Time of flight mass spectrometer

The Mars rover carried an on board mass spectrometer to analyse rock and soil samples.

A mass spectrometer is used to identify unknown substances, to determine the composition of mixtures and to accurately measure the relative amounts and masses of substances present. It can for example be used to find the masses and abundances of isotopes present in an element and from this it is relatively straightforward to calculate the relative atomic mass of the element. The mass spectrometer also has many uses in the chemical, engineering and space industries, for example the Rovers which NASA sent to the planet Mars all had mass spectrometers on board to analysis Martian rocks, minerals and gases in the atmosphere.

In the A-level chemistry specifications there are two main types of mass spectrometers that you will need to know about. If you are studying the AQA specification you will need to be able explain the working of a time of flight mass spectrometer and carry out some calculations based on this method of mass spectroscopy. So let's start here. For details on the other type of mass spectrometer, the single beam mass spectrometer and its operation click here or use the link above.

Time of flight mass spectrometer (TOF-MS)

The time of flight mass spectrometer was developed during the 1950. These mass spectrometers are smaller, less expensive and more compact than traditional single beam mass spectrometers. To analyse the sample of the unknown substance under examination we need to consider what happens in each of 4 separate key stages in the operation of this type of mass spectrometer. These 4 stages are:

Ionisation
Acceleration
Ion-drift
detection

Stage 1- ionisation.

The sample under test may be injected at the sample point (see diagram below) under low pressure and high temperature to ensure that the sample will vapourise and form a gas. This is important since the mass spectrometer cannot analyse liquids or solids. If the sample is a solid it will be heated to vapourise it or it may be dissolved in a solvent before being vapourised and placed in the mass spectrometer

Ionisation is one of the key steps that happen inside the mass spectrometer. In this step the sample atoms or molecules will be turned into ions with a +1 charge. There are 2 common methods used to ionise the sample, these are two methods are:

electron impact ionisation
electrospray ionisation

The image below shows how electron impact ionisation works. Here an electron gun, which is essentially just a wire that is heated up to a very high temperature; around 2000⁰C to 2500⁰C, at this high temperature the hot wire or filament will emits a steady stream of high energy fast moving electrons. These electrons are attracted to a positively charged plate opposite the electron gun. This positively charged plate will attract and accelerate the electrons given off by the electron gun.

Time of flight mass spectrometer with an electron gun which is used to ionise the sample

If we imagine the electrons as being like fast moving solid particles or balls/bullets; then when the molecules or atoms in the injected sample meet these fast moving electrons, they will have 1 of their outer electrons removed or knocked off, this means they will have been ionised. This will leave a positively charged ion behind, now almost all of the ions produced will have a +1 charge (this is shown in the image opposite). When the sample under test is ionised in this way to form ions with a +1 charge the ion formed is often referred to as the molecular ion.

fast moving electrons from the electron gun knock electrons off the
atoms in the sample to form positively charged ion If we call the injected sample X, then we can show this as:

X_(g) → X⁺_(g) + e

Where e represents the electron being knocked off the sample X. You may also see this equation written as:

X_(g) + e → X⁺_(g) + 2e

Here the first e represents the electron from the electron gun which impacts the sample X, forming a positively charged ion ( X⁺_(g)) and the 2e on the product side represent the one electron lost by the sample X and also the electron from the electron gun.

For example the equations below represent the ionisation of neon gas and hydrogen gas:

Ne_(g) + e → Ne⁺_(g) + 2e
or simply:
Ne_(g) → Ne⁺_(g) + e

And for hydrogen gas we have:

H_2(g) + e → H_2(g)⁺ + 2e
or simply:
H_2(g) → H_2(g)⁺ + e

Electrospray ionisation

The second method of ionising the sample uses a method called electrospray ionisation. This method is often preferred for larger molecules which may be blasted to pieces by an electron gun while electrospray ionisation rarely results in fragmentation. Here the sample is dissolved in a volatile polar solvent (volatile means it evaporates easily) such as water or methanol, next it is injected into the sample point under high pressure and through a very fine hypodermic needle which has a high voltage (around 4000V) applied to it. This results in the sample being ionised and forming fine droplets or a mist containing the ionised sample. The solvent being volatile quickly evaporated leaving the positively charged sample. This is shown in the diagram below

details of how electro-spray ionisation in a TOF mass spectrometer works

The sample X becomes ionised not by having electrons knocked off it or removed from it as is the case in electron impact ionisation, instead the sample under test gains a hydrogen ion (H⁺) from the solvent. This means that the mass of the sample molecule will increase by 1 unit due to the addition of a hydrogen ion. We can show this as:

X_(g) + H⁺ → XH⁺_(g)

All this takes place in the needle on the end of the injection point. This is also shown below:

TOF mass spectrometer uses electro-spray ionisation to ionise the sample

Step2 - acceleration

The next key step in the mass spectrometer is acceleration of the ions formed. There is one vital assumption that we will make: we will assume that all the ions formed in the ionisation step have a charge of +1. The positively charged ion will be now be accelerated up the tube by an electric field, they will be attracted to and accelerated towards the negatively charged plates.

One of the main pieces of information that the mass spectrometer provides is the A_r or M_r of the substance under analysis. If the sample contains a mixture of substances it would be very useful if we could obtain the M_r for each substance present. Now after the ionisation step we may have a range of different substances all with a charge of +1. The mass spectrometer will give you a read out of the mass to charge ratio, often called m/z ratio of any substance it detects. Now if the charge (z) is simply equal to +1, then the mass to charge ratio (m/z) will simply be the mass.

In the acceleration stage in the mass spectrometer would you expect the heavy or light ions to be accelerated quickest up the tube? Or put another way, if you pushed a golf ball or a bowling ball, which would move with the greatest velocity or speed? Obviously the lightest ions will be accelerated quickest up the tube towards the charged plates. This is outlined in the image below, here three isotopes of the metal magnesium are shown, ²⁴Mg⁺, ²⁵Mg⁺ and ²⁶Mg⁺. All three magnesium ions will have the same kinetic energy after the acceleration stage but the lighter ²⁴Mg⁺ ions will have the largest velocity and will therefore reach the detector first, whereas the heavier and slower ²⁶Mg⁺ ions will be last to reach the detector. The lighter ions are accelerated to higher velocities than heavier ions in a time of flight mass spectrometer Now you may remember from your physics lessons that the kinetic energy of an object can be calculated from the formula:

Kinetic energy (KE) = ¹/₂ mv²

Where: m =mass in kilograms (kg), v= velocity in metres per second (ms^-1) and the KE = kinetic energy in joules (J).

A key feature of this type of mass spectrometer is that all ions, no matter their mass will all gain the same amount of kinetic energy during the acceleration stage. The kinetic energy of the ions will depend on their mass and velocity, so lighter faster moving ions will have the same kinetic energy as heavier slower moving ions.

The kinetic energy of the ions is the same in a TOF spectrometer

Stage 3 - ion-drift

The ion drift stage in a TOF mass spectrometer is where the separation of ions based on their mass truly takes place. Once the ions travel through the slits in the acceleration plates and they are no longer being actively accelerated. The ions now enter a long flight tube (see diagran below) of know length and the time it takes the ions to reach the detector is carefully recorded, this flight tube is essentially a long vacuum chamber. This region is devoid of any electric fields that could influence the motion of the ions, here the ions rely solely on the kinetic energy they gained during the acceleration stage to travel or "drift" along the flight tube. I always find this name "drift area" a bit unhelpful since drift implies a slow lumbering motion, whereas in reality the flight times to the detector can often be less than a nanosecond as the ions are moving with very high velocities.

Now since the ions all have the same kinetic energy after the acceleration stage the key factor that determines their travel time along the flight tube becomes their mass.

Lighter ions: With their higher velocity from the acceleration stage, they travel the length of the flight tube faster.
Heavier ions: Due to their lower velocity, they take a longer time to travel the same distance up the flight tube.

Essentially, the lighter ions "drift" through the flight tube quicker compared to their heavier counterparts. This difference in travel times is what allows us to measure the mass-to-charge ratio (m/z) of the ions later. It's important to note that the ion-drift stage relies entirely on the initial kinetic energy provided during the acceleration stage. The longer the flight tube, the more time the ions have to separate based on their mass, leading to better resolution in the final mass spectrum. The accelerating ions now enter a portion of the mass spectrometer called the flight tube. Diagram of a time of flight (TOF) mass spectrometer

Diagram of a time of flight (TOF) mass spectrometer

Stage 4-detection

The detector plate at the end of the flight tube has a negative charge due to an excess electrons being placed on it from an electrical source, now when the positively charged ions arrive at the detector plate they gain an electron and are reduced. This reduction reaction involves the movement of electrons, or a flow of electrical current. The more electrons that flow the more ions are present; that is their abundance is high, this will be recorded by a computer connected to the detector. Remember the ions will arrive at the detector plate at various times since their flight time down the flight tube will obviously depend on how fast they are travelling and this as previously mentioned depends on their mass to charge ratio; or simply their mass if the charge on the ion is +1.

The onboard computer in a mss spectrometer can produce a mass spectrum of the sample By knowing the distance the ions travelled (that is the fixed length of the flight tube) and measuring their arrival times; the computer can calculate the velocity of each ion and using the equation for kinetic energy (where the kinetic energy is constant for all ions due to the acceleration stage) the computer can then determine the mass-to-charge ratio (m/z) of each ion that hits the detector. Finally the software creates a mass spectrum. This spectrum is a plot of the m/z values on the x-axis versus the intensity (proportional to the number of ions) on the y-axis. The mass spectrum provides a visual representation of the different ions present in the sample and their relative abundances.

Equations to learn

In the exam your exam you could be asked to calculate any one from the list below. It is often necessary to rearrange formulae, I have given some examples below but I would try the practice questions and complete as many of the examples as possible to ensure you are completely confident with these questions.

The kinetic energy of the particles in joules (J) using the formula:
Kinetic energy (KE) = ¹/₂ mv²
Here the mass must be in kilograms (kg) and the velocity in metres per second (ms^-1).
The time of flight of the ions. That is the time the ions take to move through the ion-drift area. This will be in seconds (s). This is simply calculated from:
time (s) = distance (d in metres) / velocity ( v in ms^-1)
The distance (d) is simply the length of the ion-drift area (see diagram above) and the velocity is simply how fast the ions are moving. This will obviously depend on the mass of the particles, the heavier particles will be moving slowly and the lighter particles will be moving much faster.
To calculate the velocity of the particles it may be necessary to rearrange the formula we have for KE, this is outlined below:
To calculate the time for the ion to travel along the flight path (ion-drift area) in the mass spectrometer we simply use the equations above but rearrange them to make time (t) the subject of the formula this time:

This equation tells us that time of flight (t) is proportional to the square root of the mass (√m), so lighter ions arrive at the detector before heavier ones.

To calculate the mass of the particle we simply do a little more arithmetic and rearrange the formula we used above to give:
To calculate the length of the flight tube(d) we simply use the formula below:

Key Points

The four key steps which in the operation of a TOF mass spectrometer are:

ionisation

acceleration

ion-drift

detection

You should be able to describe what happens in each of the 4 stages and in particular the difference between electron impact ionisation and electro-spray ionisation.
Learn the formulae above or know how to rearrange formula to arrive at the required equations to answer the exam questions.

Time of flight mass spectrometer