Mass and size determination of nanometer particles by means of mobility analysis and focused impaction

Aerosol Science 34 (2003) 79 – 98 www.elsevier.com/locate/jaerosci

Mass and size determination of nanometer particles by means of mobility analysis and focused impaction J. Fern'andez de la Moraa , L. de Juana , K. Liedtkeb , A. Schmidt-Ottc;∗ a

Mechanical Engineering Department, Yale University, New Haven, CT 06520-8286, USA University of Duisburg, Institute of Combustion and Gas Dynamics, D-47048 Duisburg, Germany c Delft University of Technology, Faculty of Applied Sciences, Particle Technology, Julianalaan 136, NL-2628 BL Delft, Netherlands b

Received 11 October 2001; accepted 5 August 2002

Abstract Particles in the size range of a few nanometers are characterized by means of a di5erential mobility analyzer (DMA) of the Eichler type in tandem with a focusing impactor with electrostatic blowing. One application of the DMA-impactor combination is determination of particle mass mp without knowledge of the relation Z(dp ) between particle mobility Z and diameter dp . With Z(dp ) known, also the size and density p of spherical particles can be determined. A mobility versus diameter relation Z(dp ) for the range of a few nanometers is derived from the literature. It considers the e5ect of the :nite diameter d of gas molecules, neglected in conventional studies. According to this relation, plots of Z −1=2 versus mp1=3 yield straight lines, and the intersection with the Z −1=2 axis is linearly related to the e5ective diameter d of the carrier gas molecules. Experimental data recorded with the DMA-impactor combination for silver particles are consistent with this relation. The same applies for values from literature for fullerenes and proteins. For air, d is approximately 0:53 nm, not far from the 0:6 nm estimated by Tammet (1995). The particle density p is derived from mp and the diameter inferred from Z(dp ). Measurement of p on silver particles showed that charging devices may introduce contamination leading to formation of an adsorbed layer on the particles, reducing their measured density. The DMA-Impactor combination applied has su>cient resolving power to observe occurrence of di5erent shapes of particles prepared by vapor condensation. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Mobility; Impactor; Mass spectrometer

∗

Corresponding author. Tel.: +31-15-278-3577; fax: +31-15-278-4452. E-mail addresses: [email protected] (J. Fern'andez de la Mora), [email protected] (L. de Juan), [email protected] (K. Liedtke), [email protected] (A. Schmidt-Ott). 0021-8502/03/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 1 - 8 5 0 2 ( 0 2 ) 0 0 1 2 1 - 0

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Nomenclature An A5 A6 B d dm dM dp I Imax k m p pa p50 q Qa S∗ T U Za Z  p

Wetted area of the fullerene molecule Cn Surface of pentagon Surface of hexagon Mechanical mobility E5ective molecular diameter for collisions with particles Mass equivalent particle diameter Mobility equivalent particle diameter Geometric particle diameter Impactor current Maximum impactor current Boltzmann constant Molecular mass Gas pressure Atmospheric pressure Critical impactor pressure at 50% capture e>ciency Particle charge Volume Iow at atmospheric pressure Critical Stokes number Absolute temperature Mean Iow velocity in impactor nozzle Electrical mobility at atmospheric pressure Electrical mobility Accommodation coe>cient Particle density (mean)

1. Introduction A suitable quanti:er of size for a particle of mass mp and density p is the mass diameter, which is de:ned as the diameter of a sphere of that density with the same mass. In principle, mp is directly measurable in a mass spectrometer, although few such instruments suitable to cover the full range from 1 to 10 nm exist (for several notable exceptions see Hendricks, 1962; Krohn, 1961; Zimmerman, Malinowski, Naher, Frank, & Martin, 1994; Alvarez, Vezmar, & Whetten, 1998). The particle density p is also measurable, for instance, via electron di5raction, as demonstrated by sophisticated studies on the increase of p with size in the nanometer range (El-Shall & Edelstein, 1996). El Shall et al. demonstrate that compression of the lattice constant occurs for particles smaller than 2 nm, but the use of bulk density values is appropriate above that. In the present paper we will show that the combination of a di5erential mobility analyzer (DMA) with an inertial spectrometer can be used for mass determination over a wide range. In the free-molecule range, i.e. at sizes much smaller than the mean free path of the gas molecules, the electrical mobility of a particle suspended

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in a gas is a key descriptor, closely related to its wetted area (Fern'andez de la Mora, 2002). On the other hand, particle size rather than mobility is the principal magnitude governing many of the unusual properties of nano-materials. Since the dimensions of a particle are di>cult to determine directly, especially in the nanometer size range, a reliable relation between size and mobility is of vital interest for nano-particle characterization. Such a relation will be derived from literature and corroborated experimentally. It will enable us to determine an e5ective particle density from the combined DMA and impactor measurement. Deviations of the measured density from the density of the particle material will be interpreted as a deviation from sphericity or reveal the presence of contaminants.

2. A mobility-size relation in the nanometer regime The sharp contrast between the di>culties involved in the determination of size and the straightforward measurement of an electrical mobility has led to the widespread use of the concept of a “mobility equivalent diameter” (Kasper, 1982), which we will denote here by dM . It is based on an established relation between the diameter and the electrical mobility Z of a sphere, which takes the following form in the free-molecule range (Friedlander, 1977; Tammet, 1995): Z = 0:441

q(kT=m)1=2 ; pd2M

(2.1)

where p; T and m are the pressure, absolute temperature and molecular mass of the gas, k is Boltzmann’s constant and q is the electrical charge on the particle. This relation has been widely tested for spherical particles, but rarely at diameters below 10 nm. The serious problems involved in using Eq. (2.1) in the region of a few nanometers have been addressed by Tammet (1995), who calls for three main corrections accounting for: (i) the e5ective diameter d of the gas molecules; (ii) charge-induced dipole interaction, and (iii) the transition between the inelastic collisions typically arising in gas–particle impacts and the elastic collisions appropriate for the interaction between atoms or between small molecules. Tammet (1995) argues that the last two e5ects enter into the picture at diameters smaller than 1 or 2 nm. The dominant modi:cation required in Eq. (2.1) above 2 nm therefore consists simply in the substitution dM = dp + d:

(2.2)

In Tammet’s work d = 2 + 2h has two components. 2 is the diameter of the molecules of the suspending gas based on viscosity data, and estimated as 0.373 and 0:369 nm for N2 and air at 300 K, respectively. The “extra distance” 2h, estimated as 0:23 nm, is introduced to account for experimentally observed mobilities of various molecular substances. It could perhaps be interpreted as the di5erence between the e5ective hard sphere diameter of the gas molecules inferred from viscosity measurements (gas–gas collisions) and the corresponding value for gas–particle collisions. Here we will refer to d simply as the e5ective diameter of the gas molecule for its collision with the particle, or just the gas molecule diameter. This quantity is d ∼ 0:37 nm + 0:23 nm = 0:60 nm in Tammet’s estimate. The e5ect of a non-zero gas molecule diameter and mass is easily incorporated

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for the case of elastic collisions via the Chapman–Enskog (C–E) theory. Its result for a hard-sphere interaction is ZHS =

3q(kT=2)1=2 ; 2p(d + dp )2

=

mmp : m + mp

(2.3)

In reality, collisions of gas molecules with particles are not necessarily elastic. The gas may be brieIy adsorbed on the particle surface before coming o5, leading to a larger drag and a smaller Z. In the limit of a large ratio mp =m, this e5ect is accounted for in the model of Epstein (see Friedlander, 1977) in terms of a momentum accommodation coe>cient , or fraction of the impinging gas molecules which transfer all their momentum to the surface before being di5usely re-emitted: ZE =

3q (kT=2m)1=2 : 2pd2p (1 + =8)

(2.4)

Epstein’s expression coincides with Eq. (2.1) for the case of an accommodation coe>cient =0:911, though this number must have a certain dependence on the gas, the surface, and temperature. The coe>cient 0.441 in Eq. (2.1), from which the value  = 0:911 originates, is not precise. It depends on the sum of two quantities a + b appearing in the drag law, which Tammet (1995) takes as 1.70 while Friedlander (1977) gives it as 1.657. In the present study, we will be concerned with singly charged particles with diameters above 2 nm, for which Tammet (1995) has argued that polarization e5ects are negligible and collisions in air are inelastic. The mobility should therefore be given by the following hybrid between the C–E (2.3) and the Epstein (2.4) results Z=

3q (kT=2m)1=2 2p(d + dp )2 (1 + =8)

(2.5)

and the main indeterminacy is the value of the quantity d. In rigor, m should be substituted by  in Eq. (2.5) (as in all binary collision processes), but the di5erence is negligible at particle sizes above 2 nm. To our knowledge, Eq. (2.5) has never been veri:ed directly against experiments before the present study.

3. Verication of the Z (dp ) relation by using literature data on large molecular species Our test of Eq. (2.5) will be based on experimental values of mp and Z taken from the literature. Assuming a spherical shape, the diameter can be derived from the particle mass mp through dp = (6mp =p )1=3 :

(3.1)

Here p is the particle density. Strictly speaking, Eq. (3.1) de:nes the mass equivalent diameter dM , so that it implicitly contains the assumption dM = dp , justi:ed for spherical particles. Combining Eqs. (2.5) and (3.1) leads to a linear relation between Z −1=2 and mp1=3 . Thus, if such

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experimental curves are straight lines for an aerosol of spherical particles of constant density, the proportionality Z ∼ (d+dp )−2 predicted by Eq. (2.5) will be directly con:rmed. The extrapolation of such a line to zero mass determines d, provided that the value of  = 0:91 (see Section 2) is correct. We test this approach :rst by means of various published data, and then with new experiments using nano-particles formed by condensation of silver vapors (Section 4). For air, these measurements will yield the value of d ∼ 0:53 nm, not far from Tammet’s estimated 0:6 nm. Tammet has extracted his value of the “extra distance” h from a series of data for various ions with known mobilities and masses. The problem with such data is that the ionic densities are unknown, which leaves dm incompletely speci:ed. Tammet hence makes the provisional assumption that the density is the same for all the data, and determines it together with h through a best :t condition. However, many of these ions have widely di5erent natures and hence densities. Data for a series of less heterogeneous substances would be more desirable for such a :tting procedure, and, in fact, at least two such series have become available recently. One involves the fullerenes from C30 to C70 . The other comprises a diversity of globular proteins. Although the analysis of these data in terms of shape and density still involves some ambiguity, this uncertainty is nonetheless much narrower than in earlier work. 3.1. Fullerenes We reinterpret the fullerene measurements of Gotts, von Helden, and Bowers (1995). These data are taken in He, whose low polarizability justi:es ignoring ion-induced dipole attraction even at sub-nanometer diameters. The approximation m =  is justi:ed as well due to the small mass of the He atom. A fullerene molecule consists of n carbon atoms positioned at the corners of a polyhedron composed of 12 pentagons and a variable number of hexagons. De:ning the “surface” of the polyhedron by the centers of n carbon atoms, its total area is given by An = 12A5 + (n − 20)A6 =2

(n ¿ 20);

(3.2a)

where A6 = 6a2 =(4 tan(=6)) and A5 = 5a2 =(4 tan(=5)) are the surface of a hexagon and a pentagon, respectively. The edge length a is the distance between two adjacent C atom centers. The area of the polyhedron may be more conveniently written as An = (n − n0 )A6 =2

(n ¿ 20)

(3.2b)

with n0 = 20[1 − tan(=6)=tan(=5)] = 4:1069:

(3.2c)

Given that the free-molecule mobility of isometric particles of high enough symmetry is equal to the mobility of a sphere with the same surface area (Fern'andez de la Mora, 2002), Eq. (2.5) can be modi:ed via dp2 = An . Under the assumption  = 0 for the molecule–noble gas collisions, we obtain for the mobility of the polyhedron: Z −1 =

√ 2p {[A6 (n − n0 )=2]1=2 + d }2 : 1=2 3q(kT=2m)

(3.3)

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J. Fern6andez de la Mora et al. / Aerosol Science 34 (2003) 79 – 98 0.50

1/Z-1/2 [(Vs)1/2/cm]

0.48 0.46 0.44 n0 = 0 0.42

n0 = 4.107

0.40 0.38 5

6

7 (n-n0

8

9

)1/2

Fig. 1. Mobilities Z of the fullerenes Cn in the range 30 ¡ n ¡ 70 represented in the form Z −1=2 vs. (n − n0 )1=2 (using data from Gotts et al., 1995).

If Eq. (3.3) is applied to fullerene molecules (where the polyhedron is de:ned by the atomic centers), the correction d should include the diameter of the carbon as well as the He atoms. According to Eq. (3.3), a plot of Z −1=2 versus (n−n0 )1=2 should be a straight line, whose intersection with the Z −1=2 axis yields d. The data of Gott’s et al. (1995) (extracted from their published graphs) are shown in Fig. 1 for two values of n0 together with the two corresponding linear :ts. The case n0 = 0 simply ignores the fact that some of the faces are pentagons. With Z in cm2 =V s, these √ of the −fullerenes − 1=2 1=2 :ts yield Z = 0:21971 + 0:032175 n and Z = 0:23920 + 0:030731(n − 4:107)1=2 , respectively. U as for graphite, the theoretical slope is 0.0336 (0.0330 for a = 1:39 A, U as in Taking a = 1:42 A, aromatic compounds). Thus, it agrees with the :t reasonably well in both cases. The disagreement would be made worse (even larger theoretical slope) by taking some of the collisions to be inelastic ( ¿ 0), lending force to the hypothesis that  = 0 for particles with sub-nanometer diameters, at least in helium. The d values obtained from the two linear :ttings by extrapolating to n = n0 are 0.597 and 0:650 nm for n0 = 0 and n0 = 4:107, respectively. Both diameter shifts are comparable to the dimensions of the fullerenes themselves. They are almost identical to twice the Lennard–Jones U in graphite, as compiled by Mesleh, Hunter, Shvartsburg, radius for He–C collisions (He–C=2:98 A Schatz, & Jarrold, 1996). The reasoning leading to Eq. (3.3) oversimpli:es the collision surface, which resembles the surface of a mulberry rather than a polygon. A far more rigorous analysis of the mobility problem may be found in Mesleh et al. (1996). Nevertheless, the fullerene data of Gotts et al. together with our simple polygon-model represent a strong corroboration of Eq. (2.5). Note that the value d ∼ = 0:6 nm resulting from theory as well as experiment applies to fullerenes in helium. The numerical similarity with Tammet’s estimation for the diameter of air molecules is purely coincidental. 3.2. Large electrospray and MALDI ions Until recently, large involatile ions could rarely be brought into a gas. The situation has changed thanks to the availability of electrospray ionization (Fenn, Mann, Meng, Wong, & Whitehouse, 1989)

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85

and matrix assisted laser desorption ionization (MALDI, Karas and Hillenkamp, 1988). The second technique has been used mainly (though not exclusively) for producing ions in a vacuum. However, it is possible to :rst mass analyze these ions in a mass spectrometer, and then inject them into a gas cell to determine their mobility (von Helden, Hsu, Kemper, & Bowers, 1991; von Helden, Wyttenbach, & Bowers, 1995a, b). Both matrix-assisted laser desorption ionization and electrospray ionization have been developed to transfer molecular ions from a liquid into a gas. These molecular species can be so large as to cover the entire size range from less than 1 nm up to beyond 20 nm. Wittmer, Chen, Luckenbill, and Hill Jr. (1994) :rst used electrospray ionization to measure the mobilities of a variety of large singly charged species (such as octadecyl4 –N+ ) as well as multiply charged cytochrome c ions (mp = 12; 300 amu), though without direct identi:cation of the charge state with a mass spectrometer. von Helden et al. (1995a, b) have investigated the mobilities of polyethylene glycols (fairly non-spherical) with direct measurement of both mp (up to almost 1000 amu) and Z (in He). Their earlier study (1991) on the mobility of carbon clusters, including fullerenes, used conventional ionization techniques, but is also of great interest. These authors have had considerable success in predicting electrical mobilities for a variety of species in He, some with fairly complex geometries. Several groups have studied electrosprayed multiply charged protein ions with direct measurement of both Zp and mp . (Clemmer, Hudgins, & Jarrold, 1995; Shelimov and Jarrold, 1996, 1997; Shelimov, Clemmer, Hudgins, & Jarrold, 1997; Clemmer and Jarrold, 1997; Liu, Valentine, Counterman, Hoaglund, & Clemmer, 1997, etc.; see also the related review by Fernandez de la Mora, 2000). Rosell, Loscertales, Bingham, and Fern'andez de la Mora (1996) and Seto, Okuyama, de Juan, and Fern'andez de la Mora (1997) have used electrospray to measure the mobilities of a variety of substances as massive as dodecyl4–N+ , with dM up to 2 nm. Their results are in approximate agreement with those of Wittmer et al. (1994). Most relevant here is the work of (Kaufman, Skogen, Dorman, Zarrin, & Lewis, 1996a,b; see also Kaufman, 1998), where large singly (rather than multiply) charged ions of globular proteins were produced via electrospray followed by partial neutralization. They do not measure the mass, but :nd approximate agreement between the mass diameter (p = 0:8 g=cm3 ) and the mobility diameter dM , indicating that their gas phase ions must have been closely related to the proteins in their liquid sample. The poorer agreement found for the smallest species investigated, insulin (mp = 5730 amu), may be an indication that the :nite crust of solvent impurity attached to the ions is not negligible when dM ¡ 3:5 nm (Kaufman, 2000). Notice that the data of Kaufman et al. (1996a,b) must be corrected from an error in the voltage measurement not reported in the original paper (Kaufman, Skogen, Dorman, Zarrin, & Lewis, 1996a,b). The corrected data are shown in Fig. 2 as plots of Z −1=2 versus mp1=3 . When  = 0:91 (see Section 2), the linear regression :t shown corresponds to p = 1:28 g=cm3 and d = 0:53 nm. The latter value is not far from the 0:6 nm estimated by Tammet for air. The di5erence between the density of 1:28 g=cm3 in our :t versus the 0:8 g=cm3 inferred by Kaufman et al. is mainly due to their identi:cation of the mobility diameter dM and the mass diameter dm . If the latter is equal to the geometrical diameter, dp , this is equivalent to saying d=0 (Eq. (2.2)). Several more recent published data for globular (Kaufman et al., 1998) as well as non-globular species (Mouradian et al., 1997) are not included in the :gure. Also missing are the very recent data of Bacher et al. (2001), which yield d = 0 and p ∼ 0:6 g=cm3 . The later value is too far from the established density of protein crystals (p ∼ 1:3 g=cm3 ), perhaps indicating a very high level of hydration (Fernandez de la Mora, 2000).

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10 Hard sphere, α = 0.91; d = 0.53nm self-charging UV charger ρp = 5.86 g/cc neutralizer Proteins ρp = 7.9 g/cc

Z-1/2 (cm2/Vs)-1/2

7.5

ρp = 10.5 g/cc 5

ρp = 1.28 g/cc

2.5

0 0

0.02

0.04

0.06

0.08

0.1

0.12

m1/3 (fg1/3) Fig. 2. Z −1=2 versus m1=3 plot for the protein data of Kaufman, Skogen, Dorman, Zarrin, & Lewis, (1996a,b), and our p own silver data. The :tted straight lines are based on Eq. (2.5). The three sets of silver data correspond to three di5erent charging schemes. Self-charging denotes particles nucleated on ions emitted naturally by the heated silver wire acting as the vapor source.

4. Determination of mass, mobility, size and density from DMA and impactor measurements One purpose of this chapter is to demonstrate the application of a DMA-impactor combination for particle mass mp determination. The experimental relation of mobility and mass will then be used for further corroboration of the Z(dp ) relation (2.5). This relation will then be used for experimental determination of the particle density, using the volume equivalent to dp and mp . Deviations from the material density will reveal contamination and/or non-sphericity. Agreement with the material density under clean conditions will represent another veri:cation of Eq. (2.5) and the value used for the e5ective molecular diameter d. The fullerene data under Section 3.1 is already a strong support for Eq. (2.5). The data previously compiled by Tammet and those obtained by Kaufmann and colleagues for proteins verify the proportionality Z ∼ 1=(d + dp )2 predicted by Eq. (2.5) and yield a diameter shift d between 0.5 and 0:6 nm for particles suspended in air. However, d is inferred in both cases from the hypothesis that all the particles in the series have the same density and shape, which is unlikely to hold strictly for the heterogeneous materials used in both cases. In addition, the protein data discussed have a certain ambiguity in the mobility, associated to the limited resolution of the DMA used. Furthermore, these two data sets are non-overlapping. The largest mass included by Tammet is below 3000 amu, while the lowest protein mass datum exceeds 5000 amu, and is unreliable due to clustering with solid residues from the electrospray drops. It is therefore highly desirable to create similar new sets of

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87

data for particles of :xed shape and density, ideally covering continuously the size range from 2 nm up to at least some 10 nm. For metallic particles produced by condensation of the vapor, the density and shape variables are expected to be better de:ned. We have therefore measured the mass and mobility for silver clusters in the range of sizes above 2 nm. 4.1. The DMA impactor combination as a nanoparticle mass spectrometer In the following we explain, how the particle mass can experimentally be determined using a DMA-impactor combination. Such a combination has formerly been used with aerosols in the nanometer size range for the purpose of determining their size and density (Fern'andez de la Mora, Hering, Rao, & McMurry, 1990; Fern'andez de la Mora & Schmidt-Ott, 1993; Hering & Stolzenburg, 1995; Schleicher, KVunzel, & Burtscher, 1995), or to infer their shape, including fractal analysis of agglomerates (KVutz & Schmidt-Ott, 1990; Schleicher, KVunzel, & Burtscher, 1995). Here we note that the anomalous particle densities observed in several such studies were due in a large measure to improper identi:cation of the particle diameter with the Millikan diameter, i.e. d = 0. We also show that a DMA-impactor combination can be used for an absolute determination of particle mass, i.e. for mass spectrometry, independently of whether or not the relation Z(d) is known. This result was advanced by Fern'andez de la Mora, de Juan, Eichler, and Rosell (1998) in their review of an earlier unpublished version of the present paper. Some of these conclusions have been mentioned independently by Loscertales (2000). Using Tammet’s (1995) Z(d) relation to reinterpret earlier hypersonic impactor data, Loscertales shows that they collapse on top of each other in excellent agreement with theory. An impactor is a device in which an aerosol is accelerated through a nozzle to form a jet that impinges on a plate. Particles above a certain aerodynamic size impact on the plate. The threshold condition separating collected from escaping particles can be expressed by S ∗ = mp

Z U ; q dn

(4.1)

where dn is the nozzle diameter and S ∗ is the critical Stokes number of the impactor under the operating conditions (Iow velocity, pressure). The Iow velocity through the nozzle is U=

4Qa pa d2n p

(4.2)

with the volume Iow at atmospheric pressure Qa . pa is atmospheric pressure and p is the impactor pressure (behind the nozzle). In the free molecular regime, the mobility Z at p is related to the mobility at atmospheric pressure, Za , through pa (4.3) Z = Za : p If the pressure p = p50 is determined, at which the transition between particle impaction and escape occurs, i.e. the pressure, where 50% of the particles are collected, Eq. (3.1) yields the product of the mechanical particle mobility B = Z=q and the particle mass mp . When a DMA precedes an impactor, the former :xes the electrical mobility Za , and mp =q can directly be determined. For nanoparticles, where q of a charged particle is rarely di5erent from unity, mp is unambiguously

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Fig. 3. Experimental set-up (MFC = mass Iow controller, HV = high voltage, HWG = hot wire generator).

determined, independently of particle shape. Note that this result is independent of the relation Z(dp ). It is interesting that for multiply charged particles, the DMA-impactor combination yields the charge over mass ratio, exactly as a mass spectrometer. Its range, however, is far wider than that of most mass spectrometers. Its resolution is smaller than the resolution typical for mass spectrometers, but not necessarily smaller than the one of existing mega-Dalton mass spectrometers (Alvarez et al., 1998). For wire generated silver particles 5 nm in diameter, the impactor step width corresponds to a mass resolution of about 15% (see Section 4.2), but di5erent discrete masses can typically be distinguished within one or a few percent. 4.2. Experiment for measurement of mp and Z The experimental set-up is shown in Fig. 3. The aerosol is generated by a heated silver wire as done earlier for instance by Schmidt-Ott, Schurtenberger, and Siegmann (1980). Luczak (1996) has given a detailed description of the generator. 2 l=min of Ar was highly puri:ed to a contaminant level around 0:1 ppm (purity 7.0) by a Messer Griessheim multisorb unit. Alternatively, nitrogen of purity 5.0 was applied. The gas was passed through the heated wire generator and immediately sampled into a tube (4 mm inner diameter). In initial experiments, the silver wire was held in a brass housing with teIon insulator pieces. In some of the experiments we made use of the fact that a fraction of the particles carries charge from production. In other experiments, the silver aerosol was irradiated with either a UV lamp or via passage through a 85 Kr source of alpha radiation (TSI Neutralizer 3077) or alternatively a 210 Po radioactive source. It was then introduced into an Eichler DMA (Eichler, 1997; Fern'andez de la Mora et al., 1998). The monodisperse fraction of this aerosol sampled out of the DMA was then fed into a focusing impactor with electrostatic blowing, which

J. Fern6andez de la Mora et al. / Aerosol Science 34 (2003) 79 – 98

89

Fig. 4. Collection e>ciency vs. Impactor pressure I=Imax (p) for 5:05 nm silver particles with pure and contaminated carrier gas.

incorporates a variety of improvements over its predecessors (Fern'andez de la Mora, 1996; de Juan, 1997; de Juan and Fern'andez de la Mora, 1998). It functions as a size spectrometer by scanning over the pressure p in the chamber upstream the nozzle (at :xed aerosol mass Iow rate), and measuring the associated current I of collected particles. p varies inversely as the average jet velocity U , so that each particle size undergoes a sharp transition between being captured and escaping at a certain critical value of p (Fig. 4). A repelling voltage is established between the nozzle and the collector in order to reduce deposition of sub-critical particles by Brownian motion (de Juan et al., 1997). This feature is essential to achieve high resolution with the rather small particles of interest to this work. A voltage jump anywhere in the path of the aerosol would lead to large losses and has been avoided. The inner DMA electrode and the aerosol exit line leading to the impactor were held at ground. The outer DMA electrode was held at a potential VDMA identical to that of the inlet aerosol line, which was maintained at only a few volts below that of the silver wire. This di5erence is required to extract the self-charged particles. The power source used to heat up the wire had therefore to be Ioated at a voltage near VDMA . This was achieved with the design of Liedtke (1998). Since the combination of the DMA and the impactor yields the ratio mass over charge, it is essential to establish unambiguously that the particles analyzed are singly charged. The presence of multiply charged particles of the same mobility in the output of the DMA manifests itself clearly through the appearance of several steps in the I (p) curve produced by the impactor (Fern'andez de la Mora, 1996). The absence of a second step in the measurements on silver particles demonstrates conclusively that all the particles are singly charged with the three charging schemes used. The critical pressure p50 , from which the particle mass will be inferred, is the value of p where I (p) has reached 50% of the total step height. The mass resolution achievable with the

90

J. Fern6andez de la Mora et al. / Aerosol Science 34 (2003) 79 – 98

Fig. 5. Curves of normalized impactor current versus pressure for silver particles using the sources as bipolar chargers as well as self-charging. The particle diameter is 6:94 nm.

85

Kr and

210

Po radioactive

DMA-impactor combination depends in principle on the resolutions of both instruments. The resolving power of the DMA is much larger than the impactor’s, however. This was established by varying the DMA’s resolution by changing the aerosol to sheath gas ratio, which did not show any e5ect on the slope of the I (p) curves. For example, the step width Wp=p is between 7% and 8.5% for silver particles with mobility diameters between 4 and 8 nm. Here Wp is de:ned as the interval where the capture e>ciency varies from 80% to 20%, i.e. Wp=p = (p80 –p20 )=p50 . From Eqs. (4.1) to (4.3) it follows that the mass resolution Wmp =mp is related to the broadness of the I (p) curve, Wp=p, through Wmp =mp ≈ 2Wp=p:

(4.4)

The mass resolution for silver particles 4 –8 nm in diameter was thus 14 –17%. Note that the precision with which the impactor actually determines the mean mass mp is not given by Wm=m but depends on the precision with which p50 can be determined as the value at half the step height. This relative error is much smaller than Wm=m for most applications and depends on the signal-to-noise ratio, given by the particle concentration and measuring time. The noise level in the present study (as in Figs. 4 and 5) was such that the mean mass could be determined with a precision of a few percent. Calibration of the impactor consists in experimental derivation of the critical Stokes number S ∗ , by applying well-characterized particles. Dioctil(2-Ethylhexyl)Sebacate (DOS) and Dioctyl(2-ethylhexyl) Phtalate (DOP) oil droplets of known density (p = 0:912 and 0:985 g=cm3 , respectively) with mobility diameters dM between 17.7 and 116:3 nm were used. Monodisperse fractions of these droplets were selected by a DMA (TSI Inc.) and fed into the impactor. In this size range, the size-mobility relation is well established. The Za (dM ) relation given by Friedlander (1977) accurately yields dp =dM because the inIuence of a :nite gas molecule diameter is negligible here. Using the same Za (dM ) relation, Z is calculated for the pressure in the impactor. Eq. (3.1) gives mp , and Eqs. (4.1) – (4.3)

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yield the correct critical Stokes number S ∗ . Due to electrostatic blowing, S ∗ is not size independent, and this is why a range of droplet sizes has been used. The calibration procedure is described in more detail in Liedtke (1999) The silver particles measured are some ten times smaller than the oil droplets but are captured in the same pressure range, because of their higher density. In view of the fact that the Iow of sheath gas in the DMA does not reduce the impactor step size beyond a certain 1 limit, we have used aerosol to sheath gas Iow ratio values as large as 10 , for which the signal to noise is more favourable than at higher DMA resolution. 4.3. The relation between mp and Z for silver nanoparticles Three series of data taken with silver particles to test Z ∼ 1=(d+dp )2 (Eq. (2.5)) and to determine d are shown in the Z −1=2 versus mp1=3 plots of Fig. 2, together with the data for proteins mentioned in Section 3.2. The :rst set made use of self-charging, i.e. the fact that a fraction of the particles emitted by the wire generator carry single elementary charges. This group of data covers the largest range of mobilities and is shown together with a linear regression curve. The linearity of the Zp−1=2 vs. m1=3 representation of the data referring to self-charging is a nice veri:cation of Z ∼ 1=(d + dp )2 . Interestingly, the intersection with the vertical axis is indistinguishable from that corresponding to the protein data, leading to d = 0:53 nm, and indicating again that the gas molecule diameter is not far from Tammet’s value of 0.6 for air. The closeness of the coincidence is probably fortuitous, mainly because the density of the protein molecules cannot be regarded as uniform. The value of the density for the self-charged silver particles derived from the slope of the Z −1=2 vs. mp1=3 plots (or Eqs. (3.1) and (2.5)) was 7:9 g=cm3 , 25% lower than the theoretical density of silver of 10:5 g=cm3 . The most probable explanation for this discrepancy is contamination. This will be con:rmed below by putting greater emphasis on clean conditions (see Section 4.4). The data points in Fig. 2 referring to the case using the 85 Kr neutralizer gave the most intense signal, which made it possible to record impactor I (p) spectra with rather large mobilities (0:3 cm2 =V=s). The smallest measurable size in this case was not imposed by the decay of collected current with decreasing particle size, but rather by the lower limit of the impactor, :xed at the pressure at which the jet becomes sonic. Both the 85 Kr bipolar charger data and the photoelectric charging data show discrepancies with respect to the self-charged particles. These appear small in the representation of Fig. 2 but are very signi:cant in relation to the small scatter of the data points. Independently of any possible inaccuracy in calibration, this deviation clearly indicates that the apparent density of the particles that have undergone bipolar or photoelectric charging is lower than that of self-charged particles by a factor of about 0.74. This result is of great signi:cance for any research on nano-particles in the gas phase, since this phenomenon will hardly :nd any explanation that does not involve contamination (see Section 4.4.2). It demonstrates how sensitive properties of particles sized a few nanometers are to contamination. 4.4. Determination of the density of silver nanoparticles under conditions of improved purity We have developed experimental means of determining particle mass in aerosols (Section 3). Through establishing an experimentally veri:ed mobility versus size relation (Section 2), a method of measuring particle size and density in the nanometer regime is provided, and it is now a major

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goal to investigate the role of contamination in the observed density di5erences for silver particles. These di5erences are namely the absolute deviation from silver density and the relative density reduction associated with charger application. In contrast to the brass–teIon particle generator applied in all measurements of Section 4.3, a completely new evaporation chamber was built, using only stainless steel, glass, and ceramic insulators, and copper gaskets and electrodes. Before the measurements, this chamber was outgassed for 24 h at 200◦ C, with a small Iow of high purity nitrogen under low pressure. The complete absence of air leaks was tested by introducing gas at 1.73 mbar and checking that the pressure remained unchanged for long periods. Each time the silver :lament was changed, it was heated resistively for several hours in order to remove any volatile impurities introduced on the wire surface. It was possible to further clean the carrier gas by passing it through a liquid nitrogen trap, held slightly above the temperature of liquid nitrogen. These precautions were introduced mainly to avoid possible co-condensation of a contaminant component with the silver. After cleaning the generator walls with solvents for removal of organic contaminants, further :ngerprints were avoided. Even very low partial pressures of organic vapors could pyrolize at the glowing wire, possibly causing carbon contamination of the silver particles. As an alternative charging mechanism, a 210 Po bipolar charger (Kaufman et al., 1996a) was applied. While the 85 Kr charger had previously been used in the calibration procedure with the oil droplets (and was not cleaned for the present experiments), the 210 Po charger had never been subjected to liquid organic particles. This alternative thus removes another contaminant source of potential relevance. The following measurements are carried out with nitrogen instead of argon. This allows application of the liquid nitrogen trap, which is now used to freeze out contaminants e5ectively. A DMA di5erent from the one used to obtain the results in Section 4.3. but of the same type is used. This is not expected to have any inIuence on the results. 4.4.1. The e>ect of impurities in the carrier gas Considering that the silver vapor pressure at the wire, su>cient to produce particles, corresponds to less than 1 ppb, the amount of impurity required to modify the particle density is tiny! It is well known from atmospheric chemistry that UV radiation induces reactions that lead to species of low volatility that condense to form particles (gas to particle conversion). Previous unpublished experiments with UV lamps emitting at wavelengths around 200 nm showed that gas to particle conversion occurs even in nitrogen of high purity grade (1 ppm impurities). This may lead to formation of a surface layer of low-density material on the particles. Its source may have been the glue used to join various parts of the UV charger. The results in Section 4.3 obtained with the 85 Kr bipolar charger suggest that a similar e5ect could also be induced by high-energy radiation from radioactive decay in bipolar chargers. This radiation must also lead to gas excitation and radical formation from impurities and Nitrogen that could react to form products of low volatility. A molecular monolayer of some contaminant species on the particle surface may even be formed by vapors that are far below saturation. This means that radical reactions are not even necessary to explain the particle growth observed in the present study, which was probably below a monolayer. Perhaps DOP or DOS wall contamination in the Kr charger from previous experiments form a su>cient vapor pressure for molecules to adsorb to the particle surface. The inIuence of the carrier gas purity on the measurement response is experimentally tested. The :rst set of data (“pure nitrogen”) in Fig. 4 showing I (p) curves for silver particles of mobility

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Fig. 6. Electron micrographs of spherical (a) and elongated (b) silver particles from hot wire generator (from Kirsch, 2000).

equivalent diameter 5:05 nm refers to the cleanest possible conditions, i.e. using nitrogen of initial purity 5.0 further cleaned with the liquid nitrogen trap, and with the hot wire generator chamber in an outgassed condition. The second set of data (“impure nitrogen”) was taken with the trap removed and with nitrogen of purity 4.0. The hot wire generator chamber was opened before this measurement and subjected to the laboratory atmosphere. No charger was applied, i.e. the self-charging mechanism was used. The I (p) curves show surprising invariance with respect to the carrier gas impurities introduced. A series of measurements up to 8 nm mobility diameter was taken, and the results for pure and impure condition always agreed. We can conclude that the degree of gas purity has no inIuence on silver particle density or structure for the unde:ned but probably typical contaminants in industrial gases. The degree of purity did have an inIuence on the yield of self-charged particles provided by the generator, which was a factor of 1.8 higher in the more contaminated case for the 5:05 nm particles. This is not surprising, since trace gases are expected to strongly inIuence the ion species formed in an inert gas. 4.4.2. The particle density derived from a single I (p) measurement Typical I (p) curves are shown in Figs. 5 and 6. We derive p50 from them. This value yields the particle mass mp , applying Eqs. (4.1) to (4.3) together with the appropriate value for S ∗ derived in the calibration procedure and the mobility de:ned by the DMA, Za . From the results displayed in Fig. 2, we obtained the value d = 0:53 which is practically independent of the issues discussed in connection with the “wrong” densities in Section 4.3. We use this value to obtain dp from Za ( = 0:91). The de:nition (3.1) then yields the particle density p , listed in Table 1 for the self-charged and the 85 Kr neutralized particles.

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Table 1 Densities derived from single I (p) curves, under the assumptions that the particles are spherical,  = 0:91, and d = 0:53 nm Mobility diameter dM (nm)

Density p (g=cm3 ) (selfcharged)

Density p (g=cm3 ) (85 Kr-charged)

5.36 6.94 8.01

10.22 10.42 10.24

9.12 9.20 9.13

For the self-charged particles the average value of 10.29 is now very close to the silver density of 10.53. The 85 Kr bipolar charger induces a parallel shift of the curve corresponding to an 11% density reduction. The reduction of the mean particle density corresponds to a coating thickness of 10% of the particle radius, if a density of 1 g=cm3 of the presumably organic coating component is assumed. For a 5 nm particle that is 0:5 nm. This could be a molecular monolayer or less. Since the apparent density reduction is independent of the impurity situation at the gas source, contamination of the 85 Kr bipolar charger is the suspected source of lower density material, which adsorbs to the particles. The curves for the 210 Po charger exhibit interesting structure, as the example of Fig. 5 shows. Such structure points to the occurrence of particles of slightly di5erent density in the mobility selected. Note that both the mobility expression (2.5) and the density de:nition (3.1) assume spherical particles. Any deviation from spherical shape corresponds to an apparent reduction in density. This indicates that more than one shape or composition exists. The high pressure ends of the I (p) curves coincide more or less with the self-charged case, indicating that particles as clean and as sphere-like as in the self-charging case are present. Particles of lower apparent density must also occur to explain multiple steps. The most likely explanation is the presence of di5erent shapes of uncontaminated particles. In connection with a di5erent study carried out by Hans Kirsch, 2001 (Ph.D. thesis), di5erent morphologies of silver particles were found in the aerosol produced by the wire generator under similar conditions. Hans Kirsch developed a method of separating 2 species appearing in the same mobility class by photoelectric charging, and Fig. 6 shows micrographs of the two groups of particles. Those in Fig. 6a appear round, or moderately ellipsoidal with aspect ratios between 1 and 1.35. In contrast, those in Fig. 6b are far more elongated, many of them with aspect ratios of 3, and a few as large as 4. These twins or multiple twins have most likely been formed by coalescence of two or more round neutral particles. Indeed, self-charged particles form by heterogeneous condensation on ions emitted from the wire. They have high initial mobilities and quickly move away from the :lament in the imposed :eld. Hence, they have a lower probability of coagulation than originally neutral particles, which helps understand the absence of twins from the self-charged sample. In contrast, initially neutral particles do have enough time to coagulate, but the associated twins are neutral and can only be detected when passed through a charging device. The alternative interpretation of selective coating of certain particles by contaminants, but not of others, appears as less likely. The primary source of contamination from the charger is in the charging region, where residence times are identical for originally self-charged and neutral particles. Notice :nally that Kirsch’s photographs show no aggregates of touching spheres, but only sintered aggregates, evidently joined by chemical bonds. This gives further circumstantial evidence of

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uncontaminated particles, since an organic overlayer would tend to impede metallic bonds between the primary spheres. The qualitative considerations just made lend strong support to the hypothesis that morphology di5erences are responsible for the structure in the I (p) curves in Fig. 5. More quantitative support for this interpretation follows from calculating the di5erences in mass that may be expected from mono-mobile particles of :xed density exhibiting shape distributions comparable to those shown in Kirsch’s images. In spite of the considerable width of the narrowest of the steps seen in Fig. 5, one can clearly assign mean positions to the two steps for the data using the 210 Po charger. They appear at mean pressures that di5er from each other by 6% or 7%, corresponding to mass variations of 12% to 14% (Eq. (4.4)). The step most to the right appears at the same position as for self-charged particles, and corresponds to uncontaminated nearly spherical ones. The smaller step to its left is therefore associated to particles with an average mass 12% smaller. Calculations for the mass variation of mono-mobile ellipsoids according to Fern'andez de la Mora (2002) have been performed. They show that, for the realistic limit of nearly inelastic collisions, a mass 12% below that for a sphere of the same mobility requires ratios of major to minor axis as large as 3. This value is in fact consistent with Kirsch’s images. In conclusion, the experiments with no neutralizer or with a clean neutralizer show that contamination can be avoided without extreme measures, and shows the importance of shape in the interpretation of DMA and impactor data. The experiments with the contaminated Kr neutralizer show the complete absence of dense uncontaminated particles, for the same particle source for which we know that dense, almost spherical particles are in fact produced. This shows conclusively that all the dense particles originally produced have been coated with a lighter material. Although the particles passed through the UV charger have not been investigated with the improved source, it is reasonable to attribute the associated low densities observed in Fig. 2 to the same causes as those just discussed for the Kr charger.

5. Conclusions The following important conclusions may be drawn: (i) The combination of an Eichler DMA and a focusing impactor yields unambiguously the mobility Z and the mass mp of aerosol particles in the nanometer range. (ii) Following Tammet (1995), we propose a Z(dp ) relation for the nanometer range (Eq. (2.5)). (iii) The data of Gotts et al. for fullerenes give strong support for a Z(dp ) according to Eq. (2.5). (iv) The curves Z −1=2 versus mp1=3 obtained (Fig. 2) are close to straight lines and corroborate Z ∼ 1=(d + dp )2 , consistent with Eq. (2.5). (v) The extrapolation of these lines to zero mass can be interpreted as the e5ective diameter d of the gas molecules for collision with the particles. The values obtained lead to d ∼ 0:53 nm for air, quite close to Tammet’s estimate of 0:6 nm. Ignoring the :nite value of d in the Z(dp ) relation is a serious source of error for dp ¡ 10 nm. This problem is particularly acute in tandem studies with impactors and DMA’s where the traditional interpretation contains an error by a factor (1 − d=dM )3 in the particle density inferred, even for spherical particles. The results of previous impactor studies with dp ¡ 10 nm need to be re-analyzed as in Loscertales (2000).

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(vi) Applying Eq. (2.5) to the data obtained for silver particles with the DMA-impactor combination yields the correct density in a case, where high purity conditions were applied. This veri:es the correctness of the measurement method. All previous measurements have used traditional neutralizers and shown reduced density, pointing to contamination. (vii) Structure in the impactor curves reveals occurrence of di5erent particle morphologies. (viii) Even under fairly pure conditions of the source gas, species adsorbing to the silver particle surface are produced both by the UV lamp and the 85 Kr radioactive neutralizer and form a coating of signi:cant thickness on the particles, which probably depends on the history of charger application. This e5ect must be considered in future charger development for nanoparticle application. Chargers should be cleanable and outgasable. Ultra-clean systems are probably essential in most situations involving controlled use of nanometer size particles with traditional chargers. Acknowledgements We are in great debt with Mr. Thilo Eichler (O5enburg), without whose DMA design this work would have been impossible, and to Hans Kirsch, who allowed reproduction of his micrographs in Fig. 6. Support from the US National Science Foundation grants CTS-9319151 and CTS-9871885 and from Deutsche Forschungsgemeinschaft (DFG) (SFB 445) is gratefully acknowledged. References Alvarez, M. M., Vezmar, I., & Whetten, R. (1998). On-line sampling and intact mass-analysis of nanometer size aerosols via time-of-Iight high-mass spectrometry. Journal of Aerosol Science, 29, 115–127. Bacher, G., Szymanski, W. W., Kaufman, S. L., Zollner, P., Blaas, D., & Allmaier, G. (2001). Charge-reduced nano electrospray ionization combined with di5erential mobility analysis of peptides, proteins, glycoproteins, noncovalent protein complexes and viruses. Journal of Mass Spectrometry, 36, 1038–1052. Clemmer, D. E., Hudgins, R. R., & Jarrold, M. F. (1995). Naked protein conformations-Cytochrome-c in the gas phase. Journal of the American Chemical Society, 117, 10141–10142. Clemmer, D. E., & Jarrold, M. J. (1997). Ion mobility measurements and their applications to clusters and biomolecules. Journal of Mass Spectrometry, 32, 577–592. de Juan, L. (1997). Ph.D. thesis, Yale University, Mechanical Engineering Department. de Juan, L., Brown, S., Serageldin, K., Davis, N., Rosell, J., Lazcano, J., & Fern'andez de la Mora, J. (1997). Electrostatic e5ects in inertial impactors. Journal of Aerosol Science, 28, 1029–1048. de Juan, L., & Fern'andez de la Mora, J. (1998). Sizing nanoparticles with a focusing impactor: E5ect of the collector size. Journal of Aerosol Science, 29, 589–599. Eichler, T. (1997). A Di>erential Mobility analyzer for ions and nanoparticles: Laminar ?ow at high Reynolds numbers. Senior Graduation Thesis presented to Fachhochscule O5enburg, Germany. El-Shall, M. S., & Edelstein, A. S. (1996). In A. S. Edelstein, & R. C. Cammarata. (Eds.), “Nanomaterials: Synthesis, properties and applications (pp. 13–54). Bristol, Philadelphia: Institute of Physics Publishing. Fenn, J. B., Mann, M., Meng, C. K., Wong, S. F., & Whitehouse, C. (1989). Electrospray ionization for mass spectrometry of large biomolecules. Science, 246, 64–71. Fern'andez de la Mora, J. (1996). Drastic improvements on the resolution of aerosol size spectrometers via aerodynamic focusing: The case of variable-pressure impactors. Chemical Engineering Communications, 151, 101–124. Fernandez de la Mora, J. (2000). Electrospray ionization of large multiply charged species proceeds via Dole’s charged residue mechanism. Analytica Chimica Acta, 406, 93–104. Fern'andez de la Mora, J. (2002). Free-molecule mobilities of various convex hard-bodies. Journal of Aerosol Science, 33, 477–489.

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