Advanced Separations and Mass Spectrometry

What is the apparatus used for chromatography?

A sample is injected into the mobile phase, which then passes through the column (containing the stationary phase) and arrives at a detector.

• The sample added is the eluent.

• The mixture that passes out the column is the eluate.

What does a chromatogram look like?

The sample is injected at time 0.

• t_M represents the unretained species that doesnt interact with the column at all, also called void time.

• t_R represents the retention time of the analyte.

• t_S is the time between t_M and t_R, it represents the strength of the interaction between the sample and the stationary phase.

What is resolution?

It is how well you can tell the peaks apart.

• Defined in terms of retention times and peak width:

ΔR_s = Δt_R / W_av     or     R_s = 2(t_R2 - t_R1)/W₂+W₁

Where W_av is the average of the peak widths at the base.

What is the desired R_s value for baseline resolution?

1.5

• This is the smallest resolution at which the signal is able to go to 0 before the next peak begins.

What is the capacity factor?

k’ is the amount of time the solute spends in the stationary phase relative to the amount of time the solute spends in the mobile phase.

• The longer the component is retained by a column, the greater k’.

How do you calculate k’?

An ideal range is 1-5, however it is often around 0.5-20.

What is the selectivity factor?

α is the selectivity factor, it is the ratio of the capacity factors.

• For separation to occur, the analytes must have different capacity factors.

How do you calculate α?

It should always be above 1.

How do you rearrange the k’ equation to incorporate the equilibrium constant K?

If the column runs slowly enough at equilibrium, C_S/C_M is the equilibrium constant K.

• Because the ratio of phase volumes is constant for a given column and mobile phase, k’ is directly proportional to K.

What is migration velocity?

The speed of movement through the column, it depends on the distribution of the analyte between the mobile and stationary phase.

• If more analyte is in the mobile phase, net velocity is higher.

How do you calculate the velocity of the retained species?

u_R is the velocity of the retained species.

• n_M is the number of moles of mobile species.

• n_S is the number of moles of stationary species.

• u_M is the velocity of the mobile species.

How do you rearrange the k’ equation for u_R and u_M?

How do you rearrange the k’ equation for velocity in terms of column length and elution time?

• Column length is L.

• Elution time is t.

• Velocity= L/t.

How does the band shape change over time?

The shape of the band changes over time, however the total area under the peak remains constant.

What is the rate theory of chromatography?

As the particles move through the column, they do not move evenly. This causes a symmetrical spread of velocities around a mean value.

What are Gaussian shaped peaks?

Band broadening for Gaussian shaped peaks is a statistically random process.

• σ is standard deviation (length units)

• τ is standard deviation (time units)

• τ = W/4

• σ² = τ², this represents variance.

68% of peak area is in the range t_R ± τ

How does diffusion cause band spreading?

The diffusion coefficient measures the rate at which a substance moves randomly from a region of [high] to a region of [low].

σ² = 2Dt

• t is measured in seconds.

How does the partition coefficient K affect band shape?

• A Gaussian bandshape occurs when K is independent of the concentration of the solute on the column.

• Skewing occurs when K is dependent on concentration.

What is fronting?

When overloading occurs as too much solute is added.

• Can be corrected by using a smaller sample or diluting.

What is tailing?

When small quantities of solute are retained more strongly than small quantities.

• Can be corrected by masking strong adsorption sites on the stationary phase.

What is plate height?

The constant of proportionality between the variance of the band and the distance it has travelled.

• Can be thought of as the length of the column required for one equilibrium of solute between mobile and stationary phase.

• Has units of length.

How does variance relate to plate height?

The standard deviation for diffusive band spreading is √2Dt. If a solute has travelled a distance x at linear flow rate u_x, then it has been on the column for t = x/u_x. This can then be rearranged.

What is the plate model?

A column contains a large number of separate layers (plates). The analyte moves down the column by transfer of the equilibrated mobile phase from one plate to the next.

How does plate height relate to variance?

H = σ² / L

• Small σ means a small H

• Large σ means a large H

Why do different solutes have different plate heights?

They have different diffusion coefficients.

What plate height is desirable?

A smaller plate height means a narrower bandwidth, so a small H is good.

What is efficiency?

The theoretical number of plates.

• N = L/H

• It is dimensionless, however a big N is desired.

What factors are used to describe column performance?

• Efficiency, N: Large is desired.

• Plate height, H: Small is desired.

• Peak asymmetry

• k’

How can resolution be linked to band boradening?

As R_s = Δt_R / W_av, W = 4τ, and t_R / τ = N^1/2:

• Therefore R_s is proportional to √N.

What is the van Deemter equation?

Links plate height and flow rate.

H = A + B/u + Cu

• A represents multiple flow paths.

• B represents longitudinal diffusion.

• C represents mass transfer/equilibration time.

What is A (multiple flow paths)?

Bandspreading occurs as sample particles have multiple flow paths through the column.

• Can be reduced by using smaller stationary phase particles.

• Effect is absent in open tubular columns.

What is longitudinal diffusion (B/u)?

The sample diffuses over time as it spends longer in the column.

• Can be reduced by having a faster linear flow.

What is mass transfer (Cu)?

There is a finite time for the analyte to equilibrate between mobile and stationary phases.

• Reduced by decreasing the stationary phase thickness/column radius, or increasing temperature.

How does H vary with u?

The extent of band broadening depend on the length of time the mobile phase is in contact with the stationary phase, therefore it depends on flow rate.

• Cu increases with flow rate.

• B/u decreases with flow rate.

• The optimal flow rate gives the lowest value of H, in this example it is around 30mL/min.

How do analytes elute in gas chromatography?

Analytes elute in order of their boiling points.

• Molecules with similarity to the stationary phase are retained more strongly.

• e.g. in case (b) the molecule is less strongly retained so has a higher tendency to escape into the vapour phase.

How do you find ΔG⁰ for the gas-liquid equilbirum?

What is van’t Hoff’s isochore?

What is Trouton’s rule?

It shows that the standard entropy of vaporisation is approximately constant.

• It is around 85 Jmol^-1K^-1 for many compounds.

How is boiling point linked to retention (via equation)?

ΔG^θvap = 0 at b.p. (T_bp)

ΔH^θ = T_bpΔS^θ

• This can be substituted into the van’t Hoff isochore.

• The k’ equation can be substituted into this equation.

How does k’ change with boiling point for homologous series of analytes?

lnk’ scales with T_BP

k’ increases as T_BP increases.

How does k’ change with boiling point for all analytes?

lnk’ scales with 1/T

k’ decreases as T increases.

How can retention time be controlled by varying T?

You can use a programmed temperature range to elute analytes with a wide range of boiling points.

• e.g. a programmed temperature between 50-250^oC at a ramp rate of 8^oC/min

What are packed columns?

A column which is packed with a compound such as zeolite or alumina, creating high flow resistance.

• Has a shorter length, around 2-3m.

• Has a high phase ratio (V_S/V_M)

• Has low efficiency.

• No overloading possible.

What are open tubular columns?

A column that has an open centre, similar to a capillary.

• Has low flow resistance.

• High length, around 15-100m.

• Low phase ratio.

• High efficiency.

• Can be overloaded if too much analyte is injected.

What is the order of elution in reverse phase liquid chromatography?

Analytes elute in order of their hydrophobicity, most hydrophobic analytes elute last.

• HPLC has a polar MP and non-polar SP.

What is eluent strength?

Elution occurs when solvent displaces solute from the SP.

• Eluent strength (ε°) is the solvent adsorption energy (defined as 0 for pentane on bare silica).

• As ε° increases, solutes elute more rapidly.

How does eluent strength vary with solvents?

As solvent strength increases, ε° increases.

• e.g. MeOH has a smaller ε°, and THF has a higher ε°.

• In RP, ε° is higher for less polar solvents.

How do you control k’ in LC?

Can add an organic modifier.

log k’ = log k’_w – SΦ

• Φ is the volume fraction of OM in the mobile phase and S is related to the type of OM (solvent strength).

• k’_w is k’ in water.

log k’ decreases linearly with volume of OM.

How can you vary MP composition in HPLC and why?

By varying the MP, the magnitude of k’ can change by up to 4 orders of magnitude. This can make peaks clearer and k’ more of a reasonable value.

• Change of solvent composition in HPLC is similar to change of T in GC.

Can vary MP composition by gradient elution, e.g. vary % of OM over a set time.

• Isocratic elution is keeping the same composition throughout.

How can phase volume be changed in HPLC?

Can use porous vs non-porous silica.

• A porous silica has a high surface area and high carbon loading. The SP bonds to the internal pores.

• A non-porous silica has a lower surface area and low carbon loading. This means the phase ratio is much lower, and k’ decreases. The SP can only bond to the external surface.

What is plate height like in LC and why?

Transverse diffusion is slow in LC, therefore H is much smaller compared to GC.

• In LC, there is a parabolic flow profile due to pressure driven flow. This is because the liquid in the centre of the column moves faster than the liquid near the walls.

• This means fast equilibration is needed in the direction transverse to the flow to counteract broadening.

How does plate height change as a function of particle diameter in LC?

Reducing the particle size (d_p) reduces the plate height.

H = A + B/u + Cu

• A increases with d_p as there is a less uniform flow through the column.

• C increases with d_p as it takes longer to diffuse through the inner pores.

What are the benefits and limitations of using a smaller particle diameter in LC?

• A small diameter means a smaller plate height.

• However, a small diameter means there is a higher resistance to solvent flow.

What is UHPLC?

Ultra-High Pressure Liquid Chromatography.

• The use of a higher pressure to make elution time faster.

• This is used alongside a smaller particle size to gain higher efficiency.

How do you calculate column efficiency in HPLC?

N = L/H

• N is typically around 10⁴

How does efficiency in HPLC compare to GC?

Plate height is lower in GC by a factor of around 10-100 due to faster diffusion.

Efficiency is higher in capillary GC by a factor of around 10 , this is due to a long column being used.

How do you optimise efficiency in LC?

Use a packed column with a particle diameter as small as possible consistent with pressure limitations.

• Minimise any broadening effects.

How do you determine minimum selectivity required for baselines peak separation?

For baselines resolution, R_s > 1.5. R_s is proportional to √N

• Use 1.5 as the value for R_s to find minimum selectivity.

• Multiply by 100 to find the percentage.

What is the key objective of chromatography?

To fully resolve all peaks in minimum analysis time.

If there is no separation, what should be changed?

• In GC, change the stationary phase.

• In LC, change the stationary or mobile phase.

If only partial separation is obtained, what should be changed?

Increase efficiency:

• Increase column length.

• Change flow rate.

• Reduce SP thickness.

• Increase T.

• For a packed column, decrease particle diameter.

Why is MS used alongside chromatography?

Can tell you the mass of the parent ion and the fragmentation pattern.

How do you increase the signal to noise ratio in MS?

Use selected ion monitoring with the spectrometer bringing only ions of the desired mass to the detector