reaction cell ICP-MS: Theoretical review of principles and limitations

Spectrochimica Acta Part B 110 (2015) 31–44

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Review

Kinetic energy discrimination in collision/reaction cell ICP-MS: Theoretical review of principles and limitations Noriyuki Yamada Agilent Technologies International Japan, Tokyo, Japan

a r t i c l e

i n f o

Article history: Received 17 March 2015 Accepted 18 May 2015 Available online 30 May 2015 Edited by A Bogaerts Keywords: Inductively coupled plasma mass spectrometry ICP-MS Collision reaction cell Kinetic energy discrimination KED

a b s t r a c t Kinetic energy discrimination (KED) is one of the means to control cell-formed interferences in collision/reaction cell ICP-MS, and also a technique to reduce polyatomic ion interferences derived from the plasma or vacuum interface in collision cell ICP-MS. The operation of KED is accurately described to explain how spectral interferences from polyatomic ions are reduced by this technique. The cell is operated under non-thermal conditions to implement KED, where the hard sphere collision model is aptly employed to portray the transmission of ions colliding with the cell gas that they don't chemically react with. It is theoretically explained that the analyte atomic ions surmount the energy barrier placed downstream of the cell and the interfering polyatomic ions do not due to their lower kinetic energy than the atomic ions, resulting in polyatomic interference reduction. The intrinsic limitations of this technique are shown to lie in the statistical nature of collision processes, which causes the broadening of ion kinetic energy distribution that hinders efficient KED. The reaction cell operation with KED, where plasma-derived interferences are reduced by the reactive cell gas while cell-formed interferences are suppressed by the energy barrier, is also described in a quantitative manner. This review paper provides an in-depth understanding of KED in cell-based ICP-MS for analysts to make better use of it. © 2015 Elsevier B.V. All rights reserved.

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Collision processes in the cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Decrease of ion kinetic energy by collision . . . . . . . . . . . . . . . . . . . . . 2.2. Initial ion kinetic energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Number of collisions in the cell . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Kinetic energy and scattering angle after a collision . . . . . . . . . . . . . . . . . 2.4. Ion kinetic energy after multiple collisions . . . . . . . . . . . . . . . . . . . . . 2.5. Ion trajectories in non-thermal cells . . . . . . . . . . . . . . . . . . . . . . . . 3. KED in collision cell ICP-MS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Potential barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Efficiency of KED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Energy spread caused by multiple collisions . . . . . . . . . . . . . . . . . . . . 3.4. Ion signal dependence on collision gas density (gas flow rate) of different collision gases 3.5. KED against doubly charged ions . . . . . . . . . . . . . . . . . . . . . . . . . 4. KED in reaction cell ICP-MS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Non-thermal reaction cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Reactant ion intensity in the cell . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Kinetic energy of reactant ions in the cell . . . . . . . . . . . . . . . . . . . . . 4.4. Ar+ and Ca+ signals in H2 reaction cell ICP-MS . . . . . . . . . . . . . . . . . . . 5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

http://dx.doi.org/10.1016/j.sab.2015.05.008 0584-8547/© 2015 Elsevier B.V. All rights reserved.

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N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

1. Introduction Around the turn of the century collision/reaction cell ICP-MS was commercially developed to address the problem of spectral interferences, which had been one of the major limitations in ICP-MS. Since then, it has rapidly grown popular in analytical laboratories around the world as a versatile technique to mitigate or circumvent interfering ions. Among the different types of cells that have been developed to reduce the spectral interferences derived from the plasma or the sampling interface, there is a common issue peculiar to this technique — the formation of undesirable ions within the cell through ion-molecule reactions. These ions can be produced not only through the reactions with the cell gas (in reaction cells) but also those with residual impurity gases such as water and hydrocarbons (in both collision and reaction cells). If the product ions have the same m/z as the analyte ions of interest and no measure is taken to suppress them, they will interfere with the analyte ion, thereby ruining the reduction of the original interferences that is to be achieved by the intended collision or reaction processes in the cell. The collision/reaction cells are effectual only when the interferences from the plasma or interface and those from cell-formed product ions are suppressed at the same time. While adding gas to the cell to reduce the former, three different approaches have been used to suppress the latter, that is, the signals of the detrimental product ions. 1) The dynamic reaction cell [1] prevents the formation of undesirable reaction products by using a band-passing quadrupole as an ion guide in the cell, which quickly ejects unnecessary (low-mass) ions before they produce undesirable ions through reactions with gas molecules. 2) The most recently developed ICP-QQQ [2] removes the unnecessary ions prior to the cell using an additional quadrupole mass filter, which allows only the analyte ions of interest (and the isobaric interfering ions) into the cell, and hence restricts the unnecessary reactions that would otherwise occur and yield undesirable ions in the cell. 3) KED [3] serves to prevent the transmission of the product ions toward the detector, while allowing their formation in the cell. Since the product ions that have exited the cell have lower kinetic energy than the atomic analyte ions under non-thermal conditions, they are selectively blocked by the potential barrier of appropriate height after the cell. The barrier can simply be established by setting the DC bias voltage of the quadrupole mass filter after the cell to slightly more positive voltage than that of the ion guide in the cell. KED has been used in both collision cells and reaction cells under non-thermal conditions. In this paper, the cell is referred to as collision cell when the cell gas is unreactive with the analyte and interfering ions, and as reaction cell when the cell gas is reactive with the analyte or interfering ions. The same cell can be a collision cell or reaction cell depending on the cell gas used and the ions considered. Besides the reduction of cell-formed product ion interferences, KED also plays an essential role in collision cell ICP-MS to reduce polyatomic ion interferences that are derived from the plasma or interface. Under typical operating conditions, an ion undergoes multiple collisions with gas molecules (or atoms) while it travels through the multipole ion guide extending from the entrance to the exit of the cell. It exits the cell with reduced kinetic energy as a result of these collisions. Atomic ions (analyte ions) lose less kinetic energy than the isobaric polyatomic ions (interfering ions), thus an energy difference is produced between the two ion species of the same mass. By a potential energy barrier of appropriate height placed after the cell, the slower polyatomic ions are blocked while the faster atomic ions overcome the barrier and reach the detector. Thus polyatomic interferences are suppressed. Although any gas introduced to the cell can be considered a collision gas as long as the ions don't chemically react with it, helium appears to be the most effective gas for KED as will be discussed in Section 3.4, and has been most often used in collision cell ICP-MS. For more than a decade after the first introduction of collision/reaction cell ICP-MS, pure He collision gas had been used in limited ICP-MS

systems. Now that all the collision/reaction ICP-MS instruments commercially available provide “KED mode” using 100% He gas, KED has undoubtedly become a standard technique. The KED technique was already discussed in 2002 as one of the means to control the appearance of the secondary reaction products in the comprehensive review of collision/reaction cell ICP-MS by S. D. Tanner et al. [4] However, the kinetic energy range considered in their paper (up to a several eV) differs from that in the He collision cells of the current ICP-MS instruments (up to ca. 20 eV), which is adopted for efficient reduction of plasma-derived polyatomic ion interferences. To the best of the author's knowledge, accurate, scientific, quantitative description of KED that reflects the current He collision cells is missing in literature. For better use of this technique, the operation principles and the limitations of KED in collision cell ICP-MS are described in this paper. To delineate how KED works for polyatomic interference reduction, it is imperative to know ion kinetic energies both for the atomic analyte ions and the polyatomic interfering ions in the cell. An ion, before it collides with a gas molecule, starts traveling in the cell with the kinetic energy determined by some instrumental conditions, and after experiencing multiple collisions it exits the cell with reduced kinetic energy due to those collisions. At the cell exit, however, the analyte ions of interest have to maintain as much kinetic energy as to overcome the potential barrier. Therefore the cell needs to operate under nonthermal conditions (the ion kinetic energy is above the thermal kinetic energy of the collision gas). In the non-thermal energy range considered here (from ca. 20 eV to a few eV), the collision can be regarded as that between two billiard balls (hard spheres) rather than as that caused by the electrical interaction between the charge (ion) and the dipole (neutral gas molecule). Then the ion kinetic energy after collisions is estimated using the hard sphere collision model, which will be discussed together with the cell conditions for the non-thermal operation. The ion's traveling direction may be altered by collision. The scattering angle, the angle between the ion velocity vectors before and after the collision, is also given by the hard sphere collision model. If they are large in non-thermal conditions, the ions are likely to scatter out of the ion guide. For ions having masses sufficiently higher than collision gas, however, the ion's scattering angle will be shown to be small enough for the ion to be confined within the ion guide. As for KED in reaction cell ICP-MS, the analyte atomic ions have to retain sufficient kinetic energy after unreactive collisions with the cell gas to overcome the energy barrier, while cell-formed product ions are blocked by the barrier and the signal intensities of the plasmabased interfering ions are reduced through chemical reactions with the cell gas. In this regard hydrogen may be the most usable reaction gas [5,6], since it has small mass to minimize the loss of the analyte ion's kinetic energy and has the sufficient reactivity toward the interfering argon and some argide ions. The operation of non-thermal reaction cell will be described, shedding light on the kinetic energy of reactant (interfering) ions as well as non-reactive analyte ions. As an example of KED for reaction cell ICP-MS, the kinetic energy of 40Ca+ (analyte) after collisions with H2 and the degree of reduction of 40Ar+ (interferent) through reaction with H2 are estimated to see how much improvement of signal-to-background ratio can be achieved. 2. Collision processes in the cell 2.1. Decrease of ion kinetic energy by collision In the current non-thermal collision cells operated with KED, the bias voltage of the multipole ion guide is typically set to −16 V [7] or slightly more negative [8], by which ions are accelerated to ca. 20 eV of kinetic energy upon entering the ion guide as will be discussed in the next section. With this rather high kinetic energy, however, an ion could not be transmitted if it entered the ion guide with the velocity having a large angle to the ion guide axis, because the ion kinetic energy in the radial direction became too high for the ion to be confined within

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

the ion guide by the multipole RF field. Only a well-collimated portion of the ion beam that is incident on the ion guide entrance will be transmitted, hence should be taken into account here. Then, the initial ion velocity in the cell can be considered to be in the axial direction. The ion travels along the central axis of the ion guide as it oscillates in the radial direction and/or rotates around the central axis. In the multipole RF ion guide used in collision cell ICP-MS, there is usually no electrical field in the axial direction. In such cases, the ion travels at a constant axial velocity until it collides with a gas molecule. In other words, the ion has the constant axial kinetic energy before the first collision. The initial kinetic energy (the kinetic energy of the ion after entering the ion guide but before the first collision) is typically ca. 20 eV as mentioned above, which is determined by some instrumental factors as described in the following section. Consider an ion, atomic or polyatomic, that does not react or dissociate in the event of a collision. After traveling some distance from the ion guide entrance, it collides with a gas molecule. Compared to the ion velocity, the gas molecule is much slower since it has only thermal kinetic energy at about room temperature (about 30 meV). Hence it can be considered that the ion collides with a stationary target. Just like the collision of two billiard balls, one moving, one at rest, the moving ion slows down after impact, imparting its kinetic energy to the stationary gas molecule. Subsequently, the ion travels farther at the reduced speed until it collides with the next gas molecule where it slows further. Thus the kinetic energy of the ion decreases step-by-step through multiple collisions. The final kinetic energy of the ion (the ion kinetic energy in the axial direction at the exit of the ion guide) depends on the initial ion kinetic energy; the loss of ion kinetic energy caused by a collision event; and the number of collision events that the ion experiences in the ion guide.

For the ions extracted from the Ar plasma into the vacuum, the ion energy is, in the absence of an applied field, given by [9,10] E0 ¼ V p þ

mi 5 kB T 0 mAr 2

ð1Þ

where Vp is the DC plasma potential. The second term (mi/mAr)(5/2)kBT0 is the kinetic energy that the ion acquired through gas expansion in the sampler–skimmer interface, where mi and mAr are the masses of the ion and an argon atom, respectively; kB is the Boltzmann constant; and T0 is plasma gas kinetic temperature. Assuming the interface is grounded, the ion kinetic energy is equal to E0 when the ion travels in a region of zero potential. The ion is accelerated when it enters a region of lower potential, that is, the ion kinetic energy increases when the potential where it travels decreases. Thus, the ion kinetic energy equals to E0 minus the potential at the ion's position. In the cell, the averaged potential is determined by the DC bias voltage applied to the ion guide. The kinetic energy before collisions (the initial kinetic energy), Ei is then expressed as Ei ¼ E0 −V guide

2.2. Number of collisions in the cell We consider an ion traveling at non-thermal velocity in the cell where there are stationary gas molecules at a number density of n. The average distance the ion travels between two collisions, known as the mean free path, is given by (σn)−1, where σ is the collision cross section for the collision between the ion and the gas molecule [10,11]. Then the average number of collision events N, that the ion experiences in the cell is given by the ion's traveling path length in the cell L, divided by the mean free path. N ¼ σ nL

ð2Þ

where Vguide is the DC potential of the ion guide. When the DC bias voltage (rod offset voltage) of the ion guide is set to −20 V for example, the singly charged positive ions gain about 20 eV of kinetic energy, since the average potential of Vguide ≈ −20 eV is established around the central axis of the ion guide where the ions travel. An As+ ion (mi = 75u), for instance, has the initial kinetic energy Ei of 24 eV for Vp = 2 eV, T0 = 5000 K and Vguide = − 20 eV. The first collision occurs with the ion kinetic energy of Ei. It should be noted that the kinetic energy in the radial direction that the ion acquires from the ion guide RF field is much smaller than Ei in this energy range, as will be shown by the ion trajectory simulation in Section 2.5, and therefore can be ignored as long as the ion is not thermalized.

ð3Þ

N depends on the distance the ion travels but not the time it spends in the cell as we consider ions traveling through the space where there are stationary gas molecules. Under typical cell conditions (non-thermal conditions), the traveling path length L is approximately equal to the axial distance that the ion covers, that is, the ion guide length. As will be shown in the Section 2.5, the ion's oscillating and rotating motions contributes little to the entire path length of the ion in the nonthermal cell, because the non-thermal atomic analyte ions reach the cell exit before oscillating or rotating as many times as their path length is affected by such motions. For an atomic ion colliding with a He atom, σ is on the order of 10−19 to 10−18 m2 [12], which corresponds to the collision diameter (bmax) of 0.2 to 0.5 nm when treating the ion and the He atom as hard spheres. In the hard sphere collision model, bmax is the sum of the radii of the two collision partners, ri + rg (see Fig. 1), which is related to the collision cross section as
2 2 σ ¼ πbmax ¼ π r i þ r g :

2.2. Initial ion kinetic energy

33

ð4Þ

Among the different definitions of atomic radii (e.g. covalent radii, and ionic radii), van der Waals radii are most appropriately employed to estimate collision cross sections, since they reflect the closest approach of two non-bonded atoms. They have been proposed for neutral atoms of most elements [13], e.g. 0.143 nm for He and 0.188 nm for As. Taking the van der Waals radii of He and As as the hard sphere radii of a He atom and an As+ ion, respectively, the cross section for the collision between them, for example, is calculated from Eq. (4) to be 3.3 × 10− 19 m2. (It should however be noted that the size of a positive ion may be smaller than that of the corresponding neutral atom because the electron cloud is contracted toward the nucleus by the excessive protons when the atom is ionized. Therefore, for the collision between a positive ion and a neutral gas molecule, the hard sphere cross section estimated from van der Waals radii may be somewhat larger than the empirically measured cross section. Having said that, van der Waals radii are used for the discussion in this paper since the absolute values of cross sections are not essential in polyatomic interference reduction, but the difference of the cross sections between the atomic and polyatomic ions is of essence as will be discussed later). For the polyatomic ions occurring in ICP-MS, the collision cross sections are not well known. However, when comparing the size of a polyatomic ion with the atomic ion of the same mass (e.g. ArO+ vs + Fe+, ArCl+ vs As+, Ar+ 2 vs Se ), the former is expected to have a larger collision cross section than the latter due to the fact that the interatomic distance (bond length) of the polyatomic ions occurring in ICP-MS is nearly as large as the radii of the constituent atoms. For example, the bond lengths of ArO+, ArCl+ and Ar+ 2 are 0.167 nm, 0.208 nm and 0.252 nm, respectively [14]. The van der Waals radii of the constituent atoms, Ar, O and Cl, are 0.183 nm, 0.150 nm and 0.182 nm, respectively [13], although they would be somewhat smaller when they form polyatomic ions. If compared with the size of the atomic 75As+ (ri ≈ 0.188nm), the size of the polyatomic 40Ar35Cl+ is apparently much

34

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

mi

mi

v’i

b

bmax=ri + rg

α

vi

θ/2

mg b

β vg=0

mg

v’g At Impact

Fig. 1. Collision between a moving sphere (mi) and a stationary sphere (mg) viewed in the laboratory frame of reference.

larger. Hence, in general, a polyatomic ion experiences more collisions than the isobaric atomic ion due to its larger cross section. The gas number density n is proportional to the flow rate of the cell gas (typically 0.1 to 10 sccm), and inversely proportional to the total area of the openings at the entrance and exit of the cell. When effusive flow through the openings is assumed, it is given by [10] n¼

4F vg A

and A is the area of the cell openings (the entrance and exit apertures of the cell). For a cell operating at room temperature with the two openings of 2 mm in diameter, n is about 1.1 × 1021 m− 3 (pressure = 4.7 Pa) at a He flow rate of 5 sccm. In this case, the average number of collision events in a 0.1 m long ion guide is at least about 10 (σnL = 10−19 m2 × 1.1 × 1021 m−3 × 0.1 m). The variance of the number of collisions that each ion experiences in the cell will be discussed in Section 3.3. 2.3. Kinetic energy and scattering angle after a collision Base on the hard sphere collision model, the kinetic (translational) energies of the ion and the gas molecule after a single collision E ' i and E ' g, respectively, are given by [15] m 2 þ mg 2 þ 2mi mg cosθ 1 2 E0 i ≡ mi v0i ¼ Ei i
2 2 mi þ mg

ð6Þ

1 2 E0 g ≡ mg v0g ¼ Ei −E0i 2

ð7Þ

where Ei is the ion kinetic energy before the collision, which is the initial kinetic energy given by Eq. (2) if the collision is the first one in the cell; mg is the mass of the gas molecule; and θ (0 ≤ θ ≤ π) is the scattering angle in center-of-mass coordinates. In these equations, the kinetic energy (velocity) of the gas molecule before the collision is assumed to be zero as it is considered as a stationary target. In the hard sphere collision, θ is related to the impact parameter b in the form of θ b ¼ 2 bmax

tanα ¼

sinθ mi =mg þ cosθ

tanβ ¼

sinθ 1− cosθ

ð5Þ

where F is the number of gas molecules flowing into the cell per unit  1=2 BT time; vg is the average speed of the cell gas molecules vg ¼ 8k ; πmg

cos

molecule) as illustrated in Fig. 1. The laboratory frame scattering angles of the ion and the gas molecule, α and β, respectively, are related to θ in the forms of

ð8Þ

The impact parameter b (0 ≤ b ≤ bmax) is the extrapolated distance between the incoming ion's path and the center of the target (gas

ð9Þ

ð10Þ

where α ranges from 0 to π, and β from 0 to π/2, being independent of ion kinetic energy. Consider how the impact parameter b affects the ion kinetic energy after collision and the ion scattering angle. When the ion collides headon with a stationary gas molecule (b = 0, θ = π, α = 0 or π, β = 0), the ion loses maximum energy, continuing forward or bouncing back depending on the ion mass relative to the gas molecule mass. When the two particles graze one another (b ≈ bmax, θ ≈ 0, α ≈ 0, β ≈ π/2), the ion loses almost no energy (E ' i ≈ Ei), and keeps moving in the original direction. For an As+ ion (mi = 75u) colliding with a stationary He atom (mg = 4u), the calculated kinetic energies after the collision and scattering angles of the two particles are shown in Fig. 2 as a pffiffiffi function of θ (as a function of b). At b ¼ bmax = 2 (the mean impact parameter, which gives θ = π/2), for example, Eq. (6) gives E ' i = 0.904 Ei, that is, 9.6% of the As+ kinetic energy is lost by the collision. At the mean impact parameter, the scattering angle α is close to the maximum when mi N mg, which is, however, only 3.1° for As+ ions colliding with He. Therefore the axial component of the As+ velocity after collision remains dominant, allowing us, to a first approximation, to ignore the radial component produced by the collision with He. 2.4. Ion kinetic energy after multiple collisions The final kinetic energy Ef, the kinetic energy of the ion after all the collisions experienced in the cell, is then given by mi 2 þ mg 2 þ 2mi mg cosθ j
2 j¼1 mi þ mg N

E f ¼ Ei ∏

ð11Þ

where
 θ j ¼ 2 cos−1 b j =bmax

ð12Þ

and bj is the impact parameter at the jth collision, N is the number of collisions that the ion experienced in the cell. A rough estimate of the final

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

0.97

0.87

0.71

0.50

0.26

0

1

As+

0.8 E'i/Ei

0.6

E'g/Ei

0.4

He

0.2 0 0

30

60

90

120

150

Center-of-Mass Scattering Angle θ

180 [o]

Scattering Angle[o] (Lab Frame)

Kinetic Energy after Collision normalized by Ei

Normalized Impact Parameter b/bmax 1

1

35

Normalized Impact Parameter b/bmax 0.97 0.87 0.71 0.50 0.26 0

90 80 70 60 50 40 30 20 10 0

α β

He

As+ 0

30

60

90

120

150

180

Center-of-Mass Scattering Angle θ [o]

Fig. 2. Kinetic energies after collision (left) and scattering angles in the LAB frame (right) calculated for As+ and He as a function of b, assuming that As+ collides elastically with a stationary He atom.

energy can be made assuming all the collisions occur at θj = 90° (at the mean impact parameter). With this assumption Eq. (11) is rewritten as ( )N m 2 þ mg 2 E f ¼ Ei
i 2 mi þ mg

ð13Þ

For an As+ ion that enters the ion guide with Ei = 24eV and experiences 10 collisions with He gas, the Ef of the As+ is 24eV × 0.90410 = 8.7eV. The interfering polyatomic ion ArCl+ (mi = 75u) enters the ion guide with about the same initial kinetic energy as As+ (see Eq. (2)), but collides with He more times than As+ because of its larger collision cross section. Assuming the cross section is twice as large as that of As+, an ArCl+ experiences 20 collisions on average in the pressurized cell where an As+ experiences 10 collisions on average. The final kinetic energy of the ArCl+ after 20 collisions is estimated from Eq. (13) to be 24eV × 0.90420 = 3.2eV, which is significantly lower than that of the As+ that experienced 10 collisions. Thus an axial kinetic energy difference is produced between the two isobaric ion species at the exit of the ion guide. Then with the post-cell potential barrier that is higher than 3.2 eV but lower than 8.7 eV, the ArCl+ ions are blocked while the As+ ion are allowed to transmit through the quadrupole mass filter that is set to select m/z = 75. It should be noted that polyatomic ions may lose more kinetic energy than expected from this hard sphere collision (elastic collision) model, because the part of collision energy can be deposited into the internal energies such as vibrational and rotational ones. Therefore the kinetic energy difference between the atomic and polyatomic ions of the same mass may be somewhat greater than what is estimated from this model. If the collision gas flow rate is increased to induce many more collisions, the kinetic energies of As+ and ArCl+ will both damped to the thermal energy of the collision gas, resulting in no difference between their kinetic energies. If the ion guide bias is made less negative for better ion transmission, the ions will have a higher tendency to be thermalized by collisions due to their lowered initial kinetic energy, leading to a smaller difference in the final kinetic energies between the two isobaric ion species. For example, if the ion guide bias is increased to −1 V [16,17], the lowered initial kinetic energy of As+ and ArCl+ (ca. 5 eV) results in the smaller difference of final kinetic energies, 1.8 eV for As+ and 0.67 eV for ArCl+, which would make efficient KED difficult as will be discussed in Section 3.2. Therefore both the gas flow rate and the ion guide bias are the important factors in producing sufficient kinetic energy difference. Of course it is desirable to minimize (thermalize) the kinetic energy of the interfering polyatomic ions, but the cell has to be in a non-thermal condition for the analyte ions to retain sufficient kinetic energy so that they can overcome the potential barrier after the cell.

It should be noted that the transmission of relatively low mass ions through the pressurized cell to the mass filter is low due to their large energy loss and scattering loss. The kinetic energy loss, or the energy transfer to the target gas molecule, is large when the relative difference between the ion mass and the gas molecule mass is small, which is the case for low mass ions in collision cell ICP-MS (Imagine that complete transfer of kinetic energy occurs when a moving hard sphere collides head-on with a stationary hard sphere of the same mass). For example, Eq. (6) indicates that the 35%, 46% and 41% of the kinetic energy of Li+ (7u) are lost via a single collision with H2 (2u), He (4u) and NH3 (17u), respectively at the mean impact parameter (Li+ doesn't react with any of these gases). With such large kinetic energy loss per collision, the analyte Li+ is nearly thermalized after several collisions as predicted from Eq. (13) and hence unable to surmount the potential barrier after the cell. The scattering angles α of Li+ calculated by Eq. (9) are 16°, 30° and 68° for a collision with H2, He and NH3, respectively, at the mean impact parameter. With such large scattering angles, a significant fraction of the post-collision kinetic energy can be in the radial direction. Assuming the velocity of a Li+ ion before collision is in the axial direction, the radial components of the post-collision kinetic energy are (sin 16°)2 = 7.6 %, (sin 30°)2 = 25 %, ( sin 68°)2 = 86 % of the total post-collision kinetic energy, respectively (note that kinetic energy is proportional to the square of speed). Due to these large radial components of post-collision kinetic energy, which are in the non-thermal energy range, the likelihood of the ion scattering out of the ion guide is high. For these reasons, even for non-reactive cell gases, signal loss of low mass ions is significant when the non-thermal cell is operated with KED. 2.5. Ion trajectories in non-thermal cells Now that the ion velocity (speed and direction) after collision can be obtained from Eqs. (6) and (9), ion trajectories through the RF ion guide in the pressurized cell can be simulated by statistically selecting the position where collision occurs and the impact parameter for each collision [15]. The length of the trajectory in the ion guide corresponds to the ion's traveling path length L in the cell that determines the number of collisions. Examples of calculated trajectories of the m/z = 75 ion colliding with He atoms in an octopole and a quadrupole are shown in the Fig. 3. The operating conditions of the two ion guides used for the calculations are summarized in Table 1, which are probably typical for the cells used in ICP-MS [18]. Without He in the ion guide, the calculated trajectories (black lines) indicate constant amplitude and period of the oscillatory motion (with more rapid but much smaller wiggles superimposed, which correspond to the radio frequencies of the voltage applied to the ion guides). In the octopole (upper), the ion, having the axial kinetic energy of 24 eV, oscillated only 2.1 times with amplitude of 1 mm during the passage through

36

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

Z-X plane

Without He

With He

Octopole Ion Guide

3.6mm

Traveling direction 100mm

X-Y plane

Z-Y plane

Z-X plane

Without He

With He

Quadrupole Ion Guide

8.2mm

leading to a longer traveling path in the ion guide. However, as shown by the red trajectories, along which the ion underwent 20 collisions, the ion oscillated slightly more times in the octopole (2.3 times) or 2 more times in the quadrupole (5.5 times) during the passage through the ion guide. And the amplitude of oscillation slightly decreased toward the ion guide exit, which reflects an effect of collisional focusing [15], though the effect is small due to the limited number of collisions with the light gas (He) for non-thermal operation of the cell. The final kinetic energy was calculated to be 4.1 eV both in the octopole and quadrupole, confirming the non-thermal conditions were maintained after 20 collisions with He gas. The lengths of the trajectories are 100.5 mm and 127.0 mm in the octopole and quadrupole, respectively, which are the same as or slightly longer than those without collisions, but still close to the ion guide length. Under non-thermal conditions ions reach the ion guide exit before oscillating so many times as the oscillatory motion contributes to the total path length. Therefore, the ion's traveling path length in the ion guide is about the same as the ion guide length in the non-thermal cell, which justifies the discussion in Section 2.2 to estimate the number of collisions. 3. KED in collision cell ICP-MS

Traveling direction 125mm

X-Y plane

Z-Y plane

Fig. 3. Examples of ion trajectories calculated with and without He gas in an octopole (upper) and a quadrupole (lower) ion guide. The black trajectories are calculated without collision (without He). The initial conditions were chosen so that the trajectories are within the Z–X plane. Using the identical initial conditions, the red trajectories are calculated with He collisions. The black dots on the red trajectories indicate where collision occurs. The blue straight lines represent the innermost position of the rod surface of the multipole ion guides. Note that the scale in the radial direction is expanded to show oscillatory motions of the ion. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

the entire ion guide of 100 mm in length. Similarly, in the quadrupole (lower), the ion oscillated about 3.5 times with amplitude of c.a. 1 mm while traveling the axial distance of 125 mm. The lengths of the trajectories are calculated to be 100.5 mm and 126.5 mm in the octopole and quadrupole, respectively, indicating that the ion path length in the ion guide is approximately the same as the ion guide length. If He gas is introduced to the ion guides, the ion slows down through collisions. Therefore it oscillates more as it spends more time in the RF ion guide,

Table 1 Ion guide used for ion trajectory simulation.

Length [mm] Inscribed diameter [mm] Frequency of voltage [MHz] RF amplitude [V] m/z of ion Ion mass [u] Initial kinetic energy (axial) [eV] Initial position Cell gas Number of collisions

3.1. Potential barrier In KED mode, the potential barrier is set up by the quadrupole mass filter that is DC biased at a voltage higher than the ion guide bias voltage. The ion has the axial kinetic energy Ef at the exit of the ion guide that is biased at a DC potential Vguide as described in Section 2.4. The (total) ion energy is Ef + Vguide, the sum of the kinetic and potential energies. Once the ion has left the cell, the ion energy is conserved (until it hits the detector), assuming that no collision occurs outside the cell. In the quadrupole mass filter biased at a DC potential Vquad, the axial kinetic energy of the ion passing through the mass filter Equad is determined by the energy conservation equation, Equad + Vquad = Ef + Vguide. Namely,
 Equad ¼ E f  V quad  V guide

ð14Þ

Therefore, if the potential difference (barrier height) Vquad − Vguide is smaller than Ef, the ion is able to pass through the mass filter with a certain axial velocity since Equad N 0. Otherwise it is blocked at the entrance of the mass filter by this potential barrier. For example, when the mass filter is DC biased at − 15 V (Vquad ≈ − 15eV) and the ion guide at − 20 V (Vguide ≈ − 20eV), the potential barrier of 5 eV is set up at the entrance of the mass filter. As discussed in 2.4, the As+ ions that have experienced 10 collisions have the Ef higher than 5 eV on average. Therefore, they surmount the barrier and travel through the mass filter set to m/z = 75, while the ArCl+ ions, which have Ef of only about 3.2 eV on average, are blocked. Obviously, if the potential barrier is too high or too low, both analyte and interfering ions are blocked or allowed to pass, resulting in no effective interference reduction. 3.2. Efficiency of KED

Octopole RF-only ion guide

Quadrupole RF-only ion guide

100 3.6 11 180 75 75 24

125 8.2 2.5 200 75 75 24

1 mm off the central axis No gas or He 0 or 20

1 mm off the central axis No gas or He 0 or 20

Even if the potential barrier is properly set up, the efficiency of kinetic energy discrimination is not 100% — some of the interfering polyatomic ions surmount the barrier and some of the atomic analyte ions are blocked by the barrier or ejected by the quadrupole fringe field [19]. There are two factors that limit the efficiency of KED; 1) the nonideal energy filtering property of the potential barrier, and more importantly, 2) the spread of the final energy caused by the statistical nature of the collision processes. Although it is easy and simple to use the quadrupole mass filter as a potential barrier, it does not have an ideal energy-filtering property, that is, 100% transmission for the ions that have Equad N 0. Slow ions

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

(Equad ≈ 0) are likely to be ejected by the fringe field of the quadrupole, even if they have sufficient kinetic energy to overcome the potential barrier. As will be discussed in the next section, the ions have a spread of final kinetic energies. Even if the average final energy is well above the barrier height, a portion of ions having lower kinetic energy may be unable to pass through the fringe field, leading to the loss of analyte ion signals. In addition, the spreads of the final energies for the atomic analyte ions and polyatomic interfering ions may result in an overlap of the energy distributions of these two ion species, that is, a portion of analyte ions and that of interfering ions have the same final kinetic energy. This incomplete energy separation hinders efficient KED. To what extent the polyatomic ions are suppressed and the atomic analyte ions are blocked by KED is discussed in the next section. 3.3. Energy spread caused by multiple collisions Unlike billiards games, occurrence of gas phase collisions is determined by the laws of probability. Even for the same ion species, the number of collisions that each ion experiences in the cell is not constant. Additionally the kinetic energy loss per collision is not constant either, as it depends on impact parameter b, which can't be controlled as a good pool player controls it to obtain the desired velocity of the balls after the collision. Therefore, the ions reaching the cell exit will have a spread of final kinetic energy. Take an extreme but good example here. The probability of an ion experiencing N collisions in the cell, P(N) is given by the Poisson distribution as P ðN Þ ¼

ðσnLÞN −σ nL e N!

ð15Þ

where σnL is an average number of collisions that the ions experience in the cell (see Eq. (3)). When the cell is pressurized to the extent that σnL = 10 for As+, 45 out of one million As+ ions pass the cell without a single collision, since P ð0Þ ¼ e‐10 ¼ 4:5  10−5. These 45 lucky As+ ions retain the initial kinetic energy. When it is 24 eV, the population of As+ ions will have a final kinetic energy distribution extending up to 24 eV while the average final energy is 8.7 eV as discussed in Section 2.4. The same is true for the interfering ArCl+, some of which will have higher final energy than their average final energy. Fig. 4 shows the probability distributions of the number of collisions for σnL = 10 and 20 calculated from Eq. (15). Only 12.5% of the ions go through 10 collisions for σnL = 10, while the rest experience more or fewer collisions than the average number of 10. The variation of the number of collisions that ions undergo is one of the factors that produce a spread of the final ion kinetic energy. Examples of final kinetic energy distributions calculated using Eq. (6) are shown in Fig. 5. For each of 100,000 ions of mass 75u traveling through a He-filled cell, statistical calculation of a traveling distance

σnL=10

0.12

σnL=20

Probability P(N)

0.10 0.08 0.06 0.04

0.02 0.00 0

10

20

30

between collisions was repeated until the ion covers the entire length of the ion guide and the impact parameter for each of the collisions was statistically selected to determine the post-collision kinetic energy[15]. The initial kinetic energy was assumed as Ei = 24eV with no energy spread (the mono-energetic ions entering the cell). Fig. 5a shows histograms of the final kinetic energies of 100,000 ions calculated under the conditions of σnL = 10 and 20, intending to emulate the energy distributions of As+ and ArCl+, respectively. The average final energies for σnL = 10 and 20 were calculated from the distributions to be 8.69 eV and 3.26 eV, respectively, which were coincident with the rough estimate of the final energies obtained from Eq. (13). Of the 100,000 ions, the ions having a final energy lower than 5 eV were 8646 for σnL = 10 (As+) and 81,879 for σnL = 20(ArCl+). Therefore, by the 5 eV potential barrier set up for KED, 8.65% of the As+ signal is lost, but 81.9% of the ArCl+ interference is removed. If this level of interference reduction is insufficient for samples containing high Cl matrix, one should increase the potential barrier height or the He flow rate (increase the He density n). Fig. 5b shows the final energy distributions when the He flow rate is doubled (σnL is 20 for As+ and 40 for ArCl+). In this condition, the ions having final energy lower than 5 eV were 81,879 for σnL = 20 (As+) and 99,994 for σnL = 40(ArCl+), which means that despite 81.9% loss of the As + signal, the ArCl + interference is reduced by more than four orders of magnitude (reduced from 100,000 to 6) by the 5 eV KED. At this high He flow rate, one may want to recover the As+ signal by reducing the barrier height. However, ArCl+ interference would increase more rapidly than the As+ signal. For example, by reducing the barrier height from 5 eV to 3 eV the As+ signal loss decreases from 81.9% to 46.8% as indicated in Fig. 5b, while the number of the ArCl+ ions surmounting the barrier increases from 6 to 153 (by more than 20 times), eventually leading to degradation of the S/B ratio. The potential barrier height for KED, set with a compromise between the analyte signal level and the degree of interference reduction, is also an important factor to determine the collision cell performance in addition to the collision gas flow rate and the ion guide bias. 3.4. Ion signal dependence on collision gas density (gas flow rate) of different collision gases In order to select the appropriate collision gas flow rate, the improvement of S/B ratio has been estimated by measuring the signals of atomic analyte ion (analyte standard sample) and polyatomic interfering ion (matrix blank) as a function of the flow rate [8]. The ions that overcome the potential barrier contribute to the ion signal observed in collision cell ICP-MS with KED. The number of collisions N that gives the ion the final energy higher than the barrier height, Vquad − Vguide, is obtained from the following condition, assuming all the collisions occur at the mean impact parameter (see Eq. (13)). m 2 þ mg 2 E f ≡Ei
i 2 mi þ mg

0.14

40

37

!N NV quad −V guide

ð16Þ

For example, N is lower than 21 for the As+ ions (mi = 75 [u], Ei = 24eV) colliding with He (mg = 4 [u]) when the barrier height Vquad − Vguide is set to 3 eV, that is, the As+ ions that have experienced 20 or fewer collisions overcome the barrier and are transmitted to the detector, and those that have experienced more than 20 are blocked by the barrier. The fraction of the As+ ions that are detected corresponds to the sum of the probabilities of the ion experiencing from zero to 20 collisions. Therefore, in general, the ion signal (intensity of the ions that overcomes the barrier) is given by

number of collisions N Fig. 4. Probability distribution of the number of collisions for the average collisions of 10 and 20 calculated from the Poisson distribution.

I=I0 ¼

Nc Nc X X ðσ nLÞN −σ nL e P ðN Þ≡ N! N¼0 N¼0

ð17Þ

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

6000

number of ions

5000

120000

a

σnL=20

100000

4000

80000

σnL=10

3000

60000

2000

40000

1000

20000

0

cumulative number of ions

38

0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Final Ion Kinetic Energy Ef [eV] 120000

30000

number of ions

b

σnL=40

100000

24000

80000

18000

60000

12000

40000

σnL=20

6000

20000

cumulative number of ions

36000

0

0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Final Ion Kinetic Energy Ef [eV] Fig. 5. Final kinetic energy distributions of the 100,000 ions of mass 75u that have traveled through the collision cell pressurized with He gas to the extent that the average collisions (σnL) are 10 for As+ and 20 for ArCl+ (a); and 20 for As+ and 40 for ArCl+ (b) (It is assumed the collision cross section of ArCl+ is twice larger than As+). The horizontal energy scale is divided into bins of 0.2 eV width. Scaled on the right Y axis are the cumulative numbers of ions for the two different σnL (circles and triangles). These cumulative distributions, shown as a function of Ef, represent the total number of ions having the energy lower than Ef.

where I0 is the intensity of the ions exiting the collision cell, I is the intensity of the ions exiting the cell that overcome the barrier, P(N) is the probability of the ion experiencing N collisions given by the Poisson distribution Eq. (15), and Nc is the maximum number of collisions that gives the ion the final energy higher than the barrier height. As the collision gas density n (flow rate) increases, the average number of collision (σnL) increases, resulting in the decrease of the probability of the ion experiencing a smaller number of collisions. Therefore the ion signal decreases with the flow rate. Fig. 6a shows the normalized signals of the ions (mi = 75u) that overcomes the barrier as a function of He number density, calculated using Eq. (17) for Nc = 20, mi = 75 [u], and L = 0.1 [m]. The collision cross section was assumed to be σ = 3.3 × 10− 19 m− 2, the value derived from the van der Waals radii of He and As atoms (see Section 2.2). For comparison, the calculations were also performed for the cross sections 1.5 and 2 times larger to emulate signals of the polyatomic interfering species. At n = 8 × 1020 [m− 3], for example, the signal of the ion with σ = 3.3 × 10−19 m− 2 (atomic analyte) decreases by one order of magnitude, while the signals of the ions having 1.5σ and 2σ (polyatomic interferences) decrease by 3 and 7 orders of magnitude, respectively, which corresponds to the S/B improvement of 2 to 6 orders of magnitude. Obviously, the greater the difference of collision cross sections, the higher the S/B improvement. For comparison the same calculations were performed for other collision gases, Ne and Ar, as shown in Fig. 6b and c, respectively. Nc is 6 for Ne and 3 for Ar, which are far fewer than 20 for He. This is because the loss of ion kinetic energy per collision is larger for heavier gas. It is clearly seen that the relative signal intensities of the ions of larger cross sections (polyatomic ions), compare to those of smaller cross sections, are higher for heavier gases, indicating that the polyatomic interference reduction by KED is less effective when using heavier collision gas. This result is solely derived from the characteristics of the Poisson distribution as it is obtained from Eq. (17) alone. Efficient KED

against polyatomic ions can be achieved at a high average number of collisions, which is possible with light collision gas. The curves in Fig. 6a, b and c, concave downwards on a semi-log graph, are in sharp contrast to the exponential decay (linear decay on a semi-log graph) of the ions reduced by the reaction with the cell gas as will be shown in Section 4.4. However, the measured ion signals often deviate from these profiles due to the collisional focusing and scattering loss. 3.5. KED against doubly charged ions Doubly charged ions act as interfering ions against certain singly charged analyte ions. For example 150Nd++ and 150Sm++ interfere with 75As+, because these doubly charged ions have the same m/z(=75) as a singly charged arsenic ion. Unfortunately doubly charged ion interference cannot be suppressed by the collision cell operating with KED. This section clarifies the reason, which seems to have long been misunderstood [20]. Using Eqs.(1) and (2), the initial kinetic energy of a (singly charged) analyte ion in the cell is expressed as Es ¼ V p þ

mi 5 kT 0 −V guide mAr 2

ð18Þ

where mi is the mass (not m/z) of the analyte ion. Likewise, the initial kinetic energy of the doubly charged interfering ion, which has the mass of 2mi, is given by Ed ¼ 2V p þ

2mi 5 kT 0 −2V guide mAr 2

ð19Þ

The initial kinetic energy of the doubly charged interfering ion is exactly twice higher than the singly charged analyte ion of the same

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

normalized signal intensity I/I0

1.E+01

a

1.E+00 σ

1.E-01 1.E-02

1.5 σ

1.E-03 1.E-04

2σ

1.E-05

1.E-06 mi=75 [u], mg =4 [u] 1.E-07

0

2E+20

4E+20

6E+20

8E+20

1E+21

-3

He number density [m ]

normalized signal intensity I/I0

1.E+01

b

1.E+00 σ

1.E-01 1.E-02

1.5 σ

1.E-03 1.E-04

2σ

1.E-05

1.E-06 mi =75 [u], mg =20 [u] 1.E-07

0

1E+20

2E+20

3E+20

4E+20

-3

charged ions. Then do doubly charged ions overcome a high potential barrier that singly charged ions cannot because of their higher kinetic energy? Is this why KED does not work for reduction of doubly charged ion interferences? It is not. The potential barrier height for the doubly charged ions to overcome is also twice higher than for singly charged ions. For example, with the DC bias voltage of the ion guide in the cell set to − 20 V and that of the quadrupole after the cell set to − 15 V, the potential barrier height Vquad − Vguide is ca. 5 eV for singly charged ion since the potential energies in the ion guide and quadrupole are about Vguide = −20 eV and Vquad = −15 eV, respectively as discussed in the Section 3.1. The barrier height for doubly charged ions is ca. 10 eV because the potential energies of the doubly charged ions are doubled (Vguide = −40 eV and Vquad = −30 eV). Therefore, with both kinetic energy and barrier height doubled, doubly charged ions have the same “difficulty” in overcoming the barrier as singly charged ions have. What about the kinetic energy loss induced by collision? There is difference in the energy loss between singly and doubly charged ions of the same m/z since it is mass-dependent as indicated by Eq. (6). For example, as has been discussed before, the kinetic energy of As+ (mi = 75u) after collision with a He atom (mg = 4u) at the mean impact parameter (cos θ = 0) is given by Eq. (6) as Ei′ = 0.904 Ei, which means 9.6% of the kinetic energy that the As+ has before the collision is lost. For an interfering Nd++ ion (mi = 150u) that collides with He in the same condition (cos θ = 0), the equation gives E ' i = 0.949 Ei. The kinetic energy loss is 5.1%, which is smaller than As+. As intuitively understood from a hard sphere collision event, heavier ions lose less kinetic energy than lighter ions at the collision with a light gas molecule. The final energy after multiple collisions should then be examined, which depends on the number of collisions (or collision cross section). Using Eq. (13), the conditions for the singly charged analyte to overcome the barrier (Vquad − Vguide) and for the doubly charged interfering ion to be blocked by the same barrier (2Vquad − 2Vguide) are given by

Ne number density [m ]

Es

normalized signal intensity I/I0

1.E+01

c

1.E+00

1.E-02

!σ 1 nL NV quad −V guide

1.E-04 2σ

1.E-05

!σ 2 nL

σ 2 ln C 1 N σ 1 ln C 2

1.E-06 mi=75 [u], mg =40 [u]

1E+20

b2V quad −2V guide

ð21Þ

ð22Þ

where

1.E-07

0

ð20Þ

where σ1 and σ2 are the collision cross sections for the singly and doubly charged ions, respectively (σ1nL and σ1nL are the average numbers of collisions for the singly and doubly charged ions, respectively). Combining the above two conditions leads to the single condition,

1.5 σ

1.E-03

mi 2 þ mg 2
2 mi þ mg

4m 2 þ mg 2 2Es
i 2 2mi þ mg

σ

1.E-01

39

2E+20

3E+20

Ar number density [m-3] Fig. 6. Normalized signals of the ions (mi = 75u) that surmount the 3 eV potential barrier, calculated as a function of He gas number density (a), Ne gas number density (b) and Ar gas number density (c). The DC bias potential of the ion guide in the cell is Vguide = −20 eV (The initial kinetic energy is 24 eV). The calculations were carried out for three collision cross sections, 3.3 × 10−19 m2 (solid lines denoted by σ), 5.0 × 10−19 m2 (dotted lines denoted by1.5σ) and 6.6 × 10−19 m2 (dashed lines denoted by 2σ). The maximum numbers of collisions that allow the ion to surmount the barrier are 20, 6, 3 for He, Ne and Ar, respectively. The difference of cross sections results in difference of ion signal intensities, which is larger for lighter collision gas.

m/z (Ed = 2Es). This is because the kinetic energy that the doubly charged ions acquire in the gas expansion and the potential energy that they have in a potential field are doubled compared with singly

m 2 þ mg 2 C1 ¼
i 2 mi þ mg

ð23Þ

4mi 2 þ mg 2 C2 ¼
2 2mi þ mg

ð24Þ

In the case of 150Nd++ (or 150Sm++) interference on 75As+, the condition of σ2/σ1 N 1.93 is derived for He collision gas. Namely, the collision cross section of Nd++ has to be at least 1.93 times larger than that of As+ in order to selectively block Nd++ by the potential barrier. The cross sections can be estimated from the radii of the collision pairs, Nd++–He and As+–He as discussed in Section 2.2. The van der Waals radii of neutral As and Nd are 0.188 nm and 0.295 nm [13] respectively. Assuming that ionic As+ and Nd++ have the same radii, 0.188 nm and

40

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

0.295 nm, respectively (most optimistic assumption), the cross section of the Nd++–He pair, calculated from Eq. (4), is still only 1.75 times larger than that of the As+–He pair. Therefore, the above requirement (Eq.(22)) for selective discrimination against Nd++ will not be met. Note that when Nd is ionized to be doubly charged, the electron cloud shrinks to a greater degree than when As+ is ionized to be singly charged. Hence the σ2/σ1 must be smaller than 1.75. When an As+ ion enters the ion guide with the initial kinetic energy of 24eV and experiences 10 collisions with He gas on average, a Nd++ ion enters the ion guide with 48eV and its average number of collisions is 18 (1.75 times the As+ collision number) at most. In this case the final kinetic energy of the As+ is 24eV × 0.90410 = 8.7eV and that for the 150 Nd++ is 48eV × 0.94918 = 18.7eV on average. When the potential barrier height is set to 19 eV to block the interfering Nd++ ions, the barrier height for As+ is 9.5 eV (the half of 19 eV), which is too high for the 8.7 eV As+ ions to surmount. It is readily understood from this example that KED does not work for doubly charged ion interferences because the kinetic energy of the doubly charged ion does not decrease sufficiently through collisions due to its heavier mass.

which the ion reacts is also examined, as it is one of the important factors to determine the reaction efficiency of the cell, which is energydependent. Finally, taking up an example of 40Ar+ interference on 40 Ca+, a loss of the analyte ion (40Ca+) signal due to KED and a reduction of the interfering ions (40Ar+) through the reaction with H2 is theoretically calculated under the conditions given in Table 2. 4.2. Reactant ion intensity in the cell The following bimolecular reaction is assumed to occur in the cell. Aþ þ B→C þ þ D

ð25Þ

where A+and B are the reactants — the interfering ion and the cell gas molecule, respectively. Using the reaction rate constant k, the reaction rate (reduction rate of A+) is then expressed as     d Aþ ¼ −k Aþ ½B dt

ð26Þ

4. KED in reaction cell ICP-MS 4.1. Non-thermal reaction cell In reaction cell ICP-MS, KED solely serves to reduce the interference caused by in-cell product ions, as many of these product ions have kinetic energies nearly as low as the thermal energies in the cell [3], and therefore can be selectively discriminated against by the potential barrier if the analyte ions exit the cell with sufficient kinetic energy to surmount the barrier. In other words, the analyte ions should not react with the cell gas and have to retain sufficient kinetic energy after unreactive collisions with the cell gas. (Obviously KED can't be applied to the mass-shift method [21], where the product ions that are deliberately produced from the reaction with the analyte ions are measured at a new m/z to circumvent the original interference). The original interfering ions, produced in the plasma, are reduced through the reaction with the cell gas. In order to achieve a desired degree of interference reduction, a high reaction gas density (flow rate) may be necessary, which will contradict the need to maintain the kinetic energy of the analyte ions. In this regard, hydrogen gas is preferred [5] because the gas molecule is light enough to minimize the ion kinetic energy loss caused by collision and have sufficient reactivity for some plasmabased interferences, e.g. Ar+ and Ar+ 2 [22]. The potential barrier height has been typically set to about 3 eV in H2 reaction cell ICP-MS, seemingly an empirically compromised value, as we have observed that lowering the barrier height leads to the increase of in-cell product ion signals, while increasing the barrier height causes the decrease of analyte ion signals. In a non-thermal reaction cell filled with reaction gas, each of the interfering ions that have entered the cell travels a certain distance with the initial kinetic energy and then collides with a gas molecule. At this collision each ion may or may not react with the gas. If it reacts, the interference of one ion is eliminated. If it does not, it will travel farther and collide with another gas molecule at a slightly reduced velocity, where, again, the reaction may or may not occur. Individual ions repeat collisions until they react with the gas or until they reach the cell exit. A fraction of the reactant ions will reach the cell exit (without reaction), which corresponds to the reduced interference signal (background signal) observed in the reaction cell ICP-MS. For better understanding of KED in reaction mode, the intensity of the interfering ions (reactant ions) at the cell exit is first derived for non-thermal reaction cells, and then their kinetic energy is calculated to examine whether they are able to surmount the barrier. As will be discussed in Section 4.3, the kinetic energy of the reactant ions differs from that of non-reactive analyte ions (the latter can be estimated in the same way as described in Section 2.4). The kinetic energy with

The density of the cell gas in the cell, [B], can be considered constant while the reactions are proceeding, since it is usually orders of magnitude higher than the ion density [A+] in the cell. In an ideal thermal reaction cell, k can also be treated as a constant value as it depends only on the cell gas temperature that determines the kinetic energy with which the reaction (reactive collision) occurs. The ion density [A+] is then obtained by integrating the above equation as  þ  þ A ¼ A 0 expð−k½Bt Þ

ð27Þ

where [A+]0 is the initial ion density before reaction, t is the reaction time. However, for a non-thermal reaction cell, where the ion kinetic energy in the cell is determined by the instrumental parameters, the energy-dependent rate constant k has to be used, which is defined as[23] ð28Þ

k ¼ vσ r

where v is the relative speed of the colliding pair (A+ and B), which is approximately the speed of the reactant ion A+ in the non-thermal cell as was discussed in Section 2.1, and σr is the reaction cross section, which is also energy-dependent (a function of v). In the non-thermal cell, the ions travel in the axial direction as they collide (and react) with the reaction gas molecules. Therefore

Table 2 Parameters and constants used for calculations.

Initial kinetic energy of 40Ca+ and 40 Ar+, Ei Potential barrier height H2 number density in the cell, n Ion guide length, L Collision cross section of Ar+ (and Ca+) for H2, σ Reaction cross section of Ar+ for H2, σr

Value

Comment

21.1 eV

Ion guide bias of −18 V

Quad mass filter bias of −15 V

3 eV 0.95 × 10

21

−3

m

0.1 m 2.83 × 10−19 m2

2 × 10−19 m2

Calculated from Eq. (5) for a typical operating condition (e.g. H2 flow rate of 6sccm) Reference [16]

Reference [27] and references therein, the value at ion kinetic energy of 20 eV

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

the reactant ion density decreases from the entrance to the exit of the cell. Taking dt as the time taken for the ion to travel a short distance dz (dz = vdt), and using Eq. (28), Eq. (26) is rewritten as     d Aþ ¼ −σ r Aþ ½B dz

41

This equation expresses the Lambert–Beer law. [A+]0 and [A+] are now considered to be the reactant ion intensities at the entrance and exit of the cell, respectively. The equation indicates that the ion intensity decays exponentially as the cell gas density n (flow rate) increases.

ð29Þ

As will be shown in Section 4.3, σr is approximately constant at any position in the cell for the gases having relatively high reactivity and low mass. In such cases the above equation can be integrated from the cell entrance (z = 0) to the cell exit (z = L).  þ  þ A ¼ A 0 expð−σ r nLÞ

ð30Þ

mi

4.3. Kinetic energy of reactant ions in the cell The kinetic energy of reactant ions in the cell pressurized with reaction gas is considered here based on hard sphere collision model. First, the kinetic energy of the reactant ions at the cell exit is derived to discuss whether the interfering (reactant) ions that have survived the reaction cell can be discriminated by the energy barrier after the cell.

Ei ri

rg mg 2

Collision Cross Section

Ei mi ri rg

Target for reaction

mg

Reaction Cross Section Fig. 7. Collision/reaction geometry between the ion (mi) and the gas molecule (mg).

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

Second, the kinetic energy that the reactant ion has when it reacts is estimated, which determines the reaction cross section. It is assumed that the hard sphere collision cross section σ and the reaction cross section σr are known for the ion–gas molecule pair. If every collision leads to reaction, σr is equal to σ, which means that the ion always reacts whenever it collides with a gas molecule. This is however not the case with usual ion-molecule reactions even if they are exothermic without activation energy, because the occurrence of reaction is affected by the kinetic energy with which the two reactants collide with each other. Therefore σr is smaller than the collision cross section σ, and is energy-dependent. Hence, the cross section for the unreactive collision is given by σ − σr, which corresponds to the gray area in Fig. 7. The average number of unreactive collisions in the cell is then give by N ¼ ðσ −σ r ÞnL

ð31Þ

For Ar+ in H2 reaction cell, N is calculated to be 7.9 using the physical constants listed in Table 2. Note that the probability of an Ar+ ion experiencing no collision (the fraction of Ar+ exiting the cell with no collision at all) is estimated from Eq. (15) as exp(−σnL) = e−27.17 = 1.59 × 10−12. The fraction of Ar+ exiting the cell without reaction is estimated from Eq. (30) as exp(− σrnL) = e−19 = 5.6 × 10−9, which is much higher than the probability of no collision at all. Therefore, most of the Ar+ ions exiting the cell (without reaction) have experienced some collisions in the cell, thereby lost a part of their initial kinetic energy. The kinetic energy after (unreactive) collision depends on the impact parameter b as discussed previously (the smaller the impact parameter, the smaller the post-collision kinetic energy). Fig. 7 implies that reaction occurs when the impact parameter is small, and unreactive collision occurs when it is large. Compared with a non-reactive pair (σ N 0, σr = 0), between which (unreactive) collisions occur at any impact parameter lower than bmax, unreactive collisions between the reactive pair (σ N σr N 0) may tend to occur at relatively larger impact parameters on average, that is, at impact parameters larger than the pffiffiffi mean impact parameter b ¼ bmax = 2 that was given to the collisions between non-reactive pairs as discussed in Sections 2.3 and 2.4. For the sake of simplicity of discussion, however, this mean impact parameter is used as a typical impact parameter for the unreactive collisions between the reactive pair to calculate the ion kinetic energy. Then using Eqs. (13) and (31), the ion kinetic energy after all the unreactive collisions experienced in the cell can be expressed as ( E f ¼ Ei

mi 2 þ mg 2
2 mi þ mg

)ðσ−σ r ÞnL

and that of the reaction not occurring (unreactive collision) is (σ − σr)/σ. Therefore, the probability of the ion reacting at the jth collision is given by P r ð jÞ ¼

σ−σ  j−1 σ r r ; j ¼ 1; 2; 3… σ σ

ð33Þ

Fig. 8 shows Pr(j) calculated for three different values of σr/σ. For σr/σ = 0.9 (highly reactive gas), the probabilities of reaction occurring at the first, second and third collision are 90%, 9% and 0.9%, respectively. Therefore, within the first few collisions most of the reactant ions react, which is true whether the cell is thermal or non-thermal. For less reactive gas, the probability of reaction occurring at later collision becomes higher, and the reaction cross section at the later collisions may be different from that at the early collisions due to the ion kinetic energy reduction caused by the preceding unreactive collisions. For the reaction between Ar + and H2 (σ r / σ ≈ 0.7), 97% of the Ar+ ions that have entered the cell react with H2 within the first three collisions. Although σr is dependent on ion kinetic energy, therefore, changes as the ion undergoes unreactive collisions, it can be approximated by the constant value at the initial kinetic energy, as will be discussed next. As the probability of reaction at each collision is given by Eq. (33), the average kinetic energy of the ion at the reactive collision is calculated as Er ave ¼

∞ X E j P r ð jÞ

ð34Þ

j¼1

where Ej is the ion kinetic energy at the jth collision, which is the kinetic energy after the ion experiences (j − 1) unreactive collisions. Using Eq. (13), it is approximately given by ( ) j−1 m 2 þ mg 2 E j ¼ Ei
i 2 mi þ mg

ð35Þ

Eq. (34) indicates that the average kinetic energy at which the ions react with the gas molecules, Er ave is determined by the initial ion kinetic energy, the masses of the reactants (ion and gas), the collision cross section and the reaction cross section. Since the reaction cross section σr is energy-dependent, Er ave and σr are mutually dependent. Therefore the two quantities should be determined self-consistently. For Ar+ in H2 reaction cell under the conditions shown in Table 2, the average kinetic energy of Ar+ ions at the reaction is estimated from Eq. (34) to be 20.3 eV, which is close to the initial kinetic energy of

ð32Þ

For 40Ar+ in H2 reaction cell under the conditions shown in Table 2, the final kinetic energy Ef is calculated to be 0.90937.9 Ei = 9.96eV, which is much higher than the typical height of the barrier set up after the cell. Compared with the analyte isobar Ca+, the finale energy of Ar+ is higher. Note that the average number of collisions with H2 that a non-reactive Ca+ ion undergoes (σnL) is higher than that of unreactive collisions that an Ar+ ion undergoes ((σ − σr)nL). The Ar+ ions having reached the cell exit, which have the kinetic energy of 9.96 eV, are able to surmount the potential barrier and eventually will strike the detector as the background signal. Hence, the reduction of Ar+ signal is solely due to the reactions with H2, not due to KED. The kinetic energy with which the interfering ions react with gas molecules can be estimated by calculating the probabilities of the ion reacting at the jth collision, where j = 1, 2, 3… For the ion that collides with the gas molecule, the probability of the reaction occurring is the ratio of the reaction cross section to the collision cross section, σr/σ,

1

Probability of reaction at the jth collision

42

0.9

r/

0.8

r/

0.7

r/

0.6 0.5 0.4 0.3 0.2 0.1 0 0

1

2

3

4

5

6

7

8

9

10

j Fig. 8. The probability of a reactant ion not reacting at any collision before the jth collision but then reacting at the jth collision. σr is assumed to be constant.

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

21.1 eV. In this calculation, the reaction cross section at ca. 20 eV was used and it is consistent with the calculated ion kinetic energy of 20.3 eV. Since most Ar+ ions react with H2 within the first few collisions and the kinetic energy loss by unreactive collision is small for light H2 gas, the kinetic energy with which Ar+ reacts is approximated by its initial kinetic energy, and hence the reaction cross section at that energy can be applied to the reactions at any position in the cell, and at any H2 density (H2 flow rate). This should be also the case with other reactant + + ions that have high reactivity toward H2, e.g. Ar+ 2 , ArH [24] and ArO [25]. +

+

4.4. Ar and Ca signals in H2 reaction cell ICP-MS As an example, theoretically reviewed in this section is 40Ar+ interference on 40Ca+, which was reported to be reduced by H2 gas to an extent of a single ppt level of BEC for calcium in non-matrix samples [26]. Typical operating conditions for Ca+ measurement in H2 mode are listed in Table 2, together with physical constants involved there. The loss of Ca+ due to KED is estimated in the same way as described in Section 3.4 by regarding H2 as collision gas of mg = 2[u]. With the initial 40Ca+ kinetic energy of Ei = 21.1eV, the number of collisions N that gives the Ca+ the final energy higher than the barrier height is obtained from Eq. (16). For a potential barrier of 3 eV in height, N is calculated to be 20 or lower for 40Ca+. Therefore, using Eq. (17), Ca+ signal intensity ICa is given by

ICa =ICa0 ¼

20 X ðσ nLÞN N¼0

N!

e−σnL

ð36Þ

where ICa0 is the Ca+ intensity of all energies after the cell, which corresponds to the Ca+ signal observed without H2 in the cell or without KED after the cell. At the H2 density n given in Table 2, the average number of collisions (σnL) that a Ca+ ion experiences with H2 in the cell is 27. At this average number, ICa/ICa0 is calculated to be ca. 0.1, indicating that 90% of the Ca+ are blocked by the barrier and 10% are detected. Ca+ signal intensity as a function of H2 number density n, calculated using Eq. (36), is shown in Fig. 9 together with Ar+ signal intensity, which will be derived next. To estimate the signal intensity of the reactant Ar+ ions, two types of reaction with H2 should be considered. One is H-atom transfer reaction

normalized signal intensity I/I0

1.E+01 1.E+00

Ca+

1.E-01 1.E-02 1.E-03 1.E-04 Ar+

1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 0

2E+20 4E+20 6E+20 8E+20 1E+21 1.2E+21 H2 number density [m-3]

Fig. 9. Normalized signals of the 40Ca ions that surmount the 3 eV potential barrier as a function of H2 gas number density and of the 40Ar ions after the cell. The DC bias potential of the ion guide in the cell is Vguide = −18 eV.

43

and the other charge transfer, both of which are exothermic, but the former is dominant in the energy range considered here [27]. Arþ þ H2 →ArHþ þ H

ð37Þ

Arþ þ H2 →Ar þ H2 þ

ð38Þ

Using the (total) reaction cross sections σr for these reactions, the Ar+ signal is expressed as (see Section 4.2), ½Arþ  ¼ ½Arþ 0 expð−σ r nLÞ

ð39Þ

where [Ar+]0 and [Ar+] are the Ar+ intensities at the entrance and exit of the cell, respectively; n is the H2 gas density, L is the cell length. Then, if σr is known, the Ar+ signal intensity can be estimated. For the above two reactions (37) and (38), the reaction cross sections have been thoroughly investigated as a function of Ar+ kinetic energy [27]. The average kinetic energy of Ar+ with which it reacts with H2 in the cell was estimated to be 20.9 eV in the previous section. At around this kinetic energy the reported reaction cross sections for Eqs. (37) and (38) are 1 to 2 × 10−19 m2 and 0.5 to 1 × 10−19 m2, respectively (The values vary from literature to literature) [27]. The sum of the two cross sections corresponds to σr in Eq. (39), which is approximately σr ≈ 2 × 10− 19 m2. Now that σr, n and L are all known, the degree of Ar+ reduction [Ar+]/[Ar+]0 is calculated from Eq. (39) to be 5.6 × 10− 9. Taking into account of the decrease of the Ca+ signal by one order of magnitude due to KED as discussed above, the net improvement of S/B ratio is 0.1/(5.6 × 10−9) = 1.8 × 107. Under normal plasma conditions without cell gas the modern quadrupole ICP-MS systems give 40Ar+ intensity of about [Ar+]0 = 1010 cps and Ca+ signal of about 100,000 cps/ppb. Then with H2, the 40Ar+ intensity is reduced to [Ar+]0 × 5.6 × 10−9 cps (ca. 60 cps), while the Ca+ is to 10,000 cps/ppb, resulting in BEC of 6 ppt. 5. Summary It has been more than a decade since the collision/reaction cell ICPMS became an essential technique in many analytical laboratories. In this period, “the KED mode” was established as a simple and easy approach to operate the cell-based ICP-MS for interference reduction. However an accurate, quantitative description of the KED approach has not been presented. Using the hard sphere collision model, the collision/reaction cells operated with KED under non-thermal conditions were depicted as accurately as possible to clarify the basic principles and limitations of this technique. They are summarized as follows. 1) Through multiple collisions with gas molecules in the collision cell, a significant difference of the average kinetic energy is produced between the ions of the same mass that have different collision cross sections. At the cell exit, the kinetic energy of the ion species having a larger cross section is lower than those having a smaller cross section, because the former experience more collisions than the latter on average. With a potential barrier set up after the cell, the former can be blocked while the latter is allowed to transmit to the detector. This is the basic principle for polyatomic ion interference reduction by KED, based on the premise that the polyatomic ions have a larger cross section than the isobaric atomic analyte ions. 2) Due to the statistical nature of collision events, multiple collisions produce a spread of kinetic energy even for the same ion species. Hence, the kinetic energy distributions of the atomic analyte ions and of the interfering polyatomic ions partly overlap each other. The intrinsic limitations of KED lie in this incomplete separation of the kinetic energies. 3) In order to achieve greater separation of the kinetic energies of the analyte and interfering ions, the initial kinetic energy has to be high enough to prevent atomic analyte ions from being thermalized

44

4)

5) 6)

7)

N. Yamada / Spectrochimica Acta Part B 110 (2015) 31–44

by the multiple collisions. For this reason, the DC bias voltage of the ion guide in the cell is often set to more negative (typically ca. −20 V) than the optimum for ion transmission. It was theoretically shown that lighter collision gas is more effective than heavier one for polyatomic ion reduction by KED. This is also due to the statistical nature of collision processes. KED against doubly charged interfering ions does not work due to their higher mass than the singly charged analyte ions. In non-thermal reaction cell ICP-MS, KED is used to suppress the signals derived from in-cell formed ions. The signals of (unreactive) analyte ions are decreased by KED due to their lowered kinetic energies through the multiple collisions with the reaction gas. For this reason, light gases, specifically H2, are favored. In H2 reaction cell ICP-MS, when the reaction cross section approximates the collision cross section, KED does not contribute to the reduction of plasma-based interfering ions, which are reduced solely through the reaction processes in the cell.

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