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The CHROMacademy Essential Guide

Quadrupole Analyzers and MS/MS Analysis

The Essential Guide from LCGC’s CHROMacademy presents an educational webcast on Quadrupole Analyzers and MS/MS Analysis. In this session, Dr. Kevin Schug (CHROMacademy LC Department Dean) and Scott Fletcher (Technical Business Development Manager, Crawford Scientific), present a definitive guide to the theory, instrumentation and application of this now common place technique. The session will initially consider the need for mass analyzers before concentrating on the quadrupole, which has become a mainstay for the majority of analytical laboratories. The impact the quadrupole design, geometry and applied voltages have on ion stability will be investigated. Special attention will be reserved for the electrostatic fields created within the quadrupole and the resulting equations of motion. Quadrupole resolution, sensitivity and mass accuracy will also be considered. We will then continue to review the additional benefits and design changes required in order to operate quadrupoles in tandem (MS/MS). Typical MS/MS experiments will then be reviewed individually and their specific operation and benefits presented and explained.

A must see for everyone undertaking, or looking to undertake, LC-MS or LC-MS/MS analysis..

  sponsored by Thermo scientific
Scott Fletcher
Technical Manager
Crawford Scientific

Kevin Schug
Assistant Professor
University of Texas at Arlington


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Topics includeMass Analyzers

  • Why are Mass Analyzers required?
  • Introduction to Quadrupole Mass Analyzers
  • Quadrupole Design and Orientation
  • Quadrupole Voltages and Electrostatic Fields
  • Stable and Unstable / Collisional Trajectories
  • Equations of Motion
  • Quadrupole Resolution and Sensitivty
  • Scan vs. Selected Ion Monitoring
  • Quadrupole Mass Accuracy
  • RF only Ion Bridges
  • Introduction to Tandem Quadrupole (MS/MS) Mass Analyzers
  • Benefits of MS/MS Mass Analyzers
  • Design of MS/MS Mass Analyzers
  • Typical MS/MS Experiments

Who Should Attend:

  • Anyone undertaking, or looking to undertake, LC-MS or LC-MS/MS analysis

Key Learning Objectives:

  • Understand what advantages mass analysis offers
  • Appreciate the specific benefits of quadrupole mass analyzers
  • Explain the design and orientation of the modern bench-top quadrupole mass analyzer
  • Understand how voltages and electrostatic fields are used to control stable and collisional trajectories of ions and the resulting equations of motion
  • Describe the levels of resolution, sensitivity and mass accuracy that can be expected from quadrupole mass analyzers
  • Discuss how quadrupoles can be operated as RF only ion bridges and other multipole arrangements that can be employed
  • Appreciate the benefits associated when operating quadrupole mass analyzers in tandem (MS/MS) and the necessary design requirements
  • Describe typical MS/MS experiments and explain their specific operations and benefits


Quadrupole mass analyzers are the most common type of mass analyzers found in analytical laboratories.   They were originally thought to be only suitable for residual gas analysis due to the limited mass range over which they operate, however with the advent of ElectroSpray Ionization (ESI) they can now be used for analytes whose masses exceed tens of thousands of Daltons, due to multiple charging effects.  Following successful hyphenation with HPLC, the original LC-MS quadrupole mass spectrometers were reserved for research laboratories.  With their cost reducing in the proceeding years alongside greater reliance on their ability to elucidate structural information and increased sensitivity they have now become the mainstay of the modern analytical laboratory. Quadrupole mass analyzers are now routinely employed for qualitative as well as quantitative work in both LC-MS and GC-MS using Electron Ionisation (EI) and Chemical Ionisation (CI).   Greater versatility has been realised with the coupling of two analyzers, most commonly two quadrupoles, however other combinations with Time of Flight and Trap mass analysers are also available.  LC-MS/MS systems can provide enhanced structural elucidation capability as well as increased sensitivity.  

sponsored by Thermo scientific




Quadrupole mass analyzers were first described and developed in 1953 by the West German physicists Wolfgang Paul and Helmut Steinwedel whilst working at the University of Bonn[1].  This was a continuation of the earlier work carried out in Athens by the electrical engineer Christophilos.  Electric fields are used to separate ions according to their mass-to-charge ratio, m/z (ratio of mass in Daltons (Da) to integer number of charges, z), as they pass along the central axis of parallel and equidistant poles or rods.  The rods have two voltages applied, one of which is a fixed direct current whilst the second, an alternating current, cycles with a superimposed radio frequency.



DC (Direct current or continuous current): Is the constsnt flow of electric charge from high to low potential.

AC (Alternating Current): is the movement of electric charge periodically reversing in direction (typically 50 – 60 Hz)

RF (Radio Frequency): The range of electromagnetic frequencies above the audio range and below infrared (from 10kHz to 300 GHz).


The magnitude of the applied electric field can be ordered such that only ions with a specific m/z ratio can travel through the quadrupole, exiting the analyser and being detected.  Ions with all other m/z would be deflected onto trajectories that would cause them to collide with the quadrupole rods and discharge, or be ejected out of the mass analyzer and removed via the vacuum.   The quadrupole is often referred to as an exclusive detector as only ions with a specific m/z are stable in quadrupole at any one time; all other ions are removed from the quadrupole and not detected.   Those ions with a stable trajectory are often referred to having non-collisional, resonant as well as stable trajectories.  Ions that are ejected from the quadrupole are often referred to as possessing unstable or collisional trajectories. 


« Figure 1 demonstrates a simplified operating principle of the quadrupole mass analyzer.


sponsored by Thermo scientific





Ideal Quadrupole Geometry


The ideal quadrupole mass analyzer consists of four rods with a hyperbolic cross section [2].   The quadrupole rods are typically constructed using molybdenum alloys due to their inherent inertness and lack of activity. 


« Figure 2 below demonstrates the ideal quadrupole geometry.


However, for ease of manufacturing many manufacturers chose to fabricate high precision hyperbolic surfaced rods by employing cylindrical poles in the four corners of an imaginary square. 

Figure 3 » exhibits the more common approach of mimicking an ideal hyperbolic geometry by employing cylindrical rods – please note that the quadrupole rods and spacing is not to scale but purely for ease of description.


Common quadrupole orientation - Figure 3 »




common quadrupole orientation

When utilizing cylindrical rods it is essential that the faces of the opposing rods are separated by a distance of 1/1.148 times the rods diameter.  This ratio ensures that the geometric center of the quadrupole approximates an ideal hyperbolic field with a resultant electric field of zero – see Figure 4 ».


Equipotential lines for a hyperbolic quadrupole field - Figure 4 »





hyperbolic quadrupole field

For the quadrupole to operate effectively very high degrees of accuracy and precision are required, in the µm region, for not only the machining of the rods but also their relative positioning.  Figure 5 » not only highlights typical rod lengths and diameters and the quadrupole radius, but also emphasizes the x, y and z axis.

  • Ions travel along the direction of the horizontal x-axis due to the quadrupole rods lying in the x-axis working in tandem.
  • Ions travel along the direction of the vertical y-axis due to the quadrupole rods lying in the y-axis working in tandem.
  • Ions will travel through the quadrupole along the z-axis due to the momentum that is provided by a pusher voltage or a potential difference applied between the quadrupole entrance and exit


Typical quadrupole geometry and axis - Figure 5 »



hyperbolic quadrupole field


The quadrupole rods lying in the x-axis are diametrically opposed to those lying in the y-axis.  Whilst it is a common misconception that the quadrupole mass analyzer consists of a pair of positive and negative rods, this is not quite the whole story.   Due to the voltage oscillating at a Radio Frequency (commonly known as the ‘RF Voltage’), each pair of rods will be successively positive then negative and then back to positive and so forth.   In essence there will always be a pair of positive and negative rods, however they will alternate over time.  Unlike simple deflection and acceleration of ions in magnetic and electric fields, the trajectory of the ions within the quadrupole is a little more complex.  Each diametrically opposed pair has two voltages applied;

  • A resolving DC voltage – U
  • A voltage oscillating at an RF frequency – Vcos(ωt)

Where;  V is the applied voltage
                  cos is the sinusoidal cycle of the wave
                  ω is the frequency
                  t is the time domain

Which pair of rods starts off as being positive or negative is dictated by the polarity of the DC voltage (sometimes known as the ‘Resolving DC’).  The voltages applied to each pair of rods can be defined by equations 1 and 2.

Equation 1

Positive rods= +[U+Vcos(ωt)]

Equation 2

Negative rods= -[U+Vcos(ωt)]

Figure 6 » demonstrates the how the opposing pairs of rods are successively change polarity over time and the resulting effect on the trajectory of the ion  Please note that the original polarity of the DC voltage, U, produces different positive and negative maxima for each pair of rods.


Figure 6 – Quadrupole voltages


In order to provide angular momentum along the z-axis through the quadrupole an accelerating voltage of around 5V is applied.



Whether an ion possesses a stable or collisional trajectory within the quadrupole is governed by the following equation [2];

Equation 3

Equation 3

Ф is the applied hyperbolic field within the analyzer
x and y are the distances along the co-ordinates axis
is the distance from the z-axis to either quadrupole surfaces (Quadrupole Radius)
All other terms are as defined in the previous section

As can be deduced from equation 3, when x = y, ∅ = 0, giving rise to the planes of zero field strength along the center of the z-axis as described previously described in Figure 4. Ions that travel along the x and y-axis will follow a stable trajectory as long as x ≤ r0 and y ≤ r0. In all other instances where x > r0and
y > r0 the ions will possess collisional trajectories and either discharge on the rods or be ejected out of the quadrupole. From Equation 3 , for any particular m/z value, the passage of ions through the quadrupole is dependent on
U, V, ω and r0. As r0 is fixed then this can simplified to U, V and ω, or put even more simply the ratio of DC to RF voltages (as the frequency of the applied AC (RF) voltage, ω , is fixed under most operating conditions). Figure 7 » can be used to visualise the ion trajectory through quadrupole when possessing both stable and collisional trajectories. Please note that the corkscrew type motion is due to maximum positive and negative voltages being different for each pair of rods.

Figure 7 – Stable and collisional trajectories



When using a Mathieu Function to solve the equations of motion for an ion within a quadrupole, two factors a and q emerge as being important in defining regions of stable ion trajectory.[4,5]

equation 4 & 5

All terms are as defined in previous sections. Figure 8 » illustrates the stability regions of ions in the x and y-axis. From the above equations we can infer that as ω and r0 are fixed, the variable parameters that can be manipulated to induce stale or collisional trajectories are U to affect the a term, and V to affect the q term.


Figure 8 » – Mathieu Stability Diagrams


sponsored by Thermo scientific





The region denoted by the letter A is often referred to as the ‘first stability region’ is the typical operating region of quadrupole mass analyzers.  When you view the exploded diagram of this region, the shaded area denotes the ratios of a against q (U against V or DC against RF) where any particular m/z value will possess a stable trajectory in the quadrupole.  The symmetrical nature of the diagram around the q axis denotes that this region can be operated when looking for both positive and negative ions.   The DC (U or a) and RF (v or q) voltages are altered in a linear relationship and this is referred to as the scan line.  Each ions stability region is bounded by the scan line and the outline of the stability diagram, representing ratios of DC and RF voltages that will result in a stable trajectory within the mass analyser.  As ion stability diagrams often overlap, particularly for similar m/z values, the scan line is adjusted such that only the apex of ion stability region is taken.  This ensures that only one m/z is stable in the quadrupole mass analyzer at any one time. 


The slope of the scan line is often referred to as the quadrupole gain and the intercept on the y-axis is often referred to as the quadrupole offset.  Figure 9 demonstrates quadrupole gain, offset and the scan line along with how the scan line affects the observed peak for each of the ions, m1, m2 and m3.


Quadrupole Gain, Offset and Scan Line Figure 9 »


  • The DC and RF voltage ratio (scan line) is adjusted such that all m/z ratios across the defined mass range possess equal peak widths.   The mass range of the mass analyzer is the difference between the highest and the lowest m/z ratios – typically from 2000 - 2 m/z.
  • As the scan lines moves toward the apex of the ions stability region an increase in mass resolution (decrease in the width of the spectral signal) is observed, and vice versa.
  • Quadrupoles are low resolution mass analyzers with resolving powers in region 500 – 2000.  They are capable of unit mass resolution whereby they can resolve adjacent m/z’s that differ by only 1Da.
  • When the scan line moves towards the apex of the ions stability region a decrease in mass sensitivity is observed, and vice versa.
  • Quadrupoles are highly sensitive instruments and are capable of detecting down to 50pg in scanning mode and 500fg in SIM mode.

Figure 10 » explains how quadruple gain and offset can be adjusted and their resulting effect on observed spectral peak shapes and hence resolution and sensitivity.  Adjusting the quadrupole offset affects all peaks to the same extent.  Adjusting quadrupole gain affects larger m/z ratios to a greater degree than smaller m/z ratios.


It is worth noting at this point that with a linear scan line through the origin the peak widths will increase geometrically with increasing m/z.  This is referred to as constant resolution mode and modern systems are scarcely operated in this way.   As you take a larger part of the ion stability region for the higher m/z ratios the peak widths increase and this will also alter the mass calibration.  Due to the characteristic shape of the ions stability region, with the leading edge increasing three times more slowly than the trailing edge decreases, the center point of the peak will move to a lower apparent mass.   Modern quadrupole instrument operate in unit mass resolution mode whereby a curved scan line will be approximated by either an electronic or software implementation. [3]

However, for ease of understanding it is simpler for us to continue to think of scan lines as linear for the remainder of this article.


Quadrupole gain and offset - Figure 10 »



When operated in scanning mode, the applied voltages are adjusted so that each m/z possess a stable trajectory for a fraction of a second, typically 10 – 100µs, across the defined mass range in 0.1Da increments, initially allowing the transmittance for ions with the largest m/z values.  When the quadrupole reaches the lower mass to charge value, it will then revert to the highest mass and restart the scanning process.  The time it takes to complete a full scan and revert to the highest mass is known as the ‘duty cycle’.  A Total Ion Current (TIC) is produced which plots the sum of all ion abundances against time.  At any point in time the individual m/z ratios that combine to produce the TIC can be extracted.  Scanning mode is often employed for qualitative purposes or for investigational work.  Figure 11 illustrates a typical scanning experiment where all m/z ratios for the ions produced by sulfamethiazole are recorded in the top spectrum for each scan.  Each scan is defined by its duty cycle and this is shown on the TIC by the red dots.  The scanning speed is defined in Hz and the greater the scanning speed the greater the sensitivity as seen at the bottom of Figure 11 ».

When the compounds of interest are known and increased sensitivity is required, quadrupole mass analyzers can be operated in Selected or Specific Ion Monitoring (SIM) mode.  Rather than scanning hundreds or thousands of m/z ratios (most of which will not be generating useful signals), only those signals known to produce a response, are observed.  This means that the quadrupoles can spend a lot longer, typically in the 100 – 300ms range, monitoring these specific ions, thus dramatically increasing sensitivity.  Additionally as only ions of interest are being transmitted through the mass analyzer, the noise is dramatically reduced thus enhancing sensitivity even more.   SIM mode is conventionally used for quantification purposes.



Figure 11 – Typical scanning experiment



When the resolving DC voltage has been removed, U = 0, the scan line will lie horizontally x-axis.  This permits all ions, irrespective of m/z, to travel the length of the quadrupole on a stable trajectory, with the RF voltage merely serving to focus the ions around the central z-axis.  These types of RF only ion bridges have two major functions; [6]

  • They are commonly employed after the source but before the mass analyzer in order to retain the ions whilst allowing the uncharged species to be pumped away.  This facilitates the pressure to step down from atmospheric conditions in the source to the high vacuum conditions, ≈10-6 torr, required for the mass analyzer to function.
  • They are also employed as the ‘collision cell’ in tandem MS/MS instruments where they operate in a very similar function described above, however they are filled with an inert gas and transport ions between the first and second mass analyzers and are filled with an inert gas.

More commonly RF only ion bridges are hexapoles or octapole arrangements due to their greater inherent ability in focussing ions.  These are sometimes referred to as higher multipoles.



Quadrupoles lend themselves very well to being coupled to a second mass analyzer – MS/MS.  This second analyzer can be an ion storage device (Trap), Time of Flight (ToF) or an additional quadrupole.  Next month’s Webcast and Essential Guide will focus on Trap and ToF analyzers whilst we will solely concentrate on tandem quadrupole instruments.  Tandem quadrupole instruments are often incorrectly referred to as triple quadrupole instruments; however the majority of manufacturers employ higher multipoles as the collision cell between the two quadrupole analyzers.  The ions exiting the first quadrupole are accelerated into the collision cell, which is filled with an inert gas, at sufficient velocity that they break internal bonds in order to fragment – this is known as Collision Induced Dissociation (CID).  The amount of gas in the collision cell is seldom adjusted and is purely turned on or off, however type of gas employed can affect the amount and / or type of CID.  The most common gases employed are Argon, Nitrogen, Xenon or Helium.   The two main benefits of coupling two mass analyzers with one another are;

  • Greater structural information
  • Enhanced sensitivity

How these benefits are achieved and typical MS/MS experiments will be discussed in the next section.



Product Ion Scanning

  • Used to illicit structural information from the parent ion
  • The first quadrupole operates in SIM mode and allows transmittance of the pre-cursor ion only
  • This is then fragmented in the collision cell
  • The second mass analyzer is operated in scanning mode in order that all products created by the prior CID are detected

Figure 12 – Product Ion Scanning


Pre-Cursor Ion Scanning

  • Can be used to confirm that product ions are unique to Pre-cursor as determined by Product Ion Scanning experiment
  • Very commonly used to isolate specific group containing compounds.  If one is only interested in identifying / quantifying compounds that contain alkyl benzene groups, the second analyzer only allows the characteristic tropylium ion (m/z 91) to pass through the mass quadrupole
  • The first mass analyzer operates in scanning mode, allowing transmittance of all ions across the defined mass range
  • These ions are then fragmented within the collision cell
  • The second mass analyzer is set to SIM mode, looking for the specific fragments


Figure 12 – Pre-cursor Ion Scanning



Constant Neutral Loss / Gain

  • Can be used to increase selectivity and sensitivity by only detecting ions that lose a specific group -  CO2 m/z 44
  • The first mass analyzer operates in scanning mode, allowing transmittance of all ions across the defined mass range
  • These ions are then fragmented within the collision cell
  • The second mass analyzer is also operating in scanning mode but with at a constant deficit offset  equal to the m/z of the expected leaving group

Figure 13 – Constant Neutral Loss / Gain



Single / Multiple Reaction Monitoring

  • The optimum for selectivity and sensitivity as not only are selected ions only allowed through the first mass analyzer, but unique fragments are only permitted through the second analyzer too
  • SRM refers to solely allowing the transmittance through the second analyzer on one specific fragment ion.  MRM is the term used to define the experiments where two or more specific fragment ions are allow to pass through the second mass analyzer.
  • The first mass analyzer operates in SIM mode, allowing transmittance of specific ions only
  • These ions are then fragmented within the collision cell
  • The second mass analyzer is also operating in SIM mode and only allowing the transmittance of the unique fragment ion or ions.

Figure 14 – Single / Multiple Reaction Monitoring



  1. W. Paul & H. Steinwedel. “Zeitschrift fur Naturforschung.” 8A, (1953), p448
  2. P.E. Miller, M. B. Denton. “Operrating Concepts of the Quadrupole MS.” J. Chem Educ. 63, (1986), 617-622.
  3. R. E. Pedder. “Practical Quadrupole Theory: Graphical Theory.” Extrel Application Note RA_2010A, (2001), p1 – 5.
  4. P. H. Dawson. “Quadrupole Mass Anlysers.” Mass Spectrum. Rev. 5, (1986), p1 – 37.
  5. R. E. March & R. J. Hughes. “ Quadrupole Storage Mass Spectroscopy.” Wiley, New York 1989
  6. M. Hail & I. C Mylchreest. Presented at the “41st ASMS Conference on Mass Spectrometry and Allied Topics” May 31st.  June 4, (1993), San Francisco, CA, 745


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The following subjects are covered in

The Theory Of HPLC
Introduction (1.5hrs)
Chromatographic Parameters (3hrs)
Band Broadening (3hrs)
Column chemistry (4hrs)
Reverse phase (partition) chromatography (6hrs)
Ion-Pair Chromatography (3hrs)
Normal phase (absorption) chromatography (3hrs)
Gradient HPLC (3hrs)
Quantitative and Qualitative HPLC (3hrs)
FAST HPLC (4.5hrs)
HILIC (3hrs)
SFC (3hrs)
Ion Chromatography(3hrs)

Theory and Instrumentation of GC
Introduction (1.5hrs)
Chromatographic Parameters (3hrs)
Band Broadening (3hrs)
Gas Supply and Pressure Control (2hrs)
Sampling Techniques (4.5hrs)
Sample Introduction (5hrs)
GC Columns (5.5hrs)
GC Temperature Programming (3hrs)
GC Detectors (2.5hrs)
SFC (3hrs)

Instrumentation of HPLC
Mobile Phase Considerations (3.5hrs)
Solvent Pumping Systems (4hrs)
Autosamplers (4.5hrs)
Detectors (4.5hrs)

Solid Phase Extraction
Molecular Properties (4hrs)
SPE Overview (3.5hrs)
SPE Mechanisms (4.5hrs)
Method Development (5.0hrs)
Primary Sample Preparation Techniques (2hrs)
Liquid / Liquid Extraction Techniques (1.5hrs) Approaches to Automation for SPE (1.5hrs)

Fundamental GC-MS
Introduction (1.5hrs)
GC Considerations (4.5hrs)
GC -MS Interfaces (2.5hrs)

Fundamental LC-MS
Introduction (1.5hrs)
Electrospray Ionisation Theory (6hrs)
Electrospray Ionisation Instrumentation (4hrs)
Mass Analyzers (9.5hrs)
Atmospheric Pressure Chemical Ionisation (3.5hrs)
Atmospheric Pressure Photoionisation (3hrs)
Solvents, Buffers and Additives (3.5hrs)
Vacuum Systems (3hrs)
Flow Rates and Flow Splitting (3hrs)
Orbitrap Mass Analyzers (3hrs)

MS Interpretation
General Interpretation Strategies (11hrs)
Intro to MS Proteomics Research (3.5hrs)

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