Mobility distribution of acetone cluster ions

Pergamon

MOBILITY

J. Aerosol

Sri., Vol. 27, No. 2, pp. 175-190, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0021.X502/96 %1.5.00 + 0.00

DISTRIBUTION

OF ACETONE

CLUSTER

IONS

Jyrki M. Mlkell,*vt Vilho Jokinen,* Terhi Mattila,$ Ari Ukkonen$ and Jorma Keskinenf *University of Helsinki, Department ‘Tampere

University

of Technology,

of Physics, P.O. Box 9, FIN-00014 University of Helsinki, Finland Physics Department P.O. Box 692, FIN-33101 Tampere, Finland

(First received 21 March 1995; and in jnal form 13 September 1995)

Abstract-Mobility distributions of both positive and negative cluster ions in acetone rich air were studied. A bipolar radioactive charger was used to irradiate air which contained acetone vapour within a wide range of concentrations (_ lot-300,000 ppm). The ion mobility distributions were measured with two instruments: a differential mobility analyzer (DMA) and a time-of-flight mobility spectrometer (TOF). Low concentrations of acetone (100-1000 ppm) appeared to set the mean mobility of the positive ions to 1.3-1.5 cmZV-‘s-’ and also to increase the unimodality of the spectrum, whereas the negative ion spectrum was affected only by acetone concentrations higher than some 1000 ppm’s. With even higher acetone vapour concentrations the mobilities of both the positive and negative ions were seen to decrease, apparently due to increased vapour molecule attachment onto the ions, and approaching each other, indicative of a thermodynamical and polarity-insensitive behaviour. The concentration range of acetone was, thus, concluded to consist of two separate ranges. The “low concentration range” is dominated by ion-molecule reactions of acetone and other impurities. At the “high concentration range” the ions were seen to behave like “pre-nucleation embryos” as expected according to ion-induced nucleation theory. At high concentrations, the large acetone cluster ions may already be considered close to charged ultrafine aerosol particles.

1. INTRODUCTION

Electrical mobilities of ions in air have been measured since the beginning of the century (e.g. Zeleny, 1901, 1929; Mache, 1903). It has been realized that the chemical composition of air (including low concentration impurities) affects the ion mobilities. At relatively low “trace’‘-concentrations of some vapours, formation of certain characteristic ions by ion-molecule reactions has been observed (see e.g. Huertas et al., 1971; Eiceman and Karpas, 1994). On the other hand, if condensable vapours are present in sufficiently high concentrations, ions are known to initiate particle formation by lowering the energy barrier of cluster growth. In connection with these cases the mobility distribution has been measured by Bricard et al. (1972) (SO2 and H,O in air), Cabane et al. (1976) (HZ0 and “impurities” in air) and Thomson and Iribarne (1977) (Hz0 with NaCI). Ions in air are electrically charged molecules, molecular clusters or aerosol particles. Atmospheric ions are generated by background radiation. Primary positive ions and free electrons are first produced by an ionization process of gas molecules. The free electrons become rapidly attached to electronegative air molecules forming negative ions. The primary positive and negative ions are not stable, but form product ions by fast ion-molecule reactions. Very often the ion-molecule reactions finally produce cluster ions with sizes of 5-30 molecules. Water vapour molecules and (polar) impurity molecules in the system have a tendency of clustering around the ions (Good et al., 1970). The final size of the ion is usually determined mainly by the concentration of water vapour and impurities in the system. From a variety of studies in ion mobility spectroscopy it is well known that several ions have characteristic narrow peaks, since the ion chemistry tends to produce only specific ion clusters due to a favoured structure of the ion. In this paper, we have chosen to work with

‘Author

to whom correspondence

should

be addressed. 175

J. M. Mlkeli

176

et al

acetone ((CH,),C=O), a widely used organic solvent known to strongly affect the ion mobility spectrum (see e.g. Huertas et al., 1971; Watts, 1991; Mattila and Keskinen, 1993; Makela and Jokinen, 1994). The behaviour of ions is mainly determined by their electrical mobility, which is generally much higher than that of aerosol particles. The mobility of traditional aerosol particles (diameter above 5 nm) is typically below 0.08 cm2 V- ’se ’ and mainly a function of particle size only. The electrical mobility of ions, on the other hand, is dependent on, e.g., ion size and structure. Ions with a mobility above 0.5 cm2 V-’ s-l are usually characterized as small ions (Israel, 1971). Ions below 0.5 cm2 V ’se’ are called large ions, respectively. In the literature, the distinction between these two categories is not always clear. In some systems the amounts of vapours and impurities can be high enough to produce larger cluster ions and ultrafine particles via nucleation and condensation processes. Above some known size (critical cluster size) the molecular clusters can stay stable already without an electrical charge. Large ions are usually treated as charged aerosol particles and most often also neutral particles of same size exist in the system. For historical reasons also concepts such as intermediate ions or Langevin ions are sometimes used to describe some cases. All in all, when dealing with nanometer sized particles, one should keep in mind that different definitions of the particle concept exist. The purpose of this study is to scan the entire concentration range of acetone vapour and follow the behaviour of the ion mobility distribution. The results are thought to be applicable to studies on the ion processes in aerosol chargers as well as to studies on ion-induced nucleation. We use two different methods to measure the mobility of small ions. On the other hand, we use time-of-flight ion mobility spectroscopy (TOF/IMS), which is a well-established technique to measure mobilities of small ions (Cohen and Karasek, 1970; Eiceman and Karpas, 1994). On the other hand, we use standard differential mobility analysis in the 1 nm size range. It has already been realized that the so-called Vienna-type Differential Mobility Analyzer is capable of operating well below 3 nm especially if a Faraday cup electrometer is used as a detector (Winklmayr et al., 1991; Make12 and Jokinen, 1994).

2. THEORETICAL 2.1. On mass us mobility

relationship

The relationship between electrical mobility and particle size (i.e. diameter) was discussed by, e.g., Porstendijrfer (1968) Kilpatrick (1971) Bricard et al. (1972) Hoppel (1978) Tammet (1992, 1995) and Ramamurthi et al. (1993). The electrical mobility of the particle is conventionally given by

(1) where i is the number of elementary charges carried by the ion, e0 is the elementary charge, D, is the diameter of the particle, 4 is the dynamic viscosity of the fluid and C,(D,) is the slip correction factor taking account of relation between ion radius and mean free path 2 (65.3 nm in air in NTP) of the gas molecules (Millikan, 1923; Fuchs, 1964): C,(D,)

= 1+ 2

Cl.246 + 0.420e-0.87(“~‘2”)]. P

Here the diameter D, is the so-called “mobility equivalent diameter”. It is generally known that this so-called Millikan-Fuchs relationship no longer applies below 2 nm. It is clear that the whole concept of particle diameter is not valid in these small cluster sizes. For this reason, in this paper, we will deal with electrical mobility and not ion diameter. Readers should note that, in any case, we are dealing with charged cluster ions of diameters well below 2 nm.

Mobility distribution of acetone cluster ions

177

The relationship between mobility and mass is also somewhat uncertain. In this work we use a fit to Kilpatrick’s data for ions in nitrogen (Kilpatrick, 1971, given within the range of 35.5-2122 atomic mass units) to convert from atomic mass to mobility: 2 = exp[ -O.O347(ln(mi))’ - 0.0376 ln(mi) + 1.46621,

(3)

where mi denotes ion mass in amu’s, and 2 ion mobility in cm2 V- ’s-l. Kilpartick’s data is one of the most frequently used data in studies on ion mass vs mobility (e.g. Cabane et al., 1976; Bricard et al., 1977; Bohringer et al., 1987). Since the data were originally obtained at p = 760 mmHg of nitrogen and T = 2OO”C,there is an ongoing discussion about proper conversion of Kilpatrick’s data to the atmospheric conditions (e.g. Bohringer et al., 1987; Tammet, 1995). However, there exists no generally accepted correction for the data, nor a new reliable set of data on mass-mobility relationship. Ion structure is also known to affect the mobility (Kim and Spangler, 1985). On the other hand, we do need to use some relationship to be able to interpret our measurements in this study. Therefore, we use Kilpatrick’s data but keep in mind their limitations. 2.2. Ion kinetics After the primary ionization process, the time required for stable ion formation is inversely proportional to reaction rate constant and trace gas concentration. For a proton transfer reaction: A+H+B

:

A+B+H,

(4)

where k is the reaction rate constant, [B] is the concentration of a polar impurity, e.g. acetone molecules and z is the reaction time. Reaction rate constants are usually in the order of 10-i’ cm3 s-l. Therefore, with trace gas concentrations in the order of ppm the stable ions are formed in less than a millisecond. However, if one considers the results of, e.g., Huertas et al. (1971), several slower reactions may take place at least for air ions, even above 1 s time scale. The proton affinity of acetone is rather high (823 kJmol_‘, Lias et al., 1984), so one could assume that the ion-molecule chemistry will take place very soon. The rate constant k for a proton transfer reaction between H,O+ ion and acetone vapour molecule is in the order of 3 x 10e9 cm3 s- 1 (Lagg et al., 1994). Thus, the reaction time for the lowest acetone concentration in this study (N 100 ppm) would be around 0.1 ps, which can be considered fast with respect to our instrumentation. The probable structure for acetone ion given by Mohnen (1977) is (CH3COH.H+CH2)~(H20)~(CH3COCH3),_i

(7)

accompanied with a suggestion of n - 1 = 2. This structure would be understandable on the basis of the proton transfer reactions between H30+ and acetone vapour molecule, such as given above. However, no concentration dependence for the cluster composition was given by Mohnen. At low concentrations of acetone both the structure and the mobility of the ions in air may also depend on small concentration impurities that cannot be controlled. 2.3. Calculation

on cluster size distribution

For the “high concentration range” of acetone, we may consider the thermodynamical cluster formation. To obtain the cluster size distribution we calculate the Gibbs free energy

178

J. M. Makela

0

(b) ChJStW

Gibbs Free Energy

(a) 40

20

et al.

Size Distribution

0.8

--/

!

1

0.6 2 .P 5

F Z ._ -20 %

m

-40

m

?? ??

.

m

.g 0.4 ii m t P

. 0.2 I

?? ??

-60

-80

L -1-l0

2

4

6

8

OL0

10

* 2

-

4 8 6 No. of Acetone molecules

No. of Acetone Molecules

* 10

Fig. 1. Calculated distribution of acetone cluster ions according to classical ion-induced nucleation theory. T = 20°C and C,,,,,,, = 10,OOOppm. Two different ions are assumed as the initial ion: (W) HsO+ and (0) CH,CO.H+CH,: (a) Gibbs free energy AYi as a function of number of acetone molecules in the cluster; and (b) cluster size distribution as a function of number of acetone molecules in the cluster

for cluster component

formation according to the classical ion-induced system (Thomson, 1906, Thomfor and Volmer,

nucleation 1938):

theory

for a single

(8) = -nkTIn~+4xr2y+ Ps

i&(1

-:)(t-$2

(9)

where n is the number of acetone molecules in the ion, Ap is the change of chemical potential from gas phase to liquid phase, $1 , is the bulk liquid surface tension, LZZis the surface area of the cluster, 4 is the charge of the ion (in %-units), a0 is the vacuum permittivity, E, is the relative dielectric constant (relative permittivity) of the cluster, Y is the radius of the cluster, and r. is the original initial radius of the ion, k is Boltzmann constant and T is the temperature in Kelvins. Note that in reality the values for y and E, may differ appreciably from the bulk values of the substance (Thomfor and Volmer, 1938). When the acetone molecules are gathered around the initial ion, the mass of the ion mi can be expressed as m, = nm, + mo,

(W

molecule and m. is the mass of initial ion where m, is the mass of acetone (CHJCO. H+CH2). To transform the radii Y and Y,, on the right-hand side of equation (9) into a function of acetone molecule number n in the cluster we need to use relationships: 4,$

= -nm, + -m0 Pa

PO

and

$7U$ =-,

m0

PO

(11)

where pa = 0.7899 gcmP3 (CRC) is the bulk liquid density of acetone and p. is the bulk liquid density of the ion compound. For the molecule mass of acetone mat a value of m, = 58.05 amu (amu = atomic mass unit) has been used. For the saturation vapour pressure y, of acetone, a value of 184.4 mmHg has been used at T = 20°C and for E, and y for acetone values of 21.45 (Conway, 1952) and 0.0233 N rn- ’ (Timmermans, 1950), respectively.

Mobility distribution of acetone cluster ions

179

At a temperature of T = 20°C and for an acetone concentration of 10,000 ppm we obtain a Gibbs free energy distribution as shown in Fig. la. Here we have used two positive initial ions namely H,Of (m) and CH3C0 .H+CH2 (0). In addition to acetone ion we have also made a calculation with H30+. Taking into account the proton affinities, this is an improbable composition, but it was used to simulate the case where the initial ion differs from the clustering molecule. In these two alternative cases the following values for initial ion properties have been used: with central ion being H,O+ (H), then p0 = 0.9982 gcmP3 and m, = 19.02 amu are used, with central ion being CH3C0. H+CH, (0) then values for acetone p. = 0.7899 gem-3 and m. = 58.05 amu have been used. The distribution for the actual ion clusters can be obtained from a probability form (e.g. Castleman and Tang, 1972):

f(n) - exp

Agdn) -F

1 .

[

(12)

The final cluster distribution is shown in Fig. lb, where a normalization of total cluster number to unity has been used. In these figures the filled squares (m) refer to central ion being H,O+ and the open squares (0) to CH3C0. H+CH2. Note that in the latter case in Fig. 1b (open squares, CH3C0. H+CH2 as the central ion), the central ions already contain one acetone molecule which generates a difference in Fig. lb but which difference vanishes when studying, e.g., mass distribution of the clusters. This result will be discussed later in connection with Fig. 6. 2.4. Mobility

correction

at high acetone concentrations

At low acetone concentrations the actual concentration of acetone is varied in the range 10-1000 ppm, i.e. it is a trace concentration. Since Kilpatrick’s data was obtained in nitrogen, equation (1) should be applicable to some extent, provided that Kilpatrick’s data show by any means a right trend. However, since the cluster size calculations are carried out as far as 400,000 ppm (= 40% of volume), we have to consider a correction procedure to the calculated ion mobilities at high acetone concentrations. This is because the acetone vapour molecules will already have a significant contribution to the mobility via the collisions with the ions. Using Blanc’s law for the diffusion coefficient in a mixture of vapours (Blanc, 1908) and, furthermore, for electrical mobility (Revercomb and Mason, 1975) we get 1 Zmirture

=F+?, a*r

ac

(13)

where X,ir and x,, are the mole fractions of air and acetone in the mixture and Zair and Z,, are the ion mobilities in pure components, respectively. Blanc’s law (equation (13)) is assumed to be valid since the ion concentrations are relatively low compared to vapour concentrations in all cases and since no significant gradients of either of the vapour components are assumed to exist. We have no relevant data of Z,, for all the ion mobilities where the calculation is carried out, so we use the Chapman-Enskog relation for the functional mass mobility dependence (e.g. Revercomb and Mason, 1975): (14)

where 0, is an average collision cross-section. Thus, the ion mobility Z,, in pure acetone for the calculation purposes may be obtained from ion mobilities Zair in “pure air”:

(15)

180

J. M. Miikelii er al

where M,, and Mai, are the molecular masses of acetone and “air” molecules. One of the simplest ways to estimate the collision cross section 0, between ion and a gas molecule, is the standard “rigid-sphere” model (e.g. Eiceman and Karpas, 1994) where Qn is expressed simply as geometrical collision area of two rigid spheres: Qn = Then the correction

factor (l/0,+,)/( -

1

R D,ac

-=A

I

I

nD,air

4n(rion

l/Q,, RD

+

rgasmokcud2.

air) in equation

air

(16)

(13) can be calculated

as (17)

a,,.~

(18)

where mron and Pion are the mass and the density of the ion, Mai, and M,, are the masses of the gas molecules in pure gas. Note, that here the densities of one gas molecule (Pair = 0.875 gem-3, pat = 0.7899 g cm- 3, are only artificial quantities (bulk liquid density used) to obtain the radius of the collision sphere of the gas molecule. 3. EXPERIMENTAL

Inside the Differential Mobility Analyzer (DMA) the particles of one polarity are driven by an electric field between two cylindrical electrodes and transported through a particle free sheath air flow. A specific narrow mobility range is directed into a small slit at the end of the inner electrode and drawn out of the instrument. By changing the voltage between the cylinders and using an appropriate detector, the whole mobility distribution can be measured (see e.g. Knutson and Whitby, 1975). Instruments similar to DMA were used for ion mobility measurements in the beginning of this century, having usually significantly larger flow rates. A schematic picture of a Vienna-type DMA with supporting flow arrangements is shown in Fig. 2a. The residence time of the particles inside the DMA is rather long, roughly few hundred milliseconds both in the analyzer and in the inlet tubes before the analyzer. Practically the age of measured particles is often in the order of 1 s. Development of time-of-flight (TOF) Ion Mobility Spectrometry as an analytical method began in the early 1970s (e.g. Karasek, 1974; Hill et al., 1990; Eiceman and Karpas, 1994). In the TOF method the ions travelled a well-defined distance in an electric field and the arrival time spectrum onto electrode was measured via an electrical current. From the TOF spectrum, the mobility distribution can be determined. The advantages of TOF as an analytical method are operation at normal pressure and a good mobility resolution. The TOF instrument of the present study is a cylindrical drift tube with axial electric field (Mattila et al., 1993). A schematic of the drift tube with necessary flow arrangements is presented in Fig. 2b. Sample gas is ionized by a radioactive 241Am x-source in the reaction region. The ions are pulsed electrically with a shutter grid to drift region, where ions travel a well-defined distance in an electric field and are separated according to their different electrical mobilities. As the output signal, one obtains ion current versus arrival time (TOF spectrum). The mobility distribution can be furthermore determined from the TOF spectrum. Most often only small ions with mobilities above 0.5 cm2 V- ’s ’ are measured. With TOF only relatively young ions are studied (ion age in the order of tens of milliseconds). Considering the measurement principle of DMA, it is apparent that when the ions in acetone-rich air are introduced into the DMA analyzer, where the sample air flow is suddenly diluted with a 5- or lo-fold larger clean air flow, the particles or ions under study will most probably experience some changes. This is a clear disadvantage of the DMAmeasurement and has been well realized and solved, e.g., in the case of humidity (McMurry and Stolzenburg, 1989). For this reason, we ensured the acetone rich conditions also in the

Mobility

distribution

of acetone

cluster

0

FCE

ions

181

Critical orifice Absolute filter Active carbon filter Pressure regulator

Compressor air supply

TOF

-_----_-----------___.

IMFCI PC

Oil filter

PA

Pressurized

air

Micro filter

EX

Excess

Rotameter

HV

High voltage source

Mass flow controller

A/D

Analog to digital converter

Personal computer

GP

Shutter grid pulse

(b) Fig. 2. The measurement instruments with supporting flow arrangements: (a) DMA: RI = 2.5 cm, Rz = 3.29 cm, L = 10.89 cm, V = 0.1-5 V; (b) TOF: L, = 5.5 cm, Ld = 6.8 cm. Positive polarity: E, = 176 Vcm-‘, Ed = 608 Vcm-‘. Negative polarity: E, = 188 Vcm-‘, I?, = 595Vcm-‘.

182

J. M. Miikeli

et al

sheath air flow. The set-up for air ion and acetone ion measurement using DMA and a Faraday Cup Electrometer was already presented in Fig. 2a. The sample gas was introduced through a ring shaped 1.84 mCi 241Am x-charger into the DMA. To support the acetone rich conditions in both sample and sheath air flows, we used a by-pass saturator for a single line which was divided into two separate lines, one for sheath air (Qsh) and one for aerosol inlet (Qa). A valve in the aerosol flow was used to control the balance between Qsh and Qa. The concentration of acetone was controlled by varying the surface area of the acetone pool in the by-pass system. The concentration of acetone was determined based on the readings of the consumption of acetone during an entire measurement period (typically 0.5-2 h) and flow rates (QSh + Qa). The flow rate measurement was carried out by an automatic soap-bubble spirometer (Gilibrator, Model PN # 80268, Gilian Instrument Corp.). For all the experiments we used compressed air followed by absolute particle filters, an active carbon filter and a silica gel filter. Using the following flow rates: sheath air Qsh = 25.0 1min- ‘, sample air (aerosol air in) Qa = 2.7 lmin-‘, and with the known dimensions of the Vienna DMA (R, = 2.5 cm, R2 = 3.3 cm and L = 10.9 cm), we obtain a residence time of 340 ms for the sample ions to pass through the DMA analyzer. For TOF measurements, the arrangement presented in Fig. 2b was used. Acetone was introduced to the sample air in a by-pass saturator. Concentrations below saturation were set by controlled dilution of the saturated flow with clean air. Proper operation of the saturator was ensured by measuring the total consumption of acetone during a measurement. We used sample flow rates between 0.2 and 1 1 min - ’ for the TOF-instrument. These flow rates are low enough to ensure that the gas velocity inside the instrument was less than 0.25% of the ion drift velocity. We can only estimate the residence time of the ions in the reaction region, as the mobility in this region is unknown. Assuming a value of 1 cm2 Vi s- *, we end up with approximately 30 ms. Exact values of the electric field in both the reaction and drift region are given in Fig. 2b. When comparing DMA and TOF, it is clear that the whole principle of sampling is different for the two instruments. Both the time scales of the ions to be measured and the measurement arrangements are different as well. Additionally, the accurate shape of DMA transfer function is not generally known at high mobilities.

4. RESULTS

AND

DISCUSSION

Most of the measurements on acetone ions using DMA and TOF were carried out separately at different institutes. As an example, the measurements on the mobility distribution of the positive ions at 20,000 ppm of acetone in air are shown in Fig. 3. The open squares refer to DMA measurements (signal current from electrometer at DMA voltage referring to known mobility), and the thick dashed line refers to TOF response. Here the values of time of flight from TOF have been directly converted to ion mobility and the response has correspondingly been normalized by ‘d In 2’ at each mobility channel. As far as resolution is concerned, we can see a large difference between DMA and TOF signals. However when the DMA data reduction is carried out, the situation becomes somewhat better. The thin dotted line represents simulated data which was obtained by using a best-fit lognormal mobility distribution. The lognormal shape was originally chosen due to its general use in aerosol science. In fact, the obtained mobility distribution is fairly narrow (GSD less than 1.20) and most probably nearly all available functions (Gaussian, Gammadistribution, etc.) would do to obtain a reasonable agreement. For the simulation, the diffusion broadened transfer functions of DMA according to Stolzenburg (1988) were used to describe DMA performance in the high mobility range. The actual best-fit lognormal distribution (dN/d In 2) for DMA measurement is shown as a solid line in Fig. 3. By comparing the DMA inverted result with the TOF raw data, one can see that in spite of fairly good agreement, a slight difference still exists. The difference may arise because of

Mobility

distribution

of acetone

cluster

ions

183

Positive ions, 20000 ppm acetone

1 Ion Mobility

2

3

[cm*A/s]

Fig. 3. Raw data on positive ions at 20,000 ppm of acetone in air. (0) DMA measurements (~. -. -) TOF raw data. The thin dashed line (~ ~ -) stands for simulated response data of DMA which refer to the best-fit mobility distribution as obtained via data reduction procedure. To obtain this simulated data a lognormal mobility distribution shown by (-) has been used.

different time scales of the measurements by the two instruments. It is understandable that different ions dominate at different time stages of the charge transfer and ion-molecule reaction scheme. A reason for the differences may, as well, arise from the differences of the data reduction processes and maybe from the ambiguity in, e.g., kernel functions of the instruments. As known, no well-established information on the DMA transfer function shape at high mobilities is presently yet available. One may get an overview of the system by looking at Figs 4a-c, where the DMA reduced distributions and the TOF raw data for positive ions have been plotted for acetone free air and for two different acetone concentrations (1200 and 20,000 ppm). For clean air (Fig. 4a), a large difference between these two spectra exist. For the DMA measurement, a mean mobility of N 0.90 cm2 V 1 s- ’ is obtained whereas TOF data show the main peaks at 1.3 and 1.5 cm2 V’ s-l. Similar spectra are obtained also for extremely low acetone concentrations, respectively. It must be kept in mind, that the measurements were carried out at separate locations using different background gases, and due to the measurement principles, the measurements have a different time scale as well. In TOF spectrum one can clearly see fine structure indicative of presence of several ion species. This is apparently also due to the better resolution of the TOF. It is expected that the aged ions measured by the DMA should differ from those measured by TOF (Huertas et al., 1971). In Fig. 4b we see spectra at 1200 ppm of acetone, where the two spectra are already approaching each other. Now DMA already gives a mean mobility of 1.21 cm2 V- 1s- ‘, but the main peak of TOF spectrum remains at 1.5 cm2 V-l sp ‘. Some fine structure is still visible in the TOF data. For the 20,000 ppm case, the mean mobilities of the two spectra are already very close to each other. Furthermore, the fine structure of TOF data has almost

.I. M. Make15 et al.

84

Acetone

800 - 0

PPm

TOF

1,4oo 1200 ppm

I\

1,200 t

2,500

5

In Air

L

1,000 500

0

0.5

1

2

3

Ion Mobility [cmWs] Fig. 4. Inverted DMA-data (-- ) with TOF raw data (-) presented at three different acetone concentrations: (a) 0 ppm; (b) 1200 ppm; and (c) 20,000 ppm. In (b) and (c) also the theoretical prediction for mobility distribution has been presented by 6’s, which have been connected with each other by a thin dotted line to guide the eye.

disappeared, showing now an almost unimodal structure. Note, that the unimodality increases with increasing vapour concentration. To obtain a comparison with theory, we calculated ion mass distributions (such as in Fig. lb) for acetone concentrations 1200 and 20,000 ppm (assuming CH3C0. H+CH2 as a central ion). The mass distributions were transformed into mobility distributions directly by calculating mobility values corresponding to each ion mass using Kilpatrick’s relationship (equation (3)). Furthermore, an appropriate normalization of the theoretical points (y-scale) was used to obtain additional comparability. As can be seen at 1200 ppm in Fig. 4b, the breadth of the theoretical spectrum is quite similar to the TOF spectrum,

Mobility distribution of acetone cluster ions

185

FCE

Fig. 5. Set-up for combined measurement by both DMA and TOF. Acetone rich conditions are set at the upper pressure (2.3 bar) of the flow system.

whereas at 20,000 ppm one could consider the theoretical spectrum being broader than the experimental one. It has to be emphasized that the theoretical spectrum is only a set of discrete values, whereas in fact, the ions are assumed to have n-mer fluctuation around the mean composition during the measurement process. Thus, this kind of comparison is to be considered only qualitative. Obviously, there may have been small amounts of trace-impurities which would lead to differences on small acetone concentrations. When acetone is added into the system, one obtains positive ion spectra as is also seen in Fig. 4. Acetone vapour once again turns the distribution into a narrow peak. Since there already exists a number of ion spectrometer studies at trace-concentrations (see e.g. Eiceman and Karpas, 1994), we do not wish to discuss all the possible processes affecting on the ion spectrum at low acetone concentration. However, in the aerosol community the mobility values of small ions (e.g. in charging calculations) are often treated as something “universally fixed”. Therefore, we want to make a note about the variability and dynamics of the ion mobility spectrum. We also carried out DMA and TOF measurements for negative ions in acetone-rich air. Here roughly 1000 ppm of acetone started to have a significant effect on the shape of the TOF spectrum, whereas for positive ions the lowest effective concentration was already around 100 ppm. A concluding presentation for the positive and negative ion mobilities at different concentrations of acetone will be given further in this chapter. In addition to separate measurements by DMA and TOF we wanted to perform a comparison measurement with both instruments at the same conditions, which, in practice, means same measurement location, same carrier gas, same vapour and same radioactive source. Only in this way we can ensure the same conditions such as impurities, etc. For the comparison method, the two instruments were coupled with each other by a short tube (see Fig. 5). The TOF electrode on the back wall of the drift tube was replaced by a fitting piece which, furthermore, was connected with DMA outlet (see Fig. 5). The flow

J. M. Mlkela

186

rr nl

Acetone

In Air

0 +

,,/

? ,,L!

_a

1,000 100

100,000 10,000

Acetone Concentration

1

,ooo,oo

[ppm]

Fig. 6. Mean mobilities of positive and negative “acetone ions” as a function of acetone concentration throughout the system: (0) DMA on positive ions; (0) DMA on negative ions; (0) TOF on positive ions; (+J TOF on negative ions. A dashed line refers to calculation with use of Kilpatrick’s data (equation (1)) for H,O+ as a central ion, solid line to CH,CO’ H+CH2 as a central ion. The two separate open squares (0) denote for DMA-data from combined measurement on positive acctonc ions.

rate through the TOF drift tube was now automatically arranged to be the same as the DMA sample inlet flow. The radioactive Am-241 was generating the ions just as previously for TOF alone. The ions were captured from the irradiation zone by the reactor voltage V, (=2 kV). This time, however, L’, = 0. This means that the age of the ions under consideration will be higher than in TOF’s case. The unipolar ions will be transported to the DMA by the flow, which will take time in the order of 1 s, totally. Thus, the ions measured by DMA are not identical to the ions measured by TOF alone. In this case it is a disadvantage of DMA measurement, since sampling will always take a finite time. However, the use of reactor field to pick up only unipolar ions is assumed to eliminate some disturbing processes such as recombination. A concluding scheme of all the measurements is presented in Fig. 6. Experimental DMA values were obtained as described previously with Fig. 3. The basis of the TOF data reduction scheme was to fit a unimodal lognormal mobility spectrum to the measured, using the instrument resolution function and a suitable fitting routine FMINS (a Matlab routine, Matlab, 1992). The criterium of the minimization was least-squares criterium. For the resulting distribution a mean mobility as well as a GSD may be determined. In the calculation of the theoretical curves, thermodynamics have been used to obtain cluster distributions such as shown in Fig. lb. These mass distributions of the clusters have been converted into mobility distributions using the formula based on Kilpatrick’s data (equation (3)). Finally, the values for geometric mean mobility of these distributions have been plotted as lines in Fig. 6. A dotted line refers to calculation with H30+ as a central ion and dashed line for CH3C0. H+CH2 as a central ion. These two lines go together in the high

Mobility

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of acetone

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187

concentration range indicating that thermodynamics is not eventually sensitive on the kind of the initial ion. Both of the curves have been corrected by the acetone concentration effects (equations (13)-(18)). The order of the correction due to increased acetone vapour concentration becomes relevant only above 30,000 ppm, and contributes only roughly 0.1 cm2V-‘s-1 at 100,000 ppm. Without correction the theoretical mobility values would be higher than what is seen in Fig. 6. Thus, the correction is of right direction, but not sufficiently to bring the theory and experiments together. The uncertainty in the mean mobility value obtained by DMA can be estimated to be around 0.04 cm2 V-i s-i at maximum, mainly due to transfer function uncertainties as well as the inaccuracies of the flow rate values and DMA length. The possible systematic error in the TOF mobility values arises mainly from errors in the measurement of the effective drift chamber length, the maximum error being on the same order as for the DMA. However, the relative TOF mobility values are expected to have an accuracy better than 1.0%. The uncertainty in the acetone vapour concentration is mainly caused by the error in the temperature inside the saturator. Assuming an inaccuracy of l.O”C this would lead to an error of roughly 5%. As was discussed earlier in this paper, we have restrained ourselves to use only Kilpatrick’s (1971) original interpretation of the mass-mobility data. For example, the interpretation of Kilpatrick’s data by Tammet (1995) will eventually move the theoretical curves in Fig. 6 upwards, and thereby separate the theory even further from experiments. In the low concentration range, the differences between DMA and TOF data are partly attributed to variations in trace chemistry caused by non-identical air supplies. Moreover, discrepancies between theory and experiments are understandable, since the thermodynamical theory should not work at low concentrations. Therefore, complete agreement among all the datapoints was not even expected at low concentrations. Note that the comparison measurement of DMA and TOF performed with the same clean air supply eventually gave the same mean mobilities for positive ions. Thus, a moderate agreement between the two devices was achieved when working in the same conditions. The measurements of DMA and TOF for negative ion mobilities give similar values with lower acetone concentrations but for higher concentrations the data differs. The determination of acetone concentration was checked carefully. It seems extremely unlikely that an error of a factor of two would have occurred. Furthermore, the DMA spectra seemed to follow the lognormal shape quite nicely. Thus, no disturbing effects due to, e.g., free electrons are assumed to have occurred. The discrepancy between DMA and TOF data cannot be explained by the authors. Quite interestingly, at the higher concentrations of acetone, the mobility of negative ions by TOF will eventually decrease and approach similar values as for positive ions. This behaviour may be expected from the thermodynamics. However, an agreement with the calculated values was not achieved. As was already discussed, the true relationship between the mass and the mobility of ions is more or less uncertain. One can, however, see that the slope of the calculated curve finally reaches the slope of the measurements for positive acetone ions. For general interest we performed an additional study by DMA, where acetone vapour was introduced into the DMA aerosol inlet flow only. The result is seen in Fig. 7. The mean mobility of the ions rises from around 1.1 cm2 V-i s-l to a value of 1.37 cm2 V-’ s- ‘. Since the sheath air flow more or less dilutes the sample air, the data has also been presented scaled to the total concentration in the DMA analyzer, as seen by open diamonds in Fig. 7. This result is to show that the behaviour is similar to the lower concentration range in Fig. 6. It is interesting to notice that a plateau in the mobility of positive ions exists as a function of acetone concentration. Based on Figs 6 and 7, one could realize that the location of the This is plateau is somewhere at - lOOO-10,000 ppm of actual acetone concentration. apparently comparable to the acetone concentration of - 104-lo5 ppm in the sample flow (at the flow rates used). In principle, one could think of generating positive ions with quite well-defined mobility and rather narrow distribution by this way.

J. M. Makela

188

Acetone

in

er (11.

DMA Sample

0

Air Flow

0

V V

+

0

??

0

+

V

.. .

10

+

1oo:ooo

100

10,000 1,000 300 3,000 30,000 30 Acetone Concentration [ppm]

Fig. 7. Mean mobility of positive “acetone ions” as a function of acetone concentration in sample air (+). Measurements carried out by DMA with following flow rates: Qsu = 25 Imin~‘, Q_ = 2.7 1 min-r. The open squares (0) denote for actual concentration in the analyzer, when the dilution effect by sheath air has been taken into account.

5.

CONCLUSIONS

The aim of this paper was to describe the behaviour of air ion mobilities throughout a large range of concentrations of one polar vapour. Possible applications concern both understanding of ion processes in aerosol chargers and studies on ion-induced nucleation. Some compounds with a high proton affinity have a tendency to dominate the positive ion kinetics in an ionized system such as an aerosol charger. Because of this high proton affinity, the ion-molecule reactions form characteristic cluster ions with well-defined size and electrical mobility. In this paper one such compound, acetone, was studied. The mobility spectrum of positive ions in “clean air” changed drastically when a small concentration of acetone was added into the system. The mobility of the positive ions was found to be dependent on acetone concentration. A similar behaviour was found out for negative ions but only in the acetone concentration range above -2000 ppm. The ion mobilities observed at low acetone concentrations were by no means in agreement with the cluster calculation from classical ion-induced nucleation theory. This is not very surprising, since ion-molecule reactions are expected to dominate at low concentration range and, thus, nucleation theory is not even expected to be valid. The importance of the result obtained at low concentrations range lies elsewhere, namely in instrumentation and application to aerosol chargers. On the basis of these results, one might discuss the use of trace impurities to “adjust” the ion mobility for instrument calibration purposes or in order to control the charging properties as already suggested by Mattila and Keskinen (1993). This applies especially in the range between low and high acetone concentrations, where the possible impurity effects tend to be suppressed by the high proton affinity of acetone.

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At high concentrations of acetone, both positive and negative ions were seen to behave like “pre-nucleation embryos”. The overall result may be partly explained by the thermodynamics of molecule clustering around ions. The more acetone in the air, the larger the ions and the smaller the mean mobility. This behaviour of the mean mobility of the ion as a function of acetone concentration is explainable by the classical theory for nucleation on ions. It is noteworthy that the TOF data on ion mobilities approach the same values independent of polarity of the ions when the acetone concentration is high enough. According to the classical theory, the ion mobility should not depend on the central ion. This, in fact, speaks for the validity of the classical theory, at least to some degree. The uncertainties in the relationship between the electrical mobility and mass of the ions, however, prevented us from fulfilling a complete comparison between experimental results and the theoretical predictions. New reliable data on mass vs mobility relationship would be urgently needed for related studies. With the modern ion instrumentation (e.g. mass spectrometers) it would be quite possible. All in all, two different ranges of acetone concentration apparently exist. At the lower end, the ion mobility is more or less determined by the kinetics of the system. In the higher concentration range, thermodynamics dominate and an increase in the vapour concentration results in vapour molecule attachment on ion clusters. Thereby a decrease in mean ion mobility is observed for both polarities. Note, that a mobility of 0.5 cm2V-‘s-1 is generally assumed to correspond to a particle size of roughly 2 nm. Then we are already approaching quite large cluster sizes at the higher concentrations of acetone. In principle, what we see here, is an intermediate region, in a sense a “transition regime”, between microscopic and macroscopic phenomena. One of the measurement instruments, namely the time-of-flight spectrometer (TOF) was initially known to give reliable data on the ions. The other instrument, DMA, was seen to observe similar trends for ion mobilities as TOF. It has to be remembered that the DMA itself is designed for a significantly lower mobility range, where it actually should be mainly used. Nevertheless, it clearly has a potential to trace the cluster growth from ions to particles. Scanning through a wide mobility range would be essential for a thorough study on ion-induced nucleation process, a pre-stage of which was obviously seen in this study. Acknowledgement-Support

of this work by the Academy

of Finland

is gratefully

acknowledged.

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