Expressions of the Fundamental Equation of Gradient Elution and a Numerical Solution of These Equations under Any Gradient Profile

Abstract

The original work carried out by Freiling and Drake in gradient liquid chromatography is rewritten in the current language of reversed-phase liquid chromatography. This allows for the rigorous derivation of the fundamental equation for gradient elution and the development of two alternative expressions of this equation, one of which is free from the constraint that the holdup time must be constant. In addition, the above derivation results in a very simple numerical solution of the various equations of gradient elution under any gradient profile. The theory was tested using eight catechol-related solutes in mobile phases modified with methanol, acetonitrile, or 2-propanol. It was found to be a satisfactory prediction of solute gradient retention behavior even if we used a simple linear description for the isocratic elution of these solutes.

Enhanced selectivity and search speed for method development using one-segment-per-component optimization strategies

“…To predict the elution times of the individual compounds, the fundamental gradient equation [25] was extended for multisegmented gradients, taking into account the instrument dwell time t D . For an n-segmented gradient this becomes:…”

“…The best "traditional" multi-segment gradient profile (determined by a starting composition 0 and a value for ˇ and t G for each segment) was determined via a similar grid search. Based on our own findings and these of Concha-Herrara et al [12], only 4-segment gradients were considered as these give the best compromise between the achievable selectivity (in gradient elution this is the ratio between the apparent gradient retention factors k eff,1 /k eff,2 [16][17][18][19][20][21][22][23][24][25][26][27]) and the required search time. The grid search was conducted considering different starting concentrations %B between 5 and 95% (step size of 0.5%) and a number of ˇ-and t G -values for each of the 4 segments (ˇ going from 0.001 to 0.2, corresponding to 0.1 to 20%B/min, i.e., ln(ˇ) between −6.9 and −0.70 and t G /t 0 between 1 and 12).…”

Prediction of the chromatographic retention of acid–base compounds in pH buffered methanol–water mobile phases in gradient mode by a simplified model

“…Some of them explain the behavior of neutral compounds in gradient mode and show several ways to predict their retention [1][2][3][4][5][6][7][8][9][10][11], others describe the isocratic retention of compounds with acid-base properties emphasizing the significance of the ionization degree of the analyte when predicting its retention [12][13][14][15], and there are some other studies that combine both the elution in gradient mode and the elution of ionizable compounds [16][17][18][19]. Combination of these two features is quite complex because the mobile phase * Corresponding author.…”

Multi-linear gradient elution optimization for separation of phenylthiohydantoin amino acids using pareto optimality method

“…K ij is the solute retention factor which corresponds to a constant mobile phase composition equal to ij. Nikitas and co-workers [10] have proved that if dwell time (t D ) is taken into account, the following equation can be achieved readily.…”

“…For this reason, an arbitrary gradient profile is approximated by small įij steps at įt time intervals, instead. Under these conditions, an analyte is eluted when the sum of įL a, the sum of the subsequent distances are traveled by the analyte inside the column at time interval equal to įt c , is equal to L. The derivation of the fundamental equations of gradient elution presented above by Nikitas et al [10] leads to the following very simple numerical solution of Eq. (2):…”