Ion Exchange as a Separations Method. IX. Gradient Elution Theory<sup>1</sup>

Freiling, E.C.

doi:10.1021/ja01613a010

Cited by 75 publications

(18 citation statements)

References 2 publications

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“…While the use of gradient elution for analytical-scale chromatographic separation is well established (Freiling, 1955(Freiling, , 1957Jandera and Churacek, 1974Jandera, 1989;Snyder, 1961Snyder, , 1964Snyder et al, 1979Snyder et al, , 1989aSnyder and Glajch, 1990;Tomellini and Hartuich, 1985;Tomellini et al, 1986), few studies have addressed the basic features of adsorption kinetics and mass-transfer characteristics of industrial uses of gradient-elution chromatography.…”

Section: Introductionmentioning

confidence: 99%

Rate parameters and gradient correlations for gradient‐elution chromatography

Luo

Hsu

1997

AIChE Journal

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Section: Introductionmentioning

confidence: 99%

Rate parameters and gradient correlations for gradient‐elution chromatography

Luo

Hsu

1997

AIChE Journal

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“…To estimate these isocratic retention times, the constants S and ln k o from equation (1), or the constants S1, S2, and ln k o from equation (2) were found. These methods were the analytical solution to equation (6), the numerical solution to equation (7), the numerical solution to equation (7) with an added correction for the gradient delay due to the void volume of the column, the numerical solution to equation (8), and the numerical solution to equation (8) with an added correction for the gradient delay due to the void volume of the column. These methods were the analytical solution to equation (6), the numerical solution to equation (7), the numerical solution to equation (7) with an added correction for the gradient delay due to the void volume of the column, the numerical solution to equation (8), and the numerical solution to equation (8) with an added correction for the gradient delay due to the void volume of the column.…”

Section: Resultsmentioning

confidence: 99%

“…In equation (5), V' is the corrected mobile phase volume. 8,9 Equation (5) has the advantage of being able to be integrated analytically when linear gradients are used. 8,9 Equation (5) has the advantage of being able to be integrated analytically when linear gradients are used.…”

Section: Kavanaghmentioning

confidence: 99%

Converting Gradient Retention Times to Isocratic Retention Times in Reversed Phase Liquid Chromatography

Kavanagh

2000

Journal of Liquid Chromatography & Related Technologies

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Various methods of converting gradient retention times in reversed phase liquid chromatography to isocratic retention times are compared. The two main methods investigated were the analytical solution to dV m = dV'/k, and the numerical solution to dV m = dV/(1+k). Other methods investigated involved using a quadratic expression for the dependence of log retention factor on mobile phase composition instead of the usual linear function and also inclusion of a correction for extra gradient delay due to void volume of the column. No method gave a good agreement between isocratic retention times estimated from gradient data and experimental isocratic retention times. The method which gave the best agreement was the numerical integration of dV m = dV/(1+k) using the usual linear relationship between log of retention factor and mobile phase composition. A modern spreadsheet was used for all calculations.

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“…for gradient elution. In the approach proposed by Freiling , the integral equation was obtained from the instantaneous solute linear velocity, r , by splitting the solute elution in multiple infinitesimal steps:

r = \frac{d l}{d t} = \frac{u}{1 + k (φ (t, l))}

where φ ( t , l ) is the instantaneous modifier content in the mobile phase, and t and l have the same meaning as in Eq. .…”

Section: Introductionmentioning

confidence: 99%

“…(1) for gradient elution. In the approach proposed by Freiling [14], the integral equation was obtained from the instantaneous solute linear velocity, r, by splitting the solute elution in multiple infinitesimal steps:…”

Section: Introductionmentioning

confidence: 99%

Some insights on the description of gradient elution in reversed‐phase liquid chromatography

Baeza-Baeza

García-Álvarez-Coque

2014

J of Separation Science

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The so-called "fundamental equation for gradient elution" has been used for modeling the retention in gradient elution. In this approach, the instantaneous retention factor (k) is expressed as a function of the change in the modifier content (φ(ts )), ts being the time the solute has spent in the stationary phase. This approach can only be applied at constant flow rate and with gradients where the elution strength depends on the column length following a f(t-l/u) function, u being the linear mobile phase flow rate, and l the distance from the column inlet to the location where the solute is at time t measured from the beginning of the gradient. These limitations can be solved by using the here called "general equation for gradient elution", where k is expressed as a function of φ(t,l). However, this approach is more complex. In this work, a method that facilitates the integration of the "general equation" is described, which allows an approximate analytical solution with the quadratic retention model, improving the predictions offered by the "linear solvent strength model." It also offers direct information about the changes in the instantaneous modifier content and retention factor, and gives a meaning to the gradient retention factor.

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Ion Exchange as a Separations Method. IX. Gradient Elution Theory¹

Cited by 75 publications

References 2 publications

Rate parameters and gradient correlations for gradient‐elution chromatography

Rate parameters and gradient correlations for gradient‐elution chromatography

Converting Gradient Retention Times to Isocratic Retention Times in Reversed Phase Liquid Chromatography

Some insights on the description of gradient elution in reversed‐phase liquid chromatography

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Ion Exchange as a Separations Method. IX. Gradient Elution Theory1

Cited by 75 publications

References 2 publications

Rate parameters and gradient correlations for gradient‐elution chromatography

Rate parameters and gradient correlations for gradient‐elution chromatography

Converting Gradient Retention Times to Isocratic Retention Times in Reversed Phase Liquid Chromatography

Some insights on the description of gradient elution in reversed‐phase liquid chromatography

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Product

Resources

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Ion Exchange as a Separations Method. IX. Gradient Elution Theory¹