B American Society for Mass Spectrometry, 2014

J. Am. Soc. Mass Spectrom. (2014) DOI: 10.1007/s13361-014-0934-8

RESEARCH ARTICLE

Description of Gas-Phase Ion/Neutral Interactions in Differential Ion Mobility Spectrometry: CV Prediction Using Calibration Runs David Auerbach, Julia Aspenleiter, Dietrich A. Volmer Institute of Bioanalytical Chemistry, Saarland University, Saarbrücken, Germany

1-PrOH

CV

1-BuOH

Intensity

O

O

F

N

EtOH

Abstract. Differential ion mobility spectrometry (DMS) coupled to mass spectrometry is increasingly used in both quantitative analyses of biological samples and as a means of removing background interferences for enhanced selectivity and improved quality of mass spectra. However, DMS separation efficiency using descriptor CV prediction: dry inert gases often lacks the required selectivity to achieve baseline separation. exp. mean: Polar gas-phase modifiers such as alcohols are therefore frequently employed to -19.9 V improve selectivity via clustering/declustering processes. The choice of an difloxacin predicted: -19.5 V optimal modifier currently relies on trial and error experiments, making method development a tedious activity. It was the goal of this study to establish a means CV of CV prediction for compounds using a homologous series of alcohols as gasphase modifiers. This prediction was based on linear regression of compensation voltages of two calibration runs for the alcohols with the lowest and the highest molecular weights and readily available descriptors such as proton affinity and gas phase acidity of the modifier molecules. All experiments were performed on a commercial quadrupole linear ion trap mass spectrometer equipped with a DMS device between electrospray ionization source and entrance quadrupole lens. We evaluated our approach using a homologous series of 4-alkylbenzoic acids and a selection of 23 small molecules of high chemical diversity. Predicted CV values typically deviated from the experimentally determined values by less than 0.5 V. Several test compounds changed their ion mobility behavior for the investigated gas phase modifiers (e.g., from type B to type A) and thus could thus not be evaluated. Keywords: Differential ion mobility spectrometry, Gas phase modifier, Ion/neutral interactions, Compensation voltage, Prediction 2 calibration runs:

OH

N

N

F

Received: 31 March 2014/Revised: 12 May 2014/Accepted: 12 May 2014

Introduction

H

yphenated differential ion mobility spectrometry (DMS)-mass spectrometry has been of growing interest to scientists in recent years, in particular for separation of isobars and for removing background interferences to enhance selectivity. The principles of ion separation in a differential ion mobility spectrometer have been comprehensively described in the literature [1–11] and only a few essential elements, which are important for the work presented here, will be briefly discussed in the following text. After entering the DMS cell, ions are subjected to a high frequency rf field during their motion through the cell. The rf field is asymmetric so that the zero to peak amplitude of the high field half cycle is higher than during the low field

Correspondence to: Dietrich A. Volmer; e-mail: [email protected]

half cycle. The area under one complete period equals zero; that is, no displacement occurs from a fixed offset. When the mobility of an ion is the same under high and low field conditions, the net displacement will be [K(E1)·E1·t1] – [K(E2)·E2·t2] = 0 and α(E/N) ~ 0 [12]. In these equations, K is the field-dependent ion mobility coefficient, E the electric field strength, α the normalized difference between high and low field mobility (=differential mobility) and N the density of the transport gas. If the ion mobilities are different for an ion during these two half cycles, the ion will move towards one of the planar electrodes and discharge. This loss of ions can be prevented by applying a small DC voltage to one of the plates (=compensation voltage, CV) [4, 8]. The differences of ion mobility seen under high/low field conditions are often rationalized by using the so-called dynamic clustering/declustering model [13, 14]. In a typical planar DMS setup, the rf field oscillates with a frequency of 3 MHz

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

and the mean residence time of ions is 5.1 ms in this instrument [3]. On average, an ion is then subjected to 15,000 rf cycles during transmission through the cell. Kafle et al. estimated that an ion of m/z ~250 will undergo three collisions with a neutral gas phase modifier present at 1% during the high field portion and G17 collisions during the low field period [15]. The selectivity of DMS separations can be greatly enhanced by adding polar neutral modifiers to the gas stream at concentrations of usually in excess of 10,000 ppm [2]. For the particular DMS instrument used in this study, the sign convention in our experiments was defined so that increased clustering and larger relative changes of ion mobility result in more negative CV values [1]. A CV scale obtained by using different chemical modifiers provides a measure of the average degree of clustering for a given analyte [2] as long as no secondary interactions/mechanisms occur. For example, Levin et al. demonstrated that a significant contribution of dimer ion formation to ion equilibria during DMS can cause smaller ion cross-sections during the clustered state given that the dimer possesses a higher cross-sectional area as the corresponding monomer neutral complex [16]. The same authors revealed that the potential influence of steric hindrances on ion mobility of analyte/modifier pairs can lead to decreased effective crosssectional areas, thus reversing the generally expected trend. DMS can achieve separation of structurally very similar compounds that may not be resolved using conventional IMS. Some examples for these separation capabilities include the separation of regioisomers of O-linked glycopeptides [17], charge isomers [18], and isomeric peptides and amino acids [19–23]. Ion mobility behavior with and without clustering agents were reported in the literature for pesticides [24], aromatic compounds [25], halogenated compounds [26, 27], hydrocarbons [28], ketones [12, 29], and organophosphorus compounds [30]. An extensive survey of the impact of six chemical modifiers on separation efficiency and orthogonality of the separation of 140 substances was provided by Schneider et al. [14]. In their experiments, isopropanol/ ethylacetate and isopropanol/acetonitrile were identified as modifiers providing the highest degree of orthogonality. However, even structurally related modifiers can readily be employed to enhance or change selectivity for a given separation. For example, it was demonstrated that both resolving power and selectivity of a separation of eight pharmaceuticals of equal nominal mass could be effectively manipulated by using methanol, ethanol, and 2-propanol [31]. Furthermore, a growing number of publications illustrate the analytical benefits of differential ion mobility. It was, for example, shown that DMS analyses of liver extracts readily allowed detection and separation of a pharmaceutical drug along with its isomeric metabolites without an additional separation step [32]. Hall et al.

successfully demonstrated quantitative analysis of drug metabolites [33]. Importantly, both these applications relied on the proper choice of an appropriate modifier. More information on applications of differential ion mobility can be found in recent reviews [34–37]. Clearly, the success of ion mobility separation often relies on the choice of a proper gas-phase clustering reagent. Unfortunately, compensation voltage values yielding optimum transfer conditions for an analyte/modifier pair cannot currently be computed and, thus, need to be determined experimentally [32]. It was, therefore, the goal of this study to systematically investigate the effects of a homologous series of primary alcohols as gas-phase modifiers on DMS separations. We also explored whether two initial calibration runs using the modifiers of highest and lowest molecular mass could predict CV values for a given compound and other members of the homologous modifier series by employing linear regression of CV values with suitable and readily available descriptors. We initially started our work using a homologous series of analytes and subsequently extended the approach to a set of more diverse small molecules.

Experimental Reagents and Chemicals Hydroxmethylbenzoic acid (hm ethyl-BA, 99%), ethylbenzoic acid (ethyl-BA, 99%), propylbenzoic acid (propyl-BA, 99%), butylbenzoic acid (butyl-BA, 99%), pentylbenzoic acid (pentyl-BA, 99%), hexylbenzoic acid (hexyl-BA, 99%), heptylbenzoic acid (heptyl-BA, 99%), pyridoxal (PAL, 99%), pyridoxal-5′-phosphate (PAL-P, 98%), pyridoxine (PIN, 98%), pyridoxamine (PAM, 98%), pyridoxamine-5′-phosphate (PAM-P, 98%), 4-pyridoxic acid (PIC-A, 98%), reserpine (99%), betulin (98%), gly-his (98%), gly-tyr (98%), gly-phe (99%), gly-leu-tyr (98%), bacitracin (mixture of 9 isoforms), noscapine (98%), nortriptyline (98%), LC-MS-grade acetonitrile, LC-MS grade formic acid (FA), LC grade absolute ethanol (EtOH, 99.8%), LC grade 1-propanol (1-PrOH, 99.9%) and LC grade 1-butanol (1-BuOH, 99.7%) were obtained from Sigma-Aldrich (Steinheim, Germany). LC-MS grade methanol (MeOH, 99.9%) was obtained from VWR (Leuven, Belgium). Prometon, desethylatrazin, 2,4-DP, coumaphos, and diuron (≥99%) were acquired from Dr. Ehrenstorfer GmbH (Augsburg, Germany). Woodtide was prepared by an in-house facility (995%). Organic-free, deionized water was generated by an Elga PureLab Ultra (Griesheim, Germany) water purification system. Stock solutions of each individual compound were prepared at a concentration of 40 ppmv in a solution of acetonitrile/water, 1:1 (v/v) + 0.1% formic acid. Stock solutions of the vitamin B derivatives were prepared

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

in 5 mM ammonium acetate buffer solution (pH 5). Prior to measurement, samples were diluted to a concentration of 1 ppmv using the respective solvent. Final dilution to 25 ppbv was achieved by T-split infusion (10 μL/min sample and 390 μL/min LC flow).

Differential Ion Mobility Spectrometry-Mass Spectrometry DMS-MS Experiments were performed on an AB Sciex QTRAP 5500 system equipped with a Selexion differential ion mobility cell. Details on the instrumental setup can be found in references[1, 3]. ESI source and MS voltage settings were as follows: ESI source temperature, 500°C; curtain gas, 40 psi; gas 1, 40 psi; gas 2, 20 psi; collision cell exit potential (CXP), 15 V. The DMS cell was operated at a temperature of 225°C with the modifier supply set to 1.5%. Density values for the pure modifiers and equimolar mixtures at a temperature of 293 K were taken from references [38, 39]. Data was acquired in MRM mode with a dwell time of 100 ms, and compound-specific parameters as listed in Table 1. Each compound was infused separately. Samples were infused using a T-piece at a flow rate of 10 μL/min for the syringe pump and 390 μL/min for the LC system. The LC system employed was a Dionex Ultimate RS3000 HPG system (Dionex, Thermo Fisher, Germering, Germany). The mobile phase used in all experiments was a mixture of water and methanol, 50/50 (v/v), +0.1% formic acid. It was tested for five substances if a mixture of water and acetonitrile, 50/50 (v/v) + 0.1% formic acid as mobile phase influenced the detected compensation voltages. No significant influence was detected for the five compounds reserpine, nortriptyline, prometon, noscapin, and desethylatrazin acquired without modifier and with MeOH as gas phase modifier (two sample t-tests, α=0.05). CV values at the peak apex were determined using the AB Sciex Analyst software after Gaussian smoothing (filter width 200, number of minimal distance between points 10). Data Analysis and curve fitting were performed using Origin Pro 9.1 (OriginLab, Northampton, UK).

Results and Discussion In the following treatment of the experimental data, some basic assumptions were made to enable correlation between observed CV values and suitable descriptors:

 The relevant dominant forces for cluster formation during the low field were strong ionic hydrogen bonds, the strength of which can be adequately described using proton affinities (PA), gas phase acidities, and gas phase basicities [40].  No specific assumptions were made for the absolute size of the cluster. Instead, it was hypothesized that consecutive

clustering reactions indeed occur, but that these are of proportional value for every alcohol. In fact, enthalpies for successive gas-phase solvation is often found to decrease proportionally by a factor of 0.6 to 0.8 and the condensation thermochemistry of the bulk solvent can be reached in only a few solvation steps (4–6) [40]. If this proportionality is of the same extent for every modifier, it should suffice to simply use a descriptor such as proton affinity or gas phase basicity.  Entropy influences were either very minor or constant. Similar assumptions have successfully been made before for treatment of DMS data [13]. This can be justified by taking into account that the main contribution to entropy is the loss of three translational degrees of freedom upon combination of two particles [41].  For a given analyte and the range of primary alcohols used as modifiers, either complete declustering occurred during the high field portion of the waveform or the declustering lead to a defined state.  Any intrinsic or external temperature effects from bulk temperature or field heating were negligible. As outlined in the Introduction, ions undergo multiple collisions during their transport through the DMS cell. Ion neutral reactions of sufficient exothermicity (or specifically, ion neutral association reactions for the experiments considered here) are known to occur at a rate that is often near the collision frequency [42–44]. Even short-lived activated complexes are effectively stabilized at high collision rates associated with the high pressure in the DMS cell [43], thus making the assumption of a quasiequilibrium viable. Vouros and coworkers, for example, found that CV values for a deoxyguanosin DNS adduct did not change upon exceeding a certain modifier concentration [15]. The predominant forces present in the ion/neutral clusters observed in our experiments were strong ionic hydrogen bonds of the order of 5–35 kcal/mol [40]. Cluster hydrogen bond energies correlate with proton affinities, gas phase acidities, and gas phase basicities [40]. Assuming that every collision effectively leads to an excited complex ([M –H]–·ROH)* that is subsequently stabilized via a further collision to yield ([M – H]–·ROH) with 100% efficiency (“strong collision” assumption [43]), then ([M – H]–·ROH) is almost immediately formed during every rf cycle. To adequately describe this process, we used the square root of the inverse reduced mass, which . is a term in the low field mobility equation:  1 2   3q 2π 1þζ E KE ¼ ð1Þ 16 μkT ΩðT Þ N where μ is the ion neutral reduced mass, q the ion charge, T the effective temperature, Ω(T) the ion-neutral cross section, N the gas density and ζ a small correction term [45]. Assuming that the effective temperature does not depend on the gas phase modifier, and by also taking into account that ion neutral cross-sections linearly correlate

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

Table 1. Compound Structures and MS Acquisition Parameters

substance

structure

precursor product m/z m/z

DP CE polarity SV [V]

4-(hydroxymethyl) benzoic acid

151

100

60

18

-

4000

4-ethylbenzoic acid

149

100

60

17

-

4000

163 177 191 205 219

100 200 100 100 200

60 60 60 60 60

17 18 20 20 20

-

4000 4000 4000 4000 4000

pyridoxine

170

100

60

47

+

3500

pyridoxal

168

100

60

32

+

3500

pyridoxamine

169

100

60

18

+

3500

pyridoxamine5‘phosphate

247

100

60

30

-

2500

pyridoxal5‘phosphate

246

100

60

20

-

2500

nortriptyline

264

233

140 25

+

4000

difloxacin

400

299

120 35

+

4000

nadifloxacin

361

343

100 35

+

4000

levofloxacin

362

261

240 35

+

4000

noscapine

414

220

150 35

+

4000

prometon

226

142

240 35

+

4000

desethyl-atrazine

188

146

140 25

+

4000

gly-his

213

110

120 25

+

3500

gly-tyr

239

165

170 23

+

4000

gly-phe

223.0

166.2

180 20

+

4000

gly-leu-tyr

352.2

182.1

220 20

+

4000

2,4-DP

233.1

160.9

100 24

-

3500

4-propylbenzoic acid 4-butylbenzoic acid 4-pentylbenzoic acid 4-hexylbenzoic acid 4-heptylbenzoic acid

n=2 n=3 n=4 n=5 n=6

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

with molecular polarizability/molecular mass for a homologous series [46], the reduced mass term should adequately describe the CV shifts obtained when applying the series of alcohols from methanol to 1-butanol as gas phase modifier. The use of the square root of the inverse reduced mass as a descriptor is equivalent to the use of Langevin rate constants (Equation 2), since polarizabilities of primary alcohols increase linearly with molecular mass [47]:  1=2 πα kL ¼ q ð2Þ με0 where μ is the ion neutral reduced mass, q the ion charge, ε0 the permittivity of free space, and α the molecular polarizability of the neutral [48]. So far, we have only considered formation of 1:1 clusters, and further clustering of this species with alcohol molecules is assumed to proceed via hydrogen bonding of the additional alcohol molecule to the O-atom of the bound alcohol. This can thus be taken into account by using the proton affinities. We suggest that the degree of this additional clustering can be described by using ratios of proton affinities. These ratios were used as a measure of the effects of additional clustering on collision cross sections. The rationale for this approach was as follows: a certain degree of multiple solvation reactions for the analyte with methanol was initially assumed, the magnitude of which is correlated with the enthalpies of solvation, as long as quasiequilibrium conditions hold true. By changing the modifier, (e.g., from methanol to ethanol), the net increase of collision cross section is then defined by the ratio of the two proton affinities as long as all aforementioned assumptions are fulfilled. The same applies for 1-propanol and 1-butanol. For curve fitting, we thus used the sum of the square root of the inverse reduced mass and the proton affinity ratios. Our second approach for prediction does not make use of the assumption that μ–1/2 is a factor which needs to be considered for formation of mono-solvated ions. Instead, the entire clustering process is thought of as being driven entirely by the equilibrium (Gibbs free energy of cluster formation). Krylov et al. used thermodynamic properties for calculation of average cluster numbers to model SV/CV behavior by assuming constant enthalpy and entropy for consecutive clustering [13]. Kafle et al. reported on an upper limit of gas phase modifier concentrations, where no further changes of CV values were observed [15]. Similar work was presented in reference [49] and it was pointed out by several authors that Uc ~ ΔK. The free energy of cluster formation is proposed as the determining factor governing the ion mobility in several references [1, 2, 16, 26]. We thus additionally analyzed our data based on the assumptions as outlined before, but only used the gas phase acidities in these calculations. Results for both approaches will be compared and contrasted in the following sections. The first set of analytes comprised the homologous series of 4-alkylbenzoic acids; 4-hydroxymethylbenzoic acid was

also included to determine whether the additional hydroxyl group was tolerated by our simple model. Figure 1 shows plots for the series of alkylbenzoic acids with pure modifiers and equimolar mixtures of modifiers. For mixtures, the mean values for PA and μ were used: PA was determined from an exponential fit of PA and molecular weight. Plots in Figure 1 are accompanied by typical examples of residual plots. From the residual plots, it is obvious that including data points from the mixtures systematically distorted the fitted line. CV values for solvent mixtures were closer to those for the larger alcohol in all cases (Figure 1). This can be explained in our model by a population of solvated ions that is shifted towards the larger alcohol. A larger fraction of the energetically favored cluster is formed and shifts the average collision cross section towards the larger alcohol. Table 2 summarizes some statistical figures of merit for the graphs shown in Figure 1. Excellent R2 values were achieved for pure modifiers and RMSE values were smaller than 1 V in all cases (Table 2). As can be seen, both approaches to data analysis delivered comparable results. In the next step, all regression calculations were repeated using only the data points for the smallest and largest homologue, methanol and 1-butanol. The resulting linear equations were then used to predict CV values for ethanol, 1propanol, and the two solvent mixtures. The results of these predictions are summarized in Table 3. Excellent accuracies of approximately 99% were achieved in all cases, except for 4-hydroxymethylbenzoic acid. The higher deviation found for this compound is likely due to problems with the assumption of formation of a 1:1 complex with 100% efficiency because another donor/acceptor functionality is present in 4-hydroxymethylbenzoic acid. Overall, however, the observed deviations readily allow very accurate CV prediction for pure alcohols with both analysis approaches. The linear regression using the second approach delivered largely comparable results with slightly larger deviations. Figure 2 illustrates prediction accuracy and observed experimental behavior. The four examples shown exhibited the highest observed deviations (0.4 and 0.5 V) between experiment and theory. The prediction accuracies achieved with our approach were comparable to those of empirical predictions of reduced ion mobilities in traditional IMS [50, 51] and are also comparable to calculated CV values from experimentally determined α values [52].

Influence of Field Strength on Correlations In our experiments, we generally observed a dependency of differential clustering on field strength that diminished with growing alkyl chain length (Figure 3). The observed trend can, in principle, be interpreted in two ways. It is either a question of reduced average cluster size for the larger alcohol modifiers or, vice versa, the reduced cluster formation can be specifically attributed to methanol and ethanol as modifier. The fact that no dependency on field strength was observed for the higher homologues from 4-

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

M eO H

-20 -24 Et O

H

-28

-40

1Pr O

H 1Bu O

-36

H

-32

residual di=(yi - ŷi) 4-hexylbenzoic acid 0.2

-48 -52 -56

4-alkylbenzoic acids ethyl propyl butyl pentyl hexyl heptyl

-60 -64 -68 -72 -76 -80 1.10

1.12

1.14

1.16

1.18

residuals di

CVSV4000 [V]

-44 0.0

-0.2

-0.4

1.10

μ

-1/2

1.15

1.20

+ PAmethanol•PA-1modifier

1.20

μ-1/2 + PAmethanol•PA-1modifier /E tO

H

M eO

H

-20 M eO

H

-24 uO H

/1

O Pr 1-

O H Pr

H O

0.2

residuals di

-44

CVSV4000 [V]

residual di=(yi - ŷi) 4-hexylbenzoic acid

0.4

1-

Bu

0.6

1-

-40

-B

-32 -36

Et

H

O

H

-28

-48 -52

0.0

-0.2

-56

4-alkylbenzoic acids ethyl propyl butyl pentyl hexyl heptyl

-60 -64 -68 -72 -76 -80 1.10

1.12

1.14

μ-1/2 + PA

1.16

1.18

-0.4 -0.6 -0.8

1.10

μ

-1/2

1.15

1.20

+ PAmethanol•PA-1modifier

1.20

•PA-1modifier

methanol

M eO

H

-20 -24 Et O

H

-28

residual di=(yi - ŷi) 4-hexylbenzoic acid

H O Bu

0.6

1-

-36

1Pr O H

-32 -40

0.4

-48 -52 -56

4-alkylbenzoic acids: ethyl propyl butyl pentyl hexyl heptyl

-60 -64 -68 -72 -76 -80 2.68

2.69

2.70

2.71

residuals di

CVSV4000 [V]

-44

0.2 0.0

-0.2 -0.4

μ

-1/2

2.70

+ PAmethanol•PA-1modifier

2.72

exp{ΔG0acid(modifier)/ΔG0acid(MeOH)}

Figure 1. Plots of CV values acquired for 4-alkylbenzoic acids versus selected descriptors. The first and second rows show data plotted versus sum of the square root of the inverse reduced mass and proton affinities relative to methanol and respective best fit straight lines. Equimolar modifier mixtures are excluded in the first row and included in the second. Best fit straight lines in the third row were obtained using gas phase acidities relative to methanol for curve fitting. The right column shows residual plots for 4-hexylbenzoic acid corresponding to the data shown in the left diagram

heptyl to 4-pentylbenzoic acid favors the assumption of a diminished average cluster size for methanol and ethanol

and, thus, the lower homologues were responsible for the apparently higher (less negative) CV values, since 4-

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

Table 2. Fit Statistics for 4-Alkylbenzoic Acids Using Two Approaches for Data Analysis Substance

Without mixtures

CV versus μ–1/2 + PAmethanol/PAmodifier 4-Heptylbenzoic acid 4-Hexylbenzoic acid 4-Pentylbenzoic acid 4-Butylbenzoic acid 4-Propylbenzoic acid 4-Ethylbenzoic acid 4-Hydroxymethylbenzoic acid CV versus exp[ΔG0acid/ΔG0acid(MeOH)] 4-Heptylbenzoic acid 4-Hexylbenzoic acid 4-Pentylbenzoic acid 4-Butylbenzoic acid 4-Propylbenzoic acid 4-Ethylbenzoic acid 4-Hydroxymethylbenzoic acid

Including mixtures RMSE

norm of residuals

Adjusted R2

0.999 0.999 0.999 1.000 0.999 0.998 0.997

0.39 0.36 0.45 0.40 0.45 0.61 0.97

1.55 1.44 1.78 1.60 1.78 2.46 3.89

0.996 0.997 0.997 0.998 0.998 0.998 0.996

0.998 0.999 0.998 0.999 0.999 0.999 0.998

0.53 0.58 0.66 0.77 0.79 0.84 0.85

2.11 2.30 2.63 3.08 3.14 3.37 3.38

0.993 0.993 0.993 0.993 0.995 0.996 0.997

RMSE

norm of residuals

Adjusted R

0.23 0.20 0.22 0.22 0.27 0.62 0.86

0.73 0.62 0.68 0.70 0.86 1.96 2.72

0.31 0.25 0.40 0.36 0.36 0.35 0.69

0.97 0.80 1.27 1.14 1.15 1.10 2.17

alkylbenzoic acids of lower molecular weight have a considerable smaller number of internal degrees of freedom. A larger number of internal degrees of freedom means a higher probability of cluster formation, since energy transfer from vibrational modes contribute to the activation energy (cf. Lindemann versus Lindemann-Hinshelwood theory of unimolecular reaction rate). The behavior of the experimental

2

CV values for the 4-alkylbenzoic acids and a constant gas phase modifier further supported our proposal that internal degrees of freedom are responsible for the observed deviations. As discussed in the next section, plots of CV versus μ–1/2 for a given gas phase modifier and the series of 4-alkylbenzoic acids resulted in linear relationships; however, deviations were observed for ethanol and, more pronounced, for methanol at a

Table 3. CV Prediction Results for the 4-Alkylbenzoic Acids Based on Linear Regression of CV Values Acquired for Methanol and 1-Butanol (Triplicate Measurements) and Suitable Descriptors Analyte

Heptyl-BA

Hexyl-BA

Pentyl-BA

Butyl-BA

Propyl-BA

Ethyl-BA

Hmethyl-BA

Modifier

MeOH/EtOH EtOH 1–PrOH 1-PrOH/1-BuOH MeOH/EtOH EtOH 1-PrOH 1-PrOH/1-BuOH MeOH/EtOH EtOH 1-PrOH 1-PrOH/1-BuOH MeOH/EtOH EtOH 1-PrOH 1-PrOH/1-BuOH MeOH/EtOH EtOH 1-PrOH 1-PrOH/1-BuOH MeOH/EtOH EtOH 1-PrOH 1-PrOH/1-BuOH MeOH/EtOH EtOH 1-PrOH 1-PrOH/1-BuOH

CV versus μ–1/2 + PAmethanol/PAmodifier

CV versus exp[ΔG0acid/ΔG0acid(MeOH)]

CVmeasured [V]

CVpredicted [V]

Abs. dev. [V]

acc. [%]

Abs. dev. [V]

Acc. [%]

–29.36 –32.19 –37.16 –39.32 –33.98 –37.24 –42.84 –44.70 –38.90 –42.93 –49.00 –51.60 –44.70 –49.35 –56.83 –58.97 –51.05 –56.55 –65.33 –68.04 –57.66 –64.26 –74.81 –78.04 –57.65 –65.59 –78.76 –83.62

–28.95 –32.60 –37.46 –38.79 –33.21 –37.24 –42.60 –44.07 –38.16 –42.78 –48.93 –50.61 –43.68 –49.14 –56.40 –58.37 –50.14 –56.44 –64.81 –67.08 –57.16 –64.69 –74.68 –77.37 –58.47 –67.46 –79.37 –82.59

0.42 0.40 0.30 0.53 0.76 0.00 0.24 0.63 0.74 0.15 0.07 1.00 1.02 0.21 0.43 0.60 0.91 0.10 0.52 0.97 0.50 0.43 0.13 0.67 0.82 1.87 0.61 1.03

98.6 98.7 99.2 98.7 97.8 100.0 99.4 98.6 98.1 99.7 99.9 98.1 97.7 99.6 99.2 99.0 98.2 99.8 99.2 98.6 99.1 99.3 99.8 99.1 98.6 97.1 99.2 98.8

1.12 0.12 0.68 0.03 1.54 0.32 0.17 0.09 1.65 0.53 0.39 0.37 2.11 0.68 0.10 0.13 2.18 0.67 0.07 0.14 2.38 0.73 0.06 0.34 1.01 1.04 1.44 0.14

96.2 99.6 98.2 99.9 95.5 99.1 99.6 99.8 95.8 98.8 99.2 99.3 95.3 98.6 99.8 99.8 95.7 98.8 99.9 99.8 95.9 98.9 99.9 99.6 98.3 98.4 98.2 99.8

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

Figure 2. Illustration of CV prediction for 4-heptylbenzoic acid and propylbenzoic acid using data shown in Table 3 and exemplary DMS ionograms. The first column shows values predicted using the sum of the square root of the inverse reduced mass and proton affinities relative to that of methanol for correlation. Data in the second column are obtained using gas-phase acidities relative to methanol for curve fitting. (Note: these four examples illustrate the largest observed deviation of experiment and theory in our study. All other compounds gave better agreement with the experimental data)

separation voltage of 3500 V. These deviations are difficult to observe in Figure 4 because of the scaling of the figure, but it

-20 -24

CVSV3500 [V]

-28 -32

can be seen that the regression lines are almost parallel and consequently slopes are fairly similar, with the exception of methanol, where a sudden drop occurs (1-butanol: 5137, 1propanol: 5390, ethanol: 5020, methanol: 3983 V). The drop of slope supports our previous assumption of a smaller average cluster state for the lower molecular weight benzoic acids. Higher field strength resolves these issues and restores the proportionality of cluster formation and break-up for the modifier series.

-36 -40

Ethyl Propyl Butyl Pentyl Hexyl Heptyl

-44 -48 -52 -56 2.68

2.69

2.70

2.71

2.72

exp{Δ G0acid(modifier)/Δ G0acid(MeOH)}

Figure 3. Plots of CV values acquired for 4-alkylbenzoic acids versus selected descriptors at a field strength of 3500 V

Linearization of Observed CV Values for Homologous Series Homologous series of compounds were extensively investigated using traditional IMS [50, 51, 53] and separation of these compounds is of particular importance for petroleum analysis [54]. Ahmed et al. demonstrated the use of ion mobility to reveal structural relationships of crude oil constituents [53]; molecules sharing a similar core structure were found to be linearly aligned in the adjusted tdB /m/z domain. Similar results were found by Hariharan et al. in

-20 -25 -30 -35 -40 -45 -50 -55 -60 -65 -70 -75 -80 0.13

residual di=(yi - ŷi) 1-PrOH

0,6 0,4

MeOH MeOH / EtOH EtOH 1-PrOH 1-PrOH / 1-BuOH 1-BuOH

residuals di

CVSV4000 [V]

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

0,2 0,0

-0,2 -0,4

0.14

0.15

0.16

0.17

0.18

0.19

0.20

μ-1/2

0,146

0,148

μ-1/2

0,150

0,152

Figure 4. Correlation of compensation voltage and square root of inverse reduced mass for the homologous series of 4alkylbenzoic acids (heptyl to ethyl) using four pure modifiers and two equimolar mixtures. Data acquired with the respective gas phase modifier is indicated by the color code included in the picture. The right panel shows an example of a residual plot for the 1-PrOH dataset

two studies describing the linear relations for ion mobility data of primary alcohols, secondary alcohols, ketones and aldehydes [50, 51]. Krylov et al. presented the first DMS data acquired for a homologous series of ketones (without the use of gas phase modifiers) and found that the α values of homologues resembled a common curved function when plotted against the molecular mass, although the authors stated that their procedure lacked the experimental and theoretical background[12]. We examined trends of experimental compensation voltages for the homologous series of 4-alkylbenzoic acids using a single gas-phase modifier in each experiment to find a suitable descriptor that correlated in a linear fashion (Table 4). Since the gas-phase modifier was the same for every investigated benzoic acid, it was assumed that no significant change in gas phase acidity was introduced by the growing alkyl chain in the 4-position of the molecules. The chargedirected clustering should thus be approximately constant for the entire series and the only influence on ion shape can be described by the square root of the inverse reduced mass (Equation 1). Figure 4 shows the corresponding plots of CV values observed for the 4-alkylbenzoic acids for each modifier. Linear correlations were seen (cf. Figure 4, right panel) for all modifiers and adjusted R2 values were larger than 0.997. For 4alkylbenzoic acids, the extent of clustering is determined by the gas phase acidity of carboxyl group. The presence of the alkyl chain in the 4-position was expected to have little influence on binding enthalpies and thus differences seen were rationalized as diminished clustering due to a smaller number of internal degrees of freedom. Importantly, this approach combined with dedicated mass spectrometric acquisition modes could potentially be applied to plots of compensation voltage versus reduced mass of a candidate series of homologues to investigate structural relationships of fractions of complex samples. Radiation exposure biomarkers, for example, were shown to be homologous aliphatic dicarboxylic acids and DMS was readily applied for analysis [55].

Behavior of Multifunctional Small Molecules In addition to the systematic investigation of the homologous series of analytes described in the previous sections, we also investigated several other analytes for their suitability for the described prediction models. Stone et al. reported on low field ion mobilities of hydrated molecules and found that molecules protonated at an amino group are predominantly solvated by a single molecule of water. This was reasoned as a result of the higher proton affinities of amine compounds, since larger differences of proton affinities are equivalent to lower solvation enthalpies [56, 57]. We identified several compounds that were compatible with this behavior; these compounds were nitrogen protonated species, and their CV modifier dependency was found to be solely dependent on μ–1/2. As mentioned before, this is equivalent to a dependency of CV on Langevin rate constants. Compounds for which this dependency was observed were nortriptyline, desethylatrazine, prometon, gly-phe, and gly-tyr. Precursor ion mass spectra of desethylatrazine and prometon acquired at CV values corresponding to the apex of the respective DMS ionograms revealed the presence of clustered fragment ions (m/z 184+ M(alcohol) for prometon and m/z 146+M(alcohol) for desethylatrazine), indicating dissociation of both compounds during their transit through the DMS cell. No dependency of the observed behavior on field strength could be observed Table 4. Linear Fit Statistics for Correlation of Observed CV Values and μ–1/2 for the Homologous Series of 4-Alkylbenzoic Acids and the Respective Gas Phase Modifiers Modifier

RMSE

Norm of residuals

Adjusted R2

1-BuOH 1-PrOH/1BuOH 1-PrOH EtOH EtOH/MeOH MeOH

0.27 0.21 0.30 0.35 0.40 0.41

1.07 0.86 1.21 1.41 1.62 1.62

1.000 1.000 1.000 0.999 0.998 0.997

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

Table 5. CV Prediction Results for the Selection of Small Molecules, Based on Linear Regression of CV Values Acquired for Methanol and 1-Butanol (Triplicate Measurements) Analyte CV versus μ–1/2 gly-phe gly-tyr Prometon Desethylatrazine

Modifier

CVmeasured [V]

CVpredicted [V]

Abs. dev. [V]

Acc. [%]

EtOH 1-PrOH EtOH 1-PrOH EtOH 1-PrOH EtOH 1-PrOH

–34.47 –37.69 –30.94 –34.92 –15.56 –23.81 –28.27 –33.87

–33.65 –37.65 –30.97 –35.38 –16.09 –24.19 –28.45 –33.72

0.82 0.04 0.03 0.46 0.53 0.38 0.18 0.15

97.6 99.9 99.9 98.7 96.6 98.4 99.4 99.6

–15.01 –19.92 –17.77 –23.45 –16.81 –21.67 –4.06 –6.12 –24.09 –32.70 –35.49 –43.81 –31.28 –36.61 –33.13 –41.43 –40.69 –47.50 –40.45 –49.16 –14.73 –16.87 –15.46 –18.16

–14.72 –19.49 –17.75 –22.98 –16.17 –21.14 –4.26 –6.29 –24.39 –32.28 –35.56 –43.43 –31.45 –36.02 –32.92 –41.52 –40.43 –47.66 –40.14 –48.93 –14.78 –16.84 –15.69 –18.05

0.29 0.43 0.02 0.47 0.64 0.53 0.20 0.17 0.30 0.42 0.07 0.38 0.17 0.59 0.21 0.09 0.26 0.16 0.31 0.23 0.05 0.03 0.23 0.11

98.1 97.8 99.9 98.0 96.2 97.5 95.2 97.2 98.8 98.7 99.8 99.1 99.5 98.4 99.4 99.8 99.3 99.7 99.2 99.5 99.7 99.8 98.5 99.4

CV versus μ–1/2 +PAmethanol/PAmodifier Difloxacin EtOH 1-PrOH Levofloxacin EtOH 1-PrOH Nadifloxacin EtOH 1-PrOH Noscapin EtOH 1-PrOH gly-leu-tyr EtOH 1-PrOH gly-his EtOH 1-PrOH 2,4-DP EtOH 1-PrOH PAM EtOH 1-PrOH PAL EtOH 1-PrOH PIN EtOH 1-PrOH PAM-P EtOH 1-PrOH PAL-P EtOH 1-PrOH

for the two dipeptides gly-phe and gly-tyr; a linear correlation with μ–1/2 was observed in all cases. It was shown both experimentally and computationally that dipeptides of gly are present in two different internally solvated structures at a ratio of approximately 3:1 [58]. Such internal hydrogen bonds can be stable enough to survive temperatures up to 1000 K, where covalent bonds begin to break up [40]. These stable hydrogen bonds are probably the cause for the observed correlation. For the compound 2,4-DP, a migration behavior similar to that of alkylbenzoic acids was expected, since the molecule differs mainly by the additional ether moiety adjacent to the carboxylic acid group. As expected, the linear regression delivered results similar to those of the alkylbenzoic acids for both approaches. Results for all studied compounds are summarized in Table 5. Deviations of predicted values were mostly better than 0.5 V.

Nonpolar Compounds and Other Difficult Substances We also included several compounds in our investigation that are favorably ionized by APCI. It is well known that

ion/neutral interactions in DMS can lead to charge exchange and, in fact, this was suggested as a possible means of background reduction by using a modifier with a proton affinity lower than the analyte of interest, but higher than the background [1, 2]. We found that the analytical signal for alkyl benzyl ketones completely vanished after introducing methanol as a gas phase modifier while water was still tolerated with a sensitivity loss of ca. 50%. Comparison of proton affinities revealed, for example, that octanophenone with a proton affinity of approximately 840 kJ/mol [59] is a stronger base than both water (PA = 691 kJ/mol) and methanol (PA=754 kJ/mol). The same phenomenon was observed for the compounds betulin, coumaphos, and diuron after ionization by APCI. This suggests that care should be taken to use a modifier with sufficiently low gas-phase basicity since charge transfer occurs even if the difference in gas phase basicity is as high as 86 kJ/mol. Owing to these experimental limitations, the aforementioned substances were excluded from further experiments. Blagojevic et al. have recently shown, that modifier-induced proton transfer can be suppressed with suitable modifier additives [60]. Other compounds that were not amenable to our prediction approach were the alkaloid reserpine, the poly-

D. Auerbach et al.: Gas-Phase Ion/Neutral Interactions in DMS

peptides bacitracin and woodtide, and pyridoxic acid, a degradation product of vitamin B6. For all these compounds, a change in ion mobility behavior throughout the modifier series from type C to type B or from type B to type A was observed (details about the classification of ion mobility behavior can be found in the literature (e.g., reference [1]).

4. 5. 6.

Conclusions A straightforward approach to interpret and predict CV values for a homologous series of gas phase modifiers was presented. Parameters that were employed for correlations were gas-phase acidity/proton affinity and the square root of the inverse reduced mass of the ion/modifier pairs. The correlation was either expressed as the sum of the square root of the inverse reduced mass and proton affinities relative to the smallest homologue, or simply by using relative gas phase acidities. To the best of our knowledge, this is the first demonstration of CV prediction using different gas-phase modifiers by means of readily accessible descriptors. The approach was exemplified for a set of homologues alkylbenzoic acids and subsequently extended to a broader range of small multifunctional molecules. The compounds studied were vitamin B vitamers, several 4quinolones, small peptides, pesticides, and natural compounds. Excellent prediction capability with absolute deviations usually below 0.5 V and accuracies between 97% and 99% were achieved. Several of the test compounds changed their ion mobility behavior for the four gas phase modifiers, for example from type B to type A, and could thus not be evaluated. Some protonated nitrogen-containing compounds were characterized by a strict dependency of CV on the square root of the inverse reduced mass, which is equivalent to a linear correlation with Langevin rate constants. It is clear that this approach is not universally applicable to all substance classes; nevertheless it applies to a wide variety of small molecules as demonstrated here. Other structurally unrelated modifiers could not be included in our approach since differences in mobility behavior are sometimes found to be unrelated to differences in gas-phase acidity, and dipole moments may be the determining factor in these cases [15]. In our experiments, we observed that CV values determined using H2O as modifier did not follow the linear trends observed for alcohols. We are currently performing quantum mechanical calculations in conjunction with molecular mechanics simulations to further rationalize our findings.

7.

8.

9.

10. 11.

12.

13. 14. 15.

16.

17.

18. 19.

20.

21. 22.

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