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The sorption of vapor molecules onto pre-existing nanometer sized clusters is of importance in understanding particle formation and growth in gas phase environments and devising gas phase separation schemes. Here, we apply a differential mobility analyzer-mass spectrometer based approach to observe directly the sorption of vapor molecules onto iodide cluster ions of the form (MI)xM+ (x = 1-13, M = Na, K, Rb, or Cs) in air at 300 K and with water saturation ratios in the 0.01-0.64 range. The extent of vapor sorption is quantified in measurements by the shift in collision cross section (CCS) for each ion. We find that CCS measurements are sensitive enough to detect the transient binding of several vapor molecules to clusters, which shift CCSs by only several percent. At the same time, for the highest saturation ratios examined, we observed CCS shifts of up to 45%. For x < 4, cesium, rubidium, and potassium iodide cluster ions are found to uptake water to a similar extent, while sodium iodide clusters uptake less water. For x ≥ 4, sodium iodide cluster ions uptake proportionally more water vapor than rubidium and potassium iodide cluster ions, while cesium iodide ions exhibit less uptake. Measured CCS shifts are compared to predictions based upon a Kelvin-Thomson-Raoult (KTR) model as well as a Langmuir adsorption model. We find that the Langmuir adsorption model can be fit well to measurements. Meanwhile, KTR predictions deviate from measurements, which suggests that the earliest stages of vapor uptake by nanometer scale species are not well described by the KTR model.
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Analysis of heterogeneous water vapor uptake by metal iodide cluster ions via
differential mobility analysis-mass spectrometry
Derek Oberreit, Vivek K. Rawat, Carlos Larriba-Andaluz, Hui Ouyang, Peter H. McMurry, and Christopher J.
Hogan Jr.
Citation: The Journal of Chemical Physics 143, 104204 (2015); doi: 10.1063/1.4930278
View online: http://dx.doi.org/10.1063/1.4930278
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/143/10?ver=pdfcov
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THE JOURNAL OF CHEMICAL PHYSICS 143, 104204 (2015)
Analysis of heterogeneous water vapor uptake by metal iodide cluster
ions via differential mobility analysis-mass spectrometry
Derek Oberreit,1,2 Vivek K. Rawat,1Carlos Larriba-Andaluz,1,a) Hui Ouyang,1
Peter H. McMurry,1and Christopher J. Hogan, Jr.1,b)
1Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
2Fluid Measurement Technologies, Inc., Saint Paul, Minnesota 55110, USA
(Received 28 June 2015; accepted 26 August 2015; published online 14 September 2015)
The sorption of vapor molecules onto pre-existing nanometer sized clusters is of importance in
understanding particle formation and growth in gas phase environments and devising gas phase sepa-
ration schemes. Here, we apply a dierential mobility analyzer-mass spectrometer based approach to
observe directly the sorption of vapor molecules onto iodide cluster ions of the form (MI)xM+(x =1-
13, M =Na, K, Rb, or Cs) in air at 300 K and with water saturation ratios in the 0.01-0.64 range. The
extent of vapor sorption is quantified in measurements by the shift in collision cross section (CCS)
for each ion. We find that CCS measurements are sensitive enough to detect the transient binding
of several vapor molecules to clusters, which shift CCSs by only several percent. At the same time,
for the highest saturation ratios examined, we observed CCS shifts of up to 45%. For x <4, cesium,
rubidium, and potassium iodide cluster ions are found to uptake water to a similar extent, while
sodium iodide clusters uptake less water. For x 4, sodium iodide cluster ions uptake proportionally
more water vapor than rubidium and potassium iodide cluster ions, while cesium iodide ions exhibit
less uptake. Measured CCS shifts are compared to predictions based upon a Kelvin-Thomson-Raoult
(KTR) model as well as a Langmuir adsorption model. We find that the Langmuir adsorption model
can be fit well to measurements. Meanwhile, KTR predictions deviate from measurements, which
suggests that the earliest stages of vapor uptake by nanometer scale species are not well described by
the KTR model. C2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4930278]
INTRODUCTION
Vapor molecule sorption (heterogeneous uptake, defined
as the sorption of one species onto a chemically distinct spe-
cies) onto nanometer scale ions is of interest for several rea-
sons. In many gas phase environments, heterogeneous uptake
can control the rates of formation and growth of condensed
phase entities (e.g., molecular clusters and aerosol parti-
cles).16Measurement systems can be developed in which
heterogeneous uptake alters the size and structure of chemi-
cally distinct ions to varying degrees; this enables instruments
which separate ions based upon structure (e.g., low field and
high field ion mobility spectrometries) to discriminate be-
tween ions which are similar in structure in the absence of
vapor dopants but exhibit varying degrees of uptake.712 In
modeling heterogeneous uptake, it is commonplace to apply
classical models, namely, the Kelvin-Thomson model1315
and the Köhler model.1618 These models enable prediction
of equilibrium sorption coecients, which are ratios of the
number concentrations of ions with gvapor molecules sorbed
to the number concentrations with g1 sorbed at equilib-
rium and which govern the extent of uptake in controlled
vapor concentration environments. While classical calcula-
tions agree qualitatively with experimental measurements of
a)Current address: Department of Mechanical Engineering, Indiana
University-Purdue University, Indianapolis, Indiana 46202-5132, USA.
b)Author to whom correspondence should be addressed. Electronic mail:
hogan108@umn.edu. Tel.: 1-612-626-8312. FAX: 1-612-625-6069.
sorption in several instances,19 as well as with measurements
of condensed phase entity growth,14,20,21 there are a series
of experimental observations of vapor molecule uptake that
are not explained by these models, such as the influence of
ion chemical composition and polarity on the extent of up-
take14,22 and unanticipated uptake rate functional dependencies
on temperature.23,24 Further, there are quantitative dierences
in classically predicted and measured equilibrium sorption
coecients.25 As an alternative, computational approaches
can now be used to theoretically study sorption2631 without
invoking classical assumptions (i.e., that the sorbed species
has identical properties to the bulk condensed phase); however,
experiments remain necessary to better test both classical and
computational predictions.
Experiments to-date have not clearly established the link
between structure/size shifts and equilibrium sorption coef-
ficients for ions in the nanometer size range. Heterogeneous
uptake has been examined with tandem mobility analysis3235
as well as with electrodynamic balances36 and optical trapp-
ing.37,38 These methods are usually limited to ions in the >5 nm
size range (with supermicrometer particles needed for electro-
dynamic balances and optical trapping) and are further insen-
sitive to the addition or loss of a single vapor molecule from
the surface of an ion. Conversely, single vapor molecule sorp-
tion events are detectable in high pressure mass spectrometry
(HPMS) systems,19,25 yet HPMS is limited to vapor concen-
trations well below saturation, thereby limiting the number
of attached vapor molecules that can be measured.19 Field
0021-9606/2015/143(10)/104204/11/$30.00 143, 104204-1 ©2015 AIP Publishing LLC
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104204-2 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
asymmetric waveform ion mobility spectrometry-mass spec-
trometry (FAIMS-MS) systems often exploit dierential
amounts of heterogeneous uptake by ions to distinguish iso-
mers from one another.7,8As operated, existing FAIMS-MS
technology only provides separation capability; it does not
provide quantitative information on the extent of heteroge-
neous uptake. Heterogeneous uptake may also be studied in
expansion chamber based “nucleation probability” experi-
ments;14,15,39 though enabling very precise measurement of
the vapor saturation ratio, such experiments only facilitate
observation of ions after they are grown into micrometer sized
droplets, making it dicult to link measurements to the early
stages of uptake. Finally, infrared spectroscopy can be used
to quantitatively explore the structures of sorbed vapor-ion
complexes.4044 With this technique as well, there are limita-
tions to what can be probed in terms of the sizes and chemical
complexity of the ions.
There exists a “window” in the sub 2 nm size range
with vapor saturation ratios in the 0.10–1.0 range, in which
vapor sorption onto ions is of interest as both a naturally
occurring phenomenon and in the design of gas phase sepa-
ration schemes, but wherein quantification of the extent of
sorption has been dicult. In this work, we develop a method
to link the extent of vapor molecule sorption by chemically
identified ions to changes in ion size and structure. This
method involves measurements with a low field Dierential
Mobility Analyzer-Mass Spectrometer (DMA-MS a form of
ion mobility spectrometry-mass spectrometry), wherein the
DMA is used to separate and select ions based on their collision
cross sections (CCSs). The DMA-MS method is applicable
to ions in the 1 nm size range and can be used to examine
vapor molecule uptake at any vapor molecule concentration
up to saturation. In the sections titled “Experimental Methods”
and “Results and Discussion,” the DMA-MS measurement
method is described and an analysis approach linking the shift
in CCSs inferred from measurements to equilibrium sorption
coecients for successive vapor molecules is provided. The
method is applied to measurements of water vapor molecule
uptake by positively charged metal salt cluster ions of the
form (MI)xM+, where M =Cs, Rb, K, or Na and x=1-13.
These ions are chosen mainly for ease of formation in the gas
phase and the past precedent in study ions of this type.4548
The observed extents of heterogeneous uptake are compared
to modified classical theory predictions as well as to Langmuir
adsorption isotherm based models as a demonstration of how
measurements can be used to test predictions of equilibrium
sorption coecients.
EXPERIMENTAL METHODS
Differential mobility analysis-mass spectrometry
A schematic of the DMA-MS system as operated in this
study is shown in Figure 1. DMA model P5 (SEADM, Boe-
cillo, Spain) was interfaced with a QSTAR XL mass spec-
trometer (Applied Biosystems); the DMA was operated as
described previously.46,49,50 Positively charged cluster ions (the
test ions for this study) of sodium, potassium, rubidium, and
cesium iodide were produced via positive mode electrospray
FIG. 1. A schematic diagram of the dierential mobility analyzer-mass
spectrometer (DMA-MS) system used to examine vapor molecule sorption
by electrospray generated cluster ions.
ionization (ESI) of 10 mM salt solutions in high performance
liquid chromatography grade methanol and were directed into
the DMA electrostatically against a counterflow of air. Ultra-
high purity (UHP) air (Airgas) was used for the DMA sheath
flow (and correspondingly for the counterflow). Distinct from
prior studies utilizing DMA-MS measurements, to humid-
ify the sheath flow, a custom-made nebulizer was used to
introduce controlled amounts of water vapor into the sheath
flow. Details of the nebulizer design and a schematic of it
are provided in Oberreit et al.33 A chilled-mirror dewpoint
hygrometer (General Eastern, Hygro M4) was attached to the
ESI chamber and was used to determine the total water content
of the sheath and counterflow air. The sheath flow temperature
was controlled at 299-300 K using a fan cooled heat exchanger
attached to the sheath flow recirculation tubing. The combined
water vapor content and temperature control system facilitated
mobility measurements in the water saturation ratio (S)range
of 0.01–0.64.
The DMA was stepped in 10 V increments from 900
to 3600 V applied across its electrodes, with the ESI source
voltage floating above the upper electrode. Mass spectra were
collected using the time-of-flight tube of the QSTAR XL sys-
tem at each applied potential dierence in the DMA. The DMA
was calibrated through measurement of a known-mobility
standard ion;51 because the DMA is a linear-mobility spec-
trometer, the ratio V*ZS, where Vis the voltage of maximum
transmission and ZSis the ion’s mobility measured at satura-
tion ratio S, is a constant. The ion selected for calibration in
prior work has been the tetraheptylammonium+ion. However,
at the higher saturation ratios examined, we found that the
mobility of the tetraheptylammonium+ion shifted noticeably
(but only by several percent), which was indicated by an
increase in the DMA voltage required to transmit the ion.
Also at higher saturation ratios, the mass spectrometer detected
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104204-3 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
ions not only at the expected m/z (410 Da) but also at the
m/zcorresponding to tetraheptylammonium+-H2O (428 Da).
Heterogeneous uptake of water molecules may hence shift
the mobility of tetraheptylammonium+ions, rendering them
unsuitable for instrument calibration under humidified condi-
tions. We instead used the tetradodocylammonium+ion for
calibration; for this ion, a shift in the DMA voltage required
for maximal transmission was not observed and water adduct
ions were never observed. The inverse mobility (1/ZS)of the
tetradodecylammonium+ion at 293 K and near 101 kPa was
measured to be 1.401 V s cm2by Ude and Fernandez de la
Mora.51 For an ion of this inverse mobility, the influence of
gas molecule polarization (the ion induced dipole potential
between gas molecules and the cluster ion) is expected to
be minimal.46,5255 The published mobility was thus adjusted
to the measurement temperature by multiplying by the fac-
tor (293 K/T)1/2, which is based on the assumption that
tetradodecylammonium+undergoes hard sphere interactions
with the background gas molecules.
RESULTS AND DISCUSSION
Observations of heterogeneous uptake
As discussed by Ouyang et al.,46 positive mode ESI of
iodide salt solutions leads to the formation of ions of the type
(MI)x(M+)z, where M =Na, K, I, or Cs. Here, we elect to
focus on water uptake by selected ions with x =1-13, and
z=1 (the x =0 ions were also detected, but appear to bind
transiently to low concentration gas phase impurities, compli-
cating assessment of heterogeneous uptake). Uptake of water
vapor by cluster ions leads to not only a shift in ion mobility
but also a shift in mass, and ideally, it would be possible to
assess the extent of uptake by examining changes to mass
distributions. Although not shown, in our experiments, for the
smallest ions examined (x =1-2), we commonly observed ions
shifted in mass by +18 Da units, which is indeed indicative
of water sorption. However, upon being transmitted through
the DMA, ions enter a high pressure drop, high electric field
system, in which they can either (1) undergo high energy gas
molecule collisions, leading to ion heating and dissociation
of sorbed vapor molecules and loss of a cation-anion pairs,56
or (2) travel along trajectories wherein the vapor saturation
ratio increases, leading to additional condensation of water
onto ions.57 Subtle changes to inlet operating conditions have
been shown to induce appreciable amounts of either water
condensation or evaporation from hydrated ions,58 and for this
reason, the mass distributions of water molecules bound are
not reliable measures of the extent of heterogeneous uptake at
the prescribed vapor saturation ratio.
Conversely, mobilities were measured in a temperature
and pressure controlled region, with ions migrating at low
speed relative to their mean thermal speeds. Therefore, mobil-
ity shifts can be directly correlated with the extent of heteroge-
neous uptake occurring under well-defined conditions. Repre-
sentative inverse mobility spectra at 4 water saturation
ratios are shown in Figure 2for the (CsI)2Cs+,(CsI)4Cs+, and
(CsI)6Cs+ions, with inverse mobility derived from DMA cali-
bration. Plotted signal intensities (arbitrary units) are normal-
FIG. 2. Normalized inverse mobility spectra for mass selected cesium iodide
cluster ions at four discrete water saturation ratios. Shifts to larger inverse
mobilities are indicative of water vapor uptake by cluster ions.
ized for each ion; higher signal intensities were observed
for less massive ions, and with increasing S, we observed a
decrease in absolute signal intensity, particularly for the most
massive ions examined. We attribute the decreasing signal
intensity at large saturation ratios to water condensation onto
ions in the mass spectrometer inlet (after DMA measurement),
growing ions to masses larger than can be detected/transmitted
in the mass spectrometer. For all detected ions, a shift to
larger inverse mobilities is observed with increasing water
saturation ratio. To further analyze measurements, we convert
each measured inverse mobility to a mean ion-neutral CCS
(denoted as Sat saturation ratio S), via the Mason-Schamp
equation,59
S=π µ
8kT
3ze
4ρgasZS
(1)
in which zis the ion charge state, eis the unit electron charge, k
is Boltzmann’s constant, Tis the gas temperature, µis the gas
molecule-ion reduced mass (approximated in the absence of
sorbed vapor), and ρgas is the gas mass density. The Mason-
Schamp equation is itself an approximation, which is only
applicable in suciently low electric field strength systems60
as well as in instances where the ion size relative to the gas
molecule mean free path (near 66 nm here) is small.61,62 While
these criteria are met in the presented experiments, even in
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104204-4 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
the low-field limit, the CCS is a complex parameter that is
dependent not only the physical cross section of the ion but also
the measurement temperature and the interactions between gas
molecules and ions during impingement. A change in any of
these parameters will undoubtedly lead to a change in the
CCS. However, the focus of this work is to understand the
changes in CCSs due to water sorption onto ions under constant
temperature and pressure conditions; under these conditions,
the CCS is primarily a measure of ion size and structure and
heterogeneous uptake will typically lead to an increase in CCS.
For all measurements, the ratio S/0, i.e., the ratio of the
CCS measured at saturation ratio Sto the dry condition CCS,
is provided in Table S1 of the supplementary material,63 and
for ions of specific nvalues, the value of S/01 is plotted
as a function of Sin Figure 3. Several features are apparent
in these plots. First, under nearly all circumstances, we find
that S/01 versus Scurves are slightly concave down-
ward, yet CCSs appear to increase continuously with increas-
ing saturation ratio. This behavior is similar to that observed by
Rawat et al.64 for isopropanol uptake by peptide ions, though
they observed that uptake ceased beyond a critical saturation
ratio. We compare and contrast the shapes of the S/01
versus Scurves with model calculations in the sections titled
“Modeling heterogeneous uptake” and “Measurement-model
comparison.” Second, for lower values of x (1-2), we find
that ions composed of potassium, rubidium, and cesium iodide
exhibit similar uptake behavior, with noticeably less uptake
by sodium iodide cluster ions. Conversely for x 3, we find
that sodium iodide cluster ions exhibit the largest extents of
uptake, followed by potassium iodide, rubidium iodide, and
finally cesium iodide cluster ions. Third, we find that the extent
of uptake does not correlate strongly (positively or negatively)
with x for potassium and rubidium iodide clusters, while the
extent of uptake appears to increase and decrease with x, for
sodium iodide and cesium iodide cluster ions, respectively.
However, for no ion do we observe a monotonic increase or
decrease with x in the extent of uptake (which is examined in
further detail subsequently). In total, we find that the extent of
uptake depends on both cluster size and chemical composition,
and hence ion structure.
Modeling heterogeneous uptake
The goal of this study is not only to demonstrate that
DMA-MS measurements can be used to probe heterogeneous
uptake at modest saturation ratios but also to show that the
FIG. 3. The measured value of
S/01 as a function of the water
saturation ratio in the dierential
mobility analyzer for mass identified
cluster ions.
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104204-5 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
shifts in CCS can be linked directly to equilibrium sorption
coecients. To establish this link, first, we note that the number
of water molecules bound to an ion is not a constant; rather,
water molecules continuously sorb and desorb with each ion
probing the equilibrium distribution for the number of bound
vapor molecules. We define the probability of an individual ion
having gvapor molecules bound at any given instant as Pg. We
also define eective unimolecular equilibrium sorption coe-
cients (K
eq,g , dimensionless equilibrium constants) through the
relationship,
K
eq,g =ng
ng1,(2a)
where ngand ng1are the number concentrations of ions with g
and g1 water vapor molecules bound. Noting the ergodicity
of systems in equilibrium, the probability that a single ion has
gmolecules bound to it is equivalent to the fraction of ions with
gvapor molecules bound, leading to Pgdefined as
Pg=ng
n0+i=
i=1ni
.(2b)
Combining Equations (2a) and (2b),Pgcan subsequently be
expressed as
Pg=g
j=1K
eq,j
1+i=
i=1j=i
j=1K
eq,j
for g1 (2c)
and
Pg=1
1+i=
i=1j=i
j=1K
eq,j
for g=0.(2d)
Each ion traverses the DMA in a time ttot, and with a linear
electric field in a parallel-plate DMA of magnitude E, the
electrode to electrode distance (LDMA, traversed by the ions) is
equal to the product of ttot,E, and the ion’s measured mobility,
LDMA =ZSttotE=κ0t0E+κ1t1E+κ2t1E
+· · · κgtgE+· · · +κtE,(2e)
where tgdenotes the time an ion spends within the DMA with
gvapor molecules bound, and κgis the cluster ion’s mobility
specifically with g vapor molecules sorbed (in constant to ZS,
the mobility measured at saturation ratio S). With the equilib-
rium relation Pg=tg/ttot, the ratio ZS/Z0is expressed as
ZS
Z0
=
1+g=
g=1κg
κ0j=g
j=1K
eq,j
1+i=
i=1j=i
j=1K
eq,j
.(2f)
Using Equation (1) to link mobility and CCS (both for Zand
κ) enables Equation (2f) to be rewritten as
S
0
=
1+i=
i=1j=i
j=1K
eq,j
1+g=
g=10
gj=g
j=1K
eq,j
,(2g)
where gis the CCS of the cluster ion specifically with gvapor
molecules bound. Equation (2g) therefore facilitates compar-
ison between DMA-MS observed structural modifications to
ions and predictions of equilibrium sorption coecients (from
any theoretical model), provided the ratio 0/gcan be esti-
mated for all gand provided that the introduction of vapor
molecules into the DMA does not substantially alter ion mobil-
ities due to the change in gas composition (an eect which is
anticipated to be negligible for water and is addressed in the
work of Rawat et al.64).
Comparison of measurements to models of heterogeneous
uptake requires both models of the CCSs of ions with a specific
number of vapor molecules bound and methods to calculate
K
eq,g . The calculation of CCSs is non-trivial. Here, we leverage
recent developments in gas molecule scattering calculations
for air made by Larriba-Andaluz and coworkers52,53,6567 as
well as the measurements of Ouyang et al.46 of the CCSs of
bare (dehydrated) iodide salt cluster ions. Both calculations
and measurements suggest that the CCSs of iodide salt ions
of the form (MI)nM+can be approximated by the relationship,
g=ΛξPAg,(3a)
where PAgis the orientationally averaged projected area of a
cluster-gas molecule complex with g vapor molecules bound, ξ
is the momentum scattering coecient, found by Ouyang et al.
to be 1.36 for NaI, 1.27 for KI, 1.23 for RbI, and 1.19 for CsI
(dependent upon the manner in which gas molecules impinge
and are reemitted from cluster structure surfaces52,53,68,69 and
assumed independent of the extent of water vapor sorption
here). Λis a factor which accounts for the increase in the CCS
due to attractive forces between the ion and polarizable gas
molecules, defined as53
Λ1+Ψpol 0.322 +1
ξ0.0625 +0.1212ΨpolΨpol <1,
(3b)
Ψpol =παpolz2e2
8ε0kTPAg2,(3c)
where αpol is the gas molecule polarizability and ε0is the
permittivity of free space. With the approximation that ξis
independent of the extent of heterogeneous uptake, Equa-
tions (3a)(3c) lead to
0
g
=Λ0PA0
ΛgPAg
.(3d)
Prediction of 0/ghence amounts to prediction of projected
area ratios and implementation of a function accounting for
the ion-induced dipole potential. In related studies of hetero-
geneous uptake, performed with a DMA coupled to an atmo-
spheric pressure drift tube ion mobility spectrometer,33 we
quantified the extent of vapor molecules sorption onto 2–7 nm
nanoclusters through a relationship similar to Equation (2g).
We approximated all nanoclusters as spheres, linking the pro-
jected areas to nanocluster diameters, and thus linking their
size and structures to their mobilities in the manner utilized
by Ku and Fernandez de la Mora70 and Larriba et al.71 While
the spherical approximation for nanoclusters composed of 102-
103cation-anion pairs is reasonable, it is not valid for clusters
with n 13.46 We instead modeled cluster ion structures using
density functional theory (DFT) and calculated the projected
areas of DFT inferred structures. Structures for clusters of the
type (MI)xM+*(H2O)g(x =1-3, g =0-30) were generated using
the Gaussian 09 software package (Gaussian, Inc., Walling-
ford, CT), as described by Ouyang et al.46 The B3LYP den-
sity functional72 was employed with the basis set LANL2DZ,
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104204-6 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
which applies Los Alamos ECP (eective core potential) plus
DZ (double zeta).7375 Symmetry restrictions were not applied,
and vibration frequencies were calculated. All structures evalu-
ated had positive frequencies, indicating they are local minima
rather than transition states. Complete characterization of clus-
ter structures requires the determination of the number of local
minimum structures and their energy dierences.76 However,
except in rare circumstances where a cluster has both a linear
and compact stable isomer (only found at x <5), the projected
areas calculated (using the procedure noted subsequently) for
dierent isomers dier by only several percent. For computa-
tional simplicity, we based projected areas for implementation
in Equation (3d) on the lowest energy structure obtained.
Depictions of DFT calculated structures for clusters with
x=6 and with varying numbers of bound water molecules
are shown in Figure 4. All atoms are depicted as spheres with
relative radii proportional to the radii used in projected area
calculations: Na (blue): 1.16 Å, K(gold): 1.52 Å, Rb (purple):
1.66 Å, Cs (yellow): 1.81 Å, I (green): 2.06 Å, H (white):
1.20 Å, and O (red): 1.52 Å, which are in line with the ionic
radii for the charged species (cations and anions) and the van
der Waals radii for hydrogen and oxygen. Qualitatively, clus-
ters with a limited number of water molecules sorbed (g<6)
retain their core structures observed in the absence of water,
and the water molecules themselves appear to bind to clusters
FIG. 4. Depictions of (MI)6M+structures predicted via density functional
theory with selected numbers of water molecules (g)bound.
at specific sites. As the number of sorbed water molecules
increases, the cluster structures appear to open, leading to
water present in cluster interstices. However, even with 30
water molecules bound, total dissolution of most salt clusters
is not observed. Similar results were obtained for clusters with
higher and lower x, except that dissolution was possible for
the smallest xclusters. The projected areas of all structures
were calculated using the projected area calculator of the IMoS
software package (available freely from Dr. Carlos Larriba-
Andaluz and described in detail previously52) with an added
“probe radius” to account for the size of the impinging mole-
cules (1.5 Å for air). Values for PAgwhere a structure was not
predicted were found by linear interpolation of the calculated
PAgdata up to the largest calculated cluster gmax. Beyond gmax,
PAgwas approximated using the equation,
PAg=π*,PAgmax
π3/2
+3vw
4πggmax+-
2/3
,(3e)
where vwis the volume of the condensed phase vapor mole-
cule (based upon its bulk density in the liquid phase33). A
summary of the calculated PA values is provided in Table
S2 of the supplementary material,63 and corresponding plots
of g/01 for select clusters are shown in Figure 5. For
all clusters examined, the sorption of fewer than 15 water
molecules shifts the CCS by 30% or more, and we therefore
anticipate it is 100-101(time based average) water molecules
which are sorbing to clusters at the saturation ratios examined.
However, we reiterate that as each cluster migrates through
the DMA, the number of water molecules bound is transient,
leading to Equation (2g) describing the shift in mobility.
The sorption and desorption of water molecules can
be described by models of K
eq,g . We elect to compare
two such models to experimental results. First, similar to
Oberreit et al.33 and Rawat et al.,64 based upon the classical
Kelvin-Thomson model with incorporation of Raoult’s law
(the Kelvin-Thomson-Raoult (KTR) model), K
eq,g can be
expressed as
K
eq,g =S
ax
exp Eg
kT   µv, g
µv, g 11/2PAg1
PAg
×ηψD,g 1(KTR),(4a)
where Sis the saturation ratio, axis the activity coecient
of water (the sorbing vapor) over the cluster surface (with x
cation-anion pairs), µv, g is the reduced mass of the sorbing
vapor-cluster ion pair, η(ψD,g 1)is an enhancement factor
in vapor-cluster ion collision rate considering the ion-dipole
potential (significant because vapor dopants have non–
negligible dipole moments, µD), and ψD, g is the ion-dipole
energy to thermal energy ratio,
ψD,k=ze µD
4εokT PAg
.(4b)
Based upon the analysis of Su and Bowers,77 we calculate
η(ψD,k)with the equation,
η(ψD,k)=1+CψD,k(4c)
with the approximation C=0.6 (with C=1 corresponding
to complete dipole alignment and C=0 corresponds to no
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104204-7 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
FIG. 5. The values of g/01 for selected cluster ions, as predicted for model cluster structures.
dipole alignment). Egis the change in cluster ion enthalpy
associated with the sorption of a single vapor molecule (from
g1 to gmolecules sorbed), described considering the Kelvin
and Thomson influences,
Eg=4σPAgPAg1+π1/2(ze)2
8ε011
εr
×*,
1
PAg11/21
PAg1/2+-,(4d)
where σis the eective surface tension of the sorbed liquid and
εris the dielectric constant (of water). Equation (4d) is written
approximating each cluster as a sphere, which is an assumption
invoked in derivation of the Kelvin and Thomson enthalpy
changes. Second, considering Langmuir-like adsorption, K
eq,g
can be described by the equation,64
K
eq,g =S
axζx+1
g1  µv,g
µv, g 11/2PAg1
PAg
×ηψD,g 1(Langmuir),(5)
where ζxis the maximum (integer) number of water molecules
which be sorbed to a cluster. In implementing Equation (5)
with Equation (2g), it is necessary to truncate all sums and
multiplicative sums at ζx, as in the Langmuir model, no ion can
uptake more than ζxvapor molecules. In addition, unlike the
KTR model, the Langmuir model does not contain an enthalpy
term; uptake is entropically driven.
Measurement-model comparison
While we elect to use Equations (4) and (5) to compare
to experimental results, we remark that both equations are
derived under the assumption that cluster ion structure
TABLE I. A summary of the fit parameters used in Figure 6plots with the
KTR and Langmuir models.
KTR Langmuir
Cluster type x axσ(N m1)axζx
Sodium 1 0.62 0.108 0.95 5
Iodide 4 0.98 0.057 11.0 34
9 0.95 0.020 2.00 33
13 0.45 0.020 2.50 40
Potassium 1 1.00 0.090 1.20 15
Iodide 4 0.75 0.055 1.00 10
9 0.95 0.020 1.50 18
13 0.70 0.010 0.50 7
Rubidium 1 0.95 0.085 4.30 17
Iodide 4 0.80 0.040 1.50 13
9 0.50 0.010 0.85 12
13 0.60 0.015 0.50 6
Cesium 1 0.8 0.09 1.20 6
Iodide 4 0.9 0.045 4.00 10
9 0.98 0.015 2.20 10
13 0.55 0.018 1.00 4
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104204-8 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
FIG. 6. Comparison of the measured S/01 ratios for selected cluster ions to predictions based upon the KTR model with the fit parameters provided in
Table I.
negligibly aects vapor sorption, which is not consistent with
experimental results. We thus perform comparison qualita-
tively; for selected clusters with the KTR model, we attempt
to fit values of σand ax, and with the Langmuir model, we
fit values of ζxand ax. For clusters with x=1,4,9, and 13,
the fit KTR and Langmuir model parameters are provided
in Table I. Focusing first on the KTR model, comparison of
measurements and model calculations is plotted in Figure 6.
FIG. 7. Comparison of the measured S/01 ratios for selected cluster ions to predictions based upon the Langmuir model with the fit parameters provided
in Table I.
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104204-9 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
FIG. 8. The CCS weighted “Average Sorbed Water Molecules” for selected cluster ions, as a function of saturation ratio, determined by direct comparison of
measured Svalues and calculated gvalues.
For all cluster ions, predictions can be brought to be of the
same order of magnitude as measurements using fitted sur-
face tensions of similar order to the bulk surface tension of
water (0.073 N m1) and activity coecients below unity (ex-
pected for salt cluster ions). However, in all circumstances, the
shapes of the calculated curves are qualitatively dierent from
the curves derived from experimental measurements; unlike
experimental measurements, the KTR model predicted curves
are consistently concave upward (with semi-log axes). For all
clusters, better agreement is found between with Langmuir
model predictions (Figure 7). Fitted activity coecients above
unity presumably arise because of the lack of an enthalpy
barrier to uptake in the Langmuir model; because the fitting
procedure is qualitative, we elect not to modify the Langmuir
model to include an enthalpy term. That the Langmuir model
can be fit to results is further evidence that the KTR model
insuciently describes the earliest stages of heterogeneous va-
por uptake and suggests the KTR model should not be invoked
in predicting either the extent of uptake or uptake rates in this
circumstance.
As a final note, the values of ζxused in fits range from 4
to 40. Additional support that the number of water molecules
bound to clusters in experiments falls within this range (but
below ζxfor all clusters) is provided in Figure 8, which is
a plot of the CCS weighted average number of sorbed water
molecules, determined by comparison between the shift in
CCSs observed in experiments and the calculated shifts in Fig-
ure 4(with linear interpolation used when observed shifts fall
between integer numbers of water molecules bound). Though
not the true average number of water molecules bound during
transit through the DMA, these values do enable us to estimate
how hydrated each particular cluster becomes. With the excep-
tion of cesium iodide, the least hydrated cluster is found to be
the (MI)2M+cluster, with the average number of water mole-
cules below 2 for most examined saturation ratios. Conversely,
for all cluster types, the (MI)9M+is the most hydrated. Figure 8
results additionally confirm that larger sodium iodide clusters
sorb water to a larger extent than potassium iodide or rubidium
iodide, and cesium iodide clusters of all sizes sorb relatively
few water molecules. We did not observe sucient hydration
for complete dissolution of any of the examined clusters.
CONCLUSIONS
We describe an IMS-MS based approach, with a dif-
ferential mobility analyzer-mass spectrometer to examine
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131.212.251.219 On: Mon, 14 Sep 2015 15:33:42
104204-10 Oberreit et al. J. Chem. Phys. 143, 104204 (2015)
heterogeneous uptake of vapor molecules by cluster ions. We
also develop methods to link experimentally observed CCS
shifts to model predictions of equilibrium sorption coecients.
The measurement approach is applied in examining water
uptake by singly charged alkali metal iodide cluster ions, with
comparison made to KTR and Langmuir models, each with
two fit parameters. Based on these measurements, we make
the following remarks.
1. If cluster ions rapidly equilibrate with their surroundings
during mobility measurement, then the mobility measured
for a given ion at a given temperature, pressure, and vapor
concentration depends upon the distribution of vapor mole-
cules bound at equilibrium.
2. Precise mobility measurements enable detection of shifts
in CCSs as small as 1% of the baseline CCS. Such shifts
for smaller ions correspond to the transient binding of few
vapor molecules, and IMS-MS measurements provide a
means to probe vapor uptake on an individual vapor mole-
cule level. We note that the ability to detect such small
shifts in CCS are facilitated by exact mass identification
subsequent to mobility analysis. They are further made
possible because shifted peaks in mobility spectra need not
be resolved from bare ion peaks (i.e., since all ions probe
the equilibrium distribution of bound vapor molecules, all
ion CCSs shift by equal amounts).
3. Comparison between measurements and models requires
both a method to predict the CCSs of ions with specific
numbers of vapor molecules bound, as well as a model
for equilibrium sorption coecients. Here, CCSs were pre-
dicted using cluster ion structural models with an approx-
imation (Equation (3a)) based upon prior measurements
of iodide salt cluster, and equilibrium sorption coecients
were based on functional forms from the KTR model and
Langmuir adsorption model. For the cluster ions and wa-
ter saturation ratios examined, we find that the Langmuir
adsorption model can be fit reasonably well to measure-
ments at 300 K, while the KTR model shows significant
deviation from measurements. This finding is of relevance
in understanding not only vapor sorption at equilibrium
but also new particle formation in gas phase, and it sug-
gests that the earliest stages of vapor uptake are inade-
quately described by Kelvin based models (which include
the KTR model, as well as the Köhler model18). Deriva-
tions of the KTR and Köhler models invoke assumptions
of a bulk liquid layer on the surface of cluster as well as
dissolution of the cluster constituents within the sorbing
vapor (i.e., the sorbed vapor is a solvent and other cluster
components are a solute); these assumptions are not consis-
tent with the structures of clusters with a limited number
of vapor molecules bound. Future research eorts should
be devoted to developing improved approaches to equilib-
rium sorption coecient determination, including compu-
tational approaches,30,78 multilayer sorption models,79 as
well as heuristic models based on experimental measure-
ments.80 Conveniently, IMS-MS measurements (using a
dierential mobility analyzer, drift tube, or other linear
mobility spectrometer at a fixed, prescribed temperature)
of CCS shifts can be compared to any model for the equi-
librium sorption coecients, independent of the model’s
assumptions.
4. Throughout this work, we have used the terms heteroge-
neous uptake and vapor sorption to refer to the binding
of water vapor molecules to cluster ions, without making
the distinction between adsorption (binding of vapor to the
cluster ion surface) and absorption (binding of vapor in the
cluster interstitial regions). We note that measurement of
CCS shifts alone cannot be used to distinguish between
adsorption and absorption; the CCS is global structural
parameter and its determination provides little informa-
tion about internal structure. At the same time, we note
that for cluster ions composed of a limited number of
molecules/atoms, the demarcation between adsorption and
absorption becomes blurred, as most atoms are exposed on
the cluster surface.
5. Though the reported measurements were made at 300 K,
of interest are measurements across a wide temperature
range to better understand how equilibrium binding coe-
cients vary with temperature (i.e., to examine separately en-
thalpic and entropic eects). Coupled with measurements at
temperatures appreciably higher or lower than 300 K, it will
be necessary to develop appropriate methods to predict ion
mobilities under these conditions, as the method invoked
here has only been tested near room temperature.
ACKNOWLEDGMENTS
This work was supported by National Science Foundation
(NSF) Grant No. CHE-1011810. D.R.O. acknowledges sup-
port from a NSF Graduate Research Fellowship (NSF GRFP),
H.O. acknowledges support from a University of Minnesota
Doctoral Dissertation Fellowship, and C.L.A. acknowledges
support from a Ramon-Areces Fellowship.
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131.212.251.219 On: Mon, 14 Sep 2015 15:33:42
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Ion mobility spectrometry is widely used for the detection of illegal substances and explosives in airports, ports, custom, some stations and many other important places. This task is usually complicated by false positives caused by overlapping the target peaks with that of interferents, commonly associated with samples of interest. Shift reagents (SR) are species that selectively change ion mobilities through adduction with analyte ions when they are introduced in IMS instruments. This characteristic can be used to discriminate false positives because the interferents and illegal substances respond differently to SR depending on the structure and size of analytes and their interaction energy with SR. This study demonstrates that ion mobility shifts upon introduction of SR depend, not only on the ion masses, but on the interaction energies of the ion:SR adducts. In this study, we introduced five different SRs using ESI-IMS-MS to study the effect of the interaction energy and size on mobility shifts. The mobility shifts showed a decreasing trend as the molecular weight increased for the series of compounds ethanolamine, valinol, serine, threonine, phenylalanine, tyrosine, tributylamine, tryptophan, desipramine, and tribenzylamine. It was proved that the decreasing trend was partially due to the inverse relation between the mobility and drift time and hence, the shift in drift time better reflects the pure effect of SR on the mobility of analytes. Yet the drift time shift exhibited a mild decrease with the mass of ions. Valinol pulled out from this trend because it had a low binding energy interaction with all the SR and, consequently, its clusters were short-lived. This short lifetime produced fewer collisions against the buffer gas and a drift time shorter compared to those of ions of similar molecular weight. Analyte ion:SR interactions were calculated using Gaussian. IMS with the introduction of SR could be the choice for the free-interferents detection of illegal drugs, explosives, and biological and warfare agents. The suppression of false positives could facilitate the transit of passengers and cargos, rise the confiscation of illicit substances, and save money and distresses due to needless delays. Keywords: Adduction, ion mobility spectrometry, mass spectrometry, shift reagent, valinol, buffer gas modifier
... Ion mobility is sensitive to molecular geometry, enabling it to separate isomers and other species that are similar in mass, which is one of the challenges of mass spectrometry, especially as ion mass-to-charge ratios are increased (Krechmer et al., 2016). For AN measurements in particular, DMA-based separation may provide an extra advantage over typical IMS drift tubes since they operate at atmospheric pressure, near room temperature, and with a variety of carrier gases (Oberreit et al., 2015), which can result in higher cluster stability under atmospherically-relevant conditions. IMS-MS and DMA-MS have been shown to be powerful tools for measuring AN properties in laboratory experiments and an IMS-MS instrument has also been successfully deployed in the field (Krechmer et al., 2016). ...
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