The impact of sampling time on peak capacity and analysis speed in on-line comprehensive two-dimensional liquid chromatography

Abstract

Comprehensive two-dimensional liquid chromatography (2DLC) offers a number of practical advantages over optimized one-dimensional LC in peak capacity and thus in resolving power. The traditional "product rule" for overall peak capacity for a 2DLC system significantly overestimates peak capacity because it neglects under-sampling of the first dimension separation. Here we expand on previous work by more closely examining the effects of the first dimension peak capacity and gradient time, and the second dimension cycle times on the overall peak capacity of the 2DLC system. We also examine the effects of re-equilibration time on under-sampling as measured by the under-sampling factor and the influence of molecular type (peptide vs. small molecule) on peak capacity. We show that in fast 2D separations (less than 1h), the second dimension is more important than the first dimension in determining overall peak capacity and conclude that extreme measures to enhance the first dimension peak capacity are usually unwarranted. We also examine the influence of sample types (small molecules vs. peptides) on second dimension peak capacity and peak capacity production rates, and how the sample type influences optimum second dimension gradient and re-equilibration times.

Fig. 1

1/β as a function of second dimension cycle time. ¹t_g = 1500 s, ¹n_c = 100 peaks, α =3.35.

Fig. 2

Corrected (2D) peak capacity as a function of second dimension cycle time. Note the maximum in n′_c,2D at ²t_c,opt. The figure was generated using ¹t_g = 1500 s, ¹n_c = 100 peaks, α =3.35 and the relationship in Eq. 10a.

Fig. 3

a,b. Peak capacity and peak capacity production vs second dimension gradient time for phenones and peptides. Eq. 10a,b plotted (left axes) and second dimension peak capacities per minute cycle time, assuming 3 second re-equilibration times, right axes. Data points shown were used to find the equations that are plotted with the solid lines. All data are for the 2.1 mm × 30 mm Halo column described in the experimental section using Eq. 9 as the basis for the peak capacity.

Fig. 4

Plots of corrected (2D) peak capacity vs. first dimension peak capacity. ²n_c= 25 peaks, ²t_re-eq = 3 s, ²t_c = 20 s. Curve a: ¹t_g = 10 min, Curve b: ¹t_g = 25 min, Curve c: ¹t_g = 40 min.

Fig. 5

Effect of second dimension gradient time on corrected (2D) peak capacities as a function of first dimension peak capacities. Arrows point to the 90% peak capacities, beyond which only a 10% improvement in peak capacity can be expected. First dimension gradient time is 25 min. Second dimension re-equilibration time is 3 s. Second dimension peak capacities are calculated from Eq. 10. ²t_g values: Solid line = 5 s, dash = 10 s, dot = 25 s, and dash-dot = 50 s.

Fig. 6

Corrected (2D) peak capacities (n′_c,2D upper, solid) and corresponding corrected first dimension peak capacities (¹n′_c, lower, dashed) over a range in second dimension gradients times. First dimension gradient time is 25 min. Second dimension re-equilibration time is 3 s. Second dimension peak capacities are calculated from Eq. 10a.

Fig. 7

a and b. Corrected (2D) peak capacity vs. second dimension gradient time, showing the effects of α. First dimension peak capacity is 100 peaks and re-equilibration time is 3 s. ²n_c calculated with Eq. 10a. First dimension gradient time is 25 min in (a) and 50 min in (b). Solid lines α = 1.60, dash lines α = 3.35, dot lines α = 4.80.

Fig. 8

Corrected (2D) peak capacity as a function of second dimension gradient and re-equilibration time. First dimension gradient time is 25 min, first dimension peak capacity is 100. Eq. 10a used for ²n_c. ²t_reeq values: d = 0 s, c = 3 s, b = 6 s, a = 12 s.

Fig. 9

Plots of second dimension peak capacity vs. second dimension gradient time using Eq. 12 with different pre-exponential coefficients. Curve a: a = 40, b = 0.02; curve b: a = 40, b = 0.04; curve c: a = 40, b = 0.08; curve d: a = 80, b = 0.04.

Fig. 10

Second dimension peak production rate according to Eq. 12 for different coefficients. Curve a: a = 40, b = 0.04; curve b: a = 80, b = 0.04. Maxima occur at second dimension cycle time of 14 s in both cases.

Fig. 11

Second dimension peak production rate using different exponential coefficients in Eq. 12. All pre-exponential coefficients = 40, exponential coefficients for curve a: 0.02; curve b: 0.04; and curve c: 0.08.

Fig. 12

Corrected (2D) peak capacities over a range of second dimension gradient times. Plots for ¹t_g = 25 min, α = 3.35, ¹n_c = 150 peaks, ²t_re-eq = 3s. Coefficients used in Eq. 12 to calculate ²n_c in curve a: a = 40, b = 0.04; curve b: a = 80, b = 0.04.