Chromatography y Help Desk
hony.edge@avantorsciences.com hy Help Desk
hony.edge@avantorsciences.com
when bigger is best otable trend for chromatographers to use smaller and smaller e the performance of their separation, however there are problems this approach that mean on occasion bigger particles are actually e publication of the van Deemter equation it has been noted that se relationship between the particle size and the chromatographic PLC column. This has led to a gradual reduction in the particle size ding-edge separations, with the bead technology being reduced from he current state of play which is less than 2 μm. This has also led to t of ultra-high pressure pumps to accommodate the increased ements associated with the smaller particles. Thus, the maximum ures for commercially available chromatographic systems have seen m 400 bar to over 1500 bar in the last two decades.
Tony Edge,
anthony.edge@avantorsciences.com
These models do rely on a couple of assumptions though; • The concentration of the solute is very dilute • The solute molecules do not interact with each other • There are no interactions with a container of any description
g when bigger is best otable trend for chromatographers to use smaller and smaller e the performance of their separation, however there are problems h this approach that mean on occasion bigger particles are actually e publication of the van Deemter equation it has been noted that rse relationship between the particle size and the chromatographic HPLC column. This has led to a gradual reduction in the particle size ading-edge separations, with the bead technology being reduced from the current state of play which is less than 2 μm. This has also led to nt of ultra-high pressure pumps to accommodate the increased ements associated with the smaller particles. Thus, the maximum sures for commercially available chromatographic systems have seen m 400 bar to over 1500 bar in the last two decades.
suggest that for chromatographers the use of smaller particles is and that in all cases the smaller variant of particles should be used, not the case but to better understand this statement it is necessary to nd how chromatographic performance is measured. The most ach to measuring chromatographic performance is to measure the ne measure of that is the use of experimental plates, which is he following equation.
= 16 %! (
" Understanding When Bigger is Best
It has been a notable trend for chromatographers to use smaller and smaller particles to drive the performance of their separation, however there are problems associated with this approach that mean on occasion bigger particles are actually better. Since the publication of the van Deemter equation it has been noted that there is an inverse relationship between the particle size and the chromatographic effi ciency of a HPLC column. This has led to a gradual reduction in the particle size for the more leading-edge separations, with the bead technology being reduced from 10 μm down to the current state of play which is less than 2 μm. This has also led to the development of ultra-high pressure pumps to accommodate the increased pressure requirements associated with the smaller particles. Thus, the maximum operating pressures for commercially available chromatographic systems have seen an increase from 400 bar to over 1500 bar in the last two decades.
In a standard chromatography environment, the first of these two assumptions are valid. However, it is very evident that there will be a wall effect observed which will alter the effective dispersion processes within the tubing. Thus, it must be considered that when the diffusion in the mobile phase is contained in a fluidic pathway, the result will be in drag at the surfaces causing a parabolic flow profile across the tube, comparable to a bowl. Improving the radial movement of molecules will reduce this issue, as will reducing the diameter of the tubing, however for common connector dimensions the radial dispersion does not overcome the parabolic flow profile associated with the flow rates found in capillary HPLC. As a consequence of this effect increases in the flow rate will result in a greater variance, due to the frictional effects of the surface of the tubing being greater than the relative reduction in retention time within a capillary at the typical flow rates observed in capillary systems. This is typically measured by a parameter referred to as the variance.
n suggest that for chromatographers the use of smaller particles is al and that in all cases the smaller variant of particles should be used, not the case but to better understand this statement it is necessary to nd how chromatographic performance is measured. The most ach to measuring chromatographic performance is to measure the one measure of that is the use of experimental plates, which is he following equation.
n time of the analyte, measured typically from the highest point of the
width at the base of the peak being measured is the dispersion, or variance, of the analyte n the chromatographic system. This dispersion is due to the random ment of small molecules, and even though there is a general direction e mobile phase, this random nature of dispersion will result in e mobile phase moving at different linear velocities through the fluidic
dth at the base of the peak being measured is the dispersion, or variance, of the analyte n the chromatographic system. This dispersion is due to the random ment of small molecules, and even though there is a general direction e mobile phase, this random nature of dispersion will result in mobile phase moving at different linear velocities through the fluidic
Where; tr
e system Dispersion in the system
= − ∅
he system
will have a degree of energy that can be utilised for movement within they occupy. When looking at a large number of molecules there is a e molecules to preferentially move from areas of high concentration to concentration. This can be summarised by Fick’s first and second n [1], relating to spatial and temporal concentration variations, which
ll have a degree of energy that can be utilised for movement within hey occupy. When looking at a large number of molecules there is a e molecules to preferentially move from areas of high concentration to oncentration. This can be summarised by Fick’s first and second [1], relating to spatial and temporal concentration variations, which
These models do rely on a couple of assumptions though; • The concentration of the solute is very dilute • The solute molecules do not interact with each other • There are no interactions with a container of any description
= − ∅
In a standard chromatography environment, the fi rst of these two assumptions are valid. However, it is very evident that there will be a wall effect observed which will alter the effective dispersion processes within the tubing. Thus, it must be considered that when the diffusion in the mobile phase is contained in a fl uidic pathway, the result will be in drag at the surfaces causing a parabolic fl ow profi le across the tube, comparable to a bowl. Improving the radial movement of molecules will reduce this issue, as will reducing the diameter of the tubing, however for common connector dimensions the radial dispersion does not overcome the parabolic fl ow profi le associated with the fl ow rates found in capillary HPLC. As a consequence of this effect increases in the fl ow rate will result in a greater variance, due to the frictional effects of the surface of the tubing being greater than the relative reduction in retention time within a capillary at the typical fl ow rates observed in capillary systems. This is typically measured by a parameter referred to as the variance.
= 16 %! (
"
This would then suggest that for chromatographers the use of smaller particles is highly benefi cial and that in all cases the smaller variant of particles should be used, however this is not the case but to better understand this statement it is necessary to better understand how chromatographic performance is measured. The most common approach to measuring chromatographic performance is to measure the effi ciency and one measure of that is the use of experimental plates, which is obtained from the following equation.
The variance measures the amount of peak broadening and is the standard measure of how much dispersion there is within a chromatographic system. The smaller the variance, the less dispersion there will be. The degree of diffusion or dispersion has been effectively modelled by Aris and Taylor [2], resulting in this equation for a laminar flow system.
#$$ = +"" 48
n time of the analyte, measured typically from the highest point of the w is the peak width at the base of the peak
is the retention time of the analyte, measured typically from the highest point of the peak response
In fact, what is being measured is the dispersion, or variance, of the analyte molecules within the chromatographic system. This dispersion is due to the random nature of movement of small molecules, and even though there is a general direction to the fl ow of the mobile phase, this random nature of dispersion will result in elements of the mobile phase moving at different linear velocities through the fl uidic pathways.
Where; Deff is the effective dispersion coefficient U is the average linear velocity r is the internal radius of the connector D is the measured dispersion coefficient
Where;
Deff is the effective dispersion coeffi cient U is the average linear velocity r is the internal radius of the connector D is the measured dispersion coeffi cient The important parameters to consider that will affect the dispersion rate are;
The important parameters to consider that will affect the dispersion rate are; Viscosity of mobile phase
Viscosity of mobile phase
All molecules will have a degree of energy that can be utilised for movement within the space that they occupy. When looking at a large number of molecules there is a tendency for the molecules to preferentially move from areas of high concentration to areas of lower concentration. This can be summarised by Fick’s fi rst and second laws of diffusion [1], relating to spatial and temporal concentration variations, which are given by;
The mobile phase can have an effect on the dispersion processes, with the viscosity of the mobile phase being the most predominant parameter which will affect the dispersion. Thus, if a mobile phase is more viscous there is a tendency for the diffusion of the analyte to be less than that if the analyte were in a less viscous mobile phase. The change in the viscosity can be caused by a range of external effects, however the buffer concentration and also the temperature are the parameters which will have the greatest effect on the viscosity.
Diffusion coefficient of molecule
Another factor to consider is the diffusion of the molecule through the mobile phase. In this case the larger the molecule, in general, the greater will be the resistance to movement and so the diffusion coeffi cient will be lower.
Other Factors
The dispersion within the chromatographic system does not just come from the volume attributable to the volume of the tubing, but can also arise from the injection volume, the void volume of the column, the volume associated with an ill-fi tting connector as well as the detector volume and can be summarised as;
V = Vinj + Vcol + Vtubing + Vconnectors + Vdetector cell
The volumes that each of these components contributes to the dispersion process within the chromatographic system can also be expressed in terms of a system variance with the individual variances having the same form as the above equation.
σ2 total = σ2 inj + σ2 col + σ2 tubing + σ2 connectors + σ2 detector cell
If the variance associated with the column is the major component of analyte retention time then changing the particle size to reduce this will have a benefi cial effect, however if wider bore tubing is being used, or a large injection volume then the variance or dispersion associated with these components will dwarf the contribution from the column and thus changes in the particle size will not be detectable. The impact of using inappropriate connectors and tubing can be seen in Figure 1.
The mobile phase can have an effect on the dispersion processes, with the viscosity of the mobile phase being the most predominant parameter which will affect the dispersion. Thus, if a mobile phase is more viscous there is a tendency for the diffusion of the analyte to be less than that if the analyte were in a less viscous mobile phase. The change in the viscosity can be caused by a range of external effects, however the buffer concentration and also the temperature are the parameters which will have the greatest effect on the viscosity.
The variance measures the amount of peak broadening and is the standard measure of how much dispersion there is within a chromatographic system. The smaller the variance, the less dispersion there will be. The degree of diffusion or dispersion has been effectively modelled by Aris and Taylor [2], resulting in this equation for a laminar fl ow system.
INTERNATIONAL LABMATE - FEBRUARY 2023
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