Download Probing Methanol Cluster Growth by Vacuum Ultraviolet Ionization

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Probing Methanol Cluster Growth by Vacuum Ultraviolet Ionization
Biswajit Bandyopadhyay, Oleg Kostko, Yigang Fang, and Musahid Ahmed*
Chemical Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, United States
S Supporting Information
*
ABSTRACT: The ability to probe the formation and growth of clusters is key to
answering fundamental questions in solvation and nucleation phenomena. Here,
we present a mass spectrometric study of methanol cluster dynamics to
investigate these two major processes. The clusters are produced in a molecular
beam and ionized by vacuum ultraviolet (VUV) radiation at intermediate
distances between the nozzle and the skimmer sampling different regimes of the
supersonic expansion. The resulting cluster distribution is studied by time-offlight mass spectrometry. Experimental conditions are optimized to produce
intermediate size protonated methanol and methanol−water clusters and mass
spectra and photoionization onsets and obtained. These results demonstrate that
intensity distributions vary significantly at various nozzle to ionization distances.
Ion−molecule reactions closer to the nozzle tend to dominate leading to the
formation of protonated species. The protonated trimer is found to be the most
abundant ion at shorter distances because of a closed solvation shell, a larger
photoionization cross section compared to the dimer, and an enhanced neutral tetramer precursor. On the other hand, the
protonated dimer becomes the most abundant ion at farther distances because of low neutral density and an enhanced charged
protonated monomer−neutral methanol interaction. Thomson’s liquid drop model is used to qualitatively explain the observed
distributions.
■
INTRODUCTION
Understanding the formation and growth of clusters is an active
area of research as these processes in principle can capture the
dynamical transition between the isolated gas phase and bulk
medium. Cluster growth via ionic association pathways are key
processes in aerosol physics1 and low temperature interstellar
chemistry.2 The reverse process, i.e., dissociation of larger
clusters by photoionization, plays a crucial role in atmospheric
chemistry.3,4 Mass spectrometry is a powerful technique to
study these processes and we used tunable vacuum ultraviolet
(VUV) radiation to study small water clusters5,6 and mixed
methanol−water hydrogen-bonded systems7 to decipher
photoionization dynamics. Measurements of photoionization
onsets and mass spectra provided information on fragmentation
mechanisms, ion−molecule reactions, and structural rearrangements of neutral and/or ionized clusters.
Continuous supersonic expansions from a small nozzle leads
to adiabatic cooling, which results in density and temperature
drop.8,9 As the expansion proceeds through the nozzle,
numerous collisions between gas atoms produces neutral
clusters. If a “seed” is added with the buffer gas, coexpansion
produces the clusters of interest. For supersonic expansions,
cluster formation and growth have been studied by varying the
initial temperature and pressure of the expanding gas.10 Various
nozzle shapes and sizes have also been used to study the effects
on cluster formation.11 Pulsed laser vaporizations,12 electric
discharge techniques,13,14 and electron guns15 routinely
produce ionic clusters with different intensity distributions
and internal temperatures by sampling the various parts of the
© 2015 American Chemical Society
supersonic expansion. In those cases, pulsed laser or electron
gun timings are adjusted with respect to the gas pulse to sample
the regimes of ion−molecule to neutral clustering. For
continuous expansions, these regimes in principle can be
accessed by varying the photoionization distance from the
nozzle. These expansions also provide for a more stable
environment compared to pulsed sources by decoupling the
fluid dynamics and ionization. In the present work, we report
an experimental strategy to systematically study cluster growth
and decay processes which are either predominated by
ionization induced association and/or dissociation pathways.
We produced a continuous molecular beam of methanol and
photoionized it at variable distances from the nozzle to sample
different regions of the expansion.
We chose methanol because of its crucial role in
astrochemical processing of hydrocarbons,16−18 atmospheric
uptake by ice nanoparticles,19 and local structure of mixed
liquids.20 Photoionization properties of alcohol−water clusters
are also important in analytical chemistry.21 There have been
numerous mass spectrometry based studies of methanol and
methanol−water clusters produced by a variety of ionization
sources including electron impact, and multi- and single-photon
ionization.20,22−38 Photoionization dynamics of these systems
are well understood, and hence this experimental approach can
Received: January 28, 2015
Revised: April 8, 2015
Published: April 13, 2015
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are registered. The photoionization spectrum of xenon has two
converging Rydberg series 5p5ns′ and 5p5nd′, the former of
which is very narrow. PIE spectra of the 5p58s′ peak are
measured using different sizes of the T4 monochromator exit
slit and two of the PIE curves are shown in Figure 2a together
examine the effect of ionization distance on the mass
spectrometry.
■
EXPERIMENTAL SECTION
The experiments are carried out in a continuous supersonic
expansion cluster machine coupled to a three meter VUV
monochromator of a newly commissioned terminal (T4) on
the Chemical Dynamics Beamline (9.0.2), located at the
Advanced Light Source, Berkeley, California. Figure 1 shows a
Figure 1. Cross-sectional view of the molecular beam machine.
schematic of the experiment. One bar of argon is passed
through a bubbler containing 99.9% pure methanol and
expanded through a 100 μm nozzle to a differentially pumped
chamber which is kept at a pressure of 2 × 10−4 Torr during the
expansion. The molecular beam is intersected with the VUV
radiation at various axial distances from the nozzle (x = 2−25
mm) and the resulting cluster ions are sampled into a time-offlight mass spectrometer. The ionization distance is varied by
changing the nozzle position with respect to the point of
intersection of molecular and VUV beams. The VUV beam is
rectangular with a dimension of 1000 × 330 μm2. A set of four
electrodes are used to guide the ions from the ionization region
to the mass spectrometer through a skimmer. The lenses are
kept at small potentials (+5, 0, −3, and 0 V, respectively) and
the skimmer is grounded.
The mass spectrometer is kept at 2 × 10−6 Torr in a second
differentially pumped chamber. A start pulse for the TOF is
provided by pulsing the repeller and accelerator plates because
of the quasi-continuous (500 MHz) nature of the synchrotron
light. The ions are pulse-extracted by fast switching of repeller
and accelerator plates to 1100 V using a pulse width of 7.0 μs.
Ions are accelerated perpendicularly to their initial flight path
through the field free region and detected by a microchannel
plate (MCP) detector which is installed at the end of the flight
tube. Mass spectrometer settings are kept fixed while ionization
distances are varied. The time dependent electrical signal from
the detector is amplified by a fast preamplifier, collected by a
multichannel scalar card, and then integrated with a computer.
TOF spectra are measured at different positions in the photon
energy range between 9.5 and 13.0 eV. The photoionization
efficiency (PIE) curves are obtained by integrating peak
intensities at each photon energy and normalized by the
photon flux.
The molecular beam end-station is used to measure the
resolution of terminal T4’s three meter normal incidence
monochromator (McPherson, Inc., Chelmsford, MA). PIE
measurements are performed on a mixture of 2% xenon in
helium and intensities of Xe peaks in time-of-flight mass spectra
Figure 2. (a) Xenon 5p58s′ resonance shown after subtraction of
underlying broad 5p56d′ peak for two sizes of T4 monochromator exit
slit: 100 and 600 μm. Red lines represent a Gaussian function fit to
experimental data, the dependence of the full width at half-maximum
(fwhm) on width of T4 monochromator exit slit is shown in panel (b).
Error bars in panel (b) correspond to standard deviation of 2σ.
with a Gaussian fit. The dependence of full width at halfmaximum (fwhm) of the Gaussian on the exit slit size is shown
in Figure 2b. Most of the experimental data points have a linear
dependence. Only for the slit size below 100 μm do the
experimental points start to deviate from linear dependence,
converging to a maximum resolving power (E/ΔE) of 1000.
The T4 photon flux is measured by a silicon photodiode
SXUV-100 (Opto Diode Corp.) whose quantum efficiency is
known. The flux under typical operational conditions is about 2
× 1013 photons/s.
■
RESULTS
A. Mass Spectrometry of Methanol Clusters. Figure 3
displays a representative mass spectrum measured at a distance
of 10 mm from the nozzle at 11 eV photon energy. The main
ions observed in this experiment are similar to those in which
VUV ionization was performed inside the mass-spectrometer
chamber (MS-ionization).7 Protonated methanol clusters
[H+(CH3OH)n] show the most intense distribution followed
b y a m u ch w e ak e r p r o t o n a t e d m e t h a n o l− wa te r
[H+(CH3OH)nH2O]. Unprotonated species apart from methanol monomer are not observed. Intermediate sizes (n ∼ 30)
are observed for both protonated methanol and methanol−
water clusters. Protonated methanol dimethyl ether progression
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Figure 3. Mass spectrum showing various cluster distributions
measured at an ionization distance of 10 mm from the nozzle at 11
eV photon energy. Expanded view of protonated methanol and
methanol dimethyl ether distributions are shown in insets.
Figure 4. Intensity distributions of protonated methanol and
methanol−water clusters measured at x = 2, 15, 20, and 25 mm.
Ion intensities are plotted in logarithmic scale to highlight the
prominent distributions observed for these two species. Inset in the
upper trace shows the expanded view for n = 1−5.
[H+(CH3OH)n(CH3)2O] is also detected, albeit the signal is
relatively small compared to the other cluster distributions.
The appearance of protonated methanol upon ionization has
been observed previously using electron impact and single and
multiphoton ionizations.7,23,25,26,32,35,37−39 The mechanisms of
methanol and methanol−water22,34 cluster formation were
discussed in these earlier studies and here we will briefly
describe some of the key features. It has been suggested that the
ionization of neutral hydrogen bonded clusters leads to the
formation of protonated cluster ions via rapid proton transfer
and fragmentation:
distances, while the dimer is the most abundant ion at x = 20
mm. For n = 4−30, the overall ion intensities decrease with
increasing ionization distances. There are some interesting
features observed for these distances. At x = 2 mm, a gradual
slow decrease is observed for n = 4−30. Mass spectra at all
other distances show a general trend in the n = 4−30 range: a
rapid decay at smaller clusters followed by a slow rise to
intermediate sizes, and a moderate fall at larger species. As the
distance increases, the intensities of smaller clusters decay more
rapidly and an inverted-well shaped distribution is observed for
the intermediate sizes. The maximum of this well increases with
distance. For H+(CH3OH)nH2O, clusters up to n = 4 are not
detected and n = 5−6 are very weak; a plateau is observed from
n = 8−30 with a maximum around n = 15. As the ionization
distance increases, the intensity of a specific size decreases,
similar to those observed for protonated methanol clusters.
C. Photoionization Efficiency (PIE) Curves and
Appearance Energies (AE) at Various Distances. Figures
5 and 6 display the PIE curves of methanol and protonated
methanol clusters measured in the 9.5−13.0 eV region. Figure 5
depicts PIE curves for each species with distance variation while
Figure 6 shows PIE curves for different species while keeping
the distance fixed to highlight trends in the mass spectra. The
appearance energies (AE) for monomer cation and protonated
clusters evaluated from the PIE curves are tabulated in Table S1
in the Supporting Information file (SI). The AE of methanol
was found to be the same (10.8 eV) for MSand in-source
ionization. AE values obtained for protonated methanol
monomer, dimer, and trimer are in the range of 10.1−10.3,
9.8−10.1, and 9.6−10.1, respectively. Previous work from our
group has shown that the ionization energy of methanol
decreases upon clustering, reaching an asymptotic limit of
around 9.8 eV for a cluster of size ≥4.7 PIE curves of the
unprotonated monomer cation at various distances show sharp
rise at 10.8 eV and this value is exactly the same as obtained for
MS ionization. PIE curves of the protonated monomer shows a
(CH3OH)n + hν → (CH3OH)+n + e−
→ H+(CH3OH)n − 1 + CH3O + e−
(1)
Protonated methanol−water are formed either from neutral
methanol−water cluster
(CH3OH)n H 2O + hν
→ H+(CH3OH)n − 1H 2O + CH3O + e−
(2)
or from protonated methanol clusters
H+(CH3OH)n → H+(CH3OH)n − 2 H 2O + (CH3)2 O
(3)
Castleman and Garvey have suggested that reaction 3 occurs
for size n ≥ 9 since the lowest cluster size observed was
H+(CH3OH)7.23−25,34 Morgan and Castleman23 have also
suggested that this reaction does not occur for the smaller
clusters, since the formation of a methyl bound complex
intermediate is not facile. In our experimental conditions, n = 8
and 9 are more intense than n = 7 in the mixed methanol−
water cluster series indicating that the observed distribution
arises from reaction 4.
B. Intensity Distribution of Cluster Ions at Various
Distances. Figure 4 depicts the integrated intensities of
protonated methanol [H+(CH3OH)n] and methanol−water
[H+(CH3OH)nH2O] clusters at four various ionization
distances (x = 2, 15, 20, 25 mm). Intensities are shown in
logarithmic scale to highlight the interesting size distributions.
For H+(CH3OH)n, relative intensities of smaller sizes (n = 1−
3) do not change significantly at all distances. The protonated
methanol trimer is found to be the most intense ion at shorter
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Figure 5. PIE curves for methanol (M+) and protonated methanol clusters (MnH+) at various distances. Insets show the expanded view showing the
onsets of ionization.
Figure 6. PIE curves for methanol (M+) and protonated methanol clusters (MnH+) at x = 2, 15, 20 and 25 mm.
small shoulder around 10.2 eV and sharp rise at 10.8 eV. As
distance increases, AE values change slightly (on the order of
∼100−150 meV) for monomer. The change in AE values is
most prominent for trimer, where the difference in AE between
x = 2 and 25 mm is about 500 meV. PIE curves for these
species also show some interesting features as the distance and
photon energies are varied. For all distances, the methanol
cation shows a sharp rise at 10.8 eV and then a gradual decrease
up to 13 eV (Figure 5). Here, it should be noted that all the
PIE curves have an absorption due to argon (used in the gas
filter of the beamline to remove higher harmonics) at 11.8 eV.
For protonated methanol at 2 mm, after a sharp rise at 10.8 eV,
a rapid decay (around 11 eV) followed by a sharp rise (at
around 12.5 eV) is observed. At farther distances, a gradual
increase in ionization efficiency is seen (ignoring the dip at
around 11.8 eV). For dimer and trimer at 2 mm, PIE curves
show a slow rise from 9.5 to 12.5, followed by a sharp increase.
For the farthest distances, the curves show a slow rise up to
10.8 eV and then a rapid increase due to methanol absorption.
The PIE curve for the methanol cation crosses that of the
protonated methanol around 12.25 eV at all distances (Figure
6). At x = 2 mm, the dimer and trimer show a slow rise at lower
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Figure 7. (a) Schematic of a supersonic expansion. (b) A COMSOL simulation of a nozzle of diameter 100 μm. Distances are in mm.
clusters to get an idea if a liquid-like property is indicated by the
intensity distributions. A general theory of cluster growth
processes (Thomson’s liquid drop model) will be discussed for
data analysis to explain the observed distributions at various
distances.
A. Characterization of the Supersonic Expansion.
Supersonic expansion from a small nozzle leads to adiabatic
cooling, resulting in rapid temperature and density drop as the
expansion proceeds farther from the nozzle. Clusters are
formed as a result of sufficient collisions close to the exit before
the expansion becomes rarefied and cooling stops. Figure 7a
shows a schematic of a supersonic jet expansion into a region of
background pressure Pb. The gas accelerates in the nozzle
throat where Mach number (M) becomes close to 1 at the exit
and continues to accelerate (M ≫ 1) up to the Mach disc.
energies and crosses the monomer curve twice: once at 11.1 eV
and again around 12.3−12.4 eV. For all other distances after the
initial rise, dimer and trimer show steady ionization yields in
the 11.0−13.0 eV range.
■
DISCUSSION
Mass spectrometry and photoionization dynamics of methanol
clusters have been well studied, and here we will mostly discuss
the effect of variable ionization distance. In doing so, we will
first briefly describe the supersonic expansion from a small
nozzle and how cluster generation can be influenced by
changing the distance. In the following section, the intensity
distributions, PIE curves, and AEs for small clusters will be
discussed to explain the effect of distance on these features.
Finally, we will discuss the transition from small to intermediate
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and at 25 mm, the dimer is clearly the most abundant ion. The
other interesting feature is the relative populations of the
intermediate sized clusters. At 2 mm, after the initial rise from n
= 1−3, the relative population decreases gradually showing an
almost smooth distribution. On the other hand, as the distance
increases, intermediate size clusters go through a maximum. In
our previous study (MS-ionization), we found that the
protonated methanol trimer is the most stable ion up to 14
eV photon energy. This observation is consistent with several
other studies, including an electron impact26,32 one, where a
closed solvation shell is proposed around a protonated
methanol ion. In our case, the protonated trimer is the most
abundant ion at 2 mm probably because of three factors: (a)
closed solvation shell around a protonated methanol; (b)
photoionization cross section is greater than the dimer up to 14
eV energy; and (c) enhancement of the neutral tetramer
precursor at closer distances since the neutral density is higher.
The protonated dimer becomes the most stable ion above 14
eV energy (in MS ionization) and also at farther ionization
distances (in-source ionization). The dimer is most stable ion
beyond 14 eV, as discussed in our previous work, because
clusters with higher internal energies tend to fragment to lower
sizes via evaporative cooling. In the in-source ionization
scheme, the neutral density decreases as the expansion is
moved farther from the nozzle. Up to the point of ionization,
neutral clusters which are produced during the supersonic
expansion remain unperturbed. As the distance increases,
neutral density decreases and condensation around a charged
species would be more probable for monomer (making a
protonated dimer cation) rather than a dimer which would
make a protonated trimer ion.
Ion−molecule reactions involving the protonated monomer
cation is unlikely since unprotonated clusters other than
monomer cation are not observed. The AE of methanol
monomer is found to be 10.8 eV at all distances (Figures 5 and
6). The AEs of protonated clusters are shifted around 100−300
meV as a function of distance. The AE of protonated monomer
is in the range of 10.1−10.3 eV, similar to that found in the MSionization study. Since at all distances, the AEs do not shift
closer to or are greater than the IE of methanol, it is clear that
the protonated monomer is formed from fragmentation of
larger clusters. This situation is also true for the protonated
dimer and trimer, where for all distances, the AE of the
protonated dimer is less than that of the protonated monomer;
similarly, the AE of the trimer is less than that of the dimer.
Another interesting feature is that at higher energies, the
ionization yield of the monomer cation goes down at all
distances, whereas in the case of the dimer and trimer, the yield
is steady at all energies except at 2 mm ionization distance. At 2
mm, for dimer and trimer, the initial rise in the PIE curve is
slow and gradual but shows a sharp rise at higher energies
indicating that evaporative cooling from the higher cluster leads
to more dimers and trimers. The evaporative cooling effect is
not observed when the ionization is carried out at farther
distances.
Having described the nature of mass spectrometry and PIE
curves of small clusters, we now discuss the effect of ion−
molecule reactions to the cluster distributions. The thermochemistry of methanol and methanol−water clustering has been
studied by Kebarle and Meot-Ner.26−28 They have computed
enthalpy (ΔH), entropy (ΔS), and free energies (ΔG) of
formation of reaction 4
Mach disc location (xM) is related to the nozzle diameter (d),
stagnation pressure (P0), and background pressure (Pb) in a
very simple but accurate empirical form
P
xM
= 0.67 b
d
P0
We use the nozzle diameter (100 μm) and pressure values
from our experiment to the above expression and obtain a
Mach disc position of ∼67 mm. The “zone of silence” is the
core of the jet bounded by the barrel shock and the Mach disc.
This is a region of very low pressure and molecular beams are
extracted from it. Figure 7b shows a representation of the
expansion from a 100 μm nozzle by solving the Navier−Stokes
(N−S) equations using the COMSOL multiphysics software
package. We assumed that the gas flow in the interfacial region
remains at near thermal equilibrium continuum. This treatment
is similar to continuum models applied in previous studies
which used different nozzles and mass spectrometers.40,41 The
complete description and parameters used for solving this
model are provided in the SI. We have used the high Mach
number flow module in the COMSOL multiphysics, which is
valid for Knudsen number <0.1. The Knudsen number (λ/d) in
the high Mach number and low pressure region becomes high
as flow expands downstream from the nozzle. Therefore, a
continuum model is not strictly valid for our case. However, it
has been reported that even though noncontinuum effects in
high-speed expanding flow would change the thermal structure
of the gas, dynamic features such as velocity and temperature
are not strongly perturbed.42,43 Here, we present our nozzle
picture to show that velocity and temperature reach their
optimum values within 10−20 nozzle diameter (1−2 mm for
100 μm nozzle). The description is also consistent with the
Method of Characteristics calculations by Miller.8 The picture
in Figure 7b depicts an upward flow stream with nozzle situated
at 9 mm. The maximum velocity is reached at the exit of the
nozzle (800 m/s) and then falls down to subsonic speed (200
m/s). The temperature also changes rapidly from 300 to 150 K
within 1 mm distance from the nozzle diameter. Therefore, a
continuum model is not sufficient for a complete description of
the expansion.
B. Cluster Generation Mechanisms, Mass Spectra, and
PIEs as Functions of Ionization Distance. Since the
collisions are maximum right at the nozzle exit and cooling
stops within 10−20 nozzle diameter, maximum neutral
clustering occurs at that region. As the expansion proceeds,
the continuum flow quickly becomes a molecular flow where
the neutral density is quite low. A VUV photon whose energy is
greater than the ionization energy of methanol can ionize
methanol monomer producing a methanol cation. Cluster
ionization energies are generally less than that of the monomer,
and therefore neutral clusters are ionized at an energy lower
than the ionization energy of the monomer. Within the ionized
clusters, proton transfer can produce a protonated methanol
ion, and clusters then tend to rearrange around this newly
formed charged species. Similar observations can be found for
water clusters, where upon ionization protonated water clusters
form around a core H3O+.5
The relative intensities of protonated methanol clusters,
H+(CH3OH)n, change significantly with distance. As shown in
Figure 4, for distances up to 15 mm, the protonated trimer is
the most intense ion in mass spectra. At 20 mm, the relative
intensities between dimer and trimer are almost comparable,
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Figure 8. Free energy of formation (ΔG) as a function of number of molecules (n) and different supersaturation ratios (S) according to Thomson’s
model. While (a) shows a short-range of change in S, (b) shows the change from S = 1.6 to 10.
H+(CH3OH)n − 1 + CH3OH → H+(CH3OH)n
its mathematical form is correct which can provide a qualitative
picture of the process.48
Thomson’s model is based on the thermodynamics of a
liquid drop at equilibrium, which uses bulk variables such as
surface tension and dielectric constants. Therefore, application
of this model to molecular beam studies has been criticized and
Castleman et al. have shown that it does not agree with
experimental thermodynamic values for many small clusters.
This model agrees better with the experiment when the cluster
sizes are fairly large.51 Fenn et al. argued that supersonic jets are
not equilibrium systems and clustering environment changes
very rapidly as the expansion proceeds farther away from the
source. For the clustering of protonated water in a supersonic
jet, they have expressed nucleation in terms of the rate
constants of individual association reactions leading to the
formation of the ion cluster prenucleation embryos.53 Castleman et al. have shown that thermodynamic steady state and
kinetic model can be complementary at certain conditions.48 A
simple mathematical formulation of equivalence between these
two models based on Castleman’s study is given in SI.
According to Thomson’s equation, the free energy change
(ΔG) associated with formation of the nth cluster is given by
(4)
For reaction 4, the computed ΔH values are on the order of
31.6−33.1 kcal/mol for monomer to dimer formation. These
values gradually decrease as protonated methanol is solvated by
methanol molecules. The ΔH values changes from 21.0 to 14.0
kcal/mol for n = 2 → 3 to n = 3 → 4 clustering. Meot-Ner and
co-workers have suggested that the change in ΔH is due to the
closure of the first solvation shell. They have also found that the
limiting value for the higher cluster formation is 9.0 kcal/mol,
which is equivalent to the condensation enthalpy of methanol.
They have suggested that if the clustering reactions involved
only the formation of single new hydrogen bond, this limiting
value would be 5 kcal/mol. Therefore, the observed value
indicates that higher clusters possess similar intermolecular
forces as that exists in the bulk liquid. This would suggest that
hydrogen-bonding, dipole−dipole, dipole−induced dipole, and
hydrophobic interactions among the alkyl group play crucial
roles in larger clusters similar to liquid methanol. As a result,
larger clusters may not have a purely hydrogen bonded chain,
but a liquid-like structure. Recent infrared spectroscopy study
of (CH3OH)n and H+(CH3OH)n suggested that the spectrum
of protonated methanol 50 (n = 50) converges to that of liquid
methanol.44 The observed O−H frequency of liquid methanol
is slightly higher than that of the n = 50. This difference
suggests that the major hydrogen bonding network in liquid is
much shorter than n ∼ 10. Molecular dynamics simulations also
predict this perception.45,46 Discussion of our next section is
prompted by these findings.
C. Thomson’s Liquid Drop Model and Its Relation to
Intensity Distributions. Adiabatic cooling during supersonic
expansions leads to a high degree of supersaturation, and
clusters can nucleate to form droplets. Supersonic expansions in
fact have been realized as fast flow reactors and proposed as
tools to study nucleation.47,48 However, nucleation rates are
strongly dependent on the temperature, and since the
clustering environment changes so rapidly during the
expansion, it is difficult to obtain a reliable kinetic model.
Developing a complete model of cluster distribution under our
experimental photoionization condition is beyond the scope of
this study. However, we would like to propose a simplified
version based on Thomson’s liquid drop model.49−51 This
model has been used to discuss ion-induced nucleation in
molecular beams and cloud chamber experiments. Even though
Thomson’s equation is inaccurate for quantitative estimates,52
ΔGn = −nkBT ln(S) + 4πrn2σ +
q2 ⎛
1 ⎞⎟⎛ 1
1⎞
⎜1 −
⎜ − ⎟
8πε0 ⎝
ε ⎠⎝ rn
ri ⎠
(5)
where n, kB, T, and S are the number of molecules, Boltzmann
constant, temperature, and supersaturation ratio, respectively.
The first term of Thomson’s equation is the volume excess free
energy, i.e., energy gain due to the vapor → liquid phase
transition. The second term represents the surface excess
energy, i.e., energy required to form a neutral drop of radius rn.
The third term is the free energy change induced by an ion of
radius ri and charge q. ε0 and ε are the vacuum permittivity and
dielectric constant, respectively. This term represents the
energy required to solvate the charged droplet which
contributes to the lowering of the cluster free energy due to
the presence of an ion.
Figure 8 displays the free energy of formation as a function of
number of molecules for methanol clusters around a
protonated methanol ion at different temperatures and
supersaturation values according to Thomson’s model. Here
we reiterate that this model is qualitative and there is no way to
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clusters and lowering of AEs suggest that ion−molecule
reactions involving methanol monomer cation do not occur.
PIE curves at short distances show that at higher energies,
evaporative cooling produces more protonated methanol
monomer, dimer, and trimer. The evaporative cooling effect
is not observed for farther distances. The intensity distributions
at various distances are qualitatively explained by Thomson’s
liquid drop model. At closer distances, both supersaturation
and ion-induced growth reduces the free energy barrier of
formation. On the other hand, low neutral density at farther
distances increase the free energy barrier, reducing the ioninduced growth.
This experimental approach with a control on growth and
decay processes can be further implemented to new directions.
One example would be to study ion−molecule association
reactions.54 Dissociation of organic cluster molecules via
ionization can be simultaneously studied using the same
approach. An experiment would be to study the photoionization dynamics of mixed systems in which constituents
have different ionization energies, and one can tune VUV light
into different ionization regimes to see how chemistry changes
during a reaction. Toward this end, ion−molecule reactions of
mixed clusters of acetylene (IE = 11.5 eV) and ethylene (IE =
10.5 eV) are being investigated focusing on photoionization
dynamics.
ment. However, we can assume that during the expansion,
these two values are interdependent and change rapidly along
the centerline.
We use a temperature of 30 K computed using the Method
of Characteristics,8 which corresponds to a value very close to
the nozzle throat. At the lowest supersaturation value (S = 1.6),
the free energy shows a rapid decay at smaller n, followed by an
inverted well with a maximum. According to Thomson’s model,
this is referred to as the barrier of nucleation. As S increases, the
maximum in free energy decreases indicating a reduced barrier.
At higher supersaturation values, free energy decreases with no
barrier. At these S values, the process is essentially controlled by
the kinetics of cluster formation. Here, it should also be noted
that varying the temperature in eq 5 does not change the shape
of the curve, only the free energy values changes linearly if S is
fixed. The model curves show a rapid decrease in ΔG for
smaller sizes with a minimum in free energy corresponding to n
≈ 20−25 sizes, and mass spectra at all ionization distances
show an increasing trend in intensity with a maximum at n = 3.
After the initial rapid rise in intensity, distributions for n = 4−
30 show a decay followed by a maximum, which can be
described by the model, where free energy shows a small rise
followed by the barrier. The intensity distribution at different
ionization distances provides two salient features: (a) supersaturation decreases as the expansion proceeds downstream;
(b) as ionization occurs closer to the nozzle, protonated cations
induce ion−molecule reactions. On the other hand, neutral
clusters can remain unperturbed up to the ionization distance.
Now, we see that the distribution corresponding to the shorter
ionization distance (2 mm) is qualitatively similar to that of the
model curve with higher S (1.9, 4, or 10) values where the free
energy barrier virtually does not exist. This makes sense
because we expect a higher supersaturation at shorter distances,
and a lower energy barrier due to the ion-induced lowering of
free energy. The neutral density decreases with distance and
therefore the barrier increases. The supersaturation also
decreases as ionization is carried out farther from the nozzle,
resulting in an increased energy barrier.
■
ASSOCIATED CONTENT
S Supporting Information
*
Brief description of Navier−Stokes equations; boundary
conditions to solve these equations for supersonic expansion
from a small nozzle; parameters and values used to calculate
free energies using Thomson’s equation; and equivalence
between the kinetic and thermodynamic steady state models.
This material is available free of charge via the Internet at
http://pubs.acs.org.
■
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
CONCLUSIONS
We have studied intensity distributions of methanol clusters by
VUV photoionization mass spectrometry where ionization is
carried out at variable distances from the nozzle. The
photoionization of methanol produces clusters of protonated
methanol, methanol−water, and methanol dimethyl ether.
Photoionization of a neutral hydrogen bonded methanol cluster
undergo a rapid proton transfer reaction. The cluster then
condense around the newly formed protonated methanol via a
series of ion−molecule reactions. The intensity distributions at
various ionization distances change significantly for both
smaller complexes and intermediate clusters. For shorter
distances, the protonated trimer is found to be the most
abundant ion similar to the MS ionization study. This ion is the
most abundant at shorter distances because of a closed
solvation shell, a larger photoionization cross section than
that of the dimer, and an enhanced neutral tetramer precursor.
The protonated dimer becomes the most abundant ion at
farther distances because of low neutral density and an
enhanced charged protonated monomer−neutral methanol
interaction. PIE curves are measured for small complexes
from 9.5 to 13.0 eV at each distance which shows that
appearance energies are shifted to lower values due to
protonation and clustering. The absence of unprotonated
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
This work and the Advanced Light Source are supported by the
Director, Office of Science, Office of Basic Energy Sciences, of
the U.S. Department of Energy under Contract No. DE-AC0205CH11231.
■
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