CCC Chromatograms
From TheLiquidPhase
Contents |
1. General Introduction & CCC Volume Plots
Following tradition, and in most current practical implementations, chromatograms in countercurrent chromatography (CCC) are typically plotted with retention volume or time on the x-axis. As volume and time are often related by the flow are of the liquid pumping system driving the system, the majority of CCC chromatograms are plotted with volme on the x-axis (Volume Plots).
On the other hand, the distribution constant, K (sometimes syn. Kd or Kc), represents the more appropriate value for the x-axis, because K is a physicochemical property of a particular analyte in a particular solvent system. This means that K is independent of parameters that are variable among different CCC separations and instruments: key parameters like the total column volume and the stationary phase volume ratio (SF) of the column do not affect K of a given analyte.
2. K Plots in CCC
Because K can be considered a solid analytical parameter in CCC, relating the analyte to the solvent system used, plotting K on the x-axis (K Plots) is the more appropriate way to represent CCC chromatograms. However, even with today's equipment, it is the more challenging way of creating a plot, since the raw information of the CCC run and its conditions has to be mathematically converted into the K scale. Therefore, it has to be noted that generation of K chromatograms in CCC typically requires the use of digital data collection equipment. The conversion can easily be done with the help of spreadsheet software by using the standard CCC elution equation. At the same time, the spreadsheet software allows the creation of the chromatogram.
Literature providing early examples of the use of K plots in CCC:
3. ReS and ReSS Plots in CCC
Recently, a new method of generating CCC chromatograms has been proposed by Friesen & Pauli:
The concept of Reciprocal Symmetry (ReS) Plots goes one step beyond simple K plots. ReS plots position K and 1/K on either side of a line of symmetry on the x-axis. The method allows full representation of all K values, zero to infinity. ReS plots exemplify both the invertible and the symmetric nature of CCC. In addition, the interval of optimal resolution ("sweet spot") can be centered on the ReS plot. Going two steps beyond the plot of K, a focus on K values of interest can be realized with the concept of Reciprocal Shifted Symmetry (ReSS) Plots in CCC.
Both ReS and ReSS improve the grpahical representation of CCC peak shape and make allow to standardize CCC chromatograms accross platforms and separations. The ReS and ReSS plots are particularly useful in combination with Elution-Extrusion CCC.
4. A Closer Look at the Math
The objective of this project was to represent K values (a countercurrent chromatography constant) between zero and infinity on a single plot axis (x-axis or a chromatography plot).
ReS
The solution that we came up with was to divide the x-axis into two parts with a midline in the middle. To the left of the midline we have values 0 (less than or equal to) K < midline value. To the right of the midline we have midline value < K (less than or equal to) infinity. The way to represent values up to infinity is to graph their reciprocals such that the right side mirrors the left side. The obvious choice for a midline is “1” because 1/1 = 1. This also works out well with CCC because the value K = 1 has a special place in CCC theory and practice; therefore, it is fitting that it would hold the center position.
Imagine a mirror plot where K and 1/K are equidistant from the midline one: 1 - K = 1 – K’ = 1 - f(1/K). This would work if f (1/K) = K’ = 1 divided by 1/K. K and K(reciprocal) = Krc are two different values so we can call Krc = 1/K K’ = 1/Krc = K
I need numbers to see what is going on here. Let’s use K = 0.25 Krc = 1/K = 4 1/ Krc = 1/4 = 0.25 so 1–K and 1–(1/Krc) are equidistant from the midline.
How can we plot this on a continuous plot? Every value to the left of the midline is x = K Every value to the right of the midline is x = 2-(1/K) 4 is plotted at 2–(1/4) = 1.75
This is how you graph the values in Excel. Your K value data points are in one column. A adjacent column has two different equations from 0 < K < 1 the equation is K'=K from 1 < K < infinity the equation is K'= 2- (1/K). You have to set this up manually - scroll down to the row first row of 1 < K and change the equation.
You can see the relationship of the actual K value (y axis) to the reciprocal plot K value on the x axis. K approaches infinity at “2” in this case.
The only way I know to change the x axis to represent the real K values is to put the Excel graph into powerpoint and change the values to the right of the midline manually.
ReSS
How about if you want a different midline than K = 1? Can we generalize this relationship to include a multiplication factor “m” such that K and m/K are equidistant from a midline MS ? MS-K = MS–(m/K)
At the midline K = MS = m/K The relationship between m and MS is therefore: m = M(S(squared))
With plotting: x = K and x = 2MS - m/K
Let’s see if it works: MS = 4 and m = 16 K = 1 and K = 16 should be equidistant from the midline. Plot it:
Clean up the x- axis:
Why shift the symmetry midline? Shifting the symmetry midline can open up a “window” in the chromatogram that includes a larger K value interval. For example, if you divide the ReS plot into four parts and consider the middle half as the window: ReS(1) the window is 0.5 < K < 2; ReSS(2) the window is 1 < K < 4; ReSS(4) the window is 2 < K < 8 You will notice that the window also shifts to include higher K values. This is also an advantageous thing.
Value Added
In addition to ReS plots representing all of K values on one plot in a symmetric fashion, reciprocal plotting has the advantage of clearly exhibiting the invertible nature of CCC. In CCC the mobile and stationary phases can be switched for any biphasic solvent system. Therefore, the compounds can be eluted from lipophilic to hydrophilic (normal phase) or hydrophilic to lipophilic (reverse phase) depending on the choice of mobile phase. Since K is calculated by dividing the concentration of the analyte in the stationary by its concentration in the mobile phase, reversing the mobile and stationary phases in CCC will invert K values for a particular substance in a particular biphasic solvent system. For example, a compound eluting with a KD value of 0.25 with the hydrophilic phase stationary would be expected to elute with a KD value of 4 if with the hydrophilic phase mobile. This reciprocal relationship brings up the importance of K = 1 as position of symmetry in CCC: A compound with K = 1 will elute at the same K value no matter which phase is chosen as the mobile phase.
I have already done this experiment, you can see the inverse elution but the K values don’t match up as neatly as in theory.
Playing with ReS/ReSS
How does the ReS(S) plot “distort” the chromatogram? Typically eluted compounds are collected at regular time intervals by the fraction collector. The UV-vis detector readings are also done at regular time intervals and changed to volume units and ultimately K values on an excel spreadsheet. In terms of regular time/volume/K intervals, the ReS(S) plot tends to compress values to the right of the midline compared to the values on the left.
Again consider our “middle-half” window: In a ReS(1) plot the interval between the left half and the middle is 0.5 K 1 and the interval represented by the right half is 1 < K < 2. Even worse, the left outside half is 0 < K < 0.5 and the right outside half is 2 < K < infinity.
In CCC, squeezing the high K value intervals is not such as bad thing. In the regular elution behavior peaks eluting after K = 1 tend to be broad (elute with a high volume of solvent), so the ReS plots actually improves their shape.
Another aspect of CCC is also well-served by ReS(S) plots: The interesting part of the chromatogram is the “sweet spot” described elsewhere. The sweet spot of the chromatogram can be positioned so that it is featured in the middle half or middle three-quarters of the chromatogram.
The original volume plot:
The ReS plot (Excel plot x-axis): The two peaks at K = 0.2 and 0.8 are pretty broad.
ReSS(2) plot: This one looks a lot like the volume plot only now we have K value x-axis!
ReSS(3) plot: Now the “M” peak is getting too broad and the chromatogram looks distorted
Bottom Line: The plot that has nearly the same number of data points on each side of the midline usually looks the best.