Determine the HPLC System Dwell Volume (Gradient Delay Volume)

Note: The total HPLC gradient system dwell volume is different than the HPLC column’s void volume. Two different terms for two very different measurements.

When we perform gradient HPLC analysis, the mobile phase composition is changed over a period of time. The mobile phase is mixed in real time by the pump(s), mixer and/or valves, then transported to the injector and finally, on to the head of the HPLC column. The total volume of liquid contained between where the mobile phase is mixed and the head of the column helps us determine when the newly mixed solution arrives at the column head (it is not instantaneous). This delay is often referred to as the gradient delay time (or delay volume) and its value will vary for different HPLC systems due mainly to differences in tubing dimensions used, pumping system type and the design of the flow path. 

For example: If the system dwell volume is found to be 1 ml and the flow rate used is 1.000 ml/min, then the gradient delay time is one minute. 

So how do we know what the system dwell volume or gradient delay volume is? Well, we measure it of course!

Measure the ‘System Dwell Volume’ (aka: Gradient Delay Volume)*:

(1) REMOVE any HPLC column(s) and install a Zero Dead Volume Union (*ZDV) or a restriction capillary of know volume in its place.

(2) Prepare Two Different Mobile phase solutions:

Bottle ‘A’: HPLC grade Methanol (MeOH).

Bottle ‘B’: HPLC grade Methanol with 0.1% acetone added (v/v).

(3) Set your UV/VIS detector to 265 nm (8 nm Bandwidth, Reference OFF).

(4) Program a suitable system flow rate and create a simple Gradient Method (linear change) which starts at 0.0 minutes with 100% ‘A’ (HPLC grade Methanol) and 0% B (HPLC grade Methanol with 0.1% acetone added) and runs to 0% ‘A’ and 100% ‘B’ for about 10.0 minutes (actual times used will depend on your selected flow rate).

(5) Flush and degas both solutions, ‘B’ first, then ‘A’ through the system until you get a nice clean, flat baseline. Make sure their is enough backpressure on the pump (>40 bars) to obtain a stable signal (use a restrictor or back-pressure regulator if needed).

(6) No injection should occur during this method.

(7) Start the method (RUN) and observe the 265 nm signal over time. At some point you should observe the signal begin to rise. When you see this signal change occur, the acetone has finally made it from the pump head to the detector’s flow cell. Make note of the time this occurs. 

Using the known flow rate and observed signal change time, you can now estimate the total system dwell volume. 

Example: If you observe the signal start to rise steeply at 2.00 minutes and your flow rate was 1.000 ml/min. Your system dwell volume would be 2.000 mls. 

A more accurate system dwell volume value can be obtained by next running the same method with an injection of acetone (e.g. 1 ul) and noting the time at which the injection peak is first seen. That will give you the time it takes the sample (and therefore the volume needed) to go from the injector to the flow cell. If you subtract this time off the system dwell time you recorded in the last test, you will have the actual measured time from the pump head (or proportioning valve) to the head of the column (vs the flow cell). Normally the volume contained in this tubing and flow cell are very small relative to the volume in the rest of the system, so we can ignore them. However, when using some of the very low volume columns (e.g. 2.1 x 50 mm), the volume contained in these areas can become significant so when appropriate, we need to be aware of them.

Failure to take into account changes in HPLC system dwell volumes can result in methods which no longer work or provide different results. This is because the gradient rate change you program in your method may not allow enough time for the new mobile phase composition to reach and flow all the way through the column in the time that you have programmed. A common mistake we see is when users forget to adjust the gradient profile when changing column dimensions or program changes using too fast a time.

BTW: One common trick we use to improve compatibility between systems which have different dwell volumes is to include an initial (time 0.0)  isocratic hold-time into the start of each method. If all systems used have system delay volumes under 3 mls, then add a 3 minute isocratic hold time at the start of each method (if 1.000 ml/min flow rates are used), before any gradient starts. While not the best way to deal with the issue, this type of “cheat” can make it possible to quickly adapt a method for use on several different system types.

*Note: This is a generic method to determine the system dwell volume or gradient delay volume. Detector signal buffering and flow cell volume also adds to the delay and in some cases, must also be accounted for too. There are many other methods which can be used for this determination as well. This proposed example serves to illustrate the concept only.

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).

Determination of HPLC Column Void Volume / Dead Volume, Dead Time (T zero):

Column Hold-up Volume, Column Dead Time or 'Column Void Volume' (the preferred name) are all different terms we apply to find the internal volume of a packed column  (divided by the flow rate and usually expressed in minutes for the Column Void Time). You must know what this value is BEFORE starting to run an HPLC method or perform liquid chromatography. The value for column void volume changes for different column dimensions and different column support types (e.g. fully porous, superficially porous etc) .

Are you peaks or samples eluting at or near the column void volume? If so, for most modes of chromatography, this implies that no chromatography has taken place and no HPLC method has been developed (SEC/GPC separate based on hydrodynamic volume, so elution at or near the column volume means the sample(s) were excluded from the column). Individuals with little to no chromatography training or experience often make this mistake and create methods which show poor retention. Make sure your methods are designed to retain each sample for a long enough time period on the column (K prime). How do you know how long is long enough? Start by estimating the Column Void Volume (use our table or calculate it for an estimate) then, calculate the K prime value for your sample. The K prime for each peak should be at least 1.5 (>2.0 is the accepted standard for most regulatory authorities) for the method to be useful and selective. *A more accurate value of column void volume will be found by measuring the void volume of your column (please read on).

Knowing the Column Void Volume and the Flow Rate used allows you to calculate the Column Void Time (which is the most useful initial value). Determining  the column void time or T0 ("Tee Zero" as we call it), is necessary to find other important chromatography values such as: the Resolution, Separation Factor and Capacity Factor (K prime aka: "K1") in a chromatography separation. Ideally, it is measured by injecting a sample which is unretained by the column & mobile phase (it passes right through the column support with little to no interaction). It may also be easily estimated for most fully porous, spherical, bare or coated silica supports if you know a few physical specifications of the column and media used. You should first estimate it, then measure it (the two values should be close, +/- 15%). Note: A practical "tip". You can also estimate T0 by noting when the small injector valve pressure peak ('blip') appears on the baseline. It results from the pressure change which occurs from switching the injection valve from the "load" to "inject" positions. Use a low UV wavelength to observe this deflection on the baseline.

Here is short list of typical HPLC column dimensions and their associated estimated void volumes for fully porous silica supports. At a flow rate of 1.000 ml/min these values would also be the same as the void time in minutes.

COLUMN DIMENSIONS (I.D. x Length (mm))                 VOID VOLUME (ml)

                         2.1 x  50                                                                  0.12
                         2.1 x 100                                                                 0.24
                         2.1 x 150                                                                 0.37
                         2.1 x 250                                                                 0.61
                         2.1 x 300                                                                 0.73

                         4.6 x  50                                                                  0.58
                         4.6 x 100                                                                 1.16
                         4.6 x 150                                                                 1.75
                         4.6 x 250                                                                 2.90
                         4.6 x 300                                                                 3.49

                       10.0 x 100                                                                 5.50
                       10.0 x 150                                                                 8.25
                       10.0 x 250                                                               13.75
                       10.0 x 300                                                               16.49

•  Column Void Volume Equation for Std Sized, FULLY Porous Supports:

Column Volume (ul) = (d^2 *Pi * L * 0.7) / 4 ;

•  Column Void Volume Equation for SUPERFICIALLY Porous Supports (e.g. Fused-Core, Core-Shell etc):

Column Volume (ul) = (d^2 *Pi * L * 0.5) / 4 .

   Note: Column Diameter & Length are in mm. Volumes are estimates (always measure to find the actual value).

[Note: All you need is the column's length and ID to estimate it. For most fully porous supports, use a 'Pore Volume' value of 0.70 in the above equation. This is the most commonly measures pore volume found for non-encapped, fully porous spherical bare silica support (please check with the manufacturer for the actual value of your support). For superficially porous supports, use a value of 0.50. Estimating the value will often get you close to the measured value, but due to the unique chemistries used to prepare supports, it is only an approximation.

Always measure the actual void volume of your specific HPLC column with a compound which is unretained by your column. For RP applications which utilize at least 20% organic, Uracil or Thiourea are often used, but some inorganic salts (e.g. sodium nitrite and sodium nitrate) have also been shown to work as well. When determining the "Column Void Volume", you are really measuring the void volume of the column plus any extra-column volume from the injection volume plus all lines connecting the injection to the column and the column to the flow cell. Note: This is very different from the "System Dwell Volume" which includes the volume from the pump (or gradient valve) to the column head.

A more detailed version of this table with other common HPLC Column Sizes and Tubing Volumes for capillary lines are available at the following links (Link #1) or (Link #2).