Today, the editor will continue to share with you how to optimize the number of theoretical plates.
Let’s review the Van der Mutt equation related to the number of theoretical plates:
Where H represents the theoretical plate height, V represents the flow rate of mobile phase, a represents the eddy current diffusion term, b/v represents the longitudinal diffusion term, and c*v represents the mass transfer resistance term.
And n= (1/h) l, l is the column length of the chromatographic column.
How to optimize the number of theoretical plates?
- The effect of column conditions on separation
After adjusting selectivity to optimize the spacing between chromatographic peaks and maximize sample resolution, separations are generally satisfactory. However, it is also possible to further improve the separation by changing the column conditions (column length, flow rate, particle size), thereby changing the theoretical plate number of the column.
Note that in experiments with isocratic elution, the relative retention behavior and the relative spacing between columns (values of retention factor k and selectivity α) remain the same if only the column conditions are changed; therefore, no Destroys previously optimized results for chromatographic peak spacing obtained by changing α.
An increase in the value of N results in an increase in resolution, which usually means longer separation times. Conversely, decreasing the value of N allows for shorter experimental times—after optimizing selectivity, when the resolution Rs>2, it is beneficial to the experiment itself.
If other factors are equal, N should be proportional to the column length. Generally, the value of N increases as the particle size of the packing particles decreases or the flow rate of the mobile phase decreases. When the value of k varies, the experimental time is proportional to t0, which is proportional to L/v. Therefore, the experimental time will increase year-on-year as the column length increases, or as the mobile phase flow rate decreases year-on-year. Likewise, the pressure P will increase as the column length or flow rate increases, or as the particle size of the packing particles decreases.
Therefore, when changing the column conditions to improve the separation, we need to balance the experimental time, resolution and system pressure.
In addition, if changing the column conditions is to improve the resolution or speed up the experiment, it is recommended not to change the bonded phase, this is to avoid changes in column selectivity.
- Fast HPLC
Assuming we have access to suitable instrumentation and optimal column conditions, the separation time depends on the k value of the last peak and the alpha value of the least resolved chromatographic peak pair (“critical”). Once the “best” values of k and α are determined (selective optimization), the resolution and separation time are determined by the value of N. Conditions that help achieve fast separations include smaller packed particles, shorter columns, and higher mobile phase flow rates.
Further reduction of the separation time (to ensure that the value of N cannot be reduced) can be achieved by one or more of the following methods:
● Ultra-high pressure;
● higher temperature;
● Specially designed filler particles.
High pressure operation
UHPLC can be used to obtain better resolution or reduce experimental run time. It should be noted that when the column pressure exceeds 34 MPa, some of the previously thought relationships start to obviously no longer hold. The viscosity of the mobile phase increases as the column pressure increases, so the pressure can no longer increase proportionally with the flow rate. The values of k and alpha also depend on the system pressure and are therefore related to the conditions of the column; this is not apparent at low system pressures.
As a final note, heat is generated as the liquid flows through a packed column, and this heat is proportional to the pressure throughout the column. Temperature changes in the column may negatively affect peak shape and theoretical plate number, as well as further change k and alpha values.
High temperature experimental operation
The higher the temperature, the higher the N value will be. At the same time, increasing the temperature leads to a decrease in the viscosity of the mobile phase and an increase in the diffusion coefficient Dm of the solute molecules. Increasing the temperature can theoretically be used to shorten the experiment time while keeping the value of N constant, or to increase the value of N and keep the experiment time constant. The advantages of high temperature operation are also offset by some corresponding disadvantages. So the optimum temperature is usually a compromise between N max and α max.
Specially designed filter particles
In addition to the commonly used fully porous particles, there are other types of columns: pellicular or core-shell (superficially porous) particle-packed columns and monolithic columns. We have covered these pillars in other tweets.
Thin-shell and core-shell particles are particularly advantageous for the separation of macromolecules, with a reduced contribution to the mass transfer resistance term Cv in the van der Mutt equation. The thin-shell column is composed of a thin layer of porous packing coated on a solid silica column, so it is easy to overload, which makes its use limited to some very small samples (that is, the injection volume). must be small).
Core-shell columns have a thicker layer of porous packing than thin-shell columns, which enables them to carry nearly as much sample volume as fully porous columns. With other experimental conditions being equal, monolithic columns are more permeable than particle columns, which allows higher flow rates to be used and also enables faster separations.