Collision-Based Ionization: Bridging the Gap between Chemical Ionization and Aerosol Particle Diffusion Charging

Abstract

In diffusion charging theory, it is assumed that each ion–particle collision leads to the transfer of charge from ion to particle, and that charge transfer will not occur upon collision between a vapor molecule and a charged particle. However, in chemical ionization, charge transfer can occur in two directions—from charge-donating ion to vapor molecule and back from charged vapor molecule to the original charge-donating species. Both aerosol diffusion charging and chemical ionization are collision-based charge transfer processes, and for particles only slightly larger than vapor molecules (aerosol clusters), the line between diffusion charging and chemical ionization becomes blurred. We examined the charge transfer from aerosol clusters (positively charged amino acid clusters) in the ∼1.0 nm size range to neutral vapor molecules (trimethylamine) at atmospheric pressure by using a combined experimental and theoretical approach. It was found that for singly charged amino acid cluster ions composed of 1, 2, and 3 amino acid molecules, the rate of charge transfer to trimethylamine vapor molecules was clearly observable, particularly for clusters composed of 1 and 2 molecules. The charge transfer rate for singly charged clusters with 4 or more amino acid molecules was consistently close to 0, indicating that the rate of charge transfer from clusters to vapor molecules is size dependent. The charge transfer rates also varied with cluster's chemical composition. Overall, this study demonstrates that small aerosol clusters (∼0.5 nm) can lose charge through collisions with vapor molecules, which is typically not considered in diffusion charging theories.

INTRODUCTION

A central paradigm in aerosol measurement is the determination of aerosol particle size distributions through the measurement and inversion of their mobility distributions (Hoppel 1978; Alofs and Balakumar 1982; Adachi et al. 1990). Proper inversion requires that particles reach a known charge distribution, which is often a steady-state charge distribution obtained via diffusion charging (particle collisions with ions in which charge is transferred from ion to particle) in a bipolar environment (Liu and Pui 1974). For nanoparticles and submicrometer particles, particle charge distributions resulting from diffusion charging processes are typically well predicted by Fuchs’ limiting sphere theory (Fuchs 1963; Adachi et al. 1985; Hoppel and Frick 1986). However, in Fuchs’ theory, the charging rate is not calculated explicitly; only the collision rates between aerosol particles and ions are determined as functions of particle size (in most case diameter), background gas properties (temperature and pressure), net particle charge, ion electrical mobility, and ion mass. It is thus assumed that upon collision, an ion will transfer charge to a particle, regardless of the collision frame of reference energy or the orientation of the ion and particle during collision.

Conversely, in traditional chemical ionization (Bowers et al. 1973; Su and Bowers 1973), ions collide with vapor molecules, and the transfer of charge from ion to vapor molecule is highly dependent on the collision energy relative to the activation energy for charge transfer, as well as the orientation of ion and vapor molecule (steric effects) during collision. True equilibrium (as opposed to steady state) is achievable on experimentally relevant time scales in chemical ionization, as the transfer of charge can also occur from the ionized vapor molecule (charge acceptor) back to the original charge donor. Nonetheless, chemical ionization and diffusion charging are both collision-based ionization processes. In principle, they are both describable by unified charging theory, i.e., a single equation or set of equations. Despite the fact that these two charge exchange processes have been hitherto described by differing approaches (Fuchs 1963; Bowers et al. 1973), the only major difference between aerosol diffusion charging and chemical ionization lies in the size of the charge acceptor (particle or vapor molecule) relative to the donor ion. A governing theory for all collision-based ionization processes must (1) capture all the features of chemical ionization when the charge donor (ion) and charge acceptor (vapor molecule) are of similar size and (2) accurately describe aerosol particle diffusion charging when there is a considerable size difference between charge acceptor and charge donor. This requirement further suggests that for particles only slightly larger than ions (sub-2-nm diameter particles), the dynamics of ion–particle collisions will have features akin to chemical ionization, i.e., ions may not transfer charge to small particles during all ion–particle collisions, and small charged particles may transfer their charge to colliding vapor molecules when the latter are highly basic (for positive charges) or highly acidic (for negative charges).

As evidenced by a recent special issue of this journal, there is currently considerable interest in the measurement of sub-2-nm atmospheric aerosol clusters—particles composed of a limited number of molecules (Eisele et al. 2006; Kulmala et al. 2007; Winkler et al. 2008; Iida et al. 2009; Junninen et al. 2010; Zhao et al. 2010). Unfortunately, the potential for both collisions between ions and sub-2-nm aerosol clusters without charge transfer and collisions between charged clusters and neutral vapor molecules that lead to charge transfer is hitherto unexplored. The purpose of this study is to examine the latter of these two possibilities by observing the transfer of charge from sub-2-nm positively charged amino acid clusters to highly basic trimethylamine vapor molecules in the gas phase. We will refer to this charge transfer reaction as the back reaction, as more often an ionized vapor molecule transfers charge to a cluster/particle during diffusion charging. High back reaction rates for charged aerosol clusters and vapor molecules would have far-reaching effects on cluster diffusion charging kinetics. This subsequently would influence inversion routines to determine the size distributions of clusters from electrical mobility measurements, as well as the predicted rates of ion-induced nucleation in the atmosphere (Yu et al. 1998, 2008). While analyzing back reactions, we develop a kinetic relation that not only applies to the reactions examined here, but can better describe both chemical ionization as well as aerosol particle diffusion charging in the purely free molecular limit (both mass and momentum Knudsen numbers are infinitely large; Lushnikov and Kulmala 2004, 2005). Amino acids were chosen as the test clusters due to the ease of generating protonated amino acid cluster ions via electrospray ionization (ESI; Julian et al. 2002; Myung et al. 2006). Trimethylamine was chosen as the test vapor because it has an unusually large gas-phase basicity (GB = 908 kJ/mol; Wu and Fenselau 1993), thus investigation of back charging reactions with trimethylamine allows us to place an approximate upper limit on the size at which back charging is significant for positive ions in air. Furthermore, at present, amine vapors are suspected of playing a key role in new particle formation in the atmosphere, and therefore, during the bipolar charging of freshly nucleated atmospheric aerosol clusters (Barsanti et al. 2009), amine vapors are possibly present in appreciable concentrations.

While the back reactions for charged aerosol clusters and neutral vapor molecules have not been well characterized, charge transfer reactions in the gas phase have been an active area of research over several decades. We make note of such studies, as they provide precedent for the experiments we performed in this study. Many of these studies focus on evaluating gas-phase basicities and proton affinities of molecules, as these parameters provide important information on the structure and stability of gas-phase ions. Two methods have been widely used to determine relative gas-phase basicities: (1) the measurement of the equilibrium constant for a reversible proton transfer reaction and (2) the kinetic method, which relies on the rates of competitive dissociations of mass-selected cluster ions (Cooks et al. 1994; Papayannopoulos 1995; Cooks and Wong 1998). Both of these methods involve the production of protonated or deprotonated species by techniques such as ESI (Whitehouse et al. 1985), matrix-assisted laser desorption ionization (Karas and Hillenkamp 1988), or traditional chemical ionization (Tsang and Harrison 1976). Studies for these methods have been carried out extensively using systems such as ion cyclotron resonance (ICR; Aue et al. 1976), Fourier-transform (FT) ICR (Marshall and Grosshans 1991; Decouzon et al. 1996), and quadrupole ion trap mass spectrometers (MSs; Louris et al. 1987; Brodbelt-Lustig and Cooks 1989). Our study also involves the measurement of the rate of proton transfer from an electrospray-generated ion to a neutral vapor molecule with the charge transfer reaction monitored by an MS. However, unlike prior studies, the two colliding species are not confined together long enough in a reaction chamber for equilibrium to be attained. We also examine cluster–vapor interactions at atmospheric pressure and temperature, as opposed to a low-pressure environment where, in the presence of electric fields (e.g., inside a quadrupole), collisions between entities are often of significantly higher energy. Furthermore, we examined charge transfer reactions for different sized clusters in parallel, as ESI of amino acids gives rise to an array of cluster ions of varying size and charge.

EXPERIMENTAL METHODS

For experiments, trimethylamine (TMA, C₃H₉N), ammonium acetate (C₂H₃O₂NH₄), water (HPLC grade), ethanol (HPLC grade, C₂H₆O), and 5 different amino acids: l-leucine (C₆H₁₃NO₂), l-serine (C₃H₇NO₃), l-asparagine (C₄H₈N₂O₃), l-tyrosine (C₉H₁₁NO₃), and l-threonine (C₄H₉NO₃, all of reagent grade, ≥98%) were purchased from Sigma Aldrich (St. Louis, MO, USA) and used without any further purification. A schematic of the system in which these chemicals were used is shown in Figure 1. The setup includes a neutral vapor molecule source composed of two nebulizers, an ESI source to produce cluster ions and a commercial quadrupole—time-of-flight MS (API QSTAR Pulsar, Sciex, Toronto, CA, USA). For neutral vapor (TMA vapor) production, a control solution consisting of a 50:50 (by volume) ethanol–water mixture and a TMA solution (42 mM TMA dissolved in a mixture of 31%–35% in ethanol and 65%–69% water by volume) were each nebulized in separate nebulizers using in-house filtered and dehumidified air. Syringe pumps (New Era Pump Systems, Inc., Farmingdale, NY, USA) were used to control the liquid flow rates of the TMA and control solutions, such that the total liquid flow rate was maintained constant at 10 μL/min while the flow rate of the TMA vapor source was varied. The independently atomized vapor streams were mixed together before being introduced into the reaction chamber via a copper tube of inner diameter 4.37 mm with its outlet modified to resemble a nozzle. The use of a constant total flow rate ensured that the relative humidity (RH) of the vapor stream and ethanol vapor concentration was approximately constant. The RH calculated based on the operating conditions (T = 300 K) was 29.5%, which ensured that all atomized droplets completely evaporated before exiting the tube (Friedlander 2000).

Figure 1 Schematic of the system used to examine back charging reactions between TMA vapor and charged amino acid clusters. Amino acid clusters were produced by electrospray ionization, and TMA vapor was introduced into the gas phase at varying concentration by nebulizing TMA solution.

Within the reaction chamber, ESI was used to produce gas-phase cluster ions (aerosol particles). ESI solutions were made for each amino acid, which consisted of 10 mM ammonium acetate, 1 mM of the amino acid, 10 mM TMA, and 50:50 ethanol:water by volume. TMA was specifically added to ESI solutions to mitigate the potential effects of vapor absorption by ESI-generated droplets during the evaporation process. Although the outlet of the copper tube was directed away from the ESI source and when the droplets are micrometers in size, the Stefan flow created by evaporation drives gaseous species away from the droplets (Huckaby and Ray 1989; Martínez-Lozano and de la Mora 2009), it is difficult to guarantee that no vapor uptake occurred. Substantial vapor uptake could influence ion evaporation kinetics, which, in turn, could alter the size and charge distributions of the generated cluster ions (Gamero-Castano and de la Mora 2000; Gamero-Castaño and Fernández de la Mora 2000; Hogan et al. 2008; Hogan and de la Mora 2009). In these experiments, it was essential that the generated amino acid cluster size and charge distributions remained constant and independent of the TMA vapor concentration. The amount of TMA added to ESI solutions was much greater than a droplet could possibly absorb even if equilibrium conditions were reached (from Henry's law). Therefore, it prevented any adverse affects of vapor adsorption and ensured constant cluster generation. The additional TMA in the electrospray solution eventually gave rise to neutral TMA vapor molecules, which were accounted for in data analysis as described in the Results and Discussion section as well as in the supplemental information (available online). ESI solutions were dispensed from a 1.46-mm bore diameter syringe (Hamilton Company, Reno, NV, USA) with the flow rate controlled using a Harvard syringe pump. The ESI capillary needle was positioned facing the MS inlet orifice (Figure 1), which served as the ground electrode for the ESI source. The amino acid cluster ions resulting from the ESI process collided with neutral vapor molecules in the mixing zone in front of the MS inlet. A small counterflow of curtain gas (clean N₂ from an in-house N₂ generator) was present at the MS inlet; thus, only charged species entered the MS and any charge exchange reactions between the cluster ions and TMA vapor were ceased once ions entered the MS.

At varying liquid flow rates of the TMA vapor generating nebulizer, with all other system parameters held constant, mass spectra of the amino acid cluster ions were measured using the time-of-flight section of the QSTAR Pulsar. MS instrument settings were as follows: declustering potential 1−0 V, focusing potential 100 V, declustering potential 2–10 V, and curtain gas 25. The declustering and focusing potentials create electric fields that serve to increase the transmission of ions through the MS inlet, resulting in an increase in the measured signal-to-noise ratio. Nitrogen curtain gas prevents nonionized species from entering the MS orifice. Prior to setting the declustering and focusing potentials, mass spectra for different values of these potentials were obtained to evaluate the tendency of amino acid clusters to fragment. Neither changes in signal intensity nor any shift in cluster ion size distribution for a given TMA vapor concentration were observed for a wide range of potentials around the chosen values.

Figure 2 Selected mass spectra obtained when producing charged clusters of Asparagine with 3 different TMA vapor concentrations. The TMA concentration present during data collection is proportional to the flow rate of TMA solution, which is noted in the upper right corner of each plot. (Figure provided in color online.)

RESULTS AND DISCUSSION

Mass Spectra

As examples of the data obtained and subsequently analyzed in this work, Figure 2 shows the mass spectra recorded using asparagine solution and three different liquid flow rates of the TMA syringe pump. The signal intensity in these spectra is a monotonically increasing function of the number concentration of the ionic species at a particular mass to charge (m/z) ratio, and it is immediately evident that the signal intensity of the amino acid cluster ions decreases with increasing TMA liquid flow rate. A similar phenomenon is observed for all examined amino acid clusters. This suggests the occurrence of the back charging reaction wherein neutral TMA molecules “steal” charge from the amino acid cluster ions resulting in neutral clusters that do not contribute to the MS signal. The magnitude of the decrease in signal intensities with increasing TMA flow rates is largest for the smaller cluster ions, as compared with the larger ones. Using the MS data acquired by varying TMA flow rates for each ESI solution, we are able to infer information on the back reaction kinetics between neutral TMA molecules and [AA] _x [H⁺], [AA] _x [Na⁺], [AA] _x [K⁺], [AA] _x [TMAH⁺], [AA] _x [H⁺]₂, [AA] _x [Na⁺]₂, [AA] _x [K⁺]₂, and [AA] _x [TMAH⁺]₂ cluster ions (where AA denotes an amino acid molecule and x denotes the number of amino acids per cluster). The analysis performed, which is described in the following sections, is limited to examination of singly and doubly charged cluster reactions with vapor molecules. We have chosen to focus on clusters with these charge states, because in collision-based ionization of aerosol clusters, the collision rate of charged clusters and ions of the same polarity is essentially zero due to Coulombic repulsion (Fuchs 1963), and multiply charged clusters would be extremely rare in the gas phase.

Reaction Kinetics Model

We develop a model to better understand the decrease in signal intensity due to charge transfer from cluster to vapor molecule. The reaction occurring in the mixing zone (Figure 1) is represented as

where AA represents the amino acid contained in the ESI solution, x is the number of amino acid molecules in the cluster, I is the charge carrying species (H⁺, Na⁺, K⁺, or TMAH⁺), and y is the charge state of the amino acid cluster, which takes the value of 1 or 2 in our study. While other vapor species are present in the mixing zone (e.g., H₂O), they were held at near constant concentration during all experiments; thus, the change in signal intensity for the observed amino acid cluster ions can be attributed solely to their collisions with TMA vapor molecules. Depending on the orientation of the cluster ion and the TMA molecule as well as the collision frame-of-reference kinetic energy, a collision could lead to the transfer of a single charge from the cluster ion to the TMA molecule. Assuming K _B and K _F to be the backward reaction (the reaction of interest) and forward reaction rate constants, respectively, the rate of change of the amino acid cluster ion concentration can be found using Equation (2):

For sufficiently small products of the neutral vapor concentration and residence time in the mixing zone (analogous to the ion concentration × residence time product in unipolar charging), the reionization of amino acid clusters by charged TMA molecules can be neglected. This results in the following solution to Equation (2):

where t _res, a system constant, is the residence time during which the collisions between amino acid cluster ions and neutral vapor molecules occur; [(AA) _x (I⁺) _y ] _{t 0} is the concentration of cluster ions in the absence of TMA vapor molecules, and [(AA) _x (I⁺) _y ] _{t res} is the concentration of cluster ions after passing through the mixing zone and into the MS. The above equation can be reexpressed as

where [TMA]_R is the relative (dimensionless) concentration of TMA vapor expressed in terms of the liquid flow rate of TMA vapor through the nebulizer divided by the total flow rate of nebulized material (10 μL/min); A _sys is an undetermined system constant, which is the product of the residence time in the mixing zone and the change in concentration that results from conversion of TMA from the liquid to the vapor phase and has SI units of s/m³. Under the conditions employed the signal in the MS for each amino acid cluster ion should be directly proportional to [(AA) _x (I⁺) _y ] _{t res}. Since a small amount of TMA was added to the ESI solution to mitigate the effects of TMA vapor absorption by ESI droplets, the signal intensity that would be measured in the MS corresponding to an amino acid concentration of [(AA) _x (I⁺) _y ] _{t 0} was determined by extrapolating the signal intensity versus TMA flow rate curve. Details on this procedure are given in the supplemental information (available online). With this value known, the ratio [(AA) _x (I⁺) _y ] _{t 0}/[(AA) _x (I⁺) _y ] _{t res} was calculated and ln([(AA) _x (I⁺) _y ] _{t 0}/[(AA) _x (I⁺) _y ] _{t res}) was plotted as a function of the known [TMA]_R for each experiment (Figures 3–6 for various amino acid clusters with different cations bound). The initial slope of these curves gives the value K _B A _sys. Although A _sys is difficult to determine in experiments such as Hogan et al. (2009) and Hogan and Fernandez de la Mora (2010), it is a constant for all experiments; thus comparison of K _B A _sys values between clusters of different chemical composition or size allows us to examine how the back charging reaction is influenced by cluster properties.

Figure 3 Plots used in determination of the relative back reaction rate for protonated amino acid monomer, dimer, and trimer ions with TMA vapor molecules. The labels on the abscissa and ordinate are described in the text.

Figure 4 Plots used in determination of the relative back reaction rate for sodiated, potassiated, and trimethylammoniated amino acid monomer, dimer, and trimer ions with TMA vapor molecules. Negative slopes for the trimethylammoniated clusters indicate that TMA vapor molecules can stick to cluster ions upon collisions. The labels on the abscissa and ordinate are described in the text.

Figure 5 Plots used in determination of the relative back reaction rate for doubly protonated amino acid cluster ions with TMA vapor molecules. The labels on the abscissa and ordinate are described in the text.

Figure 6 Plots used in determination of the relative back reaction rate for doubly sodiated, potassiated, and trimethylammoniated asparagine cluster ions with TMA vapor molecules. The labels on the abscissa and ordinate are described in the text.

To further analyze back charging reactions, the backward reaction rate constant of Equation (1), K _B, may be decomposed as

where the chemical rate (i.e., probability that charge transfer occurs upon collision) coefficient (K _chem) is a product of the steric factor and the activation energy necessary to cause charge transfer from cluster ion to neutral vapor; here, we will not uncouple these two terms and hence use the more general term (K _chem). The physical rate constant K _phy (i.e., collision rate, normally determined in Fuchs’ theory between a particle and a point mass ion) is a product of the enhancement factor due to the attractive potential between the cluster ion and neutral vapor and the collision frequency determined in the absence of these potentials. The free molecular regime collision frequency (β) between the amino acid cluster ions and the TMA molecules in the absence of cluster–vapor molecule potentials was calculated as (Vincenti and Kruger 1965)

where A and B represent the cluster ion and the TMA molecule, respectively, R _A is the radius of the cluster ion, R _B is the radius of the TMA molecule, k is Boltzmann's constant (1.38 × 10⁻²³ J/K), T is the temperature (room temperature), and μ _AB is the reduced mass given by

with m _A and m _B as the molecular masses of the cluster ion and the vapor molecule respectively. Attractive potentials such as the image and van der Waals potentials cause an enhancement in the collision rate between charged and uncharged particles (Marlow 1980a, 1980b; Huang et al. 1990, 1991). Marlow (1980a) derived collision rate enhancement expressions accounting for attractive interactions (note the potentials considered here are attractive in nature) in the free molecular, transition, and continuum size regimes. The enhancement rate in the free molecular size regime is of interest here, E ^fm, and is given as

where x = (R _A + R _B)/r, r is the distance between the 2 particle centers, and Ø(x) is the dimensionless attractive potential between the charged and uncharged particles. We account for the combined effect of the image and van der Waals potentials in determining the amino acid cluster ion—TMA vapor molecule collision rates (K _phy). Table 1 lists the values of the constants used in our model (CRC 1999–2000; Kumar et al. 2007). The radii of the TMA molecule and the amino acid cluster were calculated assuming that they are spherical. Explicit expressions for the image and van der Waals potentials are given in the supplemental information (available online). Table 2 shows the enhancement values calculated for the various cluster ion and TMA molecule collisions. The interparticle potential effects are dominant for smaller cluster ions (monomers and dimers), and this furthers the rate of the back reactions. With increasing cluster ion size, the enhancement in collision rate decreases, eventually leading to the free molecular collision rate predicted in the absence of potential interactions.

Back Reaction Analysis

Equation (4) is plotted with ln([(AA) _x (I⁺) _y ] _{t 0}/[(AA) _x (I⁺) _y ] _{t res}) as the ordinate and [TMA]_R as the abscissa for various cluster ions examined in this study in Figures 3–6. For all clusters where the back reaction was clearly prevalent, ln([(AA) _x (I⁺) _y ] _{t 0}/[(AA) _x (I⁺) _y ] _{t res}) was, as expected, linearly proportional to [TMA]_R for small values of [TMA]_R. Linear regression was therefore performed using the first several data points in each graph, with the value of A _sys K _B equivalent to the slopes of the regression lines (lines are drawn in each plot). At sufficiently high TMA vapor concentrations, the slopes decrease below A _sys K _B; at such high concentrations, the recharging of amino acid clusters by ionized TMA vapor is nonnegligible and the solution to Equation (2) given in Equations (3) and (4) is no longer valid. The experimentally determined value of A _sys K _B and the numerically calculated value of K _phy were used to extract information on K _chem using Equation (5). Again, however, with the undetermined A _sys, only relative K _chem values are reported here. Despite this ambiguity, the combined experimental–theoretical approach allows us to better understand the size and material dependence of charge transfer between cluster ions and neutral vapor molecules.

Figures 3 and 4 and Table 2 provide information on back reaction rates for collisions between TMA molecules and singly charged amino acid cluster ions. Small quantities of sodium and potassium salts are always present as impurities in commercially available amino acid salts as well as in high performance liquid chromotography (HPLC)-grade water. As ESI-generated droplets evaporate, some of the Na⁺ and K⁺ ions stick to amino acid clusters resulting in sodiated and potassiated cluster ions. The presence of positive slopes for the curves in each graph clearly indicates that a back charging reaction occurs. In the case of singly protonated amino acid monomers, the back reaction rates are highest for asparagine followed by tyrosine, threonine, serine, and leucine. However, this order is variable with cluster size and charge-carrying cation. The observations for singly charged (cationic species being any of H⁺, Na⁺, K⁺, TMAH⁺) amino acid cluster ions are similar, i.e., the rate constants for the monomers and dimers are much higher than that of the higher-order clusters, which are negligibly small. Comparison of the rate constants for singly charged clusters with the same number of amino acid molecules but with different charge-carrying cations indicates that the protonated amino acid clusters typically have the highest back reaction rates, followed by the sodiated and potassiated amino acid cluster ions. For potassiated serine and tyrosine trimers (Figure 4), the absence of linearity may be interpreted as statistical variations about a rate constant value that is very close to zero (slope of the graph being horizontal). In the case of the trimethylammoniated species, the distinct negative slopes in the graphs can be explained by the fact that rather than mere charge transfer, some TMA molecules stick to amino acid clusters upon collision, increasing the signal intensity of trimethylammoniated clusters.

Table 1 Summary of the parameters used in the calculation of K _phy, the collision rate between vapor molecules and cluster ions

Amino acid	Density (g/cc)	Molar mass (g/mole)	Monomer radius (nm)	Dimer radius (nm)	Trimer radius (nm)	Tetramer radius (nm)	Octamer radius (nm)	Decamer radius (nm)	Dodecamer radius (nm)
Asparagine	1.543	132.118	0.32	0.41	0.47	0.51	0.65	0.70	0.74
Leucine	1.293	131.173	0.34	0.43	0.49	0.54	0.69	0.74	0.78
Serine	1.6	105.093	0.30	0.37	0.43	0.47	0.59	0.64	0.68
Tyrosine	1.456	106.093	0.31	0.39	0.44	0.49	0.61	0.66	0.70
Threonine	1.45	119.12	0.32	0.40	0.46	0.51	0.61	0.66	0.70
Hamaker constant (J)	4.112 × 10^−21
Temperature (K)	298
Dielectric constant of TMA	2.5
Radius of TMA molecule (nm)	0.445

Table 2 Summary of calculated and experimentally determined collision rate parameters for amino acid cluster ions with TMA vapor molecules

Amino acid	Cluster ion	AK B (experimental)	Enhancement	Collision frequency (l0^−18 m^3/s)	K phy (l0^−16 m^3/s)	AK chem = AK B/K phy (l0^−16 s/m^3)
Asparagine	Protonated monomer	113.98	13.64	4.10	0.56	204.12
	Protonated dimer	14955	1154	5.98	0.67	222.08
	Protonated trimer	46.79	9.93	7.59	0.75	62.06
	Protonated tetramer	1.14	9.06	9.04	0.82	1.39
Serine	Protonated monomer	80.91	14.58	3.57	0.52	155.59
	Protonated dimer	184.32	12.14	5.13	0.62	29654
	Protonated trimer	134.73	10.78	6.47	0.70	19359
	Protonated tetramer	48.00	9.86	7.68	0.76	63.41
Tyrosine	Protonated monomer	113.39	1451	3.81	0.54	209.18
	Protonated dimer	106.97	11.79	5.49	0.65	165.42
	Protonated trimer	39.66	10.44	6.92	0.72	54.85
	Protonated tetramer	−5.46	9.54	852	0.78	−6.96
Threonine	Protonated monomer	99.18	13.78	4.03	0.56	178.67
	Protonated dimer	14955	11.38	5.83	0.66	224.81
	Protonated trimer	75.45	10.06	7.38	0.74	101.58
	Protonated tetramer	24.84	9.18	8.78	0.81	30.81
Leucine	Protonated monomer	5750	13.04	4.59	0.60	95.58
	Protonated dimer	13452	10.69	6.70	0.72	187.57
	Protonated trimer	58.66	9.41	8.50	0.80	73.32
	Protonated tetramer	1.34	8.57	10.13	0.87	1.54
Doubly protonated species
Asparagine	8 with 2 H+	5750	14.12	13.99	1.98	28.96
	10 with 2 H+	24.93	13.03	16.15	2.10	11.85
	12 with 2 H+	5.42	12.18	18.17	251	2.45
Serine	8 with 2 H+	207.41	15.49	11.80	1.83	113.45
	10 with 2 H+	171.43	14.33	13.61	1.95	87.92
	12 with 2 H+	112.92	13.43	15.30	2.05	54.98
Tyrosine	8 with 2 H+	83.59	14.94	12.65	1.89	4454
	10 with 2 H+	27.11	13.81	14.58	2.01	13.47
	12 with 2 H+	14.51	12.93	16.39	2.12	6.85
Threonine	8 with 2 H+	228.37	14.33	12.50	1.79	14.33
	10 with 2 H+	135.65	1353	14.42	1.91	1353
	12 with 2 H+	82.73	12.37	1652	2.01	12.37
Leucine	8 with 2 H+	145.00	1358	15.67	2.08	69.66
	10 with 2 H+	145.13	1254	18.08	251	65.56
	12 with 2 H+	147.59	11.43	20.35	2.33	63.43
Sodiated species
Asparagine	Sodiated monomer	22.00	13.64	4.10	0.56	39.41
	Sodiated dimer	109.19	1124	5.98	0.67	162.47
	Sodiated trimer	34.10	9.93	7.59	0.75	4524
Serine	Sodiated monomer	21.92	14.58	3.57	0.52	42.14
	Sodiated dimer	51.51	12.14	5.13	0.62	82.79
	Sodiated trimer	84.47	10.78	6.47	0.70	121.18
Tyrosine	Sodiated monomer	11.94	1421	3.81	0.54	22.03
	Sodiated dimer	29.54	11.79	5.49	0.65	45.68
	Sodiated trimer	35.59	10.44	6.92	0.72	4922
Threonine	Sodiated monomer	12.40	13.78	4.03	0.56	22.33
	Sodiated dimer	100.37	11.38	5.83	0.66	151.19
	Sodiated trimer	94.92	10.06	7.38	0.74	127.79
Leucine	Sodiated monomer	13.12	13.04	4.59	0.60	21.92
	Sodiated dimer	−11.81	10.69	6.70	0.72	−16.51
	Sodiated trimer	−206.72	9.41	8.50	0.80	−258.38
Potassiated species
Asparagine	Potassiated monomer	2322	13.64	4.10	0.56	41.57
	Potassiated dimer	50.90	1124	5.98	0.67	75.73
	Potassiated trimer	26.02	9.93	7.59	0.75	34.52
Serine	Potassiated monomer	−1.84	14.58	3.57	0.52	−3.55
	Potassiated dimer	89.30	12.14	5.13	0.62	143.53
	Potassiated trimer	30.19	10.78	6.47	0.70	43.32
Tyrosine	Potassiated monomer	−4.62	1421	3.81	0.54	−8.52
	Potassiated dimer	50.64	11.79	5.49	0.65	78.32
	Potassiated trimer	−428	10.44	6.92	0.72	−5.92
Threonine	Potassiated monomer	6024	13.78	4.03	0.56	108.52
	Potassiated dimer	155.41	11.38	5.83	0.66	234.09
	Potassiated trimer	133.19	10.06	7.38	0.74	179.31
Leucine	Potassiated monomer	20.48	13.04	4.59	0.60	3423
	Potassiated dimer	−10.53	10.69	6.70	0.72	−14.72
	Potassiated trimer	55.83	9.41	8.50	0.80	69.78
Trimethylammoniated species
Asparagine	Trimethylammoniated monomer	−109.76	13.64	4.10	0.56	−196.56
	Trimethylammoniated dimer	–	1124	5.98	0.67	NA
	Trimethylammoniated trimer	−11.19	9.93	7.59	0.75	−14.84
Serine	Trimethylammoniated monomer	−165.83	14.58	3.57	0.52	−318.91
	Trimethylammoniated dimer	−176.70	12.14	5.13	0.62	−283.99
	Trimethylammoniated trimer	−25122	10.78	6.47	0.70	−360.42
Tyrosine	Trimethylammoniated monomer	−165.90	1421	3.81	0.54	−306.05
	Trimethylammoniated dimer	−324.82	11.79	5.49	0.65	−502.31
	Trimethylammoniated trimer	−382.07	10.44	6.92	0.72	−528.38
Threonine	Trimethylammoniated monomer	−240.79	13.78	4.03	0.56	−433.76
	Trimethylammoniated dimer	–	11.38	5.83	0.66	NA
	Trimethylammoniated trimer	−306.07	10.06	7.38	0.74	−412.05
Leucine	Trimethylammoniated monomer	−206.72	13.04	4.59	0.60	−345.43
	Trimethylammoniated dimer	−75.75	10.69	6.70	0.72	−105.86
	Trimethylammoniated trimer	−21.02	9.41	8.50	0.80	−2628
Doubly sodiated species
Asparagine	Doubly sodiated octamer	58.35	14.12	1359	1.98	29.54
	Doubly sodiated decamer	42.35	13.03	16.15	2.10	20.13
	Doubly sodiated dodecamer	30.84	12.18	18.17	251	13.93
Serine	Doubly sodiated octamer	–	15.49	11.80	1.83	NA
	Doubly sodiated decamer	247.52	14.33	13.61	1.95	126.95
	Doubly sodiated dodecamer	75.82	13.43	1530	2.05	36.92
Tyrosine	Doubly sodiated octamer	73.85	14.94	12.65	1.89	39.08
	Doubly sodiated decamer	21.87	13.81	14.58	2.01	10.86
	Doubly sodiated dodecamer	2.65	12.93	1639	2.12	155
Threonine	Doubly sodiated octamer	224.15	14.33	1230	1.79	125.16
	Doubly sodiated decamer	139.32	1353	14.42	1.91	73.05
	Doubly sodiated dodecamer	48.19	12.37	1652	2.01	24.02
Leucine	Doubly sodiated octamer	–	1358	15.67	2.08	NA
	Doubly sodiated decamer	7427	1254	18.08	251	33.55
	Doubly sodiated dodecamer	107.46	11.43	2035	2.33	46.18
Doubly potassiated species
Asparagine	Doubly potassiated octamer	39.06	14.12	13.99	1.98	19.77
	Doubly potassiated decamer	49.93	13.03	16.15	2.10	23.73
	Doubly potassiated dodecamer	1029	12.18	18.17	251	4.65
Serine	Doubly potassiated octamer	–	15.49	11.80	1.83	NA
	Doubly potassiated decamer	105.46	14.33	13.61	1.95	54.09
	Doubly potassiated dodecamer	90.69	13.43	15.30	2.05	44.16
Tyrosine	Doubly potassiated octamer	76.00	14.94	12.65	1.89	4052
	Doubly potassiated decamer	4858	13.81	14.58	2.01	23.98
	Doubly potassiated dodecamer	−11.37	12.93	16.39	2.12	−5.36
Threonine	Doubly potassiated octamer	237.99	14.33	12.50	1.79	132.88
	Doubly potassiated decamer	14053	1353	14.42	1.91	73.53
	Doubly potassiated dodecamer	44.78	12.37	1652	2.01	22.32
Leucine	Doubly potassiated octamer	–	1358	15.67	2.08	NA
	Doubly potassiated decamer	7457	1254	18.08	251	33.55
	Doubly potassiated dodecamer	107.46	11.43	20.35	2.33	46.18
Doubly trimethylammoniated species
Asparagine	Doubly trimethylammoniated octamer	59.16	14.12	1359	1.98	29.95
	Doubly trimethylammoniated decamer	24.79	13.03	16.15	2.10	11.78
	Doubly trimethylammoniated dodecamer	9.36	12.18	18.17	251	453
Serine	Doubly trimethylammoniated octamer	–	15.49	11.80	1.83	NA
	Doubly trimethylammoniated decamer	−20.19	14.33	13.61	1.95	−1035
	Doubly trimethylammoniated dodecamer	−108.35	13.43	1530	2.05	−52.76
Tyrosine	Doubly trimethylammoniated octamer	3556	14.94	12.65	1.89	18.66
	Doubly trimethylammoniated decamer	−4.72	13.81	14.58	2.01	−2.34
	Doubly trimethylammoniated dodecamer	24.50	12.93	1639	2.12	11.56
Threonine	Doubly trimethylammoniated octamer	–	14.33	1230	1.79	NA
	Doubly trimethylammoniated decamer	104.14	1353	14.42	1.91	54.60
	Doubly trimethylammoniated dodecamer	2959	12.37	1652	2.01	14.60
Leucine	Doubly trimethylammoniated octamer	−20.18	1358	15.67	2.08	−9.70
	Doubly trimethylammoniated decamer	−18.70	1254	18.08	251	−8.45
	Doubly trimethylammoniated dodecamer	–	11.43	2035	2.33	NA

The mass spectra recorded were also used to extract information on the back reaction rates for doubly charged amino acid clusters (Figures 5 and 6). We note that the signal intensities of the doubly charged cluster ions were substantially lower than the singly charged clusters under all conditions. Therefore, although the back reaction for the doubly charged clusters leads to the formation of singly charged clusters, they appeared with such low signal intensity (and at larger masses than the singly charged clusters of interest), that they did not interfere with singly charged cluster analysis. Similarly, triply charged clusters were near-undetectable and did not interfere with doubly charged cluster analysis. However, quite often, a doubly charged cluster and a singly charged cluster were of the same m/z, and it was necessary to isolate singly charged cluster signal from doubly charged cluster signal. Distinguishing singly and doubly charged cluster ion signal intensities was possible by examining the isotopic distribution of all measured ions, which is described in detail in the supplemental information (available online).

Phenomena similar to those seen for singly charged clusters are observed for the doubly charged clusters wherein decreasing reaction rate constants are observed with increasing cluster size. Dependency of the reaction rate constant on the charge-carrying cation is evident as well. In general, the doubly protonated octamers have higher back reaction rate constants compared with other doubly charged clusters. Unlike the singly protonated clusters, for a particular doubly protonated cluster size, there is a strong variation in the reaction rate constant among different amino acids. The doubly protonated asparagine octamers have an AK _B ∼ 57, while their threonine counterparts have an AK _B ∼ 228.37. Similarly, a wide disparity between the highest and the lowest back reaction rate was found for the doubly protonated decamers and dodecamers. This can be contrasted to the singly protonated amino acid clusters where the differences in AK _B values were less than 100 for all cases.

Table 2 provides values of A _sys K _chem calculated for the various TMA and cluster ion reactions using Equation (5). The value of A _sys K _chem decreases with increasing cluster size for all examined amino acid cluster and charge-carrying cation combinations, implying that the influence of the coupled product of the steric factor and activation energy on the collision rate is less for larger clusters. Somewhat surprisingly, quite often, A _sys K _chem for dimer cluster ions is higher than that of monomer ions, indicating that the back reaction rate is the highest for amino acid dimers. Although K _phy also decreases with increasing cluster size, the reduction of A _sys K _chem is more drastic, leading to a net reduction in the reaction rate constant. For singly protonated species, A _sys K _chem decreases by several orders of magnitude (note that some data for tetramer and pentamer ions are not shown, as there was no decrease in signal intensity observed for these clusters upon interaction with TMA vapor) for clusters greater than a size of ∼0.5 nm, indicating that above this size, the back reaction rate is negligibly small. As TMA vapor molecules are extremely basic in the gas phase (although we note that this does not necessarily ensure that back charging reactions with TMA vapor molecules would be faster than reactions with other vapor molecules), this size can be considered as an approximate threshold value below which back reactions need to be considered for positively charged cluster ions. We thus conclude that the rate of charge transfer from only the smallest cluster ions (with sizes close to that of the vapor molecules themselves) to vapor molecules is no longer negligible. Above this critical size, however, it is simply sufficient to calculate the forward reaction rate to determine aerosol particle charging rates. In the purely free molecule regime, the model described here [Equation (2) generalized for any cluster–vapor combination], in which the charge transfer rate constants are decomposed to K _chem and K _phy, effectively describes charge transfer processes in both the diffusion charging (large particle size, K _chem → 0) and chemical ionization (K _chem > 0) regimes.

We must strongly emphasize that the reported critical size of ∼0.5 nm is an estimate based on the data taken for amino acid clusters with charge removal via collisions with TMA vapor molecules. The chemicals chosen for analysis here were simply chosen for ease of use and merely to examine whether back charging occurs with a vapor of high gas-phase basicity. The considerable variation in back charging rate for different amino acid clusters suggests that there is a strong material dependency to this process. Therefore, to determine if a back reaction will occur between a particular charged particle and a vapor molecule (for example, atmospheric aerosol clusters), controlled studies such as the one described here need to be undertaken. Furthermore, with our available data, it appears that the rate of the back reaction decreases as a smooth function of size; thus, any definition of a critical size is somewhat qualitative. Finally, while the assessment of the back reaction rate performed here allows us to better understand the dynamics of aerosol cluster charging, a complete model of cluster charging needs to take into account the probability of ionization of an aerosol cluster by a vapor ion (K _chem for the forward reaction) and further examination of aerosol cluster charging dynamics is necessary.

CONCLUSIONS

The occurrence and the size dependency of back charging reaction rates in collisions between cluster ions and gas molecules were determined for the first time. The procedure developed can be used to estimate a critical particle size below which back reaction rates have a considerable effect on charging kinetics for collision-based reactions between neutral vapor molecules and charged aerosol particles. In this study, measurement of back reaction rates for collisions between charged amino acid clusters ([(AA) _x (I) _y ⁺], x denotes the cluster size and y = 1 or 2 in our study) and uncharged TMA molecules was carried out. The model was developed to describe this process in which the enhancement in the collision rate due to the presence of attractive potentials such as image and van der Waals potentials between charged clusters and uncharged TMA molecules were accounted for. The coupled product of this enhancement factor and the collision frequency, K _phy, along with the measured relative rate constants, K _B A _sys, helped extract qualitative information on the chemical rate coefficient, K _chem (where K _chem = steric factor × activation energy).

On the basis of this study, we draw the following conclusions:

1.	Back reactions can occur during collisions between TMA molecules (neutral molecules) and both singly and doubly charged amino acid cluster ions (charged particles).
2.	The rate constants for these back charging reactions are dependent on the amino acid cluster size and the material of the cationic species charging the amino acid cluster. The reaction rates are surprisingly found to be highest for amino acid dimers.
3.	In the case of both singly and doubly charged amino acid clusters, the back reaction rate constants are higher for the smaller amino acid clusters compared with the larger ones. With increasing cluster size, the rate of the back charging reaction drops, indicating that the back reaction is energetically unfavorable. For a particular cluster size, the singly protonated cluster had the highest back reaction rate constants, but sodiated and potassiated clusters can also lose charge to vapor molecules. Likewise, in the case of doubly charged clusters, those that were doubly protonated ones had the highest back charging rate constants.
4.	An approximate critical size for collisions between TMA molecules and singly protonated amino acid clusters is ∼0.5 nm, implying that back charging reaction rates need to be accounted for when studying collision kinetics for cluster sizes below 0.5 nm.
5.	While a size dependency of the back charging rate was to be expected given the success of the limiting sphere theory alone in describing nanoparticle charging in the gas phase, our work here does little to elucidate the underlying reason for which the K chem for the back reaction decreases with size. A plausible explanation is that the electrostatic capacity of a particle is linearly proportional to its radius and thus a larger particle can more easily retain excess charge. This would also explain the occurrence of the back reaction for larger doubly charged clusters, which also decreases with increasing size. At present, however, this is only speculation.

Acknowledgments

This work was partially supported by the National Science Foundation award CHE-1011810.

[Supplementary materials are available for this article. Go to the publisher's online edition of Aerosol Science and Technology to view the free supplementary files.]