HPLC Column Support Pore VOLUME

If an HPLC column had no packing material inside it, then the volume of liquid contained in the cylinder could be calculated using the formula for the volume of a cylinder as follows: 

      Volume of Cylinder = Pi * r² * L;     

          [where Volume is in ul; Pi = 3.14; r = column radius (mm) and L= column length (mm)]

  Example: Using the above formula, a 4.6 mm x 250 mm column would have an empty volume of 4,155 ul (~ 4.16 mls).

For most chromatography applications we pack the column with a high surface area porous media. Often this is a silica based support. This support media fills the empty space inside the column reducing the total volume accessible by a liquid (or to the samples). If the media used was not porous, it would fill most of the space (depends on size and shape of media). Most commonly used chromatography supports are porous and leave about 70% (0.7) of the original volume available to the mobile phase and sample [Pore Volume = Surface Area (m²/g) x Pore Diameter  (Å) / 40,000]. Based on this information, we use a value of 0.7 as the average pore volume for a packed chromatography column (some supports will have pore volumes which are larger or smaller than this value. The manufacturer will often measure it and provide the value on their published specification sheet).


Using a typical 4.6mm x 250mm column we found the total volume to be 4,155 ul (4.16 mLs). If we now multiply this empty column volume by 0.7 (note: use 0.7 or 70% for columns with fully porous particles and 0.55 or 55% for superficially porous particles) we obtain 2,908ul total volume (2.9 mLs). This is the estimated volume of the fully packed column. This value is very important as it provides an estimate of what the column dead volume will be so we can calculate the 'T' zero time of an unretained analyte. This estimate will depend on the column dimensions, using our HPLC method (be sure and take into account the measured flow rate to determine the column "dead time"). This is one of the very first calculations you make when starting or modifying an HPLC method and is critical information to know at all stages of method development. All chromatographers should know how to estimate this value before using an HPLC system. *You should confirm this estimate by injecting an unretained sample onto the column and measure the retention volume, then compare the two values. The measured value is the most important number (the one we use for calculations), but the estimate should be close (+/- 15%). The estimate is still useful for troubelshooting and method development as when combined with K prime, it provides a quick measure if chromatography has occurred (retention).

For more information on the importance of knowing the HPLC Column Dead Time, please refer to this article link. 

Notes: The measured support pore Diameter (SIZE) is important for determining if the sample will have access to the inside of the support (e.g. A support with a pore size of 80Å will be too small for most large peptides or proteins, but a support that is 300Å will allow access to many, not all, larger molecules). A support with too small a pore diameter will not allow the sample to access the high surface area inside the support. Instead, the sample will be unretained and pass by it eluting at the column's void volume. This is the basis of SEC or GPC analysis where we use columns with different pore sizes to "filter" samples based on size. Large pores for large Mw samples and small pores for low Mw samples. A general rule is use 300Å or larger pores for samples with Mw > 10,000 and 80Å to 150Å for smaller samples.

More info on pore volume can be found at this article link: https://hplctips.blogspot.com/2014/12/hplc-column-pore-volume-or-pore.html

Using Smaller Diameter HPLC Columns (Calculate Linear Velocity)

Lots of 2.1mm ID chromatography columns are appearing on the market right now. Since most of us are using 4.6 mm ID columns to develop HPLC and UHPLC methods, use of these smaller ID columns requires a few adjustments be made to the method and often, the HPLC system. If gradient elution is used, then the gradient profile must be changed to compensate for changes in void volume of the column and the dwell volume of the system. Injection volume must also be adjusted in a linear fashion too. Additionally, to maintain the same initial mobile phase linear velocity through the column as we had before (to obtain the same approximate retention times), the flow rate must also be adjusted. *We will discuss how to calculate the change in flow rate in this installment.

In order to reproduce your original method, we must first adjust the flow rate for the new, narrower bore column. The formula to do this is very simple. We decrease the flow rate by using the square of the ratios of the column diameters times the flow rate.

Linear Velocity Change Formula:

( C₁  / C₂ )² x original flow rate (ml/min) = new flow rate (ml/min).

Where:  C₁  =  Diameter (mm) of new (smaller) column;
              C₂ =   Diameter (mm) of original column.
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Example #1: Find the new linear flow rate if we use a 2.1 mm ID column in place of a 4.6mm column with an initial flow rate of 1.000 ml/min.

              ( 2.1 / 4.6 ) ² x 1.000 = 0.208 (208 ul/min)


Example #2: Find the new linear flow rate if we use a 2.1 mm ID column in place of a 4.6mm column with an initial flow rate of 2.000 ml/min.

              ( 2.1 / 4.6 ) ² x 2.000 = 0.416 (416 ul/min)



Example #3: Find the new linear flow rate if we use a 1.0 mm ID column in place of a 4.6mm column with an initial flow rate of 1.500 ml/min.

              ( 1.0 / 4.6 ) ² x 1.500 = 0.071  (71 ul/min)



If we assume that the original flow rate is 1.000 ml/min then we can also use this table to get an idea of how the flow rate changes with decreasing column diameter (same particle size and support).

Column I.D. (mm)                 Flow Rate (ul/min)
            4.6                                          1,000
            2.1                                             208
            1.0                                               47
            0.3                                                 4
            0.15                                               1



Summary: Scaling down a method which was originally developed on a 4.6 mm ID column for use on a 2.1 mm ID column (with the same particle size) requires that the flow path of the HPLC system be optimized (reduced) to minimize diffusion and the flow rate reduced five time to achieve the same linear velocity. If the particle size is also going to be reduced from 5u to 2.5u or smaller, then increases in the flow rate may be considered to take advantage of the optimized plate counts using optimized linear velocities (which are much higher for smaller particles).

HPLC to UHPLC Conversion Notes (Column Dimensions, Flow Rate, Injection Volume & System Dispersion)

The use of ultra-high performance liquid chromatography (UHPLC) columns to reduce analysis times and sometimes improve detection limits is a hot topic. UHPLC presents a number of new issues. The incorporation of smaller 1.9 to 3.0 micron particles and smaller frits will raise backpressures and increase system wear and tear. Smaller diameter lines are often used (I.D. of 0.12mm or less) which can increase blockages and clogs if you do not filter your mobile phase and samples through a 0.45 or 0.2 micron filters. Piston seals and valve rotors can wear out early due to the very high pressures, heating and stress imposed on them. You should monitor your HPLC system carefully over time and consider increasing the frequency of preventative maintenance and inspection services as well. However, the smaller particle sizes can provide better resolution in some applications so they are well worth evaluating.

I must answer twenty or so questions each week in the area of UHPLC. The most common questions deal with selection of an UHPLC column and making adjustments to a method for the changes which effect: (1) Column Dimensions; (2) Flow Rate; (3) Injection Volume and (4) System Dispersion. The good news is that some of these questions can be answered with some basic math while others just require a basic understanding of how the system works.

(1) COLUMN DIMENSIONS: Let's start by making things as simple and brief as possible (this is supposed to be a "hint & tip", not a thirty page article). When initially converting from a convention HPLC column (e.g. with 5 micron particles) to an UHPLC column (e.g. with 1.9 to 3 micron particles), initially select a column with the same I.D. and length for the calculation. This way only the particle size changes. *I like to change one variable at a time. If you would like to change the column length to take advantage of some of the increased efficiency (and decrease the pressure!) which results from smaller particles, then please refer to the following equation.

     EQUATION A:  'Lc2' = ('Lc1' * 'p2') / 'p1'

[ 'Lc1' = Length of Column #1 in mm; 'Lc2' = Length of Column #2 in mm; 'p1' = particle size of Column #1 in microns; 'p2' = particle size of Column #2 in microns].
                    
   Example: Column # 1 is a standard HPLC column;  4.6 mm x 250 mm (5u) Column. You want to find out the length of an equivalent column which uses 1.9 micron particles instead of the 5 micron particles.

   'Lc2' = (250 * 1.9) / 5 ; Answer is: 'Lc2' = 95 mm. *So a 10 cm long column would be a good choice here.


(2) FLOW RATE: Flow rate is directly proportional to column diameter and as we saw above in Equation A, the particle size can also affect it too. If you keep the column length and internal diameter the same, then the linear flow will be unchanged with the same particle size. A change to the particle size alone will change the flow rate as follows: 'Fc2' = 'Fc1' x ('p1'/'p2').

A change to a smaller diameter column to compensate for the improved efficiency will require a change to the original flow rate to preserve the linear velocity. Please refer to the following equation.

     EQUATION B:   'Fc2' = ('d2' / 'd1')^2 * 'Fc1'

['Fc1' = Flow Rate of Column #1 in ml/min; 'Fc2' = Flow Rate of Column #2 in ml/min; 'd1' = Column #1 Diameter in mm; 'd2' = Column #2 Diameter in mm].
                     
   Example: Column # 1 is a standard 4.6 mm ID Column. You want to find out what the linear flow rate should be if you use a smaller diameter column (2.1mm in this example).

   'Fc2' = (2.1/4.6)^2 * 1.000 ; Answer is: 'Fc2' = 0.208 ml/min. *A flow rate of 200 ul/min would be fine. 

However, one other factor should be considered. The optimum flow rate for sub 2.5u particles are often about double that of the "normal" linear flow rate used with conventional particles (>2.5u). Evidence for this has been shown through analysis of the van Deemter curve with the tiniest particles showing much flatter curves. Retention (K prime) can often be maintained by combining twice the normal flow rate and speeding up the gradient time by a factor of 2. So a method utilizing std sized particles with a linear flow rate of 0.200 ml/min might benefit from a faster flow rate of 0.400 ml/min and a twice as fast gradient composition change.


(3) INJECTION VOLUME: A change in the column dimension may require a change to the injection volume (note: "volume" and concentration are two different things. If the solution concentration remains the same and you inject less, the on-column sample concentration will also be less). The smaller the internal volume of the column, the smaller the injection volume. To calculate the linear change in volume, please refer to the following equation.

     EQUATION C:   'V2' = 'V1' * {('d2'^2 * 'L2') / ('d1'^2 * 'L1')}

['V1' = Injection Volume #1 in ul; 'V2' = Injection Volume #2 in ul; 'L1' = Column #1 Length in mm; 'L2' = Column #2 Length in mm; 'd1' = Column #1 Diameter in mm; 'd2' = Column #2 Diameter in mm].
                     
   Example: Current injection volume is 10 ul. Column # 1 is a standard 4.6 mm ID x 250 mm Column. You want to find out what the equivalent injection volume should be for a 2.1 mm ID x 150 mm column.

   'V2' = 10 * (2.1^2 * 150) / (4.6^2 * 250) ; Answer is: 'V2' = 1.25 ul.



(4) SYSTEM DISPERSION: When converting HPLC methods to "UHPLC" methods, few parameters effects the results obtained more than the HPLC system's System Dispersion. The volume of liquid that is contained between the injector needle and flow cell (with the column removed or by-passed) is know as the system dispersion volume. This volume is determined by how the specific HPLC is designed and plumbed. On most HPLC systems, it can be easily changed and optimized to fit the specific application desired and only requires that you have a solid understanding of how the HPLC system works. The choice of connection tubing ID and length, how the autoinjector is programmed, its loop size and the detector's flow cell volume all contribute to the system dispersion volume. In the same way that changes to the total column volume can effect the peak shape and resolution, the internal system dispersion volume also contributes to the results. 

With standard sized analytical columns (i.e. 4.6 x 250 mm), the typical HPLC's system volume is so small relative to the volume of the column (e.g. 100 ul system dispersion vs 2900 ul column volume, or 3.5%) that it does not negatively impact the chromatography. However, anytime we utilize a tiny HPLC column whose column volume is a fraction of that found in a standard column (i.e. 100 ul system dispersion vs 2.1 x 50 mm column with 120 ul volume), diffusion and band spreading can quickly become so significant that effective plate numbers are quickly reduced below values found on a standard sized column. As column volume decreases (and approaches the system volume) the total system dispersion volume must also decrease. In general, try and keep the system dispersion volume at or below 10% of the column dead volume. This is most easily accomplished by reducing the number of connections and fittings used, reducing the lengths of all tubing used, using much narrower ID tubing (e.g. 0.12 mm vs 0.17 mm ID), reducing flow cell volume and reducing the flow-through volume in the autoinjector (i.e. loop size, needle seat, etc). The injector is often the largest contributor to the system dispersion so concentrate efforts here (e.g. after injection, switch the loop out of the flow path).