Number of theoretical plates (N), Calculation Formulas

Number of theoretical plates (N):

Often used to quantify the efficiency (performance) of a column (HPLC or GC). "Plates" are expressed per meter of column length and should be calculated based on a retained peak with ideal peak shape or symmetry. 

   N = Plates; tr = Retention Time of Peak; w = Peak width;  w_0.5 = Peak width measured at half height.

Two popular formulas are:

Tangent: USP (United States Pharmacopeia / ASTM)

Best for Gaussian peaks. Peak width is often determined at 13.4% of the peak height (w). Inaccurate for peaks which are non-Gaussian, poorly resolved or tail.

   N = 16 (tr / w)²

Half Peak Height: (European Pharmacopeia)

For peaks which are less Gaussian in appearance, using a slightly different formula with the peak width measurement made at the half-height (W_0.5). Less accurate for peaks which are poorly resolved or tail.

   N = 5.54 (tr / w_0.5)²

 

• Other formulas, not included, for calculating Plate numbers include: Half Width, Variance Method, Area / Height & Exponential Modified Gaussian (EMG).
• Caution. HPLC column "Plate" values should not be used for a final determination of efficiency unless you are comparing all results on the same exact HPLC system, which is setup and run under identical conditions each time. Since the result is based on many possible variables, including how your HPLC system is plumbed (dwell volume & tubing ID), the peak's Kprime and symmetry, the detector used, sampling rate, integration quality, flow cell volume, flow rate, actual column used (to name a few), it can easily be manipulated to be very large or small.

The HPLC Restriction Capillary; Troubleshooting, Qualification and Running Without A Column:

Most types of HPLC pumps will not operate properly without 30 or more bars of back-pressure on their outlets to prevent cavitation and excessive pulsation. Columns play a vital role in stabilizing the baseline during an analysis. In this application, they not only aid retention, but act as a cushion or buffer.

When we want to closely replicate the operation of an HPLC system under "normal" conditions and do not want to use an HPLC column in-line (because a column adds variability), we install a "restrictor" such as a restriction capillary in its place. A restriction capillary is often a very narrow ID section of long tubing (capillary) which will restrict the flow of mobile phase through it. For most HPLC systems, a restrictor which is sized to provide about 1,000 to 2,000 psi (~ 70 to 140 Bars) of back-pressure will closely replicate normal operating conditions. The restrictor can be chosen based on length, ID, volume and your flow rate to create this level of back-pressure. You could place a high pressure rated, zero-dead-volume union its place, but in doing so, the system back-pressure may be extremely low ( a few bars) and show poor pump performance. We need to replicate actual analysis conditions during testing or the results obtained may be invalid and unscientific. An HPLC column, with its densely packed small particles inside acts as a pressure pulse buffer and adds a great deal of back-pressure to the HPLC system. That back-pressure greatly improves the stability of the pump operation and overall baseline. HPLC Columns prevents pulsations by acting as a dampener and/or system buffer.

There will be times when you need to operate the HPLC system without an HPLC column installed.

For Example: 

• Troubleshooting sources of contamination, carryover or artifact peaks on a column;
• Measuring the HPLC system delay volume (gradient delay);
• Testing the performance of the injector;
• Testing the performance of the pump (measure % ripple); 
• Testing the performance of a detector module (measure S/N);
• Running HPLC Operational Qualification Tests (OQ);
• Running HPLC Installation Qualification Tests (IQ);
• Running Performance Verification Tests on a Module (PV);
• Running many of the ASTM Tests (e.g. "Baseline Noise & Drift Test").

Example of a commercially available Restriction Capillary (Agilent P/N G1312-67500). You will want to include any needed details of the restriction capillary chosen for your work in the SOP's that you write which utilize it as part of any test (P/N, source, dimensions, volume...).

Vespel, Tefzel or PEEK Valve Rotor Seals ?

One of the most common HPLC preventative maintenance parts is the injector valve rotor seal. Worldwide, the majority of these chromatography parts are produced by Rheodyne (IDEX) or Valco Instruments (VICI) and used by the major instrument manufacturers in their products. These valve seals are critical to maintaining a leak free, high pressure seal inside the injector. They are subjected to a lot of wear and chemical exposure with use. They have a finite lifetime which may be very short, in some applications (a few months) or last for many years in others. *The most common reason for rotor seal damage is a lack of flushing when buffers are used. Regular flushing down of the flow path (without the buffer) is required to maintain a clean flow path. Buffer deposits and crystals scratch and damage the rotor surfaces. Depending on the specific use and application, rotor seals are often replaced as a preventative measure once every 6 or 12 months. They should also be replaced whenever they are scratched, heavily worn, no longer sealing well, leak or become contaminated. Failure to maintain your injector's parts may lead to HPLC carry-over contamination problems.

The choice of rotor seal material should be based on: (1) the types of chemicals it will come into contact with; (2) the working pH range; (3) the temperature range.

• Note: When choosing a valve rotor seal material, please refer to the valve manufacturer's information, compatibility and advice. Blends and properties may vary between vendors so always verify compatibility with them before use.

 
Common HPLC Rotor Seal Material Types:

 Vespel ^®: Chemically, this is a polyimide blend (DuPont). One of the most widely used materials for HPLC valve rotor seals. It has excellent chemical compatibility with most HPLC mobile phases, excellent temperature stability and a pH limit of 10. An excellent choice for most applications.

Tefzel ^®: Chemical name, ethylene-tetrafluoroethylene (aka, "ETFE"). It has excellent chemical compatibility with most HPLC mobile phases and a higher pH limit of 14. Tefzel's preferred applications are where very high (>9) or very low (<3) pH solutions or mobile phases are used. Not compatible with some chlorinated solvents and in most forms it has a temperature limit of 50°C.

PEEK: Chemical name, polyether-ether ketone. Known for applications where biocompatibility and / or high temperatures are of concern. Like Tefzel, it has excellent chemical compatibility at room temperature with most HPLC mobile phases. Most vendors report a working pH range between 1 and 14. Unlike Tefzel, it has a much higher temperature limit (i.e. 100°C or higher), but its resistance to some chemicals appear to degrade with increasing temperature. Contraindicated where it will come into contact with solutions of THF, methylene chloride, DMSO or concentrated acids (i.e. nitric or sulfuric). Some sources have observed problems with chloroform as well, especially with PEEK tubing, so it may not be recommended for those applications.

 

For more information on troubleshooting HPLC injector valves, please refer to this linked article, "Troubleshooting HPLC Injectors (Manual and Automated)". 

HPLC Baseline Stabilization Tips for Refractive Index Detectors (RI or RID)

If you use refractive index detection (RID) for your HPLC samples, then you are already familiar with the very long equilibration periods needed to stabilize the system and associated baseline drift. Initial equilibration can take several hours. In fact, re-equilibration takes far longer to achieve with this detection mode than most others (i.e. UV/VIS, FLUOR, EC). While there is no quick cure for these delays, there are a number of things that you may be able to do to minimize or reduce these wait times. Here are a few to consider.

• ROOM TEMPERATURE: Locate the RID in a quiet, stable location. If the room temperature in which your HPLC system with RID system is located fluctuates by even one degree C, that can effect the stabilization of the system. The ideal room to use RID will be away from any windows, drafts, doorways, direct sunlight and HVAC vents or ducts. It should be located in a quiet area away from people walking by it. All of these things can contribute to temperature instability, which is what you want to avoid.

• INSULATION of HPLC CAPILLARY LINES: All of those stainless steel capillary lines leading from your column outlet to the RID's flow cell are loosing heat to the surrounding air (cooling). To reduce this thermal effect, insulate any metal lines with plastic tubing to reduce the heat loss. Most any type of laboratory grade, thick walled plastic tubing can be used. Pass the SS tubing through the plastic insulated tubing or use a section of split-tubing to cover it. Cover as much of the exposed tubing as possible, right up to the fittings. - Note: Sometime the HPLC system's solvent bottles may be subjected to varying temperature changes too. In these cases you can wrap the bottles with an appropriate insulating material to reduce the effects.

• FLOW CELL TEMPERATURE: Modern RID units have a heated flow cell with thermostat to control the temperature of the flow cell. This helps stabilize the temperature inside the flow cell as well as minimize the unintended effect that the heat given off by the RID's electronics has on the temperature inside the flow cell. If the flow cell temperature does not stabilize, then the baseline will drift in response to it. For most methods, select a flow cell temperature which is at least 10 degrees C above ambient (since most of these units can heat only, not cool). Factor in any column temperature used too. If you are maintaining your column at 40C, then try to maintain your flow cell at the same temperature to minimize any differences. Feel free to experiment to find the best temperature for your flow cell. Try different temperatures (in 5 degree C intervals), wait for the system to fully equilibrate, then measure the baseline S/N ratio. You may find best results using different column and flow cell temperatures. Sometimes the room temperature effect can be countered by using an optimized flow cell temperature (higher or lower). Always factor in your mobile phase boiling point (b.p.) into your method and keep the column and flow cell temperatures well below the b.p.

• DEGASSING / DECREASING DISSOLVED OXYGEN: Reduce and stabilize the amount of dissolved gas inside the mobile phase and you may achieve faster equilibration times with a RID. You do not need to remove all the dissolved gas (in fact, a reduction of 50% is often enough). The amount of dissolved gas inside the mobile phase effects the measured refractive index. As it changes, so does your baseline. High percentages of mobile phase dissolved gas = lower RI; Less dissolved gas = higher RI. Now water holds less dissolved gas than non-polar organic solvents (e.g. THF) so this effect is more pronounced when you are running non-aqueous GPC separations, but maintaining a stable dissolved gas level for all mobile phase types is important to reduce baseline drift. Stability is our goal. Continuous degassing of the mobile phase either through sparging with high purity helium gas (best for non-aqueous separations) OR using an inline vacuum degasser should provide you with a way to control the amount of dissolved gas in the solution and reduce drift.

These are a few of the factors which can effect the equilibration and drift times of an HPLC system equipped with a refractive index detector (RID). Careful selection of the instrument module's location, insulating the exposed capillary lines and bottles, optimizing the column and flow cell temperatures, maintaining a steady and controlled temperature in the environment, plus removing dissolved gas from the mobile phase may all contribute to more stable baselines and better quality peak integration. It is also a good idea to review training in the correct operation of the RI detector too. Learning to correctly operate the flush and optional recycle valves on these detectors is critical to their operation. Failure to properly flush the reference cell before each analysis with fresh mobile phase may lead to baseline changes or artifacts.

Another article which may help you improve your analysis method can be found on this site. "Diagnosing & Troubleshooting HPLC Pressure Fluctuation Problems (Unstable Baseline)".