Chromatography was invented by the Russian botanist Mikhail Tswett shortly after the tum of this century. He passed solutions containing plant pigments,

such as chlorophyUs and xantbopbylls, through glass columns packed with fi nely diviaed oalcium carbonate. The separated species appeared as colored bands on the column, which accounts

for the name he chQse for the method (Greek: chroma meani:ng "color" and graphein meaning "to write ").

Chromatography is a technique in which the components of a mhture are separated based on the rates at which they are carried through a stationary

phase by a gaseous or liquid mobile phase.

Planar and column chromatography are

based on the same types of equilibria.

490

CHAPTER 26 --

AN INTRODUCTION TO CHROMATOGRAPHIC METHODS

Chromatography is an analytical method that is widely used for the separation, identification, and determination of the chemical components in complex mix­tures. No other separation method is as powelful and generally applicable as is chromatography. 1

.

26A A GENERAL DESCRIPTION OF CHROMATOGRAPHY

The term chromatography is difficult to define rigorously because the name has been applied to such a variety of systems and teclmiques. All of these methods, however, have in common the use of a stationary phase and a mobile phase. Components of a mixture are carried through the stationary phase by the flow of a gaseous or liquid mobile phase, separations being based on differences in migration rates among the sample components.

26A-l Classification of Chromatographic Methods

Chromatographic methods are of two lypes. In column chromatography, the stationary phase is held in a narrow tube and the mobile pha5e is forced through the tube under pressure or by gravity. In planar chromatography, the stationary

I General references on chromatography include: Chromatography: FU/ldamentals and Applications of Chromatography a/ul Eleclropliolometric Methods, Part A Fundamentals, PorI B Applications, E. Heftmann. Ed. New York: Elsevier, 1983; P. Sewell and B. Clarke, Chromatographic Separations. New Yo(k: Wiley, 1988; Chromatographic Theory and Basic Principles, J. A. Jonsson, Ed . New York: Marcel Dekker, 1987; J. C. Giddings. Unified Separation Sciellce. New York: Wiley, 1991.

----

tion, rrux­as is

: has lads, lase. flow ~s in

the )ugh

nary

rlions rions, riolls. New 99l.

26A A General Description of Chromatography 491

-r:-phase is supported on a flat plate or in the pores of a paper. Here the mobile phase moves through the stationary phase by capillary action or under the influence of gravity. We will deal with column chromatography only.

As shown in the first column of Table 26-1, chromatographic methods fall into three categories based on the nature of the mobile phase. The three types of phases include liquids, gases, and supercritical fluids. The second column of the table reveals that there are five types of liquid chromatography and three types of gas chromatography that differ in the nature of the stationary phase and the types of equilibria between phases .

26A-2 Elution Chromatography

Figure 26-1 shows how two components , A and B, are resolved on a column by elution chromatography. Elution involves washing a solute through a column by additions of fresh solvent. A single pOl1ion of the sample dissolved in the mobile phase is introduced at the head of the colurrm (at time to in Figure 26-1), where components A and B distribute themselves between the two phases. Introduction of additional mobile phase (the eluent) forces the dissolved portion of the sample down the coluIID1, where further partition between the mobile pha~~e and fresh portions of the stationary phase occurs (time II)' Partitioning between the fresh solvent and the stationary phase takes place simultaneously at the original site of the sample.

Further additions of solvent cany solute molecules down the column in a continuous series of transfers between the two phases. Because solute movement can occur only in the mobile phase, the average rate at '!Vhich a solute migrates depends on the fraction of time it spends in that phase. This fraction is small

Table 26-1 CLASSIFICATION OF COLUMN CHROMATOGRAPHIC METHODS

General Classification Specific Method Stationary Phase

Liquid chromatography can be performed

in columns and 011 planar surfaces, but gas chrom atography is restricted to column pro ­cedures.

Elution is a process in which solutes are washed through a stationary phase by the movement of a mobile phase.

An eluent is a solvent used to can'Y the

components of a mixture through a sta­tionary phase.

Type of Equilibrium

Liquid chromatography

(LC) (mobile phase:

liquid)

Liquid-liquid, or partition Liquid adsorbed on a solid Partition between immisci­

ble liquids

Gas chromatography (GC)

(mobile phase: gas)

Supercritical-fluid chroma­

tography (SFC) (mobile

phase: supercritical fluid)

Liquid-bonded phase

Liquid-solid , or adsorption

Ion exchange

Size exclusion

Gas-liquid

Gas-bonded phase

Gas-solid

Organic species bonded to a

solid surface

Solid

Ion-exchange resin

Liquid in interstices of a

polymeric solid

Liquid adsorbed on a solid

Organic species bonded [0 a

solid surface

SoUd

Organic species bonded to a

solid surface

Partition between liquid

and bonded surface

Adsorpt.ion

Ion exchange

Partition/sieving

Partition between gas and

liquid

Partition between liquid

and bonded surface

Adsorption

Partition between supercriti­

cal fluid and bonded sur­

face

492 Chapter 26 An Introduction to Chromatographic Methods

Figure 26-1 (a) Diagram showing the separation of a mixture of components A and B by column elution chromatography. (b) The output of the signal detector at the various stages of elution shown in (a).

A chromatogram is a plot of some func­tion of solute concentration versus elu­tion time or elution velume. -

Sample

A+B

Packed column

..... ~ ~~

to

B A

Mobile phase

(a)

A

8 I

O·~ L-L __________ ~ _________ ~ ________ ~ __________ ~ to

Time

(b)

Detector

for solutes that are strongly retained by the stationary phase (component B in Figure 26-1, for example) and large where retention in the mobile phase is more likely (component A). Ideally, the resulting differences in rates cause the components in a mixture to separate into bands, or' zones, along the length of the column (see Figure 26-2). Isolation of the separated species is then accom­plished by passing a sufficient quantity of mobile phase through the column to cause the individual bands to pass out the end (to be eluted from the column), where they can be collected (times t3 and t4 ill Figure 26-1).

Chromatograms

If a detector that responds to solute concentration is placed at the end of the column and its signal is plotted as a function of time (or of volume of added mobile phase), a series of symmetric peaks is obtained, as shown in the lower part of Figure 26~1. Such a plot, called .a chromatogram, is useful for both

.ector

Bin se is ~ the th of ~om­

m to ron),

,f the .dded ower both

26B Migration Rates of Solutes 493

t

Distance migrated

qualitative and quantitative analysis. The positions of the peaks on the time axis can be used to identify the components of the sample; the areas under the peaks provide a quantitative measure of the amount of each species.

The Effects of Relative Migration Rates and Band Broadening on Resolution

Figure 26-2 shows concentration profiles for the bands containing solutes A and B on the column in Figure 26-1 at time It and at a later time t3.

2 Because B is more strongly retained by the stationary phase than is A, B lags during the migration. Clearly, the distance between the two increases as they move down the column. At the same time, however, broadening of both bands takes place, whjch lowers the efficiency of the column as a separating device. While band broadening is inevitable, conditions can often be found where it occurs more slowly than band separation. Thus, as shown in Figure 26-2, a clean separation of species is possible provided the column is sufficiently long.

Several chemical and physical variables influence the rates of band separation and band broadening. As a consequence, improved separations can often be realized by the control of variables that either (1) increase the rate of band separation, or (2) decrease the rate of band spreading. These altematives are illustrated in Figure 26-3.

The variables that influence the relative rates at which solutes migrate through a stationary phase are described in the next section. Following this discussion, we tum to those factors that playa part in zone broadening.

26B MIGRATION RATES OF SOLUTES

The effectiveness of a chromatographic column in separating two solutes depends in part on the relative rates at which the two species are eluted. These rates are in tum determined by the partition ratios of the solutes between the two phases.

26B-1 Partition Ratios in Chromatography

All chromatographic separations are based on differences in the extent to which solutes are partitioned between the mobile and the stationary phase. For the solute

2 Note that the relative positions of the bands for A and B in the concentration profile in Figure 26-2 appear to be reversed from Iheir positions in the lower part of Figure 26- [. The difference is that the abscissa is distance along the colunm in Figure 26-2 but time in Figure 26-1. Thus, in Figure 26-1. the /1'0111 of a peak lies to 1he left and Ihe tail (0 the right; in Figure 26-2. the reverse is true.

Figure 26-2

Concentration profiles of solute bands A and B at two different times in their migration down the column in Figure 26-1. The times I, and t3 are indicated in Figure 26-1.

1

, ___ -"M---(C) Time

Figure 26~3 Two-component chromatograms illus­trating two methods of improving sepa­ration: (a) original chromatogram with overlapping peaks; improvement brought about by (b) an increase in band separation; and (c) a decrease in bandwidth .

494 Chapter 26 An Introduction to Chromatographic Methods

The retention time tR is the time between injection of a sample and the appearance of a solute peak at the detec­tor of a chromatograpbic column.

The dead time tM is the time it takes for an un retained species to pass through a column.

Figure 26-4 A typical chromatogram for a two­component mixture. The small peak on the left represents a solute that is not retained on the column and so reaches the detector almost immedi­ately after elution is started. Thus its retention time 1M is approximately equal to the time requjred for a mole­cule of the mobile phase to pass through the column.

species A, the equilibrium involved is described by the equation

The equilibrium constant K for this reaction is called a partition ratio, or partition coefficient, and is defined as

(26-1 )

where Cs is the molar analytical concentration of a solute in the stationary phase and CM is its analytical concentration in the mobile phase. Ideally, the prutition ratio is constant over a wide range of solute concentrations; that is, Cs is directly proportional to CM'

268-2 Retention Time

Figure 26-4 is a simple chromatogram made up of just two peaks. The small peak on the left is for a species that is not retained by the stationary phase. The time tM after sample injection for this peak to appear is sometimes called the dead time. The dead time provides a measure of the average rate of migration of the mobile phase and is an important parameter in identifying analyte peaks. Often the sample or the mobile phase will contain an unretained species. When they do not, such a species may be added to aid in peak identification. The larger peak on the right in Figure 26-4 is that of an analyte species. The time required for this peak to reach the detector after sample injection is called the retention time and is given the symbol tn.

The average Unear rate of solute migration, V, is

(26-2)

where L is the length of the column packing. Similarly, the average linear velocity, U, of the molecules of the mobile phase is

(26~3)

Time

?n

1)

lse on tly

tali 'he the ion ks. len ger red ion

.-2)

:ity,

)-3)

268 Migration Rates of Solutes 495

268-3 The Relationship Between Migration Rate and Partition Ratio

In order to relate the rate of migration of a solute to its partition ratio, we express the rate as a fraction of the velocity of the mobile phase:

v = u X fraction of time solute spends in mobile phase

This fraction, however, equals the average number of moles of solute in the mobile phase at any instant divided by the total number of moles of solute in the column:

_ moles of solute in mobile phase v = Ll X ------------"---

total moles of solute

The total number of moles of solute in the mobile phase is equal to the molar concentration, CM, of the solute in that phase multiplied by its volume, VM •

Similarly, the number of moles of solute in the stationary phase is given by the product of the concentration, cs, of the solute in the stationary phase and its volume, Vs . Therefore, ~-

Substitution of Equation 26-1 into this equation gives an expression for the rate of solute migration as a function of its partition ratio as well as a function of the volumes of the stationary and mobile phases:

_ I v=uX----­

I + KVslVM (26-4)

The two volumes can be estimated from the method by which the column is prepared .

26B-4 The Capacity Factor

The capacity factor is an important experimental parameter that is widely used to describe the migration rates of solutes on columns. For a soLute A, the capacity factor k~ is defined as

(26-5)

where KA is the partition ratio for the species A. Substitution of Equation 26-5 into 26-4 yields

_ 1 v=uX--

1 + k~ (26-6)

Michael Tswelt (1872-1919), a Rus­sian botanist, discovered the basic prin­ciples of column chromatography. He separated plant pigments by eluting a mixture of the pigments on a column of calcium carbonate. The various pig­ments separated into colored bands; hence the name chromatography.

496 Chapter 26 An Introduction to Chromatographic Methods

Ideally , the capacity factor for analytes in a sample is between 1 and 5.

The selectivity factor for !wo analytes in a column provides a measure of how well the column will separate the !Wo.

In order to show how k~ can be derived from a chromatogram, we substitute Equations 26-2 and 26-3 into Equation 26-6:

L L 1 -=-x--tR IN! 1 + k~

(26-7)

This equation reananges to

(26-8)

As shown in Figure 26-4, til and tM are readily obtained from a chromatogram. When the capacity factor for a solute is much less than unity, elutl0n occurs so rapidly that accurate determination of the retention times is difficult. When the capacity factor is larger than perhaps)O to 30, elution times become inordinately long. Ideally, separations are peIformed under conditions in which the capacity factors for the solutes in a mixture are in the range between] and 5.

The capacity factors in gas chromatography can be varied by changing the temperature and the column packing. In liquid chromatography, capacity factors can often be manipulated to give better separations by varying the composition of the mobile phase and the stationary phase.

268-5 Relative Migration Rates: The Selectivity Factor

The selectivity factor a of a column for the two species A and B is defined as

(26-9)

where KB is the partition ratio for the more strongly retained species Band KA is the constant for the less strongly held or more rapidly eluted species A. According to this definition, a is always greater than unity.

Substitution of Equation 26-5 and the analogous equation for solute B into Equation 26-9 provides after reanangement a relationship between the selectivity factor for two solutes and their capacity factors:

ks a= - (26-10)

k~

where k~ and k~ are the capacity factors for B and A, respe.ctively. Substitution of Equation 26-8 for the two solutes into Equation 26-10 gives an expression

:e

-8)

TI.

so he :ly .ty

he )rs on

as

-9)

nto lity

10)

tion ;ion

26C The Efficiency of Chromatographic Columns 497

that penn its the determination of a from an experiJT\~ntal chromatogram:

(26-11 )

In Section 26D- l we show how we use the selectivity factor to compute the resolving power of a column.

26C THE EFFICIENCY OF CHROMATOGRAPHIC COLUMNS

The efficiency of a chromatographic column refers to the amount of band broaden­ing that occurs when a compound passes through the column. Before defining column efficiency in more quantitative tenns, let us examine the reasons that bands become broader as they move down a column.

26C-l The Rate Theory of Chromatography

The rate theory of chromatography describes the shapes and breadths of elution peaks in quantitative terms based on a random-walk mechanism for the migration of molecules through a column. A detailed discussion of the rate theory is beyond the scope of this book. 3 We can, however, give a qualitative picture of why bands broaden and what variables improve column efficiency.

If you examine the chromatograms shown in this and the next chapter, you will see that the elution peaks look very much like the Gaussian or normal error curves that you encountered in Chapters 4 and 5. As shown in Section 4B, normal error curves are rationalized by assuming that the uncertainty associated with any single measurement is the summation of a much larger number of small, individually undetectable and random unceltainties, each of which has an equal probability of being positive or negative. In a similar way, the typical Gaussian shape of a chromatographic band can be attributed to the additive combination of the random motions of the myriad molecules making up a band as it moves down the column.

It is instructive to consider a single solute molecule as it undergoes many thousands of transfers between the stationary and the mobile phases during elution. Residence time in either phase is highly irregular. Transfer from one phase to the other requires energy, and the molecule must acquire this energy from its surroundings. Thus, the resjdence time in a given phase may be transitory for some molecules and relatively long for others. Recall that movement down the column can occur only while the molecule is in the mobile phase. As a consequence, certain particles travel rapidly by virtue of their accidental inclusion in the mobile phase for a majority of the time, whereas others lag because they happen to be incorporated in the stationary phase for a greater-than-average length of time. The result of these random individual processes is a symmetric spread of velocities around the mean value, which represents the behavior of the average analyte molecule.

J See J . J. Hawkes, 1. Chern. Educ .• 1983. 60, 393 .

Some chromatographic peaks are non ideal and exhibit tailillg or frollting . In the for­

mer case the tail of the peak, appearing to the right on the chromatogram, is drawn out while the front is steepened . Wi th front­

ing, the reverse is the ca~e. A common cause of tailing and fronti ng is a nonlinear distribution coefficient. Fronting also

occurs when Ule sample introduced onto a

column is too large. Distort ions of this kind are undesirable because they lead to poorer separations and less reproducible

elu tion times. In our discuss ion we assume Ulat tailing and fronting are minimal.

498 Chapter 26 An Introduction to Chromatographic Methods

The plate height H is also known as the height equivalent of a theoretical plate (HETP).

The efficiency of a column is great when H is small and N is large.

Figure 26·5

Flow direction

!

Typical pathways of two molecules during elution. Note that the distance traveled by molecule 2 is greater than that traveled by molecule 1. TIlUs,-mol· ecule 2 will arrive at B later than mole­cule 1.

Diffusion also contTibutes to band broadening. Recall from Section [9A-2 that molecules tend to diffuse from a more concentrated part of a solution to a more dilute, the rate being proportional to the concentration difference. In the center of a chromatographic band, the concentration of a species is high, while at the two edges the concentration approaches zero. Therefore, molecules tend to migrate to either edge of the band. Band broadening is the result. Note that half of the diffusion will be in the direction of flow and the other half in an opposed direction.

Another cause of band broadening is shown in Figure 26-5, which shows that indi vidual molecules in the mobile phase follow paths of different lengths as they traverse the column. Thus, their arrival time at the detector differs, and bands are broader as a consequence.

The breadth of a band increases as it moves down the column because more time is allowed for spreading by these valious mechanisms to occur. Thus, zone breadth is directly related to residence time in the column and inversely related to the flow velocity of the mobile phase.

26C-2 A Quantitative Description of Column Efficiency

Two related tenus are widely used as quantitative measures of the efficiency of chromatographic columns: (1) plate lieight Hand (2) number of theoretical pLates N. The two are related by the equation

N = LIH (26-12)

where L is the length (usually in centimeters) of the column packing. Feature 26-1 describes how these measures of column efficiency got their names.

The efficiency of chromatographic columns increases as the number of plates becomes greater and as the plate height becomes smaller. Enonnous differences

Feature 26-1 WHAT IS THE SOURCE OF THE TERMS PLATE AND PLATE HEIGHT?

The 1952 Nobel Prize for chemistry was awarded to two Englishmen, A. J. P. Martin and R. L. M. Synge, for their work in the development of modern chromatography. In their theoretical studies, they adapted a model that was first developed in the early 1920s to descIibe separations on fractional distilla­tion columns. Fractionating columns, which were first used in the petroleum industry for separating closely related hydrocarbons, consisted of numerous intercOlmected bubble-cap plates (see Figure 26-A) at whlch vapor-Liquid equilibria were established when the column was operated under reflux conditions.

Martin and Synge treated a chromatographic column as if it were made up of a series of contiguous bubble-cap-like plates, within which equilibrium conditions always prevail. This plate model successfully accounts for the Gaussian shape of ebromatographle peaks as well as for factors that influence differences in solute-migration rates. The plate model is totally incapable of accounting for zone broadening, however, because of its basic assumption

tat

Ire :er '10

to he In. Lat as nd

,re

ne ed

of

2)

.re

:es es

26C The Efficiency of Chromatographic Columns 499

+1

Bubble cap plate column Figure 26-A

P1ates in a fractionating column.

that equilibrium conditions prevail throughout a column during elution. Th.is assumption can never be valid in the dynamic state that exists in a cJu'omato­graphic column, where phases are moving past one another at sLlch a pace that sufficient time is not available for equilibration.

in efficiencjes are encountered in columns, depending on their type and the kinds of mobile and stationary phases they con.tain. Efficiencies in (enns of plate numbers can vary from a few hundred to several hundred thousand; plate heights from a few tenths to one thousandth of a centimeter or smaller are not uncommon.

Definition of Plate Height, H

Tn Section 4C-2, we pointed out that the breadth of a Gaussian curve is described by the standard deviation (J" and the variance cr. Because chromatographic bands are also Gaussian and because the efficiency of a column is reflected in the breadth of chromatographic peaks, the variance per unit length of column is used by cIu'omatographers as a measure of column efficiency. That jo, the column

Stamp in honor of biochemists Archer 1. P. Martin (b . J 9 10) and Richard L. M. Synge (b . 1914) who were awarded the 1952 Nobel PLize in chemistry for their contributions to the development of modern chroma­tography.

500 Chapter 26 An Introduction to Chromatographic Methods

Figure 26~6 Definition of plate height H = c?/L.

Figure 26-7 Determination of the standard devia­tion T from a chromatographic peale W = 47".

(b)

(a)

Sample In

efficiency H is defined as

Analyte profile at end of packing

L Distance migrated-

., H=(T

L

Detector

(26-13)

This definition of column efficiency is illustrated in Figure 26-6a, which shows a column that has a packing L cm in length. Above this schematic is a plot showing the distribution of molecules along the length of the column at the moment the analyte peak reaches the end of the packing (that is, at the retention time tR)' The curve is Gaussian, and the locations of L + 1 (J" and L - to" ate indicated as broken vertical lines. Note that L calTies units of centimeters and a1 units of centimeters squared; thus H represents a linear distance in centimeters as well (Equation 26-13). In fact, the plate height can be thought of as the length of column that contains a fraction of the analyte that lies between Land L - 0".

Because the area under a nom1al error curve bounded by ± 0" is about 68% of the total area (page 62), the plate height, as defined, contains 34% of the analyte.

Experimental Determination of the Number of Plates in a Column

The number of theoretical plates, N, and the plate height, H, are widely used in the literature and by instrument manufacturers as measures of column pedor­mance. Figure 26-7 shows how N can be determined from a chromatogram. Here, the retention time of a peak tR and the width of the peak at its base W (in units of time) are measured. It can be shown (see Feature 26-2) that the number of

\ I

!.-------tR--------i~~X

o Time-

J)

vs ot le

)0

re ld ~rs

:th CT. of teo

re, lits of

26C The Efficiency of Chromatographic Columns 501

plates can then be computed by the simple relationship

(t )2

N= 16 ; (26-14)

To obtain H, the length of the column L is measured and Equation 26-12 applied.

Feature 26-2 DERIVATION OF EQUATION 26-14

The variance of the peak shown in Figure 26-7 has units of seconds squared because the abscissa is time in seconds (or sometimes in minutes) . This time-based variance is usually designated as r to distinguish it from fil, which has units of centlineters squared. The two standard deviations 'T and (J' are related by

(26-15)

where LJ tR is the average linear v~locity of the solute in centimeters per second.

Figure 26-7 illustrates a simple means for approximating 'T from an experi­mental chromatogram. Tangents at the inflection points on the two sides of the chromatographic peak are extended to fmm a triangle with the base line. The area of this triangle can be shown to be approximately 96% of the total area under the peak. In Section 5B-2 it was shown that about 96% of the area under a Gaussian peak is included within plus or minus two standard deviations (± 2CT) of its maximum. Thus, the intercepts shown in Figure 26-7 occur at approximately ±27 from the maximum, and W = 47, where W 1S the magnitude of the base of the triangle. Substituting this relationship into Equation 26-15 and rearranging yields

LW u=-

4tR

Substitution of tills equation for a' into Equation 26-13 gives

(26-16)

To obtain N, we substitute into Equation 26-12 and rearrange to get

Thus, N can be calcuJated from two time measurements, tR and W; to obtain H, the length of the column packing L must also be known.

502 Chapter 26 An Introduction to Chromatographic Methods

Figure 26-8 Effect of mobile-phase flow rate on plate height for (a) liquid chromatogra­phy and (b) gas chromatography.

26C-3 Variables that Affect Column Efficiency

Band broadening, and thus loss of coluITUl efficiency, is the consequence of the finite rate at which several mass-transfer processes occur during migration of a solute down a coluITUl. Some of the variables that affect these rates are controllable and can be exploited to improve separations.

The Effect of Mobile-Phase Flow Rate

The extent of band broadening depends on the length of time the mobile phase is in contact with the stationary phase. Therefore, as shown in Figure 26-8, column efficiency depends on the rate of flow of the mobile phase. Note that for both liquid and gas-liquid chromatography, minimum plate heights (or maximum efficiencies) occur at relatively low flow rates. Maximum efficiency for liquid chromatography occurs at rates that are well below those for gas chromatography. [n fact, the minima for liquid chromatography are often so low that they are not observed under ordinary operating conditions.

Generally, liquid chromatograms are obtained at lower ft.ow rates than gas chromatograms. Furthermore, as shown in Figure 26-8, plate heights for liquid chromatographic colunms are an order of magnitude or more smaller than those of gas chromatographic columns. Offsetting this advantage, however, is the difference in lengths of the two types of columns. Gas chromatographic columns can be 50 m or more in length. Liquid columns, on the other hand, can be no longer than 25 to 50 cm because of the high pressure drops along their lengths. As a consequence, the number of plates, N, in a gas chromatographic column may exceed that in a liquid chromatographic column by a factor of several hundred.

0.4 (a) Liquid chromatography

0.3

8 S 0.2 ~

0.1

o 0.5 1.0 1.5 Linear flow rate, cm/s

8.0 (b) Gas-liquid chromatography 7.0

El 6.0 El

5.0 ~

4.0

3.0

0 2.0 4.0 6.0 8.0

Linear flow rate, cm/s

§ 0.2

~ .0 00

0.6-0.8 mm

'0 ..d Q)

0.3-0.4 mm

~ 0.1 p...

5 10 15 20 Linear velocity, cm/s

Other Variables

It has been found that column efficiency can be increased by decreasing the particle size of column packings, by employing thinner layers of the immobilized film (where the stationary phase is a liquid adsorbed on a solid), and by lowering the mobile-phase viscosity, Increases in temperature also reduce band broadening under most circumstances. Figure 26-9 illustrates how particle size affects plate heights of gas-liquid chromatographic columns.

26D COLUMN RESOLUTION

The resolution Rl of a column provides a quantitative measure of its ability to separate two analytes. The significance of this term is illustrated in Figure 26-10, which consists of chromatograms for species A and B on three columns with different resolving powers. The resolution of each column is defined as

R = 2ilZ 2[(tR)a - (tR)A] .~ WA + WB WA + WB

(26-17)

where all of the terms on the right side are as defined in the figure. It is evident from the figure that a resolu tion of 1.5 gives an essentially complete

separation of A and B, whereas a resolution of 0.75 does not. At a resolution of 1.0, zone A contains about 4% B and zone B contains about 4% A. At a resolution of 1.5\ the overlap is about 0.3%. The resolution for a given stationary phase can be improved by lengthening the column, thus increasing the number of plates. An adverse consequence of the added plates, however, is an increase in the time required for the resolution.

26D-1 Effect of Capacity and Selectivity Factors on Resolution

A useful equation is readily derived that relates the resolution of a column to the number of plates it contains, as well as to the capacity and selectivity factors

260 Column Resolution 503

Figure 26-9 Effect of particle size on plate height. The numbers to the right are particle diameters. (From J. Boheman and J. H. Purnell, in Gas Chromatography 1958, D. H. Desty, Ed. New York: Academic Press, 1958. With pennis­sion of Butterworths, Stoneham, MA.)

504 Chapter 26 An Introduction to Chromatographic Methods

Figure 26-10 Separation at three resolutions: Rs =

2AZ/(WA + WIl ) .

Rs = 0.75

a

1 ~

.~ .... 0 0 t) ~ i (tR)H cO I Cl

1.5

O '--~

o Time-

of a pair of solutes on the column. It can be shown4 that for the two solutes A and B in Figure 26-10, the resolution is given by the equation

R = VN(~)(~) s 4 lX 1 + k~

(26-18)

where k~ is the capacity factor of the slower-moving species and Ol. is the selectivity factor. This equation can be rearranged to give the number of plates needed to realize a given resolution:

N = 16R; _CX_ _ _B ( )2(1 + kl)2 lX - 1 ks

(26-19)

260-2 Effect of Resolution on Retention Time

As mentioned earlier, the goal in chromatography is the highest possible resolution in the shortest possible elapsed time. Unfortunately, these goals tend to be incom­patible; consequently, a compromise between the two is usually necessary. The

4 See D. A. Skoog and J. J. Leary, Principles of Instrumenfal Analysis, 4th ed., pp. 592-593. Philadelphia: Saunders College Publishing, 1992.

•

~.

time (tR)B required to elute the two species in Figut~ 26-10 with a resolution of Rs is given by

t _ 16R;H (_0'._)2 (1 + k~)3 ( R)B - U a - 1 (k~? (26-20)

where u is the linear velocity of the mobile phase.

Example 26-1

Substances A and B have retention times of 16.40 and 17.63 min, respectively, on a 30.0-cm column. An unretained species passes through the column in 1.30 min. The peak widths (at base) for A and B are 1.11 and 1.21 min, respectively. Calculate (a) column resolution, (b) average number of plates in the column, (c) plate height, (d) length of column required to achieve a resolution of 1.5, and (e) time required to elute substance B on the longer column.

(a) Employjng Equation 26-17, we find

R.l = 2(17.63 -16.40)/(1.11 + 1.21) = 1.06

(b) Equation 26-14 permits computation of N:

N = 16 (16.40)2 = 3493 and N = 16 (17.63)2 = 3397 1.11 1.21

N~v = (3493 + 3397)/2 = 3445 = 3.4 X 103

(c)

H = LIN = 30.013445 = 8.7 X 10-3 em

(d) k' and a do not change greatly with increasing N and L. Thus, substituting N, and N2 into Equation 26-19 and dividing one of the resulting equations by the other yields

(R,.) , ~ (R\)2 Vii;

where the subscripts 1 and 2 refer to the original and to the longer column, respectively. Sub!\tituting the appropriate values for N" (R s)" and (RJ2 gives

1.06 V3445

1.5 Vii;

N, = 3445 U~6)' = 6.9 X 10'

26D Column Resolution 505

506 Chapter 26 An Introduction to Chromatographic Methods

A hyphenated technique is an analytical method in which two instrumental tech­niques are coupled to produce a more powerful analytical proGedure. Exam­ples include gas chromatography/mass spectrometry. liquid chroma:tography / voltammetry, and inductively coupled plasma/mass spectrometry.

But

L = NH = 6.9 X 103 X 8.7 X 10-3 = 60 cm

(e) Substituting (RJ, and (RJ2 into Equation 26-20 and dividing yields

(ll?)1 _ (Rs)i _ 17.63 _ (1.06)2 (tRh - (Rs)~ - (tRh - (1.5)2

(t1?)2 = 35 min

Thus, to obtain the improved resolution, the separation time must be doubled.

26E APPLICATIONS OF CHROMATOGRAPHY

Chromatography is a poweIiul and versatile tool for separating closely related chemical species. In addition, it can be employed for the qualitative identification and quantitative determination of separated species.

26E-1 Qualitative Analysis

Chromatography is widely used for recognizing the presence or absence of components in mixtures that contain a limited number of species whose identities are known. For example, 30 or more amino acids in a protein hydrolysate can be detected with a reasonable degree of certainty by means of a chromatogram. On the other hand, because a chromatogram provides but a single piece of information about each species in a mixture (the retention time), the application of the technique to the qualitative analysis of complex samples of unknown composition is limited. This limitation has been largely overcome by linking chromatographic columns cfuectly with ultraviolet, infrared, and mass spectrome­ters. The resulting hyphenated instruments are powerful tools for identifying the components of complex mixtures.

It is important to note that while a chromatogram may not lead to positive identification of the species in a sample, it often provides sure evidence of the absence of species. Thus, failure of a sample to produce a peak at the same retention time as a standard obtained under identical conditions is strong evidence that the compound in question is absent (or present at a concentration below the detection limit of the procedure).

26E-2 Quantitative Analysis

Chromatography owes its enonnous growth in part to its speed, simplicity, rela­tively low cost, and wide applicability as a tool for separations. However, it is doubtful that its use would have become so widespread had it not been for the fact that it can also provide quantitative information about separated specjes.

Quantitative chromatography is based on a comparison of either the height or the area of an analyte peak with that of one or more standards. If COD-

ed.

ed on

of es U1

n. )f In

n g

e

e e

26E Applications of Chromatography 507

ditions are controlled properly, both of these parameters vary linearly with concentration. ",.

Analyses Based on Peak Height

The height of a chromatographic peak is obtained by connecting the base lines on the two sides of the peak by a straight line and measuring the perpendicular distance from this line to the peak. This measurement can ordinarily be made with reasonably high precision and yields accurate results, provided variations in column conditions do not alter peak width during the period required to obtain chromatograms for sample and standards. The variables that must be conb:olled closely are column temperature, eluent flow rate, and rate of sample mjection. In addition, care must be taken to avoid overloading the column . The effect of sample-injection rate is particularly critical for the early peaks of a chromatogram. Relative errors of 5% to 10% due to this cause are not unusual with syringe injection.

Analyses Based on Peak Area

Peak area is independent of broadening effects caused by the variables mentioned in the previous paragraph. From this standpoint, therefore, area is a mor~ satisfac­tory analytical parameter than peak height. On the other hand, peak heights are more easily measured and, for narrow peaks, more accurately determined.

Most modem chromatographic instruments are equipped with electronic inte­grators that provide precise measurements of relative peak areas. If such equip­ment is not available, a manual estimate must be made. A simple method that works well for symmetric peaks of reasonable widths is to multiply peak height by the width at one-half peak height.

Calibration with Standards

The most straightforward method for quantitative chromatographic analyses involves the preparation of a series of standard solutions that approximate the composition of the unknown. Chromatograms for the standards are then obtained, and peak heights or areas are plotted as a function of concentration. A plot of the data should yield a straight line passing through the origin; analyses are based on this plot. Frequent standardization is necessary for highest accuracy.

The Internal-Standard Method

The highest precision for quantitative chromatography is obtained by using inter­nal standards because the uncertainties introduced by sample injection, ft.ow rate, and variations in column conditions are m.ini:nUzed. In this procedure, a carefully measured quantity of an internal-standard is introduced into each standard and sample, and the ratio of analyte peak area (or height) to internal-standard peak area (or height) is the analytical parameter. For this method to be successful, it is necessary that the internal-standard peak be well separated from the peaks of all other components in the sample, but it must appear close to the analyte peak. With a suitable internal standard, precisions of 0.5% to 1 % relative are reported.

508 Chapter 26 An Introduction to Chromatographic Methods

26F QUESTIONS AND PROBLEMS

26-1. Define *(a) elution.

(b) mobile phase. *( c) stationary phase.

(d) partition ratio.

*(e) retention time . (f) capacity factor.

*(g) selectivity fac(or. (h) plate height.

26-2. List the variables that lead to zone broaderung.

*26-3. What is the difference between gas-liquid and liquid­liquid chromatography?

26-4. What is the difference between liquid-liquid and liquid­solid chromatography?

*26-5. Describe a method for detennining the number of plates in a column.

26-6. Name two general methods for improving the resolution of two substances on a chromatographic colunm.

*26-7. The following data are for a liquid chromatographic column:

Length of packing Flow rate Vu Vs

24.7 cm 0.313 mL/min 1.37 mL 0.164 mL

A chromatogram of a mixture of species A, B, C, and D provided the following data:

Nonretained A B C D

Calculate

Retention Time, min

3.1 5.4

13.3 14.1 21.6

Width of Peak Base (W), min

OA1 1.07 1.1 6 1.72

(a) the number of plates from each peak. (b) the mean and the standard deviation for N. (e) the plate height for the column.

*26-8. From the data in 26-7, calculate for A, B, C, and D (a) the capacity factor. (b) the partition coefficient.

. *26-9. From the data in 26-7, calculate for species B and C (a) the resolution. (b) the selectivity factor. (c) the length of column necessary to separate the two

species with a resolution of 1.5. (d) the time required to separate the two species on the

column in (c).

*26-10. From the data in 26-7, calculate for species C and D (a) the resolution,

(b) the length of column necessary to separate the two species with a resolution of 1.5.

26-11. The following data were obtained by gas-liquid chroma~ tography on a 40-cm packed column;

Compound tR, min W1/2 ' min

Air 1.9 Methy 1cyclohexane 10.0 0 .76 Methylcyc10hexene 10.9 0.82 Toluene L3.4 1.06

Calculate (a) an average number of plates from the data. (b) the standard deviation for the average in (a). (c) an average plate height for the column . (d) the capacity factor for each of the three species.

26-12. Refer to 26-11 and calculate the resolution for (3) methylcyclohexene and methylcyclohexane. (b) methy1cyclohexene and toluene. (c) methylcyc10hexane and toluene.

26-13. If a resolution of 1.5 is desired in separating mcthylcyclo­hexane and methylcyclohexene in 26-11, (3) how many plates are required? (b) how long must the column be if the same packing is

employed? (c) what is the retention time for methylcyc10hexene on

the column in 26-11 b?

*26-14. II Vs and Vu for the column in 26- J 1 arc 19.6 and 62.6 mL, respectively, and a nonretained air peak appears after 1.9 min, calculate the (a) capacity factor for each compound. (b) partition coefficient for each compound . (c) selectivity factor for methy1cyclohexane and methyl­

cyclohexene.

*26-15. From distribution studies, species M and N are known to have waterlhexane partition coefficients of 6.01 and 6.20 (K = [M]H20/[M]neJ. The two species are to be separated by elution with hexane in a column packed with silica gel containing adsorbed water. The ratio VSIVM for the packing is 0.422. (a) Calculate the capacity factor for each solute. (b) Calculate the selectivity factor. (c) How many plates are needed to provide a resolution

of 1.5? (d) How long a column is needed if lhe plate height of

the packing is 2.2 X 10-3 cm? (e) If a flow rate of 7.1 0 cm/min is employed, how long

will it take to elute the two species?

26-16. Repeat the calculations in 26-15 assuming /(M = 5.81 and KN = 6.20.

* Answers to the asterisked problems are given in the answers section at the back of the book.

J