1 an introduction to chromatographic separations

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An Introduction to Chromatographic Separations

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An Introduction to Chromatographic Separations

It was Mikhail Tswett, a Russian botanist, in 1903 who first invented and named liquid chromatography. Tswett used a glass column filled with finely divided chalk (calcium carbonate) to separate plant pigments. He observed the separation of colored zones or bands along the column, hence name chromatography, where Greak chroma means color and graphein means write.

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The development of chromatography was slow for reasons to be discussed later and scientists waited to early fifties for the first chromatographic instrument to appear in the market (a gas chromatograph). However, liquid chromatographic equipment with acceptable performance was only introduced about two decades after gas chromatography.

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General Description of Chromatography

In a chromatographic separation of any type, different components of a sample are transported in a mobile phase (a gas, a liquid, or a supercritical fluid). The mobile phase (also called eluent) penetrates or passes through a solid or immiscible stationary phase. Solutes (eluates) in the sample usually have differential partitioning or interactions with the mobile and stationary phases. Since the stationary phase is the fixed one then those solutes which have stronger interactions with the stationary phase will tend to move slower (have higher retention times) than others which have lower or no interactions with the stationary phase will tend to move faster.

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Therefore, chromatographic separations are a consequence of differential migration of solutes. It should be remembered that maximum interactions between a solute and a stationary phase take place when both have similar characteristics, for example in terms of polarity. However, when their properties are so different, a solute will not tend to stay and interact with the stationary phase and will thus prefer to stay in the mobile phase and move faster; a polar solvent and a non polar stationary phase is a good example.

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According to the nature of the mobile phase, chromatographic techniques can be classified into three classes:

1. Liquid chromatography (LC)2. Gas chromatography (GC)3. Supercritical fluid chromatography (SFC)Other classifications are also available where

the term column chromatography where chromatographic separations take place inside a column, and planar chromatography, where the stationary phase is supported on a planar flat plate, are also used.

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Elution Chromatography

The term elution refers to the actual process of separation. A small volume of the sample is first introduced at the top of the chromatographic column. Elution involves passing a mobile phase inside the column whereby solutes are carried down the stream but on a differential scale due to interactions with the stationary phase. As the mobile phase continues to flow, solutes continue to move downward the column. Distances between solute bands become greater with time and as solutes start to leave the column they are sequentially detected.

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The time a solute spends in a column (retention time) depends on the fraction of time that solute spends in the mobile phase. As solutes move inside the column, their concentration zone continues to spread and the extent of spreading (band broadening) depends on the time a solute spends in the columns. Factors affecting band broadening are very important and will be discussed later. The dark colors at the center of the solute zones in the above figure represent higher concentrations than are concentrations at the sides. This can be represented schematically as:

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Chromatograms

The plot of detector signal (absorbance, fluorescence, refractive index, etc..) versus retention time of solutes in a chromatographic column is referred to as a chromatogram. The areas under the peaks in a chromatogram are usually related to solute concentration and are thus very helpful for quantitative analysis. The retention time of a solute is a characteristic property of the solute which reflects its degree of interaction with both stationary and mobile phases. Retention times serve qualitative analysis parameters to identify solutes by comparison with standards.

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Migration Rates of Solutes

The concepts which will be developed in this section will be based on separation of solutes using a liquid mobile phase and an immiscible liquid stationary phase. This case is particularly important as it is a description of the most popular processes.

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Distribution Constants

Solutes traveling inside a column will interact with both the stationary and mobile phases. If, as is our case, the two phases are immiscible, partitioning of solutes takes place and a distribution constant, K, can be written:

K = CS/CM (1)

Where; CS and CM are the concentrations of solute in the stationary and mobile phases, respectively. If a chromatographic separation obeys equation 1, the separation is called linear chromatography. In such separations peaks are Gaussian and independent of the amount of injected sample

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The time required for an analyte to travel through the column after injection till the analyte peak reaches the detector is termed the retention time. If the sample contains an unretained species, such species travels with the mobile phase where the time spent by that species to exit the column is called the dead or void time, tM. Solutes will move towards the detector in different speeds, according to each solute’s nature.

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Chromatography Chromatography Retention TimesRetention Times Chromatography ChromatographyRetention TimesRetention Times

tM = retention time of mobile phase (dead time)tR = retention time of analyte (solute)tR

’ = time spent in stationary phase (adjusted

retention time)L = length of the column

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Chromatography: Chromatography: VelocitiesVelocitiesLinear rate of solute migrationLinear rate of solute migration!!

:Chromatography :ChromatographyVelocitiesVelocitiesLinear rate of solute migrationLinear rate of solute migration!!

M

R

t

L

t

Lv

Velocity = distance/time length of column/ retention times

Velocity of solute:

Velocity of mobile phase:

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average linear velocity of a solute, v, can be written as:

v = L/tR (2)Where, L is the column length and tR is the

retention time of the solute. The mobile phase linear velocity, u, can be written as:

u = L/tM (3) The linear velocity of solutes is a fraction of the

linear velocity of the mobile phase. This can be written as:

v = u * moles of solute in mp/total moles of solute

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Chromatography Chromatography Velocity/Retention time and KcVelocity/Retention time and Kc

Chromatography Chromatography Velocity/Retention time and KcVelocity/Retention time and Kc

SSMM

MM

VcVc

Vcv

v

v

solute of moles total

phase mobile in solute of moles

phase mobile in timeof fraction

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This can be further expanded by substitution for the moles of solute in mp, CMVM, and the total number of moles of solute, CMVM + CSVS.

v = u * CMVM / (CMVM + CSVS)Dividing both nominator and denominator by

CMVM we get

v = u * 1/ (1 + CSVS/ CMVM) (4) Now, let us define a new distribution constant,

called the capacity or retention factor, k’, as:

k’ = CSVS/ CMVM = K VS/VM (5)

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Substitution of 1,2 and 5 in equation 4 we get:

L/tR = L/tM * {1/(1 + k’)}

Rearrangement gives:

tR = tM (1+k’) (6)

This equation can also be written as:

k’ = (tR – tM)/tM

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The Selectivity Factor

For two solutes to be separated, they should have different migration rates. This is referred to as having different selectivity factors with regard to a specific solute. The selectivity factor, , can be defined as:

= kB’/kA’ (7)Therefore, a can be defined also as:

= (tR,B – tM)/ (tR,A – tM) (8) For the separation of A and B from their mixture, the

selectivity factor must be more than unity.

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The Shapes of Chromatographic Peaks

Chromatographic peaks will be considered as symmetrical normal error peaks (Gaussian peaks). This assumption is necessary in order to continue developing equations governing chromatographic performance. However, in many cases tailing or fronting peaks are observed.

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Gaussian peaks (normal error curves) are easier to deal with since statistical equations for such curves are well established and will be used for derivation of some basic chromatographic relations. It should also be indicated that as solutes move inside a column, their concentration zones are spread more and more where the zone breadth is related to the residence time of a solute in a chromatographic column.

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Plate Theory

Solutes in a chromatographic separation are partitioned between the stationary and mobile phases. Multiple partitions take place while a solute is moving towards the end of the column. The number of partitions a solute experiences inside a column very much resembles performing multiple extractions. It may be possible to denote each partitioning step as an individual extraction and the column can thus be regarded as a system having a number of segments or plates, where each plate represents a single extraction or partition process.

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Therefore, a chromatographic column can be divided to a number of theoretical plates where eventually the efficiency of a separation increases as the number of theoretical plates (N) increases. In other words, efficiency of a chromatographic separation will be increased as the height of the theoretical plate (H) is decreased.

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Column Efficiency and the Plate Theory

If the column length is referred to as L, the efficiency of that column can be defined as the number of theoretical plates that can fit in that column length. This can be described by the relation:

N = L/H

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The plate theory successfully accounts for the Gaussian shape of chromatographic peaks but unfortunately fails to account for zone broadening. In addition, the idea that a column is composed of plates is unrealistic as this implies full equilibrium in each plate which is never true. The equilibrium in chromatographic separations is just a dynamic equilibrium as the mobile phase is continuously moving.

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Definition of Plate Height

From statistics, the breadth of a Gaussian curve is related to the variance 2. Therefore, the plate height can be defined as the variance per unit length of the column:

H = 2/L (9)In other words, the plate height can be defined

as column length in cm which contains 34% of the solute at the end of the column (as the solute elutes). This can be graphically shown as:

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The peak width can also be represented in terms of time, t, where:

t = /v (10)

t = /(L/tR) (11)The width of the peak at the baseline, W,

is related to t by the relation:W = 4t where 96% of the solute is

contained under the peak.

s = L t/tR

s = LW/4tR (12)

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2 = L2W2/16tR2

2 = HL

H = LW2/16tR2

N = 16(tR/W)2 (13) Also, from statistics we have:

W1/2 = 2.354 t (14)2 = LH

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= L t/tR

= L (W1/2/2.354)/tR

2 = L2 (W1/2/2.354)2 /tR2 (15)

Substitution in equation 9 gives:

LH = L2 (W1/2/2.354)2 /tR2

H = L (W1/2/2.354 tR)2

N = L/H

N = 5.54 (tR/W1/2)2 (16)

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Asymmetric PeaksThe efficiency, N, can be estimated for an asymmetric chromatographic peak using

the relation:

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N = 41.7 (tR/W0.1)2 / (A/B + 1.25) (17)

Draw a horizontal line across the peak at a height equal to 1/10 of the maximum height.

Where W0.1 = peak width at 1/10 height = A + B

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Band Broadening

Apart from specific characteristics of solutes that cause differential migration, average migration rates for molecules of the same solute are not identical. Three main factors contribute to this behavior:

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Longitudinal Diffusion

Molecules tend to diffuse in all directions because these are always present in a concentration zone as compared to the other parts of the column.

This contributes to H as follows:

HL = K1DM/V

Where, DM is the diffusion of solute in the mobile phase. This factor is not very important in liquid chromatography except at low flow rates.

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This contributes to H as follows:

HL = K1DM/V

Where, DM is the diffusion of solute in the mobile phase. This factor is not very important in liquid chromatography except at low flow rates.

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Resistance to Mass Transfer

Mass transfer through mobile and stationary phases contributes to this type of band broadening.

1. Stationary Phase Mass Transfer This contribution can be simply attributed to

the fact that not all molecules penetrate to the same extent into the stationary phase. Therefore, some molecules of the same solute tend to stay longer in the stationary phase than other molecules

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Quantitatively, this behavior can be represented by the equation:

Hs = K2 ds

2 V/Ds

Where ds is the

thickness of stationary phase and Ds is the diffusion coefficient of solute in the stationary phase.

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Mobile Phase Mass Transfer

Solute molecules which happen to pass through some stagnant mobile phase regions spend longer times before they can leave. Molecules which do not encounter such stagnant mobile phase regions move faster. Other solute molecules which are located close to column tubing surface will also move slower than others located at the center. Some solutes which encounter a channel through the packing material will move much faster than others.

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HM = K3dp2V/DM

Where dp is the particle size of the packing.

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Multiple Path Effects Multiple paths which

can be followed by different molecules contribute to band broadening.

Such effects can be represented by the equation:

HE = K4 dp

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The overall contributions to band broadening are then,

Ht = HL + HS + HM + HE

Where; Ht is the overall height equivalent to a theoretical plate resulting from the contributions of the different factors contributing to band broadening.

Ht = k1dp + k2DM/V + K3 ds2 V/Ds + K4 dp

2 V/DM

Ht = A + B/V + CSV + CMV•

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H = A + B/V+ CV It turned out that resistance to mass transfer

terms (K3 ds2 V/Ds and K4 dp

2 V/DM) are most important in liquid chromatography and thus should be particularly minimized. This can be done by:

1. Decreasing particle size2. Decreasing the thickness of stationary

phase3. Working at low flow rates4. Increase DM by using mobile phases of low

viscosities.

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On the other hand, the longitudinal diffusion term (k2DM/V) is the most important one in gas chromatography. Reducing this term involves:

1. Working at higher flow rates

2. Decreasing DM by using carrier gases of higher viscosities

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Van - Deemter Equation

From the abovementioned contributions to band broadening, the following equation was suggested to describe band broadening in liquid chromatography (LC)

H = A + B/V+ CV

Where; A represents multiple path effects, B/V accounts for longitudinal diffusion, and CV accounts for resistance to mass transfer. The figure below shows a plot of H against the different factors in the equation

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The optimum flow rate can be found by taking the first derivative of equation 23.

dH /dV = O - B/V2 + C

V is optimum when dH /dV= O , therefore,

C = B/V2optimum

Voptimum = {B/C}1/2 (24) This theoretically calculated velocity is always small

and in practice almost twice as much as its value is used in order to save time.

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The relation of H and the flow rate of the mobile phase is highly dependent on particle size. H will become almost independent on flow rate at very small particle size. In this case, faster separations can be achieved, using higher flow rates, without affecting H, and thus band broadening. The figure below shows such an effect:

Particle size and flow rate

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Resolution

One of the basic and most important characteristic of a chromatographic separation is undoubtedly the resolution term. Resolution between two chromatographic peaks is a measure of how well these peaks are separated from each other, which is the essence of the separation process. Resolution of the two peaks in the figure below are different and one finds no trouble identifying that the lower chromatogram has the best resolution while the top one has the worst resolution:

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Chromatography: Chromatography: Peak ResolutionPeak ResolutionChromatography: Chromatography: Peak ResolutionPeak Resolution

Poor resolution

More separation

Less band spread

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Chromatography Chromatography Determining the Number Determining the Number

of Theoretical Platesof Theoretical Plates

Chromatography Chromatography Determining the Number Determining the Number

of Theoretical Platesof Theoretical Plates

2

2/1

2

54.5

16

pates ofnumber

W

tN

W

tN

N

R

R

W1/2

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Resolution can be defined from the following figure as:

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R = Z/(WA/2 + WB/2) = 2 Z/(WA + WB) (18) R = 2(tR,B – tR,A)/(WA + WB) (19) For a separation where WA = WB = W, we can write: R = (tR,B – tR,A)/W

However, we have the equation:N = 16 (tR/W)2, or for peak B we have:W = 4 tR,B /N1/2

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R = (N1/2/4)(tR,B – tR,A)/tR,B

We can now substitute for the retention time using the equation derived earlier:

tR = tM (1+k’)Thus we have:

R = (N1/2/4){(tM(1+kB’) - tM(1+kA’)) /tM(1+kB’)}Rearrangement gives:

R = (N1/2/4)(kB’ – kA’)/(1+kB’)

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Dividing both nominator and denominator by kB’:

R = (N1/2/4)(1 – kA’/kB’)/{(1+kB’)/kB’}

However, = kB’/kA’

R = (N1/2/4)(1 – 1/) (kB’)/(1+kB’)

R = (N1/2/4){(kB’)/(1+kB’)}{( – 1)/)} (21)

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Therefore, resolution can be viewed as a composite contribution of three terms:

a. Efficiency term where R is proportional to

N1/2

b. Retention term where R is proportional to k’/(1+k’) which suggests that the retention parameter should be optimized. A value for k’ in the range from 5-10 is preferred as smaller values (low retention) results in bad resolution while a very high k’ value means very long retention with exceedingly small improvements in resolution:

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These data can be better viewed as a plot where as k’ was increased, almost a plateau was realized.

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The overlap of two Gaussian peaks of equal area and amplitude, at various values of resolution (R) is presented below:

(a) R = 0.50 Overlap of two peaks = 16% (c) R = 1.00 Overlap of two peaks = 2.3% (d) R = 1.50Overlap of two peaks = 0.1%

c. Resolution is dependent on a selectivity term {( – 1)/)}. As the selectivity is increased, resolution increases as well. When = 1, resolution is zero.

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Effect of Other Parameters on Resolution

a. The resolution of a column is proportional to the square root of its length since N = L / HETP.

R = (L1/2/4H1/2){(kB’)/(1+kB’)}{(–)} (22)

b. Retention time as related to resolution can be obtained by the following treatment:

N = L/H

tM = NH/u

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tR,B = tM (1+kB’)

tR,B = (NH/u) (1+kB’)

N = 16R2{(1 + kB’)/kB’}2{)}2

Substitution gives:

tR,B = (16R2H/u){(1 + kB’)3 /kB’2}{)}2

Therefore, one can also write:

tR,A/tR,B = RA2/RB

2

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To obtain a high resolution, the three terms must be maximised. An increase in N, the number of theoretical plates can simply be done by lengthening the column. This leads to two opposing effects where resolution is increased but at the same time this causes an increase in retention time and thus increased band broadening. In addition, a longer column may not always be available. An alternative is to increase the number of plates, the height equivalent to a theoretical plate by adjusting elution variables (mobile phase composition), and other factors affecting selectivity.

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Chromatographic RelationshipsChromatographic Relationships

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It is often found that by controlling the capacity factor, k', separations can be greatly improved. This can be achieved by changing the temperature (in Gas Chromatography) or the composition of the mobile phase (in Liquid Chromatography).

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When a is close to unity, optimising k' and increasing N is not sufficient to give good separation in a reasonable time. In these cases, a is increased by one of the following procedures:

1. Changing mobile phase composition 2. Changing column temperature 3. Changing composition of stationary

phase 4. Using special chemical effects (such as

incorporating a species which complexes with one of the solutes into the stationary phase or use of surfactants)

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The General Elution ProblemLook at the chromatogram below in which six

components are to be separated by an elution process:

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It is clear from the figure that the separation is optimized for the elution of the first two components. However, the last two components have very long retention and appear as broad peaks. Using a mobile phase composition that can optimize the elution of the last two compounds will, unfortunately, result in bad resolution of the earlier eluting compounds as shown in the figure below where the first two components are coeluted while the resolution of the second two components becomes too bad:

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One can also optimize the separation of the middle too components by adjusting the mobile phase composition. In this case, a chromatogram like the one below can be obtained:

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However, in chromatographic separations, we are interested in fully separating all components in an acceptable resolution. Therefore, it is not acceptable to optimize the separation for a single component while disregarding the others. The solution of this problem can be achieved by consecutive optimization of individual components as the separation proceeds. In this case, the mobile phase composition should be changed during the separation process.

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First, a mobile phase composition suitable for the separation of the first eluting component is selected, and then the mobile phase composition is changed so that the second component is separated and so on. The change in mobile phase composition can be linear, parabolic, step, or any other formula. The chromatographic separation where the mobile phase composition is changed during the elution process is called gradient elution. A separation like the one below can be obtained:

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Qualitative Analysis

Usually, the retention time of a solute is the qualitative indicator of a specific analyte. The retention time of an analyte is thus compared to that of a standard. If both have the same retention time, this may be a good indication that the identity of the analyte is most probably that of the standard. However, there can be important uncertainties since some different compounds have similar retention. In such cases, it is not wise to use the retention time as a guaranteed marker of the identity of compound, except in cases where the sample composition is known.

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Development in qualitative analysis in chromatography involves use of detectors that can give structural details of solutes, like diode array, Fourier transform infrared, mass spectrometers, etc. In such cases, qualitative analysis with high degree of certainty can be accomplished. It should therefore be clear that a similar retention time of a component and standard does not imply a100% identification but rather a good possibility. However, if the retention time of a compound in question does not match that of the standard, we are 100% sure that the anticipated compound is either absent or present at a concentration below the detection limit of the instrument.

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Quantitative Analysis

Chromatographic separations provide very good and reliable information about quantitative analysis of sample constituents. Either the peak height or peak area can be used for quantitative analysis. Peak heights are easier and faster to use and usually result in good precision, especially when reproducible sample injections are made. However, late eluting peaks may have small peak heights but large width which may cause large errors. Peak areas are better for quantitative analysis as the area under the peak is integrated which is an accurate measure of concentration.

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The Internal Standard Method

Uncertainties in sample injection can be overcome by use of an internal standard. In this method, a measured quantity of an internal standard is added to both standard and sample, and the ratio of analyte signal to internal standard is recorded. Any inconsistency in injection of the sample will affect both the analyte and internal standard.

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Properties of the internal standard should include:

The retention times of internal standard and analyte should be different and the two peaks must be well separated, R >1.25

The detector response factor for the analyte and the internal standard should be the same.

Using internal standards can significantly improve precision to better than 1%.

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The Area Normalization Method

This technique can also overcome the uncertainties associated with sample injections. In this method, complete elution of all components is necessary where areas of all eluted peaks are computed and calculated areas are corrected for detector response. The concentration of the analyte is thus the ratio of its corrected peak area to total corrected areas of all peaks. The method is not as versatile as the internal standard method. The definition of the response factor and how it is calculated is very important to correctly solve problems

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Two definitions can be used:Weight response factor = %wt (standard)/Area

(standard) In this case the response factor should be

multiplied by the area of the unknown.Or: Detection response factor = Area (standard)/wt

(standard) In this case the response factor should be

divided by the area of the unknown.