Mass spectrometry (MS) is an analytical technique that is used to measure the molecular weight of the compounds. The results are typically presented as a mass spectrum, a plot of intensity as a function of the mass-to-charge ratio.
2. Mass
Spectrometry
Separation and analysis of the
fragments provides information about:
Molecular
weight
Structure
Mass spectrometry (Mass Spec or MS)
uses high energy electrons to break a
molecule into fragments.
4. Background
• The impact of a stream of high energy
electrons causes the molecule to lose an
electron forming a radical cation.
– A species with a positive charge and one
unpaired electron
+ e
-
C H
H
H
H H
H
H
H
C + 2 e
-
Molecular ion (M+)
m/z = 16
5. Background
• The impact of the stream of high energy
electrons can also break the molecule or the
radical cation into fragments.
(not detected by MS)
m/z = 29
molecular ion (M
+
) m/z = 30
+ C
H
H
H
+ H
H
H C
H
H
C
H
H
H C
H
H
C
H
H
H C
H
H
+ e
-
H C
H
H
C
H
H
H
6. Background
• Molecular ion (parent ion):
– The radical cation corresponding to the
mass of the original molecule
• The molecular ion is usually the highest mass
in the spectrum
– Some exceptions w/specific isotopes
– Some molecular ion peaks are absent.
H
H
H
H
C H C
H
H
C
H
H
H
8. Background
• Only cations are detected.
– Radicals are “invisible” in MS.
• The amount of deflection observed depends
on the mass to charge ratio (m/z).
– Most cations formed have a charge of +1
so the amount of deflection observed is
usually dependent on the mass of the ion.
9. Background
• The resulting mass spectrum is a graph of the
mass of each cation vs. its relative abundance.
• The peaks are assigned an abundance as a
percentage of the base peak.
• the most intense peak in the spectrum
• The base peak is not necessarily the same as
the parent ion peak.
10. Background
The mass spectrum of ethanol
SDBSWeb : http://riodb01.ibase.aist.go.jp/sdbs/ (National Institute of Advanced
Industrial Science and Technology, 11/1/09)
base peak
M+
11. Background
• Most elements occur naturally as a mixture of
isotopes.
– The presence of significant amounts of
heavier isotopes leads to small peaks that
have masses that are higher than the
parent ion peak.
• M+1 = a peak that is one mass unit higher
than M+
• M+2 = a peak that is two mass units higher
than M+
12. Easily Recognized Elements in MS
• Nitrogen:
– Odd number of N = odd MW
SDBSWeb : http://riodb01.ibase.aist.go.jp/sdbs/ (National Institute of Advanced
Industrial Science and Technology, 11/2/09)
CH3CN
M
+
= 41
13. Easily Recognized Elements in MS
Bromine:
M+ ~ M+2 (50.5% 79Br/49.5% 81Br)
SDBSWeb : http://riodb01.ibase.aist.go.jp/sdbs/ (National Institute of Advanced Industrial Science and Technology,
11/1/09)
2-bromopropane
M+ ~ M+2
14. Easily Recognized Elements in MS
• Chlorine:
– M+2 is ~ 1/3 as large as M+
SDBSWeb : http://riodb01.ibase.aist.go.jp/sdbs/ (National Institute of Advanced
Industrial Science and Technology, 11/2/09)
Cl
M+
M+2
15. Easily Recognized Elements in MS
• Sulfur:
– M+2 larger than usual (4% of M+)
SDBSWeb : http://riodb01.ibase.aist.go.jp/sdbs/ (National Institute of Advanced
Industrial Science and Technology, 11/1/09)
S
Unusually
large M+2
M+
16. Easily Recognized Elements in MS
• Iodine
– I+ at 127
– Large gap
ICH2CN
SDBSWeb : http://riodb01.ibase.aist.go.jp/sdbs/ (National Institute of Advanced
Industrial Science and Technology, 11/2/09)
Large gap
I+
M+
17. Fragmentation Patterns
• The impact of the stream of high
energy electrons often breaks the
molecule into fragments, commonly a
cation and a radical.
– Bonds break to give the most stable
cation.
– Stability of the radical is less
important.
18. Fragmentation Patterns
• Alkanes
– Fragmentation often splits off simple alkyl
groups:
• Loss of methyl M+ - 15
• Loss of ethyl M+ - 29
• Loss of propyl M+ - 43
• Loss of butyl M+ - 57
– Branched alkanes tend to fragment forming
the most stable carbocations.
21. IONISATION
METHODS
Electron Ionization (EI)
Chemical Ionization (CI)
• Secondary ion Mass Spectrometry (SIMS)
• Fast atom bombardment (FAB)
• Matrix Assisted Laser Desorption Ionization
(MALDI)
Desorption Ionisation Techniques
Electro Spray Ionization (ESI)
22. ELECTRON IONISATION (EI)
AIM: To convert sample into charge particle
A beam of electrons (from Tungsten filament) strikes the molecule in Ion Chamber
Collision b/w electrons and sample molecules, strips (eject) an electron from the
molecule creating a cation (positively charged species)
A repeller plate (+ve potential thus repel + ions, which carries low positive electrical
potential directs or expel the newly created ion towards a series of accelerating
plates.
These cations are directed towards a series of accelerating plates (i.e. a large
potential (is applied across these plates produces a beam of rapidlly travelling +
ions) (negative potential so as to attract the +ions)
Neutral molecule or unionized molecules if produced are drawn off by a vacuum pump
near the ion chamber and –vely charged ions are absorbed by repeller plates.
Further focusing slits directs the ions into uniform Beam going towards Mass
analyzer.
24. ELECTRON
IONISATI
ON (EI)
The energy required to remove an electron from
an atom or molecule is its Ionization Potential
or Ionization Energy.
Most organic compounds need 8-15 ev potential
but to produce reproducible pattern a
standard beam of 70 ev is needed.
Only about 103
the molecules present in the
sample are ionized. Excess energy imparted
to the sample during EI process leads to the
significant fragmentation of the molecular
ion.
Benefits
• well-understood & can be applied to virtually
all volatile compounds
• reproducible mass spectra
• fragmentation provides structural
information
• libraries of mass spectra can be searched
for EI mass spectral "fingerprint"
Limitations
• sample must be thermally volatile and stable
• the molecular ion may be weak or absent for
many compounds.
25. CHEMICAL IONISATION (CI)
Need for new technique: Electron ionization (EI) leads to fragmentation of the
molecular ion, which sometimes prevents its detection.
Chemical ionization (CI):
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. Consequently, chemical ionization is
complementary to electron ionization.
Sample molecules are combined with an ionized reagent gas (Primary ions) (present
in excess w.r.t. to the sample.
Collision of these primary ions produce stable population of secondary ions by
various mechanism- 1. Proton Transfer 2. Electron Transfer 3. Adduct
Formation
Almost any readily available gas or high volatile liquid can be used for CI. Common
ionizing reagent are methane, ammonia, isobutane and methanol.
26. CHEMICAL IONISATION (CI)
Methane as CI reagent gas:
The predominant ionization event is proton transfer from CH5
+
ion to the sample. The
methane is converted to ions as follows:
CH4 + e CH4
+*
+ 2e ----------------------( 1)
CH4
+*
+ CH4 CH5
+
+ *CH3 --------------------- (2)
Due to high pressure in the chemical ion source, there is every possibility of molecular ion
of the reagent gas (CH4
+*
) colliding with another methane molecule and most likely the
reaction is eq.2.
Now the introduction of the small amount of sample in the vapor phase in the CI Source
results into the reaction b/w reagent ion (CH5
+
) and the sample molecule leading to the
ion formation of the analyte/sample molecule.
M + CH5
+
(M+H)+ + CH4 --------------------- (3)
The (M+H)+ has one m/z value one amu (atomic mass unit) greater than that of molecular
ion.
27. Chemical Ionization
- Sample introduced to ionized reagent gas like:
Methane, Isobutane, Ammonia, others
- Collisions between sample & gas ions cause proton
transfers → produces [M+H]+ ions, not M+ ions.
- These are even electron ions
Benefits:
-Much less energy transferred <5 eV so less
fragmentation
-Abundance of molecular ions
-good for molecular weight determination
-less information about structure
28. CI Reagent Gases-Comparisions
Methane:
• good for most organic compounds
• usually produces [M+H]+, [M+CH3]+ depending on partial pressure [M+C2H5]+ adducts
• extensive fragmentation
Isobutane:
• usually produces [M+H] +
, [M+C4H9]+
adducts and some fragmentation
• adducts are relatively more abundant than for methane CI
• not as universal as methane
Ammonia:
• fragmentation virtually absent
• polar compounds produce [M+NH4]+ adducts
• basic compounds produce [M+H]+
adducts
• non-polar and non-basic compounds are not ionized
33. Desorption
Ionization
Techniques
Need: Both EI and CI requires a
relatively volatile (low mol wt)
sample.
There is need for a
technique that can ionize large
mol. wt. and non-volatile
molecules.
These are:
SIMS-secondary ion Mass
Spectrometry
FAB- Fast atom bombardment
MALDI-Matrix Assisted Laser
Desorption Technique
34. Desorption ionization techniques
In Desorption ionization, the sample to be analyzed is
dissolved or dispersed in a matrix and placed in the
path of high energy-
- beam of ions (SIMS)
- Neutral atoms (FAB)
- High intensity photons (MALDI)
- Beams of Ar+ and Cs+ are often used in SIMS
- Beams of neutral Ar or Xe atoms in FAB
- Nitrogen laser (337nm)/IR laser in MALDI
36. Desorption ionization techniques
The collision of these ions (SIMS)/Neutral atoms (FAB)/ Photons
(MALDI) with the sample ions ionizes some of the sample
molecules and ejects them from the surface.
The ejected ions are then accelerated towards the mass
analyzer.
Sample matrix- metal plate coated with viscous solution of the
sample (say in glycerol). The sample matrix should be non-
volatile, inert and a reasonably electrolytic to allow ion
formation. Common matrix compounds for SIMS and FAB
include Glycerol, Thioglycerol,3-nitrobenzyl alcohol, di and tri
ethanolamine and mix of dithiotheritol (DTT) and
dithioerytheritol. Matrix protect sample from excess energy
38. Fast atom
Bombardment
(FAB)
The analyte is dissolved in the viscous liquid and
ionization is achieved by bombardment of
fast-moving neutral atoms i.e. Xe and Ar
usually.
In order to achieve high kinetic energy (Fast
moving gaseous atoms) the atoms of the gas
are first ionized (by EI Tech.) and these ion
are passed through an electric field- ions
are accelerated under the influence of
electric field- these accelerated ion enters
into the chamber containing further gas
atoms and collision of ions and atoms (Xe
and Ar) leads to charge exchange (so as to
neutralize the charge generated) in the
collision cell. Now the fast neutral atom
produced in this process are preceded
towards sample matrix. The remaining ions
are removed before sample bombardment
by means of a deflector plate.
39. Fast atom bombardment ( FAB)
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.
Ar + e Ar+ acceleration (5-15 KeV)
Ar+ + Ar Ar + Ar+
fast slow + 8 KeV slow
fast
(This fast atom will attack)
45. Fast atom Bombardment
Ionization from Protonation (M+H)+, cation enhancement
(M+23(Na)+) or deprotonation (M-H)-
Both negative and positive ions are produced in matrix
desorption techniques. Either of these two can be
analyzed by selecting proper exit slit method.
Observed peaks in FAB are those of matrix cluster ions,
analyte ions (M+ and M-), impurities, and ions of
matrix modifiers.
But the stability of carbocations are more, so +ve ion
analysis is better.
46. Matrix
assisted
Laser
Desorption
Technique
(MALDI)
Laser desorption methods use a pulsed
laser to desorb species from a target
surface.
The analyte is dissolved in a solution
containing excess of matrix such as
cinnamic acid that has a chromophore
that absorbs at a laser wavelength.
A small amount of this solution is placed
on the laser target. The matrix absorbs
the energy from the laser pulse and
produces a plasma that results in
vaporization and ionization of sample
analyte.
47. MALDI: Matrix Assisted Laser
Desorption Ionization
1. Sample is mixed with matrix
(X) and dried on plate.
2. Laser flash ionizes matrix
molecules.
3. Sample molecules (M) are
ionized by proton transfer:
XH+ + M MH+ + X.
48. Matrix
assisted
Laser
Desorption
Technique
(MALDI)
Laser desorption methods use a pulsed
laser to desorb species from a target
surface.
The analyte is dissolved in a solution
containing excess of matrix such as
cinnamic acid that has a chromophore that
absorbs at a laser wavelength.
A small amount of this solution is placed on
the laser target. The matrix absorbs the
energy from the laser pulse and produces
a plasma that results in vaporization and
ionization of sample analyte.
50. MALDI: Matrix Assisted Laser
Desorption Ionization
Benefits
- rapid and convenient molecular weight determination
Limitations
• MS/MS difficult
• requires a mass analyzer that is compatible with
pulsed ionization techniques
• not easily compatible with LC/MS
Mass range
• Very high Typically less than 500,000 Da.
51. Electrospray
Ionization
(ESI)
More useful tech. for studying high
mol wt biomolecules and other
labile and non-volatile compounds
In this spray techniques- A soln
containing analyte is sprayed at
atm. pressure, through an
interface into the vacuum of the
ion source chamber. A combination
of thermal (heat) and pneumatic
(gas) means is used to desolvate
the ions as they enter the ion
chamber.
Two types of spray techniques:
1. ESI 2. TSI
52. Electrospray
ionization
(ESI)
Electrospray ionization (ESI) is a technique used
in mass spectrometry to produce ions using
an electrospray in which a high voltage is applied to a
liquid to create an aerosol.
It is especially useful in producing ions
from macromolecules because it overcomes the
propensity of these molecules to fragment when
ionized.
ESI is different than other atmospheric pressure
ionization processes (e.g. MALDI) since it may produce
multiply charged ions, effectively extending the mass
range of the analyser to accommodate the kDa-
MDa orders of magnitude observed in proteins and
their associated polypeptide fragments.
53. Spray Ionization (SI)
In ESI, The capillary through which the solution passes
has high voltage potential across it’s surface and
small, charged droplets are expelled into the ion
chamber. In this chamber liquid nitrogen (drying gas)
evaporates the solvent molecule from droplets until
only solvent free sample ions are left in the gas
phase.
In TSI, occurs through similar mechanism but
relies on a preheated capillary rather than one with
an electrostatic potential to initially form the
charged droplets.
54. Electrospray ionization (ESI)
Benefits
- rapid and convenient
molecular weight
determination
Limitations
• MS/MS difficult
• requires a mass analyzer
that is compatible with
pulsed ionization techniques
• not easily compatible with
LC/MS
Mass range
• Very high Typically less
than 500,000 Da.
57. Spray
Ionization
(SI)
These spray techniques produces
multiply charged ions with number of
charge tending to increase as the mol
wt increases. e.g ESI-MS spectrum of
lysozyme from a chicken egg white
The formation of multiply charged ions
is particularly useful in the analysis of
proteins. Typical protein carry many
protons due to the presence of basic
amino acid side chains, resulting in
peaks at 600-2000 m/z for a protein
with mol wt of 20000 amu.
58. Spray
Ionization
(SI)
ESI-MS is not limited to study of
large biomolecules however many
small molecules with mol. Wt. in
the 100-1500 range can be studied
Compounds that are too volatile to
be introduced by direct probe
methods or are too polar or
thermally labile to be introduced by
GC-MS method are ideal for study
by LC-MS using ESI technique
62. MASS
ANALYZER
The region of mass spectrometer
where the ions are separated
according to their m/z ratio.
There are different type of mass
analyzers:
1. Magnetic Sector Mass Analyzer
2. Double Focusing Mass Analyzer
3. Quadrupole Mass Analyzer
4. Quadrupole Ion Trap Mass
Analyzer
5. Time of Flight (TOF) Analyzer
65. The
Magnetic
Sector mass
analyzer
Separation in this way is effected by the
application of a magnetic field perpendicular to
the motion of the ions leaving the ion-source.
The charged particle is deflected to a circular
motion of a unique radius in a direction
perpendicular to the applied magnetic field.
Deflections of about 30 to 180 degrees are
achieved
Ions in the magnetic field experience two equal
forces; force due to the magnetic field and
centripetal force.
66. The Magnetic Sector mass analyzer
In this type of mass analyzer, the ions are passed
between the poles of the magnet. In the magnetic
field, charged particles describes a curved flight
path (Recall NMR Spectroscopy).
The K.E of an accelerated ion will be:
1/2mv2 = ZV ----------- (1)
The radius of this path will be:
r= mv/ZB -------------- (2)
B- strength of magnetic field
67. The Magnetic Sector mass analyzer
Combining above two eq. we get:
m/z = B2r2/2V ------ (3)
From eq. 3, greater the value of m/z, the larger the radius of
curved path.
But the analyzer have a fixed radius of curvature. A particle
with correct m/z ratio can negotiate the curved analyzer
tube and reach the detector. While particles having m/z
ratio that are either too high or too small, strikes the
sides of the analyzer tube and do not reach the detector.
Means ions of only one mass is detected- which is not
useful. Therefore, to solve this problem magnetic strength
is continuously varied( called Magnetic field scan) so that
all the ions produced in the ionization chamber can be
detected.
68. The Magnetic Sector mass analyzer
Basically, the ions of a certain m/z value will have a unique
path radius which can be determined if both magnetic
field magnitude B, and voltage difference V for region of
acceleration are held constant. when similar ions pass
through the magnetic field, they all will be deflected to
the same degree and will all follow the same trajectory
path. Those ions which are not selected by V and B values,
will collide with either side of the flight tube wall or will
not pass through the slit to the detector. Magnetic sector
analyzers are used for mass focusing, they focus angular
dispersions.
69. The
Electrostatic
Sector mass
analyzer
Separates the ions using an electric field.
Electrostatic sector analyzer consists of two curved
plates of equal and opposite potential.
As the ion travels through the electric field, it is
deflected and the force on the ion due to the
electric field is equal to the centripetal force on
the ion.
Here the ions of the same kinetic energy are
focused, and ions of different kinetic energies are
dispersed.
Electrostatic sector analyzers are energy focusers,
where an ion beam is focused for energy.
70. Double Focusing Mass Analyzers
Electrostatic and magnetic sector analyzers when employed
individually are single focusing instruments. However, when
both techniques are used together, it is called a double
focusing instrument., because in this instrument both the
energies and the angular dispersions are focused.
• A double focusing mass analyzer can be considered to exists
of two stages: electrostatic sector and magnetic sector
• Better Resolution due to additional electrostatic sector.
• The electrostatic sector acts as a kinetic energy selector. By
narrowing the range of the kinetic energy of the ions that
enter the mass analyzer part, the paths of these ions is more
focused, and results in a better resolution.
72. Quadrupole
Mass Analyzer
• Has four parallel metal rods arranged
parallel to direction of the ion beam
• A combination of RF and DC voltages is
applied to the rods generating an oscillating
electrostatic field in the region between the
rods
• Depending upon the RF amplitude to DC
voltage, ions acquire an oscillation in this
electrostatic field
• Ions with incorrect m/z ratio (too small or
too large) undergo unstable oscillation
• The amplitude of oscillation continues to
increase until the particles strike on of the
rods.
• Ions with correct m/z ratio undergoes
stable oscillation and travel down the
quadrupole axis with a “cork-screw
trajectory” and not strike any four rods and
pass through analyzer to reach the detector
(one mass pass through at a time).
• Can scan through all masses or sit at one
fixed mass.
73. Quadrupol
e Mass
Analyzer
• Quadrupole
analyzers can be
scanned from high to
low values of m/z.
• Found generally in
GC-MS system
• Low resonance
instrument incapable of
providing exact
elemental composition
of the sample
74. Double Focusing Mass Analyzers
mass scanning mode
m1
m3
m4 m2
m3
m1
m4
m2
single mass transmission mode
m2 m2 m2 m2
m3
m1
m4
m2
76. Quadrupole
Ion Trap
Mass
Analyzer
Operates by similar principles as the linear quadrupole
described earlier
The ion trap consists of three cylindrically symmetrical
electrodes: two end cap electrodes, A and B (connected to
each other), and a ring C.
An alternating DC and RF potential is applied between the end
caps and the ring electrodes.
In Linear quadrupole mass analyzer, ions of different m/z ratio
are allowed to pass in turn through quadrupole by adjusting
the RF and DC Voltage. But in Ion Trap, Ions of all M/Z value are
in trap simultaneously, oscillating in concentric trajectories
The use of an r.f. voltage causes rapid reversals of the field
direction so the ions are alternately accelerated and
decelerated in the axial (z) direction and vice versa in the radial
direction.
77. Ion Trap Mass Analyzer
The sweeping the RF potential in this way results in the removal
of the ions with increasing m/z value (Lighter ions will leave
first). Ejected from trap in the axial direction towards the
detector- Process is known as Resonant Ejection.
Spectra is complicated- b’ coz the ion trap contains ions of all
values of m/z at the same time (as well as neutral molecule
that were not ionized prior to entering to trap), ion trap mass
analyzers are also sensitive to overload and ion molecule
collision is possible. These neutral molecule moves in a random
path in the trap and collide with ions. This event result in
further ionisation and is known as self CI.
Self CI can be minimized-by increasing ionization efficiency
Reducing the number of ions in the ion trap( by injecting less
sample)
78.
79. Time of
Flight
(TOF)
Mass
Analyzer
Time-of-flight (TOF) is the least
complex mass analyzer in terms of its
theory
The TOF mass analyzer is based on the
simple idea that velocities of two ions
created at the same instant with the
same kinetic energy, will vary depending
on the mass of the ions- the lighter ion
will have the higher velocity.
Ions are given a defined kinetic energy
and allowed to drift through a field-free
region (0.5 to several meters)
Ions are separated on the basis of the
time t needed to travel a path L.
If these ions are travelling towards the
detector, the faster (lighter) ion will
strike the detector first.
The time ions arrive at the detector is
measured and related to the m/z ratio
80. Time-of-flight (TOF) Mass Analyzer
+
+
+
+
Source Drift region (flight tube)
detector
V
• Ions are formed in pulses.
• The drift region is field free.
• Measures the time for ions to reach the detector.
• Small ions reach the detector before large ones.
81. TOF Concept
• A packet of stationary ions is accelerated to
a defined kinetic energy and the time
required to move through a fixed distance is
measured.
• First TOF design published in 1946 by W.E.
Stephens
Detector
82. TOF
advantages
•Ions are not trapped (quad, IT, FTICR) nor are their flight paths curved
(BE sectors)
•Detection efficiencies induce practical limits of a few hundred kDa (M+H)+
Theoretically unlimited mass range
•Analysis is very rapid (40+ kHz acquisition possible)
•Wide range of m/z’s can be measured with good sensitivity
Instrument is not scanning (it is dispersive)
Moderate to high resolving powers (5,000-20,000+)
Moderate cost ($100k to $500k)
Relatively high duty cycle
Couples extremely well with pulsed ion sources (e.g.
MALDI)
83. TOF Disadvantages
• Requires high vacuum (<10-6 torr)
• Coupling to continuous ion sources (e.g. ESI or EI) not
straight forward
• Requires complex and high-speed electronics
– High acceleration voltages (5-30 kV)
– Fast detectors (ns or faster)
– GHz sampling digital conversion
– Large volumes of data can be generated quickly
• Limited dynamic range
– Often 102 or 103 at most
• High resolution instruments can get rather large
84. Time-of-Flight Theory
From Physics 1: (1) KE = ½mv2
From Physics 2: (2) KE = z*U = ½mv2
All ions accelerated by the same voltage, U
From Physics 1: (3) ΔX= v0TOF + ½aTOF2
(5) TOF = ΔX/v0
1,000 Th ion @ 19 kV, v ≈ 60 km/sec
ΔX same for all ions = D (flight tube length)
No acceleration in flight tube. TOF α U-1 α (m/z)½
2
/
1
0
*
*
2
)
4
(
m
z
U
v
z
m
U
X
TOF tube
flight *
*
2
)
6
( _
85. Mass Scale Calibration
• TOF α (m/z)1/2 or m/z α TOF2
• Mass scale is calibrated measuring flight times known
m/z ions and fitting them to a polynomial equation
• (7) TOF = a*(m/z)1/2 + b also
– Higher order calibrations are often used
• 5th order on some commercial instruments
• Form can be (7a) m/z = A*TOF2 + B*TOF + C
86. Real-
world
TOF MS
Previous examples all
assumed ions formed at rest,
at the same time, and all at
the same position in the
source
In reality, ions are formed
throughout the source at
various times, in various
locations, with a range of
initial kinetic energies
Practical TOF instrument
design relies on minimizing
the contributions of each of
these realities