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.

Do your HPLC Methods Meet Good Chromatography Fundamentals? HPLC Training: RETAIN, SEPARATE and RESOLVE

When an HPLC or LC-MS method is not developed properly, it may not be selective for the sample and may not show any retention on the column. When this happens, everything injected may elute out at the same time and appear to be 100% pure . *These types of errors are easy to spot by anyone with formal training and experience in chromatography concepts (note: "years" on the job are not the same thing as years of practical knowledge and/or formal training in the technique. We routinely provide consulting services to clients with 10 or more years on the job performing chromatography analysis, but whom have not received any formal training during this time and make errors of this type).

Developing HPLC Methods which follow good chromatography guidelines and fundamentals should be key goals of HPLC method development. When developing an HPLC ("UHPLC") method, you must develop an analysis method which is selective for the compound of interest. 'Selectivity' is the most important variable to focus on when developing methods. Your method must demonstrate that it can: (1) Retain; (2) Separate and (3) baseline Resolve all peaks present (and any possible impurities or related substances), in a reliable and repeatable way. Failure to demonstrate that your HPLC method meets these basic requirements AND is selective for the sample being analyzed means your method is invalid.  

*You may be surprised to know that many HPLC methods (including some published papers and "Validated" Methods) do not meet these basic requirements. In this case, knowledge is truly power. If you have the practical knowledge and understanding of this technique, you will be able to easily spot these invalid methods. Make sure you review other methods as part of your training. Never assume because someone else published it or "did it that way", that it is valid. It may not be. An average of 20% of the methods I review do not meet these basic requirements and are invalid.

• Do your HPLC methods meet these requirements? 
• Can you demonstrate to others, who are knowledgeable in the technique, that your method follows good fundamentals? 

You should be able to demonstrate knowledge of these basic principles and have confidence in them.

Proper HPLC method development training must include and stress the following three practical, fundamental concepts of Retain, Separate and Resolve:

• Demonstrate that using your HPLC Method, that the sample is RETAINED on the Column. *Screen many columns to find the best one, early in the process. For most modes of chromatography, you do this by first estimating then measuring the column void volume. How do you know if it is retained long enough? Next, you calculate the K prime (Capacity Factor) of your sample to insure it meets basic chromatography guidelines (or regulations). * K prime > 1.5 (or > 2.0 for most regulated environments). Note: While retention is required, K prime is not applicable to SEC modes of chromatography.

• When satisfactory retention is achieved (K prime), begin optimizing the method to SEPARATE and baseline RESOLVE all compounds. This is achieved using proper HPLC Method Development techniques plus the practical knowledge and experience which comes from good training. Please refer to these two linked articles for more information; "Modern HPLC Method Development Tips (PART I)" and "Modern HPLC Method Development Tips (PART II)".

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 switching peak ('blip') appears on the baseline. It results from the change 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).

Modern HPLC Method Development Tips (PART II):

This is the second of two articles (Part I) which will provide suggestions on how to improve the HPLC (UHPLC) method development process. - PART II

INITIAL METHOD DEVELOPMENT:

1. Before you start, learn what you can about your sample, its hazards, solubility and properties. Conduct a quick literature and/or keyword search on the web using a popular search engine (e.g. GOOGLE). You can often find many journal articles, white papers, application notes and chemical data on the web in just a few minutes.
2. Determine which liquids your compound(s) are soluble in. Use a pipette and several glass vials or tubes with different solutions (pH is important too). This will narrow down the types of mobile phase and chromatography modes that you can use.
3. Column choice is the most important part of method development. The stationary phase that you choose has the single greatest effect on selectivity! Select the right column and mode of chromatography. Most RP methods should start with at least a modern ultra high purity, metal free type B silica column with a C8 or C18 support (*But you must select the column type that best suits your application). For small molecules (<1,000 Daltons) select a standard sized analytical column with a 2.5 to 5.0 micron particle size and pore size between 60 and 120 Å (e.g. 4.6 x 150 mm; 3.0 x 100 mm). *For larger peptide or protein molecules you will need a particle with a large pore size (~ 300 Å). For optimal results, columns with very small internal volumes should be paired with HPLC systems with similar ultra-low internal delay volumes. Your HPLC system should be optimized to balance the needs of good mixing, low delay volume and proper sampling rate for your method. If the method is likely to be transferred to different types of HPLC systems, then you may want to initially stay away from the < 2.1 u particle supports for your method development. At this time, these tiny particles can not be reliably packed into columns as well as the larger sized particles and generally have much poorer %RSD values than larger particles (i.e. 2.5 to 5 u). Method development is initially easier & generally more rugged using conventional particle sizes [Keep things simple when starting out. You can always change later on]. Once you have selected a column and decided on a flow rate, make sure you calculate and measure the actual column void volume to find the 'Tzero value' (column dwell volume). You will need this value to find out if your compound has been retained on the column (K prime) and to also determine most of the needed performance calculations and parameters.
4. Once you have selected an HPLC column (if possible, please start with a brand new column) you will need to test it and establish a baseline to show that it meets both the manufacturer’s specifications and, far more importantly, that it meets your method’s requirements. In most cases, do not use the manufacturer’s QC test solution for this. Those stds are designed to allow the column to easily pass manufacturing QC, not the more critical requirements that you may need to prove. We prefer to use a real sample mixture (~2 compounds) that are similar to the type proposed for the method. They must be well retained on the column (K prime of > 2), easy to prepare, stable and reliable. This std and the specific method you develop for it, will be used to prove the column’s performance (i.e. R, S, K prime, Tzero, Plates). It will be used again, when the column’s performance is called into question.  
5. Notes on Mobile phase and additives: Keep it simple. Avoid the use of any additives such as ion-pairing reagents when first starting out. They are overused in general and can cause problems later on. If required, they can always be added later on. Use only HPLC grade solvents, fresh RO HPLC grade Water and the highest purity acids, bases and/or additives, if required. Use only filtered (0.22u) products. Always dissolve samples in the mobile phase (or a weaker solution) for injection. For many RP methods a low pH mobile phase (~ pH 2.5) provides a good starting place. Samples with a pKa far enough away from this value are likely to be retained, stable and unaffected by small changes in pH. *pH is usually one of the last parameters which is optimized.
6. Use a Gradient Method to find the approximate elution conditions of the mixture AND make sure you are detecting all of the compounds injected onto the column [For dedicated RP isocratic methods, start with a high organic mobile phase % (i.e. 95%) and record the results. Continue to reduce the organic content in steps of 10% and observe where the best compromise exists between retention and elution]. For RP gradient methods, start with a very high aqueous % (e.g. 98%) and run your gradient, slowly, to a very high organic % (e.g. 95% or 98%, not 100%!) to make sure you retain, hold, and then elute everything. Your mobile phase conditions must be strong enough to elute everything off the column during the gradient portion of the run (long enough hold time). Please Do NOT include the gradient reversal portion back to initial conditions (wash and re-equilibration) of the gradient as part of the same analysis method. The method should end after the gradient has reached and been held at its maximum level for a period of time (we refer to this as the "hold time"). It should NOT switch back to the initial conditions to re-equilibrate the column. Don't make this novice mistake. Column flushing and re-equilibration should be a separate method and/or step, separate from your analysis method. If you include your column flushing (washing) and re-equilibration steps as part of your analysis method, you are also forcing the baseline's slope to change radically. This may interfere with integration plus include extra peaks and baseline changes that you are going to have to integrate, identify and explain to others (e.g. auditors). Additionally, including these wash steps as part of the same method wastes time as you must wait for these steps to complete before you can start to process the data obtained in the analysis method. Summary: Develop methods like the professionals do and create separate Analysis and Flush/Re-Equilibration Methods (or steps).
7. If your compounds can be seen with a UV/VIS detector, then make sure you are using a Diode Array Detector (aka, DAD or PDA) set to scan a wide range of wavelengths (e.g. 210 - 410 nm). Method development should not be performed using a single or multi-wavelength detector. This invites errors, limits the utility of the method and does not result in any cost savings. You must have a full scanning detector so you can detect all possible peaks at the same time. If you use a single or dual wavelength detector you may not know if an impurity has been introduced or if you have a co-eluter (because you will have no way to detect it). Generic starting settings for Wavelength Bandwidth should be ~ 8 nm, software based Reference Wavelength OFF and the sampling rate must be set to collect at least 20+ peaks/sample peak of the narrowest sample peak observed and integrated (at ½ height). Run with scanning turned 'on' for all analysis methods and review the spectral data for each run. This provides important qualitative data about the compounds which may be used for purity determination and also to demonstrate how the method is selective for the compound(s) of interest. *If your compounds do not absorb well (weak chromophores), then you may still want to have a UV/VIS detector inline (first) with a secondary detector second. The UV/VIS detector will still be very useful for troubleshooting and detecting other compounds. Select an appropriate type of detector and compatible mobile phase as required for the secondary detector (e.g. RID, EC, FLD, ELSD, CAD, MS...). Note: If available, LC-DAD-MS is one of the most useful instrument setups for LC method development.
8. This needs to be repeated (from Part I)....  Before starting ANY HPLC analysis, the HPLC pump must be running and operating with no problems, achieving a stable baseline, steady flow rate with as little pulsation as possible (~ 1% ripple or less). Accuracy depends on this. Do not begin any HPLC analysis unless the HPLC pumping system is working perfectly.