Daniel N Mortensen1, Evan R Williams. 1. Department of Chemistry, University of California , Berkeley, California 94720-1460, United States.
Abstract
Double-barrel wire-in-a-capillary electrospray emitters prepared from theta-glass capillaries were used to mix solutions during the electrospray process. The relative flow rate of each barrel was continuously monitored with internal standards. The complexation reaction of 18-crown-6 and K(+), introduced from opposite barrels, reaches equilibrium during the electrospray process, suggesting that complete mixing also occurs. A simplified diffusion model suggests that mixing occurs in less than a millisecond, and contributions of turbulence, estimated from times of coalescing ballistic microdroplets, suggest that complete mixing occurs within a few microseconds. This mixing time is 2 orders of magnitude less than in any mixer previously coupled to a mass spectrometer. The reduction of 2,6-dichloroindophenol by l-ascorbic acid was performed using the theta-glass emitters and monitored using mass spectrometry. On the basis of the rate constant of this reaction in bulk solution, an apparent reaction time of 274 ± 60 μs was obtained. This reaction time is an upper limit to the droplet lifetime because the surface area to volume ratio and the concentration of reagents increase as the droplet evaporates and some product formation occurs in the Taylor cone prior to droplet formation. On the basis of increases in reaction rates measured by others in droplets compared to rates in bulk solution, the true droplet lifetime is likely 1-3 orders of magnitude less than the upper limit, i.e., between 27 μs and 270 ns. The rapid mixing and short droplet lifetime achieved in these experiments should enable the monitoring of many different fast reactions using mass spectrometry.
Double-barrel wire-in-a-capillary electrospray emitters prepared from theta-glass capillaries were used to mix solutions during the electrospray process. The relative flow rate of each barrel was continuously monitored with internal standards. The complexation reaction of 18-crown-6 and K(+), introduced from opposite barrels, reaches equilibrium during the electrospray process, suggesting that complete mixing also occurs. A simplified diffusion model suggests that mixing occurs in less than a millisecond, and contributions of turbulence, estimated from times of coalescing ballistic microdroplets, suggest that complete mixing occurs within a few microseconds. This mixing time is 2 orders of magnitude less than in any mixer previously coupled to a mass spectrometer. The reduction of 2,6-dichloroindophenol by l-ascorbic acid was performed using the theta-glass emitters and monitored using mass spectrometry. On the basis of the rate constant of this reaction in bulk solution, an apparent reaction time of 274 ± 60 μs was obtained. This reaction time is an upper limit to the droplet lifetime because the surface area to volume ratio and the concentration of reagents increase as the droplet evaporates and some product formation occurs in the Taylor cone prior to droplet formation. On the basis of increases in reaction rates measured by others in droplets compared to rates in bulk solution, the true droplet lifetime is likely 1-3 orders of magnitude less than the upper limit, i.e., between 27 μs and 270 ns. The rapid mixing and short droplet lifetime achieved in these experiments should enable the monitoring of many different fast reactions using mass spectrometry.
Rapid mixing
of two or more
solutions is often required to investigate the kinetics of fast chemical
and biochemical reactions.[1−3] Mixers that are commonly used
for this purpose include laminar,[4,5] turbulent,[6,7] and chaotic[8−10] flow mixers, where the dead time decreases with increasing
flow rate.[4,11] The performance of these types of mixers
has been extensively reviewed.[12,13] A dead time of 8 μs
has been achieved with a flow rate of ∼100 nL/s using laminar
flow mixers.[14] The use of mass spectrometry
(MS) to monitor reactions in mixing experiments has the advantage
of high chemical specificity. Several in-line mixers have been coupled
to MS, including continuous,[15,16] stopped,[17,18] and laminar[3] flow mixers. The shortest
dead time reported for mixers coupled to MS is 200 μs.[3]Numerous techniques have also been used
to mix solutions during
the electrospray process, including fused-droplet electrospray,[19,20] multiple channel electrospray,[21,22] extractive
electrospray,[23−25] and dual-sprayer microchips.[26−28] Both desorption
electrospray ionization[2,29−31] and ambient
ion soft landing[32] techniques have been
used to carry out solution-phase reactions in charged microdroplets.
Similarly, mixing from theta-glass emitters (double-barrel wire-in-a-capillary
emitters made from theta glass) has been used to form noncovalent
complexes,[33] conduct hydrogen/deuterium
exchange reactions,[33] unfold proteins,[34] and introduce supercharging reagents to protein
solutions,[34] all during the electrospray
process. Mixing in microdroplets has the potential advantage of minimizing
sample volume,[35−37] but reported mixing times in microdroplets are greater
than those in laminar flow mixers. For example, complete mixing of
two 80 μm diameter ballistic droplets takes ∼10 ms to
occur,[38] and complete mixing within a 25
μm diameter droplet generated by flowing multiple streams of
aqueous reagent solutions into an inert stream of water immiscible
oil occurs in ∼2 ms.[37]Microdroplets
formed in atmosphere can undergo desolvation, and
the droplet lifetime depends on the evaporation rate. Evaporation
rates of heptane, octane, and xylene electrospray droplets ranging
in initial size from 3 to 60 μm have been measured using phase
Doppler anemometry,[39] and the evaporation
rate depends on both the solvent and the square of the initial droplet
diameter. The initial diameter of electrospray droplets generated
using capillaries with outer diameters as small as 12.5 μm[40] to as large as a centimeter[41,42] have been measured using various techniques, including optical microscopy,[42,43] flash shadowgraph techniques,[44−46] phase Doppler techniques,[39,44,47−50] scanning mobility particle sizers,[51,52] and white light particle counters.[41] Electrospray
droplets have been observed from an electrospray capillary with an
outer diameter (o.d.) as small as 12.5 μm using a stereomicroscope,[40] but droplets from a capillary with an o.d. of
<1 μm were too small to be visualized.[40] The initial size of an electrospray droplet can depend
on the tip diameter for a given solution, but heptane droplets generated
from an electrospray capillary with an outer diameter of 0.45 mm can
have initial diameters of ∼200 μm,[46] whereas ethylene glycol droplets generated from a 10 mm
o.d. electrospray capillary can have initial diameters as small as
∼1.5 μm.[40] Therefore, the
exact relationship between the size of the electrospray capillary
and the initial size of the droplet depends on many factors. There
are several models[42,53−55] that have been
reported for determining the size of droplets generated using electrospray
based on the flow rate and various other solution and instrumental
conditions. Schmidt et al.[40] compared several
of these models and reported that they predicted droplet diameters
differing by 4 orders of magnitude (7.7 × 10–8 to 1.4 × 10–4 m) for the same water/methanol/acetic
acid solution under otherwise identical conditions.As droplets
evaporate, the surface area to volume ratio and the
concentration of reagents increase and up to a 4 unit change in the
pH can occur.[56,57] These factors can increase the
rate of product formation in droplets by 1–3 orders of magnitude
over bulk solution rates.[31,58−60] The relative contribution of each of these factors to the increased
rate of product formation is unknown.In this study, theta-glass
emitters were used to mix solutions
during nanoelectrospray ionization (nano-ESI). The extent of mixing
between solutions loaded into opposite barrels was measured by carrying
out a fast complexation equilibrium reaction, and an apparent droplet
lifetime was obtained by monitoring a fast redox reaction with a known
forward rate constant. On the basis of increased rates of product
formation in droplets compared to rates in bulk solution measured
by others, the droplet lifetime is estimated to be less than ∼27
μs.
Experimental Section
Mass spectra were acquired using
a 9.4 T Fourier-transform ion
cyclotron resonance mass spectrometer that is described in detail
elsewhere.[61] Nanoelectrospray ionization
was performed using premium theta glass (Warner Instruments, LLC,
Hamden, CT) pulled into tips using a model p-87 Flaming/Brown micropipette
puller equipped with an FB330B square box filament (Sutter Instruments
Co., Novato, CA). Theta glass is a borosilicate glass capillary divided
into two separate barrels by a borosilicate glass wall. Platinum wires
connected to the ground of the instrument were brought into contact
with the solution in each barrel, and electrospray was initiated by
applying a potential of ∼−700 V to the heated capillary
of the nanoelectrospray interface. A backing pressure of ∼10
psi (CO2) was applied to the solutions during electrospray
using a pressure regulator. A schematic of this experimental setup
is shown in Scheme S-1 in the Supporting Information. A Hitachi tabletop microscope TM-1000 scanning electron microscope
(Hitachi High-Technologies Co., Tokyo, Japan) was used to image the
tips. All reported uncertainties are one standard deviation from three
replicate measurements. Diffusion coefficients used to model the diffusion
of K+, Na+, and 18C6 in water are 0.00196,[62] 0.00163,[63] and 0.00060
μm2/μs,[64] respectively.Leu-enkephalin acetate salt hydrate, met-enkephalin acetate salt
hydrate, l-ascorbic acid, and 18-crown-6 were obtained from
Sigma-Aldrich (St. Louis, MO), KCl was from Mallinckrodt Baker, Inc.
(Phillipsburg, NJ), HCl 0.1 N was from EMD Millipore Chemicals (Darmstadt,
Germany), and 2,6-dichloroindophenol Na salt and NaCl were from Fisher
Scientific (Fair Lawn, NJ). All chemicals were used without further
purification, and all solutions were prepared in 18.2 MΩ water
from a Milli-Q integral water purification system (Millipore, Billerica,
MA).
Results and Discussion
Characterization of Theta-Glass ESI Emitters
Theta-glass
capillaries are divided into two separate barrels by a central divider,
which after the pulling process extends to the end of the tip (Figure 1a; tip oriented so that the divider is perpendicular
to the sample stand). Thus, solutions loaded into opposite barrels
do not mix until flow is initiated by applying a potential to the
capillary of the nanoelectrospray interface and a backing pressure
is applied to the solutions. The tip o.d. is 1.71 ± 0.04 μm
perpendicular to the divider (Figure 1a) and
1.36 ± 0.02 μm along the axis of the divider (Figure 1b). The thickness of the outer wall is uniform in
both orientations (0.16 ± 0.02 μm) and is the same as the
inner divider thickness (0.16 ± 0.01 μm). The length of
the emitters is 5.47 ± 0.05 cm.
Figure 1
Electron micrographs of the tips of theta-glass
emitters with the
inner divider (a) perpendicular to and (b) parallel to the sample
stand.
Electron micrographs of the tips of theta-glass
emitters with the
inner divider (a) perpendicular to and (b) parallel to the sample
stand.
Measuring Relative Flow
Rates of Individual Barrels
The overall flow rate from both
barrels was obtained by measuring
the change in volume and mass of an aqueous solution of 500 μM
NaCl and 500 μM 18-crown-6 after spraying for ∼10 min
(density of 1.0 mg/mL for water containing less than 1% NaCl).[65] The flow rate is 1.4 ± 0.4 nL/s, which
is 2 orders of magnitude lower than the flow rates of common mixers
in which high mixing efficiency is achieved on the order of tens of
microseconds.[13] The flow rate remains relatively
constant when the backing pressure is doubled and when the ionic strength
of the solution differs by more than an order of magnitude (data not
shown).In order to obtain quantitative information from mixing
experiments preformed using theta-glass emitters, the flow rate of
each barrel must be measured individually. To determine the relative
flow rate of each barrel, 10 μM solutions (pH = 2) of Leu-enkephalin
(L-Enk) and Met-enkephalin (M-Enk) (polypeptides YGGFX, X = L and
M, respectively) were prepared and loaded into the separate barrels.
The protonated forms of the peptides were observed in the mass spectra
at a ratio of 1.8 ± 0.1 to 1, L-Enk to M-Enk (Figure 2a). To determine the relative ionization efficiencies
of these peptides, an equimolar mixture of L-Enk and M-Enk was prepared
(5 μM, pH = 2) and loaded into both barrels of the theta-glass
emitters. On the basis of the relative abundances of the protonated
forms of the peptides, the relative ionization efficiency of L-Enk
to M-Enk is 1.7 ± 0.1 (Figure 2b). Although
these peptides differ by only a single amino acid, even minor differences
in structure can lead to significant differences in ionization efficiencies.[66] The relative flow rates of the individual barrels
were established using the relative abundances and ionization efficiencies
of the internal standards, and in this experiment, the relative flow
rate of the L-Enk solution to the M-Enk solution was 1.1 ± 0.1
to 1, suggesting that relative flow rates are nearly even and are
highly reproducible between tips.
Figure 2
Representative ESI mass spectra of L-Enk
and M-Enk solutions (a)
loaded into separate barrels of a theta-glass emitter and (b) premixed
and loaded into both barrels.
Representative ESI mass spectra of L-Enk
and M-Enk solutions (a)
loaded into separate barrels of a theta-glass emitter and (b) premixed
and loaded into both barrels.
Mixing Efficiency
In order to determine the extent
of mixing that occurs in these experiments, a fast complexation equilibrium
reaction was performed using the theta-glass emitters. If incomplete
mixing occurs in these experiments, only a portion of the reagents
loaded into the opposite barrels will interact during the electrospray
process and the ratio of products to reactants in the mass spectra
will be lower than that at equilibrium. Complexation of 18-crown-6
(18C6) with K+ in water has a forward rate constant of
2.45 × 109 mol s–1 and an equilibrium
constant of 116.4 (values are averages of values measured by others).[67] Protonated 18C6 is not observed in the mass
spectra, so the product to reactant ratio cannot be measured directly.
For this reason, 18C6 is mixed with Na+ to form the complex
[18C6 + Na]+, which has an equilibrium constant of 7.0
(average of values measured by others).[67]A solution (A) containing 100 μM 18C6 and 500 μM
NaCl (pH = 2) was mixed with solutions (B) containing between 50 and
1000 μM KCl (pH = 2). A calibration curve for the ratio [18C6
+ K]+/[18C6 + Na]+ was generated as a function
of the initial concentration of K+ over the initial concentration
of Na+ in solution ([K]o/[Na]o) (Figure 3a). A representative mass spectrum of a premixed
solution of A and B, where the initial concentrations of Na+ and K+ are equal, is inset into Figure 3a. To determine how the relative abundances of the two complex
ions reflect the corresponding abundances in solution, an equilibrium
ratio is derived from the equilibrium constants of the two complexes.
The equilibrium constants of these complexes arewhere
M = Na+ or K+, KM is the equilibrium constant of the reaction
involving M, [18C6 + M]eq and [18C6]eq are the
equilibrium concentrations of the complexed and uncomplexed forms
of 18C6, respectively, and [M]eq is the equilibrium concentration
of M. In all experiments, <1% of M is complexed with 18C6, so [M]eq is approximated as the initial concentration of M, [M]o. Solving eq 1 for both Na+ and K+, rearranging, and dividing [18C6 + K]eq by [18C6 + Na]eq gives eq 2:The ratio [18C6 + K]eq/[18C6 +
Na]eq as a function of the ratio [K]o/[Na]o is linear with a slope of 16.8 (Figure 3a), which is nearly the same as the expected value of KK/KNa = 16.6. This result
indicates that the ratios of abundances of the two complex ions are
approximately equal to their relative abundances in solution.
Figure 3
(a) The ratio
[18C6 + K]+/[18C6 + Na]+ in
the mass spectra of premixed solutions (circles) and predicted by
eq 2 (dashed green line), both as functions
of the ratio [K]o/[Na]o. The inset is a representative
mass spectrum of a solution containing Na+/K+/18C6 at a ratio of 1:1:0.05. (b) The ratio [18C6 + K]+/[18C6 + Na]+ in the mass spectra from the theta-glass
emitters as a function of the same ratio predicted by a linear fit
to the calibration curve data (open circles). The dashed green line
is a 1:1 correspondence between the axes. Black lines in both panel
a and panel b are linear fits to the data.
(a) The ratio
[18C6 + K]+/[18C6 + Na]+ in
the mass spectra of premixed solutions (circles) and predicted by
eq 2 (dashed green line), both as functions
of the ratio [K]o/[Na]o. The inset is a representative
mass spectrum of a solution containing Na+/K+/18C6 at a ratio of 1:1:0.05. (b) The ratio [18C6 + K]+/[18C6 + Na]+ in the mass spectra from the theta-glass
emitters as a function of the same ratio predicted by a linear fit
to the calibration curve data (open circles). The dashed green line
is a 1:1 correspondence between the axes. Black lines in both panel
a and panel b are linear fits to the data.The extent of mixing between two solutions loaded into opposite
barrels of the theta-glass emitters was determined by loading solution
A into one barrel and solutions of B into the other barrel. L-Enk
and M-Enk were used as internal standards in these respective solutions
to determine the relative flow rates of the two barrels. The initial
concentrations of Na+ and K+ in the droplets
were determined from the initial concentrations of the ions in the
respective solutions and from the respective flow rates. The ratio
[18C6 + K]+/[18C6 + Na]+ in the mass spectra
of the solutions mixed from the theta-glass emitters as a function
of the same ratio determined from the linear fit to the calibration
curve data results in a line with a slope of 0.99 and a correlation
coefficient of 0.97 (Figure 3b). These results
indicate that the complexation of 18C6 with K+ reaches
equilibrium during nano-ESI and that complete mixing occurs between
solutions sprayed from opposite barrels of the theta-glass emitters.
Estimates of the Mixing Time
An estimate of the maximum
time required for mixing to occur in the electrospray droplets was
made by assuming that the mixing time is diffusion-limited. Concentration
profiles in the droplet are modeled as a function of both the distance
from the center of the droplet, d, and time, t, using the classical solution to Fick’s second
law of diffusion for finite boundary conditions:where c(d,t) is the concentration as a function of d and t, co is the concentration
at t = 0, co/2 is the
equilibrium concentration (assuming even flow
from both barrels), erf is the error function, and D is the diffusion coefficient. Only diffusion in the direction perpendicular
to the solution interface is considered, and the outer boundaries
correspond to the droplet radius. Because there is significant uncertainty
in the initial droplet size in these experiments, mixing times are
calculated for droplets with initial diameters of one-half and one-tenth
the outer diameter of the tip of the electrospray capillary (o.d.).
Because mixing should occur across the interface between the solutions
in the absence of turbulent flow, the tip diameter of 1.71 μm,
measured perpendicular to the inner divider, is used as the o.d.The concentration of K+, Na+, and 18C6 as a
function of the distance from the center of a 0.86 μm droplet
(one-half the o.d.) at 0, 23, and 732 μs are shown in Figure 4a–c, respectively. The relative concentrations
of [18C6 + K]+ and [18C6 + Na]+ were calculated
as a function of the distance from the center of the droplet using
the concentration profiles in Figure 4a–c
and the equilibrium constants (eq 1). Relative
concentrations of the complexes as a function of the distance from
the center of a 0.86 μm droplet at 0, 29, and 732 μs are
shown in Figure 4d–f, respectively.
From these data, the ratio [18C6 + K]+/[18C6 + Na]+ as a function of time can be determined. At 23 and 732 μs
for all initial concentrations of K+ in solution B, this
ratio is ∼42% and ∼90% of the equilibrium ratio, respectively.
On the basis of the standard deviations of the calibration curve data
(∼10% of the average values, Figure 3a), the ratio of the complexes at 732 μs would be nominally
the same within the uncertainty of the measurement as that from a
premixed solution and mixing would appear complete. Similar extents
of diffusion-limited mixing in a 0.17 μm droplet (one-tenth
the o.d.) would take 0.9 and 29 μs to occur, respectively. These
mixing times are upper limits because droplet evaporation reduces
the droplet radius[39] and, therefore, the
distance material must diffuse. Turbulence in the droplet will also
significantly increase the rate of mixing over that of a diffusion-limited
system.
Figure 4
Concentrations of K+ (blue line), Na+ (red
dots), and 18C6 (green dashes) as a function of the distance from
the center of a 0.86 μm droplet at (a) 0, (b) 23, and (c) 732
μs. Relative abundances of [18C6 + K]+ (blue dots
and dashes) and [18C6 + Na]+ (red double-dashes) as a function
of the distance from the center of the droplet at (d) 0, (e) 23, and
(f) 732 μs. Initial concentrations used to calculate relative
abundances are 500 μM Na+ and 100 μM 18C6 in
solution A and 250 μM K+ in solution B. Horizontal
dashed, gray lines represent equilibrium concentrations (a–c)
and abundances (d–f).
Concentrations of K+ (blue line), Na+ (red
dots), and 18C6 (green dashes) as a function of the distance from
the center of a 0.86 μm droplet at (a) 0, (b) 23, and (c) 732
μs. Relative abundances of [18C6 + K]+ (blue dots
and dashes) and [18C6 + Na]+ (red double-dashes) as a function
of the distance from the center of the droplet at (d) 0, (e) 23, and
(f) 732 μs. Initial concentrations used to calculate relative
abundances are 500 μM Na+ and 100 μM 18C6 in
solution A and 250 μM K+ in solution B. Horizontal
dashed, gray lines represent equilibrium concentrations (a–c)
and abundances (d–f).The effect that turbulence might have on the mixing times
in these
experiments is estimated by comparing the calculated diffusion-limited
mixing times to the measured mixing times of coalescing ballistic
microdroplets, studied by Graceffa et al.[38] In that study, 80 μm diameter ballistic droplets were generated
using two synchronized drop-on-demand inkjet systems, and droplets
containing aqueous cytochrome c were collided with
droplets containing aqueous sodium acetate buffer. Stroboscopic synchrotron
radiation microbeam small-angle X-ray scattering was used to image
the redistribution of cytochrome c within the newly
formed 100 μm droplets, and cytochrome c was
uniformly distributed after ∼10 ms. Diffusion of 18C6, K+, and Na+ in a 100 μm droplet would take
∼10 s to form the complexes [18C6 + K]+ and [18C6
+ Na]+ at 90% of the equilibrium ratio, indicating that
turbulence increased the mixing rate in the ballistic microdroplets
by 3 orders of magnitude over the rate of diffusion-limited mixing.
If turbulence contributes equally to mixing from the theta-glass emitters,
complete mixing could occur in well under a microsecond.To
estimate the extent of mixing that occurs in the Taylor cone
prior to droplet formation, the volume of solution in the Taylor cone
is estimated as the volume of a cone with a height 4 times the o.d.[68] and with a radius equal to the o.d. At the measured
flow rate of 1.4 ± 0.4 nL/s, a reagent molecule spends less than
11 μs in the Taylor cone prior to droplet formation. This suggests
that a significant extent of mixing will occur prior to droplet formation
if contributions from turbulent mixing are significant, but mixing
will primarily occur in the droplet if mixing is diffusion-limited.
Droplet Lifetimes
An upper limit to the lifetime of
a droplet can be obtained by measuring the extent to which a reaction
with a known rate constant occurs during nano-ESI. The reduction of
2,6-dichloroindophenol (DCIP) by l-ascorbic acid (L-AA) (Scheme 1) has a forward rate constant of 5.6 × 104 L mol–1 s–1 at pH = 3.[69] A solution (C) containing 10 μM DCIP (pH
= 3) was loaded into one barrel of the theta-glass emitters, and solutions
(D) containing between 10 and 50 mM L-AA (pH = 3) were loaded into
the other barrel. Figure 5a shows a representative
mass spectrum resulting from mixing solutions C and D (50 mM L-AA)
from the theta-glass emitters. Due to the large excess of L-AA in
solution, L-AA carries away a substantial fraction of the available
charge in the form of protonated L-AA (m/z 177.039, data not shown), resulting in a low signal-to-noise
ratio for DCIP. The protonated oxidized and reduced forms of DCIP
have overlapping isotope distributions, but these ions can be readily
resolved (inset to Figure 5a, the third isotope
peak of oxidized DCIP and the first isotope peak of reduced DCIP are
shown). The fraction of DCIP that is reduced increases as a function
of the concentration of L-AA in solution D (Figure 5b).
Scheme 1
Reduction of 2,6-Dichloroindophenol by l-Ascorbic
Acid
Figure 5
(a) Representative mass spectrum of a
10 μM DCIP solution
mixed with a 50 mM L-AA solution (both pH = 3) from a theta-glass
emitter. The inset shows the third isotope peak of oxidized DCIP and
the first isotope peak of reduced DCIP. (b) The fraction of DCIP reduced
as a function of the concentration of L-AA in the opposite barrel.
(c) Reaction times calculated from the relative abundances of oxidized
and reduced DCIP using eq 6 as a function of
the initial concentration of L-AA in solution.
(a) Representative mass spectrum of a
10 μM DCIP solution
mixed with a 50 mM L-AA solution (both pH = 3) from a theta-glass
emitter. The inset shows the third isotope peak of oxidized DCIP and
the first isotope peak of reduced DCIP. (b) The fraction of DCIP reduced
as a function of the concentration of L-AA in the opposite barrel.
(c) Reaction times calculated from the relative abundances of oxidized
and reduced DCIP using eq 6 as a function of
the initial concentration of L-AA in solution.Because the initial concentration of L-AA is in large excess
of
the initial concentration of DCIP, this reaction can be modeled using
pseudo-first-order reaction kinetics. The pseudo-first-order integrated
rate law for this reaction iswhere [L-AA]o is
the initial concentration of L-AA, kf is
the forward reaction rate constant, t is the reaction
time, and [oDCIP]o and [oDCIP] are the concentrations of oxidized DCIP at times 0 and t, respectively. The initial concentration of oxidized DCIP in the
droplet was determined using the initial concentration of oxidized
DCIP in solution C and the relative abundances of the internal standards
(L-Enk in solution C and M-Enk in solution D). [oDCIP] was calculated from the abundances of the oxidized
and reduced forms of DCIP using the equationwhere AoDCIP and ArDCIP are the abundances
of the oxidized and reduced forms of DCIP, respectively, and iDCIP is the relative ionization efficiency of
the oxidized form of DCIP relative to the reduced form. iDCIP was measured separately (Figure S-1, Supporting Information) and is 1.0 ± 0.2,
which is in good agreement with a previously published value[2] of 1.09 ± 0.08. Combining eq 4 with eq 5 gives eq 6:which was
used to determine the apparent reaction
time. On the basis of the rate constant from bulk solution, the average
apparent reaction time is 274 ± 60 μs. This value does
not appear to change as a function of the concentration of L-AA in
solution D (Figure 5c).The average apparent
reaction time is an upper limit to the droplet
lifetime because the rates of chemical reactions in rapidly desolvating
droplets are greater than in bulk solution.[58] The rapid desolvation of a droplet leads to increased reagent concentrations,
a larger surface area to volume ratio, and a decrease in pH. Cumulatively,
these factors can increase the rate of product formation within a
rapidly desolvating droplet by between 1 and 3 orders of magnitude,[58] but the relative contributions of each of these
factors are poorly characterized. The forward rate constant for the
reduction of DCIP by L-AA increases by less than 3% from pH = 3 to
pH = 1,[69] so pH changes likely have little
impact on the rate of product formation in these experiments. However,
increases in reagent concentrations and the surface area to volume
ratio within the droplet occur, so the true average lifetime of a
nano-ESI droplet may be between 10 and 1000 times less than the average
apparent reaction time based on the bulk solution rate. Thus, mixing
and reactions in these experiments likely occur between about 27 μs
and 270 ns. Some product formation will occur in the Taylor cone,
which will contribute to a greater apparent droplet lifetime, so the
actual droplet lifetime is likely less than 27 μs. This same
reaction was previously used to characterize a continuous flow mixing
system combined with desorption electrospray (DESI) mass spectrometry
of the subsequent liquid jet stream. A mixing time of 2.5 ms was reported,
with an instrumental time resolution of 300 μs at longer times
obtained by increasing the distance between the mixer and the DESI
source. The mixing time we report for this reaction is at least 2
orders of magnitude lower.The mixing time in conventional mixers
is typically controlled
by varying either the solution flow rate or the geometry of the mixing
region.[13] In nano-ESI, the droplet lifetime
depends on the initial droplet diameter,[39] and thus on the diameter of the tip of the electrospray capillary[40] as well as the solution flow rate.[42,53−55] It should be possible to acquire kinetic data at
multiple time points using theta-glass emitters by varying either
the diameter of the tip of the emitters or the backing pressure to
control the solution flow rate.
Conclusions
Theta-glass
emitters were used to mix two different solutions during
the electrospray process at a flow rate of 1.4 ± 0.4 nL/s. This
flow rate is 2 orders of magnitude less than typical flow rates for
common mixers in which mixing is achieved in tens of microseconds.[13] On the basis of probable sizes of electrospray
droplets, rates of diffusion, and mixing times of coalescing ballistic
microdroplets, complete mixing from theta-glass emitters likely occurs
within a few microseconds. Thus, mixing from theta-glass emitters
is competitive with the fastest mixers reported in the literature[14] and 2 orders of magnitude faster than any mixer
previously coupled to MS.[3]The reduction
of DCIP by L-AA performed using the theta-glass emitters
was monitored with the mass spectrometer to obtain a lifetime of nano-ESI
droplets. The resulting value of 274 ± 60 μs is an upper
limit to the droplet lifetime because both the reagent concentrations
and the surface area to volume ratio increase as the droplet evaporates
and because some product formation likely occurs in the Taylor cone
prior to droplet formation. On the basis of previously reported results
that show that reaction rates in droplets can be 10–1000-fold
higher than rates in bulk solution, we estimate that the true droplet
lifetime is between 27 μs and 270 ns. The rapid mixing and short
droplet lifetime achieved using these theta-glass emitters should
make it possible to monitor fast reactions using MS. Because the initial
droplet diameter, and therefore the droplet lifetime, depends on both
the size of the tip of the electrospray capillary and the solution
flow rate, the acquisition of reaction data at multiple time points
should be possible by either using theta-glass emitters with variously
sized tips or by changing solution flow rates.
Authors: Saša M Miladinović; Luca Fornelli; Yu Lu; Krzysztof M Piech; Hubert H Girault; Yury O Tsybin Journal: Anal Chem Date: 2012-05-11 Impact factor: 6.986
Authors: Feifei Zhao; Sarah M Matt; Jiexun Bu; Owen G Rehrauer; Dor Ben-Amotz; Scott A McLuckey Journal: J Am Soc Mass Spectrom Date: 2017-07-11 Impact factor: 3.109