secondary electrospray ionization of complex vapor mixtures. theoretical and experimental approach

B American Society for Mass Spectrometry, 2012DOI: 10.1007/s13361-012-0369-z

J. Am. Soc. Mass Spectrom. (2012) 23:1085Y1096

RESEARCH ARTICLE

Secondary Electrospray Ionization of ComplexVapor Mixtures. Theoretical and ExperimentalApproach

Guillermo Vidal-de-Miguel,1,2 Ana Herrero1

1SEADM S.L., Valladolid, Spain2Energy and Fluid Mechanics Engineering Department, Valladolid University, Valladolid, Spain

AbstractIn secondary electrospray ionization (SESI) systems, gaseous analytes exposed to anelectrospray plume become ionized after charge is transferred from the charging electrosprayedparticles (the charging agent) to the vapor species. Currently available SESI models are valid forsimplified systems having only one type of electrosprayed species, which ionizes only one singlevapor species, and for the limit of low vapor concentration. More realistic models requireconsidering other effects. Here we develop a theoretical model that accounts for the effects ofhigh vapor concentration, saturation effects, interferences between different vapor species, andelectrosprays producing different types of species from the liquid phase. In spite of the relativelyhigh complexity of the problem, we find simple relations between the different ionic speciesconcentrations that hold independently of the particular ion source configuration. Our modelsuggests that an ideal SESI system should use highly concentrated charging agents composedpreferably of only one dominating species with low mobility. Experimental measurements with aMeOH-H2O-NH3 electrospray and a mixture of fatty acids and lactic acid served to test thetheory, which gives good qualitative results. These results also suggest that the SESI ionizationmechanism is primarily based on ions rather than on charged droplets.

Key words: Electrospray, Vapor ionization, Vapor analysis, SESI

Introduction

The ionization of vapors by means of electrosprays orcoronas is playing an increasingly important role in

vapor analysis applications such as explosives detection orbreath analysis.

Secondary electrospray ionization (SESI), first introducedby Fenn et al. [1–3] and later worked on by Wu et al. [4],takes place when an electrospray cloud (the charging agent)comes into contact with a gas carrying vapors (the samplevapors), resulting in the formation of vapor ions (sampleions) at atmospheric pressure. Unlike corona discharges orradioactive ionizers, SESI is a soft ionization process.Furthermore, the charging agent’s affinity can be selected

so as to ionize only vapors below certain ionization affinity.This limits the types of molecules that can be ionized (onlypolar molecules), but has the advantage of reducingchemical noise produced by the carrying gas or otherundesired vapors. Recent experiments [5, 6] show sensitiv-ities below the ppt level, and ionization probabilities pi ofthe order of 10–4, as defined in equation (1):

pi ¼ ns Ns;= ð1Þwhere ns is the concentration of sample ions and Ns is theconcentration of sample neutral vapors.

Whether vapor charging takes place directly via contactwith the droplets, or indirectly by charge transfer from ionsreleased from the droplets, remains unclear [7]. Recentstudies [8] using a secondary electrospray ionization,differential mobility analyzing and mass spectrometry(SESI-DMA-MS) analyzer with a charging electrosprayReceived: 24 September 2011Revised: 30 January 2012Accepted: 25 February 2012Published online: 17 April 2012

Correspondence to: Guillermo Vidal-de-Miguel; e-mail: [email protected]

of formic acid, and vapors containing different types ofamides, suggest that the ions option is more likely to behappening. In this case, the charge transmission reactiontaking place would be: formiate–+amide → amide–+formic. The exact charge transfer mechanism in a moregeneral case still depends on many factors. However, forsmall ES droplets or at high temperature, when the dropletsare quickly evaporated, it is reasonable to hypothesize thatvapor charging will be attributable primarily to chargingions rather than droplets.

The ionization probability measured by Mesonero et al.[6], though achieving limits of detection in the range of partsper trillion, is as low as pi=10–4. As explained by de laMora [7], the major factor limiting the ionization probabilitywhen the sample is ionized by means of a concentratedunipolar charge emitter such as electrospray is the spacecharge effect, which dilutes the ions at the same rate assample ions are produced. De la Mora noticed that the strongionic velocities produced by the space charge needed to beaccounted for [7]. According to de la Mora’s reasoning,sample ions are produced at a rate proportional to theconcentration of charging ions (nc) but, because spacecharge is also produced primarily by the charging ions,sample ions are diluted at a rate also proportional to theconcentration of charging ions. In stationary conditions,these two effects reach an equilibrium in which the balancebetween the production of new sample ions and the dilutionattributable to space charge leads to a simple expression forthe ionization probability:

pi ¼kcs"0Zs�e ð2Þ

[7]where e is the charge of the ion, ε0 is the permittivity ofthe vacuum, Zs is the mobility of the sample ion, and kcs isthe reaction rate coefficient for the charge transfer reactionfrom the charging ions to the sample molecule. It isremarkable how such a simple expression might describe aphenomenon apparently so complicated. Further compari-sons of the measured values of pi with those predicted byequation 2 show that this equation agrees, at least in theorder of magnitude, with experimental data [6, 7].

The low theoretically predicted value of pi indicates that theionization probability achievable in practice is highly limited.On the other hand, the fact that the amount of sample ions isproportional to the amount of available molecules can be usefulto estimate quantitatively the concentration of sample vapors.Unfortunately, experiments using complex mixtures of vaporsshow that there is a dependence of the sample ions produced onthe concentration of other vapors. For instance, following theexperiments by Martínez-Lozano [9, 10], we tried to improvebackground levels and enhance the sensitivity of an online skinodor analyzer by collecting the skin vapors in an enclosedchamber through which clean nitrogen was first put in contactwith the skin and was then directed to the SESI ionizer. Whenwe brought the skin closer to the apparatus, instead ofimproving the sensitivity, the signals of many species

originally present in the background dropped, whereas lacticacid produced a huge signal. We concluded that lactic acid,which was more concentrated in our closed set-up, could beinterfering with the ionization of other compounds.

While de la Mora’s model [7] is valid in the greatlydiluted limit, the purpose of the present study is to develop atheory with which to estimate the ionization probability inmore complex samples. Here, we consider finite vaporconcentration and associated suppression and saturationeffects. In multicomponent vapors, the more concentratedspecies tend to consume the available charging agents aswell as minority ionized vapors having lower ion affinity.These effects lower the probability of ionization, precludequantification of original vapor concentration, and couldeven blind the analyzers which, as a result, cannot detect theless concentrated species, which is often of more interest foranalysis. These effects are studied here, both theoreticallyand experimentally. In particular, we deal with the situationswhere a major species interferes with and reduces theionization probability of the minor sample species, andwhere the ionization source is working near saturation.Despite the complexity of the subject, we find that in mostsituations of interest, the concentration of the differentionized vapors can be expressed as a function of theconcentration of charging ions independently of the partic-ular ionizer configuration. As an extension of the theory, weare also analyzing the effect of electrospray plumes emittingcomplex mixtures of charging ions and other types ofuseless particles. Our model suggests that an ideal SESIshould use highly concentrated charging agents composedpreferably of only one dominating species having lowmobility. The results also suggest that in MeOH-H2O-NH3

electrosprays, ions rather than charged droplets are primarilyresponsible for the ionization of lactic acid vapors. Togetherwith this theoretical approach, experimental measurementsare also carried out to quantify the effect of lactic acid in agroup of fatty acids already found in the skin vapors, and tocheck the validity of the theory.

MethodsThe objective of the experiments is to provide qualitativedata for the behavior of the specific studied species as wellas some experimental support for the proposed theory.Vapors generators allow the production of vapors of thedesired species at minute, controlled, and known concen-trations. In a vapor generator, an electrospray of ultra puremethanol and water (1:1), and a known concentration of agiven species (the sample), is produced in a heated chamberwhere the nanodrops are mixed with a flow of gas (nitrogenin this study). Nanodrops are quickly evaporated and thesample species stay vaporized and neutral within thecarrying gas. The flow of gas is controlled and measuredusing a flow-meter. Assuming a Poiseuille flow, the pressuredrop along the electrospray capillary permits us to controlthe flow of the desired species. The electrospray thus used to

1086 G. Vidal-de-Miguel and A. Herrero: Secondary Electrospray Ionization of Vapor Mixtures

generate vapors at minute concentrations is called secondaryelectrospray [5, 6]. Two vapor generators are coupled withan ionization chamber, which is in turn coupled to an in-house modified Qstar XL used in single TOF MS mode. Inthis case, the species used have been lactic acid and severalfatty acids. In order to prevent sample vapor deposition inthe inner walls of the tubes, every part of the system isheated using proportional integral derivative (PID) control-lers. The ionization chamber is composed of a plate holdingan electrospray needle and an inlet and an outlet tube placedupstream of the curtain plate of the MS atmospheric pressureinterface (API). This scheme is similar to that alreadyproposed by Martínez-Lozano [11] except for a tube insidethe chamber that guides the sample flow towards the ESIplume, allowing lower flow-rate operation (2 lpm versus6 lpm in [11]). The primary electrospray at the ionizationchamber produces negative ions (in negative mode) resultingfrom an ammonium-methanol–water dissolution. Samplevapors flow continuously through the ionization chamber;vapors enter through the inlet tube, pass in front of theelectrospray tip, and exit, along with the counterflow gas,through the outlet tube, so that the cloud of charging agentsproduced by the charging electrospray is in close contactwith the sample gas before ions are driven towards theanalyzer inlet by the strong electric fields produced by theelectrospray. Figure 1 shows schematically the hardwareused for the experiments in this study.

The purpose of these experiments is to establish therelationship between the concentration of vapors and theconcentration of ions produced in the ionization region.Vapor concentration can be easily controlled. In this respect,two main regions can be distinguished: (1) a sample gasregion affected by the vapor jet, and (2) a clean gas region,affected by the counterflow gas. Turbulence in the tubesensures that the concentration of vapors in the sample gasregion is approximately uniform. Variations of the vaporconcentration can be expected only in the narrow shear layerbetween the sample gas jet and the counterflow gas region.Sample ions are only produced in the sample gas regionwhere charging agents are in contact with the sample vapors.Our goal in this study is to find relationships between vaporand ion concentrations in this region. But how can we inferthe concentration of sample ions here if we are detectingthem after they have crossed the clean gas region, thevacuum interface, and all the mass spectrometer optics?

The rate of ions ingested by the MS is proportional totheir concentration at the MS inlet. Once ions reach the sonicMS inlet, they pass through the API interface, the quadru-poles, and the TOF system until they are finally detected.Most of them are lost in this journey, but we hypothesizethat for the range in which we are interested, the fractionreaching the sensor is fixed (independent of m/z). In thisrespect, we know that the QStar XL mass analyzer gain isapproximately constant through this mass range [8]. Becausethe gas is clean in the clean region (from the sample gasregion to the MS inlet), ions are only affected by spacecharge repulsion, but this effect can be minimized as long asthe electrostatic field is stronger than the Coulomb repulsion.And this can be easily achieved as long as the primaryelectrospray tip is separated from the curtain plate to ensurethat charging ions are already sufficiently diluted when theyreach the clean region. We have, therefore, positioned theelectrospray tip in the farthest position possible (2 cm fromthe curtain orifice). Under these conditions, the concentra-tion of sample ions reaching the sonic MS inlet isapproximately equal to the concentration in the boundaryseparating the sample and counterflow regions, and thereforethe ion signal is proportional to the concentration of ions inthis boundary.

TheoryCharging Vapors in the Linear Regime,Theoretical Approach

Under the assumptions already explained by de la Mora(stationary regime, negligible fluid velocity, uniform vaporconcentration, negligible loss of available vapor moleculesand charging ions attributable to sample ion productionchemical reactions, and negligible concentration of sampleions on the electric fields), we already know that sample ionconcentration reaches the equilibrium given by equation 2.But is this equilibrium solution valid for all configurations?

Figure 1. Hardware used to study the behavior of anelectrospray-based vapor ionization system comprising twovapor generators

G. Vidal-de-Miguel and A. Herrero: Secondary Electrospray Ionization of Vapor Mixtures 1087

If it were so, the ionization efficiency of all charge transfertechniques should be the same no matter the configuration ofthe ionizer, as long as the same charging ions are used.Applying the mass conservation equation for each species(the charging and the sample ions), the time derivative of theconcentration of each ion is equal to the production rate ofions minus the convective dilution due to space charge.Assuming that the proportion of charging ions lost by chargetransfer reactions is negligible compared with space chargedilution, the set of equations for the two species reads as:

dnsdts

¼ kcsNsnc � nsr� Zs E!þ V

!f

� �

dncdtc

¼ �ncr� Zc E!þ V

!f

� �ð3a; bÞ

where E is the electric field, Vf is the fluid velocity of the gasdragging the ions, and τ is the time of each infinitesimallysmall volume following the ionic streamlines at avelocity Vf+ZE. Note here that dn/dτ in equations 3, not tobe confused with Eulerian notation, refers to the Lagrangiantime derivative of the concentration of an infinitesimallysmall volume following the ions at the same speed of theions. Although dns/dτ differs from zero, the configurationmight be in a stationary state. Because each type of ionhas a different mobility, the streamlines of species isdifferent and τ cannot be directly simplified. But if thefluid velocity is negligible, or if both the sample ion and thecharging ion have the samemobility, they both follow the sametrajectory (though they might travel at different speeds).Fortunately, these conditions apply in our ionizer, at least inthe sample gas region, where the flow travels smoothly, andvery intense electric fields are applied producing ionicvelocities as high as 100 m/s (near the electrospray tip). Underthese conditions, the set of equations can be simplified andfurther integrated (details in Appendix I), and the relationbetween the concentration of sample and charging ions along ageneric streamline can be expressed as:

ns ¼ n�s 1� ncnc0

� �þ ns0

ncnc0

ð4Þ

where n�s ¼ Nskcs"0Zs�e and ns0 and nc0 are, respectively, the

concentrations of sample and charging ions in a referencesection of the streamline.

In the case of an electrospray, two main regions have tobe distinguished. In the first region, the apex of theelectrospray emits nearly monodisperse droplets, whichquickly evaporate and reduce their size, producing asequence of Coulombic explosions [12]. This process iseminently dynamic and the shape of the charging agentsvaries, but eventually the charging agents reach a stablecondition of well defined clusters. Equation 4 is only validin the second region, where the composition of the chargingagent is stable. But, in the case of interest, dropletevaporation is a very fast process taking place in a very

narrow region near the cone apex. As the first region is verysmall, the charging agents entering the second region arehighly concentrated and tend to be quickly diluted byCoulombic repulsion. As a result, it is reasonable to assumethat the inequality nc/nc0GG1 holds in the second region.Obviously, there are no clear boundaries between the tworegions defined, but the assumption nc/nc0GG1 permits us toneglect the effect of the first region. Under these circum-stances, equation 4 reduces to ns=ns

*, yielding the ioniza-tion probability previously predicted [7].

In the case of a corona discharge, two main regions wouldalso have to be distinguished, one region closer to the needle tipwhere a bipolar plasma is formed, and the other farther from theneedle tip, where only ions of one polarity are expelled. Thesame reasoning referred to above would apply to the case ofcoronas as long as the plasma region is small.

The effect of diffusion can be ignored because, for thecase of interest, the convective velocity is much higher thanthe diffusive velocity. The convective velocities are of theorder ZE, while diffusive velocity (VD) is, using theEinstein’s relation, VD=ZkBT/e·l, where kB is the Boltzmannconstant, T is the temperature of the gas, Z is the mobility, Eis the electric field, and l is the size of the region studied.The ratio of the two velocities is the dimensionlessparameter P=E·l/(kBT/e) which, in the case of an electro-spray, is typically very high (E·l is around a few kV whilekBT/e~0.026 V at ambient temperature).

Charging Vapors Comprising a Major Speciesand a Minor Species, Theoretical Approach

One interesting consequence of expressions 2 and 4 is thatthe concentration of sample ions is, on a first approximation,independent of the concentration of charging ions as long asnc/nc0GG1. The charging ions produce a strong backgroundin the analyzer, which it would be better to minimize.Naturally one concludes that the charging ions should bediluted as much as possible in order to achieve this, and thiscan be achieved by simply positioning the emitter fartheraway from the analyzer inlet. But charging ions cannot bediluted too much because, eventually, the ions would bedepleted and no new sample ions would be produced. So, anew question arises: How much can the charging ions bediluted to improve the background before losing perfor-mance? Answering this question requires considering realworld samples often composed of substances at verydifferent concentrations. A common scenario is a samplecontaining a major substance and other minor substancesmore difficult to detect. For instance, complex biomedicalsamples such as skin emanations include fatty acids at muchsmaller concentrations than lactic acid [9]. In this example,as one would expect, the minimum concentration ofcharging ions would be limited by the lactic rather than thefatty acids.

One objective of this study is to describe and predict thebehavior of a sample comprising one major species and


other minor species. This could be useful to establish howmuch one can dilute charging ions before performance loss.It could also be useful for estimating the interference ofdifferent species and for calculating the original sampleconcentration from measurements where the ionized speciesinterfere with each other.

As minor species at low concentrations do not affectother species, only one minor species will be consideredin the theoretical approach. In order to clarify thenomenclature, and because the major species reducesthe signal produced by the minor species, the majorspecies is termed buffer (subscript b), and the minorspecies is simply termed sample (subscript s). Bufferspecies might interfere with the ionization of the samplein two main ways. Buffer vapors can deplete the amountof charging ions available by charging to buffer chargetransfer reactions, and they can also neutralize samplevapors by sample to buffer charge transfer reactions. Forsimplicity, only one charging species and one bufferspecies will be considered here.

In the regime of interest, the electric field is producedby both the charging and the buffer ions, and theproduction of buffer ions is also reflected in a non-negligible destruction of charging ions. The amount ofsample vapors will be considered sufficiently small sothat its effect on both the neutralization of charging ionsand the electric field are negligible. Sample ions areproduced by transfer reactions from charging ion to thesample vapor and are neutralized by charge reactionsfrom sample ions to neutral buffer vapors. The set ofequations governing the behavior of the charging, thebuffer, and the sample ions becomes:

dnsdts

¼ kcsNsnc � ksbnsNb � nsr� Zs E!þ V

!f

� �

dncdtc

¼ �kcbNbnc � ncr� Zc E!þ V

!f

� �

dnbdtb

¼ kcbNbnc � nbr� Zb E!þ V

!f

� �

ð5a; b; cÞ

rE!¼ e

"0nc þ nbð Þ ð6Þ

where nb is the concentration of buffer ions, Nb is theconcentration of buffer vapors, Zb is the mobility of bufferions, and kcb and ksb are the reaction rate constants forcharge transfer from the charging ions to the buffermolecule, and from the sample ions to the buffer molecules,respectively.

Again, if the fluid velocity is negligible, or if the sample,the buffer, and the charging ions have the same mobility, allions follow the same streamlines (though they might havedifferent velocities). The variable τ can then be furthersimplified and the concentration of both buffer and sample

ions can be expressed as a function of the charging ion (seedetails in Appendix II):

d�bd�c

¼ �c � �b �c þ �bð Þ��cZbc � �c �c þ �bð Þ

d�sd�c

¼ �c � �sZbck � �s �c þ �bð Þ��cZbc � �c �c þ �bð Þ

ð7a; bÞ

where n�s ¼ Nskcs"0Zs�e and n�b ¼ Nb

kcb"0Zb�e are parameter groups

having dimensions of concentration, �s ¼ �s ��s ; �c ¼�

�c ��b ; �b ¼ �b n�b��

: are dimensionless concentrations,zbc=Zb/Zc is the buffer to charging mobility ratio, andκ=ksb/kcb· is the ratio of reaction rate constants. Buffer vaporreduces the ionization of minor species by (1) competing forthe available charging ions and by (2) neutralizing alreadyionized minor sample ions. The ratio κ represents the relativeimportance of these two different processes.

This set of equations 7 can be numerically integratedgiven a set of initial conditions (ns0, nb0, and nc0). In the caseof an electrospray having a singular source of charging ions,one would expect to see the asymptotic behavior alreadypredicted by de la Mora [7] near the cone apex, where theconcentration of charging ions tends to infinity. To recoverthis behavior, equations 7 are integrated numerically bystarting the integration at the source �c ! 1 with theequilibrium initial condition that �s ! 1 and �b ! 1.

Charging Vapors when the Electrospray PlumeProduces Charging Agents, and Also ChargedParticles, which Reduce Performance, TheoreticalApproach

Our discussion has so far been limited to the case wherethe charging agent is composed of only one ion type. Inmore realistic situations, the electrospray might produceseveral types of ions and clusters. Electrosprays tend toproduce, once droplets are evaporated, single ions aswell as dimers, trimers, and many types of clustersdepending on each particular solution [12]. Some ofthese charging agents will produce ions when combinedwith the sample vapors, but other species produced bythe spray will not react to produce vapor ions, or willsimply react differently, producing other adducts that willappear in a different peak in the spectrum. Such specieswould not produce sample ions, but would still dilute thesample by space charge. How exactly would thesespecies affect our sample? For simplification, only onetype of charging ion is considered to produce the desiredsample ions, whereas other electrosprayed species wouldnot produce the desired sample ions. The only effect ofthose useless charged particles is to increase the electrostaticrepulsion of the ions.

The objective of the present study is to evaluate the effectof complex electrospray plumes on the probability ofionization. For simplicity, we only consider one samplespecies at very low concentration (sufficiently low to ignore


its effects on space charge and charging ion concentration).The set of equations governing the behavior of the chargingions, the useless electrosprayed ions, and the sample ionsare:

dnsdts

¼ kcsNsnc � nsr� Zs�E!þ V!

f

� �

dncdtc

¼ �ncr� Zc�E!þ V!

f

� �

dnidt i

¼ �nir� Zi�E!þ V!

f

� �

ð8a; b; cÞ

rE!¼ e

"0nc þ

Xni

� �ð9Þ

where the useless electrosprayed ions are denoted withsubscript i, ni is the concentration of the useless electro-sprayed particle of type i, and Zi is its mobility. Again, if allparticles travel along the same streamlines, the equations canbe simplified (see Appendix III):

dnsdnc

¼ n�snc � ns nc þP

nið Þ�nc nc þ

Pnið Þ

dnidnc

¼ ninc

ð10a; bÞ

Equation 10b can be directly integrated showing that theconcentration ratio of each species remains constant: ni/nc=Ci. Equation 10a can also be integrated analytically yielding:

ns ¼ n�s1þP

Ci1� nc

nc0

� �þ ns0

ncnc0

ð11Þ

Equation 11 shows that the ideal single-charging concentrationns

* is actually reduced by a potentially large factorg ¼ 1þP

Ci. This factor shows that charging agents shouldbe composed preferably of only one ion type. Whether thisfactor could also explain the strong dependence of the ionizationprobability on other parameters affecting the structure of thecharging electrospray plume (such as humidity, temperature, orother parameters) is a question that needs further study.

Results and DiscussionBoth experimental results and theoretical results have to bepresented in a way that allows comparison and validation.The theoretical approach shows the relationships betweenthe charging ions and the vapor sample ions. Basically, thenumerical solution to equation 7 provides the functions�s $ �c and �b $ �c for different values of the mobilityratio zbc and the kinetic ratio κ. But experimental dataprovide only vapor concentration and sample ion signals.

In the experiments we have varied the concentration ofinterfering lactic acid. For a given ionization configuration,

the concentration of minor sample ions in the boundaryseparating the sample gas region and the clean counterflowregions depends on the concentration of the major vapor. Ona first approximation, if the charging and buffer ions havesimilar mobilities, the structure of the electrospray plumeand the concentration of total charge, governed by the totalemitted current and the mobility of the ions within the plume[13], would be unaffected even if the charge is transferredfrom one species to another, and the sum of the concentra-tion of charging plus buffer ions would not depend on theconcentration of buffer ions. It is therefore reasonable toassume that for zbc close to one, the concentration ofcharging plus buffer ions in this boundary remains constant(ntot ¼ nb þ nc ¼ constant, where ntot is the total amount ofavailable ions). Figure 2a and b, reconstructed from dataobtained by numerical integration of equation 7, illustratethe fraction of buffer ions among the total amount ofavailable ions nb ntot= and the dimensionless concentration ofsample ions ns n�s

�as a function of the dimensionless

concentration of buffer vapors n�b ntot= (note here that n*bis, by definition, proportional to the concentration of buffervapors). As expected, sample ions produce lower signals,whereas buffer ions produce higher signals and tend towardsaturation at increasing buffer vapor concentrations.

Figure 2b shows the results for different values of κ, andfor zbc=1 (buffer and charging ions having the samemobility). Curves corresponding to the evolution of thebuffer ion are collapsed because its behavior does notdepend on κ. As expected, at higher κ (when the bufferneutralizes the minor sample species), the concentration ofsample ions falls very quickly, even before charging ions aredepleted, and the buffer ions signal still behaves linearlywith buffer concentration.

Comparison of Theoretical and ExperimentalData

The data obtained in the experiments is the signal of thesample ions Ss (fatty acids) and the buffer ions Sb (lacticacid) versus buffer vapor concentration Nb at a given samplevapor concentration Ns. As expected, the behavior of thebuffer ion signal at increasing buffer vapor concentrationsshows a linear regime, a saturation regime, and a transitionregime.

In the saturation regime, the buffer signal is constant (Sb,max).In this regime, it is reasonable to assume that the signal isproportional to the total concentration of ions available:Sb;max ¼ ntot�G, where G is the gain of the analyzer and isunknown. Assuming that Sb=Nb·G, the dimensionless param-eter nb ntot= can be estimated experimentally as:

nb ntot ¼ Sb Sb;max

�� ð12Þ

On the other hand, in the linear regime, the signal isproportional to the concentration of buffer vapors being


Sb ; l ¼ pb;l G�Nb , where pb,l is the probability of ionizationof the buffer species in the linear regime. Though G isunknown, the value pb,lG can be easily calculated by asimple linear regression in the linear region of the Sb(Nb)curve. Using the relation between pb,l and n�b (nb ¼ pb;lNb bydefinition), the dimensionless parameter n�b ntot= can also beestimated experimentally as:

n�b ntot= ¼ pb;l�G Sb;max�Nb

� ð13Þ

With regard to the sample ions, the ratio ns/n*s can also

be estimated experimentally assuming that in the absence oflactic acid, the concentration of sample ions approaches theideal concentration n�s and that signals are proportional to ion

concentration. The dimensionless parameter ns/n*s can be

experimentally estimated as:

ns n�s ¼ Ss Ss Nb¼0ð Þ�� ð14Þ

As for the behavior of the buffer ions, our ionizer starts tobecome saturated at lactic acid concentrations near 10~20 ppb. Figure 3 shows both the theoretical and theexperimental nb ntot $ n�b ntot=

�curves together. Due to the

way experimental data are processed, the behavior forn�b ntot= ! 1 and n�b ntot= ! 0 is constrained and fitted tothe theoretical values. Differences between experimental andtheoretical behavior can be seen only in the transition region,which should be somewhere near n�b ntot= 1. Note here thatthe shape of the curve depends only on the parameter zbc. In


Figure 2. (a) and (b): theoretically calculated evolution of the buffer and the minor sample ion concentrations as a function ofthe buffer vapor concentration: and dimensionless curves for different values of zbc near zbc=1 (a), and for different values ofκ (b)

Figure 3. Experimental and theoretical curves. Dimensionless buffer ion concentration as a function of dimensionless buffervapor concentration

this case, the value for zbc=1 has been chosen arbitrarilyunder the hypothesis that lactic acid ions and charging ionswould have a fairly similar mobility. It would have beenuseful to know the exact charging agent but, unfortunately,we could not find a dominating peak in the MS spectruminversely correlated with the lactic acid signal, and we stilldo not know the exact ionization mechanism. We hypoth-esize that the ionization agent is very light and its mass istoo small to be detected by our mass spectrometer (almostblinded for ions smaller than 30 ~40 Da). However,although the charging agent still remains unknown, thebehavior shown in Figure 3 suggests that the mobility of thecharging agent is similar to or slightly smaller than that ofthe lactic acid, so the charging agent might be a clustercomprising an OH– ion and a few molecules of water ormethanol. This result is in agreement with recent studies byMartínez-Lozano [8], and also supports the original hypoth-esis that we cannot detect the charging agent simply becauseit is too small for our analyzer.

Figure 4 shows the curves ns n�s� $ n�b ntot= (sample ion

concentration as a function of buffer vapor concentration)evaluated both theoretically and experimentally for differentsaturated fatty acids at concentrations near 1 ppb acting assample species (where C1 here stands for the moleculehaving only one C atom, C2 for the fatty acid moleculehaving two C atoms, and so on) and lactic acid acting asbuffer (at concentrations up to 30 ppb). Table 1 shows the

concentration of fatty acids and the gain (signal/concentra-tion) produced when no lactic acid is introduced. Interest-ingly, bigger molecules are sensed more efficiently. Thiscould be partly because bigger molecules, having lowermobility, have higher probability of ionization. As expected,Figure 4 shows how the signal of fatty acids falls as theconcentration of lactic acid is increased.

In accordance with the results of Figure 3, theoreticalcurves are computed for zbc =1. As for κ, in a firstapproximation, charge transfer will always occur if twoparticles collide and the charge affinity difference isfavorable for the reaction. Under this hypothesis, thedifferent reaction rate constants should be of the same orderand κ ~1 (or κ ~0 if the reaction is not favorable). On theother hand, for favorable reactions, buffer vapors will havethe highest charge affinity, followed by the sample vapors,while the charging agent has the lowest charge affinity. Thecharge to buffer reaction would therefore tend to be strongerthan the sample to buffer reaction, and the ratio κ would thusbe smaller than one (κG1). Continuous and dashed theoret-ical lines in Figure 4 correspond, respectively, to κ=0.1 andκ=0.3. Post-processed experimental data are forced to meettheoretical curves at the point (0, 1), but there are no otherrestrictions. Most experimental data fall between the twotheoretical curves (κ=0.1 and κ=0.3), suggesting that botheffects (1) charge transfer reactions from fatty acid to lacticacid, and (2) charging agent depletion is important andcommensurable in our set-up.

ConclusionsThe developed model hypothesizes that charging agentshave constant composition. Although this holds true at leastfor highly conductive electrosprays producing very smalldroplets that quickly evaporate and produce ions, it is notnecessarily always the case. Luckily, comparison of theoret-ical and experimental data suggest that in our specific

Table 1. Number of Carbons, Maximum Signal, Concentration of Vapors,and Overall Gain of the Different Fatty Acids Analyzed

Carbons Ss (cps) Ns (ppt) Gain (cps/ppt)

1 70 1917.9 3.65E – 022 129 1462.4 8.82E – 023 1169 1181.7 9.89E – 015 7840 853.94 9.18E+006 9042 749.93 1.21E+017 10838 656.21 1.65E+018 12409 591.94 2.10E+01


Figure 4. Experimental and theoretical curves. Dimensionless sample ion concentration as a function of dimensionless buffervapor concentration

configuration, ionization agents are highly mobile and thattransfer reaction from sample ions (ionized by chargetransfer reactions from charging agents) and charging agentdepletion are commensurable effects for the case of amixture of fatty acids and lactic acid. Although this is notconclusive evidence, our data support the hypothesis thatSESI mechanism is, at least in this case, based on ion tomolecule rather than droplet to molecule reactions.

Another interesting theoretical result is that low mobilitycharging agents would be much less affected by chargedepletion. According to our model, when the mobility of thecharging agents is much lower than the mobility of the ionizedvapors, the behavior of the ionizer is perfectly linear until thecharge is totally depleted. This interesting result suggests thatSESI ionizers should use preferably low mobility chargingagents to improve the linear response over a wider sampleconcentration range. An improved model including time-varying charging agent properties would be useful for a betterunderstanding of this hypothetically more efficient regime.

AcknowledgmentsThe authors are most grateful to Juan F. de la Mora forhis valuable insights and comments. They are alsograteful to Pablo Martínez-Lozano for many fruitfulconversations and to their colleagues at SEADM, andespecially to Ernesto Criado, for his help during theexperiments. This work was developed under the projectEMOCION funded by the Plan AVANZA (Gobierno deEspaña). The authors also thank Gonzalo F. de la Morafor his support for this project.

Appendix I - Charging Vaporsin the Linear RegimeIn a very first approximation, we shall consider only onereaction where the charging agent is composed of ions ofonly one type transferring their charge to the samplemolecules to produce sample ions. As already noted byJ. F. de la Mora [7], as the measured probability ofionization is very low, one can simplify the equations byassuming that the concentration of sample vapor remainsconstant and homogeneous (only a tiny part of the totalmolecules are ionized). Equations are also simplified byassuming that the concentration of charging ions is muchhigher than the concentration of sample ions. Thisimplies that the electric field is only (or mainly) drivenby the concentration of charging ions, and that thedestruction rate of charging ions attributable to chargetransfer reactions can also be ignored. These assumptionsare reasonable in the limit of interest when one is tryingto measure the sensitivity of a system because undersuch conditions the concentration of sample ions is verylow. Applying these assumptions to the sample ion massconservation equation of an infinitesimally small volumetraveling at the velocity of the sample ions, and similarly

to the charging ion mass conservation equation of asimilarly and equally infinitesimal small volume travelingat the velocity of the charging ions yields:

dnsdts

¼ kcsNsnc � nsr� Zs~E þ ~V f

� �

dncdtc

¼ �ncr� Zc~E þ ~V f

� �ðaI� 1a; bÞ

Where dτs is the time required by the sample ions totravel an infinitesimally short distance dl and dτc is thetime required by the charging ions to travel the samesimilarly infinitesimal short distance dl. Note here thatdn/dτ in equations (aI-1a, b), not to be confused withEulerian notation, refers to the Lagrangian time deriva-tive of the concentration of an infinitesimally smallvolume following the ions at the same speed of theions. Although dns/dτ differs from zero, the configurationmight be in a stationary state. Because each type of ionhas a different mobility, the streamlines of species aredifferent and τ cannot be directly simplified. But underspecial circumstances where dτs and dτc are related,equations (aI-1a, b) can be further simplified. If the fluidvelocity is negligible or if both the sample ion and thecharging ion have the same mobility, the charging andthe sample ions follow the same trajectory even thoughthey might travel at different speeds. Under suchcircumstances, dτs and dτc are related as follows:

dtc ¼ dtZs

Zc

dts ¼ dt

ðaI� 2a; bÞ

and the variable τ can be further simplified by dividing equations(aI-1a) and (aI-1b), using the relationsr~E ¼ nce "0;= and (aI-2),and assuming that the flow is incompressible:

dnsdnc

¼ kcsNsnc � nsZse"0nc

ZsZc

�ncZce"0nc

� � ðaI� 3Þ

Rearranging the expression of equation (aI-3) and usingthe parameter n�s ¼ Ns

kcs"0Zs�e (having dimensions of concen-

tration), yields a very simple equation:

dnsns � n�s

¼ dncnc

ðaI� 4Þ

that can be easily integrated for a given initial condition (ns0and nc0), leading to the result already presented in the maintext as equation 4:

ns ¼ n�s 1� ncnc0

þ ns0ncnc0

� �ðaI� 5Þ


Appendix II - Charging VaporsComprising a Mayor Speciesand a Minor Species, TheoreticalApproachIn the regime of interest, the electric field is produced byboth the charging and the buffer ions, and the productionof buffer ions is also reflected in a non-negligibledestruction of charging ions. The amount of samplevapors will be considered sufficiently small to assumethat its effect on both the neutralization of charging ionsand the electric field is negligible. Sample ions areproduced by transfer reaction from charging ion tosample vapor and are neutralized by charge reactionsfrom sample ions to neutral buffer vapors. The set ofequations governing the behavior of the charging, thebuffer, and the sample ions become:

dnsdts

¼ kcsNsnc � ksbnsNb � nsr� Zs~E þ ~V f

� �

dncdtc

¼ �kcbNbnc � ncr� Zc~E þ ~V f

� �

dnbdtb

¼ kcbNbnc � nbr� Zb~E þ ~V f

� �

ðaII� 1a; b; cÞ

r�~E ¼ e

"0nc þ nbð Þ ðaII� 2Þ

where nb is the concentration of buffer ions, Nb is theconcentration of buffer vapors, Zb is the mobility of bufferions, kcb and ksb are the reaction rate constants for chargetransfer from the charging ions to the buffer molecule, andfrom the sample ions to the buffer molecules, respectively,and dτb is the time required by the buffer ions to travel aninfinitesimally short distance dl.

Again, if the fluid velocity is negligible, or if all thesample, buffer, and charging ions have the same mobility, allions follow the same trajectory even though they mighttravel at different speeds. Under such circumstances, dτs, dτb,and dτc are related to dτ similarly as in equation (aI-2):

dtc ¼ dt ZbZc

dts¼ dt ZbZs

dtb¼ dtðaII� 3a; b; cÞ

and the variable τ can be further simplified by dividingequations (aII-1c) and (aII-1b), and equations (aII-1a)and (aII-1b), using the relations (aII-2) and (aII-3), and

assuming that the velocity field is incompressible:

dnbdnc

¼ ncn�b � nb nb þ ncð Þ�ncn�b

ZbZc� nc nb þ ncð Þ

dnsdnc

¼ n�snc � n0bns � ns nb þ ncð Þ

�ncn�bZbZc� nc nb þ ncð Þ

ðaII� 4Þ

where n�s ¼ Nskcs"0Zs�e ; n�b ¼ Nb

kcb"0Zb�e and n

0b ¼ Nb

ksb"0Zs�e . Rear-

ranging equations (aII-4) and using the dimensionlessparameters �s ¼ ns n�s

�; �c ¼ nc n�b ; �b ¼ nb n�b

��Zbc ¼ Zb=

Zc:, and k ¼ ksb kcb= yields:

d�bd�c

¼ �c � �b �c þ �bð Þ��czbc � �c �c þ �bð Þ

d�sd�c

¼ �c � �szbck � �s �c þ �bð Þ��czbc � �c �c þ �bð Þ

ðaII� 5Þ

This set of equations can be numerically integrated, given aset of initial conditions (ns0, nb0, and nc0). For the case of anelectrospray having a singular source of charging ions, onewould expect to find the asymptotic behavior already predictedby de la Mora [7] near the cone apex where concentration ofcharging ions tends toward infinity. To recover this behavior,equations (aII-5) are integrated numerically by starting theintegration at the source �s ! 1 with the equilibrium initialcondition that �s ! 1 and �b ! 1.

Solving these equations for κ=0 and for different valuesof zbc show that the dependence of the concentration ofbuffer ions as charging ion concentration varies is lower forzbc 991. This result suggests that a SESI ionizer using lowmobility charging agents (such as droplets rather than singleions) would improve the linear range of the ionizer.

In the limit when zbck ! 1, the concentration of sampleions falls when the fraction of buffer ions is still very low. Thismeans that the main mechanism reducing the sample ionconcentration is charge transfer reaction from the sample ionsto the buffer molecules rather than charging agent depletion.Obviously, equations (aII-5) cannot be integrated in thisregime, but a new set of equations can be rewritten for thismore special case where the only effect of the buffer vaporconcentration is to stead charge from the sample:

dnsdts

¼ kcsNsnc � ksbnsNb � nsr� Zs~E þ ~V f

� �

dncdtc

¼ nsr� Zc~E þ ~V f

� � ðaII� 6Þ

r�~E ¼ e

"0nc ð1Þ


Proceeding as before to eliminate the variables dτs and dτcyields:

dnsdnc

¼ n�s nc � n0bns � nsncn2c

ðaII� 7Þ

and this equation can be further simplified using thedimensionless parameters �s ¼ ns n�s

�and �c ¼ nc n

0b

�(where n

0b ¼ Nb

ksb"0Zs�e . Note that �c ¼ �czbck).

d�sd�c

¼ �c � �s � �s�c

�2c

ðaII� 8Þ

Equation (aII-8) can be integrated analytically. Imposing thecondition that the solution is bound when�c ! 1, the solutionfor equation (aII-8) is equation (aII-9), which also recovers theresult already expected when the concentration of chargingions is much higher than the concentration of buffer ions.

�s ¼ �c 1� e1�c

� �ðaII� 9Þ

For a given ionization configuration, the concentration ofcharging ions is constant (note that in the proposed limit,charging agent depletion is negligible) nc=ntot, and the ratio �c

is inversely proportional to the buffer vapor concentration. Inthe limit when �c ! 1 (very low concentration of buffervapors), �s tends to one, and in the limit when �c ! 0 (veryhigh concentration of buffer vapors), �s tends toward zero.

Appendix III - Charging Vaporswhen the Electrospray PlumeProduces Charging Agents,but Also Charged Particleswhich Reduce PerformanceFor simplicity, we shall consider only one sample species atvery low concentration. Equations are also simplifiedassuming that the concentration of electrosprayed ions ismuch higher than the concentration of sample ions and,therefore, that the electric field is only driven by theconcentration of electrosprayed ions, and that the destructionrate of charging ions is also negligible. These simplificationsyield the following set of equations:

dnsdts

¼ kcsNsnc � nsr� Zs~E þ ~V f

� �

dncdtc

¼ �ncr� Zc~E þ ~V f

� �dnidt i

¼ �nir� Zi~E þ ~V f

� �ðaIII� 1a; b; cÞ

r�~E ¼ e

"0nc þ

Xni

� �ðaIII� 2Þ

where the useless electrosprayed ions are denoted withsubscript i, ni is the concentration of the charged particle oftype i, Zi is the mobility of the charged particle i and dτi isthe time required by the i ions to travel an infinitesimallyshort distance dl. If the fluid velocity is negligible, or if allthe sample, buffer, and charging ions have the samemobility, all ions follow the same trajectory even thoughthey might travel at different speeds. Under such circum-stances, dτs, dτi, and dτc are related to τ, similarly as inequations (aI-2):

dtc ¼ dt ZsZc

dt i ¼ dt ZsZi

dts ¼ dt

ðaIII� 3Þ

and the variable τ can be further simplified dividingequations (aIII-1c) and (aIII-1c), and equations (aIII-1c)and (aIII-1c), using the relations (aIII-2) and (aIII-3), andassuming that the velocity field is incompressible:

dnsdnc

¼ n�snc�ns ncþP

nið Þ�nc ncþ

Pnið Þ

dnidnc

¼ ninc

ðaIII� 4a; bÞ

Equations (aIII-4b) can be directly integrated yielding ni/nc=Ci, where Ci is the concentration ratio of each speciesthat will remain constant as long as the composition of theplume is in equilibrium; equation (aIII-4a) can also beintegrated analytically introducing the values Ci, giving theresult already presented in the main text as equation 11:

ns ¼ n�s1þP

Ci1� nc

nc0

� �þ ns0

ncnc0

ðaIII� 5Þ

List of Symbols

Symbol Definitionpi Ionization probabilityns Concentration of sample ionsNs Concentration of sample neutral vaporse The charge of the ionε0 Permittivity of the vacuumZs Mobility of the sample ionkcs Reaction rate coefficient for the charge transfer

reaction from the charging ions to the samplemolecule

E Electric fieldVf Fluid velocity of the gas dragging the ionsτ Time for each infinitesimally small volume

following each type of ionic streamline at avelocity Vf+ZE

n�s ¼ Nskcs"0Zs�e

ns0 Concentration of sample ions in a referenceSection of the streamline


References

1. Whitehouse, C.M.; Levin, F.; Meng, C.K.; Fenn, J.B. Proceedings ofthe 34th ASMS Conference on Mass Spectrometry and Allied Topics,Denver, CO, 1986; p. 507.

2. Fuerstenau, S.; Kiselev, P.; Fenn, J. B. ESIMS in the analysis of tracespecies in gases. Proceedings of the 47th ASMS Conference on MassSpectrometry, Dallas TX, 1999.

3. Fuerstenau, S. Aggregation and fragmentation in an electrospray ionsource. Ph.D. Thesis, Department of Mechanical Engineering, YaleUniversity, 1994.

4. Wu, C., Siems, W.F., Hill Jr., H.H.: Secondary electrospray ionizationion mobility spectrometry/mass spectrometry of illicit drugs. Anal.Chem. 72, 396–403 (2000)

5. Martínez-Lozano, P.; Rus, J.; Fernández de la Mora, G.;Hernández, M.; Fernández de la Mora J. Detection of explosivevapors below part per trillion concentrations with electrospraycharging and atmospheric pressure ionization mass spectrometry(API-MS). J. Am. Soc. Mass Spectrom. 20, 287–294

6. Mesonero, E.; Sillero, J.; Hernandez, M.; Fernandez de la Mora,J. Secondary electrospray ionization detection of explosive vaporsbelow 0.02 ppt on a triple quadrupole with an atmosphericpressure source. Proceedings of the 57th ASMS Conference,Philadelphia, PA(USA), May 2009.

7. Fernandez de la Mora, J. Ionization of napor molecules by anelectrospray cloud; special issue of the International Journal ofMass Spectrometry (Samy El-Shall and David Muddiman,Editors) to honor the Science and Impact of John B. Fenn;May/5/2010.

8. Martínez-Lozano P.; Criado E.; Vidal G. Mechanistic study on theionization of trace gases by an electrospray plume. Int. J. MassSpectrom. 313, 21–29 (2011)

9. Martínez-Lozano, P., Fernández de la Mora, J.: On-line detection offatty acid vapors released by human skin. J. Am. Soc. Mass Spectrom 20(6), 1060–1063 (2009)

10. Martínez-Lozano, P.: Mass spectrometric study of cutaneous volatilesby secondary electrospray ionization. Int. J. Mass Spectrom. 282(3),128–132 (2009)

11. U.S. Patent application 11/732,770; Martínez-Lozano P., Fernandez dela Mora J. Method for detecting volatile species of high molecularweight. April 4, 2006.

12. Hogan C. J. Jr.; Fernández de la Mora, J. Tandem ion mobility-mass spectrometry (IMS-MS) study of ion evaporation fromionic liquid-cetonitrile nanodrops. Phys. Chem., Chem. Phys.(36), 8079–8090 (2009)

13. Fernández de la Mora, J.: The effect of charge emissions fromelectrified liquid cones. J Fluid Mech 243, 561–574 (1992)

nc0 Concentrations of charging ions in a referencesection of the streamline

ZE Convective velocitiesVD Diffusive velocitykB Boltzmann constantT Temperature of the gasZ MobilityL Size of the region studied

P ¼ E�l kBT e=ð Þ=subscript b The major species termed buffersubscript s Minor species termed samplenb Concentration of buffer ionNb Cconcentration of buffer vaporsZb Mobility of buffer ionskcb Reaction rate constant for charge transfer from

the charging ions to the buffer moleculesksb Reaction rate constant for charge transfer from

the charging ions to the buffer molecules

n�b ¼ Nbkcb"0Zb�e

�s � ns n�s�

Dimensionless sample ion concentration

�c ¼ nc n�b�

Dimensionless charging ion concentration

�b ¼ nb n�b�

Dimensionless buffer ion concentration

zbc ¼ Zb Zc= Buffer to charging mobility ratio

k ¼ ksb kcb= Ratio of reaction rate constants

nb0 Concentrations of buffer ions in a referencesection of the streamline

subscript ‘i” Useless charging ionsni Concentration of the useless electrosprayed

particle of type iZi Mobility of the charged particle 'i'

Ci ¼ ni nc= constant concentration ratio of each species

g ¼ 1þPCi

ntot ¼ nb þ nc Total amount of available ions

Ss Signal of the sample ionsSb Signal of buffer ionsSb,max Signal of buffer ions in saturation regimeG Gain of the analyzer

Sb;l Signal of the buffer ion in the linear regime

pb;l Probability of ionization of the buffer speciesin the linear regime

Ss Nb¼0ð Þ Signal of sample ions at zero concentration ofbuffer vapors

n0b ¼ Nb

ksb"0Zs:e

�c ¼ nc n0b

�


secondary electrospray ionization of complex vapor mixtures. theoretical and experimental approach

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