Column Selection in Gas Chromatography
PART 2 PACKED-COLUMN GAS CHROMATOGRAPHY Packed columns are still utilized for a variety of applications in gas chromatog-
3.6 STATIONARY PHASES
3.6.4 Evaluation of Column Operation
constants but also observe that these two polysiloxanes have a more favorable higher temperature limit. Comparisons of this type curtailed the proliferation of phases, eliminated the duplication of phases and simplified column selection.
Many phases quickly became obsolete and were replaced by a phase having identical constants but of higher thermal stability such as a polysiloxane phase.
Today polysiloxane-type phases are the most commonly used stationary phases for both packed-column (and capillary-column) separations because they exhibit excellent thermal stability, have favorable solute diffusivities and are available in a wide range of polarities. They will be discussed in greater detail in Part 3 of this chapter.
There likewise was an impetus to consolidate the number of stationary phases in use during the mid-1970s. In 1973 Leary et al. (36) reported the application of a statistical nearest-neighbor technique to the 226 stationary phases in the McReynolds study and suggested that just 12 phases could replace the 226. The majority of these 12 phases appear in Table 3.8. Delley and Friedrich found that four phases, OV-101, OV-17, OV-225, and Carbowax 20M, could provide satisfactory gas chromatographic analysis for 80% of a wide variety of organic compounds (37). Hawkes et al. (38) reported the findings of a committee effort on this subject and recommended a condensed list of six preferred stationary phases on which almost all gas–liquid chromatographic analysis can be per- formed: (1) a dimethylpolysiloxane (e.g., OV-101, SE-30, SP-210), (2) a 50%
phenylpolysiloxane (OV-17, SP-2250), (3) poly(ethylene glycol) of molecular weight (MW) >4000 (Carbowax), (4) DEGS, (5) a 3-cyanopropylpolysiloxane (Silar 10 C, SP-2340), and (6) a trifluoropropylpolysiloxane (OV-210, SP-2401).
Chemical structures of the more popular polysiloxanes used as stationary phases are illustrated in Figure 3.6.
Another feature of the McReynolds constants is guidance in the selection of a column that will separate compounds with different functional groups, such as ketones from alcohols, ethers from olefins, and esters from nitriles. If an analyst wishes a column to elute an ester after an alcohol, the stationary phase should have a largerZ value with respect to itsYvalue. In the same fashion, a stationary should exhibit a largerYvalue with respect toZif an ether is to elute before an alcohol. The appendixes in Reference 12 list McReynolds constants in order of increasing I for each probe in successive tables that are handy and greatly facilitate the column selection process.
FIGURE 3.6 Chemical structures of popular polysiloxanes.
of solute (percent of total) versus plate number. Figure 3.7b shows the band positions after 50, 100, and 200 equilibrations with the mobile phase.
An ideal gas chromatographic column is considered to have high resolving power, high speed of operation, and high capacity. One of these factors can be improved usually at the expense of another. Sometime we may be able to achieve two of the three if we are fortunate. Thus, a number of column parameters must be discussed to enable us to arrive at an efficient operation of a column. We now consider several of these parameters and illustrate with appropriate relationships.
3.6.4.1 Column Efficiency
Two methods are available for expressing the efficiency of a column in terms of HETP: measurement of the peak width (Figure 2.18) at (1) the baseline (Equation 2.9) and (2) half-height (Equation 2.11). In determiningN, we assume that the detector signal changes linearly with concentration. If it does not, N
FIGURE 3.7 (a) Elution peaks for three solutes from various plate columns (top, 10 plates; middle, 20 plates; bottom, 50 plates); (b) plate position of components after variable number of equilibrations (top, 50 equilibrations; middle, 100 equilibrations;
bottom, 200 equilibrations).
cannot measure column efficiency precisely. If Equation 2.9 or 2.11 is used to evaluate peaks that are not symmetric, positive deviations of 10–20% may result.
Since N depends on column operating conditions, these should be stated when efficiency is determined. There are several ways by which one may calculate column efficiency other than the two equations shown (Equations 2.9 and 2.11).
Figure 3.8 and Table 3.9 illustrate other ways in which this information may be obtained.
3.6.4.2 Effective Number of Theoretical Plates
The term “effective number of plates”Neff was introduced to characterize open tubular columns. In this relationship adjusted retention volumeVR, in lieu of total retention volume VR, is used to determine plate number:
Neff=16 VR
wb
2
=16 tR
wb
2
(3.2)
FIGURE 3.8 Pertinent points on a chromatographic band for calculation of column efficiency.
TABLE 3.9 Calculation of Column Efficiency from Chromatograms Standard Deviation
Terms Measurements Plate NumberN=
A/ h(2π)1/2 tR and band areaAand heighth 2π(tRh/A)2 Wi/2 tR and width at inflection points 4(tR/wi)2
(0.607h)wi
wh/(8 ln 2)1/2 tR and width at half-heightwh 5.55(tR/wh)2
wb/4 tR and baseline widthwb 16(tR/wh)2
This Neffvalue is useful for comparing a packed and an open tubular column or two similar columns when both are used for the same separation. Open tubular columns generally have a larger number of theoretical plates. One can translate regular number of plates N to effective number of platesNeff by the expression
Neff=N k
1+k 2
(3.3)
as well as the plate height to the effective plate height:
Heff=H 1+k
k 2
(3.4)
Similarly, the number of theoretical plates per unit time can be calculated:
N
tR = u(k)2
tR(1+k)2 (3.5)
where u is the average linear gas velocity. This relationship accounts for char- acteristic column parameters, thus offering a way to compare different-type columns.
3.6.4.3 Resolution
The separation of two components as the peaks appear on the chromatogram (see Figure 2.18) is characterized by
Rs= 2tR wb1+wb2
(3.6) where tR =tR2 −tR1 . If the peak widths are equal, that is, wb1=wb2, Equation 3.6 may be rewritten
Rs= tR
wb (3.7)
The two peaks will touch at the baseline whentR is equal to 4s:
tR2 −tR1 =tR (3.8) If two peaks are separated by a distance 4s, thenRs=1. If the peaks are separated by a 6s, then Rs =1.5.
Resolution also may be expressed in terms of retention indices of two com- ponents:
Rs = I2−I1
whf (3.9)
where f is the correction factor (1.699) because 4s=wb=1.699wh.
A more useable expression for resolution is
Rs = 1 4(N )1/2
α−1 α
k 1+k
(3.10)
where N and k refer to the later-eluting compound of the pair. Since α and k are constant for a given column (under isothermal conditions), resolution will be dependent on the number of theoretical platesN. Thek term generally increases with a temperature decrease as doesα but to a lesser extent. The result is that at low temperatures one finds that fewer theoretical plates or a shorter column are required for the same separation.
3.6.4.4 Required Plate Number
If the retention factor k and the separation factor α are known, the required number of plates (nne) can be calculated for the separation of two components.
(Thek value refers to the more readily sorbed component.) Thus
nne=16Rs2 α
α−1 2
1+k k
2
(3.11)
The Rs value is set at the 6s level or 1.5. In terms of the required effective number of plates, Equation 3.11 would be
Neff=16Rs2 α
α−1 2
(3.12)
Taking into account the phaseβratio, we can write Equation 3.11 as
nne=16Rs2 α
α−1 2
β k2 +1
2
(3.13)
Equations 3.11 and 3.13 illustrate that the required number of plates will depend on the partition characteristics of the column and the relative volatility of the two components, that is, on K and β. Table 3.10 gives the values of the last term of Equation 3.13 for various values of k. These data suggest a few inter- esting conclusions. Ifk <5, the plate numbers are controlled mainly by column parameters; if k >5, the plate numbers are controlled by relative volatility of components. The data also illustrate thatk values greater than 20 cause the the- oretical number of platesN and effective number of platesNeff to be the same order of magnitude:
N Neff (3.14)
TABLE 3.10 Values for Last Term of Equation 3.11
k 0.25 0.5 1.0 5.0 10 20 50 100
(1+k/ k)2 25 9 4 1.44 1.21 1.11 1.04 1.02
The relationship in Equation 3.11 also can be used to determine the length of column necessary for a separationLne. We know that N=L/H; thus
Lne=16R2sH α
α−1 2
1+k k
2
(3.15) Unfortunately, Equation 3.15 is of little practical importance because theHvalue for the more readily sorbed component must be known but is not readily available from independent data.
Let us give some examples from the use of Equation 3.11. Table 3.11 gives the number of theoretical plates for various values of α and k, assuming Rs
to be at 6s (1.5). Using data in Table 3.11 and Equation 3.11, we can make an approximate comparison between packed and open tubular columns. As a first approximation, βvalues of packed columns are 5–30 and for open tubular columns, 100–1000—thus a 10–100-fold difference in k. Examination of the data in Table 3.11 shows that whenα=1.05 andk=5.0 we would need 22,861 plates in a packed column, which would correspond to an open tubular column with k=0.5 having 142,884 plates. Although a greater number of plates is predicted for the open tubular column, this is relatively easy to attain because longer columns of this type have high permeability and smaller pressure drop than the packed columns.
3.6.4.5 Separation Factor
The reader will recall that the separation factorαin Section 1.2 is the same as the relative volatility term used in distillation theory. In 1959 Purnell (39,40) intro- duced another separation factor term (S) to describe the efficiency of a column.
TABLE 3.11 Number of Theoretical Plates for Values ofα and k (Rs at 6σ=1.5)
k α: 1.05 1.10 1.50 2.00 3.00
0.1 1,920,996 527,076 39,204 17,424 9,801
0.2 571,536 156,816 11,664 5,184 2,916
0.5 142,884 39,204 2,916 1,296 729
1.0 63,504 17,424 1,296 576 324
2.0 35,519 9,801 729 324 182
5.0 22,861 6,273 467 207 117
8.0 20,004 5,489 408 181 102
10.0 19,210 5,271 392 173 97
It can be used very conveniently to describe efficiency of open tubular columns:
S =16 VR
wb
2
=16 tR
wb
2
(3.16) whereVR andtR =adjusted retention volume and adjusted retention time, respec- tively. Equation 3.16 may be written as a thermodynamic quantity that is char- acteristic of the separation but independent of the column. In this form we assume resolution Rs at the 6s level or having a value of 1.5. Therefore, from Equation 3.12, we obtain
S=36 α
α−1 2
(3.17)
3.6.4.6 Separation Number
We also can calculate a separation number SN or Trennzahl abbreviated as TZ as another way of describing column efficiency (41). By separation number we mean the number of possible peaks that appear between two n-paraffin peaks with consecutive carbon numbers. It may be calculated by
SN=
tR2−tR1
(wh)1+(wh)2
−1 (3.18)
This equation may be used to characterize capillary columns or for application of programmed pressure or temperature conditions for packed columns. This concept is depicted in Figure 3.9.
3.6.4.7 Analysis Time
If possible, we like to perform the chromatographic separation in minimum time.
Time is important in analysis but it is particularly important in process chro- matography and in laboratories having a high sample throughput. Analysis time
TZ 0 TZ 4 TZ 6
FIGURE 3.9 Illustration of separation number (Trennzahl).
is based on the solute component that is more readily sorbed. Using the equation for determination of retention time, we obtain
t = L(1+k) u = N H
u (1+k) (3.19)
and substituting the value for the required number of plates, nne for n (Equation 3.11), we arrive at an equation for the minimum analysis timetne:
tne=16Rs2H u
α α−1
2
(1+k)3
(k)2 (3.20)
the term H /u can be expressed in terms of the modified van Deemter equation (Section 2.3.2, Equation 2.45).
H u = A
u + B
u2 +Cl+Cg (3.21) For minimum analysis time, high linear gas velocities are used; thus the first two terms on right side of Equation 3.22 may be neglected. Therefore,
H
u =Cl+Cg (3.22)
Substituting Equation 3.11 and 3.18 into Equation 3.18 we obtain
tne=nne(Cl+Cg)(1+k) (3.23) This equation indicates that minimal separation time depends on plate numbers, capacity factor, and resistance to mass transfer. It should be pointed out that the analysis times calculated from Equation 3.21 also depend on the desired resolution. Our example calculations were made on the basis of resolution Rs = 1.5. For a resolution of 1.00, even shorter analysis times can be achieved.
Figure 3.10 gives a representation of an idealized separation of component zones and the corresponding chromatographic peaks for a three-component sys- tem. With columns of increasing number of plates, we see better resolution as column efficiency increases.