and C. The positive slope in the low-separation field portion of the alpha plot of Type B behavior indicates that a collision process identical to that of Type A ions occurs, except that the extent of clustering is less and the cluster complexes are more weakly bound. At low SV, collisions are dominated by the Type A cluster/decluster mechanism with a less-dramatic amplification of the differential mobility due to the low cluster numbers. The reduced positive slope observed in this region compared to Type A graphs can be explained by this model. At moderate field strengths, where the inflection in the graph occurs toward a negative slope, all of the weak clusters are eliminated during all portions of each period of the waveform. The collision mechanism switches to that experienced by Type C behavior at the point in the alpha curve where the slope turns negative. It should be noted that, even when transport gases are thought to be composed of pure inert gases, minute traces of water can be inadvertently present to give rise to this low level clustering effect. Another explanation of Type B behavior also invokes multiple collision mechanisms, but emphasizes polarization interactions instead of low-level clustering. At low separation fields, where the positive slope is observed in the alpha plot, collision mechanisms associated with polarization interactions between an ion and neutrals in the transport gas have been proposed as an explanation (Buryakov et al., 1993a). Under low electric-field strength conditions in gases that contain highly polarizable molecules, the long-term polar interaction forces can increase ion-molecular interaction cross sections. As the ion velocity increases with field strength, polarization effects become negligible and the mobility increases similar to, but less pronounced than, that of the clustering phenomena shown for the Mass Spectrometry Reviews DOI 10.1002/mas

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Type A situation. At higher separation fields, beginning at the inflection in the graph where the slope changes negative, the collision mechanism switches to a hard-sphere interaction process. Type B behavior can also be observed for very large proteins, and this phenomenon has been attributed to dipole alignment in the strong separation field (Shvartsburg et al., 2006a). The terms Type A, B, and C will be used throughout this manuscript, where Types A and C represent collision processes that are distinct and mechanistically well-defined as the clustering and hard-sphere models, respectively. Type B is a mixture of mechanisms, where hard-sphere collisions dominate at high SV fields and there remains some debate between polarization and low-level clustering in the low-field portion of the alpha plot. Experimentally, it would be extremely difficult to distinguish these two mechanisms, and the practical relevance of doing so is dubious, which invokes the age old philosophical question and scientific metaphor, “how many angels can sit on the head of a pin?” To complicate the debate further, Shvartsburg (2008) has suggested that Type A behavior corresponds to a special case of Type B behaviour, where the separation field has not been raised sufficiently to demonstrate hard-sphere collisions, and has proposed modification of the Type A, B, and C designations to reflect this. Because field strengths of the magnitudes suggested are difficult to control at atmospheric pressure due to discharge problems, this approach has not been generally accepted in the literature for practical reasons and will not be utilized here, although it warrants theoretical merit. An important conclusion to this discussion of the separation mechanisms is that the process is dominated by gas-phase chemical interactions, particularly with the Types A and B situations. Classical low-field or drift-tube ion mobility is also affected by clustering reactions, but not to the same extent as differential ion mobility. Low-field mobility in general tends to correlate well with molecular mass, where flight times and molecular mass fall on a continuous scale to draw a closer analogy to mass spectrometry (Shvartsburg, Mashkevich, & Smith, 2006). Conversely, with differential ion mobility, the specificity is derived from the unique chemical interactions of the analyte ion with the transport gas, and the transport gas can be deliberately varied in its chemical composition to make the separation process highly orthogonal to mass spectrometry (Schneider, Covey, & Nazarov, 2013) and to some degree more akin to other chemistry-driven separation techniques like liquid chromatography (Levin et al., 2006b). The term “ionogram” originally proposed by Roger Guevremont (Guevremont, 2004) for the data display most commonly used to show DMS and FAIMS separations is logical, because the mechanisms that underlie separation are more akin to a chromatogram than they are to a mass spectrum. In the discussion around Figure 4, we describe in more detail how the data to create ionograms are acquired. A review article by Lapthorn, Pullen, and Chowdry (2013) provides more detail regarding pros and cons of different ion mobility approaches.

IV. DESIGN OPTIMIZATION There is no particular dimension, ratio of dimensions, or RF frequency, amplitude, or waveform that can be expected to provide optimal performance for the four primary figures of merit simultaneously; those figures of merit are resolving power, peak capacity, scan speed (ion-residence time), and sensitivity

Mass Spectrometry Reviews DOI 10.1002/mas

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(ion-transmission efficiency). The design of the cell and its power supplies will accentuate some of these figures of merit, at the same time it will compromise others. A clear understanding of the desired application is required to define the performance specifications for each figure of merit to establish the general direction of the design of the cell. Section IV.A The Four Central figures of Merit: Resolving Power, Peak Capacity, Scan Speed, and Sensitivity focuses on definitions and discussion of the four central figures. Section IV.B Analyzer Design Considerations provides details about how several aspects of the DMS analyzer design affect these performance characteristics. Although the principles described throughout Section IV use a particular geometry to provide examples, the concepts can be generalized to any particular design and different examples from the literature will be provided.

A. The Four Central Figures of Merit: Resolving Power, Peak Capacity, Scan Speed, and Sensitivity.

1. Resolving Power Definition of resolving power: DMS resolving power (RP) is defined in Equation (6) as RP ¼

CoV FWHM

ð6Þ

where CoV represents the observed compensation voltage for the peak center, and FWHM is the peak width in volts at half height. Figure 4 shows data acquired at two different resolving powers in the form of ionograms. The ionogram is the primary scan mode of a DMS. With this form of data acquisition, CoV is scanned at a constant SV, while a sample is introduced over the time frame of the scan (Guevremont, 2004). The intensities of the signals from the components of the sample are recorded during the scan, and the resolving power and peak capacity of the separation can be determined. In this case, the sample is introduced by infusion, but ionograms can be acquired over HPLC peaks if the cell and data acquisition parameters are chosen to be fast enough. This aspect is elaborated in more detail in Section IV.A.3 Scan Speed. The ionograms in this Figure show a separation with two different residence times in the cell. It shows different resolving powers achieved by slowing down the transport gas flow to increase the residence time (Schneider et al., 2010a). When the resolving power is adjusted in this manner, the peak position on the CoV scale does not change. The resolving power improves with this method as the peaks narrow, but the CoV values remain constant. When resolving power is improved with increased residence time, signal intensity is lost due to an increase in the number of ions lost to the walls by diffusion rate processes. In this specific case, the signal intensity dropped in the high-resolution mode, depending on the ion monitored, from 10- to 40-fold, inversely proportional to mass, as would be expected because low-mass ions diffuse through the gas to the walls faster than higher mass ions to impart greater losses. Defocusing fields at the entrance of the cell also contribute to losses, as discussed further in Section V.D Fringe Field Effects and Simulations. 7

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FIGURE 4. Ionograms of a six-component mixture of drugs to show the resolving powers and peak capacities obtained with different residence time. Each peak is individually normalized to 1.0 to improve the visualization of the peak widths of each component. Residence time was controlled by altering the transport gas flow rate. A) 6.5 msec residence time with no throttle gas; peak capacity ¼ 6.5 and B) 20 msec residence time with throttle gas; peak capacity ¼ 22.5. The sample was composed of 1) phenylalanine, resolving power (A) ¼ 4.8, (B) ¼ 13.6 (m/z ¼ 166.1), 2); histidine, resolving power (A) ¼ 3.4, (B) ¼ 11.3 (m/z ¼ 156.1), 3) methylhistamine, resolving power (A) ¼ 2.6, (B) ¼ 8.2 (m/z ¼ 126.0), 4) minoxidil, resolving power (A) ¼ 5.5, (B) ¼ 19.5 (m/z ¼ 210.1), 5) cimetidine, resolving power (A) ¼ 6.4, (B) ¼ 21.2 (m/z ¼ 253.1), and 6) perphenazine, resolving power (A) ¼ 6.7, (B) ¼ 28.4 (m/z ¼ 404.2), infused into an electrospray ion source at 10 mL/min. The signal was monitored for each component by multiple reaction monitoring (MRM) with a 200 msec dwell for each component on a triple-quadrupole MS. See Appendix 1 for specifications of the system used for these measurements and Figure 13 for the location of the throttle gas.

As will be discussed in Section IV.A.2 Peak Capacity, other methods to improve resolution and peak capacity result in a shift of the CoV value without peak broadening, and can show more dramatic improvements in resolution and peak capacity, sometimes without significant signal loss. In the Peak Capacity section, we will also discuss why the calculated resolving power figure of merit can sometimes be misleading. Mathematical derivation of peak width: Peak width is related to resolving power, but is not the sole determinant of this figure of merit. A theoretical model can be developed for the DMS sensor parameters that affect peak width based upon the following considerations. Inside the separation cell, ions have a zigzag trajectory due to the combined effects of the SV and CoV. To transmit an ion, the CoV is set to compensate for the effect of the applied SV to result in an ion trajectory similar to that labeled #1 in Figure 5. Under these conditions, the ion’s trajectory is parallel to the axis of the sensor to provide maximum transmis8

sion for the ion of interest. When the ion trajectory deviates, ions will hit the surface of the electrodes and be neutralized, as shown with trajectories #2 and #3 in Figure 5. On the basis of these considerations, we can generate a phenomenological model for assessment of FWHM in a planar DMS. The larger the DMS gap height, the greater the acceptance angle (w) for ion trajectories. When the correct combination of SV and CoV is applied, the average radial speed of the selected ions is equal to 0. A formalized mathematical description is provided in Equation (7), hv? ðtÞi ¼

1 T

Z

T

v? ðtÞdt ¼ 0

ð7Þ

0

where n? is the component of ion velocity which is perpendicular to the DMS plates, and T is the period of the waveform. The

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DIFFERENTIAL MOBILITY SPECTROMETRY/MASS SPECTROMETRY

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FIGURE 5. Illustration of the formation of a peak in a planar DMS sensor. The ion trajectory #1 has been altered by the appropriate CoV to result in maximum transmission. The ion trajectories #2 and #3 have not been sufficiently altered by an appropriately high CoV to prevent them from hitting the electrodes.

ion velocity perpendicular to the DMS plates varies with time following the separation waveform and Equation (1). The time dependence is shown in Equation (7); however, for simplicity, the form hn?iwill be used in the subsequent equations. Figure 5 illustrates conditions for ion detection when the CoV is varied during optimal filtration conditions. Ion species will pass through the sensor if their drift velocity (n?) toward the electrode is smaller than a critical value. If we assume that ions originate at the center of the sensor gap, then the total radial displacement of the ions should be smaller than half of the height of the gap between the electrodes. Therefore, ions are transmitted under the following conditions:

where hKi is the coefficient of mobility averaged over one period of the SV. Therefore, the net velocity of the ion toward the upper and lower electrodes is provided in Equations (12a) and (12b), respectively.

v? t min  h=2

For a planar DMS design, we can assume that ion trajectories are symmetric on both sides of the gap axis, and that the velocity toward the upper or lower electrode is the same, as shown in Equation (13).

ð8Þ

where tmin is the minimum residence time of ions as they pass through the device. In the case of laminar gas flow with a parabolic distribution, axial speed is greatest on the central axis, and tmin can be written as t min ¼

l vjj;max

ð9Þ

where nk,max is the maximum axial speed. More commonly, the residence time is expressed as a function of the average axial speed, nk,av, and under laminar flow conditions, nk,av¼ 0.5 nk,max. The average radial velocity of the ions depends upon the combination of SV and CoV voltages, and can be determined by averaging Equation (1) over one period of the waveform, as shown in Equation (10). hv? i ¼

1 T

Z

T

KðEÞEdt ¼

0



1 T

Z

T

KðEÞ 0

  SV  CoV h

DðCoVÞ dt 2h

ð10Þ

Using the previously defined conditions for ion transmission (Equation 7), the first term in Equation (10) must be 0. Therefore, Equation (10) can be simplified to evaluate hn?i as a function of the small change in CoV, which we have defined as D(CoV)/2, to estimate the FWHM of the peak. Therefore, hn?i is directly proportional to D(CoV)/2, as demonstrated by Equation (11), hv? i ¼ 

DðCoVÞ hKi 2h

Mass Spectrometry Reviews DOI 10.1002/mas

ð11Þ

hv? iup ¼

þDðCoVÞ hKi 2h

ð12aÞ

hv? ibot ¼

DðCoVÞ hKi 2h

ð12bÞ

hv? idown ¼ hv? iup ¼

h 2t

ð13Þ

By substituting Equation (13) into Equation (12a) or (12b), we can determine an equation for peak width in a planar DMS, as shown in Equation (14). DðCoVÞ ¼

1 h2 hKi t min

ð14Þ

Equation (14) expresses several properties of DMS sensors, some of which are apparent in the experimental results of Figure 4. First, the ion-residence time is a key determinant of sensor performance. Peak width decreases as residence time increases. Second, the peak width depends directly on the volumetric flow rate of the transport gas and the square of gap height. Third, an increase in the length and width of the gap helps to narrow peak width. Finally, the coefficient of mobility for a given ion species averaged over one cycle of the SV waveform also affects the observed peak width. Ions with higher coefficient of mobility have narrower FWHM. This effect is apparent in the data shown in the top pane of Figure 4, where the highest mass compound with the lowest mobility has the widest peak. The validity of Equation (14) can be further confirmed by comparison with published experimental data (Schneider, Nazarov, & Covey, 2012a). The data in that paper show that variations in the volumetric flow over a range of 1.1–3.6 L/ min did not change the CoV for any of the 16 compounds tested; only peak widths and ion transmission were affected.

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2. Peak Capacity Definition of peak capacity: Peak capacity (PC) needs to be considered with reference to a defined set of compounds one desires to separate. Peak capacity for a particular separation can be defined as the ratio of the CoV range over which the specified compound set is spread divided by the average FWHM of the peaks. PC ¼

CoV max  CoV min FWHM

ð15Þ

The data in Figure 4 show that the resolving power and peak capacity improve similarly as the peaks are narrowed by increasing the residence time. When one of these figures of merit improves, so does the other to a comparable degree. Peak capacity can also be improved by means other than altering the residence time. Figure 6 provides an example when polar modifiers are added to the transport gas to affect the separation. Unlike the situation when the transport-gas velocity is altered, changing the transport gas composition changes the CoV values; however, in this case, the peak widths remained relatively constant. Under certain circumstances, changing CoV values can lead to a situation where the resolving power and peak

capacity measurements are contradictory. When the calculations for these figures of merit were used as defined here, the resolving power improved 34-fold when isopropanol was added to the transport gas (Figure 6A), but the peak capacity decreased 10fold. Clearly, reduction in peak capacity reflects reduction in separation power. The resolving power improvement in this case is misleading, and points to the importance of the peak-capacity measurement in DMS. This is a carefully selected example to demonstrate the problem with the resolving power calculation; but in the vast majority of cases, the addition of modifiers to the transport gas greatly improves the resolving power and peak capacity measurements by leveraging the differences in the gasphase ion chemistries of different species (Schneider et al., 2010c; Schneider, Covey, & Nazarov, 2013). Improvement of peak capacity with transport gas chemical modifiers: An example of the improvement in peak capacity with the use of modified transport gases is presented in Figure 7 which shows the separation of two structural isomers and one other isobaric species. In Figure 7B, the differential mobilities of all three are similar, with the inert transport gas nitrogen, as reflected in the peak capacity value and the appearance of overlapping peaks in the ionogram. This Type C separation is predominantly physical in nature, dominated by hard-sphere

1.0

Normalized Signal

A

Methionine RP: 54.7 Histidine RP: 53.4 Peak Capacity: 0.11

0.8 0.6 0.4 0.2 0.0 -80

B

-60

-40 CoV (V)

-20

0

Normalized Signal

1.0

Methionine RP: 1.6 Histidine RP: 2.8 Peak Capacity: 1.14

0.8 0.6 0.4 0.2 0.0 -80

-60

-40 CoV (V)

-20

0

FIGURE 6. Ionograms of methionine and histidine under two different transport-gas conditions; A) nitrogen that contains 1.5% isopropanol and B) 100% nitrogen. The system used is described in Appendix 1, with MRM data acquisition. Each peak is individually normalized to 1.0 to improve visualization of the separation of each component.

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FIGURE 7. Ionograms of ketorolac (MW ¼ 255.272 Da) and two structural isomers diphenhydramine and phenyltoloxamine (both MW ¼ 255.359 Da) under A) nitrogen transport gas modified with 1.5% isopropanol, peak capacity ¼ 20.4, and B) nitrogen transport gas, peak capacity ¼ 2.3. Compound 1 ¼ ketorolac, resolving power A ¼ 19.8 and B ¼ 5.7; compound 2 ¼ diphenhydramine, resolving power A ¼ 20.2 and B ¼ 6.7; compound 3 ¼ phenyltoloxamine, resolving power A ¼ 1.8 and B ¼ 7.9. The system used for separation is described in Appendix 1. Each peak is normalized to 1.0 on the “Y” axis to improve the visualization of the separation of each component. Minimal signal loss was observed with use of modifiers with these high proton affinity compounds.

collisions, as described in Section III.C Ion/Molecule Interactions and the Mechanisms of Separations. With the addition of a polar modifier as shown in Figure 7A, a Type A separation mechanism is invoked, and the subtle alterations in the clustering chemistries amplify their differential mobilities to result in a peak-capacity improvement by approximately 10-fold. The aforementioned difficulty with the resolving power value is also apparent here, where the resolving power for compound 3 degrades by a factor of 4 with the addition of modifier; however, in the context of this example, the separation power has actually increased substantially. The disjoint between resolving power and separation power is a mathematical aberration of the resolving power calculation caused by the CoV of phenyltoloxamine that moves closer to 0. There are thermodynamic limitations on the use of gasphase ion-cluster chemistry to affect separation performance. With nitrogen-containing analytes that have high gas-phase proton affinities, such as those used in Figure 6, no signal losses were observed in exchange for the increased peak capacity and separation power. However, in situations where the proton Mass Spectrometry Reviews DOI 10.1002/mas

affinity of the transport gas modifier is higher than the analyte, the charge will be transferred to the modifier to a degree that is relative to differences in the proton affinities or gas-phase basicities, depending on whether one deals with positive- or negative-ion separations. In an extreme case, all charge could be stripped from the analyte. Different modifiers can be used that have lower proton affinities or gas-phase basicities and mixtures of modifiers can be used to minimize this effect. The use of mixtures of methanol and hexanol was reported to minimize proton transfer to the transport gas. In addition, chloroform was added as a discharge-suppressing agent (Blagojevic, Koyanagi, & Bohme,2014). Volmer’s group has also considered these issues in some detail (Auerbach, Aspenleiter, & Volmer, 2014). The vast improvement in peak capacity, and the strong positive influence that gas-phase ion chemistry brings to bear on the improvement of peak capacity, is demonstrated across a diverse chemical space in Figure 8. The improvement in peak capacity when modifiers are added to the nitrogen transport gas is obvious with isopropyl alcohol improved over acetonitrile and 11

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FIGURE 8. Ionograms of a 54-component small-molecule mixture (mw range 115–530 Da) under different transport gas conditions. A) 1.5% isopropanol in nitrogen, peak capacity ¼ 91.7; B) 1.5% acetonitrile in nitrogen, peak capacity ¼ 40.6; C) 100% nitrogen, peak capacity ¼ 20.1. The list of compound names and the details of the system used for the separation are provided in Appendix 1. Detection was with MRM. Each peak is normalized to 1.0 to improve the visualization of the separation of each component.

both vastly superior to nitrogen. The CoV range expands, and the peaks maintain their FWHM. A relatively high concentration of the modifier in the transport gas is also critical to provide the maximum improvement to peak capacity and CoV stability by driving the clustering process to the maximum cluster number to amplify the difference in the high- and low-field ion mobility. Another advantage of high concentrations is that fluctuations in CoV values can occur at low concentrations (