Introduction to Modern Liquid Chromatography, Third Edition part 8 doc

A solute molecule must be present in either the mobile or stationary phase so that, if the fraction of molecules in the mobile phase is R, the fraction in the stationary phase must be 1−

where K = (C s /C m) is the equilibrium constant for Equation (2.2), and s /V m)

is the phase ratio—the ratio of stationary and mobile-phase volumes within the column We will see that k is a very important property of each peak in the chromatogram; values of k can help us interpret and improve the quality of a

separation A solute molecule must be present in either the mobile or stationary

phase so that, if the fraction of molecules in the mobile phase is R, the fraction in

the stationary phase must be 1− R; therefore from Equation (2.3) we have

k=1− R

or

The retention time (t R ) of X can be defined as distance divided by speed (or band velocity), where the distance is the column length L and the band velocity is u x:

t R= L

u x

(2.4)

Similarly the retention time of the solvent peak is

t0= L

where u is the average mobile-phase velocity Eliminating L between Equations (2.4) and (2.4a) gives

t R= t0u

which, with R = u x /u0(Eq 2.1) and Equation (2.3b), then gives

Equation (2.5) can also be expressed in terms of retention volume V R = t R F, where

F is the mobile-phase flow rate (mL/min):

Here V m is the column dead-volume, equal to t0F (see the further discussion of V m

and Eq 2.5a below)

Equation (2.5) can be rearranged to give

k=t R − t0

which allows the calculation of values of k for each peak in the chromatogram Visual estimates of k from the chromatogram (based on Eq 2.6) are often used in practice, because exact values of k are seldom needed for developing a separation (method development) or during routine analysis Thus k is equal to the corrected retention time (t R − t0), measured in units of t0, or

k=



t R

t0



As illustrated in Figure 2.3f (which corresponds to the chromatogram of Fig 2.3e), the distance t0 can be used to mark off approximate values of k, beginning at time

t0; thus k equals 1, 2, and 4, respectively, for compounds X, Y, and Z.

We will see in Section 2.4.1 that values of k between about 1 and 10 are

preferred for various reasons Therefore it is important to be able to estimate (or

calculate) values of k for the different peaks in a chromatogram, which in turn requires a value of the column dead-time t0 A value of t0 can often be obtained from a visual inspection of the initial portion of the chromatogram, as illustrated in

Figure 2.5a–b Sometimes the first baseline disturbance assumes the characteristic shape illustrated in Figure 2.5a, which is a clear indication of the unretained solvent peak This t0-disturbance is usually the result of a change in refractive index (RI)

of the mobile phase (due to differences in RI for the sample solvent vs the mobile phase), which in turn affects the amount of light that passes through the flow cell

of the detector If the sample is dissolved in the mobile phase (usually the preferred

choice), a t0peak as in Figure 2.5a may not be observed.

At other times, especially for the injection of a reaction product, environmental sample, or plant or animal extract, a very large (‘‘excipient’’ or ‘‘junk’’) peak may

be observed at the beginning of the chromatogram (Fig 2.5b) In this case t0

corresponds to the initial rise of the peak Sometimes no obvious solvent peak is

observed (Fig 2.5c), in which case a value of t0can either be measured or estimated

t0

t0

t0

t0??

thiourea

Figure2.5 Determining the column dead-time t

The most direct procedure for determining t0 is to inject a solute (dissolved in

water or the mobile phase) that is unretained (k= 0) and readily detected, as in

Figure 2.5d When UV detection below 220 nm is used, thiourea as test solute fulfills both requirements, and is therefore a good choice for the measurement of t0 Other

test solutes have also been used for measuring t0, for example, uracil or concentrated solutions of a UV-absorbing salt such as sodium nitrate [2–4] Observed values

of t0 for a given column can vary with mobile-phase composition by as much as

±10–15% for 0–100% B (%B refers to the percent by volume of organic solvent in

the mobile phase), but usually t0varies by<5% for 20–80% B [5] For approximate estimates of k as in Figure 2.3e, a value of t0measured for one value of %B can be assumed to be the same for all values of %B (when only %B is changed)

Alternatively, a value of t0can be estimated from the column dimensions and flow rate (for columns packed with fully porous particles):

t0≈ 5 × 10−4Ld2

c

Here L is the column length in mm, d c is the column inner diameter in mm, F is the flow rate in mL/min, and t0 is in minutes For several hundred different RPC

columns, it was found that Equation (2.7) agrees with experimental values of t0

with an average error of only±10% (1 SD) [6], which again is accurate enough for

practical purposes The column dead-volume V m is related to t0as

with L and d c in mm The dead-volume V m represents the total volume of mobile phase inside the column, both inside and outside of the column particles For

example, if V m = 2 mL, and F = 0.5 mL/min, then t0= V m /F = 2/0.5 = 4 min; t0

can be regarded as the time required to empty the column of the mobile phase that was originally present in the column

For the common case where the column inner diameter ≈ 4.6 mm, we can conveniently estimate values of V m(by combining Eqs 2.7 and 2.7a):

V m(mL)≈ 0.01L (for 4 to 5 mm i.d columns, with L in mm) (2.7b)

Values of t0 can then be obtained from Equation (2.7b), with t0= V m /F For

a further discussion of the measurement, accuracy and significance of column dead-time or dead-volume, see [2–4]

2.3.2 Role of Separation Conditions and Sample Composition

The relative effect of different separation conditions on sample retention k is

summa-rized in the second column of Table 2.2 Table 2.2 is applicable for different HPLC modes, but the following discussion will assume reversed-phase chromatography (RPC) The mobile phase for RPC is usually a mixture of water or aqueous buffer (A-solvent) and an organic solvent (B-solvent) such as acetonitrile or methanol As the volume-percent of organic solvent (%B) is increased, the retention of all sample

compounds decreases A mobile phase that provides smaller values of k is referred to

as a ‘‘stronger’’ mobile phase; similarly water is referred to as a ‘‘weak’’ solvent, and

Table 2.2

Effect of Different Separation Conditions on Retention (k), Selectivity (α), and Plate

Number (N)

B-solvent (acetonitrile, methanol, etc.) + ++ −

Column type (C 18 , phenyl, cyano, etc.) + ++ −

Note: ++, major effect; +, minor effect; -, relatively small effect; 0, no effect; bolded quantities denote

conditions that are primarily used (and recommended) to control k, α, or N, respectively (e.g., %B is varied

to control k or α, column length is varied to control N).

aFor ionizable solutes (acids or bases).

b Higher pressures allow larger values of N by a proper choice of other conditions; pressure per se, how-ever, has little direct effect on N (see Sections 2.4.1.1 and 2.5.3.1).

organic solvents are ‘‘strong.’’ Typically values of k decrease by a factor of 2 to 3 for

a change of+10% B; an example of the effect of %B on sample retention is shown

in Figure 2.6, for the separation of a mixture of five herbicides A mobile phase of

80% B in Figure 2.6a results in rapid elution of the sample, with small values of

k (0.3–0.8) and poor separation When %B is decreased (50% B, Fig 2.6b), separa-tion improves, separasepara-tion or ‘‘run time’’ increases (16 min vs 1.5 min in Fig 2.6a),

and peak heights are reduced because the peaks are wider Retention normally is

controlled within a desired range of k by the choice of %B The conditions of

Table 2.2 can also be varied in order to control separation selectivity (α) or column efficiency (N); see Section 2.5 for details.

Reversed-phase chromatography involves a nonpolar stationary phase or col-umn (e.g., C18) and a polar, water-containing mobile phase Polar solutes will prefer

the polar mobile phase (‘‘like attracts like’’) and be less retained (larger R, smaller k), while nonpolar solutes will interact preferentially with the nonpolar stationary phase and be more retained (smaller R, larger k) The preferential interaction of

a nonpolar solute (n-hexane) with the nonpolar stationary phase is illustrated in Figure 2.7a, while Figure 2.7b shows the preferential interaction of a polar solute (1,3-propanediol) with the polar mobile phase Figure 2.7c is a chromatogram

of several mono-substituted benzenes that vary in polarity or ‘‘hydrophobicity’’ because of the nature of the substituent group Polar (less hydrophobic) groups such

as –NHCHO, –CH2OH, or –OH reduce retention relative to the unsubstituted solute benzene (shaded peak), while less polar (more hydrophobic) groups such as chloro, methyl, bromo, iodo, and ethyl increase retention

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Time (min)

80% methanol

(0.3≤ k ≤ 0.8)

50% methanol

(4≤ k ≤ 19)

(a)

(b)

1

2 3

4

5

t0

1

0

Time (min)

Figure2.6 Separation as a function of mobile phase %B (%v methanol) Herbicide sample:

1, monolinuron; 2, metobromuron; 3, diuron; 4, propazine; 5, chloroxuron Conditions,

150× 4.6-mm, 5-μm C18column; methanol/water mixtures as mobile phase; 2.0 mL/min; ambient temperature Recreated chromatograms from data of [7]

Ionized acids and bases are much more ‘‘polar’’ and therefore less retained than their neutral counterparts A change in mobile phase pH that results in increased solute ionization will therefore lead to a decrease in retention time (Section 7.2)

2.3.2.1 Intermolecular Interactions

This section provides additional insight into sample retention as a function of the solute, column, and mobile phase; it also represents more information than is usually required in practice The reader may therefore prefer to skip to following Section 2.3.2.2, and return to this section as needed.

The attraction between adjacent molecules of a solute and solvent is the result of several different intermolecular interactions, as illustrated in Figure 2.8 In principle,

a quantitative understanding of these interactions should allow estimates—or even predictions—of retention as a function of molecular structure While this is usually not possible at the present time (see Section 2.7.7), an understanding of these interactions can prove useful in other ways; for example, when selecting a different column for a change in separation (Section 5.4)

Dispersion interactions (Fig 2.8a) result from the random, instantaneous positions of electrons around adjacent atoms of either the solvent (S) or the solute (X) Typically the arrangement of electrons around the nucleus of atom S will

be unsymmetrical at any instant of time (as in Fig 2.8a), and this will cause the electrons in adjacent atom X to move as shown (due to coulombic repulsion) The result is an instantaneous dipole moment for both S and X that favors electrostatic

attraction The strength of dispersion interactions increases with the polarizability

(a) (b)

sample molecule

H

O H

Nonpolar (hydrophobic) interaction

with the nonpolar stationary phase

Polar(hydrogen bonding) interaction with the polar mobile phase

C18 C18 C18 C18 C18 C18 C18

CH3−CH 2 −CH 2 −CH 2 −CH 2 −CH 3 HO − CH 2 −CH 2 −CH 2 −OH

H

O H

Time (min)

−OCH 3 (anisole)

benzene

−NH−CHO (benzylformamide)

−CH 2 OH (benzyl alcohol)

−OH (phenol)

−CHO (benzaldehyde)

−COCH 3 (acetophenone)

−CN (benzonitrile)

−NO2 −COOCH 3 (methylbenzoate)

−Cl+ −CH 3 (chlorobenzene + toluene)

−I −CH2CH3

−Br

(c)

Figure2.7 Sample polarity and retention Illustration of the interaction of a nonpolar

sam-ple solute with the stationary phase (a) and of a polar solute with the mobile phase (b); (c)

effect of different substituents on the retention of monosubstituted benzenes; 150× 4.6-mm

Hypersil C18column, 50% acetonitrile/water as mobile phase, 25◦C, 2 mL/min; recreated chromatogram from data of [8]

of each of the two adjacent atoms Solute polarizability increases with the size of the molecule (number of atoms or molecular weight) and with refractive index [9]; dispersion interactions are therefore stronger for aromatic compounds and for molecules substituted by atoms of higher atomic weight (sulfur, chlorine, bromine, etc.)—provided that molecules are of similar size

Dispersion interactions exist between every adjacent pair of atoms, and this interaction largely accounts for the physical attraction between molecules of all kinds (especially for less polar molecules) Because of the nonspecific and universal nature

of dispersion interactions, they are significant in both the mobile and stationary phases Dispersion interactions therefore tend to cancel, and they generally play

only a minor role in determining selective interactions of the kind that result

in changes in relative retention when the mobile phase or column is changed

Dispersion interactions contribute to hydrophobic interactions, so called because

Dispersion Dipole-dipole

.

NO2

NO2

Charge transfer ( π−π)

(e)

CH3−C≡N NO2

R

N(CH3)2

CH3O −H

.

.

O H −O

+

−

− +

Figure2.8 Intermolecular interactions that can contribute to sample retention and selectivity

of the attraction of less polar solutes to nonpolar RPC stationary phases (or their ‘‘water-fearing’’ rejection from the polar aqueous phase) As the strength of dispersion interactions increases (for larger, less polar solute molecules), the solute

is increasingly retained

Dipole–dipole interaction is illustrated in Figure 2.8b for the case of dipolar

molecules of solvent (acetonitrile, CH3C≡N) and solute (a nitroalkane, R–NO2) The functional groups (–C≡N and –NO2) in these two molecules each have a large, permanent, dipole moment, causing the two molecules to align for maximum electrostatic interaction (positive end of one molecule adjacent to the negative end of the other) The strength of dipole interaction is proportional to the dipole

moments of each of the two interacting groups (not the dipole moment of an entire,

multi-substituted molecule), because dipole interactions are only effective at very close range (i.e., adjacent atoms or groups)

Hydrogen bonding interactions are shown in Figure 2.8c, for two cases:

an acidic (or proton-donor) solvent (methanol) interacting with a basic

(proton-acceptor) solute (N,N-dimethylaniline), or an acidic solute (phenol) interacting with

a basic solvent tetrahydrofuran (THF) The strength of hydrogen bonding increases with increasing hydrogen-bond acidity and basicity of the two interacting species (Table 2.3)

Ionic (coulombic) interaction is illustrated in Figure 2.8d for a positively charged sample ion (X+) interacting with surrounding molecules of a polarizable

Table 2.3

Solvent Selectivity Characteristics Normalized Selectivitya

Solvent H-B Acidityα/ H-B Basicity β/ Dipolarity π∗/ P b ε c

Note: see Appendix I (Table I.4) for additional solvent information.

aValues from [11], where refers to the sum of values of α, β, and π∗for each solvent.

bPolarity index; values from [12].

cDielectric constant; values from [13].

solvent The positive charge on the solute ion causes a displacement of charge in the solvent molecules, for maximum electrostatic interaction The strength of ionic interaction increases for solvents with a larger dielectric constant ε (Table 2.3).

Ionic interaction can also occur between a charged sample ion and ions in either the mobile or stationary phases; see the discussion of ion-pair chromatography (Section 7.4.1) and ion-exchange chromatography (Section 7.5.1)

Charge transfer or π –π interaction is illustrated in Figure 2.8e for the π-acid

(electron-poor) solute 1,3-dinitrobenzene and the π-base (electron-rich) solvent

benzene Interactions of this kind can occur between any two aromatic (or unsat-urated) species, with the strength of the interaction increasing for strongerπ-bases

such as polycyclic aromatics (e.g., naphthalene and anthracene), and for stronger

π-acids (e.g., aromatics substituted by electron withdrawing nitro groups) The

solvent acetonitrile (a π-acid) can also interact with aromatic solutes by π –π

interaction [10]

The polar interactions of various nonionic aliphatic solvents used in HPLC can

be described by the solvent-selectivity triangle (Fig 2.9, [11]) The position of each solvent in this plot indicates its relative hydrogen-bond acidity α/, hydrogen-bond

basicityβ/, and dipolarity π*/ Thus amines are relatively strong hydrogen-bond

bases, as indicated by their position near the top of the triangle (largeβ) Similarly

H-B Basic ( β/∑)

amines

ethers

THF DMSO esters

N,N-dialkyl amides ketones

nitriles

nitro compounds

H2O

glycols formamide

alcohols

R-COOH

CH2Cl2 CHCl3

perfluoroalcohols

basic solvents

dipolar solvents

acidic

solvents

Figure2.9 Solvent-selectivity triangle for aliphatic solvents of various kinds See Table 2.3 for values of the solvent properties plotted Adapted from [11]

nitroalkanes, aliphatic nitriles, and CH2Cl2 all have groups with large dipole moments, and they are situated near the lower right-hand side of the triangle Perfluoroalcohols are especially strong hydrogen-bond donors (and simultaneously very weak acceptors); they and carboxylic acids (R–COOH) are found near the lower left of the triangle (largeα) Table 2.3 lists (1) relative contributions to solvent

polarity from dipolarity and hydrogen-bond acidity or basicity, (2) a measure of

overall solvent polarity (P), and (3) values of the dielectric constantε Larger values

ofε for the mobile phase indicate increasing ionic interaction with solute molecules

as in Figure 2.8d, increasing solubility in the mobile phase for ionic solutes, and smaller values of k for ionic solutes For a comprehensive review of intermolecular

interactions in chromatography, see [14]

More will be said about the solvent-selectivity triangle of Figure 2.9 and solvent

selectivity in Chapters 6 and 8 Section 5.4 on column selectivity provides a similar

treatment of interactions between the solute and the stationary phase

2.3.2.2 Temperature

Temperature is an important variable in HPLC, as it has a significant effect on

values of k For most solute molecules and customary separation conditions, solute

retention varies with temperature according to the Van’t Hoff equation, which can

be expressed in HPLC as

log k = A + B

T K

(2.8)

For a given solute and other conditions unchanged, A and B are temperature-independent constants, and T K is the temperature (K) Values of k usually decrease with increasing temperature (positive value of B) by 1–2% per ◦C; thus a 50◦C

increase will cause about a 2-fold decrease in k As temperature increases, separation

often worsens, while peak heights increase (similar to an increase in %B, as in Fig 2.6) It should be noted that deviations from Equation (2.8) are not uncommon,

sometimes resulting in curved plots of log k against 1/T K In a few cases, retention is

observed to increase with an increase in temperature These exceptions to Equation

(2.8) can arise for various reasons, including changes with temperature of (1) the ionization of a solute [15, 16], (2) solute molecular conformation [17], and (3) the stationary phase [18]

Temperature also affects the column plate number N and pressure drop

(see Section 2.4) The practical use of most current HPLC equipment is limited

to temperatures of <80◦C (Section 3.7.2), and HPLC column lifetimes often are shorter at temperatures>60◦C (Section 5.8) For a further discussion of the role of temperature in HPLC, see Section 2.5.3.1 and [19–20a]

As illustrated in Figure 2.3, solute molecules spread out to enclose a larger volume (or form a wider band) during their migration through the column When the band leaves the column to become a peak in the chromatogram, it will have a width that

can be defined in various ways The baseline peak width W is illustrated for the first peak i of Figure 2.10a Tangents are drawn to each side of the peak (through the

inflection points), and their intersection with the baseline determines the value of

W When referring to peak width in this book, we will assume values of baseline peak width W The relative ability of a column to furnish narrow peaks is described

as column efficiency, and is defined by the plate number N:

N= 16



t R W

2

(2.9)

For example, W for peak i in Figure 2.10a is equal to (4 00 − 3.85) = 0.15 min, and

t R = 3.93 min Therefore N = 16 × (3.93/0.15)2= 10, 980 Values of N can vary

for different samples, separation conditions, and columns (Section 2.4.1) The larger

the value of N, the narrower are the peaks in the chromatogram, and the better is

the separation

Peak width can be measured more conveniently (and precisely) by the

half-height peak width W1/2 , as illustrated for peak j in Figure 2.10a; values of

W1/2 ≡ 0.588W are reported by many data systems When the peak width at half height is used to calculate N,

N = 5.54



t R

W1/2

2

(2.9a)

Charge transfer or π –π interaction is illustrated in Figure 2.8e for the π-acid

(electron-poor)... Figure 2.8d, increasing solubility in the mobile phase for ionic solutes, and smaller values of k for ionic solutes For a comprehensive review of intermolecular

interactions in chromatography,. .. K In a few cases, retention is

observed to increase with an increase in temperature These exceptions to Equation

(2 .8) can arise for various reasons, including changes