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![1 Introduction
Electrospray Ionisation (ESI) is a process used to separate ions from a solution by applying
voltage to the capillary filled with liquid which causes the solution to fission and solvent to evap-
orate. This process is present in various applications, most well-known of which is Electrospray
Ionisation Mass Spectrometer (MS) which is used for analysing chemicals like salts or proteins
by measuring their charge and mass. There are more applications of EI which will be discussed
in the Literature Review chapter. In order to use MS and other technologies, which involve EI,
efficiently and effectively it is important to understand and be able to control this entire process.
The process can be split into three parts: Taylor Cone formation, Coulomb fission and a part
in which droplets reach very small sizes of around 10nm or less, where the process is not well
understood. Two mechanisms exist nowadays which try to explain what happens when drops
reach this size: Charge Residue Model and Ion Evaporation Model. There is a lot of debate on
which model is more applicable and whether both mechanisms act in concert. This report will
touch Taylor Cone formation and Coulomb fission to help readers understand how very small
scale droplets of 10nm size are produced, but the main focus will be on the difference between
CRM and IEM. This study will investigate how droplet temperature, charge, salt concentration
as well as the applied electric field trigger IEM or CRM of a 500-water-molecule drop. This will
be done with the help of Molecular Dynamic simulations (MDS) using an open source software
LAMMPS. Cases with very high electric field representative of a drop in the Taylor Cone region
will be covered too because ion evaporation may occur in that region according to previous stud-
ies. The basic theory behind Molecular Dynamics (MD) as well as limitations will be explained
in this report. LAMMPS script used for this study as well as values for parameters used will be
explained and justified step by step in this report as well. Some theory on CRM and IEM which
exists up to date will be explained, however it will be shown that there are limitations to theory
which do not let it to be applied on simulation results. Analysis of simulations will be done
using several state of the art MATLAB scripts created specifically for this project and using the
MD visualization software OVITO (the scripts used to generate the results in this report have
been appended in a USB). This report will aim to provide some clarity on whether IEM and
CRM occur in ESI.
2 Literature Survey
There is a broad range of applications where electrospray is used. One of them is electro-
spray propulsion, electospraying process is used to provide thrust in order of mN to position
small satellites in a required orientation [1]. This technology is known as ion thruster. Another
example is electrospray painting. Quite interestingly Dole, one of the founders and developers
of electrospraying theory [2], was trying to analyse masses of some polymers and was struggling
to find a method of separating molecular ions from solution without chemical decomposition.
Accidentally, when he visited a car manufacturer and saw car painting process using electro-
spray he realised he could use same technology for his research [3]. Since then electrosprays
became widely used in mass spectrometry (MS) for biological and chemical analysis. The other
two applications are nanofiber and nanocrystall production [4]. In the first case a long polymer
is present in the solution used in ESI with is electrospinned to form a thin fiber. The second
application is relatively new and requires more research, but the idea is to find such electrospray
parameters that the analyte forms prism-shaped crystalls after solvent is fully evaporated. Zheng
et al. [4] have studied how nanocrystalls of salt form this way and how results depend on the
applied electric field and flow rate. This application should not be confused with electrocrystal-
lization. Electrocrystallization is the process of freezing dielectric nanodroplets via applying a
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![very high electric field. Luedke et al have done a molecular dynamic study and visualized this
effect using formamide [5].
The process of ESI starts with applying voltage to a capillary tube filled with liquid solution.
There exist different designs of capillary tubes, some designs involve multiple nozzles, some
involve blowing of gas along with sprayed liquid. For this report the most simple design will be
considered with a single nozzle and no gas supply, as there is more experimental data available
for a simpler design. The design however is assumed to not have a significant effect on the
investigated part of the ESI process which is the very end of drop formation just prior reaching
the counter electrode (Figure 1a).
(a) Electrospray Ionization Process.
(b) Taylor Cone. (c) Nano-jet formation on the sur-
face of the Taylor cone.
Figure 1: Electrospray Ionization process. The main parts of the process are: Taylor Cone,
Nanojet, Coulomb fission, CRM and IEM. This study focuses on two regions: just before the
counter electrode and the region of the nanojet.
However, some ESI settings such as solution temperature and applied electric field will be dis-
cussed in this report. The liquid may consist of water or other solvent mixed with proteins,
salts or other chemicals which can form ions when dissolved. In this study only water mixture
with salt (NaCl) will be considered. Depending on the direction of the electric field negative
or positive ions get pulled out of the capillary and form a Taylor Cone, a "cap" at the end of
the capillary (Figure 1b). At some point when drops overcome surface tension they separate
from the cone. Until the size of about 10nm these droplets break up into smaller droplets via
the process called Coulomb fission. There is a lot of debate about what happens when a drop
reaches such small size. Up to date two mechanisms have been suggested which explain how
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![final ions form: Charge Residue Model (CRM) and Ion Evaporation Model (IEM). The first one
states that drops will continue to follow Coulomb fission until they reach size and properties
under which they can no longer explode, after that solvent evaporates from the drop leaving a
charged residue. The second one states that at such small scale ions can gain enough energy
to escape the droplet and evaporate in singly charged ion-solvent clusters of a very small size
(around 1-5Å). The full process of ESI is shown in Figure 1 and the difference between CRM
and IEM in Figure 2.
Figure 2: Difference between IEM and CRM.
Depending on the solvent and analyte materials the distribution of mass and charge in
exploded droplets during Coulomb fission can vary quite significantly [6]. During Coulomb
fission a droplet separates into one big and several smaller droplets. How charge and mass are
distributed in these droplets depends on chemicals involved. One study investigated Coulomb
fission for water mixed with NaCl, their experiment showed how charge and size of the droplet
change with time [6]. The driver for the Coulomb fission is the Rayleigh limit or limit at which
the electrostatic energy is twice higher than the surface energy [7]. Equation 1 was derived by
Lord Rayleigh [8] and it is a droplet surface charge above which the droplet becomes unstable,
it is well known as the Rayleigh limit.
Q = 64π2
0γR3 (1)
where Q is the maximum charge a drop can carry in units of coulomb (C), 0 is the electrical
permittivity in vacuum equal to 8.85 · 10−12F/m, γ is the surface tension and R is the radius
of the drop. Q can be converted to electric charge by multiplying by 6.242 × 1018. For clarity,
if there are k Na+ and i Cl− ions in the solution then the electric charge Q on that drop is
equal to k-i. There are some uncertainties on how accurate the expression for Rayleigh limit
is and whether it can be used at all for cases with applied external electric field and particle
aspherity [9]. Electric field will be applied on all drops in this study and particle aspherity
may have a significant effect because drop sizes considered here are very small, around 15.5Å
in radius. Previous experiments and MD simulations have also shown that droplet fission can
occur before the Rayleigh limit is reached [9–11].
CRM assumes Coulombic fission continues until the end of spraying. CRM was suggested
by Dole [12] and was considered to be the only process happening in ES for some time, however
Fenn et al. [13] has shown that singular ions can be produced without Coulomb fission and later
Iribarne and Thomson [14] have demonstrated that singular ions can gain enough energy to
escape the droplets and evaporate and started developing a theory describing ion evaporation.
There have been studies supporting that both processes may take place but no understanding
has been established yet on when one or another process is dominant and if these two processes
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![are the only processes which can take place at this scale. MD simulations have been carried out
to partially investigate these processes. There has been focus on different solvent and analyte
materials and how they affect IEM, a big variety of proteins has been tested via MD [11,15–17].
Other studies have investigated the effect of collision of droplets with surrounding gas, but
no collision of two or more drops has been investigated before [18], [19]. It has been noticed
that most papers have very little focus on CRM and that in general, more and more evidence
appears with every study supporting IEM for small ions, however CRM is more probable for large
ions like proteins. There have been two studies however which showed the entire process of salt
residue formation and observed ion evaporation only once in their simulations, but temperatures
used there were higher than expected to see on the drop of such size [11,15]. Temperatures in
those studies were set to high values of 370K and 460K and were kept the same throughout the
simulation by using a thermostat (temperature updating command in MD software).
The theory behind IEM, which was first initiated by Iribarne and Thomson [14] and then
developed further by Fernandez de la Mora [20–22] involves assumptions and is valid for limited
cases. More detail on CRM and IEM and the shortcomings of IEM theory will be given in
this report in chapter CRM and IEM Theory. Quite surprisingly electric field is not present in
any derivations by Iribarne and Thomson or Fernandez de la Mora. Moreover, only few MD
studies were found which would apply an external electric field on the drop. Two of those were
modeling very high electric field because they concentrated on the drop formation in a Taylor
cone region which will be investigated in this report too, as it has been stated that IEM can
occur in that region as well. Another study modeled a very small droplet with less than 50
water molecules [19] and focused on its collision with argon, the electric field used in the study
is however higher than 3×10−5V/Å which is a common electric field in electrosprays. The reason
why electric field is absent in most simulations might be because at such small values of electric
field it does not have much effect on drop’s behaviour, however this is just an assumption and
it may not be true. Low electric field will be applied on some drops in this study.
Because drops become smaller and smaller as they fly and fission they become harder to
track, therefore there is very little experimental data on drops below the size of approximately
0.002µm. Due to this some droplet properties which will be chosen for simulations will be based
on assumptions, some on previous MD studies on a similar topic and some on experimental data
where available. From theory on ion evaporation and from previous MD studies the factors which
could trigger CRM and IEM are: temperature, salt concentration, droplet size, droplet charge,
ion properties, solvent chemical composition. Some experiments have shown that flow rate may
also affect the ion formation process [4]. The range of chemicals and proteins which could be
used in ES is very broad, most common ones are NaCl, NaI, KI, KCl etc. Because of limitations
of MD software not all materials can be modeled, therefore only NaCl will be considered in
this report. The range of solvent materials is narrower: water, methanol, acetonitrile and
formamide are usually used, however only water will be considered as there is no model existing
in LAMMPS which would be suitable for other materials. The flow rate of solution is within
1 − 20µl/min [3, 10, 11], bath gas temperature varies from 317K to 473K [10, 23, 24], common
temperature of inlet capillary is 373 − 573K [3], the analyte concentrations lie between 10nM
and 10mM [11, 23], the applied voltages between 2 and 3kV [10, 11, 23, 24], the distance from
the needle tip to the entrance capillary is usually 1-3cm [23]. Coulomb fission and evaporation
of solvent from the drop cause reduction in temperature. Some previous studies applied a very
high temperature to an electrosprayed drop to speed up the evaporation process, however it
cannot be established with certainty if results of such simulations are realistic. There have been
no experimental studies showing the temperature change of drops during the electrospraying
process, therefore temperatures in this study were selected based on the majority of previous
MD studies.
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![calculated from the gradient of the potential, if electric field is applied, then additional force is
added on all particles according to Equation 5
F = qE, (5)
where q is the charge of atom. Lorentz-Berthelot mixing rules are used to determine σ and for
interaction of two different atoms, for example Na and Cl.
Acceleration found from the force and the selected time step t provide new velocities and
new positions for elements. In LAMMPS there is a selection of pair styles available, for example
if pair style lj/cut/coul/cut is selected then interactions between atoms will follow Equations 3
and 4 as discussed, however for different applications slight deviations to these equations need
to be applied and this can be done by selecting different pair styles. TIP4P/2005 [25] pair style
lj/cut/tip4p/long was used to model interactions with water molecules and lj/cut/coul/long pair
style was used to model interactions with Na+ and Cl−.lj/cut/coul/long is slightly different from
lj/cut/coul/cut, it applies an additional damping factor to the Coulombic term to be able to
compute long range Coulombic interactions.
Part of ESI process starting from the drop radius of approximately 15.5 Åwas modeled using
MD simulations. Simulations were split into two stages: equilibration stage at which all atoms
reach specified temperature and form a drop and applied electric field stage where a drop starts
to move.
Limitations
As can be seen from Figure 3 time increment is one of the input parameters. Simulations
with very high electric field were found to be extremely sensitive to this parameter and required
very low time increment. Simulations with low electric field ran smoothly with ∆t = 3 fs. For
readers who want to replicate the simulations it is advised to run them with selected timestep for
around 100000 timesteps to make sure they do not crash. Simulation time also depends on the
neighbor value (distance above which Coulombic interactions are neglected), number of atoms
in the simulations, domain size and processing power. The best performance was found when
simulations were running on nodes with 24 CPU cores. Slow down of simulations were noticed
when simulations were running on two parallel nodes with 16 CPU cores per node.
Another limitation is the chemicals MD software are able to model. As mentioned in the Lit-
erature Review, not only water can be a solvent in electrospray, but also methanol, acetonitrile,
formamide or other chemicals some of which may have more complicated molecular structures
than water. LAMMPS does not have an in-built pair style for methanol or acetonirtrile to date.
There have been molecular dynamic simulations done on methanol-water mixture by Koner-
mann et al. [17], however the authors used an in-house C++ code to model it. Another research
has created an ab initio model for methanol and acetonitrile [26] but this model has not been
implemented or tested using any MD software yet. Water was selected as a solvent material as
it is widely tested by other LAMMPS users. Number of experiments and studies on ESI with
water is significantly larger than on formamide, which can also be modeled using LAMMPS. If
any other salts however have similar structure to NaCl, then they can be modeled as well by
simply changing the properties of atoms in the LAMMPS script.
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![4 MD Simulations of Electrospray
In total 45 simulations were run on a 500-water-molecule-drop which vary with charge,
electric field, initial temperature and salt concentration. Three values of charge were used, the
maximum value Q = 7 corresponds to 100% Rayleigh limit according to Table 2, the limit above
which the droplet is expected to fission, the second charge Q = 4 was chosen as a middle between
the Rayleigh limit charge and neutral charge (Q = 0) and the last charge Q = 2 was selected
to see what happens when the drop is almost neutral but still has some charge. Charge was
changed by changing the number of chloride ions in the drop while keeping the sodium ions fixed.
In future studies more charge values could be investigated; as it can be seen from experiments
that there is a wide range of initial drop charges which can exist in an electrosprayed drop. Two
extremes of electric field were investigated. The low value of an electric field E = 3×10−5 V/Å is
representative of a drop separated from the cone-jet and flying between the jet and the counter
electrode. The value can easily be calculated using Equation 6.
E =
∆V
L
, (6)
where ∆V is the applied voltage and L is the distance between the capillary and the counter
electrode equal to approximately 1cm (Figure 1a).
According to Luedtke et al. [27] ion evaporation phenomenon can occur at the surface of a
flowing electrified jet in a Taylor cone region, where electric field is much higher. Magnitudes up
to 0.2V /Å have been previously tested on formamide solutions with NaI [27] and magnitudes
of 0.05 V/Å on water solutions with NaCl, KCl and CsCl [28]. This study will test three
magnitudes 0.05 V/Å, 0.14 V/Å and 0.3 V/Å. The last value was chosen to see how the droplet
behaviour changes if electric field is increased further than 0.2 V/Å. It is important to recognise
the difference between the applied electric field and surface electric field. For the benefit of
explanation let us split the applied electric field into two types: artificial and real. The real
applied electric field is the field induced by the applied voltage on the capillary. It always stays
the same and can be calculated using equation 6. This field acts on all flying drops. The surface
electric field appears due to the charge in the drop or substance. In the region of the nanojet
(Figure 1c) the surface electric field is much higher and is dominant in the direction of the real
electric field. This high surface electric field on a drop can be reproduced by applying the high
external electric field on a drop i.e. the artificial applied electric field. It was found in some
experiments that ion evaporation happens in the range 0.07 V/Å − 0.19 V/Å for surface electric
field [22] and 0.146V/Å and 0.266V/Å according to different experiments [29]. This was another
reason for choosing the specified electric field values as one of them is within the range and other
two are outside the range given. Number of water molecules in the system was chosen to be 500,
this value has not been tested before and at the same time it allows to run simulations faster
(compared to 1000 and 2000 molecules which are typically used in similar studies).
Salt concentration is a very interesting parameter, there was a lack of attention to it in any
of previous MD simulations for the same topic. It is unclear both from previous studies and
from experiments, what is the correct salt concentration to use. There is no consistency in
previous studies in salt concentration of the drops. Some previous MD studies use values such
as 10 pairs of Na+ and Cl− ions per 4000 water molecules [10], 13 or 17 pairs per 2420 water
molecules [15], 60 pairs per 1000 water molecules [11], 0 pairs and only charge per 10, 15 and
20 water molecules [19]. Another experimental study has been made which shows that almost
any salt concentration starting from 0 pairs and ending with 56 pairs per drop can be present in
final drops which get into the mass spectrometer, but not all charges. Charges of 4 and above
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![are not very common according to the mentioned experimental study [30]; however it is not
clear if the distance of Mass Spectrometer from the capillary can have an effect on those results.
It was decided to first test two extremes of salt concentration because it was initially unclear
what effect it will have on drop behaviour and then nine more cases were run with medium salt
concentration (Table 1). It was noted that salt concentration has a significant effect on drop
behaviour.
Temperature values of 300K and 320K are commonly used in previous studies. Higher values
are used too and could be used in future studies but they would affect the starting condition of
the droplet. It was aimed to have similar starting conditions for all simulations, i.e. no ion or
water evaporation present in the domain but higher temperatures would lead to ion evaporation
even at the equilibration stage where no electric field is applied. Therefore two temperatures
with 20K difference were selected which are 300K and 320K. However for the case of 15 sodium
atoms and Q = 7 the evaporation effect could still not be eliminated.
Table 1: Timestep used (top value) and length (bottom value) of each simulation.
Water Molecules 500
Temperature 300K 320K
Electric Field 0.05 V/Å 0.14 V/Å 0.3 V/Å 0.00003 V/Å 0.05 V/Å 0.14 V/Å 0.3 V/Å
NumberofNa+andCl−ionsinadrop
65Na+ 58Cl− 0.3fs
1230ps
0.1fs
1000ps
0.05fs
400
-
0.3fs
960ps
0.1fs
1000ps
-
65Na+ 61Cl− 0.3fs
1260ps
0.1fs
1000ps
0.05fs
400
-
0.3fs
540ps
0.1fs
1000ps
-
65Na+ 63Cl− 0.3fs
960ps
0.1fs
1000ps
0.05fs
400
-
0.3fs
600ps
0.1fs
1000ps
-
40Na+ 33Cl− -
0.1fs
284ps
0.05fs
92ps
- - -
0.05fs
78.2ps
40Na+ 36Cl− -
0.1fs
295ps
0.05fs
90ps
- - -
0.05fs
85.2ps
40Na+ 38Cl− -
0.1fs
300ps
0.05fs
96ps
- - -
0.05fs
77.8ps
15Na+ 8Cl− 0.3fs
329ps
0.1fs
126ps
0.05fs
50ps
3.0fs
3600ps
0.3fs
363ps
0.1fs
100ps
0.05fs
50ps
15Na+ 11Cl− 0.3fs
864ps
0.1fs
141ps
0.05fs
50ps
3.0fs
3600ps
0.3fs
1463ps
0.1fs
142ps
0.05fs
50ps
15Na+ 13Cl− 0.3fs
630ps
0.1fs
203ps
0.05fs
50ps
3.0fs
3600ps
0.3fs
1430ps
0.1fs
141ps
0.05fs
50ps
Two scripts would be used to create a drop. The first one randomly fills a sphere of radius
R with point masses and applies type number to them, e.g. 1 is Oxygen, 2 is Hydrogen, etc. In
case of water molecule atoms it puts them at an angle and distance to each other required for
the TIP4P water model, rigid water model (bonds do not displace) with shifted mass which is
available in LAMMPS (Figure 4). It is one of the most commonly used liquid water models and
statistically provides very accurate results.
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![Figure 4: TIP4P Rigid Water Model
Radius of each drop was calculated as following:
R =
m
4
3πρ
1/3
(7)
Where ρ is the density of water, and m is its mass calculated using equation
m =
nM
N
, (8)
where n is the number of water molecules, M is the molar mass of water and N is Avogadro
number equal to approximately 6.022 × 1023. Radius would then be increased by 2.5% to avoid
squeezed or overlapping atoms. A maximum charge on it was then calculated according to the
Rayleigh limit (Equation 1). Surface tension is present in Equation 1 and its values are listed in
a table for different droplet setups according to experiments and previous MD studies on surface
tension, it will later be shown that it plays an important role in fission and ion evaporation of
drops. MD seems to underrate the surface tension γ [31] and this is supported in this study
as well. It will be seen later that ion evaporation of the drop seems to match with theory
better when surface tension values obtained from MD simulations are used. At the lowest salt
concentration Q=7.0 taking γ values from MD simulation results and Q=7.5 taking γ from
experiments [31]. Values for γ which were not found in sources were linearly extrapolated..
Density of the solution changes with salt concentration as well but the change is negligible.
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![Step 15 Compute kinetic and potential energies of all atoms.
Step 16 Create trajectory files which store information about positions, velocities and
energies of atoms. Create a restart file every 100000 timesteps in case the
simulation stops. This allows to run the simulation from the last saved restart
file. A detailed script can be found in Appendix B.
5 CRM and IEM theory
CRM states that solvent (water) evaporates from the drop and reaches the Rayleigh limit
at which it explodes and simultaneously produces several charged drops. It also states that
if Rayleigh limit cannot be reached solvent will evaporate from the drop and leave only the
analyte residue (salt). Such CRM with full evaporation was observed by several MD studies
on drops of around 1000 molecules. It was mainly observed in drops containing large protein
molecules which do not break up [32, 33]. Another MD study has been done showing that
drops containing salt experience such CRM but the simulations were conducted at much higher
temperatures than what is used used in this study and under different boundary conditions as
well i.e. particles would disappear when they reach boundaries (while this study uses periodic
boundaries) and no external electric field was applied to the drop either [15]. It was not expected
to see any drop fission due to the size of the drop used, however full evaporation of solvent was
expected. Gamero-Castano et al. [12] stated that Coulomb explosions could only produce drops
of macroscopic size and can be suppressed in the case of sufficiently small initial drops. They
also stated that very small scale drops can remain below the Rayleigh limit by getting rid of
small singly charged clusters i.e. experience ion evaporation.
Iribarne and Thomson [14] were the first who tried to describe IEM analytically. They stated
that an ion cluster must overcome an energy barrier in order to leave a charged drop. They
built the expression for energy barrier which would consist of two terms: energy of solvation
and electrostatic energy. Energy of solvation is the energy required to dissolve an ion cluster of
radius Ri in a drop of radius R. Energy of solvation can thus be split into two terms, the first
term is due to overcoming the surface tension and the second is the energy required to charge
an ion in a dielectric continuum ∆GBorn also known as Born’s equation.
Fernandez de la Mora et al [20–22] then improved this derivation and added a curvature
correction term. Their studies give step by step derivation of the activation energy ∆. Activation
energy ∆ is the difference in energy of the entire system between after and before an ion cluster
separates from the main drop and this is what Iribarne and Thomson meant by the energy
barrier as well. They started from assuming that the drop is infinitely large and its charge is 0.
In this case Born’s equation summed with a surface energy term can be used to calculate the
energy required to bring an ion from the solution into a vacuum. That energy sum depends on
the radius of the escaping ion drop Ri and assuming that evaporating drop follows the path of
least resistance, ion evaporation happens at the minimum value of ∆GBorn. They then found
an expression for the radius of an escaping drop Ri based on ∆GBorn:
R3
i =
e2(1 − −1)
64π2γ 0
, (9)
where e is an ion charge, is the dielectric constant of the solution, 0 is the electrical permittivity
in vacuum equal to 8.85 × 10−12F/m and γ is the surface tension of the solution. As Fernandez
de la Mora et al [21] pointed in their study, quite interestingly this expression is very similar
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![to the expression for the radius of the drop at the Rayleigh limit which can be derived from
Equation 1. They further expanded the expression for activation energy ∆ to account for drop’s
charge and curvature, full expression for which contained five terms:
∆ = U + Ui + W∗
− U0 + ∆Us (10)
where U is the energy of the drop (after separation of ion), Ui is the energy of the separated
ion cluster, W∗ is the interaction energy between the main drop and the separated ion drop, U0
is the energy of the full drop before ion is separated and ∆Us is the surface energy created by
detaching two spherical drops. Full expressions for these can be found in Equations 11-13, 15,
16.
U =
z2e2
8π 0R
(11)
Ui =
e2
8π 0Ri
(12)
U0 =
(z + 1)2
8π 0[R3 + R3
i ]1/3
, (13)
where z is the number of charges remaining in the drop after ion evaporates. Expression z + 1
can be met quite often in these derivations because Fernandez de la Mora et al [20–22] assumed
that the separating ion cluster contains only one ion. Interaction energy W depends on the
distance between the primary and the secondary drop and can be expressed using Equation 14,
it reaches its maximum value W∗ at a distance x∗ (Equation 15).
W(x) =
e2
4π 0R
z
x
−
1
2x2(x2 − 1)
(14)
W∗
=
e2
4π 0R
[z − F(z)] (15)
In Equation 15, F(z) is the field ionization function defined as F(z) = z1/2 −7/8+O(z−1/2).
It was derived by Gamero-Castano and Fernandez de la Mora [12] to account for the effect
of curvature on a drop and the remaining charge z on the drop. The final term ∆Us can be
calculated as following:
∆Us = 4πγ R2
i −
2R3
i
3R
(16)
Full expression then becomes
∆ =
e2
8π 0Ri
+ 4πγR2
i −
e2(2F(z) + 1)
8π 0R
+ 4πγ
2R3
i
3R
(17)
For water drops at room temperature ion evaporation would start at ∆ around 0.4eV [21].
Radius of the drop which leads to the smallest loss in energy is then
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![R3
i =
e2
64π2γ 0
(18)
We can see that the only variable contained in the expression for Ri which changes is the
surface tension. Thus from this equation for Ri it is expected to see that radius of an ion cluster
does not change with temperature, charge or electric field. There are some shortcomings which
make it hard to apply the presented analytical model on the results of MD simulations:
• The applied electric field on a drop was not taken into account in any derivations how-
ever it will be seen later that the difference in electric field can cause a difference in ion
evaporation.
• An assumption has been made that the evaporated drop contains only one ion however it
will later be seen in the Results chapter that some escaping drops can contain two or three
ions or even five. It is not certain if Ri can be multiplied by two or three in these cases.
• Collision with other drops is not taken into account, neither is the presence of vapor or
gas in the system. All derivations were made assuming full vacuum. Periodic boundary
conditions which were used in MD simulations mean that the system is not full vacuum,
in some simulations as the drop would evaporate and brake up some vapour would occur
around the drop.
• An assumption has been made that the radius of the evaporated ion cluster is much smaller
than the radius of the initial drop, however for the case of strong electric fields we will
see that some evaporating ions might not satisfy this assumption as they are quite large
relative to the primary drop.
• Curvature correction function F(z) is only valid if z is large, z >> 1. It is not certain what
is the minimum value of z at which Equations 15-17 can still be used.
• There has been some evidence that this analytical model works well for stationary drops to
which no electric field has been applied but no such evidence with an electric field applied.
Despite the shortcomings and despite the fact that this analytical model for IEM was devel-
oped years ago, it is the best model which exists up to date and which can describe and predict
ion evaporation to some extent. Another important parameter which was not mentioned before
is the rate of evaporation dz
dt which according to Iribarne and Thomson [14] can be calculated
using the following equation:
dz
dt
= −
kT
h
(z + 1) exp −
∆
kT
, (19)
where k is Boltzmann’s constant, T is the absolute temperature and h is Planck’s constant.
Again, there is no term describing the applied electric field on a drop. It can also be noticed
that ion evaporation rate depends on temperature while the expression for radius of an escaping
ion cluster and activation energy do not contain a temperature variable. Loscertales et al. [22]
have concluded in their studies that the rate of ion evaporation is related to the rate of solvent
evaporation from the drop. Thus at lower temperatures and higher salt concentrations ion
evaporation rate is expected to be slower.
21](https://image.slidesharecdn.com/dissertationfinal3-190407142222/85/My-Dissertation-22-320.jpg)
![Figure 5: Visualising evaporation in MATLAB. Purple circles - vapour, blue - liquid, Na+ and
Cl− are marked as "+" and "-" respectively.
6 Simulation Analysis
Open source visualisation software OVITO was used for visualizing results and creating
animations. Several state of the art MATLAB scripts were created for analysing simulations.
Each simulation in LAMMPS produces a trajectory file containing the history of drop’s positions,
velocities, potential and kinetic energies which were recorded every 200 fs or so. More attributes
could be exported from LAMMPS if required however the listed ones are the only ones which
will be used for analysis. MATLAB scripts can read information about each timestep from the
trajectory file and analyse temperatures, distinguish between vapour and liquid (Figure 5), keep
track of the ratio between the two, track potential energy, track escaping ions and their potential
energy, make plots and animations. Some MATLAB codes can also identify both vapour and
liquid drops and apply group IDs to them and recognise periodic boundary conditions. The
strength of MATLAB is its ability to manipulate efficiently with matrices, therefore loops were
avoided where possible and mainly matrix operations were carried out to make the code faster
and more efficient.
One of the scripts was created to analyse the vapour formation during simulation. According
to Zhang et al [31] water is in vapour state when there are less than 10 water molecules sur-
rounding it in a radius of 6.3Å. To make the script faster and easier to process hydrogen atoms
were removed from the trajectory matrix by MATLAB script. This does not affect the results of
analysis. The script would check distances between every pair of atoms in the domain and select
all atoms, which are within the distance of 6.3Åto each other. Once the loop is over MATLAB
sums all these atoms and checks if their number is more or equal to 10 and labels each atom
ID as liquid if it satisfied the condition and as vapour otherwise by assigning a number 1 or 0
respectively.
Similarly to liquid identification MATLAB script can identify particle groups using the same
limit distance of 6.3Å. MATLAB can identify both vapour and liquid groups and can also
recognise periodic boundary conditions by copying the domain and coordinates of particles on
three perpendicular sides of the domain as shown in Figure 6.
Because the system studied is very dynamic and drops explode at a fast rate and into a large
number of smaller drops, it is quite hard if not impossible to keep group IDs the same from
22](https://image.slidesharecdn.com/dissertationfinal3-190407142222/85/My-Dissertation-23-320.jpg)
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My Dissertation
- 1. The University ofEdinburgh MEng Individual Project Final Report PROBING THE NANOSCALE MECHANICS OF ELECTROSPRAY IONISATION Author: Nadezda Avanessova Matriculation Number: s1449529 Supervisor: Rohit Pillai April 4, 2019
- 2. Personal Statement • Thisproject is new, it is not a continuation from previous years. • This project was very challenging because it involved chemistry, the subject I am not so strong at. It also involved working with LAMMPS, the MD software which was the main tool for my project. I have never worked with LAMMPS before or any other software which did not have GUI and even with the help of my supervisor found it quite difficult to learn. My supervisor Rohit Pillai helped me a lot throughout the project and was always my main contact point. He helped me with learning necessary LAMMPS commands and running simulations. I have also received IT support for the project from Angela (from the University IT Support). • This project was derived by my supervisor Rohit Pillai and it is an original work. There are works which focused on the similar problem and they will be discussed in this paper. Some simulation setup settings were however taken from similar papers, the report will discuss which settings and why they were used. It is important to note here that there is a lack of experimental data available which could be used for the project because experiments and data collection for such study can be very difficult and expensive, therefore assumptions were used where there was no data available. • This project did not need any experimental work, only MD simulations were conducted using LAMMPS. Supercomputers ARCHER and Eddie as well as VLX servers were used for simulations. As it is stated in one of the objectives, the simulations were performed with assistance from the supervisor. Around 90% of in.equilibrate and in.efield scripts used for simulations were written by Rohit Pillai, however I gained a full understanding of the scripts and explained what they do step by step in this report. By the end of the project I felt confident with the script and can modify it if needed for different or more complex simulations related to the topic of this report. • The theoretical part of the project progressed well, there is a lot of theoretical material available online. Some of it was hard to understand, I felt that theory behind electrosprays is very different from everything I learnt in my degree however I found it very interesting and challenging. I enjoy learning something new and this was one of the reasons I put this project high in my preference list. It was quite unfortunate that the simulations would crash for quite a while until one of the parameters (timestep) was decreased. That led to very slow simulations, with those I needed at least a couple of days to finish them. Mistakes in the script were also made quite often, which means I had to rerun simulations several times. 1
- 3. Summary Probing the NanoscaleMechanics of Electrospray Ionisation Author: Nadezda Avanessova Date: 04/04/2019 Background: Electrospray Ionisation is a process used to separate ions from a solution by applying voltage to the solution which causes the solution to explode and solvent to evaporate. This processes present in various applications, most well-known of which is Electrospray Ionisa- tion Mass Spectrometry which is used for analysing chemicals like salts or proteins by measuring their charge and mass. Aims: • To read through the literature and develop an understanding of molecular dynamics(MD) and electrospray ionization. • To perform simulations of electrospraying nanodroplets using LAMMPS, with as-sistance from the supervisor. • To analyze the data obtained from MD simulations. • To quantitatively describe the process for the system studied and possibly comparewith reported experimental results. • To provide a set of recommendations for ESI equipment design. Methods: Molecular Dynamic Simulations were run using LAMMPS. Analysis was carried out using several state-of-the-art MATLAB scripts. Results and Discussion: Only 15 simulations out of all which run successfully showed any results and they are listed in the Results chapter. More and longer simulations need to be run to achieve more accurate results. This work however shows that the effects of electric field and salt concentration on drop’s behaviour are stronger than the effects of charge or temperature. Conclusions: (1) A logarithmic relationship is suspected between the time of first ion evap- oration and electric field in high electric field cases (2) salt concentration plays an important role in studied processes, high salt concentrations can reduce ion evaporation rate as well as solvent evaporation significantly, (3) equations generally used in IEM theory cannot be applied on high electric field cases, (4) increase in charge may cause ion evaporation even in the absence of electric field in low salt concentration cases and also speeds up explosion of the drop when electric field is applied, (5) high electric field causes strong collisions which lead to complete evaporation of drops unlike (6) low electric field cases, where repulsive forces between escaped ion and a drop overcome the electric field force and thus collisions are less likely (7) neither IEM nor CRM were observed for low electric field cases for 4ns. 2
- 4. Acknowledgements I would liketo acknowledge my brothers Sergei, Aleksei, Ivan and my sister Jelena for their continuous support throughout my studies. I would also like to use this opportunity to say special thanks to my mother Tatjana, who started studying in college at the age of 57 while having two jobs, and my father Andrei, who ran his first marathon at the age of 51. They showed me that everything is possible no matter when and where you started. 3
- 5. Nomenclature Abbreviations CRM Charge ResidueModel ESI Electrospray Ionisation IEM Ion Evaporation Model LJ Leonard-Jones MD Molecular Dynamics MDS Molecular Dynamic Simulations MS Mass Spectrometry PBC Periodic Boundary Conditions Other Symbols ∆ Activation Energy Dielectric Constant 0 Permittivity in a vacuum γ Surface Tension ρ Density e Electron Charge h Planck’s Constant k Boltzmann’s Constant L Length M Molar Mass m Mass n Number of Atoms q Atom Charge Ri Radius of an Ion Cluster T Temperature Ts Starting Temperature V Voltage v Velocity 4
- 6. E Electric Field QCharge R Radius of the drop U Energy 5
- 7. Word Count Chapter WordCount Introduction 422 Literature Review 1680 MD using LAMMPS 930 MD on Electrospray 2125 CRM and IEM Theory 1260 Simulation Analysis 926 Results and Discussion 1664 Conclusin 384 Total 9391 6
- 8. Contents 1 Introduction 8 2Literature Survey 8 3 MD Using LAMMPS 12 4 MD Simulations of Electrospray 14 5 CRM and IEM theory 19 6 Simulation Analysis 22 7 Results and Discussion 24 8 Conclusion 40 Appendix A Equilibration Script 41 Appendix B Electric Field Script 42 7
- 9. 1 Introduction Electrospray Ionisation(ESI) is a process used to separate ions from a solution by applying voltage to the capillary filled with liquid which causes the solution to fission and solvent to evap- orate. This process is present in various applications, most well-known of which is Electrospray Ionisation Mass Spectrometer (MS) which is used for analysing chemicals like salts or proteins by measuring their charge and mass. There are more applications of EI which will be discussed in the Literature Review chapter. In order to use MS and other technologies, which involve EI, efficiently and effectively it is important to understand and be able to control this entire process. The process can be split into three parts: Taylor Cone formation, Coulomb fission and a part in which droplets reach very small sizes of around 10nm or less, where the process is not well understood. Two mechanisms exist nowadays which try to explain what happens when drops reach this size: Charge Residue Model and Ion Evaporation Model. There is a lot of debate on which model is more applicable and whether both mechanisms act in concert. This report will touch Taylor Cone formation and Coulomb fission to help readers understand how very small scale droplets of 10nm size are produced, but the main focus will be on the difference between CRM and IEM. This study will investigate how droplet temperature, charge, salt concentration as well as the applied electric field trigger IEM or CRM of a 500-water-molecule drop. This will be done with the help of Molecular Dynamic simulations (MDS) using an open source software LAMMPS. Cases with very high electric field representative of a drop in the Taylor Cone region will be covered too because ion evaporation may occur in that region according to previous stud- ies. The basic theory behind Molecular Dynamics (MD) as well as limitations will be explained in this report. LAMMPS script used for this study as well as values for parameters used will be explained and justified step by step in this report as well. Some theory on CRM and IEM which exists up to date will be explained, however it will be shown that there are limitations to theory which do not let it to be applied on simulation results. Analysis of simulations will be done using several state of the art MATLAB scripts created specifically for this project and using the MD visualization software OVITO (the scripts used to generate the results in this report have been appended in a USB). This report will aim to provide some clarity on whether IEM and CRM occur in ESI. 2 Literature Survey There is a broad range of applications where electrospray is used. One of them is electro- spray propulsion, electospraying process is used to provide thrust in order of mN to position small satellites in a required orientation [1]. This technology is known as ion thruster. Another example is electrospray painting. Quite interestingly Dole, one of the founders and developers of electrospraying theory [2], was trying to analyse masses of some polymers and was struggling to find a method of separating molecular ions from solution without chemical decomposition. Accidentally, when he visited a car manufacturer and saw car painting process using electro- spray he realised he could use same technology for his research [3]. Since then electrosprays became widely used in mass spectrometry (MS) for biological and chemical analysis. The other two applications are nanofiber and nanocrystall production [4]. In the first case a long polymer is present in the solution used in ESI with is electrospinned to form a thin fiber. The second application is relatively new and requires more research, but the idea is to find such electrospray parameters that the analyte forms prism-shaped crystalls after solvent is fully evaporated. Zheng et al. [4] have studied how nanocrystalls of salt form this way and how results depend on the applied electric field and flow rate. This application should not be confused with electrocrystal- lization. Electrocrystallization is the process of freezing dielectric nanodroplets via applying a 8
- 10. very high electricfield. Luedke et al have done a molecular dynamic study and visualized this effect using formamide [5]. The process of ESI starts with applying voltage to a capillary tube filled with liquid solution. There exist different designs of capillary tubes, some designs involve multiple nozzles, some involve blowing of gas along with sprayed liquid. For this report the most simple design will be considered with a single nozzle and no gas supply, as there is more experimental data available for a simpler design. The design however is assumed to not have a significant effect on the investigated part of the ESI process which is the very end of drop formation just prior reaching the counter electrode (Figure 1a). (a) Electrospray Ionization Process. (b) Taylor Cone. (c) Nano-jet formation on the sur- face of the Taylor cone. Figure 1: Electrospray Ionization process. The main parts of the process are: Taylor Cone, Nanojet, Coulomb fission, CRM and IEM. This study focuses on two regions: just before the counter electrode and the region of the nanojet. However, some ESI settings such as solution temperature and applied electric field will be dis- cussed in this report. The liquid may consist of water or other solvent mixed with proteins, salts or other chemicals which can form ions when dissolved. In this study only water mixture with salt (NaCl) will be considered. Depending on the direction of the electric field negative or positive ions get pulled out of the capillary and form a Taylor Cone, a "cap" at the end of the capillary (Figure 1b). At some point when drops overcome surface tension they separate from the cone. Until the size of about 10nm these droplets break up into smaller droplets via the process called Coulomb fission. There is a lot of debate about what happens when a drop reaches such small size. Up to date two mechanisms have been suggested which explain how 9
- 11. final ions form:Charge Residue Model (CRM) and Ion Evaporation Model (IEM). The first one states that drops will continue to follow Coulomb fission until they reach size and properties under which they can no longer explode, after that solvent evaporates from the drop leaving a charged residue. The second one states that at such small scale ions can gain enough energy to escape the droplet and evaporate in singly charged ion-solvent clusters of a very small size (around 1-5Å). The full process of ESI is shown in Figure 1 and the difference between CRM and IEM in Figure 2. Figure 2: Difference between IEM and CRM. Depending on the solvent and analyte materials the distribution of mass and charge in exploded droplets during Coulomb fission can vary quite significantly [6]. During Coulomb fission a droplet separates into one big and several smaller droplets. How charge and mass are distributed in these droplets depends on chemicals involved. One study investigated Coulomb fission for water mixed with NaCl, their experiment showed how charge and size of the droplet change with time [6]. The driver for the Coulomb fission is the Rayleigh limit or limit at which the electrostatic energy is twice higher than the surface energy [7]. Equation 1 was derived by Lord Rayleigh [8] and it is a droplet surface charge above which the droplet becomes unstable, it is well known as the Rayleigh limit. Q = 64π2 0γR3 (1) where Q is the maximum charge a drop can carry in units of coulomb (C), 0 is the electrical permittivity in vacuum equal to 8.85 · 10−12F/m, γ is the surface tension and R is the radius of the drop. Q can be converted to electric charge by multiplying by 6.242 × 1018. For clarity, if there are k Na+ and i Cl− ions in the solution then the electric charge Q on that drop is equal to k-i. There are some uncertainties on how accurate the expression for Rayleigh limit is and whether it can be used at all for cases with applied external electric field and particle aspherity [9]. Electric field will be applied on all drops in this study and particle aspherity may have a significant effect because drop sizes considered here are very small, around 15.5Å in radius. Previous experiments and MD simulations have also shown that droplet fission can occur before the Rayleigh limit is reached [9–11]. CRM assumes Coulombic fission continues until the end of spraying. CRM was suggested by Dole [12] and was considered to be the only process happening in ES for some time, however Fenn et al. [13] has shown that singular ions can be produced without Coulomb fission and later Iribarne and Thomson [14] have demonstrated that singular ions can gain enough energy to escape the droplets and evaporate and started developing a theory describing ion evaporation. There have been studies supporting that both processes may take place but no understanding has been established yet on when one or another process is dominant and if these two processes 10
- 12. are the onlyprocesses which can take place at this scale. MD simulations have been carried out to partially investigate these processes. There has been focus on different solvent and analyte materials and how they affect IEM, a big variety of proteins has been tested via MD [11,15–17]. Other studies have investigated the effect of collision of droplets with surrounding gas, but no collision of two or more drops has been investigated before [18], [19]. It has been noticed that most papers have very little focus on CRM and that in general, more and more evidence appears with every study supporting IEM for small ions, however CRM is more probable for large ions like proteins. There have been two studies however which showed the entire process of salt residue formation and observed ion evaporation only once in their simulations, but temperatures used there were higher than expected to see on the drop of such size [11,15]. Temperatures in those studies were set to high values of 370K and 460K and were kept the same throughout the simulation by using a thermostat (temperature updating command in MD software). The theory behind IEM, which was first initiated by Iribarne and Thomson [14] and then developed further by Fernandez de la Mora [20–22] involves assumptions and is valid for limited cases. More detail on CRM and IEM and the shortcomings of IEM theory will be given in this report in chapter CRM and IEM Theory. Quite surprisingly electric field is not present in any derivations by Iribarne and Thomson or Fernandez de la Mora. Moreover, only few MD studies were found which would apply an external electric field on the drop. Two of those were modeling very high electric field because they concentrated on the drop formation in a Taylor cone region which will be investigated in this report too, as it has been stated that IEM can occur in that region as well. Another study modeled a very small droplet with less than 50 water molecules [19] and focused on its collision with argon, the electric field used in the study is however higher than 3×10−5V/Å which is a common electric field in electrosprays. The reason why electric field is absent in most simulations might be because at such small values of electric field it does not have much effect on drop’s behaviour, however this is just an assumption and it may not be true. Low electric field will be applied on some drops in this study. Because drops become smaller and smaller as they fly and fission they become harder to track, therefore there is very little experimental data on drops below the size of approximately 0.002µm. Due to this some droplet properties which will be chosen for simulations will be based on assumptions, some on previous MD studies on a similar topic and some on experimental data where available. From theory on ion evaporation and from previous MD studies the factors which could trigger CRM and IEM are: temperature, salt concentration, droplet size, droplet charge, ion properties, solvent chemical composition. Some experiments have shown that flow rate may also affect the ion formation process [4]. The range of chemicals and proteins which could be used in ES is very broad, most common ones are NaCl, NaI, KI, KCl etc. Because of limitations of MD software not all materials can be modeled, therefore only NaCl will be considered in this report. The range of solvent materials is narrower: water, methanol, acetonitrile and formamide are usually used, however only water will be considered as there is no model existing in LAMMPS which would be suitable for other materials. The flow rate of solution is within 1 − 20µl/min [3, 10, 11], bath gas temperature varies from 317K to 473K [10, 23, 24], common temperature of inlet capillary is 373 − 573K [3], the analyte concentrations lie between 10nM and 10mM [11, 23], the applied voltages between 2 and 3kV [10, 11, 23, 24], the distance from the needle tip to the entrance capillary is usually 1-3cm [23]. Coulomb fission and evaporation of solvent from the drop cause reduction in temperature. Some previous studies applied a very high temperature to an electrosprayed drop to speed up the evaporation process, however it cannot be established with certainty if results of such simulations are realistic. There have been no experimental studies showing the temperature change of drops during the electrospraying process, therefore temperatures in this study were selected based on the majority of previous MD studies. 11
- 13. 3 MD UsingLAMMPS General Theory For this projet an open source MD software LAMMPS was used. In MD the interaction between atoms is generally described via the sum of the Leonards-Jones (LJ) potential Uij(r) and the Electrostatics potential Ue(r). Uij(r) is the difference between a potential due to a Figure 3: Simulation flow of the MD software repulsive force between particles which appears when electron orbitals of two atoms overlap (represented by the first term in the square brackets of Equation 3) and a van der Waals force potential (which corresponds to the second term in the square brackets of Equation 3). van der Waals force is an attractive force between polar molecules. U(r) = Uij(r) + Ue(r) (2) Uij(r) = 4 σ r 12 − σ r 6 (3) In Equations 2-3 r is the distance between atoms, σ is the distance between atoms at which LJ potential becomes 0, is the minimum LJ potential. These values were found according to the selected solvent and analyte i.e. water and salt. The Electrostatic potential (Equation 4) describes an interaction between atoms due to their charge. If the charge of two atoms has the same sign then there is a repulsive force between them, opposite charges cause an attractive force. Ue(r) = e2 4π 0 a,b qaqb rab (4) In Equation 4 for the electrostatic potential e is the proton charge, qa and qb are the charges of interacting atoms and rab is the distance between them. LAMMPS as any other MD soft- ware utilizes these force potentials U(r) to simulate the movement of elements using numerical integration method which is schematically explained in Figure 3. The force on each element is 12
- 14. calculated from thegradient of the potential, if electric field is applied, then additional force is added on all particles according to Equation 5 F = qE, (5) where q is the charge of atom. Lorentz-Berthelot mixing rules are used to determine σ and for interaction of two different atoms, for example Na and Cl. Acceleration found from the force and the selected time step t provide new velocities and new positions for elements. In LAMMPS there is a selection of pair styles available, for example if pair style lj/cut/coul/cut is selected then interactions between atoms will follow Equations 3 and 4 as discussed, however for different applications slight deviations to these equations need to be applied and this can be done by selecting different pair styles. TIP4P/2005 [25] pair style lj/cut/tip4p/long was used to model interactions with water molecules and lj/cut/coul/long pair style was used to model interactions with Na+ and Cl−.lj/cut/coul/long is slightly different from lj/cut/coul/cut, it applies an additional damping factor to the Coulombic term to be able to compute long range Coulombic interactions. Part of ESI process starting from the drop radius of approximately 15.5 Åwas modeled using MD simulations. Simulations were split into two stages: equilibration stage at which all atoms reach specified temperature and form a drop and applied electric field stage where a drop starts to move. Limitations As can be seen from Figure 3 time increment is one of the input parameters. Simulations with very high electric field were found to be extremely sensitive to this parameter and required very low time increment. Simulations with low electric field ran smoothly with ∆t = 3 fs. For readers who want to replicate the simulations it is advised to run them with selected timestep for around 100000 timesteps to make sure they do not crash. Simulation time also depends on the neighbor value (distance above which Coulombic interactions are neglected), number of atoms in the simulations, domain size and processing power. The best performance was found when simulations were running on nodes with 24 CPU cores. Slow down of simulations were noticed when simulations were running on two parallel nodes with 16 CPU cores per node. Another limitation is the chemicals MD software are able to model. As mentioned in the Lit- erature Review, not only water can be a solvent in electrospray, but also methanol, acetonitrile, formamide or other chemicals some of which may have more complicated molecular structures than water. LAMMPS does not have an in-built pair style for methanol or acetonirtrile to date. There have been molecular dynamic simulations done on methanol-water mixture by Koner- mann et al. [17], however the authors used an in-house C++ code to model it. Another research has created an ab initio model for methanol and acetonitrile [26] but this model has not been implemented or tested using any MD software yet. Water was selected as a solvent material as it is widely tested by other LAMMPS users. Number of experiments and studies on ESI with water is significantly larger than on formamide, which can also be modeled using LAMMPS. If any other salts however have similar structure to NaCl, then they can be modeled as well by simply changing the properties of atoms in the LAMMPS script. 13
- 15. 4 MD Simulationsof Electrospray In total 45 simulations were run on a 500-water-molecule-drop which vary with charge, electric field, initial temperature and salt concentration. Three values of charge were used, the maximum value Q = 7 corresponds to 100% Rayleigh limit according to Table 2, the limit above which the droplet is expected to fission, the second charge Q = 4 was chosen as a middle between the Rayleigh limit charge and neutral charge (Q = 0) and the last charge Q = 2 was selected to see what happens when the drop is almost neutral but still has some charge. Charge was changed by changing the number of chloride ions in the drop while keeping the sodium ions fixed. In future studies more charge values could be investigated; as it can be seen from experiments that there is a wide range of initial drop charges which can exist in an electrosprayed drop. Two extremes of electric field were investigated. The low value of an electric field E = 3×10−5 V/Å is representative of a drop separated from the cone-jet and flying between the jet and the counter electrode. The value can easily be calculated using Equation 6. E = ∆V L , (6) where ∆V is the applied voltage and L is the distance between the capillary and the counter electrode equal to approximately 1cm (Figure 1a). According to Luedtke et al. [27] ion evaporation phenomenon can occur at the surface of a flowing electrified jet in a Taylor cone region, where electric field is much higher. Magnitudes up to 0.2V /Å have been previously tested on formamide solutions with NaI [27] and magnitudes of 0.05 V/Å on water solutions with NaCl, KCl and CsCl [28]. This study will test three magnitudes 0.05 V/Å, 0.14 V/Å and 0.3 V/Å. The last value was chosen to see how the droplet behaviour changes if electric field is increased further than 0.2 V/Å. It is important to recognise the difference between the applied electric field and surface electric field. For the benefit of explanation let us split the applied electric field into two types: artificial and real. The real applied electric field is the field induced by the applied voltage on the capillary. It always stays the same and can be calculated using equation 6. This field acts on all flying drops. The surface electric field appears due to the charge in the drop or substance. In the region of the nanojet (Figure 1c) the surface electric field is much higher and is dominant in the direction of the real electric field. This high surface electric field on a drop can be reproduced by applying the high external electric field on a drop i.e. the artificial applied electric field. It was found in some experiments that ion evaporation happens in the range 0.07 V/Å − 0.19 V/Å for surface electric field [22] and 0.146V/Å and 0.266V/Å according to different experiments [29]. This was another reason for choosing the specified electric field values as one of them is within the range and other two are outside the range given. Number of water molecules in the system was chosen to be 500, this value has not been tested before and at the same time it allows to run simulations faster (compared to 1000 and 2000 molecules which are typically used in similar studies). Salt concentration is a very interesting parameter, there was a lack of attention to it in any of previous MD simulations for the same topic. It is unclear both from previous studies and from experiments, what is the correct salt concentration to use. There is no consistency in previous studies in salt concentration of the drops. Some previous MD studies use values such as 10 pairs of Na+ and Cl− ions per 4000 water molecules [10], 13 or 17 pairs per 2420 water molecules [15], 60 pairs per 1000 water molecules [11], 0 pairs and only charge per 10, 15 and 20 water molecules [19]. Another experimental study has been made which shows that almost any salt concentration starting from 0 pairs and ending with 56 pairs per drop can be present in final drops which get into the mass spectrometer, but not all charges. Charges of 4 and above 14
- 16. are not verycommon according to the mentioned experimental study [30]; however it is not clear if the distance of Mass Spectrometer from the capillary can have an effect on those results. It was decided to first test two extremes of salt concentration because it was initially unclear what effect it will have on drop behaviour and then nine more cases were run with medium salt concentration (Table 1). It was noted that salt concentration has a significant effect on drop behaviour. Temperature values of 300K and 320K are commonly used in previous studies. Higher values are used too and could be used in future studies but they would affect the starting condition of the droplet. It was aimed to have similar starting conditions for all simulations, i.e. no ion or water evaporation present in the domain but higher temperatures would lead to ion evaporation even at the equilibration stage where no electric field is applied. Therefore two temperatures with 20K difference were selected which are 300K and 320K. However for the case of 15 sodium atoms and Q = 7 the evaporation effect could still not be eliminated. Table 1: Timestep used (top value) and length (bottom value) of each simulation. Water Molecules 500 Temperature 300K 320K Electric Field 0.05 V/Å 0.14 V/Å 0.3 V/Å 0.00003 V/Å 0.05 V/Å 0.14 V/Å 0.3 V/Å NumberofNa+andCl−ionsinadrop 65Na+ 58Cl− 0.3fs 1230ps 0.1fs 1000ps 0.05fs 400 - 0.3fs 960ps 0.1fs 1000ps - 65Na+ 61Cl− 0.3fs 1260ps 0.1fs 1000ps 0.05fs 400 - 0.3fs 540ps 0.1fs 1000ps - 65Na+ 63Cl− 0.3fs 960ps 0.1fs 1000ps 0.05fs 400 - 0.3fs 600ps 0.1fs 1000ps - 40Na+ 33Cl− - 0.1fs 284ps 0.05fs 92ps - - - 0.05fs 78.2ps 40Na+ 36Cl− - 0.1fs 295ps 0.05fs 90ps - - - 0.05fs 85.2ps 40Na+ 38Cl− - 0.1fs 300ps 0.05fs 96ps - - - 0.05fs 77.8ps 15Na+ 8Cl− 0.3fs 329ps 0.1fs 126ps 0.05fs 50ps 3.0fs 3600ps 0.3fs 363ps 0.1fs 100ps 0.05fs 50ps 15Na+ 11Cl− 0.3fs 864ps 0.1fs 141ps 0.05fs 50ps 3.0fs 3600ps 0.3fs 1463ps 0.1fs 142ps 0.05fs 50ps 15Na+ 13Cl− 0.3fs 630ps 0.1fs 203ps 0.05fs 50ps 3.0fs 3600ps 0.3fs 1430ps 0.1fs 141ps 0.05fs 50ps Two scripts would be used to create a drop. The first one randomly fills a sphere of radius R with point masses and applies type number to them, e.g. 1 is Oxygen, 2 is Hydrogen, etc. In case of water molecule atoms it puts them at an angle and distance to each other required for the TIP4P water model, rigid water model (bonds do not displace) with shifted mass which is available in LAMMPS (Figure 4). It is one of the most commonly used liquid water models and statistically provides very accurate results. 15
- 17. Figure 4: TIP4PRigid Water Model Radius of each drop was calculated as following: R = m 4 3πρ 1/3 (7) Where ρ is the density of water, and m is its mass calculated using equation m = nM N , (8) where n is the number of water molecules, M is the molar mass of water and N is Avogadro number equal to approximately 6.022 × 1023. Radius would then be increased by 2.5% to avoid squeezed or overlapping atoms. A maximum charge on it was then calculated according to the Rayleigh limit (Equation 1). Surface tension is present in Equation 1 and its values are listed in a table for different droplet setups according to experiments and previous MD studies on surface tension, it will later be shown that it plays an important role in fission and ion evaporation of drops. MD seems to underrate the surface tension γ [31] and this is supported in this study as well. It will be seen later that ion evaporation of the drop seems to match with theory better when surface tension values obtained from MD simulations are used. At the lowest salt concentration Q=7.0 taking γ values from MD simulation results and Q=7.5 taking γ from experiments [31]. Values for γ which were not found in sources were linearly extrapolated.. Density of the solution changes with salt concentration as well but the change is negligible. 16
- 18. Table 2: Propertiesof each solution. Note that the solubility of salt in water is 36% under atmospheric temperature and pressure. Water Molecules 500 Temperature 300K 320K SolutionCon- centration SurfaceTension(Ex- periment)(mN/m) SurfaceTension (MD)(mN/m) RayleighCharge Limit(Experiment) RayleighCharge Limit(MD) SurfaceTension(Ex- periment)(mN/m) SurfaceTension (MD)(mN/m) RayleighCharge Limit(Experiment) RayleighCharge Limit(MD) NumberofNa+and Cl−ionsinadrop 65Na+ 58Cl− 39.4% 87.5 78.9 8.2 7.8 77.0 69.4 7.7 7.3 65Na+ 61Cl− 40.6% 88.0 79.4 8.3 7.9 77.4 69.9 7.8 7.4 65Na+ 63Cl− 41.4% 88.3 79.7 8.3 7.9 77.7 70.1 7.8 7.4 40Na+ 33Cl− 23.2% 81.0 72.7 7.9 7.5 71.3 64.0 7.4 7.1 40Na+ 36Cl− 24.4% 81.5 73.2 7.9 7.5 71.7 64.4 7.5 7.1 40Na+ 38Cl− 25.2% 81.8 73.5 8.0 7.6 72.0 64.7 7.5 7.1 15Na+ 8Cl− 7.0% 74.5 66.6 7.6 7.2 65.6 58.6 7.1 6.8 15Na+ 11Cl− 8.2% 75.0 67.0 7.6 7.2 66.0 59.0 7.2 6.8 15Na+ 13Cl− 9.0% 75.3 67.3 7.7 7.2 66.2 59.2 7.2 6.8 Another C++ script applies properties to these dots and creates a readable input file for LAMMPS. The script follows the procedure below: • Apply the periodic boundary conditions (PBC), in all cases it is 250Å × 150Å × 150Å. PBC are used to save computational time and this way it is not a complete vacuum but the model will assume that there is an infinite number of same drops in all three directions. When any particle moves outside the domain on one side it will be copied and appear on the other side. • Position the created drop inside the domain. Droplet was positioned centrally in all cases. • Define a mass of each atom type. • Create a list of atoms. Apply a unique ID to each atom and to each water molecule, apply charge values and XYZ coordinates to each atom. • Create a list of bonds. Define which connections are rigid and the type of the bond. Tip4p requires rigid connection between oxygen and hydrogen atom in a molecule. • Create a list of angles. Apply the tip4p angle type to each molecule of water, define where the angle is located. • Create a file readable by LAMMPS which contains all previously listed information. Then at the equilibration stage temperature is applied to all drops. The following describes step by step what the script does, but if a reader wants to replicate the problem it is advisory to visit Appendix A where an example of the script is provided. 17
- 19. Step 1 Definethe set of units as real. Select the atom style as full in order to encom- pass necessary attributes: bonds, angles, charge. Step 2 Define the distance at which Coulomb interactions are negligible. Step 3 Read the data file with atom coordinates created previously. Step 4 Group atoms according to their type and name the groups. Step 5 Create two pair styles, one for water-water interaction, another for all other interactions. Define the accuracy of Coulombic interactions as 1 × 10−6. Shift LJ potential at a specified cutoff distance to 0.0. Step 6 Apply a suitable pair style between each pair of atoms depending on their type. Apply the well depth and the characteristic diameter to each pair. Step 7 Define the O-H bond distance as 0.9572A and an H-O-H angle as 104.52. Define the stiffness of the bond and the angle as very high, making it a rigid model. Step 8 Move atoms and molecules so that the distance between them does not cause unrealistic behaviour, very high velocities for example. Step 9 Apply a fix, all fixes are commands which last until the end of the simulation or until they are unfixed. This fix resets bonds and angles to their equilibrium lengths and angular values with a tolerance of 0.0001. Step 10 Set the timestep value (Table 1). Step 11 LAMMPS creates a log file while running a simulation to keep track of the simulation without having to upload a trajectory file. These lines define what information and how often it is uploaded to the log file. Step 12 Apply constant temperature to the entire system. By the end of equilibration energy of all atoms must equilibrate so that the temperature of the system is either 300K or 320K. Step 13 Create trajectory files which are files which store information every set number of timesteps for all atom types. For equilibration storing only atom coordi- nates was required. Equilibration of the droplet was run for 100000 timesteps with 2.0fs timestep for most of the files with some exception to low salt con- centration cases.These files can later be read in OVITO, where animations can be produced or in a newly developed MATLAB scripts created for analysis. Then the final trajectory data was converted into a new LAMMPS input file. Similar script to equilibration (Appendix B) was created to apply an electric field on the equilibrated drop. All steps were kept the same apart from Step 12, which was replaced by the following: Step 12 Input file does not store velocities and therefore the temperatures either, apply velocity to all atoms so that the temperature of the system is 300K or 320K. Step 13 Apply a fix which would keep the energy of the system constant throughout the simulation. Step 14 Apply a fix which would apply a constant electric field in X direction. 18
- 20. Step 15 Computekinetic and potential energies of all atoms. Step 16 Create trajectory files which store information about positions, velocities and energies of atoms. Create a restart file every 100000 timesteps in case the simulation stops. This allows to run the simulation from the last saved restart file. A detailed script can be found in Appendix B. 5 CRM and IEM theory CRM states that solvent (water) evaporates from the drop and reaches the Rayleigh limit at which it explodes and simultaneously produces several charged drops. It also states that if Rayleigh limit cannot be reached solvent will evaporate from the drop and leave only the analyte residue (salt). Such CRM with full evaporation was observed by several MD studies on drops of around 1000 molecules. It was mainly observed in drops containing large protein molecules which do not break up [32, 33]. Another MD study has been done showing that drops containing salt experience such CRM but the simulations were conducted at much higher temperatures than what is used used in this study and under different boundary conditions as well i.e. particles would disappear when they reach boundaries (while this study uses periodic boundaries) and no external electric field was applied to the drop either [15]. It was not expected to see any drop fission due to the size of the drop used, however full evaporation of solvent was expected. Gamero-Castano et al. [12] stated that Coulomb explosions could only produce drops of macroscopic size and can be suppressed in the case of sufficiently small initial drops. They also stated that very small scale drops can remain below the Rayleigh limit by getting rid of small singly charged clusters i.e. experience ion evaporation. Iribarne and Thomson [14] were the first who tried to describe IEM analytically. They stated that an ion cluster must overcome an energy barrier in order to leave a charged drop. They built the expression for energy barrier which would consist of two terms: energy of solvation and electrostatic energy. Energy of solvation is the energy required to dissolve an ion cluster of radius Ri in a drop of radius R. Energy of solvation can thus be split into two terms, the first term is due to overcoming the surface tension and the second is the energy required to charge an ion in a dielectric continuum ∆GBorn also known as Born’s equation. Fernandez de la Mora et al [20–22] then improved this derivation and added a curvature correction term. Their studies give step by step derivation of the activation energy ∆. Activation energy ∆ is the difference in energy of the entire system between after and before an ion cluster separates from the main drop and this is what Iribarne and Thomson meant by the energy barrier as well. They started from assuming that the drop is infinitely large and its charge is 0. In this case Born’s equation summed with a surface energy term can be used to calculate the energy required to bring an ion from the solution into a vacuum. That energy sum depends on the radius of the escaping ion drop Ri and assuming that evaporating drop follows the path of least resistance, ion evaporation happens at the minimum value of ∆GBorn. They then found an expression for the radius of an escaping drop Ri based on ∆GBorn: R3 i = e2(1 − −1) 64π2γ 0 , (9) where e is an ion charge, is the dielectric constant of the solution, 0 is the electrical permittivity in vacuum equal to 8.85 × 10−12F/m and γ is the surface tension of the solution. As Fernandez de la Mora et al [21] pointed in their study, quite interestingly this expression is very similar 19
- 21. to the expressionfor the radius of the drop at the Rayleigh limit which can be derived from Equation 1. They further expanded the expression for activation energy ∆ to account for drop’s charge and curvature, full expression for which contained five terms: ∆ = U + Ui + W∗ − U0 + ∆Us (10) where U is the energy of the drop (after separation of ion), Ui is the energy of the separated ion cluster, W∗ is the interaction energy between the main drop and the separated ion drop, U0 is the energy of the full drop before ion is separated and ∆Us is the surface energy created by detaching two spherical drops. Full expressions for these can be found in Equations 11-13, 15, 16. U = z2e2 8π 0R (11) Ui = e2 8π 0Ri (12) U0 = (z + 1)2 8π 0[R3 + R3 i ]1/3 , (13) where z is the number of charges remaining in the drop after ion evaporates. Expression z + 1 can be met quite often in these derivations because Fernandez de la Mora et al [20–22] assumed that the separating ion cluster contains only one ion. Interaction energy W depends on the distance between the primary and the secondary drop and can be expressed using Equation 14, it reaches its maximum value W∗ at a distance x∗ (Equation 15). W(x) = e2 4π 0R z x − 1 2x2(x2 − 1) (14) W∗ = e2 4π 0R [z − F(z)] (15) In Equation 15, F(z) is the field ionization function defined as F(z) = z1/2 −7/8+O(z−1/2). It was derived by Gamero-Castano and Fernandez de la Mora [12] to account for the effect of curvature on a drop and the remaining charge z on the drop. The final term ∆Us can be calculated as following: ∆Us = 4πγ R2 i − 2R3 i 3R (16) Full expression then becomes ∆ = e2 8π 0Ri + 4πγR2 i − e2(2F(z) + 1) 8π 0R + 4πγ 2R3 i 3R (17) For water drops at room temperature ion evaporation would start at ∆ around 0.4eV [21]. Radius of the drop which leads to the smallest loss in energy is then 20
- 22. R3 i = e2 64π2γ 0 (18) Wecan see that the only variable contained in the expression for Ri which changes is the surface tension. Thus from this equation for Ri it is expected to see that radius of an ion cluster does not change with temperature, charge or electric field. There are some shortcomings which make it hard to apply the presented analytical model on the results of MD simulations: • The applied electric field on a drop was not taken into account in any derivations how- ever it will be seen later that the difference in electric field can cause a difference in ion evaporation. • An assumption has been made that the evaporated drop contains only one ion however it will later be seen in the Results chapter that some escaping drops can contain two or three ions or even five. It is not certain if Ri can be multiplied by two or three in these cases. • Collision with other drops is not taken into account, neither is the presence of vapor or gas in the system. All derivations were made assuming full vacuum. Periodic boundary conditions which were used in MD simulations mean that the system is not full vacuum, in some simulations as the drop would evaporate and brake up some vapour would occur around the drop. • An assumption has been made that the radius of the evaporated ion cluster is much smaller than the radius of the initial drop, however for the case of strong electric fields we will see that some evaporating ions might not satisfy this assumption as they are quite large relative to the primary drop. • Curvature correction function F(z) is only valid if z is large, z >> 1. It is not certain what is the minimum value of z at which Equations 15-17 can still be used. • There has been some evidence that this analytical model works well for stationary drops to which no electric field has been applied but no such evidence with an electric field applied. Despite the shortcomings and despite the fact that this analytical model for IEM was devel- oped years ago, it is the best model which exists up to date and which can describe and predict ion evaporation to some extent. Another important parameter which was not mentioned before is the rate of evaporation dz dt which according to Iribarne and Thomson [14] can be calculated using the following equation: dz dt = − kT h (z + 1) exp − ∆ kT , (19) where k is Boltzmann’s constant, T is the absolute temperature and h is Planck’s constant. Again, there is no term describing the applied electric field on a drop. It can also be noticed that ion evaporation rate depends on temperature while the expression for radius of an escaping ion cluster and activation energy do not contain a temperature variable. Loscertales et al. [22] have concluded in their studies that the rate of ion evaporation is related to the rate of solvent evaporation from the drop. Thus at lower temperatures and higher salt concentrations ion evaporation rate is expected to be slower. 21
- 23. Figure 5: Visualisingevaporation in MATLAB. Purple circles - vapour, blue - liquid, Na+ and Cl− are marked as "+" and "-" respectively. 6 Simulation Analysis Open source visualisation software OVITO was used for visualizing results and creating animations. Several state of the art MATLAB scripts were created for analysing simulations. Each simulation in LAMMPS produces a trajectory file containing the history of drop’s positions, velocities, potential and kinetic energies which were recorded every 200 fs or so. More attributes could be exported from LAMMPS if required however the listed ones are the only ones which will be used for analysis. MATLAB scripts can read information about each timestep from the trajectory file and analyse temperatures, distinguish between vapour and liquid (Figure 5), keep track of the ratio between the two, track potential energy, track escaping ions and their potential energy, make plots and animations. Some MATLAB codes can also identify both vapour and liquid drops and apply group IDs to them and recognise periodic boundary conditions. The strength of MATLAB is its ability to manipulate efficiently with matrices, therefore loops were avoided where possible and mainly matrix operations were carried out to make the code faster and more efficient. One of the scripts was created to analyse the vapour formation during simulation. According to Zhang et al [31] water is in vapour state when there are less than 10 water molecules sur- rounding it in a radius of 6.3Å. To make the script faster and easier to process hydrogen atoms were removed from the trajectory matrix by MATLAB script. This does not affect the results of analysis. The script would check distances between every pair of atoms in the domain and select all atoms, which are within the distance of 6.3Åto each other. Once the loop is over MATLAB sums all these atoms and checks if their number is more or equal to 10 and labels each atom ID as liquid if it satisfied the condition and as vapour otherwise by assigning a number 1 or 0 respectively. Similarly to liquid identification MATLAB script can identify particle groups using the same limit distance of 6.3Å. MATLAB can identify both vapour and liquid groups and can also recognise periodic boundary conditions by copying the domain and coordinates of particles on three perpendicular sides of the domain as shown in Figure 6. Because the system studied is very dynamic and drops explode at a fast rate and into a large number of smaller drops, it is quite hard if not impossible to keep group IDs the same from 22
- 24. Figure 6: MATLABscript can recognise boundary conditions with the help of copying the domain and its contents on three sides of the original domain X,Y and Z timestep to timestep. This makes it challenging to recognize escaping ion drops. Escaping ion drops can be tracked when a drop has a relatively large diameter, but when there are a lot of small droplets of almost equal size then MATLAB is quite ineffective at tracking escaping ions or exploding droplets because there is no identifier like size for example to track the droplets, therefore for the case of small droplets any explosions should be tracked by manually manipulat- ing the MATLAB code or by observing the results in OVITO. Another script selects the largest drop in the domain and tracks it until it breaks up. It then runs the script again from the point of interest and shows the location of atoms which later escape the drop as shown in Figure 22. Temperature was calculated per drop using a formula for the average molecular kinetic en- ergy (see Equation 20), also this equation accounts only for translational motion of the particles, yet this is another reason for removing hydrogen atoms from analysis (rotational velocities are not taken into account). 1 2 mv2 = 3 2 kT (20) In Equation 20 m is the mass of the body, v is its velocity, k is the Boltzmann constant and T is the temperature of the body. The expression for temperature of a drop can then be derived as: T = ma v2 nk (21) Where ma is the average mass of a particle in a drop, v2/n is the average squared velocity magnitude (where n is the number of atoms) and k is the Boltzmann constant. It is not certain what is the minimum number of molecules to which Equation 21 can still be applied. In this study for simplicity there is no limit, but in reality this equation cannot be used for very small molecular clusters containing about 30 atoms. Code check was done on Final trajectory files to see if temperature calculation part of the script was done correctly, after successful testing it was applied to all other simulations. The script was used to check the temperatures of drops in the simulation and check under what conditions freezing or overheating of the drop occur. It was used to check if temperatures in the beginning of each simulation were correct i.e. equal to 300K or 320K. 23
- 25. As was shownin CRM and IEM Theory chapter, energies play an important role in the electrospray problem, the developed analytical model contains energy parameter ∆. MATLAB scripts in Two MATLAB scripts are capable of plotting changes in energy with time. Created MATLAB scripts can not only be used for analysing this particular problem, users can utilise these for any other problems which involve water and two other types of atoms i.e. it is not only limited to Na+ and Cl−. Some additional changes to each script may be required for analysing more chemicals or a different solvent, but as long as trajectory files are written in the same style it should not be too complicated. Scripts are easy to use and reading of the files does not have to start from the very first timestep, but can be started and finished at any timestep of interest, timesteps can also be skipped by a specified number if required. 7 Results and Discussion Only 15 simulations out of all listed in Table 1 showed any results or changes during simu- lations, these were mainly low salt concentration cases. Some highly salt concentrated droplets did not evaporate at all and did not show much change with varying electric field, charge or temperature. Either longer simulations or increase in temperature is required for these cases. If number of salt molecules is desired to be kept untouched, number of water molecules could be increased to decrease salt concentration. Another option is to add more drops into the do- main or simulate gas flow as well, as collisions may trigger fission and evaporation of highly salt concentrated drops. Effect of Charge During equilibration of the drop significant differences between final drop shapes were found due to charge. These differences can be visualized in Figures 11-12. For the cases of drops with largest amount of salt in them (Figure 13) the shapes of drops changed only slightly and almost no difference was observed with varying Q. For the cases with low salt concentration (Figure 11) increase in charge caused ion evaporation even in the absence of electric field and even for cases below Rayleigh limit according to Table 2. Due to this effect these simulations are labeled as 14Na+ instead of 15Na+. 24
- 26. Figure 7: Caption Figure8: Caption 25
- 27. The results forthe time at which the first ion cluster separated from the drop are presented in Figure 7. When results are put on a logarithmic scale a descending trend on a graph can be noticed; separation time is proportional to positive charge value. This was an expected result as the higher is the charge on a drop the closer it is to the Rayleigh limit. No significant effect of charge on the number of molecules in the first ion cluster was observed (Figure 8), except for two cases with Q = 2 and one case with Q = 4. In these cases the escaped ion cluster had more or equal to 100 water molecules, which is 20% of the entire drop. Because these cases are close to neutral charge it was expected to see such behaviour. Absolutely neutral drops elongate under the applied electric field because it pushes negative and positive ions in opposite directions thus causing a water drop to brake into several drops approximately equal in size. Simulations show that this effect may occur for low positive charges Q < 4 as well (Figures 9-10). Figure 9: Drop with characteristics:15Na+ 13Cl− Ts = 300K E = 0.3V/Å, starts elongating. Figure 10: Drop with characteristics:15Na+ 13Cl− Ts = 300K E = 0.3V/Å, starts braking up. 26
- 28. (a) 15Na+ 8Cl− 300K (b)15Na+ 8Cl− 320K (c) 15Na+ 11Cl− 300K (d) 15Na+ 11Cl− 320K (e) 15Na+ 13Cl− 300K (f) 15Na+ 13Cl− 320K Figure 11: How equilibration varies with charge and temperature for cases with 15Na+ 27
- 29. (a) 40Na+ 33Cl− 300K (b)40Na+ 33Cl− 320K (c) 40Na+ 36Cl− 300K (d) 40Na+ 36Cl− 320K (e) 40Na+ 38Cl− 300K (f) 40Na+ 38Cl− 320K Figure 12: How equilibration varies with charge and temperature for cases with 40Na+ 28
- 30. (a) 65Na+ 58Cl− 300K (b)65Na+ 58Cl− 320K (c) 65Na+ 61Cl− 300K (d) 65Na+ 61Cl− 320K (e) 65Na+ 63Cl− 300K (f) 65Na+ 63Cl− 320K Figure 13: How equilibration varies with charge and temperature for cases with 65Na+ Effect of Salt Concentration Increase in salt concentration lowered the chances of evaporation of both water and ions from the drop. Maximum length of simulations with 65Na+ was 1ns, so it is possible that some water evaporates from the drop later but it is clear that the rate of evaporation is very low. Even evaporation of solvent from the drop did not occur in high salt concentration cases. This means that in those cases surface tension is high enough to not let even the highest electric field pull an ion cluster from the drop. Not all cases with 40Na+ experienced ion evaporation either, only cases with E = 0.3 V/Å and one case with E = 0.14 V/Å and Q = 7. The lack of any ion cluster separation from high salt concentration cases makes it difficult to analyse the trend between ion evaporation rate and salt concentration. However it is clear that the higher the salt concentration the slower is evaporation and this was expected because the higher the surface tension the higher is the activation energy required to extract an ion cluster. 29
- 31. Salt concentration wasfound to have a significant effect on the size of the escaping ion cluster. Ion clusters produced with weaker surface tension were found to generally have much bigger size (Figure 15). Figure 14: How first ion cluster separation time varies with MD surface tension (according to Table 2) Figure 15: How separated ion cluster size varies with MD surface tension (according to Table 2) 30
- 32. Figure 16: Rapidfreezing occurs right after the start of the simulation. An example shown is 15Na+ 8Cl− 300K E = 0.3 V/Å, was plotted using MATLAB.Na+ are marked with "+", Cl− with "-" Effect of Temperature Surprisingly temperature did not have the expected effect on the behaviour of droplets. It can be seen from Table 3 that full evaporation and first ion evaporation time can be slower or faster for higher temperature, there is no trend. This is assumed to be a wrong result as temperature increase should cause faster evaporation. Rapid freezing of the drop was also observed during the first few iterations in each simulation (Figure 16). The reason for this is an error in LAMMPS script. The minimize command used in LAMMPS decreased the energy of the system and thus the temperature. For more accurate results simulations with applied electric field should be rerun without the minimize command. Table 3: Time when the entire drop is fully evaporated. Water Molecules 500 Temperature 300K 320K Electric Field 0.05V/Å 0.14V/Å 0.3V/Å 0.05V/Å 0.14V/Å 0.3V/Å NumberofNa+and Cl-ionsinadrop 40Na+ 33Cl− - - - - - 22.8 ps 40Na+ 36Cl− - - 8.8 ps - - 46.4 ps 40Na+ 38Cl− - - - - - 18.2 ps 15Na+ 8Cl− 40 ps - 28.0 ps 253.0 ps 100.0 ps 23.0 ps 15Na+ 11Cl− - - 30.0 ps 1330.0 ps - 22.3 ps 15Na+ 13Cl− - - 37.4 ps - - 30 ps It was noticed however that collisions cause rapid increase in temperature and lead to full evaporation (Figure 17). 31
- 33. (a) Just beforethe collision. (b) At the time of collision. Figure 17: Collision of an ion cluster with a drop in case: 15Na+ 8Cl− 300K E = 0.3 V/Å Effect of Electric Field in Nanojet region High electric field was found to overcome attractive forces between molecules and atoms and pull out big ion clusters out of the drop. It is concluded that high electric field cases cannot be explained by the usual theory on ion evaporation as evaporating ion clusters are much bigger than clusters which would be expected to appear due to IEM and some results were characterisctic of CRM despite the fact that these simulations were below the Rayleigh limit and its size was too small to expect a CRM. Compared to low electric field cases there were also strong collisions present which in most cases resulted in complete evaporation of the entire drop. Therefore, in nanojet regions as long as salt concentration is below approximately 25%, complete evaporation of the entire drop is expected due to strong collisions. 32
- 34. There is alack of results for high salt concentration cases, therefore it cannot be established with certainty that there is a logarithmic relationship between first ion cluster evaporation time and electric field however it can be noticed by observing the graph that such relationship is highly probable (Figure 18). It can be seen that within the simulated time only drops with low salt concentration were able to extract an ion cluster at medium and low electric fields of 0.14V/Å and 0.05V/Å respectively. Some cases with medium salt concetration were however observed and analysed in OVITO and it is likely that these cases may experience ion evaporation within about a nanosecond. Very high salt concentration cases (with 65Na+) are not expected to experience ion evaporation within that time, it is therefore advised for such cases to increase the simulation temperature to be able to find out if logarithmic trend is valid for these cases too. No dependency of the number of water molecules in an escaped ion cluster on the applied Figure 18: How first ion cluster separation time varies electric field. electric field was observed. Figure 19 shows that any number between 10 and 130 is possible and it does not depend on the applied electric field. Effect of Low Electric Field For cases with 15Na+ ions no ion evaporation was observed (except for equilibration cases discussed earlier). Electric field was found to not be strong enough to pull out ion clusters from drops. This is why higher salt concentration cases were not run with low electric fields. An additional simulation with 8Na+ ions and 1Cl− ion was run for 4ns to see if lower salt concentration can speed up the process. For that additional case temperature error mentioned earlier was also fixed, however still no ion evaporation was observed. Water would also not tend to evaporate from that drop. This means that to simulate a 500-water-molecule drop, either very long simulations or increase in temperature are needed. It was also noticed in two cases with Q = 7 that low electric field cannot overcome repulsive forces between a drop and an ion cluster and thus collisions do not occur like they do in high electric field cases. 33
- 35. Figure 19: Howseparated ion cluster size varies with electric field. Figure 20: Additional case with 8Na+ and 1Cl−, Ts = 300K, E = 3 × 10−5V/Å Escaping Ion Cluster Tracking MATLAB script was found to not be very efficient at tracking escaping ions but it can be improved. Figure 22 however shows some cases where MATLAB was successfully used for tracking an ion cluster. Water molecules which escaped the drop seem to surround sodium atoms from the very beginning of simulations. There is however no trend observed in the initial shape of ion cluster while it is inside the drop, however if MATLAB script is improved it can be used in future studies and more analysis on ion cluster shape could be done. Table 4 compares the theoretical radius of an escaped cluster to the actual radius obtained via simulations. It can be seen that the differences are significant, especially for low temperature cases. 34
- 36. Figure 21: Ioncluster and droplet repel each other. Electric field cannot overcome the repelling force. Table 4: Comparison of radius calculated using Equation 18 and values from Table 2 with an effective radius calculated from the number of water molecules in an escaped ion cluster. Simulation Characteristics Number Of Ions Number Of Water Molecules Ratio Effective Radius (Å) R (Equation 18) (Å) 14Na+ 8Cl− Ts = 320K E = 0.05 V/Å 3 91 30 8.7 4.1 15Na+ 11Cl− Ts = 320K E = 0.05 V/Å 2 20 10 5.2 4.1 14Na+ 8Cl− Ts = 320K E = 0.14 V/Å 3 73 24 8.1 4.1 15Na+ 11Cl− Ts = 320K E = 0.14 V/Å 5 125 25 9.6 4.1 14Na+ 8Cl− Ts = 320K E = 0.14 V/Å 3 50 17 7.1 4.1 15Na+ 11Cl− Ts = 320K E = 0.3 V/Å 3 58 19 7.5 4.1 15Na+ 13Cl− Ts = 320K E = 0.3 V/Å 6 125 21 9.6 4.1 40Na+ 33Cl− Ts = 320K E = 0.3 V/Å 2 18 9 5.0 0.4 40Na+ 36Cl− Ts = 320K E = 0.3 V/Å 1 7 7 3.7 0.4 40Na+ 38Cl− Ts = 320K E = 0.3 V/Å 3 23 8 5.5 0.4 14Na+ 8Cl− Ts = 300K E = 0.05 V/Å 1 15 15 4.8 0.4 14Na+ 8Cl− Ts = 300K E = 0.3 V/Å 2 50 25 7.1 0.4 15Na+ 11Cl− Ts = 300K E = 0.3 V/Å 2 23 12 5.5 0.4 15Na+ 13Cl− Ts = 300K E = 0.3 V/Å 3 100 33 8.9 0.4 40Na+ 33Cl− Ts = 300K E = 0.3 V/Å 3 30 10 6.0 0.4 35
- 37. IEM or CRMDiscussion Overall, the cases which showed any results experienced ion evaporation, however the escap- ing ion clusters contained more than one ion which is not commonly described by IEM as IEM assumes singular ions in the escaping drop. Potential energy difference between before and after ion evaporation was several orders of magnitude higher than what was expected with theory (Figure 23). It should be recalled however that theory neglected electric field and does not in- clude it into derivations which may be valid for low electric field cases with E = 3×10−5V/Å but not for cases with several orders of magnitude higher electric fields. Process similar to CRM was however observed in three cases shown in Figure 24. Sodium and chloride ions stayed together after the first ion evaporation for a long part of the simulation while solvent evaporated from the drop almost completely. In other simulations collisions would cause Na+ and Cl− to separate and so this effect was not observed. 36
- 38. (a) 15Na+ 8C− Ts =320K E = 0.14V/Å (b) 40Na+ 33C− Ts = 300K E = 0.3V/Å (c) 40Na+ 36C− Ts = 300K E = 0.3V/Å Figure 22: Tracking escaped ion clusters (yellow) back in time using MATLAB. 37
- 39. (a) Before ionevaporation. (b) After ion evaporation Figure 23: Potential Energy plot for 15Na+ 8C− Ts = 300K E = 0.3V/Å case. 38
- 40. (a) 15Na+ 8C− Ts =300K E = 0.05V/Å (b) 15Na+ 11C− Ts = 320K E = 0.05V/Å (c) 40Na+ 36C− Ts = 320K E = 0.14V/Å Figure 24: Cases which show similar behaviour to CRM. 39
- 41. 8 Conclusion In thisstudy the effect of charge, salt concentration, temperature and electric field on the formation of pure ions and ions with salt residue were evaluated. This study focused on two regions: nanojet and the end of the ESI process just prior reaching the counter electrode. Key findings from the current study include (1) suspected logarithmic relationship between the time of first ion evaporation and electric field in high electric field cases (2) salt concentration plays an important role in studied processes, high salt concentrations can reduce ion evaporation rate as well as solvent evaporation significantly, (3) equations derived by Fernandez de la Mora et al. cannot be applied on high electric field cases, (4) increase in charge may cause ion evaporation even in the absence of electric field in low salt concentration cases and also speeds up explosion of the drop when electric field is applied, (5) high electric field causes strong collisions which lead to complete evaporation of drops unlike (6) low electric field cases, where repulsive forces between escaped ion and a drop overcome the electric field force and thus collisions are less likely (7) neither IEM nor CRM were observed for low electric field cases for 4 ns. Previously only few studies investigated the effect of electric field on a drop, usually only a stationary drop is simulated. This study showed that the applied electric field does matter for very high electric fields which are present in nanojets, but for low electric fields which drops experience when they leave the Taylor Cone more simulations need to be run to be able to say with certainty that it does not affect droplet’s behaviour. Previous studies also did not investigate the effect of salt concentration or initial charge on drops behaviour, but some findings are listed here which should help with continuation of research in this topic. It is highly recommended to vary the size of the drop and the size of the domain as well, these two parameters were set constant in this study and their effect is unknown. Other chemicals can be tested with an example of this study, however there are limitations to what materials it is possible to model using LAMMPS or any other MD software. For solvents more complex than water in-house codes would need to be written and coupled with MD software. 40
- 42. Appendix A EquilibrationScript Equilibration Script 41
- 43. Appendix B ElectricField Script Electric Field Script 42
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