Adjusting the HPLC Gradient Time For Changes in Column Diameter and/or Length (same particle size)

Changes to the column diameter (to scale the method up or down) can be calculated. For an established HPLC method using the same support type (same exact material and particle size) where the column dimensions and flow rate are known. Note: If only the diameter changes and the lengths remain the same (proper linear flow rates used in both cases), then the resulting gradient times will also be similar. If the column lengths change, then the gradient time will change.

Changes to the Gradient Time (Tg2) used for a second column which has a different diameter, "Dc2" and/or length, "Lc2" can be calculated if you know: 

• Tg1 [Time, of initial Gradient on Column #1];
• Tg2 [Time of second Gradient on Column #2];
  
• Fc1 [Flow Rate of Column 1] ;
• Fc2 [Flow Rate of Column 2];
• Dc1 [Diameter of Column 1]
• Dc2 [Diameter of Column 2];
• Lc1 [Length of Column 1];
• Lc2 [Length of Column 2].

        Tg2 = Tg1 x (Fc1 / Fc2) x (Dc2² / Dc1²) x (Lc2 / Lc1)

 

Example: Initial Method utilizes a 4.6 x 150 mm, 5u column run at 1.00 mL/min with a 10 minute gradient program and we wish to transfer this gradient method over to a column with a 2.1 mm diameter (ID) x 100 mm column run at 200 ul/min.

   Tg2 = 10 x (1 / 0.2) x (2.1² / 4.6²) x (100 /150)

   Tg2 = 10 x (5) x (4.41/21.16) x (0.67) 

   Tg2 =  50 x 0.208 x 0.67

   Tg2 =  6.97 minutes.

The gradient time used on the 2.1 x 100 mm column run at 0.200 mL/min would be ~ 7 minutes (vs 10 minutes on the 4.6 x 150 mm column at 1 mL/min).

 

NOTE: A note about optimized flow rates. If the Column PARTICLE SIZE changes, esp from greater than 3.5 u to less than 3.5 u, then the optimized flow rate may also change too. Please refer to my article; 

• "Speed Up HPLC Analysis Time Using Higher than "Normal" Flow Rates with SMALLER Particles" for more information.

HPLC to UHPLC Conversion Notes (Gradient Time Program Adjustment)

In an earlier article we discussed how to adjust the flow rate, injection volume and column dimensions when scaling an HPLC method UP or Down. The formula's needed to do this are fairly simple. If we adjust for changes in the column dimensions or flow rate, what types of changes are needed to adjust the gradient time? The formula to make this adjustment is also very simple. Here is the information you need.

Terms Used in Formula:

Time in minutes, Gradient (Initial): Tg1

Time in minutes, Gradient (New):   Tg2

Flow Rate in mL/min, Column (Initial): Fc1

Flow Rate in mL/min, Column (New): Fc2

Column Diameter, mm (Initial): Dc1

Column Diameter, mm (New): Dc2

Column Length, mm (Initial): Lc1

Column Length, mm (New): Lc2

• Tg2 = Tg1 x (Fc1/Fc2) x ((Dc2²) / (Dc1²)) x (Lc2 x Lc1)

Here is an example problem to solve for. 

If we start with a flow rate of 1.000 mL/min (Fc1) on a 4.6 x 250 mm column with 5 micron support (Dc1 & Lc1) and have an initial Gradient Time of 10 minutes (Tg1), then what would the new gradient time be if we switched to a sub 2 micron support in a 2.1 x 50 mm column (Dc2 & Lc2) at 0.200 mL/min (Fc2)? 

To solve the equation we will plug-in the values for each part of the equation separately, then multiply them to obtain the result.

  (Fc1/Fc2):    1.000/0.200 = 5

  (Dc2²) / (Dc1²)  4.41/21.16 = 0.21

   (Lc2 x Lc1) = 50/250 = 0.20

  Tg2 = 10 x 5 x 0.21 x 0.20 

  Tg2 = 2.10 (or 2.10 minutes)

If a 2.1 x 50 mm column was substituted for the 4.6 x 250 mm AND the flow rate was changed from 1.000 mL/min to 0.200 mL/min, then the initial programmed gradient time of 10 minutes would be changed to 2.1 minutes

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 K Prime. Also known as: Retention Factor, Capacity Factor): One of the Single Most Important HPLC Parameters of All

The role of Capacity Factor / Ratio (K prime) in liquid chromatography is to provide a calculation or ratio which defines how much interaction the solute (sample peak) has with the stationary phase material relative to the mobile phase (IOW: the relative time the sample spends interacting with the support vs. the mobile phase). If this interaction is too short (i.e. K prime less than 1.0), then no chromatography has taken place and you have just developed a "flow-injection" method (the same as if no column was used) instead of a chromatography method. The method fails all validation and is NOT fit for purpose. Sample Retention must be long enough to demonstrate that the method developed is specific to the sample and shows good selectivity (retention) for the sample analyzed. This is true for most, but not all modes of liquid chromatography (3). 

• New and ever 'experienced' users lacking training in HPLC often make this error, developing methods where the sample has little to no retention on the column. We routinely review methods where the actual K prime of the key sample is measured to be at or near 0, failing to show any chromatography took place in the method (*The Journals are filled with thousands of examples of invalid HPLC methods of analysis). This mistake is made because the author(s) have no formal training in liquid chromatography and do not understand the basics of the technique. 
• Note: Slowing down the flow rate to "show" a later elution time DOES NOT increase K prime (a very common novice mistake) !!! 
  

Observance of the fundamentals of chromatography are key to developing high quality HPLC methods. For most modes of HPLC, highest on this list of basic fundamentals is that the sample(s) be retained on the HPLC column used and not eluted out at or near the column's void volume (we often refer to this time in minutes as, "T-zero" or "t0"). Many chromatography methods fail this simple test of retention and are invalid as written. Knowing what a compound's retention or capacity factor is allows us to be confident that it has been retained and eluted past this critical point, but to first calculate K prime, we first need to know the HPLC column's void volume. 

Calculation and/or measurement of the Column Void Volume should be one of the very first chromatography method development tasks you learn to perform. Knowing the column void volume allows you to determine the retention time of an unretained sample and the resulting retention factor (K prime) of each sample eluted after it. To do this, you must calculate the column void volume AND inject a sample which will not be retained by the column to determine what time an unretained sample will be eluted off the column. This establishes the 'T' zero time, or T(0). The time it takes an unretained compound to elute off the column is critical to know. If your HPLC method does not retain the sample on the column long enough past this time, then you are not allowing any chromatography to occur. Once you have this T(0) value, you can then determine the retention factor (the "K Prime") of your actual sample(s) using the simple ratio formula below. Your final method should baseline separate all compounds apart and, if properly developed, each sample peak will often have K Prime values between 2.0 and 10.0. K prime values of greater than 10 are acceptable, but often show minimal improvements to resolution. Try and insure that the earliest eluting peak in your sample has a K Prime of  >1.5. Do not develop methods which only result in K Primes of less than 1.5 (an indication of poor quality chromatography). 

Note 1: Many regulatory agencies (e.g. The USA FDA) requires that K prime values for HPLC separations be equal to or greater than 2.0 to meet Specificity acceptance criteria (System Suitability/Method Validation). After all, if it elutes at or near the void volume, then your method is not specific for anything. Besides being unscientific in design, your method will fail System Suitability and fail validation. IOW: It does not meet this basic requirement.

• K Prime, K1 (Capacity Factor or Retention Factor) Formula:

       k1 = [T(R) - T(0)] / T(0)

• (where T(R) equals the retention time of the peak in minutes and T(0) is
  the retention time of an unretained peak). 
• *The 'K Prime' of your sample must be > 1.00. A value greater than 1.5 should be your goal.

Example #1: 
 T(0) found to be 2.90 minutes and the sample elutes at 5.80 minutes. k1 = 5.80 - 2.90 / 2.90. k1 = 1.00.

Example #2:
 T(0) found to be 2.90 minutes and the sample elutes at 9.10 minutes. k1 = 9.10 - 2.90 / 2.90. k1 = 2.13.

Example #3:
 T(0) found to be 1.75 minutes and the sample elutes at 1.74 minutes. k1 = 0. No retention and no chromatography have taken place at all. The method is invalid.


Note 2: I see and read published HPLC methods (including "Validated Methods" !) every week which ignore this fundamental requirement and present data showing little to no retention of the primary sample on the column. Most are RP methods run on popular C18 columns and show the main peak of interest eluting out as a nice sharp peak right at the void volume.  These methods often describe the sample analyzed as "100% pure" and are fully validated (because the person doing the work may not have had any HPLC experience or training)! A mixture will always look like a single peak by HPLC when no 'chromatography' is employed to separate out all of the possible components. The sample must be retained on the column for a period of time before we can conclude anything about its purity by the method employed.

Note 3: In some cases, when other modes of chromatography are utilized (e.g. ion exchange, size exclusion chromatography (SEC / GPC), K prime is not as relevant. The mode of chromatography can affect the interpretation. For example: This is because size exclusion chromatography relies on the sample's interaction with well defined pores inside the support (inclusion/exclusion) to separate based on molar size. A variety of pore sizes can be used to "filter" the sample. So a large K prime value might be normal for a molecule that is low in molecular weight and spends a lot of time working its way through the column. A high molecular weight sample might just "shoot" through the column due to little or no interaction with the pores. You still need to have retention on the column, but now it is determined by how long it takes the sample to find its way out of the column. SEC columns are bracketed by Pore Size (e.g Mw. Excluding all samples that do not "fit"). With size exclusion columns, determine the Retention and Exclusion times, not the K prime). This article is specific to thr more common cases where traditional HPLC NP or RP modes are used. In these cases, low K prime values indicate no retention took place and the method fails all claims of specificity for the sample (selectivity is absent or poor). HPLC methods with little to no selectivity fail scientifically as no chromatography has taken place.

HPLC Column PORE SIZE (or Pore Diameter) and Retention Time

Think of your typical porous bare silica support as a big sponge full of holes. All of those holes (pores) are where the sample will migrate through before emerging out the other side. With conventional chromatography supports, most of the interaction takes place inside the particle, not on the surface. The size and number of these openings relate to retention time. Besides particle size (particle diameter), pore size is one of the most important characteristics of silica based chromatography supports.


The pore size or pore diameter is often expressed in Angstroms (i.e. 80 A = 8 nm). The degree of porosity relates to the hydrodynamic volume of your sample and is inversely related to the surface area of the support. The larger the surface area of the support (smaller pore size), the longer the possible retention of the sample. For small drug molecule samples under 1,000 daltons (an estimate only) we often use high surface area supports with small pore sizes between 60 and 150 Angstroms (~ 200 to 500 square meters per gram). These provide high retention characteristics useful in separating apart many small compounds in one analysis run. For larger molecules (i.e. peptides and proteins), we employ supports with larger pore sizes (~300 Angstroms). Particles with small pores have larger surface areas which can provide more interaction with the sample. Note: Pore size is often determined using the BET Nitrogen adsorption/desorption equation. Due to endcapping of the support (e.g. C8 or C18), the actual value obtained is often 20-30% less than the original value.

When comparing bare silica columns or trying to identify similar conventional columns for use in a method, pore size must be considered. Manufacturer's publish the pore size in Angstroms (*sometimes in nm) for their different supports. Choosing columns with similar pore sizes is just one of many parameters needed to provide similar retention characteristics. 

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).