Combustion, Explosion, and Shock Waves, Vol. 48, No. 5, pp. 516–525, 2012.

Original Russian Text c© A.N. Hayhurst.

Mass Spectrometric Sampling of a Flame

UDC 662.612+543.51A. N. Hayhursta

Translated from Fizika Goreniya i Vzryva, Vol. 48, No. 5, pp. 27–38, September–October, 2012.Original article submitted October 1, 2011.

Abstract: Some of the more important perturbations of the gas composition in samples taken formass spectrometric analysis are considered. In particular, the flame is cooled by passing up to theinlet hole at the tip of a relatively cool sampling nozzle; cooling occurs in thermal boundary layersbefore the sample reaches the local speed of sound at the throat of the sampling orifice. Certainly,the sample also cools just because of attaining its sonic velocity. Finally, there is a sudden fall intemperature and density in the supersonic expansion into the first vacuum chamber. It is shownhere that perturbations in the external boundary layer are much reduced by using a larger inlethole. However, a bigger sampling orifice causes the supersonic expansion to last for a longer time,thereby increasing the likelihood of a sampling perturbation inside the expansion duct. Theseeffects are demonstrated experimentally in studies of ions in various flames, where the cooling inthe boundary layer was measured to be up to 400 K. This means that the total cooling can be up toat least 700 K. In addition, the effects of burning a flame at a reduced pressure and also of changingthe ratio of the principal specific heats of the flame gas are considered. If there is a falsification ofa mass spectrometric measurement, corrections can be made by extrapolating the measurementsto that for either an infinitely large sampling orifice or one of zero diameter, depending on whetherthe sample is perturbed in the boundary layer or in the supersonic expansion. It also has provedpossible to deduce the rate constant of reactions occurring during supersonic expansion, e.g., forH3O

+ + H2O + M → H3O+·H2O + M.

Keywords: flame sampling, mass spectrometry, ions in flames, perturbation of the sample’scomposition and temperature, molecular beam sampling.

DOI: 10.1134/S0010508212050036

INTRODUCTION

Mass spectrometers have an unrivalled sensitivityin that they have the capability of detecting a singlemolecule or radical. They must operate at pressureslow enough for the mean free path to exceed any internaldimension characteristic of the spectrometer. Roughlyspeaking, the mean free path in air at T = 300 K andp = 10−8 bar is 7 m, so that a flame burning at p = 1 barhas to be expanded to a pressure of 10−8 bar or less,before a mass spectrometric analysis of the flame’s con-stituents can be acquired. This huge reduction in pres-sure is achieved in 2–3 stages of pumping. If neutral

aDepartment of Chemical Engineering and Biotechnology,University of Cambridge, Pembroke Street, Cambridge,CB2 3RA, England; anh1000@cam.ac.uk.

species in a flame are being studied, at some stage theyhave to be ionised before injecting them into the massspectrometer. Usually this is done by directing a beamof electrons at a molecular beam of species from theflame, so that a molecule or radical M ionises in thereaction: M + e− → M+ + 2e−. Thereafter, usingelectric fields, it is easy to direct and focus the posi-tive ions M+ into either a magnetic or radio-frequency(quadrupole) spectrometer. The experiments reviewedbelow are studies of ions in a flame, so that the massspectrometer was simpler, because of not requiring adevice to produce ions. Whether ions or neutrals in aflame are being studied, the gases in a flame have tobe expanded down to a pressure of at least 10−8 bar.It will be seen below that this usually involves adia-batically expanding the flame gases through a pin-hole

516 0010-5082/12/4805-0516 c© 2012 by Pleiades Publishing, Ltd.

Mass Spectrometric Sampling of a Flame 517

Fig. 1. Apparatus for burning an almost flat flame at atmospheric pressure against a water-cooledsampling plate housing a metallic sampling nozzle. Ions of chosen sign are weakly focused into thesecond vacuum chamber housing a quadrupole mass spectrometer. For more details, see [9, 11].

into an expansion duct to form a molecular beam insidea vacuum chamber. Inevitably, there is a concomitantcooling of the sample. A chemical equilibrium in a flameat p = 1 atm must have a time constant less than ≈5 μs.Below it will be shown that only an equilibrated chem-ical is fast enough to respond to these rapidly fallingtemperatures, thereby falsifying the sample’s composi-tion. This is the major perturbation of the measure-ments and is reviewed in some detail below.

The mass spectrometry of molecular beams from aflame was reviewed by Biordi in 1977 [1] and by Ko-robeinichev in 1980 [2]. An excellent discussion of someof the problems of sampling a flame for mass spectrome-try dates from Smith’s publication in 1995 [3]. Samplinga flame to investigate the ions in it was reviewed by Fi-alkov in 1997 [4] and by Guo and Goodings in 2010 [5].It will become clear that, to a large extent, the difficul-ties of mass spectrometrically studying ions and neutralspecies in a flame are qualitatively identical.

APPARATUS

Figure 1 shows a very typical apparatus [6–9] forburning a nearly flat flame at atmospheric pressureagainst a water-cooled sampling plate, at the centre ofwhich is a hollow sampling cone electroformed from ei-ther chromium (with the melting point of 1860◦C) for afuel-rich flame or nickel (melting at 1455◦C) for eithera rich or lean one. In this study [10], fuel-rich mix-tures of H2 + O2 + Ar (or N2) were passed down 150hypodermic stainless steel tubes (with the inner andouter diameters equal to 0.6 and 0.8 mm, respectively)bonded together with epoxy in a tightly packed array.

Table 1. Description of flames studied

Flamenumber

Mole fractionratios in theunburnt gas

T [K]at a distance of Mole

fraction H2O

H2 O2 N2 Ar 3 mm 20 mm

1 2.74 2.95 — 2250 2400 0.176

1a 2.74 — 4.69 2220 2400 0.134

2 3.18 4.07 — 1923 2080 0.275

2a 3.181.0

— 6.49 1904 2080 0.206

3 3.09 4.74 — 1874 1980 0.255

3a 3.09 — 7.53 1841 1980 0.188

4 3.12 5.77 — 1798 1820 0.224

4a 3.12 — 9.17 1767 1820 0.151

The compositions of the various horizontal flames stud-ied are listed in Table 1, together with their temper-atures at 3 and 20 mm from the tip of the reactionzone, which extended some 1.0–1.5 mm from the flatface of the burner. The hot gas from these reactionzones merged into a cylindrical column (≈14 mm in di-ameter) of a burnt gas, where, apart from the edges,there was a laminar flow for at least 25 mm. The veloc-ity in the burnt gas varied from ≈30 m/s in the hottestflame to ≈10 m/s in the coolest flame.

A flame was burnt against a cooled vertical sam-pling plate (see Fig. 1). The sampling cone had aninternal angle of 60◦, and the thickness of its walls was≈0.08 mm. Quite importantly, very many samplingplates were available with differently sized inlet orifices,whose diameters ranged from 0.05 to 0.22 mm. Initially,

518 Hayhurst

the orifices were surrounded by a sharp-edged metal togive an internal length of zero, but with continued usesome rounding occurred. These sampling nozzles andtheir supporting plates were electrically grounded, butthe electrical potential of the burner was variable. In thework described here, the burner was actually earthed.Depending on the thickness of its wall, the tempera-ture at the tip of a sampling cone was estimated tobe ≈1400 K from its red glow, when in a flame at2400 K. A small fraction of the gas on the flame’s axis(0.1–2.0 ml/s at standard pressure and temperature,depending on the flame and also the hole diameter)passed through the inlet orifice and supersonically ex-panded into the first vacuum chamber, pumped downto a pressure of ≈10−3 mbar. The huge pressure ra-tio of ≈106 across the inlet meant that the velocity atthe narrowest part (the throat) was sonic for the lo-cal conditions there. In an expansion duct, the flow issupersonic [11], until the continuum flow becomes col-lisionless after ≈0.1–1.5 μs, when the gas has travelled6 nozzle diameters down the expansion duct. Thus, theKnudsen number (the ratio of the mean free path to thelocal diameter of the duct) increases from 10−2–10−3 atthe throat to more than 3 at the exit of the Cr nozzle.

In the first vacuum chamber (see Fig. 1), an elec-trode (its size and shape were similar to a wedding ring)had a voltage of −15 V for the study of positive ions.Consequently, any negative ions and free electrons fromthe flame were stopped. Many positive ions and someneutral species entered the second chamber, whose wallswere held at −300 V. This arrangement meant that thewedding ring acted as an immersion lens to give somemodest focusing of positive ions into the second cham-ber, pumped to a pressure of ≈ 2 · 10−6 mbar. Thebeam of positive ions was then shifted and focused intoa quadrupole mass spectrometer, measuring the abun-dance of each ion [6–9]. Negative ions could be studiedby reversing the signs of the accelerating potentials; cal-ibration techniques are available to enable absolute ionicconcentrations to be measured [8, 12]. It is importantto note that the sampling plate could be easily replacedby another with a differently sized inlet orifice. For this,the vacuum in the second chamber was maintained by avalve [6, 7] sealing the entrance to this chamber, whilstair at 1 atm was admitted to the first chamber. A differ-ent arrangement has been used by Goodings et al. [13]for exchanging sampling orifices.

Trace quantities of metals were added to a flame bynebulising an aqueous solution of a soluble salt into thegas supplied to the burner [12]. Typically, a 0.1 M solu-tion of NaCl resulted in a total mole fraction of all Na-containing species in a flame of ≈10−6. In that case, themajor positive ion was Na+, with some Na+·H2O and

Fig. 2. Streamline showing the amount of the flamebeing samples through relatively large (left) andsmall (right) inlet orifices.

traces of higher hydrates present. Thermal ionisation ofNa atoms [14] is responsible for producing Na+ ions, butsome originate from the reaction with the natural flameion, H3O

+ in: H3O+ +Na→ Na+·H2O + H [15]. Even

so, the measured ratio (see below) of [Na+·H2O]/[Na+]can be as high as 0.05 [10], which is larger than expectedgiven a temperature above 1800 K (see Table 1) and themole fractions of H2O quoted in Table 1. The suspicionis that ion hydrates form during excessive cooling of theflame gases during their sampling.

SOME SAMPLING CONSIDERATIONS

Figure 2 shows two sampling cones (note theshort length of the entrance channel) and approximatesketches of the flow fields of the gas approaching thesenozzles with either a relatively large or small inlet ori-fice. The streamlines in Fig. 2 were obtained by assum-ing a potential flow [16] up to the throat of the inletorifice. This assumption is justified by the Reynoldsnumber at the throat being ≈ 200 for an orifice diam-eter of 0.2 mm [9], so that any effects of viscosity canbe neglected. There is always a stagnation streamline,which separates the gas entering the first vacuum cham-ber (i.e., the sample) from that which does not. At thethroat, the flow is inevitably choked, so the local Machnumber is equal to unity. Assuming that the flow isadiabatic, the pressure p, density ρ, and temperature Tof the sample (assumed to be a perfect gas) are relatedto their initial values pbg, ρbg, and Tbg in the burnt gasof the flame by the formulae [11]

p

pbg=

(ρ

ρbg

)γ

=

(T

Tbg

)γ/(γ−1)

, (1)

Tbg/T = 1 + (γ − 1)M2/2, (2)

Mass Spectrometric Sampling of a Flame 519

Table 2. Aerodynamic cooling along each

of the flames of Table 1

Flamenumber

Tbg − Tthroat, K [H2O]throat

[H2O]bg3 mm 20 mm

1 97 104 0.58

1a 290 314 0.55

2 174 190 0.56

2a 282 309 0.54

3 211 223 0.56

3a 306 329 0.53

4 213 216 0.55

4a 314 324 0.52

where M is the Mach number, i.e., the ratio of thegas velocity to the local velocity of sound, given by(γRuT/Mw)

1/2. Here γ is the ratio of the principalspecific heats of the gas whose mean molecular mass isMw and Ru is the gas constant. Equations (1) and (2)apply particularly to the supersonic flow inside the ex-pansion duct of the sampling cone. At the throat of thenozzle, we have M = 1, so the temperature there is

Tthroat = 2Tbg/(1 + γ). (3)

This means the sample experiences aerodynamic cooling

Tbg − Tthroat = Tbg(γ − 1)/(γ + 1) (4)

solely because of the sample’s acceleration to a Machnumber of unity. The same acceleration is responsiblefor the decrease in the ratio [H2O]throat/[H2O]bg. Thebehavior of both quantities is illustrated in Table 2. Ofcourse, the sample also cools, because of heat transfer tothe tip of the cooler sampling nozzle. Even so, Table 2reveals that, if these additional heat losses are ignored,the concentrations are almost halved when a samplemoves to the throat. Also, the cooling is enhanced whenargon is the diluent in the flame instead of nitrogen,because of the higher value of γ for Ar. Nevertheless,these unavoidable coolings are in the range from 100 Kto at least 300 K.

The flow fields in Fig. 2 show that the gas on theaxis of symmetry simply accelerates to M = 1 at thethroat. However, the gas in the sample initially awayfrom the axis moves farther from the axis and then re-turns, with some gas moving very closely over the metal-lic cone. This means that the gas passing through thethroat has experienced a variety of residence times inthe burnt gas, the spread of times being ≈20 μs [16].This creates uncertainty in the “age” of the sample.Also, there are boundary layers on the high-pressure

side of the sampling nozzle, covering its surface. How-ever, to some extent these boundary layers are “suckedinto” the first vacuum chamber; in fact, this effect isshown below to be more pronounced with a larger in-let orifice. The result is that, with a bigger hole, theboundary layer is thinner; hence, a smaller fraction ofthe sample is affected by the proximity of the coolermetallic surface. Figure 2 illustrates the approximatepositions of these boundary layers, illustrating that the“boundary-layer cooling” of the sample (i.e., that in ad-dition to the aerodynamic cooling discussed above) islarger with a smaller inlet orifice. Of course, a largersampling orifice leads to the subsequent supersonic ex-pansion lasting much longer, before collisions cease in-side the Cr nozzle. This means that the cooling of asample in the external boundary layer and in the near-adiabatic expansion have opposite dependences on theorifice’s diameter.

Calculations of the flow fields and boundary layereffects in Fig. 2 are difficult, as also is a computation ofthe cooling in the boundary layers. Even so, attemptshave been made [17, 18] to do so. The results of suchan attempt [17] confirm that this cooling in the exter-nal boundary layer is greater with a smaller inlet hole.Also, for a smaller orifice (0.085 mm in diameter), amean residence time in the external boundary layer of≈0.4 μs was estimated [17] and confirmed by measure-ments [9]. This residence time is smaller for a largersampling orifice and vice versa.

The fact that the residence times in the supersonicexpansion and external boundary layer have similar or-ders of magnitude leads to a clear conclusion: if a chemi-cal reaction in a flame has a time constant less than 1 μs,it will be at equilibrium in the burnt gas and also, atleast in principle, fast enough to shift its position duringthe cooling when either traversing the boundary layer (ifthe inlet orifice is small) or expanding supersonically (ifthe hole is large). When there is a fall in temperature,the equilibrium shifts in its exothermic direction with aconsequential change in the sample’s composition. Onthe other hand, any chemical equilibrium with a timeconstant exceeding 5 μs will probably not be at equi-librium in the flame and will be too slow to respond tothe quickly falling temperatures during molecular beamsampling (see Figs. 1 and 2). One example consideredbefore [19] is the equilibrium

OH+H2 = H2O+H (I)

with an exothermicity of about 63 kJ/mol. This meansthat its equilibrium constant increases by a factor of 3.5if a sample from a flame is cooled from 2000 to 1500 K.Of course, if the exothermicity were larger, the shiftwould be greater. Thus, an equilibrium like (I) contin-ues to adjust to the increasingly lower temperatures ex-

520 Hayhurst

perienced during sampling, but this process stops whenthe time constant becomes longer than the time remain-ing before collisions cease. As for reaction (I), its timeconstant [19] at T = 2000 K and p = 1 atm is ≈0.13 μs,so that, when sampling such a flame at p = 1 atm, reac-tion (I) will shift somewhat to produce H atoms at theexpense of OH radicals. What about a flame burningat a sub-atmospheric pressure p < 1 atm? A reductionin pressure to, e.g., 0.04 atm will not affect the externalflow field [16] between the burner and sampling noz-zle, because the effects of viscosity can be neglected.However, in the absence of suction, the boundary layerthickness is inversely proportional to the square root ofthe pressure, so one might expect an increase in the res-idence time there to ≈1 μs, bearing in mind that onlya fraction of the sample passes through the boundarylayer. Of course, the residence time in the supersonicexpansion before collisions cease is considerably reducedby burning a flame at a lower pressure. Consequently,in a flame at T = 2000 K and p = 0.04 atm, the timeconstant of (I) is 0.13 · 25 ≈3.3 μs, which is longer thanthe new residence times in the boundary layer and su-personic expansion. Thus, a sampling perturbation ofreaction (I) is not expected with a flame burning atT = 2000 K and p = 0.04 atm. Also, the above discus-sion indicates that one only has to be concerned aboutexothermic reactions, with fairly low activation energiesand large exothermicities, occurring during sampling.One example is the reaction

H + O2 +M = HO2 +M (II)

with a large rate constant [20], which varies with pres-sure. In an oxygen-rich flame at, say, T = 2000 K andp = 0.04 atm, the time constant of the forward stepin (II) is less than 1 μs. This is low enough for reaction(II) to be shifted towards producing anomalous amountsof HO2 radicals, even in the supersonic expansion froma flame burning at, e.g., 0.04 atm.

There are other problems of sampling a flame intoa vacuum chamber. For example, the background pres-sure in the first chamber of Fig. 1 varies linearly with thearea of the inlet orifice [21] and is typically 0.17 N/m2

for a nozzle 0.14 mm in diameter. Such a pressure ishigh enough for some attenuation (by scattering) of anion beam to occur, whilst it traverses the first cham-ber. These effects have been studied, and correctionswere made in the work described below to compensatefor different species having different scattering cross-sections [21]. Another feature, particularly of samplingflames of H2 + O2, is that the temperature at the tipof the sampling nozzle is much hotter when samplingclose to the flame reaction zone than later in the burntgas. Visual observations indicate that, when samplingthe reaction zone, the temperature at the tip can be as

Fig. 3. Values of 1/R plotted against the reciprocalof the sampling hole diameter: the notation of flames isthe same as that in Table 1; the distances (3 or 20 mm)downstream of the reaction zone in each flame are in-dicated in brackets; chromium sampling nozzles wereused [10].

much as 400◦C above that when sampling downstream.This means that the cooling in the boundary layer isleast, when sampling near a reaction zone. These effectscan be attributed to the flame radicals, H, OH, and O,recombining on the sampling cone, thereby, of course,constituting a sampling perturbation of the flame’s com-position. Another sampling problem is that with theflow fields in Fig. 2 it appears that the effect of suctionon the flame is to shift the point of sampling slightlyupstream [3, 22, 23]. This poses difficulties when at-tempting to match computed and measured concentra-tion profiles along the flame.

RESULTS AND DISCUSSION

The charged species in H2 + O2 flames (see Ta-ble 1) were the H3O

+ ion, its hydrates, and free elec-trons, with mole fractions of no more than 10−8. Whenan alkali metal such as sodium, was added in traceamounts by atomising an aqueous solution of NaCl, thepositive ion Na+ was detected, together with its hy-drates [10]. Measurements were made of [Na+] and[Na+·H2O] along the flame, with interest focused onthe ratio R = [Na+]/[Na+·H2O] whose values were cor-rected for these ions being scattered to different extentsin the first vacuum chamber [21]. Figure 3 shows plots of1/R = [Na+·H2O]/[Na+] at 3 and 20 mm downstreamof the reaction zone of each flame. Measurements are

Mass Spectrometric Sampling of a Flame 521

Fig. 4. Plots of lnK against 1/Tthroat to check theVan’t Hoff equation.

presented for different diameters of the sampling ori-fice used. It is clear from Fig. 3 that the experimentalresults can be fitted by straight lines, except possiblyfor the measurements made with the smallest samplingholes in the hotter flames. Also, Fig. 3 shows that theratio [Na+·H2O]/[Na+] measured at 3 mm downstreamof the reaction zone always exceeds that measured at20 mm. This is probably a reflection of the temper-ature at 3 mm downstream of the reaction zone beingless than at 20 mm (see Table 1). Because, according toFig. 3, more hydrates are detected with a smaller inletorifice, it looks as if some of the monohydrate is formedin the external boundary layer, but not at all signif-icantly in the supersonic expansion. In that case, onewould expect the sampling perturbation to be least withthe largest sampling orifice. The linear portions of Fig. 3were accordingly extrapolated to an infinite hole size,when there are no boundary layer effects, and the sam-ple is altered only by the changes in pressure, density,and temperature for an acceleration to the unit Machnumber at the throat of the sampling nozzle. In thatcase, it will be assumed that the ionic ratios obtainedby the above-described extrapolation refer to this well-defined situation, where the temperature is 2Tbg/(1+γ)when sampling a flame of temperature Tbg.

To test this hypothesis of the equilibrium Na+ +H2O = Na+·H2O freezing at the throat of the sam-pling cone, the equilibrium constant of this reactionK = (1/R)[H2O]throat was calculated from the valuesof 1/R extrapolated in Fig. 3, together with [H2O]throatderived from Table 2. The resulting constants are plot-

Table 3. Value of ΔH0 and ΔS0 for monohydration

of a positive ion I+ in the reaction I+ + H2O = I+·H2O

Ion

−ΔH0,kJ ·mol−1

−ΔS0,J ·mol−1 ·K−1

thiswork

[6] [24] [25, 26] thiswork

[25, 26]

Na+ 111 117 119 100 92 92

K+ 81 73 73 71 89 83

Rb+ 67 — 59 67 84 88

CaOH+ 144 — — — 90 —

SrOH+ 125 — — — 90 —

NO+ 95 — — 77 100 96

ted logarithmically for several positive ions in Fig. 4.It is seen that the CaOH+ ion dominates [10]. Someresults for nickel sampling nozzles have also been in-cluded, but they do not constitute an identifiable anddifferent set of measurements. The data for each ion arefitted by straight lines in Fig. 4, with the slope yieldingΔH0 for monohydration of the ion and the interceptproviding ΔS0. These values are listed in Table 3, for amean temperature of 1600 K, together with other pub-lished values [6, 24] derived from studying flames (butcorrected to absolute zero). Also included are the quiteindependent results of Dzidic and Kebarle [25] and Ke-barle [26], whose values of ΔH0 and ΔS0 refer to 298 K.The values from this work and from [25, 26] come froma second law analysis of measurements for several tem-peratures; the other values [6, 24] were derived using athird law analysis of one measurement of K at a partic-ular temperature.

The errors in the values of ΔH0 from this studyare ±18 kJ ·mol−1. Also, one has to remember thatTable 3 has data for different reference temperatures.Thus, to compare this work with the results of [25, 26],one can use ΔH0

1600 − ΔH0298 ≈ −10 kJ ·mol−1 and

ΔS01600 −ΔS0

298 ≈ −5 J ·mol−1 ·K−1. This means thatthe values of ΔS0 measured in this work have correctmagnitudes. Also, the values of ΔH0 and ΔS0 at aparticular temperature are not expected to vary muchfrom one ion to another; the values of ΔS0 from thisstudy have errors of ±10 J ·mol−1 ·K−1, but all lie be-tween 90 and 100 J ·mol−1 ·K−1. Thus, the above-madekey assumption that monohydration of a variety of pos-itive ions is frozen at equilibrium in the throat of thesampling nozzle and yet does not proceed farther in thesubsequent supersonic expansion seems to be confirmed.

522 Hayhurst

The above-made conclusion means that the timeconstant for hydration of an I+ ion in:

I+ +H2O+M → I+ ·H2O+M (III)

(M is any molecule, is ≈0.2 μs in the flame). Con-sequently, 1/{k × 0.2 × (3.7 · 1018)2} ≈ 2 · 10−7 s ork ≈ 7 · 10−31 mol−2 ·ml2 · s−1 at T = 2000 K. Here k isthe rate constant for three-body hydration of a positiveion, 0.2 is the mole fraction of H2O, and the total con-centration of molecules in the flame at p = 1 atm andT = 2000 K is 3.7·1018 molecules/ml. Such a value of k,estimated for a temperature of 1600 K, is quite accept-able, being of the correct order of magnitude. It mightalso be noticed that one reason why three-body hydra-tion of a positive ion is unlikely to occur very far into asupersonic expansion is because its local rate dependson the square of the total concentration of all species,which, of course, is falling extremely rapidly inside theexpansion duct.

The values of ΔH0 and ΔS0 in Table 3 providea relationship between the equilibrium constant (as isplotted in Fig. 4) and temperature. This means thatthe ion ratios R, as is presented in Fig. 3 for Na+ andreal sampling situations, can be used to estimate thetemperature at the throat of a sampling nozzle of di-ameter d. Let, when sampling a particular flame, thetemperature of the gas entering the sampling nozzle (ofdiameter d) be Td. If that temperature for sampling thesame point in the same flame is T∞ for a hole of infinitediameter, Van’t Hoff’s equation gives

lnK(T∞)

K(T )= −ΔH0

Ru

(1

T∞− 1

Td

).

The ratio of the equilibrium constant at the tempera-tures T∞ and Td is known from the relation

K(T∞)

K(Td)=

R(Td)

R(T∞)

(pH2O)d(pH2O)∞

where (pH2O)d and (pH2O)∞ are the partial pressures ofH2O at the throats with, respectively, finite and infinitediameters. The ratio of these two partial pressures ischaracterised by Td, which accordingly can be derived,knowing the ionic ratios R(Td) and R(T∞), and by solv-ing the above-given equations.

Figure 5 shows the results for the mean coolingof the sample in the boundary layer T∞ − Td plottedagainst the diameter of the sampling nozzle for three dif-ferent flames, each with Ar as a diluent. It must be em-phasized that these boundary layer coolings in Fig. 5 donot include the “aerodynamic cooling” discussed above,so the actual cooling is the sum of the two and conse-quently can add up to over 700 K for a smaller orificewith a hotter flame. The experimental points have beenomitted from Fig. 5, but they seldom deviate from the

Fig. 5. Plots of T∞ − Td versus the diameter of thesampling orifice, which show the mean cooling of thesample in the boundary layer alone (i.e., with the“aerodynamic cooling” being omitted): the measure-ments were made by sampling at a distance of 20mm downstream of the reaction zones of the flames;argon was used as the diluent; chromium samplingnozzles were used [10].

plotted curves by more than 40 K. There is no system-atic variation of the measured values of (T∞ −Td) fromion to ion. This agreement for different ions confirmsthe above-made assumption that monohydration of allthese positive ions freezes at the throat of one of thesesampling nozzles. It is, thus, legitimate to consider anaverage plot for each of the three flames in Fig. 5. Thefall in boundary layer cooling with an increase in thediameter of the inlet orifice is entirely as expected [17].Qualitatively, the plots in Fig. 5 indicate fairly similarcoolings to those calculated previously [17].

It was noticed in Fig. 3 that the overall cooling ina flame diluted with argon exceeds that with nitrogenas a diluent. For these sampling systems, it has beendeduced that the boundary layer thickness is propor-tional to the square root of the kinematic viscosity ofthe gas [16]. However, the kinematic viscosity of nitro-gen is only ≈7% greater than for argon. Likewise, thethermal conductivity of argon is 30% less than that ofnitrogen at room temperature. Given that there was nochange in the velocity of the burnt gas, when nitrogenand argon were interchanged, it appears that flames like2 and 2a in Table 1 are cooled by similar extents in theboundary layer. Hence, the plots in Fig. 5 for cooling inthe boundary layer are approximately true for the cor-responding flames diluted with nitrogen. However, as isseen in Table 2, a flame diluted with argon undergoes a

Mass Spectrometric Sampling of a Flame 523

Fig. 6. Ratio [H3O+ ·H2O]/[H3O

+] measured at thetip of the reaction zone of four different flames versusthe diameter of the sampling orifice: the ratio forflame 1a (see Table 1) is increased by a factor of 10for clarity [10].

greater aerodynamic cooling than one with nitrogen asa diluent, because of the sensitivity of Eqs (1)–(4) to γ.

Hydration of the genuine flame ion, H3O+, turns

out to be more complicated than that of the smallerions in Table 3. Thus, Fig. 6 shows plots of[H3O

+·H2O]/[H3O+, as measured close to the reaction

zone of four flames and plotted against the diameter ofthe Cr sampling nozzle used. Curve 3 for the flame di-luted with nitrogen typical of every flame with this dilu-ent is not showing a minimum, but instead a gradualfall as d is increased. This situation is similar to Fig. 3and also for every ion in Table 3, when the only sam-pling perturbation is caused by cooling in the externalboundary layer. However, the plots in Fig. 6 for flamesdiluted with argon show a minimum, so that with thelarger sampling holes, the perturbation is greater witha yet bigger inlet orifice, so the dominant perturbationoccurs in the supersonic expansion. In such a case, themeasurements with large sampling orifices must be ex-trapolated to a hole size of zero to acquire an indicationof conditions at the nozzle throat. This means that

the value of [H3O+·H2O]/[H3O

+] for the equilibriumstate at the throat of the sampling orifice, when unaf-fected by either boundary layers or supersonic expan-sion, lies below the minimum for the particular flamein Fig. 6. Of course, hydration in the supersonic ex-pansion is conspicuous with argon, but not nitrogen, asa diluent, because γ is then larger. Interestingly, suchan increase in γ results in a slower expansion insidethe sampling nozzle, so that the residence times thereare longer before collisions cease and the flow becomesmolecular. The Li+ ion behaves like H3O

+ [10] in thatminima for plots as in Fig. 6 are obtained for flamesdiluted with argon. Of course, H3O

+ and Li+ have thelargest values of ΔH0 [26, 27] for their monohydration.Also, the rate constant of reaction (III) is larger for Li+

and H3O+ than, e.g., for other alkali metals; this fact

enables these two ions to hydrate at low temperaturesand pressures far down the supersonic expansion. Sucha situation contrasts with that in a fuel-rich flame ofC2H2 + O2 with CO2 as a diluent, when the burnt gashas a relatively low value of γ [27]. This ability to varyγ by changing the diluent from Ar to N2 to CO2 is animportant feature.

It is also worth noting that measurements like thosein Fig. 6 have been interpreted by matching the mea-sured and computed perturbations [11] in the supersonicexpansion, to deduce that the rate constant for H3O

+

undergoing hydration inside the supersonic expansionvia reaction (III) is ≈7 · 10−28 molecule−2 ·ml2 · s−1

at 300 K and ≈ 1 · 10−30 molecule−2 ·ml2 · s−1 at2000 K [28]. This is slightly larger than that estimatedvery roughly above for monohydration of, e. g., Na+.The technique has been also used in [9] to measure therate constants of H + X− → HX + e−, where X is Cl,Br, or I. This reaction occurs during the supersonic ex-pansion and is responsible for fewer halide ions beingdetected than expected.

It is clear that these very significant samplingperturbations have not inhibited thermodynamic stud-ies of ionic species in flames, such as Li+ ·CO [27],Li+ · (H2O)2 [27], and NH+

4 ·H2O [29] and measure-ments of the proton affinities of NH3 [29], CO andCO2 [28]. In each case, a chemical reaction was at equi-librium in a flame and was also perturbed. By extrap-olating the observations to an infinite diameter for thesampling nozzle, the effects of the boundary layer couldbe allowed for and so annulled. Alternatively, if thesample is perturbed only in the supersonic expansion,an extrapolation of the observations to zero diameter forthe inlet hole yields information for a situation wherethe sample is only affected by being accelerated to theMach number M = 1 at the nozzle throat. In addition,much kinetic information has been obtained for reac-

524 Hayhurst

tions occurring in the supersonic expansion, i.e., whenthe inlet orifice is relatively large or γ is has a highvalue.

As for sampling a general flame, it is most impor-tant to repeat every relevant observation using othersampling nozzles with a range of diameters. If the mea-surement is unaffected by changing the size of the inletorifice, there are no sampling perturbations, and thatmeasurement most probably is one made at the undis-turbed temperature of the flame, roughly at five ori-fice diameters [16] upstream of the tip of the samplingprobe. If the measurement, e. g., of the ratio of con-centrations does depend on the size of the hole in thesampling cone, it will be possible to identify the fastexothermic equilibrium being shifted during sampling.Furthermore, it should be possible to deduce whetherthe perturbation occurs in the external boundary layeror in the supersonic expansion. Such information en-ables one to extrapolate the measurements to those fora hole size of either zero or infinity and, thereby, cor-rect for the sampling perturbation. In that case, thecorrected measurements will refer to conditions at thethroat of the sampling nozzle, where the temperature,pressure, and density are all significantly below theirvalues in the flame. It is clear that the test for whetheror not a sample has been perturbed is to simply repeatan observation or measurement using differently sizedinlet orifices.

CONCLUSIONS

There are many different ways in which a gas froma flame might have its composition falsified, when itis continuously sampled into a mass spectrometer foranalysis. This paper has concentrated mainly on per-turbations caused by the sample being cooled: (i) in theboundary layer on the high-pressure side of the sam-pling nozzle, (ii) on being accelerated to the velocity ofsound at the throat of the inlet orifice, and (iii) duringthe supersonic expansion on entering the first vacuumchamber of the spectrometer. To respond to these dropsin temperature, an exothermic chemical reaction musthave a time constant of 1 μs or less for conditions in theflame, i.e., it must be equilibrated in the flame. Cool-ing in the external boundary layer has been shown tobe greater with a smaller inlet orifice. This fact con-trasts with cooling in the supersonic expansion, whichis more pronounced with a bigger sampling hole. Ofcourse, the cooling accompanying the sample being ac-celerated to a Mach number of unity at the throat of theorifice is inevitable and independent of the inlet diame-ter. To test whether or not a particular observation has

been falsified by such cooling, the experiment in ques-tion should be repeated with sampling holes of differentsizes. If the observation or measurement is not affectedby such a change of the inlet orifice, the observation isgenuine; otherwise, the sample has been perturbed. Ifthe perturbation is more pronounced with a smaller in-let hole, the exothermic chemical equilibrium has shiftedand falsified the composition within the thermal bound-ary layer on the exterior of the sampling nozzle. If theperturbation is greater with a bigger orifice, the samplewas perturbed by a chemical reaction proceeding in thesupersonic expansion into the first vacuum chamber.

Measurements of the cooling experienced by a sam-ple in the boundary layers are reported and discussed.The cooling in cases (i) and (ii) can add up to at least700 K; that in case (iii) can be even larger. The im-portance of γ, the ratio of the principal specific heatsof the samples, in determining the extent of cooling isdiscussed. It proved possible to vary γ by changingthe flame diluent from Ar to N2 to CO2. Exampleshave been discussed of thermodynamic parameters be-ing derived for rapid reactions using mass spectrometricsampling, in spite of the perturbations. Also, there areseveral instances of the rate constant being deduced forreactions fast enough to occur during sampling.

REFERENCES

1. J. C. Biordi, “Molecular Beam Mass Spectrometry for

Studying the Fundamental Chemistry of Flames,” Prog.

Energ. Combust. Sci. 3, 151–173 (1977).

2. O. P. Korobeinichev, “The Use of Mass Spectrometry

for Studying the Fundamental Chemistry of Flames,”

Usp. Khim. 49, 945–965 (1980).

3. O. I. Smith, “Probe Sampling from Combustion Sys-

tems,” in Flame Structure and Processes, Ed. by

R. M. Fristrom (Oxford Univ. Press, Oxford, 1995),

pp. 168–195.

4. A. B. Fialkov, “Investigations on Ions in Flames,” Prog.

Energ. Combust. Sci. 23, 399–528 (1997).

5. J. Z. Guo and J. M. Goodings, “Diagnostic Studies

of Flames by Mass Spectrometry,” in Elemental and

Isotope Ratio Mass Spectrometry: The Encyclopedia of

Mass Spectrometry, Ed. by M. L. Gross and R. M. Capri-

oli, Vol. 5 (Elsevier, 2010), pp. 279–290.

6. A. N. Hayhurst and T. M. Sugden, “Mass Spectrometry

of Flames,” Proc. Roy. Soc. London, Ser. A 293, 36–50

(1966).

7. A. N. Hayhurst, F. R. G. Mitchell, and N. R. Telford, “A

Quadrupole Mass Filter Designed for Flame Ionization

Studies,” Int. J. Mass Spectrom. Ion Phys. 7, 177–187

(1971).

Mass Spectrometric Sampling of a Flame 525

8. A. N. Hayhurst and N. R. Telford, “Mass Spectromet-

ric Sampling of Ions from Atmospheric Pressure Flames.

I: Characteristics and Calibration of the Sampling Sys-

tem,” Combust. Flame 28, 67–80 (1977).9. N. A. Burdett and A. N. Hayhurst, “Kinetics of For-

mation and Removal of Atomic Halogen Ions X− by

HX + e− ↔ H + X− in Atmospheric Pressure Flames

for Chlorine, Bromine and Iodine,” Proc. Roy. Soc. Lon-

don, Ser. A 355, 377–405 (1977).10. N. A. Burdett and A. N. Hayhurst, “Hydration of Gas-

Phase Ions and the Measurement of Boundary-Layer

Cooling during Flame Sampling into a Mass Spectrom-

eter,” J. Chem. Soc., Faraday Trans. I 78, 2997–3007

(1982).11. A. N. Hayhurst and N. R. Telford, “The Occurrence of

Chemical Reactions in Supersonic Expansions of a Gas

into a Vacuum and its Relation to Mass Spectrometric

Sampling,” Proc. Roy. Soc. London, Ser. A 322, 483–

507 (1971).12. J. Guo, J. M. Goodings, A. N. Hayhurst, and S. G. Tay-

lor, “A Simple Method for Measuring Positive Ion Con-

centrations in Flames and the Calibration of a Nebu-

lizer/Atomizer,” Combust. Flame 133, 335–343 (2003).13. J. M. Goodings, C. S. Hassanali, P. M. Patterson, and

C. A. Chow, “A New Flame-Ion Mass Spectrometer:

Chemi-Ionization of Lanthanum Observed in Hydrogen–

Oxygen–Argon Flames,” Int. J. Mass Spectrom. Ion

Processes 132, 83–96 (1994).14. A. F. Ashton and A. N. Hayhurst, “Kinetics of Colli-

sional Ionization of Alkali Metal Atoms and Recombina-

tion of Electrons with Alkali Metal Atoms and Recom-

bination of Electrons with Alkali Metal Ions in Flames,”

Combust. Flame 21, 69–75 (1973).15. C. J. Butler and A. N. Hayhurst, “The Kinetics of Gas-

Phase Ionisation of an Alkali Metal, A, by the Elec-

tron and Proton Transfer Reactions: A + H3O+ →

A+ ·H2O + H and AOH + H3O+ → AOH+

2 + H2O

in Fuel-Rich Flames at 1800–2250 K,” J. Chem. Soc.,

Faraday Trans. 94, 2729–2734 (1998).16. A. N. Hayhurst, D. B. Kittelson, and N. R. Telford,

“Mass Spectrometric Sampling of Ions from Atmo-

spheric Pressure Flames. II: Aerodynamic Disturbance

of a Flame by the Sampling System,” Combust. Flame

28, 123–135 (1977).17. A. N. Hayhurst and D. B. Kittelson, “Mass Spectromet-

ric Sampling of Ions from Atmospheric Pressure Flames.

III: Boundary Layer and Other Cooling of the Sample,”

Combust. Flame 28, 137–143 (1977).

18. P. A. Skovorodko, A. G. Tereshchenko, O. P.

Korobeinichev, D. A. Knyaz’kov, and A. G. Shmakov,

“The Perturbations of a Flame by a Sampling Probe.

I. Peturbations of the Flow’s Gasdynamic Structure,”

Khim. Fiz. 25, 23–32 (2006).19. S. D. T. Axford and A. N. Hayhurst, “The Sampling of

Ions from an Atmospheric Pressure Flame into a Vac-

uum Chamber,” Bull. Soc. Chim. Belg. 99, 451–459

(1990).20. J. Troe, “Detailed Modeling of the Temperature and

Pressure Dependence of the Reaction H + O2(+M) →HO2(+M),” Proc. Combust. Inst. 28, 1463–1469 (2000).

21. N. A. Burdett and A. N. Hayhurst, “Mass Spectromet-

ric Sampling of Ions from Atmospheric Pressure Flames.

IV: Scattering Processes in Molecular Beams from Su-

personic Expansions,” Combust. Flame 34, 119–134

(1979).22. A. C. Yi and E. L. Knuth, “Probe-Induced Concentra-

tion Distortions in Molecular-Beam Mass-Spectrometric

Sampling,” Combust. Flame 63, 369–379 (1986).23. P. A. Skovorodko, A. G. Tereshchenko, O. P.

Korobeinichev, D. A. Knyaz’kov, and A. G. Shmakov,

“The Perturbations of a Flame by a Sampling Probe. II.

Peturbations of the Distributions of Concentration for

the Components,” Khim. Fiz. 25, 33–41 (2006).24. A. N. Hayhurst, “Alkali-Metal Ions and their Monohy-

drates in the Gas Phase,” in The Alkali Metals, Special

Publ. 22 (The Chem. Soc., London, 1967), pp. 139–146.25. I. Dzidic and P. Kebarle, “Hydration of the Alkali Ions

in the Gas Phase. Enthalpies and Entropies of Reactions

M+(H2O)n−1 + H2O = M+ · (H2O)n,” J. Phys. Chem.

74, 1466–1474 (1970).26. P. Kebarle, “Ion Thermochemistry and Solvation from

Gas Phase Ion Equilibria,” Annu. Rev. Phys. Chem. 28,

445–476 (1977).27. A. N. Hayhurst and S. G. Taylor, “The Stabilities of the

Gas-Phase Ions Li+ ·H2O, Li+ · (H2O)2 and Li+ ·CO,

as Measured by Mass Spectrometric Sampling of Fuel-

Rich Flames of C2H2 + O2,” Phys. Chem. Chem. Phys.

5, 1610–1618 (2003).28. A. N. Hayhurst and S. G. Taylor, “The Proton Affini-

ties of CO and CO2 and the First Hydration Energy of

Gaseous H3O+ from Mass Spectrometric Investigations

of Ions in Rich Flames of C2H2,” Phys. Chem. Chem.

Phys. 3, 4359–4370 (2001).29. A. N. Hayhurst and S. G. Taylor, “The Ions in Fuel-

Rich Hydrogen Flames with Added Ammonia: Measure-

ments of the Proton Affinity of NH3 and the Enthalpy

of Monohydration of NH+4 ,” Phys. Chem. Chem. Phys.

4, 561 — 570 (2002).