Chromatography Introduction GENERAL THEORY OF COLUMN CHROMATOGRAPHY Introduction

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Chromatography : Introduction GENERAL THEORY OF COLUMN CHROMATOGRAPHY

Chromatography : Introduction GENERAL THEORY OF COLUMN CHROMATOGRAPHY

Introduction • Of the two methods for bringing the stationary and mobile phases into

Introduction • Of the two methods for bringing the stationary and mobile phases into contact, the more important is column chromatography. • In this section we develop a general theory that we may apply to any form of column chromatography. • With appropriate modifications, this theory also can be applied to planar chromatography.

Chromatographic separation Progress of a column chromatographic separation showing the separation of two solute

Chromatographic separation Progress of a column chromatographic separation showing the separation of two solute bands Typical chromatogram of detector response as a function of retention time

Chromatogram tr Detector Signal Retention time tr Retention volume Vr Baseline width Wb void

Chromatogram tr Detector Signal Retention time tr Retention volume Vr Baseline width Wb void time, tm void volume Vm tm w Injection time • Chromatogram is a plot of the detector’s signal as a function of time or volume of eluted mobile phase. • It consists of a peak for each of the separated solute bands.

Chromatographic Resolution: is a quantitative measure of the degree of separation between two chromatographic

Chromatographic Resolution: is a quantitative measure of the degree of separation between two chromatographic peaks

Resolution value and degree of peak overlap 0. 13 %

Resolution value and degree of peak overlap 0. 13 %

How to improve resolution Poor resolution improved selectivity narrow band selectivity is unchanged

How to improve resolution Poor resolution improved selectivity narrow band selectivity is unchanged

How to improve resolution • From later equation, it is clear that resolution may

How to improve resolution • From later equation, it is clear that resolution may be improved either by increasing ∆tr or by decreasing w. A or w B. • We can increase ∆tr by enhancing the interaction of the solutes with the column or by increasing the column’s selectivity for one of the solutes. • Peak width is a kinetic effect associated with the solute’s movement within and between the mobile phase and stationary phase. • The effect is governed by several factors that are collectively called column efficiency.

Fundamental equation of resolution Factors affecting resolution Efficiency Selectivity Retention • The fundamental equation

Fundamental equation of resolution Factors affecting resolution Efficiency Selectivity Retention • The fundamental equation of resolution indicates that the resolution is affected by three parameters 1. Selectivity (separation) factor (α) 2. Efficiency 3. Retention (capacity factor, k)

Column efficiency • The plate number N (column factor) can be increased by lengthening

Column efficiency • The plate number N (column factor) can be increased by lengthening the column, decreasing the packing particle diameter, or optimizing flow rate. • However, improving resolution by increasing N is expensive in time. • Doubling the column length doubles the elution time, solvent consumption, and pressure while only increasing Rs by 1. 4. • Likewise, reducing the particle diameter increases the resolution but may exceed the maximum allowable pressure.

Capacity factor • It is a measure of how strongly a solute is retained

Capacity factor • It is a measure of how strongly a solute is retained by the stationary phase (k'). tm is the retention time of the non retained compound t`r Adjusted retention time. Retention (capacity) factor • How to change the capacity factor: Change the mobile phase strength (polarity in reversed phase chromatography)

Significance of K` Capacity factor Results k` = 0 a component is unretained k`

Significance of K` Capacity factor Results k` = 0 a component is unretained k` < 2 all peaks are packed together too closely at the beginning of the chromatogram. k` is between 2 and about 10 good separations are observed k` > 10 peaks are separated, but they take too long to elute, have become wider and lower, and if close to baseline noise in magnitude, they may become difficult to distinguish from it.

Column Selectivity The selectivity (or separation factor) is the ability of the chromatographic system

Column Selectivity The selectivity (or separation factor) is the ability of the chromatographic system to distinguish between the sample components α = if the solutes elute with identical retention times, α> 1 when t r, A > t r, B

Effect of selectivity on resolution The selectivity α can be increased by 1. changing

Effect of selectivity on resolution The selectivity α can be increased by 1. changing columns to a different stationary phase or 2. by imposing secondary equilibria through changes in mobile-phase p. H 3. or the addition of complexing agents to the mobile phase, .

Peak asymmetry Asymmetry factor (AF) = b/a 0. 95 – 1. 15

Peak asymmetry Asymmetry factor (AF) = b/a 0. 95 – 1. 15

Non ideal asymmetrical chromatographic bands (a) Sharp peak (b) Broad peak (c) Fronting (d)

Non ideal asymmetrical chromatographic bands (a) Sharp peak (b) Broad peak (c) Fronting (d) Tailing • fronting is most often the result of overloading the column which will lead to poor trapping of the analyte, too much ‘dead volume’ in the chromatographic sample some and sample decomposition. • tailing, system molecules of the analyte are adsorbed strongly onto active sites in the stationary phase.

COLUMN EFFICIENCY

COLUMN EFFICIENCY

COLUMN EFFICIENCY • At the beginning of a chromatographic separation the solute occupies a

COLUMN EFFICIENCY • At the beginning of a chromatographic separation the solute occupies a narrow band of finite width. • As the solute passes through the column, the width of its band continually increases in a process called band broadening. • Column efficiency provides a quantitative measure of the extent of band broadening. • Column efficiency can be explained by two theories: 1. PLATE THEORY OF CHROMATOGRAPHY 2. RATE THEORY OF CHROMATOGRAPHY

PLATE THEORY OF CHROMATOGRAPHY • Resolution is a measure of the efficiency of the

PLATE THEORY OF CHROMATOGRAPHY • Resolution is a measure of the efficiency of the column. • There another parameter which defines the efficiency as the number of theoretical plates, N. • Consider a column that is divided into N segments of equal length, and that each segment is just long enough to allow complete equilibration of solute partitioning between the stationary phase and the mobile phase, according to its partition coefficient. Each of these segments is called a theoretical plate. . • It is important to remember that a theoretical plate is an artificial construct and that no such plates exist in a chromatographic column.

The relationship between column length, number and height of theoretical plates • The relationship

The relationship between column length, number and height of theoretical plates • The relationship between column length (L), number of theoretical plates, N, and the height of a theoretical plate, H; are give by the following equation; • The greater the number of plates for a given column length, the shorter the height equivalent to a theoretical plate, H, and the more efficiently the column. • A column’s efficiency improves with an increase in the number of theoretical plates or a decrease in the height of a theoretical plate.

Calculation of number of theoretical plates • The number of theoretical plates in a

Calculation of number of theoretical plates • The number of theoretical plates in a chromatographic column is obtained by using the following equations: • An advantage of N as a measure of efficiency is that – it may be calculated from measurements on a single peak. Unlike Rs, it does not require a pair of peaks and is independent of their relative selectivity . – It may be calculated using either the peak width at base, wb, or peak width at half the peak height, wh. – The latter (wh) is sometimes better, whenfor broadened peak, fronting or the effects of adsorption (tailing).

Notes on the number of theoretical plates • A ‘‘good’’ column will have large

Notes on the number of theoretical plates • A ‘‘good’’ column will have large N values (104 ->105), and a small HETP. • Columns packed with a small-particle stationary phase have been shown to yield higher N values than those packed with larger particles. • In fact, the number of theoretical plates depends on both the properties of the column and the solute. • As a result, the number of theoretical plates for a column is not fixed and may vary from solute to solute.

RATE THEORY OF CHROMATOGRAPHY • The plate theory assumes that complete equilibration occurs in

RATE THEORY OF CHROMATOGRAPHY • The plate theory assumes that complete equilibration occurs in each of the N segments of the column. • This assumption is not applicable to all solutes, and because of this, the rate theory was developed. • The rate theory takes into account the finite rate at which the solute can equilibrate between the mobile and stationary phases. • The value of the HETP depends on flow rate of the mobile phase (µ), according to van Deemter equation and broadening H = A + B/µ + Cµ • In this equation, H accounts for height equivalent of theoretical plate, A for multiple paths, B/u for longitudinal diffusion, and Cu for the resistance of solute’s mass transfer in the stationary and mobile phases.

Multiple path (Eddy diffusion) • Solute molecules passing through a chromatographic column travel separate

Multiple path (Eddy diffusion) • Solute molecules passing through a chromatographic column travel separate paths that may differ in length. • Because of these differences in path length, solute molecules injected simultaneously elute at different times. • The principal factor contributing to this variation in path length is – a non-homogeneous packing of the stationary phase in the column, – differences in particle size and – packing consistency. – dp : average diameter of the particulate packing material • A smaller range of particle sizes and a more consistent packing produce a smaller value for A. • Note that for an open tubular column, which does not contain packing material, Hp is 0.

Longitudinal Diffusion: • If a band of molecules or atoms are placed in a

Longitudinal Diffusion: • If a band of molecules or atoms are placed in a container such as a tube at the center of its length, the molecules will diffuse in the direction of lower concentration. • Clearly this occurs in all directions but in a tube the walls are a limit and so our concern is along the axis of movement caused by the mobile phase and this is referred to as longitudinal molecular diffusion. • Even if the mobile phase velocity is 0, solute molecules are constantly in motion, diffusing through the mobile phase. • Since the concentration of solute is greatest at the center of a chromatographic band, more solute diffuses toward the band’s forward and rear edges than diffuses toward the band’s center. • The net result is an increase in the band’s width and broadening

Factors affecting on longitudinal diffusion • The magnitude of Hd is affected by: –

Factors affecting on longitudinal diffusion • The magnitude of Hd is affected by: – the solute’s diffusion coefficient in the mobile phase, – u is the mobile phase velocity, – column packing. • The effect of Hd on the height of a theoretical plate is minimized by – a high mobile-phase velocity. • Because a solute’s diffusion coefficient is larger in a gaseous mobile phase than in a liquid mobile phase, longitudinal diffusion is a more serious problem in gas chromatography.

Resistance to mass Transfer • A chromatographic separation occurs because solutes move between the

Resistance to mass Transfer • A chromatographic separation occurs because solutes move between the stationary and mobile phases. • For a solute to move from one phase to the other, it must first diffuse to the interface between the two phases in a process called mass transfer. • A contribution to band broadening occurs whenever the solute’s movement to the interface is not fast enough to maintain a true equilibrium distribution of solute between the two phases. • Thus, solute molecules in the mobile phase move farther through the column than expected before passing into the stationary phase. • Solute molecules in the stationary phase, on the other hand, take longer time than expected to cross into the mobile phase.

Factors affecting on resistance to mass transfer • There are two factors for resistance

Factors affecting on resistance to mass transfer • There are two factors for resistance to mass transfer; one in the stationary phase, Hs, and the other one for resistance to mass transfer in the mobile phase, Hm, • The Hs is affected by: – df is the thickness of the stationary phase, – Ds is the solute’s diffusion coefficient in the stationary phase, – q is a constant related to the column packing material, • The Hm is affected by – Dc is the column’s diameter, – Dm is the solute’s diffusion coefficient in the mobile phase, – dp is the average diameter of the particulate packing material • Both Hs and Hm ar affected by u is the mobile phase velocity

How to increase column efficiency van Deemter equation • To increase the number of

How to increase column efficiency van Deemter equation • To increase the number of theoretical plates without increasing the length of the column, it is necessary to decrease one or more of the terms in van Deemter equation. • The easiest way to accomplish this is by adjusting the velocity of the mobile phase. • At a low mobile-phase velocity, column efficiency is limited by longitudinal diffusion, whereas at higher velocities efficiency is limited by the two mass transfer terms. • As shown in next Figure, the optimum mobile-phase velocity corresponds to a minimum in a plot of H as a function of µ.

Plot of the height of a theoretical plate as a function of mobile-phase velocity

Plot of the height of a theoretical plate as a function of mobile-phase velocity using the van Deemter equation

Van Deemter equation in gas chromatography • There are two types of columns in

Van Deemter equation in gas chromatography • There are two types of columns in GC: packed GC columns vs open tubular capillary columns. • The theoretical considerations are different for both columns.

Open tubular capillary column • For an open tubular capillary column the eddy diffusion

Open tubular capillary column • For an open tubular capillary column the eddy diffusion coefficient does not play a part in band broadening and the C term is largely composed of the diffusion coefficient in the gas phase since the liquid film coating of the capillary column wall is typically 0. 1 -0. 2% of the internal diameter of the column. • B/u is most favorable for nitrogen (diffusion coefficients of molecules are lower in nitrogen than in the other commonly used carrier gases hydrogen and helium),

 • However, nitrogen only gives better efficiency where u is small since the

• However, nitrogen only gives better efficiency where u is small since the size of the term Cu is governed by the resistance to transverse diffusion which is greatest for nitrogen, the, fast flow rates of nitrogen reduce the interaction of the analyte with the stationary phase, • Most often helium is used as a carrier gas in capillary GC since it gives a good efficiency without having to reduce the flow rate, which would give long analysis times. • Longitudinal diffusion effects are reduced by reducing the internal diameter of a capillary column and thus the smaller the internal diameter of a column, the more efficient it is.

Packed GC column • With a packed GC column the separation efficiency is lower

Packed GC column • With a packed GC column the separation efficiency is lower because, although the longitudinal diffusion coefficient is lower, the eddy diffusion coefficient (A) causes band broadening. • In addition, resistance to mass transfer are greater for a packed column because of the irregular structure of the particles of packing and the consequent uneven coating of a relatively thick liquid phase. • However, whatever type of GC column is used. the CH, term is not as significant as that in liquid chromatography because of the high diffusion coefficient of molecules in the gas phase. • Therefore, GC have much more efficiency than that for HPLC.