1. Introduction
1.1 Principles of Mass Spectrometry
1.2 Terminology
1.3 Parts of Mass Spectrometer
1.4 Measures of Performance
1.5 Applications
2. Ion sources
2.1 Ionization
2.2 Electron ionization
2.3 Chemical ionization
2.4 SIMS and Fast atom/ion bombardment
2.5 Laser desorption ionization and MALDI
2.6 Electrospray
3. Mass analyzers
3.1 Quadrupolar Analyzers
3.2 Quadrupole Ion Trap
3.3 Time-of-flight Analyzers
3.4 Magnetic and Electromagnetic Analyzers
4. Detectors
Lecture on mass spectrometry
Lenka Zajíčková (Faculty of Science & CEITEC MU)
more details in the course F7360
Characterization of surfaces and thin films
spring semester 2018
1. Introduction
Literature
• E. de Hoffmann and V. Stroobant, Mass Spectrometry: Principles and Applications, Wiley 1999
• J. H. Gross, Mass Spectrometry, Springer 2011
1. Introduction
Mass spectrometry (MS) is analytical technique for the determination of the composition
of a sample or molecule and elucidation of the chemical structures of molecules, such as
peptides and other chemical compounds.
“Smallest scale” in the world, not because of the mass spectrometer size but because of
the size of what it weighs - molecules.
1.1 Principles
1. Introduction
What information can be determined?
 Molecular weight
 Molecular formula
 Structure (from fragmentation fingerprint)
 Isotopic incorporation / distribution
 Protein sequence (MS-MS)
1. Introduction
1.2 Terminology
consist of nucleons (protons + neutrons) and electrons
 Z - atomic number (number of protons), N – number of neutrons
 chemical properties determined by the number of electrons (atomic number)
 physical properties - mass number A (A = Z + N)
X
state of ioniz.
No. of atoms in molecule
A
Z
 atom with a determined number of neutrons
4He => 2 protons + 2 neutrons = mass number 4
3He => 2 protons + 1 neutron = mass number 3
 positively charged => electrons removed from the particle
He+, N2
+, CO2
+, 38Ar+ , 40Ar+, N2
++
 negatively charged => electrons attached to the particle
O-, OH-
Atoms
Isotopes
Ions
Generally in mass spectrometry, the ion charge q is
indicated in multiples (z) of the elementary charge e
(charge of 1 electron in absolute value
1 e = 1.602 177×10−19 C)
q = z e
and the mass m is indicated in atomic mass units
(1 u = 1.660 540×10−27 kg).
For simplicity, a new unit, the Thomson, with symbol
Th, has been proposed
1. Introduction
1.2 Terminology
Example of mass spectrum:
methanol CH3OH analyzed by
electron impact ionization:
The mass spectrum depends on m/z
1. Introduction
1.2 Terminology
 m - mass in atomic mass units (u) or daltons (Da),
1u = 1 Da = 1.660 540×10−27 kg
 u / Da used in different contexts:
 u – masses referring to the main isotope of each element as used in mass
spectrometry
 Da – mean isotopic masses as generally used in stoichiometric calculations
 The mass number A gives rough figure for the atomic mass because of
approx. equality of the proton and neutron masses (1.007277u and 1.008665u,
respectively) and the relative insignificance of the electron mass (5.48×10-4u).
X
state of ioniz.
No. of atoms in molecule
A
Z
Mass
 For stoichiometric calculations chemists use the average mass calculated using the
atomic weights of atoms composing the molecule (weighted averages of the atomic
masses for the differently abundant isotopes).
Let us consider CH3Cl as an example:
Chlorine atoms: mixtures of two isotopes, 34.968 852 u and 36.965 903 u with
relative abundances 75.77% and 24.23 %.
The atomic weight of chlorine atoms is the weighted average mass:
(34.968 852×0.7577+36.965 903×0.2423) = 35.453 Da.
The average mass of CH3Cl is 12.011+(3×1.00 794)+35.453 = 50.4878 Da.
Carbon and hydrogen also are composed of isotopes, but at much lower abundances. They
are neglected for this example.
1. Introduction
1.2 Terminology
Mass
 In mass spectrometry, the nominal mass or the monoisotopic mass is generally used.
 The nominal mass is calculated using the mass of the predominant isotope of each
element rounded to the nearest integer value that corresponds to the mass number,
also called nucleon number.
 Exact masses of isotopes are not exact whole numbers (differ weakly from the summed
mass values of their constituent particles that are protons, neutrons and electrons).
These differences, which are called the mass defects, are equivalent to the binding
energy that holds these particles together. Every isotope has a unique and characteristic
mass defect. The monoisotopic mass takes into account these mass defects and is
calculated by using the exact mass of the most abundant isotope for each
constituent element.
Let us consider again CH3Cl as an example:
The monoisotopic mass is 12.000 000+(3×1.007 825)+34.968 852 = 49.992 327 u.
When the mass of CH3Cl is measured with a mass spectrometer, two isotopic peaks will
appear
first peak m/z=(34.968852+12.000000+3×1.007825) = 49.992327 Th, rounded to m/z 50.
second peak m/z=(36.96590+12.000000+3×1.007825) =51.989365 Th, rounded to m/z 52.
The abundance at this latter m/z value is (24.23/75.77)=0.3198, or 31.98% of that observed
at m/z 50.
1. Introduction
For molecules of very high molecular weights, the differences between the different masses can become notable. Let us
consider two examples.
The first example is human insulin, a protein having the molecular formula C257H383N65O77S6.
The nominal mass of insulin is 5801 u using the integer mass of the most abundant isotope of each element, such as 12 u for
carbon, 1u for hydrogen, 14 u for nitrogen, 16 u for oxygen and 32 u for sulfur.
Its monoisotopic mass of 5803.6375 u is calculated using the exact masses of the predominant isotope of each element such
as C=12.0000 u, H=1.0079 u, N=14.0031 u, O=15.9949 u and S=31.9721 u.
Finally, an average mass of 5807.6559 Da is calculated using the atomic weight for each element, such as C=12.011 Da,
H=1.0078 Da, N=14.0067 Da, O=15.9994 Da and S= 32.066 Da.
The second example masses of two alkanes having the molecular formulae C20H42 and C100H202 are calculated.
For the smaller alkane, its nominal mass is (20×12)+(42×1)=282 u, its monoisotopic mass is (20×12)+(42×1.007
825)=282.3287 u rounded to 282.33 and its average mass is (20×12.011)+(42×1.007 94)=282.5535 Da.
The differences between these different types of masses are small but are more important for the heavier alkane. Indeed, its
nominal mass is (100×12)+(202×1)=1402 u, its monoisotopic mass is (100×12)+(202×1.007 825)=1403.5807 u rounded
to 1403.58 and its average mass is (100×12.011)+(202×1.007 94)=1404.7039 Da.
In conclusion, the monoisotopic mass is used when it is possible experimentally to distinguish the isotopes, whereas the
average mass is used when the isotopes are not distinguishable. The use of nominal mass is not recommended and should
only be used for low-mass compounds containing only the elements C, H, N, O and S to avoid to making
mistakes.
1. Introduction
The difference between the average mass, the nominal mass and the monoisotopic
mass can amount to several Da, depending on the number of atoms and their isotopic
composition. The type of mass determined by mass spectrometry depends largely on
the resolution and accuracy of the analyzer.
 The most intense peak – base peak (normalized 100%)
 Ions provide information concerning the nature and the
structure of their precursor molecule. In the spectrum of a
pure compound, the molecular ion, if present, appears at
the highest value of m/z (followed by ions containing
heavier isotopes) and gives the molecular mass of the
compound.
 The term molecular ion refers in chemistry to an ion
corresponding to a complete molecule regarding occupied
valences. This molecular ion appears at m/z 32 in the
spectrum of methanol, where the peak at m/z 33 is due to
the presence of the 13C isotope, with an intensity that is
1.1% of that of the m/z 32 peak.
 In the same spectrum, the peak at m/z 15 indicates the
presence of a methyl group. The difference between 32
and 15, that is 17, is characteristic of the loss of a neutral
mass of 17 Da by the molecular ion and is typical of a
hydroxyl group.
 In the same spectrum, the peak at m/z 16 could formally
correspond to ions CH4
•+, O+ or even CH3OH2+, because
they all have m/z values equal to 16 at low resolution.
However, O+ is unlikely to occur, and a doubly charged
ion for such a small molecule is not stable enough to be
observed.
1. Introduction
Example of mass spectrum:
methanol CH3OH analyzed by
electron impact ionization:
1. Introduction
1.3 Parts of Mass Spectrometer
14N+  “14”
15N+  “15”
14N2
+  “28”
14N15N+  “29”
14N2
2+  “14”
A mass spectrometer is an apparatus which
 produces a beam of gaseous ions from a sample,
 sorts out the resulting mixture of ions according to
their mass-to-charge ratio m/z (z = n e) and
 provides output signals which are measures of the relative abundance of each
ionic species present
sample
gas
unresolved accelerated
ion beam
resolved focused
ion beams
high vacuum
1. Introduction
1.4 Measures of Performance
 A measure of ability to separate and identify ions of slightly
different masses Usually defined in terms of the largest mass at
which a given criterion is met.
 The most popular “valley” definition: highest mass at which
two adjacent peaks of equal height M, differing in mass by W,
exhibit a valley between the peaks not greater than a certain
percentage such as 2 or 10 %, of the peak height.
R = (WxM) / DW = M / DW (for W=1)
 In practice, resolution must often be determined using an
isolated peak. Then DWis often taken as the width of the peak
at 50 % peak height level (FWHM).
For example resolving power of 2500 is required to separate the N2
+ peak (mass =
28.006148) from CO+ peak (mass = 27.994915), even though the nominal mass is
only 28.
1. Introduction
1.4 Measures of Performance
 A measure of the instrument’s response to ions of a particular component at
an arbitrary m/z value. It is expressed for a particular peak and a particular
sample
 various materials exhibit different efficiencies for ionization in the source,
 there might be differences in the efficiencies of the transmission of ions
through the mass analyzer
 the detector may exhibit a higher or lower efficiency for a particular mass or
type of ion.
instrument noise level, i.e. the spurious instrument response not due to ions
striking the ion collector – signal-to-noise at least 2:1 for good measurement
instrument background, instrument response, at a given mass, without the
sample
Sensitivity
Mass range Scan rate
Sensitivity and resolving power are inversely proportional!
1. Introduction
1.5 Applications
Typical applications are:
 leak detection
 determination of gas-specific desorption and adsorption rates of materials
for vacuum system components
 mass-selective leak testing of serial production components in the automotive
industry
 partial pressure measurements in high vacuum systems
 quantitative determination of the composition and purity of porcess gases
 monitoring of the gas composition in vacuum coating processes
 end point determination in vacuum etching
 complex analysis of catalytic reactions on the surface of solid bodies
 investigation of biochemical substance transformations
 mass-resolved determination of neutral particles and ions in plasma processes
2. Ion sources
2.1 Ionization
Ionization
Although both positive and negative ions can be studied by mass spectrometry,
the majority of instruments are used to investigate positive ions because in most
ion sources they are produced in larger number (approx. 103) than negative ions.
ionization potential (energy) – minimum energy provided in order for ion
formation to occur. The first ionization potential – a valence e- from the
highest occupied atomic or molecular orbit is removed to form the
corresponding atomic or molecular ion (parent ion) in its ground state. To
remove 2nd, 3rd etc. electron additional energy is needed (2nd, 3rd, ... ionization
potentials).
 by electron impact AB + e- -> AB+ + 2e
by photon AB + hn -> AB+ + eultraviolet
light, lasers (multiphoton absorption), synchroctron radiation
2. Ion sources
2.1 Ionization (contin.)
 by impact of high mass particle
like ion
like fast neutral
chemical ionization
Penning ionization
AB + C+ -> AB+ + C
AB + C -> AB+ + e- + C
AB + RH* -> ABH+ + R
AB + C* -> AB+ + e- + C
 by field emission
 by thermal ionization
gas-phase excited-state atom or molecule C*
Collisions would produce a deviation of the trajectory and the ion would lose its charge against the walls of the
instrument. On the other hand, ion–molecule collisions could produce unwanted reactions and hence increase
the complexity of the spectrum.
According to the kinetic theory of gases, the mean free path L (in m) is given by
where k is the Boltzmann constant, T is the temperature (in K), p is the pressure (in Pa) and σ is the collision
cross-section (in m2); σ =πd2 where d is the sum of the radii of the stationary molecule and the colliding ion (in
m).
In fact, one can approximate the mean free path of an ion under normal conditions in a mass spectrometer
(k=1.38×10−21 JK−1, T ≈ 300 K, σ ≈ 45×10−20 m2) using either of the following equations where L is in
centimetres and pressure p is, respectively, in pascals or milliTorrs:
2. Ion sources
2.1 Ionization (contin.)
 In a mass spectrometer, the mean free path should be at least 1 m and hence the maximum pressure
should be 6.6 10-3 Pa. In instruments using a high-voltage source, the pressure must be further reduced to
prevent the occurrence of discharges. In contrast, some trap-based instruments operate at higher pressure.
 In the same way, producing efficient ion–molecule collisions requires the mean free path to be reduced to
around 0.1 mm, implying at least a 60 Pa pressure in a region of the spectrometer.
 These large differences in pressure are controlled with the help of an efficient pumping system using
mechanical pumps in conjunction with turbomolecular, diffusion or cryogenic pumps. The mechanical
pumps allow a vacuum of about 10−1 Pa to be obtained. Once this vacuum is achieved, the operation of the
other pumping systems allows a vacuum as high as 10−8 Pa to be reached.
 Samples are often introduced without compromising the vacuum using direct infusion or direct insertion
methods. For direct infusion, a capillary is employed to introduce the sample as a gas or a solution. For
direct insertion, the sample is placed on a probe, a plate or a target that is then inserted into the source
through a vacuum interlock.
 For the sources that work at atmospheric pressure and are known as atmospheric pressure ionization
(API) sources, introduction of the sample is easy because the complicated procedure for sample
introduction into the high vacuum of the mass spectrometer is removed.
2. Ion sources
2.1 Ionization (contin.)
Ionizing a neutral molecule in the gas phase through electron ejection, electron capture, protonation, deprotonation,
adduct formation or by the transfer of a charged species from a condensed phase to the gas phase.
Electron ionization
Chemical ionization gas-phase ionization
Field ionization
limited to compounds sufficiently volatile and thermally stable.
However, a large number of compounds are thermally labile or do not have sufficient vapour pressure. Molecules of
these compounds must be directly extracted from the condensed to the gas phase.
Liquid-phase ion sources
Electrospray, atmospheric pressure chemical ionization and atmospheric pressure photoionization sources
Solid-state ion sources
the analyte is in an involatile deposit irradiated by energetic particles or photons that desorb ions near the surface of
the deposit. These ions can be extracted by an electric field and focused towards the analyser.
Matrix-assisted laser desorption,secondary ion mass spectrometry, plasma desorption and field
desorption sources
2. Ion sources
2.1 Ionization (contin.)
widely used in organic mass spectrometry
works well for many gas-phase molecules but induces extensive fragmentation so that the molecular ions are not
always observed
This wavelength is 0.27nm for a kinetic energy of 20 eV and
0.14 nm for 70 eV. When this wavelength is close to the bond
lengths, the wave is disturbed and becomes complex. If one
of the frequencies has an energy hv corresponding to a
transition in the molecule, an energy transfer that leads to
various electronic excitations
In the case of organic
molecules, a wide
maximum appears
around 70 eV
2 Ion sources
2.2 Electron ionization
2 Ion sources
2.2 Electron ionization (contin.)
Ionization
2. Ion sources
2.2 Electron ionization (contin.)
Ionization
2. Ion sources
2.2 Electron ionization (contin.)
Fragmentation during ionization AB + e- -> A+ + B + 2eappearance
potential (AE) – minimum energy required for creation of
particular fragment ion.
cracking (fractal) pattern – the array of peaks in the complete spectrum
of a pure substance.
Peak heights in a spectrum are usually normalized by taking the largest
peak in the spectrum (base peak) as 100. Every chemical compound has
its own distinctive cracking pattern (“fingerprint”).
Ionization efficiencies and appearance potentials can be used in many ways
to study electron impact phenomena:
 mechanism of ionization and dissociation
 calculation of chemical bond strengths
 energy states of atoms, molecules, free radicals
 theory of mass spectra
2. Ion sources
2.2 Electron ionization(contin.)
Fragmentation during ionization
2. Ion sources
2.2 Electron ionization (contin.)
Chemical ionization (CI) is a technique that produces ions with little excess energy. Thus this technique presents the
advantage of yielding a spectrum with less fragmentation in which the molecular species is easily recognized.
Chemical ionization is a lower energy process than electron ionization.
Chemical ionization consists of producing ions through a collision
of the molecule to be analyzed with primary ions present in the
source (with ions of a reagent gas that are present in the ion
source). Ion–molecule collisions will thus be induced in a definite
part of the source. In order to do so, the local pressure has to be
sufficient to allow for frequent collisions.
(1) EI/CI switch; in EI mode, the box serves as a pusher; (2)
microswitch; (3) entrance for the reagent gas;
(4) Flexible capillary carrying the reagent gas;
(5) diaphragm; (6) filament giving off electrons; (7) path of the
ions towards the analyser inlet; (8) hole for the ionizing
electrons in CI mode; (9) sample inlet;
(10) box with holes, also named ‘ion volume’.
The pumping speed is sufficient to maintain a 60 Pa pressure
(mean free path is about 0.1 mm) within the box. Outside, the
usual pressure in a source, about 10−3 Pa, will be maintained.
2. Ion sources
2.3 Chemical Ionization
 An electron entering the box will preferentially ionize the reagent gas molecules
through electron ionization.
 The resulting ion will then mostly collide with other reagent gas molecules, thus
creating an ionization plasma through a series of reactions.
 Both positive and negative ions of the substance to be analyzed will be formed by
chemical reactions with ions in this plasma. This causes proton transfer reactions,
hydride abstractions, adduct formations, charge transfers, and so on.
 This plasma will also contain low-energy electrons, called thermal electrons. These
are either electrons that were used for the first ionization and later slowed, or
electrons produced by ionization reactions. These slow electrons may be associated
with molecules, thereby yielding negative ions by electron capture.
 Ions produced from a molecule by the abstraction of a proton or a hydride, or the
addition of a proton or of another ion, allow the determination of the molecular mass
of the molecules in the sample.
2. Ion sources
2.3 Chemical Ionization (contin.)
 When analyte molecules M are introduced in the ionization plasma, the reagent gas ions GH+ can often
transfer a proton to the molecules M and produce protonated molecular ions MH+.
 acid–base reaction: the reagent gas ions GH+ and the analyte molecules M being Brönsted acid (proton
donor) and Brönsted base (proton acceptor).
 The proton affinity (PA) is the negative enthalpy change for the protonation reaction. The observation of
protonated molecular ions MH+ implies that the analyte molecule M has a proton affinity much higher than
that of the reagent gas: PA(M) > PA(G)
 If the reagent gas has a proton affinity much higher than that of an analyte (PA(G)>PA(M)), proton transfer
from GH+ to M will be energetically too unfavourable.
 The energetics of the proton transfer can be controlled by using different reagent gases. The most common
reagent gases are methane (PA=5.7 eV), isobutane C4H10 (PA=8.5 eV) and ammonia (PA=9.0 eV).
 Fragmentation may occur with methane while with isobutane or ammonia the spectrum often presents
solely a protonated molecular ion because these reagent gases is considerably less exothermic than
protonation by methane.
Proton Transfer
2. Ion sources
2.3 Chemical Ionization (contin.)
isobutane
Mass spectra of butyl methacrylate
C8H14O2 or CH2C(CH3)COO(CH2)3CH3
The ionization techniques (EI vs CI) and the reagent gases
(methane vs isobutane) influence the amount of
fragmentation and the prominence of the protonated
molecular ions detected at 143 Th.
2. Ion sources
2.3 Chemical Ionization
(Proton transfer contin.)
EI
methane CI
isobutane CI
 In chemical ionization (CI), all the ions are liable to associate with polar molecules to form adducts, a kind
of gas-phase solvation. The process is favoured by the possible formation of hydrogen bonds.
 For the adduct to be stable, the excess energy must be eliminated, a process which requires a collision with
a third partner.
 Ions resulting from the association of a reagent gas molecule G with a protonated molecular ion MH+ or
with a fragment ion F+, of a protonated molecular ion MH+ with a neutral molecule, and so on, are often
found in CI spectra.
 Every ion in the plasma may become associated with either a sample molecule or a reagent gas molecule.
 A mixture of two species M and N can give rise to associations such as (MH+N)+, (F+N)+ with (F+M)+, and
so on.
 It is always useful to examine the peaks appearing beyond the ions of the molecular species of a substance
thought to be pure. If some peaks cannot be explained by reasonable associations, a mixture must be
suspected.
Adduct Formation
2. Ion sources
2.3 Chemical Ionization (contin.)
An adduct is a product of a direct addition of two or more distinct molecules,
resulting in a single reaction product containing all atoms of all components.
When interpreting the results, one must
always keep in mind that a mixture that is
observed may result from the presence of
several constituents before the vaporization or
from their formation after the vaporization.
It is always useful to examine the peaks
appearing beyond the ions of the molecular
species of a substance thought to be pure. If
some peaks cannot be explained by reasonable
associations, a mixture must be suspected.
Two examples of chemical ionization
(isobutane) spectra. The top spectrum is that of
a pure compound. The bottom spectrum is that
of a mixture of two compounds with masses
261 and 270. They correspond respectively to
the loss of hydrogen cyanide (HCN) and water.
2. Ion sources
2.3 Chemical Ionization(contin.)
Adduct Formation (contin.)
Rare gases, nitrogen, carbon monoxide and other gases with high ionization potential react by charge
exchange:
A radical cation is obtained, as in EI, but with a smaller energy content. Less fragmentation is thus observed. In
practice, these gases are not used very often.
A radical (more precisely, a free radical) is an atom, molecule, or ion that has unpaired valence electrons.
An anion is an ion with more electrons than protons, giving it a net negative charge.
A cation is an ion with fewer electrons than protons, giving it a positive charge.
Charge-Transfer Chemical Ionization
2. Ion sources
2.3 Chemical Ionization(contin.)
Almost all neutral substances are able to yield positive ions, whereas negative ions require the presence of acidic
groups or electronegative elements to produce them. This allows some selectivity for their detection in mixtures.
Negative ions can be produced by capture of thermal electrons by the analyte molecule or by ion–molecule reactions
between analyte and ions present in the reagent plasma.
Any excess of energy from the negative molecular ion as it is formed must be removed by collision. Thus, in CI
conditions, the reagent gas serves not only for producing thermal electrons but also as a source of molecules for
collisions to stabilize the formed ions.
Negative Ion Formation
2. Ion sources
2.3 Chemical Ionization(contin.)
 The associative resonance capture that leads to the formation of negative molecular ions
needs electrons in the energy range 0–2 eV, whereas the dissociative resonance capture is
observed with electrons of 0–15 eV and leads to the formation of negative fragment ions.
 Ion pair production is observed with a wide range of electron energies above 15 eV. It is
principally this process that leads to negative ion production under conventional EI
conditions. Ion pair production forms structurally insignificant very low-mass ions with a
sensitivity that is 3–4 orders of magnitude lower than that for positive ion production.
 Negative ions can also be formed through ion–molecule reactions with one of the plasma
ions. These reactions can be an acid–base reaction or an addition reaction through adduct
formation.
 Note the different behaviours that the electron can adopt towards the molecules.
Electrons at thermal equilibrium, that is those whose kinetic energy is less than
about 1 eV (1 eV=98 kJ mol−1), can be captured by molecules and yield negative
radical anions.
 Those whose energy lies between 1 and a few hundred electronvolts behave as a
wave and transfer energy to molecules.
 Finally, molecules will be ‘transparent’ to the electrons with higher energies: here
we enter the field of electron microscopy.
2. Ion sources
2.3 Chemical Ionization(contin.)
2. Ion sources
2.3 Chemical Ionization (Reagent gas)
Methane
2. Ion sources
2.3 Chemical Ionization (Reagent gas)
Methane
2. Ion sources
2.3 Chemical Ionization (Reagent gas)
Isobutane
2. Ion sources
2.3 Chemical Ionization (Reagent gas)
Amonia
Secondary ion mass spectrometry (SIMS) analyses the secondary ions emitted when a surface is irradiated
with an energetic primary ion beam.
 mostly used with solids and is especially useful to study conducting surfaces. High resolution chemical
maps are produced by scanning a tightly focused ionizing beam across the surface.
 Static SIMS – low energy beam (less damage),
 Dynamic SIMS – high energy beam (erosion, profiling)
Fast atom bombardment (FAB) and liquid secondary ion mass spectrometry (LSIMS)
a high primary current beam of neutral atoms/molecules or ions focused on the sample, respectively. The sample
must be dissolved in a non-volatile liquid matrix. In practice, glycerol is most often used, while mnitrobenzylic
alcohol (MNBA) is a good liquid matrix for non-polar compounds, and di- and triethanolamine
are efficient, owing to their basicity, in producing negative ions. Thioglycerol and a eutectic mixture of
dithiothreitol and dithioerythritol (5:1 w/w), referred to as magic bullet, are alternatives to glycerol.
 The energetic particles hit the sample solution, inducing a shock wave which ejects ions and molecules
from the solution. Ions are accelerated by a potential difference towards the analyser. These techniques
induce little or no ionization. They generally eject into the gas phase ions that were already present in the
solution.
 The neutral atom beam at about 5 keV is obtained by ionizing a compound, most often argon, sometimes
xenon. Ions are accelerated and focused towards the compound to be analysed under several kilovolts
 Using a ‘caesium gun’, one produces a beam of Cs+ ions at about 30 keV. It is claimed to give better
sensitivity than a neutral atom beam for high molecular weights. However, the advantage of using neutral
molecules instead of ions lies in the avoidance of an accumulation of charges in the non-conducting
samples.
2. Ion sources
2.4 SIMS and Fast atom/ion bombardment
More details in the course F7360 Charakterizace povrchů a tenkých vrstev
spring semester 2018
1, Ionization of argon; the resulting ions are accelerated and focused by the lenses 2. In 3, the argon ions exchange
their charge with neutral atoms, thus becoming rapid neutral atoms. As the beam path passes between the
electrodes 4, all ionic species are deflected. Only rapid neutral atoms reach the sample dissolved in a drop of
glycerol, 5. The ions ejected from the drop are accelerated by the pusher, 6, and focused by the electrodes, 7,
towards the analyzer, 8.
This method is very efficient for producing ions from polar compounds with high molecular weights. Ions up to
10 000 Da and above can be observed, such as peptides and nucleotides. Moreover, it often produces ion beams
that can be maintained during long periods of time, sometimes several tens of minutes, which allows several types
of analysis to be carried out.
2. Ion sources
2.4 SIMS and Fast atom/ion bombardment
(contin.)
Softer than EI and CI. Ions are produced by
bombardment with heavy atoms. Gives
(M+H)+ ions and little fragmentation. Good
for more polar compounds.
Fast atom bombardment
2. Ion sources
2.5 Laser Desorption (LD)
 Laser desorption (LD) is an efficient method for producing gaseous ions. Generally, laser
pulses yielding from 106 to 1010 Wcm−2 are focused on a sample surface of about 10−3–10−4
cm2, most often a solid.
 This technique is used in the study of surfaces and in the analysis of the local composition of
samples, such as inclusions in minerals or in cell organelles. It normally allows selective
ionization by adjusting the laser wavelength. However, in most conventional infrared LD
modes, the laser creates a thermal spike, and thus it is not necessary to match the laser
wavelength with the sample.
 Since the signals are very short, simultaneous detection analysers or time-of-flight analysers
are required. The probability of obtaining a useful mass spectrum depends critically on the
specific physical proprieties of the analyte (e.g. photoabsorption, volatility, etc.).
 Furthermore, the produced ions are almost always fragmentation products of the original
molecule if its mass is above approximately 500 Da. This situation changed dramatically with
the development of matrix-assisted laser desorption ionization (MALDI)
 A widespread and powerful source for the production of intact gas-phase ions from a broad range of large,
non-volatile and thermally labile compounds such as proteins, oligonucleotides, synthetic polymers and
large inorganic compounds.
 The method is characterized by easy sample preparation and has a large tolerance to contamination by salts,
buffers, detergents, and so on.
 MALDI is achieved in two steps. In the first step, the compound to be analysed is dissolved in a solvent
containing in solution small organic molecules, called the matrix. These molecules must have a strong
absorption at the laser wavelength. This mixture is dried before analysis and any liquid solvent used in the
preparation of the solution is removed. The result is a ‘solid solution’ deposit of analyte-doped matrix
crystals. The analyte molecules are embedded throughout the matrix so that they are completely isolated
from one another.
 The second step occurs under vacuum conditions inside the source of the mass spectrometer. This step
involves ablation of bulk portions of this solid solution by intense laser pulses over a short duration.
Irradiation by the laser induces rapid heating of the crystals by the accumulation of a large amount of
energy in the condensed phase through excitation of the matrix molecules. The rapid heating causes
localized sublimation of the matrix crystals, ablation of a portion of the crystal surface and expansion of the
matrix into the gas phase, entraining intact analyte in the expanding matrix plume.
Matrix-Assisted Laser Desorption Ionization (MALDI)
2. Ion sources
2.5 MALDI
 Among the chemical and physical ionization pathways suggested for MALDI are gas-phase
photoionization, excited state proton transfer, ion–molecule reactions, desorption of
preformed ions, and so on.
 The most widely accepted ion formation mechanism involves proton transfer in the solid
phase before desorption or gas-phase proton transfer in the expanding plume from
photoionized matrix molecules.
2. Ion sources
2.5 MALDI(contin.)
 MALDI is more sensitive than other laser ionization techniques. Indeed, the number of matrix molecules
exceeds widely those of the analyte, thus separating the analyte molecules and thereby preventing the
formation of sample clusters that inhibit the appearance of molecular ions.
 The matrix also minimizes sample damage from the laser pulse by absorbing most of the incident energy
and increases the efficiency of energy transfer from the laser to the analyte.
 It is not necessary to adjust the wavelength to match the absorption frequency of each analyte because it is
the matrix that absorbs the laser pulse.
 Because the process is independent of the absorption properties and size of the compound to be analysed,
MALDI allows the desorption and ionization of analytes with very high molecular mass in excess of 100
000 Da. For example, MALDI allows the detection of femtomoles of proteins with molecular mass up to
300 000 Da.
 Typical MALDI spectra include mainly the monocharged molecular species by protonation in positive ion
mode. More easily deprotonated compounds are usually detected in negative ion mode.
 Compounds that are not easily protonated can be cationized instead, often by adding a small quantity of
alkali, copper or silver cations to the sample.
2. Ion sources
2.5 MALDI (contin.)
 Generally, the power density required corresponds to an energy flux of 20 mJ cm−2
 The laser spot diameter at the surface of the sample varies from 5 to 200 μm.
 It is important to determine the threshold irradiance, the laser pulse power that results in the
onset of desorption of the matrix.
 When an IR laser is used, only less fragmentation is observed, indicating that the IR-MALDI
is somewhat cooler.
 On the other hand, IR-MALDI induces a larger depth of vaporization per shot that leads to
shorter lifetime of the sample. Compared with UV-MALDI, a somewhat lower sensitivity is
observed.
 The MALDI matrix selection is based on the laser wavelength used. In addition, the most
effective matrix is strongly related to the class of analyte and may differ for analytes that have
apparently similar structures.
 The matrix should have strong absorbance at the laser wavelength, low enough mass to be
sublimable, vacuum stability, ability to promote analyte ionization, solubility in solvents
compatible with analyte and lack of chemical reactivity.
2. Ion sources
2.5 MALDI (contin.)
Dried-droplet methode consists of mixing some saturated matrix solution (5–10 μl) with a smaller volume (1–2
μl) of an analyte solution. Then, a droplet (0.5–2 μl) of the resulting mixture is placed on the MALDI probe,
which usually consists of a metal plate with a regular array of sites for sample application. The droplet is dried at
room temperature and when the liquid has completely evaporated to form crystals, the sample may be loaded into
the mass spectrometer.
2. Ion sources
2.5 MALDI (contin.)
 MALDI suffers from some disadvantages such as low shot-to-shot reproducibility and strong dependence
on the sample preparation method.
 High concentrations of buffers and other contaminants commonly found in analyte solutions can interfere
with the desorption and ionization process of samples.
 Prior purification to remove the contaminants leads to improvements in the quality of mass spectra. For
instance, the removal of alkali ions has proven to be very important for achieving high desorption efficiency
and mass resolution.
 Matrix-free direct laser desorption ionization method, good results were obtained with surface-activated
laser desorption ionization (SALDI) which uses graphite as the surface.
 But the use of porous silicon as a new surface is more promising and has led to the development of a new
method called desorption ionization on silicon (DIOS).
 The structure of porous silicon allows the analyte molecules to be retained while its strong UV absorption
allows the desorption ionization of the sample under UV laser irradiation.
 DIOS mass spectra do not present interference in the low-mass range, while signals due to the matrix are
observed in MALDI. It allows small molecules (100–3000 Da) to be easily analysed. Furthermore, DIOS is
equivalent to MALDI in sensitivity, but is more tolerant of the presence of salts or buffers.
2. Ion sources
2.5 MALDI (contin.)
There are essentially three different types of fragmentations that generate fragment ions in MALDI spectra.
1) Fragmentations taking place in the source are called in-source decay (ISD) fragmentations. To be precise,
fragmentation at the sample surface that occurs before or during the desorption event (on a time scale of a few
picoseconds to nanoseconds) is called prompt fragmentation.
2) Fragmentation occurring in the source after the desorption event but before the acceleration event (on a time scale
of a few nanoseconds to microseconds) is called fast fragmentation.
3) Fragmentation that occurs after the acceleration region of the mass spectrometer is called post-source decay
(PSD) fragmentation. It corresponds to the fragmentation of metastable ions, which are stable enough to leave the
source but contain enough excess energy to allow their fragmentation before they reach the detector.
Acquisition of an excess of internal energy can be due to the direct interaction photon/molecule, to ionization energy
and to activation of molecules in solid state. Another important mechanism consists of the multiple collisions that
ions undergo in the source. These collisions can be controlled by the strength of the electric field used to extract the
ions from the source.
ISD fragmentations lead to product ions that are always apparent in the MALDI spectra, whereas the observation of
product ions from PSD fragmentation needs certain instrumental conditions. This induces a broadening of the peaks
with a concomitant loss of mass resolution and sensitivity.
Fragmentations
2. Ion sources
2.5 MALDI (contin.)
As the transfer of ions into the mass spectrometer is
relatively inefficient, the total sample consumption is higher
for AP-MALDI than for vacuum MALDI.
Because of the fast and efficient thermalization of the ion
internal energy at atmospheric conditions, AP MALDI is a
softer ionization technique compared with conventional
vacuum MALDI and even softer than vacuum IR-MALDI.
Ions produced by this method generally exhibit no
fragmentation but tend to form clusters with the matrix.
These unwanted adducts between matrix and analyte can be
eliminated by increasing the energy transferred to the ions in
the source. For instance, increasing the laser energy or some
API parameters, such as capillary temperature, increases the
analyte-matrix dissociation process.
As a result of the almost complete decoupling of the ion desorption from the mass analyser, the performance of the
instrument (calibration, resolution and mass accuracy) is not affected by source conditions (type of sample matrix,
sample preparation method and location of the laser spot on the sample). This allows much greater experimental
flexibility. It is possible, for instance, to use long-pulse lasers to increase the overall sensitivity without observing
deterioration in resolution.
Atmospheric Pressure MALDI
2. Ion sources
2.5 MALDI (contin.)
ESI is produced by applying a strong electric field, under atmospheric
pressure, to a liquid passing through a capillary tube with a weak flux
(normally 1–10 μlmin−1). The electric field is obtained by applying a
potential difference of 3–6 kV between this capillary and the counterelectrode,
separated by 0.3–2 cm, producing electric fields of the order of
106 Vm−1
A gas injected coaxially at a low flow rate allows the dispersion of the spray
to be limited in space.
These droplets then pass either through a curtain of heated inert gas, most often nitrogen, or through a heated
capillary to remove the last solvent molecules.
The spray starts at an ‘onset voltage’ that, for a given source, depends on the surface tension of the solvent. In a source
which has an onset voltage of 4 kV for water (surface tension 0.073Nm−2), 2.2 kV is estimated for methanol
(0.023Nm−2), 2.5 kV for acetonitrile (0.030Nm−2) and 3 kV for dimethylsulfoxide (0.043Nm−2).
2. Ion sources
2.6 Electrospray (ESI)
A decomposing droplet in an electrospray source,; q,
charge; ε0, permittivity of the environment; γ, surface
tension and D, diameter of a supposed spherical droplet.
Breakdown of the droplets can occur before the limit given by the Rayleigh equation is reached because the
droplets are mechanically deformed, thus reducing the repulsion necessary to break down the droplets. The solvent
contained in the droplets evaporates, which causes them to shrink and their charge per unit volume to increase.
2. Ion sources
2.6 Electrospray (ESI) (contin.)
If one examines with a microscope the nascent drop forming at the tip of the capillary while increasing the voltage,
at low voltages the drop appears spherical, then elongates under the pressure of the accumulated charges at the tip in
the stronger electric field; when the surface tension is broken, the shape of the drop changes to a ‘Taylor cone’ and
the spray appears.
 From this Taylor cone, about 20 smaller droplets are released. Typically a first-generation droplet from the
capillary will have a diameter of about 1.5 μm and will carry around 50 000 elementary charges, or about 10−14 C.
The offspring droplets will have a diameter of 0.1 μm and will carry 300 to 400 elementary charges. The total
volume of the offspring droplets is about 2% of the precursor droplet but contain 15% of the charge. The charge
per unit volume is thus multiplied by a factor of seven. The precursor droplet will shrink further by solvent
evaporation and will produce other generations of offspring.
 These small, highly charged droplets will continue to lose solvent, and when the electric field on their surface
becomes large enough, desorption of ions from the surface occurs. Sensitivity is higher for compounds whose
concentration at the surface is higher, thus more lipophilic ones.
 When the droplet contains very large molecules, like proteins for example, the molecules will not desorb, but are
freed by evaporation of the solvent. This seems to occur when the molecular weight of the compounds exceeds
5000 to 10 000 Da.
 The ions obtained from large molecules carry a greater number of charges if several ionizable sites are present.
Typically, a protein will carry one charge per thousand daltons approximately, less if there are very few basic
amino acids. Small molecules, say less than a thousand daltons, will produce mainly monocharged ions.
 ESI can also be used in the case of molecules without any ionizable site through the formation of sodium,
potassium, ammonium, chloride, acetate or other adducts.
ESI has important characteristics: for instance, it is able to produce multiply charged ions from large molecules. The
formation of ions is a result of the electrochemical process and of the accumulation of charge in the droplets.
2. Ion sources
2.6 Electrospray (ESI) (contin.)
ESI spectrum of phage lambda lysozyme. The molecular
mass is measured as being 17 828±2.0 Da.
The ESI mass spectra of biological macromolecules
normally correspond to a statistical distribution of
consecutive peaks characteristic of multiply
charged molecular ions obtained through
protonation (M+zH)z+, or deprotonation
(M−zH)z−, with minor if any contributions of ions
produced by dissociations or fragmentations.
Consider a positive ion with charge z1 whose massto-charge
ratio is measured as being m1 Th, issued
from a molecular ion with mass M Da to which z1
protons have been added. We then have
where mp is the mass of the proton
An ion separated from the first one by (j−1) peaks, in increasing order of mass-to-charge ratio, has a measured ratio
of m2 Th and a number of charges z1 – j, so that
2. Ion sources
2.6 Electrospray (ESI) (contin.)
Using the peaks at m/z 939.2 and 1372.5 (j = 6), we obtain z1 =6(1372.5−1.0073)/(1372.5−939.2)=19 and we can
number all the peaks measured according to the number of charges. M can be calculated from their mass. This
technique allowed the determination of the molecular masses of proteins above 130 kDa with a detection limit of
about 1 pmol using a quadrupole analyser
Product ion spectrum of the [M + 7H]7+ ion from
the following peptide:
ALVRQGLAKVAYVYKPNNTHEQHLRKSEA
QAKKEKLLNIWSEDNADSGQ.
Notice that fragment ions having lower charge
number z may appear at higher m/z values than
the precursor, which indeed occurs in the
spectrum shown. The inset shows that, owing to
the high resolution, the isotopic peaks are
observed separated by 1/6 Th, and thus 1/z = 1/6
or z = 6. As neighbour peaks differ by 1Da, the
observed distance between them will be 1/z,
allowing the direct determination of the charge
state of the corresponding ion.
2. Ion sources
2.6 Electrospray (ESI) (contin.)
Charges of ions generated by ESI do not reflect the charge state of compounds in the analysed solution, but are the
result of both charge accumulation in the droplets and charge modification by electrochemical process at the probe
tip.
The negative ion spectrum of myoglobin at pH 3 shows a better signal-to-noise ratio than the same spectrum at pH
10.
pH is a measure of the acidity or basicity of an aqueous solution. Solutions with a pH less than 7 are said to be
acidic and solutions with a pH greater than 7 are basic or alkaline. Pure water has a pH very close to 7.
2. Ion sources
2.6 Electrospray (ESI) (contin.)
Another feature of ESI is its sensitivity to
concentration, and not to the total quantity
of sample injected in the source, as is the
case for most other sources.
The sensitivity increases somewhat when the flow entering the source is reduced. This remains true up to flows as
low as some tens of nanolitres per minute. When flow rates higher than about 500 μl min−1 are used, the sensitivity
is reduced. Lower flow rates also allow less analyte and buffer to be injected in the source, reducing contamination.
Furthermore, for the same amount of sample, an HPLC column with a lower diameter, and using smaller flow
rates, will give an increased sensitivity because the concentration of the sample in the elution solvent is increased.
Based on this concentration dependence, modifications of the technique, called microelectrospray (μESI), or
nanospray (nESI), which use much lower flow rates down to some tens of nanolitres per minute, have been
developed using adapted probe tips. Detection limits in the range of attomoles (10–15 moles) injected have been
demonstrated.
2. Ion sources
2.6 Electrospray (ESI)
Sensitivity to Concentration
When positive ions are extracted for analysis, electrons have to be
provided in the circuit from the capillary. The same number of
negative charges must be ‘pumped’ out of the solution as positive
charges are extracted to the analyser, thus an oxidation occurs. For
negative ions, electrons have to be consumed, and thus a reduction
occurs.
A major consequence is that the total number of ions per unit time
that can be extracted to the spectrometer is actually limited by the
electric current produced by the oxidation or reduction process at the
probe tip.
This limiting current is not dependent on the flow rate, up to very
low flow, and this explains why ESI is only concentration
dependent. In practice, the total ion current is limited to a maximum
of about 1 μA.
Ions, either positive or negative, of an analyte A will be desorbed from the droplets, producing a theoretical ion current
IA =kA[A], where kA is a rate constant depending on the nature of A. Let us suppose that another ion B is produced from
the buffer, at a rate IB =kB[B].
The total ion current for these two ions IT =(IA +IB), but this total ion current is limited by the oxidation, if positive ions
are desorbed, or reduction process that occurs at the probe tip.
2. Ion sources
2.6 Electrospray (ESI) (contin.)
2. Ion sources
2.6 Electrospray (ESI) (contin.)
 The ESI source is a constant-current electrochemical cell. The important consequence is that
there will be a constant current IM carried by the ions.
 If there are too many ions from salts in the flow, they will suffice to produce IM and the ions of
the sample will be either at low abundances or not observed.
 On the other hand, if the solution is very dilute and at very low flow (below 1 μl), the ion flow
from the capillary can be insufficient to provide IM.
 The electrochemical process at the probe tip will then produce additional ions by oxidation (or
reduction in negative ion mode) of either the solvent or the sample depending on their
respective oxidation (reduction) potentials.
This will lead to the observation of radical cations or radical anions in the spectrum.
Let us consider that [B] remains constant, but the analyte concentration [A] varies; then two limiting cases are to
be considered. First, for kA[A] « kB[B],
This means that the intensity detected for A will be proportional to its concentration, but the sensitivity will be
inversely proportional to [B].
The other extreme case leads to
IA remains constant, and quantitation of [A] is no longer possible. The intensity of the signal for B will become
weaker as [A] increases.
2. Ion sources
2.6 Electrospray (ESI) (contin.)
This limiting current is symbolized IM, and IT = IM if no other ionic species are present. The current for each ion
will be proportional to its relative desorption rate
In a solvent containing NH4
+ and Na+ ions at constant
concentrations, an increasing amount of morphine
chlorhydrate is added. The graph shows on top the
number of amperes at the capillary tip, and below the
intensity monitored at the mass of protonated morphine
and the sum of the intensities for the NH4
+ and Na+ ions.
Linearity is observed at low concentrations, but from
about 5×10−6 significant curvature is observed (note that
the scales are logarithmic) the intensity for morphine is
constant, and the signal for the other ions diminishes.
At still higher concentrations, the intensity levels out.
2. Ion sources
2.6 Electrospray (ESI) (contin.)
Measuring the performance of a mass analyser
Mass range limit- The mass range determines the limit of m/z over which the mass analyzer can measure ions.
It is expressed in Th, or in u for an ion carrying an elementary charge, that is z = 1.
Analysis speed- The analysis speed, also called the scan speed, is the rate at which the analyzer measures over
a particular mass range. It is expressed in mass units per second (u s−1) or in mass units per millisecond (u
ms−1).
Transmission-The transmission is the ratio of the number of ions reaching the detector and the number of ions
entering the mass analyzer.
Mass accuracy- Mass accuracy indicates the accuracy of the m/z provided by the mass analyzer. It is the
difference that is observed between the theoretical m/z (mtheoretical) and the measured m/z (mmeasured). It can be
expressed in millimass units (mmu) but is often expressed in parts per million (ppm).
3. Mass Analyzers
Resolution-Resolution or resolving power is the ability of amass analyzer to yield distinct signals for two ions with
a small m/z difference.
Two peaks are considered to be resolved if the valley between them is equal to
10 % of the weaker peak intensity when using magnetic or ion cyclotron
resonance (ICR) instruments and 50% when using quadrupoles, ion trap,
TOF, and so on. If Δm is the smallest mass difference for which two peaks with
masses m and m+Δm are resolved, the definition of the resolving power R is
R=m/Δm. Therefore, a greater resolving power corresponds to the increased
ability to distinguish ions with a smaller mass difference.
The resolving power can also be determined with an isolated peak. Indeed, the
resolving power is also defined using the peak width Δm at x% of the peak
height. Often x is taken to be 50% and Δm is designated as full width at half
maximum (FWHM). The relationship between the two definitions is obvious for
two peaks with equal intensities.
The resolution full width at x% of the peak height is equal to the resolution at
2x% for the valley.
3. Mass Analyzers
(contin.)
Relationship between the two definitions of resolution, resolution full width at x% of the peak height or
resolution at y% of the valley. As the bottom of the valley is the sum of the intensities at the cross, y = 2x.
If δm is taken at half maximum height, two peaks having amass difference equal to this width will cross at
50% height. As the valley depth will be two times this height, it will be at 100 %. There is thus no separation.
3. Mass Analyzers
(contin.)
The quadrupole analyzer is a device which uses the stability of the trajectories in oscillating electric fields
to separate ions according to their m/z ratios. The 2D or 3D ion traps are based on the same principle.
Φ0 ~ potential applied to the rods.
ω ~ the angular frequency (in radians per second=2πv, where v is the frequency of the RF field).
U ~ the direct potential (500 to 2000V).
V ~ the ‘zero-to-peak’amplitude of the RF voltage, 0 to 3000V (from −3000 to +3000V peak to peak).
3. Mass Analysers
3.1 Quadrupole Analyzers
Equations of Motion
Differentiating and rearranging the terms leads to the following equations of the movement (Paul equation):
3. Mass Analyzers
3.1 Quadrupole Analyzers (contin.)
The trajectory of an ion will be stable if the values of x and y never reach r0, thus if it never hits the rods. The
following equation was established in 1866 by the physicist Mathieu in order to describe the propagation of waves in
membranes:
u stands for either x or y. Comparing the preceding equations with this one, and taking into account that the potential
along y has opposite sign to the one along x, the following change of variables gives to the equations of the
movement the form of the Mathieu equation. First, ξ is defined as being
In the first term of the Paul equation, replacing t2 by ξ2 introduces a factor ω2/4. To compensate for this factor, the
whole equation must be multiplied by the reverse, 4/ω2. In the cosine term, 2ξ is equal to ωt, as needed in the Paul
equations. Incorporating these changes and rearranging the terms yields the following expressions:
As long as x and y, which determine the position of an ion from the centre of the rods, both remain less than r0, the
ion will be able to pass the quadrupole without touching the rods.
3. Mass Analyzers
3.1 Quadrupole Analyzers (contin.)
Stability areas for an ion along x or y and
along x and y; u represents either x or y. The
four stability areas are labelled A to D and are
circled.
The area A is that used commonly in mass
spectrometers.
In practice, the highest detectable m/z ratio is
about 4000 Th, and the resolution hovers
around 3000. Thus, beyond 3000 u the isotope
clusters are no longer clearly resolved.
Usually, quadrupole mass spectrometers are
operated at unit resolution, that is a resolution
that is sufficient to separate two peaks one
mass unit apart.
Quadrupoles are low-resolution instruments.
3. Mass Analyzers
3.1 Quadrupole Analyzers (contin.)
The last terms of both the U and V equations is a constant for a given quadrupole instrument, as they operate at
constant ω. We see that switching from one m/z to another results in a proportional multiplication of au and qu, which
means changing the scale of the drawing in U, V coordinates; thus the triangular area A will change from one mass to
another, like proportional triangles.
Stability areas as a function of U and V for ions with
different masses (m1 < m2 < m3). Changing U linearly
as a function of V, we obtain a straight operating line
that allows us to observe those ions successively.
A line with a higher slope would give us a higher
resolution, so long as it goes through the stability
areas.
Keeping U = 0 (no direct potential) we obtain zero
resolution. All of the ions have a stable trajectory so
long as V is within the limits of their stability area.
3. Mass Analyzers
3.1 Quadrupole Analyzers (contin.)
These quadrupoles also have the property of focusing the
trajectory of the ions towards the centre of the quadrupole.
It goes down the potential ‘valley’ with respect to the negative rods,
and acquires some kinetic energy in that direction. However, the
potentials quickly change, so that the kinetic energy is converted
into potential energy and the ion goes back to the centre of the rods,
as would happen for a ball on a horse’s saddle that is turned quickly.
The name ‘saddle field’ is an allusion to this phenomenon.
The time for crossing the analyzer is short compared with the time
necessary to switch from one mass to the other,
The ions remain long enough between the rods for a few oscillations
of the alternative potential to occur. This means that the kinetic
energy at the source exit must range from 1-100 eV.
3. Mass Analyzers
3.1 Quadrupole Analyzers (contin.)
When U is equal to zero (quadrupole operating in the RF only mode) all of the ions with a mass higher than a
given limit selected by adjusting the value of the RF voltage V have a stable trajectory.
But the transmission of ions with high masses suffers from their poorer focusing. Indeed, the efficiency of
focusing depends on the depth of the effective potential well, which is inversely proportional to m/z.
Consequently, ions with high m/z are weakly focused and may be lost on the rods.
To increase the transmission of ions with high masses by a more efficient focalization, the RF voltage V is
increased. Indeed, the depth of the effective potential well, which influences the efficiency of focusing, is
proportional to V2. However, all heavy ions are poorly focused when V is low and all light ions are lost when
V is high.
The quadrupoles operating in RF-only mode have the property to focus the trajectory of ions. The use of
quadrupoles as ion guides or ion focusing devices has been extended to other multipoles as hexapoles and
octapoles. An RF voltage V is applied to the rods, with a polarity inverted from one rod to the next one.
Ion Guide and Collision Cell
As an ion moves from the centre of the multipole towards any one of the rods, the potential increases to reach a
maximum at the surface of the rod. For the quadrupole (n = 2), the potential varies as (r/r0)2, whereas the hexapole
(n = 3) and the octapole (n = 4) have potentials that vary as (r/r0)4 and (r/r0)6, respectively.
3. Mass Analyzers
3.1 Quadrupole Analyzers (contin.)
 While the octapole has a softer potential around the centre but a steeper potential close to the rods. Furthermore,
for the same conditions, the maximum potential generated by an octapole has an amplitude that is four times
higher than the potential generated by a quadrupole.
 The extent of the mass range for simultaneous transmission of ions is not important when the ion guide is
combined with a scanning analyzer.
 TOF measure all the ions simultaneously, requires ion guides that transmit all the ions together at the same time in
the entire mass range of the analyzer.
3. Mass Analyzers
3.1 Quadrupole Analyzers (contin.)
An ion trap is a device that uses an oscillating electric field to store
ions. The ion trap works by using an RF quadrupolar field that traps
ions in two or three dimensions.
3D ion trap - Paul ion trap
2D ion trap - Four rod quadrupole ending in lenses that reflect
ions forwards and backwards in that quadrupole.
Conceptually, a Paul ion trap can be imagined as a quadrupole bent in
on itself in order to form a closed loop. The inner rod is reduced to a
point at the centre of the trap, the outer rod is the circular electrode,
and the top and bottom rods make up the caps.
In quadrupole instruments, the potentials are adjusted so that only ions
with a selected mass go through the rods.
The principle is different in this case. Ions of different masses are
present together inside the trap, and are expelled (by applying a
resonant frequency along z) according to their masses so as to obtain
the spectrum.
3. Mass Analyzers
3.2 Quadrupole ion traps (QITs).
To avoid ion losses by expansion, a pressure of helium gas which removes excess energy from the ions by
collision. This pressure hovers around 10−3 Torr (0.13 Pa). A single high-vacuum pump with a flow of about 40 l s−1
is sufficient to maintain such a vacuum compared with the 250 l s−1 needed for other mass spectrometers.
In the Paul ion trap the motion of the ions under the influence of
the applied potentials occurs in three dimensions, x, y and z. The z
motion resulting from the kinetic energy of the ions when they
enter the quadrupole field. However, due to the cylindrical
symmetry x2 + y2 = r2, it can also be expressed using z, r
coordinates.
Mathieu equation, whose solutions are known, is
3. Mass Analyzers
3.2 Quadrupole ion traps (contin.).
To have a stable trajectory, the movement of the ions must be such that during this time the coordinates never reach
or exceed r0 (r-stable) and z0 (z-stable). The complete integration of the Mathieu equation by the method of
Floquet and Fourier requires the use of a function e(α+iβ). Real solutions correspond to a continuously increasing,
and thus unstable, trajectory. Only purely imaginary solutions correspond to stable trajectories. This requires both
α = 0 and 0 <βu < 1
A simpler approximate equation holds for qu values lower than 0.4:
The iso-β lines for βu =0 (solid lines) and βu =1 (dotted lines)
3. Mass Analyzers
3.2 Quadrupole ion traps (contin.).
Typical stability diagram for a 3D ion trap. The value at βz =1 along the qz axis is qz = 0.908. At the upper
apex, az =0.149 998 and qz =0.780 909.
3. Mass Analyzers
3.2 Quadrupole ion traps (contin.).
The ions will not oscillate at this same ‘fundamental’ v frequency because of their inertia, which causes them to
oscillate at a ‘secular’ frequency f , lower than v, and decreasing with increasing masses. It should be noted that au
and qu, and thus β, are inversely proportional to the m/z ratio.
As the maximum value of β for a stable trajectory is β =1, the maximum secular frequency fz of an ion will be
half the fundamental v frequency.
The second important parameter which is a function of qz is the Dehmelt pseudopotential well. The trapping
efficiency of ions injected in the trap can be described using the pseudopotential well given by the following
equation:
3. Mass Analyzers
3.2 Quadrupole ion traps (contin.).
Ion trap with an RF voltage applied to the ring electrode,
providing the fundamental frequency v and its associated
variable amplitude V. Instead of injecting ions, electrons
may be injected for internal ionization. Variable RF
voltage can be applied to the end caps for ion excitation
or ion ejection.
As no DC voltage is applied, the 3D trap will be operated
along the qu axis, au =0.
qz is given by the following equation:
qz will increase if V increases, and decrease if m
increases.
3. Mass Analyzers
3.2 Quadrupole ion traps (contin.).
If V is increased, all the ions will have a higher qz value. If
this value is equal to 0.908, β = 1, and the ion has reached its
stability limit. A slight increase of V will cause this ion to
have an unstable trajectory, and will be expelled from the
trap in the z direction.
Thus 50% of the expelled ions will reach the detector.
This allows the ions present in the trap to be analyzed.
See the example at page No. 109 Hoffmann
Thus, besides trying to increase V at higher values without
arcing, the maximum observable mass can be increased by
reducing the size of the trap or using a lower RF frequency v.
3. Mass Analyzers
3.2 Quadrupole ion traps (contin.).
TOF analyser is well suited to the pulsed nature of the laser desorption ionization. The development of matrix-assisted
laser desorption/ionization TOF has paved the way for new applications not only for biomolecules but also for synthetic
polymers and polymer/biomolecule conjugates.
As all the ions acquire the same kinetic energy,
ions characterized by a distribution of their masses
present a distribution of their velocities.
Mass-to-charge ratios are determined by
measuring the time that ions take to move
through a field-free region between the source
and the detector.
Before it leaves the source, an ion with mass m
and total charge q = ze is accelerated by a potential
Vs. It electric potential energy Eel is converted into
kinetic energy Ek:
3. Mass Analyzers
3.3 Time-of-Flight Analyzers (TOF).
 In principle, the upper mass range of a TOF instrument has no limit, which makes it especially
suitable for soft ionization techniques. For example, samples with masses above 300 kDa have
been observed by MALDI-TOF.
 Another advantage of these instruments is their high transmission efficiency that leads to very
high sensitivity. For example, the spectrum from 10−15 mol of gramicidin and the detection of 100–
200 attomole amounts of various proteins have been obtained with TOF analyzers.
 All the formed ions are in principle analyzed contrary to the scanning analyzers that transmit ions
successively along a time scale.
 The analysis speed of TOF analyzers is very fast and a spectrum over a broad mass range can be
obtained in micro-seconds. So, it is possible in theory to produce in 1 second several thousand TOF
mass spectra over a very wide mass range.
 But in practice, for most of the applications, the weak number of ions detected in each individual
spectrum is insufficient to provide the required precision of mass or abundance measurement.
 It is actually impossible to record all these individual spectra one by one at such a rate without
exceeding the speed of data transfer and the capacity of data storage of most computers. Thus,
recorded spectra are generally the addition of a number of individual spectra.
3. Mass Analyzers
3.3 Time-of-Flight Analyzers (contin.).
Interesting characteristic of the TOF analyser lies in its easy mass calibration with only two reference points.
The terms in parentheses can be replaced with the constant A. A constant B is added to produce a simple equation for
a straight line. This constant B allows correction of the measured time zero that may not correspond exactly with the
true time zero.
Therefore, the conversion of flight times to mass supposes a preliminary calibration with two known molecules
(standards). Using their known m/z ratios and their measured flight times, this equation is solved for the two
calibration constants A and B. As long as the points are not too close together, a simple two-point calibration is
usually accurate.
Internal calibration is a method in which the flight times of the standard and unknown ions are measured from the
same spectrum providing the best possible match of experimental conditions for the three species involved. The
highest degree of mass accuracy is usually achieved through internal calibration.
Δm and Δt are the peak widths measured at the 50% level on the mass and time scales, respectively and Δx is the
thickness of an ion packet approaching the detector.
3. Mass Analyzers
3.3 Time-of-Flight Analyzers (contin.).
 The only way to have both high resolution and high sensitivity is to use a long flight tube
with a length of 1 to 2 m for a higher resolution and an acceleration voltage of at least 20 kV
to keep the sensitivity high.
 The most important drawback of the first TOF analysers was their poor mass resolution.
Mass resolution is affected by factors that create a distribution in flight times among ions with
the same m/z ratio.
 These factors are the length of the ion formation pulse (time distribution).
 The size of the volume where the ions are formed (space distribution).
 The variation of the initial kinetic energy of the ions (kinetic energy distribution), and so on.
 The electronics and more particularly the digitizers, the stability of power supplies, space
charge effects and mechanical precision can also affect the resolution and the precision of the
time measurement.
 The quality of its pulsed ion beam from MALDI is insufficient to obtain the high resolution
and high mass accuracy. This situation is substantially improved with the development of two
techniques: delayed pulsed extraction and the reflection.
3. Mass Analyzers
3.3 Time-of-Flight Analyzers (contin.).
Delayed Pulsed Extraction
The extraction pulse applied after a certain delay transmits more
energy to the ions which remained for a longer time in the source.
Consequently, the initially less energetic ions receive more kinetic
energy and join the initially more energetic ions at the detector.
So, delayed pulsed extraction corrects the energy dispersion of the
ions leaving the source with the same m/z ratio and thus improves the
resolution of the TOF analyser.
Lower pulse voltages or shorter delays are required to focus ions of
lower m/z ratio. In general, for a given m/z and initial velocity
distribution, greater voltage pulses require shorter time delays and
vice versa.
Delayed extraction complicates the mass calibration procedure.
MALDI-TOF experiments, optimum focusing conditions depend on
laser pulse width and fluence, the type of sample matrix, the sample
preparation method, and even the location of the laser spot on the
sample.
3. Mass Analyzers
3.3 Time-of-Flight Analyzers (contin.).
In the continuous extraction mode the ions with the same m/z ratio but with
different kinetic energy reach the detector at slightly different times,
resulting in peak broadening.
Reflectrons  Ions with more kinetic energy and hence with
more velocity will penetrate the reflectron more
deeply than ions with lower kinetic energy.
 Consequently, the faster ions will spend more time
in the reflectron and will reach the detector at the
same time than slower ions with the same m/z.
 However, the reflectron increases the mass
resolution at the expense of sensitivity and
introduces a mass range limitation.
The performance of the reflectron may be improved by using a two-stage reflectron, to reduce the size and to
improve the homogeneity of the electric field.
In this reflectron, two successive homogeneous electric fields of different potential gradient are used. The first stage is
characterized by an intense electric field responsible for the strong deceleration of the ions while the second stage is
characterized by a weaker field.
These two-stage reflectrons have the advantage of being more compact devices because of the strong deceleration of
the ions at the first stage, but they suffer from a lower transmission.
3. Mass Analyzers
3.3 Time-of-Flight Analyzers (contin.).
Changing B as a function of time allows successive
observations of ions with various values of m/q.
Instead of positioning a guide tube and detecting the ions
successively while scanning the magnetic field, it is also possible
to use the characteristic that ions with the same kinetic energy but
different m/q ratios have trajectories with different r values.
The ions with identical charge and mass are dispersed by a magnetic field according to their kinetic energy. In order to
avoid this dispersion, which alters the mass resolution, the kinetic energy dispersion must be controlled. This is
achieved with an electrostatic analyzer.
The magnetic analyzer is fundamentally a momentum analyzer.
3. Mass Analyzers
3.4 Electromagnetic Analyzers
Suppose a radial electrostatic field is produced by a cylindrical condenser. The trajectory is then circular and the
velocity is constantly perpendicular to the field.
Since the trajectory is independent of the mass, the electric field is not a mass analyzer, but rather a kinetic energy
analyzer, just as the magnetic field is a momentum analyzer.
Resolution depends inversely on the dispersion at the analyzer outlet. Three factors favour the dispersion, and thus the
loss of resolution:
1. If the ions entering the field do not have the same kinetic energy, they follow different trajectories through the field.
This is called energy dispersion.
2. If the ions entering the field follow different trajectories, this divergence may increase during the trip through the
field. This is called angular dispersion.
3. The incoming ions do not originate from one point, but issue from a slit. The magnetic or electric field can only
yield, at best, a picture of that slit. The picture width depends on the width of the slit and on the
magnifying effect of the analyzer.
3. Mass Analyzers
3.4 Electromagnetic Analyzers(contin.).
The electric sector separates the ions according to their kinetic energy.
 An ion entering the magnetic field along a trajectory
perpendicular to the field edge follows a circular trajectory.
 An ion entering at an angle α with respect to the previous
perpendicular trajectory follows a circular trajectory with an
identical radius and thus converges with the previous ion
when emerging from the sector.
 An ion entering the electric sector perpendicular to the field
edge follows a curved trajectory.
 However, if the ion trajectory at the inlet is not perpendicular
to the edge, its trajectory is longer if it enters the sector
closer to the outside and shorter if it enters the sector closer
to the inside.
3. Mass Analyzers
3.4 Electromagnetic Analyzers(contin.).
When a beam of ions with different kinetic energies
issues from the source, the electric and magnetic sectors
produce an energy dispersion and a direction focusing.
If two sectors with the same energy dispersion are
oriented, the first sector dispersion energy is corrected by
the second sector convergence.
Double focusing instruments use this principle.
3. Mass Analyzers
3.4 Electromagnetic Analyzers(contin.).
 The magnetic instrument’s sources must function with potentials Vs of about 10 kV. The vacuum in the source
must thus be very high so as to avoid arcing.
 Classical magnets were not well suited to fast scanning because of the hysteresis phenomenon and the magnet
heating up by the Foucault currents induced by rapidly changing magnetic fields. Lamellar magnets avoid such
inconveniences; they have been well developed and are now widely used.
 It can be shown that magnetic instruments function at constant resolution R=m/δm. As a result, δm varies in
proportion to m. In the low-mass range δm is small, while in the high-mass range it is large.
 Peak matching technique consists of comparing the masses of two compounds that are simultaneously ionized
in the spectrometer source: one is unknown and its exact mass is sought; the other is a reference and its mass is
known with accuracy.
 This comparison is achieved by a very rapid alternative modification of the acceleration voltage so as to focus the
two ions, the intensities of the magnetic and electric fields being kept constant. The match is perfect when the
two masses’ profiles exactly overlap.
 If the acceleration voltages necessary for the focusing of the two ions are known with accuracy, the mass of the
unknown compound can be determined with accuracy.
3. Mass Analyzers
3.4 Electromagnetic Analyzers(contin.).
Detectors are able to generate from the incident ions an electric current that is proportional to their abundance.
Detection of ions is always based on their charge, their mass or their velocity.
Faraday cup: based on the measurement of direct charge current that is produced when an ion hits a surface and
is neutralized.
Electron multipliers or electro-optical ion detectors: based on the kinetic energy transfer of incident ions by
collision with a surface that in turn generates secondary electrons, which are further amplified to give an
electronic current.
FTICR or orbitrap (OT): consists of a pair of metal plates within the mass analyzer region close to the ion
trajectories. Ions are detected by the image current that they produce in a circuit connecting the plates.
Significant amplification is often necessary to obtain a usable signal. 10 incident ions per second at the detector
corresponds to an electric current of 1.6×10−18 A.
Point ion collectors - made to count ions of a single mass at a time and therefore they detect the arrival of all ions
sequentially at one point.
Array collectors - photographic plates, image current detectors or array detectors, have the ability to count
multiple masses and detect the arrival of all ions simultaneously along a plane.
Efficiency generally decreases when the mass of the ion increases. The signal decreases exponentially with
increasing mass.
4. Detectors
Photographic Plate
Ions sharing the same m/z ratio all reach the plate at the same place and the position of the spots allows the
determination of their m/z values after calibration. The darkness of the spots gives an approximate value of their
relative abundance. This detector, which allows simultaneous detection over a large m/z range, has been used for many
years but is obsolete today.
Faraday Cup Because the charge associated with an electron leaving the wall of
the detector is identical to the arrival of a positive ion at this
detector, secondary electrons that are emitted when an ion strikes
the wall of the detector are an important source of errors if they are
not suppressed. The accuracy of this detector can be improved by
preventing the escape of reflected ions and ejected secondary
electrons.
The cup is coated with carbon because it produces few secondary ions. The shape of the cup and the use of a weak
magnetic field prevent also any secondary electrons produced inside to exit.
The disadvantages of this simple and robust detector are its low sensitivity and its slow response time.
FC generally used in the measurement of highly precise ratios of specific ion species as in isotopic ratio mass
spectrometry (IRMS) or in accelerator mass spectrometry (AMS).
4. Detectors
(contin.).
Electron Multipliers
The most widely used ion detector in mass spectrometry.
The discrete dynode electron multiplier is made up of a
series of 12 to 20 dynodes that have good secondary
emission properties. Thus a cascade of electrons is created
and the final flow of electrons provides an electric current at
the end of the electron multiplier that is then increased by
conventional electronic amplification.
A type of continuous-dynode electron multipliers (CDEM),
which is called a channeltron, is made from a lead-doped
glass with a curved tube shape that has good secondary
emission properties.
4. Detectors
(contin.).
 The amplifying power is the product of the conversion factor (number of secondary particles emitted by the
conversion dynode for one incoming ion) and the multiplying factor of the continuous dynode electron multiplier.
 Their lifetime is limited to 1 or 2 years because of surface contamination from the ions or from a relatively poor
vacuum.
 The conversion factor is highly dependent on the impact velocity of the detected ions and on their nature (mass,
charge and structure), so these detectors are not as precise as Faraday cups.
 Because of their slower velocity, large ions produce fewer secondary electrons and thus the efficiency decreases
when the mass of the ion increases.
 Conversion dynodes are thus very useful for detecting high-mass ions, especially with analyzers delivering ions
at low kinetic energy, such as quadrupoles or ion traps.
The microchannel plate (MCP)
It is a plate in which parallel cylindrical channels have been
drilled. The channel diameter ranges from 4 to 25 μm with a
centre-to-centre distance ranging from 6 to 32 μm and a few
millimetres in length.
The plate input side is kept at a negative potential of about 1
kV compared with the output side.
4. Detectors
(contin.).
 Electron multiplication is ensured by a semiconductor substance covering each channel
and giving off secondary electrons.
 The snowball effect within a channel can multiply the number of electrons by 105. A
plate allows an amplification of 102–104, whereas by using several plates the
amplification can reach 108.
 This detector is characterized by a very fast response time because the secondary
electron path inside the channel is very short. In consequence, it is well suited to TOF
analyzers, which need precise arrival times and narrow pulse widths.
 The large detection area of the microchannel plate allows the detection of large ion
beams from the analyzer without additional focalization.
 They are fragile, sensitive to air and their large microchannel plates are expensive.
4. Detectors
(contin.).
The microsphere plate (MSP)
 The electron multiplier consists of glass beads with diameters from 20
to 100 μm that are sintered to form a thin plate with a thickness of 0.7
mm.
 This plate is porous with irregularly shaped channels between the
planar faces. The surfaces of the beads are covered with an electron
emissive material and the two sides of the plate are coated to make
them conductive.
 A potential difference of between 1.5 and 3.5 kV is applied across the
plate, with the output side of the plate at the more positive potential.
 The microsphere plate offers some advantages over the microchannel
plate. It is less expensive and its gain of 106–107 is higher.
This higher amplification is due to the fact that nearly the entire surface of
the input side is active and therefore emits secondary electrons that will be
accelerated onto and through the plate to give the final signal. In
comparison, the surface of the microchannel plate between the
microchannels, which corresponds to about 50% of the entire surface, is
inactive.
4. Detectors
(contin.).
Electro-Optical Ion Detectors  This type of detector operates by converting ions to electrons
and then to photons. The most common electro-optical ion
detector is called the Daly detector.
 The phosphorescent screen surface is covered with a thin layer
of aluminum conductor to avoid the formation of a charge that
would prevent new electrons from reaching it.
 Its lifetime is longer than the lifetime of electron multipliers
because the photomultiplier is sealed in glass and held under
vacuum.
 This prevents contamination and allows the detector to
maintain its performance for a considerably longer period than
conventional electron multipliers.
 It has a fast response time and a similar sensitivity to electron
multipliers with an amplification ranges from 104 to 105.
 Another electro-optical ion detector, which is called the
electro-optical array detector, allows the simultaneous
measurement of ions spatially separated along the focal plane
of the mass spectrometer. It combines the microchannel plate
and Daly detector.
4. Detectors
(contin.).