Theory of HPLC Band Broadening - CHROMacademy

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The Theory of HPLC

Band Broadening

Aims and Objectives

Aims and Objectives

Aims

To illustrate and explain the principle of Band Broadening in HPLC

To define the Van Deemter equation and explain the terms of the equation

To demonstrate the effects of Eddy Diffusion, Longitudinal Diffusion and Mass Transfer on the Efficiency of Chromatographic Peaks

Objectives

At the end of this Section you should be able to:

To use the Van Deemter coefficients to illustrate how to optimise the Efficiency (N) of chromatographic separations and to reduce Band Broadening

© Crawford Scientific www.chromacademy.com

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Content Band Broadening 3 The Van Deemter Equation 3 Eddy Diffusion 4 Longitudinal Diffusion 5 Mass Transfer 7 Optimising Flow Rate 9 Optimising Particle Size 10 Minimising System Volumen 11 Glossary 12


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Band Broadening The Van Deemter Equation Band broadening is a phenomenon that reduces the efficiency of the separation being carried out –leading to poor resolution and chromatographic performance. This is problematical in terms of both the quality of the separation obtained and the accuracy with which sample components can be quantified. The degree of band broadening (loss of efficiency) naturally increases with the age of the chromatographic column being used, but there are measures that can be taken to slow these processes and to optimise column and instrument conditions to ensure maximum efficiency and minimum band broadening. In 1956 J.J. Van Deemter derived an equation that included the main factors contributing to column band broadening. He described the individual terms (A,B,C & D) and also derived a ‘composite’ curve which related plate height (HETP) to linear velocity of the mobile phase flowing through the column. Whilst it is not important to necessarily know and use the equation on a daily basis –it is important to understand the terms (or factors) that contribute to band broadening, so that we can optimise our separations. For example, the interactive diagram opposite shows the reduction in chromatographic performance sustained when moving from a system extra column volume of 20μL to 80μL.

The Van Deemter Equation and graphical representation of the contributing terms

Comparative chromatograms from HPLC systems with 20 and 80μL dead volume –

showing effects on efficiency and resolution.

http://www.opdac.com/hplc/HPLC_Unit_1/


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Eddy Diffusion The first of the ‘factors’ relating to band broadening is that of Eddy Diffusion. This is a generic term, often used to describe variations in mobile phase flow or analyte flow path within the chromatographic column. Eddy diffusion itself relates to the fact that an analyte molecule, within a ‘band’ of analytes, can take one of many ‘paths’ through the column. These multiple paths arise due to inhomogeneities in column packing and small variations in the particle size of the packing material. This multiple path effect tends to make the band of analytes broader as it moves through the column.

Large Particles

Small Particles

Band broadening due to Eddy Diffusion (A Term) in columns with large and small particles

– effects on chromatographic peak shape (Efficiency (N)).

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Minimise Eddy Diffusion by: Selecting well packed columns Using smaller stationary phase particles Using particles with a narrow size distribution


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In fact, the Eddy Diffusion term in the Van Deemter equation (the A term), is often called the ‘packing’ term as it reflects the quality of column packing. Laminar flow occurs with standard size HPLC column packing materials at flow rates up to approximately 4mL/min. Non-laminar flow occurs when using very large particle size packing material (>40μm) and at high flow rates (>5mL/min.). This situation is also sometimes referred to as ‘Turbulent Flow’ and does not occur under normal HPLC conditions –customised HPLC equipment and columns are required for ‘Turbulent Flow Chromatography’.

Band broadening due to Eddy Diffusion (A Term) in columns with in Laminar and Non

Laminar mobile phase flow profiles. One other flow variation in column chromatography comes from the laminar flow profile adopted by liquids flowing under pressure through tubes. The flow profile is said to be laminar, where linear velocity near the inner walls of the tubing is lower than in the ‘centre’ of the column. This also tends to produce a broader band of analyte molecules. Longitudinal Diffusion A band of analyte molecules contained in the injection solvent will tend to disperse in every direction due to the concentration gradient at the outer edges of the band. This broadening factor is called ‘Longitudinal diffusion’ because inside tubes, the greatest scope for broadening is along the axis of flow. The band will broaden in all system tubing, but the worst effects will be encountered in the column itself. Longitudinal diffusion occurs whenever the HPLC system contains internal volumes that are larger than necessary and some instances of this are: Tubing length too long Tubing that is too wide (internal diameter) Tubing joined by unions Incorrectly connected Zero Dead Volume fittings Using the wrong column nuts and ferrules Using a detector flow cell that has a large internal volume

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http://www.opdac.com/hplc/HPLC_Unit_1/


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As can be seen, Longitudinal diffusion has a much larger effect at low mobile phase velocity (flow). Therefore, using high linear velocity (high mobile phase flow with narrow columns), will reduce the effects of this broadening factor.

Band broadening due to Longitudinal Diffusion (B Term) in columns with low and high mobile phase linear velocity – effects on chromatographic peak shape (Efficiency (N)).

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Minimise Longitudinal Diffusion by: Using higher mobile phase flow rates Keep system tubing short and as a narrow as possible

(careful with back-pressure) (<0.12mm i.d. is ideal) Use correct nuts, ferrules and fittings wherever possible


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Mass Transfer This term in the Van Deemter equation arises largely due to the fact that the stationary phase material is porous and the mobile phase within the pores is ‘stagnant’ or stationary. The packing material is porous to allow a very large surface area for separation to occur. As the analyte molecules move through the stagnant mobile phase to reach the surface of the packing material, they do so by diffusion only. Analyte molecules entering the pore, those that don’t enter the pore and those that penetrate more deeply into the pore, will all be held up at that point to different extents –causing a broadening of the band. This is the ‘C’ term.

Mass Transfer (C Term) band broadening processes in the pore structure of stationary

phase particles Further, the analyte residence time in (or on) the stationary phase is also variable – again causing a variation in elution time and band broadening. These effects may be minimised by reducing the size (diameter) of the packing material particle size to make the pores as shallow as possible. The effects of mass transfer are also lower at lower linear velocity of the mobile phase.

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Large Stationary Phase Particles

Greater possible pore distance for analyte diffusion

Diffusion time increased

Differences in diffusion times out of the pore are amplified

Peak efficiency decreases (peak broadens) Small Stationary Phase Particles

Reduced possible pore distance for analyte diffusion

Diffusion time decreased

Differences in diffusion times out of the pore are reduced

Peak efficiency increases (peak becomes narrower)

Effect of mobile phase linear velocity (top) and stationary phase particle size (bottom) on

Mass Transfer effects and peak shape (Efficiency (N))

Minimise Mass Transfer effects by: Using smaller (diameter) stationary phase particles Using lower mobile phase flow rates Heating the column (at higher temperatures the diffusion

processes are speeded up and the differences in elution time from the particle pore are reduced)


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Optimising Flow Rate Let’s look at the composite Van Deemter curve and equation once again – this time using real world examples - to investigate options for minimising band broadening and optimising peak efficiency. During the previous pages you have seen that the mobile phase velocity and the particle size of packing material used, have a fundamental effect on efficiency (and therefore band broadening).

Van Deemter relationship between mobile phase flow rate and peak efficiency in HPLC

The On-line course contains an interactive

experiment in which the eluent flow rate can be changed to alter the HETP parameter

Although the change in particle size does not appear to have a marked effect on the efficiency and resolution of this separation, you should study the results carefully

Reducing particle size (even when using traditional column internal diameters), has a marked effect on plate height, which can be usefully used to improved the resolution of separations, especially where selectivity options have failed to produce baseline separated peaks

The plate heights obtained with very small particles are extremely low. By combining short columns with traditional internal diameter (0.46cm), and small diameter silica packing material (1.8μm) – very short analysis times may be achieved.

When using smaller diameter column packing materials, system backpressure should be carefully observed as increased backpressure results from the use of small silica particles

Starting with an investigation of mobile phase flow (linear velocity) – you should see that the mobile phase flow rate can have an effect on band broadening, plate height and hence resolution. It’s important to note that there is an optimum flow rate for each separation (the minimum point on the curve –corresponding to the lowest plate height). Whilst this effect is noticeable, it is minor in comparison with other variables affecting resolution –and therefore flow rate would be used to ‘fine tune’ a separation only. Of course, if you have enough efficiency (and resolution) to run at higher flow rates – then this will make the analysis time shorter – however, care should be taken not to exceed the pressure limit of your HPLC pump!

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Optimising Particle Size Another important factor to consider regarding band broadening is the particle size of the

stationary phase used. We have seen several instances where the use of smaller diameter particles is advantageous to both efficiency and resolution.

Van Deemter relationship between stationary phase particle size and peak efficiency in HPLC

The On-line course contains an interactive experiment in which the effects of changing particle diameter (dp)

on efficiency (band broadening) and resolution are presented

Although the change in particle size does not appear to have a marked effect on the efficiency and resolution of this separation, you should study the results carefully

Reducing particle size (even when using traditional column internal diameters), has a marked effect on plate height, which can be usefully used to improved the resolution of separations, especially where selectivity options have failed to produce baseline separated peaks

The plate heights obtained with very small particles are extremely low. By combining short columns with traditional internal diameter (0.46cm), and small diameter silica packing material (1.8μm) – very short analysis times may be achieved.

When using smaller diameter column packing materials, system backpressure should be carefully observed as increased backpressure results from the use of small silica particles

It should be noted that whilst smaller diameter particles are favourable – there is a trade with system backpressure. Small particles may be used in conjunction with higher mobile phase flow rates to produce very fast analyses, but system backpressure needs to be carefully monitored. The use of smaller diameter silica particles (<2μm), with traditional column internal diameters (i.e. 4.6mm), means extra-column dead volume is less important than when using narrow bore columns. This can be an advantage when fast HPLC analysis is required, without having to change the analytical system hardware to very low dead volume, or very high pressure versions.

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Minimising System Volumen As previously discussed, systems containing large extra-column volume (tubing, unions, flow cell etc.), show low efficiency and hence broadened chromatographic peaks and loss of resolution. You can use the slider bar to investigate the effects of extra column volume. You may want to consider how you could reduce these volumes on your system. Typical ways might include: reduce tubing length and internal diameter / reduce the number of unions between tubing / fit column end fittings appropriate to the column type being used / reduce the injection loop volume / reduce the detector flow cell volume.

Van Deemter relationship between extra column dead volume and peak efficiency in HPLC

The system extra column volume can have a critical effect on efficiency and therefore resolution of a separation

You need to also consider the column dead volume, and if in any doubt about the quality of the column packing, use a new column. Column voids from within columns over time adding very large dead volumes to the system

Extra column dead volumes below 20μL should be easily achievable on modern HPLC systems

You should consider the volume of the detector flow cell as being a major contributor to extra column volume, along with any high pressure mixing chambers on the HPLC pump

System dead volume becomes more critical as the internal diameter, (and to a lesser extent particle size), of the column used are reduced

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Important: It is straightforward to measure the extra column volume of a system:

Remove the column and join the tubing with a Zero Dead Volume union Inject 10μL of 100% strong solvent (acetonitrile works with UV at 200nm) or a

solution of 1% acetone (monitor at 265nm) The apex retention time (tR) of the baseline perturbation due to the passage of the

solvent gives the extra column hold up time of the system (expressed in minutes) Multiply this time by the flow rate (in millilitres per minute) to obtain the extra

column volume (in millilitres)


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Apex solvent retention time used to determine extra column volume of an HPLC system.

Glossary Linear Velocity – The linear velocity of the mobile phase across the average cross-

section of the chromatographic bed or column. It can be calculated from the column flow-rate at column temperature (Fc ), the cross-sectional area of the column (Ac ) and the interparticle porosity ( ε):

= Fc /(εAc) In practice the mobile phase velocity is usually calculated by dividing the column length (L) by the retention time of an unretained compound (tM)

= L/tM System Extra Column Volume – the volume of the HPLC system from the point of injection to the point at which the sample passes out of the detector, MINUS the column dead volume. This typically includes the injection loop, any tubing and unions as well as the detector flow cell where appropriate. Tubing Unions – Fittings which allow the coupling of two pieces of tubing in HPLC. May be made from Stainless Steel or and inert polymeric material such as PEEK (polyether ether ketone).

Zero Dead Volume – refers to a fitting in which the nut, ferrule and tubing exactly match the internal volume of the fitting, leaving no ‘dead’ space. This ‘dead volume’ tends to cause band broadening in HPLC by artificially holding up analyte molecules in the stagnant (not moving) phase that resides in the ‘dead volume’ within the fitting.


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Wrong column nuts and ferrules - each column manufacturer uses particular end fitting types. Specially design stainless nuts and ferrules must be used in order to obtain a satisfactory ‘zero dead volume’ union with the column. Some workers use PEEK fittings that deform to fit the internal geometry columns from any manufacturer. However, these fittings do loose their ‘plasticity’ and should be regularly replaced to avoid band broadening.

Incorrect ferrule and tubing fitting

Dead Volume

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Theory of HPLC Band Broadening - CHROMacademy