Once analyte ions are formed in the gas phase, a variety of mass analyzers are available and used to separate the ions according to their mass-to-charge ratio (m/z). Mass spectrometers operate with the dynamics of charged particles in electric and magnetic fields in vacuum described by the Lorentz force law and Newton’s second law of motion (9):
F = z(E + v x B) (Lorentz force equation)
F = ma (Newton’s second law of motion)
where F is the force applied to the ion, m is the mass of the ion, a is the acceleration, q is the ionic charge, E is the electric field, and v x B is the vector cross product of the ion velocity and the magnetic field. Combining those equations results in the equation that describes the motion of charged particles:
(m/z)a = E + v x B
Two particles with the same physical quantity m/z behave identically, and all mass spectrometers measure m/z rather than m. Types of mass analyzers include: magnetic or electric sectors, time-of-flight instruments (TOF), quadrupoles (Q), ion traps (IT), and instruments that perform Fourier Transformations of image currents of ion trajectories (FT), but they all operate according to this same law or equation. Some mass spectrometers use two or more mass analyzers for tandem mass spectrometry.
A sector mass analyzer uses an electric and/or magnetic field to change the direction of the paths of ions accelerated through the mass analyzer (Figure 5). Ions enter a magnetic or electric field that bends the ion paths depending on their mass-to-charge ratios (9, 22). This results in greater deflection of ions with low m/z values compared to those with higher m/z values. The relative abundances of ions that reach the detector are measured. The analyzer can select a narrow or range of m/z values or scan through a range of values to catalog the ions.
Figure 6 illustrates the operating principles of time-of-flight (TOF) mass analyzers, which are often used in conjunction with MALDI ion sources (15, 16). When kinetic energy is imparted to a group of ions with various m/z values by application of an electric field and the ions are allowed to drift in a region of constant electric field, they traverse the path from the ion source to the detector in a time that depends upon their m/z ratios. Under ideal conditions, identical kinetic energy is imparted to all ions in the group:
KE = [mv2]/2 = zeEs
where KE = kinetic energy; m = ion mass; v = ion velocity; z = number of charges; e = the charge on an electron in coulombs; E = electric field gradient; and s = the distance from ion source to detector).
Rearranging the above equation reveals that:
m/z = (2eEs)/v2
Since v2 is inversely proportional to m/z, ions with lower m/z values travel with greater velocity (and thus arrive at the detector more rapidly) than those with higher m/z values. Early TOF mass analyzers had relatively poor resolution (R), which is the ability to distinguish m1/z from m2/z. (If the difference between those values is Dm and their mean is M, then R is defined as M/Dm.) The low R reflected deviation from the ideal condition that identical KE is imparted to all ions in the group. Various factors create some spread among KE values, even among ions with identical m/z values. Two developments have greatly increased the resolving power of modern TOF mass analyzers: delayed extraction and the reflectron (15).
Among the factors that might contribute to KE spread are collisions with neutrals or other ions in the plume created above the analyte + matrix spot of laser beam impact that causes ion formation. This could cause differences in initial velocities among individual ions of identical m/z value. A fraction of the final velocity achieved by ions of a given m/z value as they are accelerated out of the ion source into the field free region includes this initial velocity component. Delayed extraction involves interposing a brief interval between ion creation by the laser flash and ion acceleration by application of the electric field. This allows the dense plume of MALDI-generated ions/neutrals to dissipate before ions are accelerated out of the ion source, and it reduces the broadening of ion velocity distribution from collisional processes in the ion source. This results in narrower ion arrival time distributions at the detector and better mass resolution. The reflectron provides an additional means to compensate for the broadening of the range of flight times among ions of identical m/z by focusing the ion packets in space and time at the detector.
Quadrupole mass analyzers (Figure 7) use oscillating electrical fields to selectively stabilize or destabilize ions passing through a radio frequency (Rf) quadrupole field and are essentially mass filters that transmit only ions of a selected m/z value to achieve a stable trajectory that allows them to arrive at the detector (23). Ions of other m/z values collide with the rods or walls of the apparatus and are destroyed/not detected. The quadrupole consists of four parallel metal rods. Each opposing rod pair is connected together electrically and a Rf alternating current voltage is applied between one pair of rods and the other. A direct current voltage is then superimposed on the Rf voltage, and this causes the ions to adopt an irregular, oscillatory trajectory as they traverse the region bounded by the rods. For a given ratio of voltages, only ions of a specific m/z value reach the detector, and other ions with unstable trajectories are collisionally annihilated. This allows selected monitoring of ions of a particular m/z value, or a mass spectrum can be obtained by scanning through the m/z range of interest over time.
Quadrupole ion trap mass analyzers (Figures 8 & 9) operate on the same physical principles as quadrupole mass analyzers, but the ions are trapped in stable orbits and then sequentially ejected (23-26). Both 3D (Paul Trap) and linear ion traps use DC and radio frequency (Rf) oscillating AC electric fields to trap ions. The 3D trap consists of two hyperbolic metal electrodes with their foci facing each other and a hyperbolic ring electrode halfway between the other two electrodes (Figure 8). The ions are trapped in the space between these 3 electrodes by AC (oscillating, non-static) and DC (non-oscillating, static) electric fields. The AC radio frequency voltage oscillates between the two hyperbolic metal endcap electrodes if ion excitation is desired. The driving AC voltage is applied to the ring electrode. The ions are first pulled up and down axially while being pushed in radially. The ions are then pulled out radially and pushed in axially (from the top and bottom). In this way the ions move in a complex motion that generally involves the cloud of ions being long and narrow and then short and wide, back and forth, oscillating between the 2 states (Figure 9).
Illustrated in Figure 10 is a mechanical model of dynamic stabilization in the trap in which equipotential lines form a saddle surface. When a small ball is placed on the surface, its position is unstable and it rolls down. If, however, the disk is rotated with a frequency appropriate to the potential parameters and the mass of the ball, it remains on the surface making small oscillations. Figure 11 illustrates the trajectory of a trapped ion.
There are many methods to separate and isolate ions of specific m/z values using ion traps. One commonly used is the mass instability mode in which the Rf potential is ramped so that orbits of ions with a mass a > b are stable while ions with mass b become unstable and are ejected on the z-axis onto a detector (23-25). Ions can also be ejected by resonance excitation, whereby a supplemental oscillatory excitation voltage is applied to the endcap electrodes, and the trapping voltage amplitude and/or excitation voltage frequency is varied to bring ions into a resonance condition in order of their m/z values. Since the mid-1980’s most 3D traps have used ~1 mtorr of helium as a damping gas.
Linear (2D) ion trap mass analyzers (Figures 12 & 13) use a set of quadrupole rods to confine ions radially and a static electrical potential on end electrodes to confine ions axially (26). The linear form of the trap can be used as a selective mass filter, as described above, or as a trap by creating a potential well for ions along the axis of the electrodes. Advantages of the linear trap design are increased ion storage capacity, faster scan times, and simplicity of construction. Thermo Fisher’s LTQ (Linear Trap Quadrupole) is an example of a linear ion trap, and its overall configuration is illustrated in Figure 12 (26). Figure 13 illustrates the voltages necessary to operate the 2D ion trap, which include: three DC voltages applied to the separate sections of each rod to produce an axial trapping field; two phases of the primary Rf voltage applied to the rod pairs to produce the radial trapping field; and two phases of supplemental AC voltage applied across the X rods for isolation, activation & ejection of ions.
Fourier transform ion cyclotron resonance mass analyzers (Figure 14) measures m/z by detecting the image current produced by ions accelerated outwards from a common center along a spiral path (i.e., cyclotroning) in a magnetic field. Instead of measuring the deflection of ions with a detector such as an electron multiplier, the ions are injected into a Penning trap (a static electric/magnetic ion trap illustrated in Figure 14, left panel) where they effectively form part of a circuit (27-29). Detectors at fixed positions in space measure electrical signals from ions that pass near them over time producing cyclical signals. The center and right panels of Figure 14 illustrates the trajectory of an ion in a Penning trap. Since the cycling frequency of an ion is determined by its mass-to-charge ratio, the cyclical signal can be deconvolved by performing a Fourier transform (FT) on the signal. FTMS has the advantage of high sensitivity (since each ion is ‘counted’ more than once) and extremely high resolution and thus precision.
The principle of ion cyclotron resonance (ICR) is that ions have a fundamental oscillation frequency (resonant frequency) in a magnetic field. Ions trapped in the ICR cell are excited by a resonant excitation pulse into a coherent orbit (Figure 15). The excitation amplifier is then turned off and the ions continue to orbit at their final radius. Ions moving near electrodes cause an image charge to form on these electrodes to balance the ions’ electric field. In the case of a circular orbit, this image charge will oscillate at the ion’s resonant frequency and can be detected by a sensitive preamplifier circuit, digitized, and stored in computer memory. To detect all ions in the spectrum, a sweep is performed through all expected frequencies, and the image current is deconvolved using Fast Fourier Transformation to generate the mass spectrum (Figure 16).
In an Orbitrap mass analyzer (Figure 17), ions are electrostatically trapped in an orbit around a central, spindle-shaped electrode (30). The electrode confines the ions so that they both orbit around the central electrode and oscillate back and forth along the central electrode’s long axis. This oscillation generates an image current in the detector plates that is recorded by the instrument. As described above, the frequencies of these image currents depend on the m/z ratio of the individual ions, and mass spectra are obtained by Fourier transformation of the recorded image currents just as for ion cyclotron resonance (ICR) mass spectrometers. Both ICR and Orbitrap Fourier Transform instruments have extremely high resolving power, mass accuracy, sensitivity, and dynamic range.